the neoaorta in patients with transposition … · figure 1.3 - schematic representation of the...

POLITECNICO DI MILANO

Facoltà di Ingegneria Industriale e dell’Informazione

Corso di Laurea Specialistica in Ingegneria Biomedica

THE NEOAORTA IN PATIENTS WITH

TRANSPOSITION OF THE GREAT ARTERIES

AFTER ARTERIAL SWITCH OPERATION:

IMAGING AND COMPUTATIONAL STUDY

Relatore: Prof. Francesco MIGLIAVACCA

Correlatore: Ing. Daria COSENTINO

Ing. Silvia SCHIEVANO

Ing. Giovanni BIGLINO

Tesi di Laurea Specialistica di:

Matteo CASTELLI, matr. 765535

Lorenzo DE NOVA, matr. 765741

Anno Accademico 2011-2012

Index

SUMMARY I

SOMMARIO XVI

CHAPTER 1 – INTRODUCTION : THE CLINICAL PROBLEM 1

1.1 TRANSPOSITION OF THE GREAT ARTERIES ............................................... 2

1.2 SURGICAL REPAIR OF TGA: THE ARTERIAL SWITCH

OPERATION......................................................................................................... 4

1.3 POSTOPERATIVE COMPLICATIONS .............................................................. 7

1.4 SURGICAL REPAIR OF TGA: AN ALTERNATIVE

OPERATION......................................................................................................... 9

CHAPTER 2 – AIM OF THE STUDY 12

CHAPTER 3 – STATE OF THE ART 14

3.1 4D MAGNETIC RESONANCE IMAGING ...................................................... 15

3.1.1 PRINCIPLES ............................................................................ 15

3.1.2 PREVIOUS WORK .................................................................. 16

3.2 COMPUTATIONAL ANALISYS ...................................................................... 19

3.2.1 COMPUTATIONAL FLUID DYNAMICS ............................. 19

3.2.2 LUMPED PARAMETER NETWORK (LPN) ........................ 20

3.2.3 MULTI-DOMAIN APPROACH .............................................. 22

3.2.4 PREVIOUS WORKS ............................................................... 23

CHAPTER 4 – MATERIALS AND METHODS I : EXPERIMENTAL 26

4.1 ANATOMICAL MODELS ................................................................................. 27

4.2 HYDRAULIC CIRCUIT ..................................................................................... 31

4.2.1 PUMP ....................................................................................... 32

4.2.2 ARTERIAL COMPLIANCE .................................................... 34

4.2.3 VASCULAR RESISTANCE .................................................... 35

4.2.4 ATRIAL RESERVOIR ............................................................ 38

4.2.5 PRESSURE MEASURING EQUIPMENT .............................. 38

4.2.6 FLOW MEASURING EQUIPMENT ...................................... 40

4.2.7 DATA ACQUISITION AND DATA ANALYSIS .................. 43

4.3 MAGNETIC RESONANCE (MR) ..................................................................... 44

4.3.1 ACQUISITION ......................................................................... 44

4.3.2 DATA EXTRACTION ............................................................. 46

4.4 ASSESSING THE EFFECT OF COMPLIANCE: COMPLIANT

TGA MODEL ...................................................................................................... 49

CHAPTER 5 – MATERIALS AND METHODS II :

COMPUTATIONAL 52

5.1 ANATOMICAL MODELS ................................................................................. 53

5.1.1 AN ADDICTIONAL CASE ..................................................... 53

5.2 MESH AND SENSITIVITY ANALYSIS .......................................................... 54

5.3 CFD SIMULATION............................................................................................ 57

5.3.1 WORKING HYPOTHESIS ...................................................... 58

5.3.2 BOUNDARY CONDITIONS .................................................. 58

CHAPTER 6 - RESULTS 65

6.1 EXPERIMENTAL RESULTS ............................................................................ 66

6.1.1 CONSIDERATIONS ON TEMPORAL RESOLUTION FOR

4D FLOW ACQUISITIONS ................................................................ 66

6.1.2 4D FLOW RESULTS: TGA AND CONTROL GEOMETRIES

68

6.1.3 THE EFFECT OF COMPLIANCE: DISTENSIBLE

PHANTOM .......................................................................................... 70

6.2 COMPUTATIONAL RESULTS ........................................................................ 72

6.2.1 MODEL VALIDATION .......................................................... 73

6.2.2 QUALITATIVE COMPARISON BETWEEN 4D FLOW AND

CDF SIMULATIONS .......................................................................... 81

6.2.3 THE EFFECT OF THE AORTIC ARCH GEOMETRY: CFD

COMPARISON BETWEEN TGA, CONTROL AND SPIRAL

GEOMETRIES ..................................................................................... 86

CHAPTER 7 - DISCUSSION 99

CHAPTER 8 – CONCLUSIONS AND FUTURE WORK 108

REFERENCES 114

List of Figures Figure 1.1 - Schematic representation of the heart with TGA, highlighting the origin of the

great vessels from the incorrect ventricle [yorksandhumberhearts.nhs.uk]. .............................. 2

Figure 1.2 - Rashkind procedure: the balloon catheter is inserted into the septal defect and

inflated. After inflation, the catheter is pulled back through the hole [http://www.hakeem-

sy.com]......................................................................................................................................... 5

Figure 1.3 - Schematic representation of the arterial switch operation, including relocation of

coronary buttons [http://radiology.rsna.org]. ............................................................................. 7

Figure 1.4 - Fluoroscopy visualisation of an acute aortic arch, or gothic arch, as a result of

arterial switch operation. The enlarged aortic root (indicated by the yellow arrow) and the

indentation resulting from repositioning of the pulmonary arteries following the Lecompte

procedure (red arrow) can also be appreciated. Image modified from [Agnoletti et al., 2007]. . 9

Figure 1.5 - Comparison between normal heart (C), TGA (A), ASO with Lecompte (B) and spiral

ASO (D). It is possible to appreciate how the spiral procedure restores a more physiological

anatomy than the traditional arterial switch operation [image form Chiu et al.,2002]. ........... 10

Figure 3.1 - 3D flow visualisation of a control patient highlighting cohesive systolic streamlines

[Baker er al., 2012]. ................................................................................................................... 16

Figure 3.2 - Particle traces emitted from the SVC show how the blood is distributed between

the p-RPA, d-RPA and main PA [Bachler et al.,2012]. ................................................................ 18

Figure 3.3 - A simple example of LPN model (top) and its electrical-hydraulic analogy (bottom):

flow (f) and pressure (P) are represented by electric current (i) and voltage (V). ...................... 20

Figure 3.4 - Lumped model of a short pipe: flows and pressures in the district are regulated by

the NS equations [Laganà, 2002]. ............................................................................................. 22

Figure 3.5 - Inlet (left) and outlet (right) lumped parameter network used to study the fluid

dynamics in the aortic arch [Kim et al., 2008]. .......................................................................... 23

Figure 3.6 - Velocity magnitude at peak systole (A), late systole (B), diastole (C). .................... 24

Figure 3.7 - Mean wall shear stress at peak systole. ................................................................. 24

Figure 4.1 - Screenshot of the Mimics interface, showing anatomical reconstruction of the TGA

aortic arch. 3D geometry (bottom right panel) is reconstructed from 2D MR images (top and

bottom left panels). ................................................................................................................... 28

Figure 4.2 - Detail of the port for the pressure catheter. It allows for access the aortic arch in a

very easy way. ........................................................................................................................... 29

Figure 4.3 - Control (left) and TGA (right) models manufactured by means of rapid prototyping.

It is possible to appreciate geometries differences among the two models: the yellow arrow

highlights the enlarged aortic root in the TGA model; the red arrows point the different aortic

arches. The green arrow indicates the point of insertion of a pressure catheter on the

ascending aorta (on the TGA model). Finally silicone was used to attach the model to Tygon

tubes, as can also be appreciated from these images. .............................................................. 30

Figure 4.4 - Experimental circuit: II indicates the compliant chambers, III one of the four taps

implementing the resistances, and IV the atrial reservoir. ........................................................ 31

Figure 4.5 - Schematic representation of the circuit. P represents the pulsatile pump, C the

compliant chambers, R the non-linear resistances. The arrow indicates the direction of the

flow. ........................................................................................................................................... 32

Figure 4.6 - Harvard Apparatus pulsatile blood pump used for the experiments: A) inlet, B)

outlet. Also indicated, the position of the ball valve that regulates the flow. ........................... 33

Figure 4.7 - Inflow waveform: it is obtained setting the stroke volume and the heart rate

respectively at 90 ml and 70 bpm. ............................................................................................. 34

Figure 4.8 - Schematic representation of the circuit using for characterising the resistances.

The red and the blue arrow indicate the position of the pressure catheters to measure pressure

values before and after the tap. ................................................................................................ 36

Figure 4.9 - Characteristic curves, with the respective equations, of the resistances: carotid

(blue), innominate and subclavian (red), descending aorta (green). ......................................... 38

Figure 4.10 - Catheter tip dimension compared with a match. ................................................. 39

Figure 4.11 – Pressure catheter manual calibration: on the ‘x’ axis the output of the console in

Volts (V) and on the ‘y’ axis the associated pressure in mmHg. ................................................ 39

Figure 4.12 - Catheter position: the yellow arrow indicates the dedicated port for the pressure

catheter. It is possible to see the light blue little pipe, fixed to the model with silicone, along

which the catheter is guided into the model. ............................................................................ 40

Figure 4.13 - Transit time ultrasound theory of operation: a schematic representation. On the

left: cross-talk between the crystals mounted inside the probe. On the right: position of the

probe, snugly clumped to the Tygon tube. ................................................................................ 41

Figure 4.14 - Flow-probe calibration: on the ‘x’ axis the output of the flow-meter in Volts (V)

and on the ‘y’ axis the associated flow in L/min. ....................................................................... 41

Figure 4.15 - The yellow arrow points at the flow-probe position, which is the inlet of the

phantom. ................................................................................................................................... 42

Figure 4.16 - The yellow arrow underlines the flow-probe artefact in MR scan, visible in the

aortic root. ................................................................................................................................. 43

Figure 4.17 - AcqKnowledge interface: pressure curve is shown in purple, flow curve in red. .. 44

Figure 4.18 - Data extraction via Osirix : magnitude (right) and phase (left). The enlightened

circles in the left image are the inlet (top) and the descending aorta (bottom), while the two

big grey circles are the two bottles full of water positioned in the scanner to simplify the

identification of the model. ....................................................................................................... 47

Figure 4.19 - 3D mask and planes in the TGA model. The numbers indicate the planes for the

velocity analysis: 1-2 inlet, 3 aortic roots, 4 ascending aorta, 5-6 descending aorta. ............... 48

Figure 4.20 - Particle seeds at different locations along the 3D model then used to generate

streamlines and pathlines. ......................................................................................................... 49

Figure 4.21 - Compliant TGA geometry. Clearly the new model was printed starting from the

same STL file used for the rigid one. Thus the only differences are the properties of the two

different materials. .................................................................................................................... 50

Figure 5.1 - Comparison of three different geometries: TGA, control and “spiral”. Images at the

bottom represent the 3D volumes recostructed in Mimics. The aorta is shown in red and the

pulmonary arteries are shown in blue. ...................................................................................... 54

Figure 5.2 - Mesh example at the inlet of the model: it is possible to notice the 5 layers of

prisms. ....................................................................................................................................... 55

Figure 5.3 - Sensitivity analysis: variation of the power dissipation index with the number of

elements in the mesh. There is no significant difference between 900000 elements mesh and

1200000 element mesh. ............................................................................................................ 56

Figure 5.4 - Control (right), TGA (central) and spiral (left) geometries meshed with tetrahedral

elements. The different colours represent different portions of the models separated by planes

used to evaluate the fluid dynamics at 1)aortic root, 2)ascending aorta, 3)descending aorta. 57

Figure 5.5 - TGA geometry: inlet (A) and outlets (B, C, D, E). ..................................................... 59

Figure 5.6 - TGA (top) and control (bottom) velocities imposed at the inlet of the 3D

geometries during the CFD simulation. ..................................................................................... 60

Figure 5.7 - 3D geometry of the TGA patient coupled with the LPN. ......................................... 60

Figure 5.8 - LPN implemented at each of the outlet branch: Qin, Qin2, Qt, Qx represent the

flows, P, Pt, Patrium the pressures; R2 and Rt are linear resistances, while R1 is flow-

dependant; C and Ct are compliances. ...................................................................................... 61

Figure 6.1 – Flows at the inlet of the model acquired with the Standard (blue) and High

Resolution (red) 4D Flow sequences, compared with the OsiriX 2D acquisition (green). .......... 67

Figure 6.2 – Qualitative comparison of the streamlines of the High Resolution (left) and the

Standard (right) 4D flow sequences. The first image shows a noisier background and visibly

less number of streamlines than the Standard one. .................................................................. 68

Figure 6.3 - Streamlines in the TGA geometry (left) compared with streamlines in the control

geometry (right) at t= 0.2 s (systolic peak). The range of velocity goes from 0 to 1.38 m/s for

both images. The yellow arrow indicates the jet impinging the aortic root. ............................. 69


geometry (right) at t= 0.6 s (diastole). The range of velocity goes from 0 to 1.38 m/s for both

images. ...................................................................................................................................... 69

Figure 6.5 - TGA compliant model (left) and TGA rigid model (right). As expected there are no

shape differences between the two phantoms. The only difference is represented by the

material used for the rapid prototyping process. ...................................................................... 71

Figure 6.6 – The compliant TGA model (left) is connected with the pulsatile pump. The

pressure effect is clearly visible, as the model did not retain its original shape, especially in the

aortic root. The TGA rigid model (right) was placed next to the compliant one in order to

better appreciate the geometric differences. ............................................................................ 71

Figure 6.7 - Pressure waveform comparison between the rigid TGA model (red) and the

compliant one (blue). As expected the second one in more damped than the first one, as a

result of the additional proximal compliance implemented by the distensible phantom.......... 72

Figure 6.8 - Computational (red) and experimental (blue) flow waveforms comparison in TGA’s

subclavian for a cardiac cycle (T=0.8 s). .................................................................................... 75

Figure 6.9 - Computational (red) and experimental (blue) flow waveforms comparison in TGA’s

innominate for a cardiac cycle (T=0.8 s). ................................................................................... 76

Figure 6.10 - Computational (red) and experimental (blue) flow waveforms comparison in

TGA’s carotid for a cardiac cycle (T=0.8 s). ................................................................................ 76


TGA’s descending aorta for a cardiac cycle (T=0.8 s). ............................................................... 77


control’s subclavian for a cardiac cycle (T=0.8 s). ...................................................................... 77


control’s innominate for a cardiac cycle (T=0.8 s). .................................................................... 78


control’s carotid for a cardiac cycle (T=0.8 s). ........................................................................... 78


control’s descending aorta for a cardiac cycle (T=0.8 s). ........................................................... 79

Figure 6.16 - Computational (red) and experimental (blue) pressure waveforms comparison in

TGA’s aortic arch for a cardiac cycle (T=0.8 s). .......................................................................... 80


control’s aortic arch for a cardiac cycle (T=0.8 s). ..................................................................... 80

Figure 6.18 - Temporal instants considered for the comparison displayed in the cardiac cycle. :

t1 represents the early systole, t2 the systolic peak, t3 the late systole and t4 the diastole. ...... 81

Figure 6.19 - 4D flow streamlines (left) compared with CFD streamlines (right) at t1= 0.1 s

(early systole) in the TGA model. The range of velocity is the same for both images. .............. 82

Figure 6.20 – 4D flow streamlines (left) compared with CFD streamlines (right) at t2= 0.2 s

(peak systole), in the TGA model. The range of velocity is the same for both images. It is clearly

visible in both of them the flow jet hitting the wall. .................................................................. 82

Figure 6.21 – 4D flow streamlines (left) compared with CFD streamlines (right) at t2= 0.4 s (late

systole), in the TGA model. The range of velocity is the same for both images. Once again in

both of them it is possible to appreciate a flow jet impinging on the aortic wall...................... 83

Figure 6.22 – 4D flow streamlines (left) compared with CFD streamlines (right) at t2= 0.6 s,

(diastole), in the TGA model. The range of velocity is the same for both images. ..................... 83


(early systole) in the control model. The range of velocity is the same for both images. .......... 84


(peak systole), in the control model. The range of velocity is the same for both images. It is

clearly visible in both of them the flow jet flowing smoothly towards the upper branches. ..... 85

Figure 6.25 – 4D flow streamlines (left) compared with CFD streamlines (right) at t2= 0.4 s (late

systole), in the control model. The range of velocity is the same for both images. Once again in

both of them it is possible to appreciate a flow jet flowing towards the subclavian artery. ..... 85


(diastole), in the control model. The range of velocity is the same for both images ................. 86

Figure 6.27 - CFD innominate flow waveforms comparison between TGA (red), control (blue)

and spiral (green) geometries for a cardiac cycle (T=0.8 s). ...................................................... 88

Figure 6.28 - CFD carotid flow waveforms comparison between TGA (red), control (blue) and

spiral (green) geometries for a cardiac cycle (T=0.8 s). ............................................................. 89

Figure 6.29 - CFD subclavian flow waveforms comparison between TGA (red), control (blue)

and spiral (green) geometries for a cardiac cycle (T=0.8 s). ...................................................... 89

Figure 6.30 - CFD descending aorta flow waveforms comparison between TGA (red), control

(blue) and spiral (green) geometries for a cardiac cycle (T=0.8 s). ............................................ 90

Figure 6.31 - Control (left), TGA (central) and spiral (right) velocity streamlines at t=0.1 s. ..... 91

Figure 6.32 - Control (left), TGA (central) and spiral (right) velocity streamlines at t=0.2 s. .... 92

Figure 6.33 - Control (left), TGA (central) and spiral (right) velocity streamlines at t=0.4 s. ..... 93

Figure 6.34 – Control (left), TGA (central) and spiral (right) velocity streamlines at t=0.6 s. .... 94

Figure 6.35 - Front view of the WSS in control (left), TGA (central), spiral (right) models. The

range of wall shear stress goes from 0 to 35 Pa. ....................................................................... 95

Figure 6.36 - Lateral view of the WSS in control (left), TGA (central), spiral (right) models. The

range of wall shear stress goes from 0 to 35 Pa. ....................................................................... 95

Figure 6.37 –Velocity vectors at peak systole (t=0.2s) in the control model . ............................ 97

Figure 6.38 - Velocity vectors at peak systole (t=0.2s) in the TGA model . ................................ 97

Figure 6.39 - Velocity vectors at peak systole (t=0.2s) in the spiral model. ............................... 98

Figure 7.1 - Control (right), TGA (central) and spiral (left) geometries. ................................... 104

Figure 7.2 - WSS in control (left), TGA (central), spiral (right) models. .................................... 105

Figure 8.1 - Coarsen mesh on the inlet face of the TGA model, used for the pixel by pixel

imposition of the velocity......................................................................................................... 113

List of Tables

Table 4.1 - Compliance values per each outlet of the model. .................................................... 35

Table 4.2a - Pressure drop in carotid. ........................................................................................ 36

Table 4.2b - Pressure drop in innominate and subclavian. ... Errore. Il segnalibro non è definito.

Table 4.2c - Pressure drop in descending aorta .................... Errore. Il segnalibro non è definito.

Table 5.1 - Pressure drop (ΔP) across each non-linear resistance. Q indicates flow-rate. ......... 62

Table 5.2 - Linear resistances of the LPN. .................................................................................. 63

Table 5.3 - Compliances of the LPN. .......................................................................................... 63

Table 6.1 - Mean flows calculated by OsiriX software (left) and Fluent simulation (right) at

every outlet for the TGA model. ................................................................................................. 73


every outlet for the control model. ............................................................................................ 74

Table 6.3 - Flow split calculated by OsiriX software (left) and Fluent simulation (right) at every

outlet for the TGA model. The following percentages are computed relatively to the inlet flow.

................................................................................................................................................... 74

Table 6.4 - Flow split calculated by OsiriX software (left) and Fluent simulation (right) at every

outlet for the control model. The following percentages are computed relatively to the inlet

flow. ........................................................................................................................................... 75

Table 6.5 - Mean flows calculated by Fluent at every outlet of the TGA (left), control (central)

and spiral (right) models. ........................................................................................................... 87

Table 6.6 - Flow split calculated by Fluent at every outlet of the TGA (left), control (central) and

Spiral (right) models. The following percentages are computed relatively to the inlet flow. .... 87

Table 6.7 – Mean pressure calculated at each outlet of the control (left), TGA (central) and

spiral (righ) models. ................................................................................................................... 96

List of Abbreviations


2D : Two-Dimensional

3D : Three-Dimensional

4D : Four-Dimensional

ASO : Arterial Switch Operation

BAV : Bicuspid Aortic Valve

BSA : Body Surface Area

CFD : Computational Fluid Dynamics

LPN : Lumped Parameter Network

MR : Magnetic Resonance

MRI: Magnetic Resonance Imaging

ODE : Ordinary Differential Equation

PA : Pulmonary Artery

ROI : Region of Interest

RPA : Right Pulmonary Artery

SVC : Superior Vena Cava

TGA : Transposition of the Great Arteries


UDF : User Defined Function

VA : Ventriculo-Arterial

WSS : Wall Shear Stress

SNR : Signal to Noise Ratio

HR : Heart Rate

SV : Stroke Volume

Summary

I

SUMMARY

Summary

II

INTRODUCTION

Transposition of the Great Arteries (TGA) is the most common cyanotic

congenital heart disease in neonates. The incidence of the disease is estimated

as 20-30 cases per 100,000 live births every year, with a 60-70% male

predominance. It involves ventriculo-arterial (VA) discordance, with the aorta

originating from the right ventricle and the main pulmonary artery (MPA) from

the left ventricle. The pulmonary and systemic circulations thus function in

parallel rather than in series, resulting in insufficient oxygen supply to the

tissues and excessive right and left ventricular workload. This scenario is

incompatible with prolonged survival unless oxygenated and deoxygenated

blood is mixed at some anatomic level. As soon as the condition of the

newborn is stabilised, typically by an atrial septostomy facilitating blood

mixing, it is possible to proceed with the arterial switch operation (ASO),

repositioning the great vessels in their physiological site.

Although ASO restores normal blood flow, several long-term complications

can arise and the long-term effects are not fully appreciated yet as this

procedure was introduced in the 1980s. In particular the hemodynamics might

be greatly affected by anatomical features such as enlarged aortic root and

acute aortic arch angulation, typical of TGA repaired by ASO.

AIM OF THE STUDY

The aim of this work is to create a validated computational model of the neo-

aorta following ASO and use this validated model to compare the local fluid

dynamics in different anatomies.

Particular attention was given to the result of the Lecompte maneuver, during

which the main pulmonary artery and its branches are brought forward and the

aorta is moved posteriorly, generating a greatly different anatomical

arrangement. It has been suggested that retaining the spiral shape of the aorta,

otherwise compromised during the Lecompte manoeuvre, could be beneficial,

so this scenario was also explored.

The workflow adopted in this study is summarised in Figure a: starting from

clinical data, 3D models are generated both for the experimental and the

Summary

III

computational study, using the experimental data to validate the computational

model and taking forward the study in-silico, evaluating different geometries.

Figure a – Summary of the workflow adopted in this study.

MATERIAL AND METHODS I: EXPERIMENTAL

An experimental approach was chosen because an in-vitro study can provide

controllable and reproducible data.

Anatomical models:

The study was carried out at a patient-specific level. A patient with TGA

corrected with ASO and an age-matched healthy control case were selected (15

years old, 1.7 m2 BSA, male). Both patients underwent MR examinations and

their anatomies were reconstructed in 3D from MR data using commercial

software (Mimics, Materialise, Leuven, Belgium). The final models include the

aortic root, the ascending and descending aorta, and the brachiocephalic

branches (i.e. innominate, left carotid and left subclavian arteries).

The 3D volume can be exported as a Standard Triangle Language (STL) file

compatible with the rapid prototyping technique known as PolyJet technology,

allowing to manufacture 3D models. A transparent and robust resin (Watershed

11122; DSM Somos, Elgin, IL) was used for the printing process (Figure b).

Summary

IV

Figure b - Control (left) and TGA (right) models manufactured by means of rapid prototyping

from MR data, showing the indentation on the ascending aorta (AAo) in the TGA model.

Hydraulic circuit:

The models are inserted in a mock circulatory loop (Figure c), consisting of a

pulsatile pump with adjustable stroke volume and heart rate, four Windkessel

elements and four metered needle-pinch valves at every outlet of the model, in

order to replicate arterial compliance and vascular resistance, respectively,

and a reservoir implementing atrial pressure (= 9 mmHg).

Figure c - Schematic representation of the circuit.

Summary

V

Each Windkessel component consists of a Perspex cylinder, with a 3-way valve

fitted at the top in order to control the volume of air, regulating the stiffness of

the circuit. The range of pressure at the inlet was set to 115/60 mmHg

according to cuff pressure data measured in the TGA patient. The resistance

elements have the advantage of being easily adjustable, albeit strongly flow-

dependent, thus implementing non-linear curves. They were previously

characterized imposing a range of flows and measuring the pressure drop

across the tap . They were set in order to split the flow physiologically: 55% to

the descending aorta and 45% to the upper branches.

As the circuit had to be inserted inside the MR scanner for 4D flow

acquisitions, all the ferromagnetic parts were located in the control room,

adjacent to the scanner. In order to guarantee hygiene and safety of the scanner

in the event of leakages, water was the flowing medium for performing the

experiments. Hydraulic seal between the model, the pipes and the compliant

chambers was ensured using silicon.

The measuring equipment consisted of a high-fidelity factory-calibrated fiber

optic catheter (Samba Preclin; Vastra Frolunda, Sweden) and an ultrasonic

flow probe (Transonic; Ithaca, NY, USA), both accurately calibrated before the

experiments. Pressure and flow tracings were recorded with a data acquisition

system (BIOPAC, Goleta, CA, USA) at 250 Hz.

Magnetic Resonance:

MR acquisitions were performed with a 1.5 T scanner (Avanto; Siemens,

Erlangen, Germany). Firstly, phase-contrast data was acquired for 2D

quantification of flow-velocity. The images were taken in 4 different planes,

always perpendicular to the flow: inlet, descending aorta, innominate and

subclavian arteries. Moreover, 4D (i.e. 3 spatial dimensions in time)

acquisitions were performed. Two different sequences were tested: a standard

sequence (provided by Siemens, 15 minutes acquisition) and a higher temporal

and spatial resolution sequence (1 hour 10 minutes acquisition). OsiriX

Imaging Software (Pixmeo; Geneva, Switzerland), a DICOM viewer

specifically designed for navigation and visualization of medical images, was

used for quantification of flow from phase-contrast data using a previously

Summary

VI

validated in-house written plug-in. Mean velocity for the 4 above-mentioned

planes were obtained dividing each flow by the area of the region of interest

(ROI). The difference between the inlet and the other 3 measured flows

provided a measure of carotid flow. 4D data were analysed by means of the

Siemens 4D Flow software. A 3D mask was created and 6 planes of interest

were drawn (two at the inlet of the model, one in the aortic root, one before and

one after the upper branches, and one in the descending aorta) gathering

information on flow and velocity. The evolution of particle traces and

streamlines, originated by particle seeds placed in the 3D mask, was recorded

in order to obtain temporal information.

Assessing the effect of compliance:

The main shortcoming of using a rigid model is that the compliant behaviour of

blood vessels is not considered. In order to account for this and evaluate how

local fluid dynamics are affected, a compliant TGA phantom was also

manufactured, using a rubber-like commercially available compound

compatible with PolyJet rapid prototyping, namely TangoPlus FullCure 930.

The new compliant TGA geometry was connected to the same hydraulic circuit

used for the rigid models, so that the only difference in the experiment was

represented by the material of the phantom.

MATERIALS AND METHODS II: COMPUTATIONAL

Anatomical models:

The two geometries used for the CFD simulations were the same as those

printed for the in-vitro study. In order to better understand how geometric

differences could affect the hemodynamics in the aortic arch and to better

evaluate the effect of the Lecompte maneuver, an additional patient with a

different anatomical arrangement was taken into consideration. This patient

had TGA repaired with ASO but the Lecompte maneuver was not performed in

this instance. This resulted in the aorta preserving a more spiral curvature

(Figure d). This case presented an enlarged aortic root, typical of TGA patients,

but the aortic arch is more similar to the control geometry, and is hereby

referred to as “spiral” geometry.

Summary

VII

Figure d - Comparison of three different geometries: TGA, control and “spiral”. The aorta is

shown in red and the pulmonary arteries are shown in blue.

CFD simulations:

The STL files of the geometries obtained from Mimics were imported in ICEM

(Ansys Inc., Canonsburg, PA), in order to build the finite volume mesh

(900,000 tetrahedral elements with 5 boundary prism layers) as shown in

Figure e.

Figure e - Control (left), TGA (centre) and spiral (right) geometries meshed with tetrahedral

elements. The different colour is due to the presence of three planes, created in order to

evaluate the fluid dynamics at these positions.

Summary

VIII

Computational simulations were run using commercial finite volumes software

(Ansys Fluent 14, Fluent Inc.©, Lebanon, NH). The second order upwind

method was chosen to solve the convective terms of the Navier-Stokes

equations in 3D fluid domains, with SIMPLE algorithm to solve the pressure-

velocity coupling. The solver is an implicit “Least square cell method” (1st

order, temporal increment = 10-4

s). Water was used as flowing medium (ρ=

1000 Kg/m3, μ= 1 cP) and laminar flow motion conditions were observed in all

cases. In order to reach asymptotic behaviour in the results, 5 cardiac cycles

per simulation were replicated for a total of 400,000 time-steps.

Each of the 3 aortic models (TGA, control and spiral) presented 5 boundary

faces: one aortic inlet, three brachiocephalic outlets (Innominate, Carotid,

Subclavian), and one descending aorta outlet. An 11 term Fourier series was

used to impose at the inlet of the model the same velocities measured during

the experiments (Vmean = 0.9 m/s, ranging from -0.8 m/s and 2.8 m/s). In order

to provide the necessary boundary conditions, each outlet was coupled with a

lumped parameter network (LPN, in Figure f). The LPN reproduced exactly the

experimental circuit described above.

Figure f - LPN implemented at each outlet branch. The first part of the network is different for

each outlet: C stands for the compliant chamber, R1 represents the non-linear resistance of the

taps, R2 the distributed resistances of the tubes. The second part of this LPN is common to

every outlet: Ct and Rt represent the overall compliance and resistance of the circuit.

EXPERIMENTAL RESULTS AND DISCUSSION

All hydrodynamic experiments and data acquisition were performed

successfully. The mock circuit proved to be suitable for the representation of

the downstream districts of the circulatory system and pressure and flow values

are in the physiological range, setting adequate boundary conditions.

Summary

IX

Consideration on temporal resolution for 4D flow acquisition:

There were no substantial differences between the flows acquired with the two

sequences. In both cases the mean flow (OsiriX Qmean= 5.5 L/min, Standard

Qmean= 5.5 L/min, HighRes Qmean= 7 L/min) and the amplitude of the signals

(OsiriX Qpeak= 17 L/min, Standard Qpeak= 15 L/min, HighRes Qpeak= 20 L/min)

were comparable with those measured with OsiriX from traditional 2D

Cartesian phase-contrast flow acquisitions, which represented our reference

values. The high resolution sequence was noisier and slightly overestimated the

systolic peak. From a qualitative point of view, images from the high resolution

sequence did not provide any additional information compared to the standard

one, and exhibited a noisier background, likely due to compromised signal-to-

noise ratio (SNR), as well as a smaller number of streamlines, which could not

represent adequately the fluid dynamics in the arch. As the results obtained

from the 15 minute acquisition were satisfactory as validation data for the

computational study, these were further analysed.

4D flow results: TGA vs. control anatomy:

Qualitative fluid dynamics differences between different geometries can be

appreciated thanks to 4D flow visualisation, in particular streamlines analysis.

Overall, the TGA model exhibited more chaotic flow in both systolic and

diastolic phases. In systole (Figure g) a high velocity jet was clearly visible,

impinging on the enlarged aortic root wall. This was not observed in the

control model.

Summary

X

Figure g - Streamlines in the TGA geometry (left) compared with streamlines in the control

geometry (right) at systole.

Compliant TGA model:

Noticeable geometric changes were observed in the compliant model, once

pressurised, due to the highly distensible nature of TangoPlus. The geometry

did not retain its original shape. As the aim of the work is to study the effect of

a specific geometry on the fluid dynamics, this material was deemed as not

suitable. The model was also prone to tear and, prior to inserting the model in

the MR scanner for data acquisition, structural failure of the material occurred

in correspondence of the aortic arch. Pressure data was acquired prior to

failure, showing a damped pressure waveform, as expected due to the

additional proximal compliance.

COMPUTATIONAL RESULTS AND DISCUSSION

Model validation:

There were no substantial differences between the flows acquired during the

experiments and the one calculated by the CFD simulations, both for the TGA

and the control geometries. The computational model replicated appropriately

the experimental hydrodynamic environment. Flow distribution results were in

excellent agreement, with a maximum difference in the flow split in the TGA’s

subclavian of 3.5%. Overall distributions and flow tracings in the

computational models were in good agreement with in-vitro data. Satisfactory

Summary

XI

agreement was also noted in terms of pressure tracings and pressure values:

experimental and computational mean pressures matched both in the TGA

model (84.6 mmHg vs. 85.7 mmHg) and in the control model (87.0 mmHg vs.

83.2 mmHg).

Qualitative comparison between 4D flow and CFD simulations:

A good agreement between 4D flow and CFD was assessed for both TGA and

control geometries (Figure h). In particular, CFD showed the same flow jet

impinging at the top of the aortic root wall in the TGA model, and the

surrounding whirl visible in 4D flow images. In the control model it is possible

to observe the uniform flow jet in the aortic root, smoothly reaching the upper

branches, as in the 4D flow data. All the ranges of velocities are comparable in

terms of magnitude and distributions, both in systole and in diastole.

Figure h – 4D flow streamlines (left) compared with CFD streamlines (right) at systole for the

TGA (top) and the control (bottom) geometries.

CFD anatomical assessment: TGA, control and spiral geometries

The mean flows at each outlet and the flow split in the three geometries are

comparable: the difference is around 1%, with a maximum of 1.1% in the

Summary

XII

subclavian arteries. Pressures in the TGA model are similar to the control, with

a maximum difference in the subclavian artery (3.7%). Comparing the spiral

and the control geometries, the difference in flow split is around 1%, with the

largest variation in the carotid (2.5%) and differences in flow and pressure

waveforms are negligible at every face of the models.

Streamlines highlighted the differences between the geometries. In systole

(Figure i), the control model exhibited a streamlines pattern which follows the

geometry, while in the TGA and the spiral geometries the flow jet, surrounded

by low-velocity whirling streamlines, hits the wall, losing velocity before

reaching the upper branches and causing a chaotic trend of the flow. In diastole

it is possible to underline a more chaotic streamlines trend in the enlarged root

of both the TGA and spiral geometries compared to the control.

This fluid dynamic feature, characterized by low velocities and recirculation,

could be important from a clinical point of view, since it can promote particles

deposition and consequently thrombus, clotting and plaques formation, thus

increasing long-term risk of atherosclerosis.

Figure i - Control (left), TGA (central) and spiral (right) velocity streamlines at systole.

In TGA and spiral geometries the area interested by a WSS > 25 Pa

(green/yellow) is more extended than in the control model, reaching values

Summary

XIII

around 35 Pa (red), particularly where the root narrows (Figure l). The risk of

high WSS is a mechanical damage of the inner vessel wall, which could

weaken the vessel and possibly initiate a lesion.

Figure l - WSS in control (left), TGA (central), spiral (right) models.

In both TGA and spiral roots the velocity vectors (Figure m) showed more

complex dynamics than in the control model, with presence of secondary

flows. While higher velocities in the control model are clustered in the centre

of the surface, in the other two they have a random distribution. In the

ascending aorta, the effect of the sudden shrinking after the enlarged root is

clearly visible.

Figure m – Velocity vectors in control (left), TGA (central), spiral (right) anatomies.

Summary

XIV

CONCLUSIONS

This study provides a reliable methodology for hemodynamic evaluations in

patient-specific models, highlighting how new techniques like 4D MR flow can

help in clinical analysis. Moreover CFD simulations, validated against in-vitro

data, proved to be a useful tool to study complex geometries in order to help

clinicians to evaluate the patients’ conditions and potentially assess novel

procedures. This methodology provides results that are coherent with clinical

ranges from patients’ data and from the literature. The results thus have clinical

relevance. The anatomical features of TGA, mainly the enlarged aortic root

(common to the “spiral” model, in which the Lecompte maneuvre was not

performed), have an unfavourable hemodynamic effect.

FUTURE WORK

Statistical analysis:

It is important to include more patients in the study in order to draw

conclusions on the statistical significance of the findings. Additional patients

can be implemented in the CFD simulations, whose reliability has been proven

in the validation study. Increasing the number of both TGA and healthy cases,

it is possible to characterize this congenital heart disease with statistical

confidence and potentially gather insight into long-term effects which at

present are lacking due to the absence of long-term follow up clinical data.

Compliant model:

A compliant model, reflecting the distensible behaviour of real vessels, would

be helpful to further understand the fluid dynamics, especially local

hemodynamics in the aortic root. The material must be deformable but also

able to withstand physiological pressures for the whole duration of the MR

acquisition. In this study Tango Plus suffered structural failure, so finding

alternative materials warrants future investigation.

Provided that significant differences are observed between rigid and compliant

phantoms, it is possible to account for such compliant behaviour also in the

computational simulations, using a fluid-structural interaction (FSI) approach.

One problem typically related to this tool is the lack of information on the

Summary

XV

elastic characteristics of natural vessels. However, using an artificial material,

thoroughly characterised experimentally, all the elastic characteristics could be

implemented in the FSI simulations.

Pixel by pixel inlet imposition:

4D MR flow is a novel technique providing a breath of hemodynamic

information, and it is appealing to try and develop methods of data extraction

in order to refine the computational simulations. For example, imposing

velocities values to each element of the mesh at the inlet of the computational

model, instead of the spatial average, could allow to obtain a more detailed

characterization of complex fluid dynamics. It is possible, from MR data, to

extract the velocity in each of the pixels of the inlet face, in the three

components x, y and z. The effect of this different inlet on the local fluid

dynamics, such as better characterising whirling and recirculation in the aortic

root, warrants further study.

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SOMMARIO

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INTRODUZIONE

La Trasposizione delle Grandi Arterie (TGA) è una grave cardiopatia

congenita, cianotica che si manifesta alla nascita. Tale patologia, la cui

incidenza è stimata intorno ai 20-30 casi all’anno per ogni 100.000 nati vivi ha

una predominanza per il sesso maschile del 60-70%. È caratterizzata da una

discordanza arterio-ventricolare, con l’aorta che ha origine dal ventricolo

destro e l’arteria polmonare dal ventricolo sinistro. La configurazione

anatomica che ne risulta prevede un funzionamento in parallelo tra circolazione

polmonare e sistemica, piuttosto che in serie.

Questa situazione è incompatibile con la vita, a meno di comunicazioni tra i

due circoli, polmonare e sistemico, che permettano al sangue deossigenato di

miscelarsi con il sangue ossigenato. Per questo motivo, in tali pazienti, viene

eseguita una settostomia atriale alla nascita, necessaria per stabilizzare le

condizioni del neonato prima di procedere con l’operazione che riposiziona i

grandi vasi nei loro siti fisiologici, chiamata appunto “operazione di inversione

arteriosa” (Arterial Switch Operation, ASO). Nonostante l’operazione di

inversione delle grandi arterie ripristini una normale disposizione delle

strutture cardiache, numerose complicazioni a lungo termine possono insorgere

e per di più gli effetti a lungo termine non sono ancora ben noti dal momento

che il primo caso di ASO è stato riportato all’inizio degli anni Ottanta. In

particolare, è stato notato come le caratteristiche anatomiche tipiche di pazienti

TGA trattati con ASO, quali la radice aortica allargata e la acuta angolazione

dell’arco aortico, potrebbero influenzare l’emodinamica nel distretto aortico.

OBIETTIVO DELLO STUDIO

L’obiettivo di questo lavoro è di creare un modello computazionale della

neoaorta a seguito di ASO, di validarlo, e infine di usarlo per valutare come

differenti anatomie possono influenzare la fluidodinamica locale.

Particolare attenzione è stata posta sulla Lecompte maneuver, manovra

chirurgica nella quale l’arteria polmonare e le sue diramazioni vengono

spostate anteriormente all’aorta, generando una inusuale disposizione

anatomica con l’aorta in posizione posteriore e compressa dalle arterie

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polmonari. In letteratura è stato suggerito che il mantenimento di una

disposizione più fisiologica potrebbe giovare da un punto di vista

emodinamico: è stato pertanto suggerito di ricreare la curvatura naturale

dell’arco aortico, altrimenti compromessa dalla Lecompte maneuver. In questo

lavoro è stata modellata e analizzata anche questa anatomia.

In Figura a è stato riportato uno schema riassuntivo del lavoro svolto: partendo

da dati clinici, sono stati generati i modelli 3D da usare sia per lo studio

sperimentale che per quello computazionale. I risultati sperimentali sono stati

usati per validare il modello computazionale che, una volta validato, è stato

applicato allo studio delle diverse anatomie indagate.

Figura a – Rappresentazione schematica del lavoro svolto.

MATERIALI E METODI SPERIMENTALI

E’ stato scelto un approccio sperimentale dato che uno studio in-vitro è in

grado di fornire dati controllabili e riproducibili.

Modelli anatomici:

Lo studio è stato svolto a livello patient-specific. Per apprezzare le differenze

emodinamiche, sono stati selezionati due soggetti della stessa età e con

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XIX

caratteristiche fisiche comparabili (15 anni, 1.7 m2 BSA, maschi): un paziente

TGA corretto con ASO e un controllo sano.

Di entrambi i pazienti, i dati di risonanza magnetica erano disponibili e sono

stati utilizzati per ricostruirne le anatomie 3D, usando un software

commerciale (Mimics, Materialise, Leuven, Belgium). I modelli finali

includono la radice aortica, l’aorta ascendente e discendente e le arterie

brachiocefaliche (anonima, carotide sinistra e succlavia sinistra).

Il volume 3D creato per ogni modello può essere esportato come un file

Standard Triangle Language (STL), compatibile con la tecnica di

prototipazione rapida, conosciuta come tecnologia PolyJet, che permette di

stampare modelli fisici 3D. Per il processo di stampaggio è stata scelta una

resina rigida e trasparente (Watershed 11122; DSM Somos, Elgin, IL) (Figura

b).

Figura b – Modello di controllo (sinistra) e TGA (destra) stampati con la tecnica di

prototipazione rapida a partire da immagini di MR, che mostrano la posizione dell’aorta

ascendente (AAo) nel modello TGA.

Circuito idraulico:

I modelli sono stati montati in un circuito idraulico (Figura c), consistente in

una pompa pulsatile con un volume di eiezione e un range di frequenza

cardiaca regolabili, quattro elementi Windkessel e quattro valvole a rubinetto

ad ogni uscita dei modelli, per riprodurre rispettivamente la distensibilità delle

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arterie e la resistenza vascolare, e una riserva il cui battente idraulico

rappresenta la pressione atriale (9 mmHg).

Figura c – Rappresentazione schematica del circuito.

Ogni componente Windkessel è costituita da un cilindro in Perspex, con una

valvola a tre posizioni nella parte superiore per controllare il volume di aria

contenuto nel cilindro, regolando così la rigidezza del circuito. Le valvole a

rubinetto sono state regolate in modo da ottenere un intervallo di pressione

all’ingresso del circuito di 115/60 mmHg, in accordo con la pressione misurata

nel paziente TGA, e una divisione fisiologica del flusso con il 55% in aorta

discendente e 45% nei vasi brachiocefalici. Gli elementi resistivi utilizzati

hanno il vantaggio di essere facilmente controllabili, sebbene fortemente

dipendenti dal flusso. Le loro curve caratteristiche non lineari sono state

ottenute imponendo diversi flussi e misurando la caduta di pressione a cavallo

del rubinetto.

La parte centrale del circuito è progettata priva di componenti metallici in

modo da poter essere inserita ed usata in uno scanner per risonanza magnetica.

I componenti ferromagnetici come la pompa, le console degli strumenti di

misurazione e il laptop sono stati posizionati nella stanza adiacente allo

scanner. Per questioni di sicurezza e igiene dello scanner nell’eventualità di

perdite, come fluido di prova è stato scelto di utilizzare acqua durante gli

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esperimenti. Le guarnizioni idrauliche, i modelli, i tubi e le camere complianti

sono state sigillate utilizzando silicone.

La strumentazione per le misurazioni è composta da un catetere di pressione a

fibra ottica (Samba Preclin; Vastra Frolunda, Sweden) e un flussimetro ad

ultrasuoni (Transonic; Ithaca, NY, USA), entrambi accuratamente calibrati

prima degli esperimenti. Pressioni e flussi sono stati registrati con un sistema di

acquisizione di dati (BIOPAC , Goleta, CA, USA) a 250 Hz.

Risonanza Magnetica:

Le acquisizioni sono state effettuate con uno scanner da 1.5 T (Avanto;

Siemens, Erlangen, Germany). Per prima cosa sono stati acquisiti dati a

contrasto di fase per le quantificazioni 2D di flusso e velocità in 4 diversi piani,

scelti perpendicolari al flusso in corrispondenza dell’ingresso del modello,

dell’aorta discendente, anonima e succlavia. Successivamente sono state

acquisite due diverse sequenze 4D (le 3 dimensioni spaziali nel tempo): una

standard (fornita dalla Siemens, della durata di 15 minuti) e una con

risoluzione spaziale e temporale aumentate (della durata di 1 ora e 10 minuti).

Il software OsiriX Imaging (Pixmeo; Geneva, Switzerland), progettato per la

navigazione e la visualizzazione di immagini mediche, è stato utilizzato per la

quantificazione di flussi da dati a contrasto di fase usando un plug-in

precedentemente scritto e validato dal gruppo di ricerca del Great Ormond

Street Hospital di Londra. Le informazioni sulle velocità nei quattro piani

descritti prima sono state ottenute dividendo i flussi per l’area delle rispettive

regioni di interesse (ROI). La misura del flusso in carotide è stata ottenuta

sottraendo al flusso in ingresso i 3 flussi calcolati alle altre uscite. I dati 4D

sono stati analizzati per mezzo del software Siemens 4D Flow. Dopo aver

creato una maschera 3D, sono stati disegnati 6 piani di interesse (2 all’ingresso,

1 in radice aortica, 2 lungo l’arco aortica, rispettivamente prima e dopo i vasi

brachiocefalici e uno in aorta discendente) per estrarre dati su velocità e flussi.

Infine, per studiare l’evoluzione temporale delle particelle di flusso lungo

l’arco aortico e le sue diramazioni, sono state riprodotte le streamlines

registrate nel modello scegliendo opportuni piani di origine nella maschera 3D.

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XXII

Stima dell’effetto della distensibilità:

Il principale limite nell’uso di modelli rigidi consiste nel trascurare la

deformabilità fisiologica dei vasi. Per studiarne l’effetto sulla fluidodinamica

locale, è stato perciò stampato lo stesso modello TGA ma con un un materiale

gommoso, e quindi distensibile, commercialmente disponibile e compatibile

con la prototipazione rapida, chiamato Tango Plus FullCure 930. La nuova

geometria TGA deformabile è stata connessa allo stesso circuito idraulico

utilizzato per i modelli rigidi, in modo da valutare la sola influenza del

materiale.

MATERIALI E METODI COMPUTAZIONALI

Modelli anatomici:

Le stesse due anatomie stampate per gli studi in-vitro sono state utilizzate per

le simulazioni CFD. Per meglio comprendere come le differenze geometriche

possono influenzare l’emodinamica nell’arco aortico e valutare l’effetto della

Lecompte maneuver, è stato considerato un ulteriore paziente, con una diversa

disposizione anatomica. È un paziente TGA che ha subito una ASO senza

Lecompte maneuver. Il risultato è una disposizione anatomica differente

(Figura d), con l’aorta che mantiene una curvatura più fisiologica. Anche

questo caso presenta una radice aortica allargata, tipica dei pazienti TGA, ma

l’arco aortico è più simile alla geometria di controllo. Questa geometria è

definita, nel nostro studio, con il nome di “spiral”.

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XXIII

Figura d - Confronto tra le tre diverse geometrie: TGA, controllo e “spiral”. L’aorta è colorata

in rosso, mentre l’arteria polmonare in blu.

Simulazioni CFD:

I file STL delle geometrie, ottenuti da Mimics, sono stati importate in ICEM

(Ansys Inc., Canonsburg, PA), per creare le mesh a volumi finiti (900000

elementi tetraedrici con 5 strati di prismi al contorno), come mostrato in Figura

e.

Figura e - Controllo (sinistra), TGA (centrale) and spiral (destra) con mesh ad elementi

tetraedrici. I diversi colori corrispondono a 3 piani, creati in ciascuna geometria per valutare la

fluidodinamica in quelle posizioni.

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XXIV

Le simulazioni computazionali sono state effettuate con un software

commerciale per simulazioni a volumi finiti (Ansys Fluent 14, Fluent Inc. ©,

Lebanon, NH). Il metodo scelto per risolvere i termini convettivi delle

equazioni di Navier-Stokes nel dominio fluido 3D è il metodo Upwind di

secondo ordine, con l’algoritmo SIMPLE per risolvere l’accoppiamento

pressione-velocità.

Il metodo di risoluzione adottato è il metodo “Least square cell” (primo ordine,

incremento temporale = 10-4

s). Il fluido scelto per le simulazioni è l’acqua (ρ=

1000 Kg/m3, μ= 1 cP) e condizioni di moto laminare sono state verificate in

ogni simulazione. Per raggiugere un comportamento asintotico dei risultati,

sono stati simulati 5 cicli cardiaci, corrispondenti a 40000 passi temporali.

Ognuno dei 3 archi aortici modellati (TGA, controllo e spiral) presenta 5 facce:

una di ingresso, e quattro di uscita (anonima, carotide, succlavia e aorta

discendente). Le velocità misurate durante gli esperimenti sono state imposte

come ingresso del modello grazie a una serie di Fourier a 11 termini (Vmedia =

0.9 m/s, con intervallo da -0.8 m/s e 2.8 m/s). Per fornire le adeguate

condizioni al contorno ogni uscita è stata accoppiata ad una rete a parametri

concentrati (Figura f). Questa rete riproduce esattamente il circuito

sperimentale precedentemente presentato.

Figura f - Rete a parametri concentrati ad ogni uscita del modello.La prima parte della rete è

diversa per ogni uscita: C indica la camera compliante, R1 rappresenta la resistenza non lineare

del rubinetto, R2 la resistenza distribuita dei tubi. La seconda parte della rete è in comune tra

tutte le uscite: Ct e Rt rappresentano la complianza e la resistenza totali del circuito.

RISULTATI SPERIMENTALI E DISCUSSIONE

Tutti gli esperimenti idrodinamici e le acquisizioni sono stati condotti con

successo. Il circuito idraulico si è rivelato adatto a rappresentare i distretti a

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XXV

valle del sistema circolatorio. Le pressioni ed i flussi ottenuti si trovano tutti in

un intervallo di valori fisiologico.

Considerazioni sulla risoluzione temporale delle acquisizioni 4D flow:

Non sono state notate differenze sostanziali tra i flussi acquisiti con le due

sequenze. I valori di flusso medio (OsiriX Qmedio=5.5 L/min, Standard

Qmedio=5.5 L/min, HighRes Qmedio=7 L/min) e l’ampiezza dei segnali (OsiriX

Qmax=17 L/min, Standard Qmax=15 L/min, HighRes Qmax=20 L/min) sono

confrontabili con quelli estratti da OsiriX tramite l’acquisizione standard 2D in

contrasto di fase, utilizzata come termine di paragone. La sequenza ad alta

risoluzione ha fornito risultati più rumorosi e ha leggermente sovrastimato il

picco sistolico.

Da un punto di vista qualitativo le immagini estratte tramite l’acquisizione ad

alta risoluzione non hanno fornito nessuna informazione aggiuntiva rispetto

alla sequenza standard, e addirittura hanno mostrato uno sfondo rumoroso,

dovuto al rapporto segnale-rumore compromesso, e un numero inferiore di

streamlines, che potrebbero quindi non rappresentare in modo completo la

fluidodinamica nell’arco aortico.

Risultati del 4D flow: anatomia TGA vs. controllo:

Le differenze qualitative tra le due diverse geometrie possono essere

apprezzate grazie alla visualizzazione del 4D flow, e in particolare tramite

l’analisi delle streamlines. Complessivamente, il flusso nel modello TGA

risulta essere più caotico sia in sistole che in diastole. In sistole (Figura g), il

getto ad alta velocità che impatta contro la parete della radice aortica,

chiaramente visibile nella geometria patologica, è assente nel modello di

controllo.

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XXVI

Figura g - Streamlines durante la sistole nella geometria TGA (sinistra) confrontate con il

modello di controllo (destra).

Modello TGA distensibile:

Una volta messo sotto pressione, sono stati osservati importanti cambiamenti

nella forma del modello distensibile, a causa della grande deformabilità del

materiale. In particolar modo la radice aortica ha perso la forma originale. Dal

momento che lo scopo del lavoro è studiare gli effetti di una specifica

geometria sulla fluidodinamica, questo materiale si è rivelato inadatto. Prima di

inserire il modello dentro lo scanner, inoltre, il materiale è andato incontro a

cedimento strutturale. I valori di pressioni sono stati acquisiti prima del

cedimento, mostrando, come previsto, una forma d’onda più smorzata a causa

dell’aumento della compliance prossimale.

RISULTATI COMPUTAZIONALI E DISCUSSIONE

Validazione del modello:

Non essendoci differenze sostanziali tra i flussi acquisiti durante gli

esperimenti e quelli calcolati dalle simulazioni CFD, né per la geometria TGA

né per quella di controllo, possiamo affermare che il modello computazionale

replica correttamente le condizioni idrauliche sperimentali. Le distribuzioni dei

flussi tra le uscite sono in ottimo accordo, con una differenza massima del

3.5% nell’arteria succlavia del modello TGA. L’andamento temporale dei

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XXVII

flussi conferma che la simulazione CFD riproduce in maniera soddisfacente le

condizioni del set-up sperimentale. Inoltre è apprezzabile una soddisfacente

corrispondenza per quanto riguarda le pressioni medie e il loro tracciato nel

tempo, sia per il TGA (85.7 mmHg dal test sperimentale vs. 84.6 mmHg dalla

simulazione) che per il controllo (87.0 mmHg dal test sperimentale vs. 83.2

mmHg dalla simulazione).

Confronto qualitativo tra il 4D flow e le simulazioni CFD:

La corrispondenza tra i risultati del 4D flow e quelli computazionali è ottima,

sia per il modello TGA che per il controllo (Figura h). In particolare il CFD

mostra lo stesso getto che impatta contro l’apice della radice aortica nel

modello TGA e gli stessi vortici circostanti che si notano nelle immagini del

4D flow. Nel modello di controllo è possibile osservare il getto, uniforme

lungo l’intero arco aortico, che scorre verso le arterie brachiocefaliche, identico

a quello mostrato dal 4D flow. Gli intervalli di velocità sono confrontabili sia

in termini di valore assoluto che di distribuzione, in sistole come in diastole.

Figura h – Confronto tra le streamlines ottenute dal 4D flow (sinistra) e quelle ricavate dalla

simulazione CFD (destra) in sistole nel modello TGA (in alto) e nel controllo (in basso).

Sommario

XXVIII

Confronto CFD tra i modelli TGA, di controllo e “spiral” :

Il flusso medio ad ogni uscita e la sua ripartizione sono confrontabili nelle tre

geometrie: la differenza è intorno all’1%, con un massimo di 1.1% in

succlavia. La pressione nel modello TGA è molto simile a quella nel controllo,

con una variazione massima in succlavia (3.7%). Confrontando la geometria

spiral con il controllo, la differenza è intorno all’1%, con la più grande

variazione in carotide (2.5%). La stessa situazione si può osservare per le

forme d’onda di flussi e pressioni, dove le differenze sono trascurabili in ogni

faccia dei modelli. Le streamlines mettono in evidenza le differenze tra le

geometrie. In sistole (Figura i) si nota come, mentre nel controllo le linee di

flusso seguono la geometria, nel modello TGA e in quello spiral un getto ad

alta velocità, circondato da vortici a bassa velocità, colpisce la parete perdendo

velocità prima di raggiungere le arterie brachiocefaliche e causando un

andamento casuale del flusso. In diastole è possibile evidenziare l’andamento

meno ordinato delle streamlines nella radice aortica del modello TGA e spiral,

se confrontate con il controllo.

Questa situazione fluidodinamica, caratterizzata da basse velocità e ricircoli,

può essere importante da un punto di vista clinico, poiché promuove la

formazione di coagulo, di trombo o placca, aumentando il rischio a lungo

termine di arteriosclerosi.

Sommario

XXIX

Figura i - Streamlines in sistole nei modelli di controllo (sinistra), TGA (centrale) e spiral

(destra)

Nelle geometrie TGA e spiral, l’area caratterizzata da valori di sforzo alla

parete più alti di 25 Pa (giallo/verde) è più estesa rispetto al modello di

controllo, e il WSS raggiunge persino valori intorno ai 35 Pa, specialmente

dove la radice si stringe (Figura l). Alti valori di sforzo alla parete possono

causare danni meccanici alla parete interna dei vasi [Chien et al., 1998 and

Shyyy ,2001], che può portare all’ indebolimento degli stessi e potenzialmente

a un inizio di lesione.

Figura l - Sforzo alla parete nel modello di controllo (sinistra), TGA (centrale) e spiral

(destra).

Sommario

XXX

I vettori di velocità (Figura m) nella radice sia del modello TGA che nello

spiral mostrano una fluidodinamica più complessa che nel controllo, con

presenza di flussi secondari. Mentre le zone ad alta velocità sono concentrate al

centro della radice del controllo, negli altri due modelli hanno una

distribuzione casuale. In aorta ascendente l’effetto del brusco restringimento è

chiaramente visibile.

Figura m – Vettori di velocità nella radice aortica, in aorta ascendente e in aorta discendente

dei modelli di controllo (sinistra), TGA (centrale) e spiral (destra).

CONCLUSIONI

Conclusioni:

Questo studio fornisce un metodo affidabile per la valutazione

dell’emodinamica in modelli patient-specific, evidenziando come la nuova

tecnica di 4D MR flow possa essere utile per l'analisi clinica. Inoltre le

simulazioni CFD, validate con i risultati in-vitro, si sono dimostrate uno

strumento valido per studiare geometrie complesse e aiutare i medici a valutare

le condizioni del paziente ed eventualmente a testare virtualmente procedure

chirurgiche innovative. Questo metodo ha fornito risultati confermati da ogni

simulazione e coerenti con gli intervalli fisiologici presenti ini letteratura. I

risultati hanno una grande rilevanza dal punto di vista clinico. Le caratteristiche

anatomiche derivanti dalla correzione della trasposizione delle grandi arterie, in

particolare la radice aortica dilatata (comune al modello “spiral”, in cui la

Sommario

XXXI

Lecompte maneuver non è stata effettuata), hanno dimostrato avere un effetto

negativo sull’emodinamica.

SVILUPPI FUTURI

Analisi statistica:

Sarebbe interessante includere ulteriori pazienti nello studio, in modo da poter

tratte conclusioni di rilevanza statistica da un punto di vista clinico. Le

simulazioni CFD, la cui affidabilità è stata provata in questo studio, sarebbero

quindi la metodologia da usare per l’analisi di nuove anatomie patient-specific.

Aumentando il numero sia di pazienti TGA che di casi fisiologici, sarà

possibile caratterizzare questa patologia cardiaca congenita con confidenza

statistica, intuendo potenzialmente gli effetti a lungo termine ad oggi ancora

sconosciuti per l’assenza di un adeguatamente esteso follow-up clinico.

L’effetto della distensibilità:

Un modello distensibile, che rispecchia il comportamento deformabile dei vasi

fisiologici, sarebbe d’aiuto per capire meglio la fluidodinamica, e in particolare

l’emodinamica locale nella radice aortica. Il materiale da usare per stampare

tali modelli deve essere deformabile, ma anche capace di resistere sotto

pressione per il tempo richiesto dalll’acquisizione delle immagini di risonanza

magnetica. In questo studio il Tango Plus ha subito un cedimento strutturale,

quindi la ricerca di materiali alternativi deve essere oggetto di eventuali

indagini future.

Purché un analisi sperimentale con un circuito idraulico mostri differenze tra i

modelli rigidi e distensibili, è possibile tenere conto del comportamento

distensibile anche nelle simulazioni computazionali, sfruttando un approccio di

interazione fluido-struttura (FSI). Un problema solitamente legato a questo

strumento è la mancanza di informazioni sulle proprietà elastiche del vaso

naturale. Utilizzando un materiale artificiale, approfonditamente caratterizzato

sperimentalmente, tutte le proprietà elastiche possono essere implementate

nelle simulazioni FSI

Sommario

XXXII

Imposizione pixel per pixel del flusso in ingresso:

Four-Dimensional MR flow è una tecnica nuova, in grado di fornire utili

informazioni emodinamiche. E’ interessante cercare di sviluppare nuovi metodi

di estrazione dei dati, in modo da migliorare le simulazioni computazionali. Per

esempio, imporre valori di velocità a ogni elemento della faccia di ingresso del

modello computazionale, invece del valore medio, potrebbe permettere di

caratterizzare la complessa fluidodinamica della radice aortica in modo più

dettagliato. Dalle immagini di risonanza magnetica è infatti possibile estrarre il

valore della velocità nelle sue tre componenti x, y e z in ogni pixel della faccia

di ingresso. L’effetto di questo tipo di ingresso sulla fluidodinamica locale, ad

esempio per caratterizzare meglio i ricircoli e i vortici all’interno della radice

aortica, potrebbe essere oggetto di studi futuri.

Chapter 1 Introduction: the clinical problem

1

CHAPTER 1

INTRODUCTION: THE

CLINICAL PROBLEM


2

1.1 TRANSPOSITION OF THE GREAT ARTERIES

Transposition of the Great Arteries (TGA) is the most common cyanotic

congenital heart disease in neonates [Lincon et al., 1984]. The incidence of the

disease is estimated as 20-30 cases per 100,000 live births every year, with a

60-70% male predominance [Kalogeropoulos et al., 2009].

Although the aetiology of this congenital disease is still unknown, some risk

factors have been identified:

- Mother’s age > 40 years

- Alcoholism

- Diabetes

- Poor nutrition during pregnancy

- Rubella or other viral illness during pregnancy.

The hallmark of TGA is ventriculo-arterial (VA) discordance, whereby the

aorta arises from the right ventricle and the pulmonary artery (PA) arises from

the left ventricle (Figure 1.1) [Warnes, 2006].

Figure 1.1 - Schematic representation of the heart with TGA, highlighting the origin of the

great vessels from the incorrect ventricle [yorksandhumberhearts.nhs.uk].


3

This anatomical arrangement impacts on the way blood circulates throughout

the body; in fact, the pulmonary and systemic circulations function in parallel

rather than in series. Oxygenated pulmonary venous blood returns to the left

atrium and left ventricle, but it is recirculated to the pulmonary vascular bed

via the abnormal pulmonary arterial connection to the left ventricle.

Deoxygenated systemic venous blood returns to the right atrium and right

ventricle where it is pumped to the systemic circulation, effectively bypassing

the lungs.

This parallel circulation results in insufficient oxygen supply to the tissues and

excessive right and left ventricular workload [Allen et al., 2007]. It is

incompatible with prolonged survival unless oxygenated and deoxygenated

blood are mixed at some anatomic level, such as in the presence of atrial or

ventricular septal defects acting as left-to-right shunts [Planche et al., 1998].

In approximately 60% of patients, the aorta is anterior and to the right of the

pulmonary artery, while a subset of patients presents the aorta located in front

and to the left of the pulmonary artery. These two types of configurations are

referred to as dextro-transposition of the great arteries (d-TGA) and levo-

transposition of the great arteries (l-TGA).

In addition, most TGA patients (regardless of the spatial orientation of the

great arteries) exhibit a subaortic infundibulum, absence of subpulmonary

infundibulum, and fibrous continuity between the mitral valve and the

pulmonary valve [Shrivastava et al., 1976]. However, several exceptions have

been observed and cannot be placed in the above classifications [Allen et al.,

2007].

With regard to ventricular morphology, the patient’s ventricles have normal

shape and thickness in presence of atrial-septal defect at birth, otherwise the

right ventricular wall is considerably thickened, with such thickening

increasing with growth. Within few weeks, the right ventricle often becomes

enlarged and hypertrophied. The wall of the left ventricle, instead, begins to

thin and becomes compressed [Planche et al., 1998].

The aortic valve plane is rightward and anterior relative to the pulmonary

trunk. The fibrous continuity of the leaflets of the atrio-ventricular and the


4

ventriculo-arterial valves is located on the right side rather than on the left side

[Planche et al., 1998].

Coronary arterial anatomy in TGA patients is not only significantly different

from the normal circulatory arrangement, but it can also vary substantially

within this patients’ group. In most cases, the coronary arteries originate from

the aortic sinuses contiguous to the pulmonary trunk and run directly toward

the atrio-ventricular groove following a normal course. In other cases, they

originate from different sinuses and have an intramural course, or can be

characterised by abnormal looping around the vessels [Planche et al., 1998].

Another anatomical consideration concerns the pulmonary trunk, which can be

larger than the descending aorta, particularly in those cases presenting a

ventricular septal defect. Either isthmic coarctation or interrupted aortic arch

are very common in hearts with ventricular septal defect [Planche et al., 1998].

Following from these considerations, TGA clearly results in a complex

anatomical and physiological arrangement and, if untreated, this pathology

leads to a 30% mortality rate in the first week of life, 50% in the first month,

and 90% by the end of the first year [Allen et al., 2007]. On the other hand,

short-term and midterm survival rate exceeds 90% in cases of successfully

palliated or corrected TGA [Allen et al., 2007].

1.2 SURGICAL REPAIR OF TGA: THE ARTERIAL

SWITCH OPERATION

Repair of TGA has been attempted since the 1950s. The most successful

procedures were introduced in 1958 by A. Senning [Senning, 1959] and in

1963 by W.T. Mustard [Mustard, 1964]. Both approaches consisted in

redirecting blood flow within the atria: the former has the advantage of not

using foreign material (i.e. atrial patch), the latter of being simpler to manage

post-operatively [Kostantinov et al., 2004]. The Senning or Mustard procedures

thus represent an ‘atrial switch’ and have been used to palliate TGA until a new

procedure, referred to as ‘arterial switch’, was introduced in 1980. The first

successful arterial switch operation (ASO) was reported by Jatene [Jatene,


5

1982], and it proved to be more beneficial than the atrial correction [Planche et

al., 1998], as it avoids arrhythmias and dysfunctions of the systemic ventricle.

This thesis will focus solely on patients who underwent ASO procedure, as

described below.

In the first day of life, the primary step undertaken to treat a newborn with

TGA defect is to perform a Rashkind balloon atrial septostomy [Warnes,

2006]. This mini-invasive procedure uses a balloon catheter to enlarge the

foramen ovale (i.e. the hole allowing communication between the atria in the

fetal circulation) in order to prevent its sealing, otherwise naturally occurring

soon after birth. This facilitates blood mixing and increases oxygen saturation

(Figure 1.2).

Figure 1.2 - Rashkind procedure: the balloon catheter is inserted into the septal defect and

inflated. After inflation, the catheter is pulled back through the hole [http://www.hakeem-

sy.com].

After 10-15 days, the aorta and main pulmonary artery can be surgically

repositioned (Figure 1.3) performing the actual arterial switch, which requires

cardiopulmonary bypass and aortic cross clamping.


6

One particularly challenging feature of ASO is the relocation of the coronary

arteries, in order to avoid cardiac hypoxemia and ischemia of the myocardium.

The left and right coronary arteries ostia are visualized and excised from the

aortic root, with adjacent aortic wall, as "buttons". In abnormal looping course

the dissection of the coronary trunk is extended, in order to avoid any stretch or

kink during the relocation. The coronary artery buttons are then shifted

posteriorly and implanted into the facing sinuses of the main pulmonary artery

root. The left coronary artery is allocated in a low position and the right

coronary artery in a high position, in order to reduce the risk of distortion. A

lateral relocation could prevent compression by the pulmonary bifurcation.

The aorta is transected in the middle of the ascending portion, in order to lessen

the amount of reconstructed aorta posteriorly below the transferred pulmonary

artery bifurcation. The pulmonary trunk is transected 5–10 mm below its

bifurcation. Next, the main pulmonary artery and its branches are brought

forward (“Lecompte maneuver”), and the distal aorta is moved posteriorly

[Planche et al., 1998]. The distal aorta is now anastomosed (termino-terminal

anastomosis) to the root of the pulmonary valve. Reconstruction of the

pulmonary artery is then undertaken, utilising a patch of cryopreserved

pulmonary artery homograft.

Closure of the atrial septal defect completes the arterial switch repair [Planche

et al., 1998].


7

Figure 1.3 - Schematic representation of the arterial switch operation, including relocation of

coronary buttons [http://radiology.rsna.org].

1.3 POSTOPERATIVE COMPLICATIONS

Although arterial switch restores normal blood flow with mixing of oxygenated

and deoxygenated blood, and 90% 10-year survival has been reported to date,

indicating the success of the surgery [Warnes, 2006], several long-term

complications can arise. It should be noted that since this procedure has been

performed for only approximately 30 years, there are no long-term survivors so

far, and the possible extent of long-term complications is not fully appreciated

yet [Cohen et al., 2010].

Aortic wall abnormalities in surgically repaired TGA are likely due to

anomalous aorticopulmonary septation, damage to the vasa vasorum, and

surgical manipulations during ASO. Vasa vasorum transections during the

procedure, with consequent blood flow inhibition, can induce necrosis followed

by dilatation, This can lead to impaired distensibility of the neoaorta, and both


8

invasive and imaging-based studies have reported reduced aortic distensibility

in this group of patients [Ntsinjana et al., 2012]. Kinking of the coronary

arteries could also occur, because of the spatial arrangement of the vessels,

which does not respect the physiological one. Physical manipulations during

ASO, such as the reimplantation of the coronary arteries and suturing of the

two main vessels, can also lead to scarring and changes in the neoaortic root

wall, resulting in progressive aortic dilatation. Aneurysm formation and aortic

dissection have also been attributed to the ASO surgical handlings [Grotenhuis

et al., 2008].

After ASO, the neoaortic wall (the former pulmonary artery) is exposed to

higher systemic pressures. Concern has been raised about the ability of the

pulmonary root to adapt to a systemic pressure load. A study by Co-Vu et al.

discussed the risk for the native pulmonary root to dilate when implanted in the

aortic position, because of the histologic differences inherent to the vessel

walls of the pulmonary and aortic arteries. Also, no evidence of stabilization in

the root dimensions has been observed yet, around 15-20 years postoperatively

[Co-Vu et al., 2012].

Both aortic distensibility and aortic dimensions are crucial parameters affecting

aortic valve dynamics. Decreased distensibility of the aortic root increases

stress and strain on the neoaortic valve leaflets, therefore predisposing for

aortic valve dysfunction [Grotenhuis et al, 2008]. In addition, the risk for

neoaortic valve regurgitation appeared to increase with length of time after the

operation, which parallels the risk for neo-aortic root dilation [Co-Vu et al.,

2012].

Furthermore, the relocation of the ascending aorta onto the pulmonary valve

might create an abnormally acute angulation of the aortic arch (Figure 1.4) as a

consequence of the Lecompte maneuver. This postoperative morphological

feature has been suggested to induce enhanced systolic wave reflection and

consequent ascending aortic dilatation [Agnoletti et al., 2007]. The acute

angulation of the aortic arch, also referred to as “gothic” arch, has been

associated with compromised exercise capacity in these patients [Ou et al.,

2008]. Furthermore, the increased impedance due to a stiffer and abnormally


9

shaped aortic arch is likely to impinge on the VA coupling, as recently

indicated by Biglino et al. Thus, it has been suggested that TGA repair by ASO

can also have consequences on pumping efficiency and energetics [Biglino et

al., 2013].

Figure 1.4 - Fluoroscopy visualisation of an acute aortic arch, or gothic arch, as a result of

arterial switch operation. The enlarged aortic root (indicated by the yellow arrow) and the

indentation resulting from repositioning of the pulmonary arteries following the Lecompte

procedure (red arrow) can also be appreciated. Image modified from [Agnoletti et al., 2007].

1.4 SURGICAL REPAIR OF TGA: AN

ALTERNATIVE OPERATION

In a normal anatomy, the aorta and the main pulmonary artery present a spiral

spatial arrangement, while the ASO with Lecompte maneuver, as described in

paragraph 1.3, does not maintain the spiral relationship of the great arteries.


10

This has been indicated as one of the main causes for some of the clinical

complications in repaired TGA [Chiu et al., 2002]. For this reason, a modified

ASO by a so-called “spiral reconstruction” (Figure 1.5) has been advocated to

potentially help in avoiding coronary kinking.

Figure 1.5 - Comparison between normal heart (C), TGA (A), ASO with Lecompte (B) and

spiral ASO (D). It is possible to appreciate how the spiral procedure restores a more

physiological anatomy than the traditional arterial switch operation [image form Chiu et

al.,2002].

The three main differences of the spiral procedure with respect to the previous

technique have been described by the group who introduced it as follows: (1)

the aorta is amputated obliquely so that a larger left lip can be used as the floor

of the pulmonary pathway; (2) the right posterior part of the pulmonary trunk is

divided to make a larger flap to be everted to the left and a more leftward

pulmonary pathway after neoaortic anastomosis and posterior attachment


11

(suturing the caudal edge of the right pulmonary artery to the posterior

neoaorta) accordingly; (3) the posterior attachment site is ascertained after

release of the aortic cross-clamp, as in the previous technique (Figure 1.6).

However, to facilitate exposure, the aorta is cross-clamped again distal to the

deepest site of attachment and then stitched from the right [Chiu et al., 2002].

Therefore, this procedure restores the high-pressure ascending aorta to its

natural location, reducing the acute angulation of the aortic arch due to the

Lecompte maneuver and all the resulting issues, such as arch hypoplasia and

neocoarctation.

Chapter 2 Aim of the study

12

CHAPTER 2

AIM OF THE STUDY

Chapter 2 Aim of the study

13

As appreciated in Chapter 1, where the clinical problem of TGA and the

associated complications were briefly presented, the anatomy and physiology

of patients with repaired TGA are clearly very complex.

From a surgical point of view, the palliation and repair of this congenital heart

defect has evolved from the Senning and Mustard procedures (i.e atrial

switches) to the ASO with Lecompte modification, and recent attempts at

improving the hemodynamics post-repair (e.g. spiral surgery) suggest that

surgery for repairing TGA could still be optimised.

Moreover, from a clinical point of view, it has emerged that morphological

implications (such as the dilated aortic root and the angulation of the aortic

arch) are likely linked with some of the complications observed in TGA

patients in their teenage or early adulthood.

Gathering additional hemodynamic information by means of engineering tools

in order to systematically evaluate the neo-aorta in this patients’ population is

thus clinically important, not only to enhance knowledge of the fluid dynamics

in TGA, but also to predict potential problems that may arise later on in life in

these patients.

Taking advantage of state-of-the-art engineering tools, both experimental and

computational, this study aims to:

1) create a validated computational model of the neo-aorta following

ASO;

2) use the validated model to highlight differences in the local fluid

dynamics in different anatomies.

From a methodological point of view, hydrodynamic experimental data will be

acquired using magnetic resonance (MR) imaging, with a novel technique

known as 4D MR flow and using patient-specific phantoms. The study is then

taken forward in-silico, whereby a multi-scale modelling approach will be

adopted, including patient-specific 3D anatomy and physiology in the

simulations. As a modelling paradigm, the computational model will be

validated against experimental data. These approaches, their advantages and

their application in this specific context are described more in detail in the

following chapters.

Chapter 3 State of the art

14

CHAPTER 3

STATE OF THE ART


15

3.1 4D MAGNETIC RESONANCE IMAGING

3.1.1 PRINCIPLES

Magnetic Resonance (MR) imaging techniques provide non-invasive, highly

accurate anatomic depictions of the heart and vessels. Traditionally, MR

imaging of flow is accomplished using methods that resolve two spatial

dimensions (2D) in individual slices, adding functional information to the

anatomical data. Quantitative flow assessment is an important element of

cardiovascular MR studies in patients with congenital heart disease, and in

many cases information about blood flow is required in multiple arterial and

venous vessels [Kilner et al., 2010]. This conventional 2D method offers the

advantage of a sequential acquisition of flow data in different vessels with

individually adjusted velocity encodings [Nordmeyer et al., 2010]. However,

repeated planning and acquisition can be time-consuming. In addition, data

analysis is limited to those vessel sections that were targeted when planning the

scan.

A new technique, i.e. four-dimensional magnetic resonance imaging flow

acquisition (4D MR flow), allows to obtain 3D morphological information as

well as blood flow velocities in 3 directions for each voxel at each measured

time point of the cardiac cycle. It thus provides detailed quantitative flow and

vessel wall parameters with complete vascular coverage, also allowing

additional measurements of hemodynamic parameters such as shear stress,

vortex formation, or pressure fields. Therefore, it is a reliable and resourceful

tool to quantify blood flow in patients with congenital heart diseases [Uribe et

al., 2009].

One major indication of using 4D flow application in congenital heart disease

would be the diagnostic work-up of complex cases that require multiple

quantitative flow acquisitions in arterial and venous vessels with normal and

abnormal flow patterns [Nordmeyer et al., 2010]. Compared to the

conventional 2D method, this reduces scan time, making the protocol less time

extensive and demanding for the patient; indeed, planning and acquisition of

imaging planes perpendicular to the target vessels are not necessary.


16

Furthermore, data analysis is not limited to the acquired single predefined 2D

imaging plane and, thus, would help avoiding incomplete or falsely registered

datasets [Nordmeyer et al., 2010].

The 4D flow software offers a new and time efficient tool to evaluate 4D data,

and has demonstrated its potential for analysis of arterial and venous

hemodynamics [Barker et al. 2010].

3.1.2 PREVIOUS WORK

Four-dimensional flow MRI analysis has been used in several recent studies to

investigate fluid dynamics in different cardiovascular application.

One example is an interesting study which exploits 4D flow acquisitions to

investigate aortic hemodynamics in bicuspid aortic valve (BAV) patients,

comparing specific valve morphology (i.e. fusion of the right-left coronary

cusp) with control cases matched for age and aortic size [Barker at al., 2012].

Steady-state free precession cine imaging has been used to identify the valve

lesion morphology in all BAV patients. Co-registration of the 2D valve images

with the flow data allowed to visualise the valve cups morphology in parallel

with the 3D blood flow pattern in the aorta. The 3D visualisation was based on

streamlines at peak systole (Figure 3.1).

Figure 3.1 - 3D flow visualisation of a control patient highlighting cohesive systolic

streamlines [Baker er al., 2012].


17

Four-dimensional flow MR can measure and visualise aortic 3D blood flow

patterns such as flow jets, vortex or helical flow patterns. It was observed that

BAV and cusps fusion morphology alter the hemodynamic environment, in

particular post-valvular blood jets. This in turn leads to abnormal wall shear

stress (WSS), with an elevated or asymmetrical WSS along the circumference

of the aortic wall, with consequent vascular remodelling. This study highlights

the utility of 4D MR flow for investigating the structure-function relationship

between a type of valve morphology and downstream flow characteristic, in a

congenital scenario.

Moreover, current quantification methods only allow measurement of net flow

through a vessel of interest. Estimation of flow contributions from a particular

vessel, when more than one source of flow is present, is not possible.

Using this 4D flow technique Bachler et al. (2012) analysed the flow

distribution in patients with pulmonary atresia and intact ventricular septum

after ‘‘one-and-a-half ventricle repair’’ with placement of a bidirectional Glenn

shunt [Bachler et al., 2012]. In particular, they estimated flow contribution

from the superior vena cava (SVC) toward the right pulmonary artery (RPA)

distal to the cavopulmonary anastomosis (d-RPA) and toward the RPA

proximal to the cavopulmonary anastomosis (p-RPA), thus avoiding any blood

flow streaming from the main pulmonary artery. Different regions of interest

(ROI) were defined and used as emitter planes of particle traces. Such particles,

travelling along the cardiovascular structures according to the velocity field

distribution acquired by the 4D flow sequence, allowed to characterise the

hemodynamic ‘‘baffle’’ between the pulmonary circulation and the Glenn

anastomosis. The blood flow distribution (Figure 3.2) suggests that the

palliated pulmonary circulation has poor efficiency because most of the blood

flow ejected by the ventricle moves back to the heart during the diastolic phase.

Furthermore, bidirectional Glenn anastomosis of the SVC showed poor

efficiency because most of its blood flow contribution was directed into the PA

and not into the lungs.


18

Figure 3.2 - Particle traces emitted from the SVC show how the blood is distributed between

the p-RPA, d-RPA and main PA [Bachler et al.,2012].

In 2012, Valverde and co-workers took advantage of 4D velocity acquisition

sequences to evaluate systemic-to-pulmonary collateral flow and flow

distributions in patients with single-ventricle physiology [Valverde et al.,

2012]. A whole-heart 4D velocity and 2D flows MR data were acquired in

aorta, caval veins and pulmonary arteries. The 4D velocity acquisition was

validated with the 2D velocity technique by comparing the flows measured in

each individual vessel, and time efficiency of both techniques was evaluated.

Good agreement was obtained in the measured flows, and significantly shorter

4D velocity acquisition-time was observed. Indeed, the duration of the single

4D velocity acquisition sequence (12:34±03:42 min) was significantly shorter

than the average time to satisfactorily obtain five individual 2D flow scans

(17:28±04:24 min), which increases with the number of scans needed.


19

3.2 COMPUTATIONAL ANALISYS

3.2.1 COMPUTATIONAL FLUID DYNAMICS

Computational fluid dynamics (CFD) is a very useful tool to investigate

complex fluid dynamic scenarios. In the last years, the considerable

improvements in computer technology increased the number of computational

studies to the detriment of in vitro analyses. The main advantage of CFD

simulations is the possibility of a complete representation of fluid dynamic

variables in 3D domains such as flows, pressures and velocity distributions,

shear stresses and energy losses. Also, from an economical point of view, costs

of computational analyses are lower than costs of experimental setups. The

major drawback of this method is the long-time taken by the simulation to

converge, which depends on the accuracy needed, on the complexity of the

problem, and on the computational resources available.

The computational method is based on the solution of the Navier Stokes (NS)

equations and of the mass balance equation in each volume of the grid in which

the 3D domain is divided. The 3D NS equations are:

{( )

}

where ρ is the fluid density, vi is the component of the velocity vector in the

specified Cartesian direction (i =x, y, z), t is the time, Fi is the vector of the

external body forces operating on the fluid, p is the pressure and μ is the fluid

viscosity [Dubini, 2009].

The continuity equation is shown below:

and becomes as follows


20

for incompressible fluids (constant density ρ).

Two are the key factors for obtaining detailed and reliable descriptions of the

fluid dynamics in any specific case: the boundary conditions and the

representation of the 3D domain. In cardiovascular applications, the boundary

conditions to be prescribed at the boundary faces of the 3D model are typically

values or tracings of pressure, velocity and flow-split derived from medical

exams such as catheterism, MR scans, echo measurements. Regarding the 3D

volume, it is possible to mimic complicated patient specific geometries,

obtained by advanced medical imaging techniques, such as magnetic resonance

(MR) and computerised tomography (CT) [Coveney et al., 2011].

Hence, in order to computationally reproduce patient-specific fluid dynamics,

medical images with high resolution and time-varying boundary conditions are

required for achieving adequate accuracy and reliable outcomes.

3.2.2 LUMPED PARAMETER NETWORK (LPN)

Lumped parameter models are efficient tools for the representation of complex

hydraulic networks like the cardiovascular system. This method is based on the

analogy with electric networks, where pressure and flow are identified with

electric voltage and electric current, while capacitors (C), resistors (R) and

inductors (L) correspond to vessel wall compliance, viscous dissipation in the

vessel, and fluid inertial features (Figure 3.3).

Figure 3.3 - A simple example of LPN model (top) and its electrical-hydraulic analogy

(bottom): flow (f) and pressure (P) are represented by electric current (i) and voltage (V).


21

The equations describing the behaviour of each lumped parameter are the

following:

( )

where L is the length of the conduit, r the radius in the undeformed

configuration, h the wall thickness, µ the fluid viscosity, ρ the fluid density, σ

the Poisson ratio and E the Young modulus [Laganà et al., 2002].

This approach allows an immediate calculation of flow distribution, pressure

drops and their waveforms in all the cardiovascular districts modelled. The

hemodynamics in each district is described through a system of differential

equations deduced from the NS equations after appropriate simplifications: the

convective terms of the NS equations are neglected; the fluid is considered

incompressible and in a laminar regime; the velocity distribution across a

section and the velocity variation along a conduit are replaced with mean

velocity values on the sections. The whole vascular tree can be split in several

essential compartments, depending on the grade of accuracy needed for the

study undertaken: a larger number of blocks accounts for a more precise

cardiovascular system description, but at the same time the number of

parameters’ values to be estimated increases.

For example, the differential equations solving the network shown in Figure

3.4 are the following:


22

Figure 3.4 - Lumped model of a short pipe: flows and pressures in the district are regulated by

the NS equations [Laganà, 2002].

If the input and all the parameters of the network (R, L, C) are known,

pressures and flows can be obtained [Laganà et al., 2002].

Because of the approximations in the NS equations previously explained, LPNs

are unable to represent 3D spatial distribution and local values of the

hemodynamic variables, but are extremely fast and low demanding in terms of

computational power.

3.2.3 MULTI-DOMAIN APPROACH

In hemodynamics, as in many other engineering or scientific fields, a problem

can show peculiar behaviours at different scales. Therefore, a crucial issue is

choosing the right scale to approach the problem, which could be too large to

observe events occurring at the microscale, or too small to evaluate accurately

macroscopic phenomena. Simulating all the relevant dimensions of a problem

would require a too large number of variables and technological resources.

A multi-domain approach could be very useful, as it consists in incorporating

the 3D geometry of the only district of interest, solved with the CFD methods,

in a LPN reproducing the whole vascular tree or just the districts proximal to

the considered 3D part. The resulting network provides the 3D geometry with

realistic boundary conditions, and the LPN with the local fluid dynamic

variables [Laganà et al., 2002].


23

The boundary conditions will thus consider the behaviour of the downstream

districts and their interaction with the upstream computational domain. Indeed,

the blood flow and the pressure in the aortic arch are strictly linked to the

values in the whole arterial system.

Lumped parameter models can be used with closed multi-domain models,

where the network provides both inlet and outlet boundary conditions, and

open multi-domain models, in which the inlet is imposed from the outside.

3.2.4 PREVIOUS WORKS

An interesting work by Kim et al. studied the fluid dynamics in a pediatric

aorta coupling the 3D volume with a LPN, and comparing the results obtained

from the model with physiological flow-rate and pressure fields [Kim et al.,

2008]. The 3D geometry (meshed with 1916167 elements) included the aortic

arch and the main upper branches (left and right carotids and left and right

subclavian arteries). The open lumped parameter networks coupled at the inlet

and at all the outlets of the 3D domain are shown in Figure 3.5.

Figure 3.5 - Inlet (left) and outlet (right) lumped parameter network used to study the fluid

dynamics in the aortic arch [Kim et al., 2008].

This model allowed the analysis of several variables, such as mean flow rates

and pressures at inlet and outlets, shear stress and velocity fields in the whole

3D geometry. The results confirmed the reliability of this multi-domain

methodology. Mean flow rates and mean pressures were evaluated in all outlet

faces along the cardiac cycle. The computed cardiac output was 3.5 L/min

compared with the 3.6 L/min of the subject. Computed pressures ranged from

62 to 106 mmHg. The upper branches, as expected, experienced retrograde

flow in diastole, while the descending aorta had positive flow in the same

a)Inlet coupled to lumped parameter heart model b)Outlets coupled to 3-element Windkessel models


24

instants. These values and all the waveforms are physiologically realistic.

Volume rendered velocity magnitude showed complex flow features related to

the high inertia of the blood, especially in late systole when the flow was

decelerating (Figure 3.6B). The mean wall shear stress increased where the

flow jet hits the wall of the vessels, and decreases in the descending aorta, as

shown in Figure 3.7.

Figure 3.6 - Velocity magnitude at peak systole (A), late systole (B), diastole (C).

Figure 3.7 - Mean wall shear stress at peak systole.


25

In 2008, Karmonik and co-workers demonstrated the potential role of CFD in

therapeutic decision making of vascular pathologies of the human aorta

[Karmonik et al., 2008]. Computational models built using patient-specific

geometries and patient-specific inflow boundary conditions obtained from MRI

were used to simulate two cases: A) a mobile thrombus in the aortic arch in a

patient with ischemic stroke, B) an abdominal aortic aneurysm repaired with an

endoluminal graft. Blood flow pathlines, wall shear stresses (WSS), dynamic

pressures, blood velocity and flow particle resident times were calculated. In

all the cases, tracings and absolute flow values obtained by CFD simulations

were in good agreement with literature. In case A, flow lines intersecting the

thrombus were found to enter the left common carotid artery, providing

additional evidence on the danger represented by the thrombus: it may be a

potential source for emboli, and in case of upstream dislocation to the cerebral

circulation via the left common carotid it may be cause ischemic stroke. Wall

shear stress magnitudes computed in correspondence of the thrombus showed

high values that are favourable for emboli shedding. Also, flows predicted by

the simulations confirmed the favourable conditions for these emboli to reach

the cerebral circulation.

In case B, the analysis was focused on the WSS distribution on the wall of an

endoluminal graft, and at healthy proximal and distal segments. The results

revealed high WSS values at the landing zone and at the section of the

endoluminal graft located in the right iliac artery. Disturbed flow patterns and

increased flow particle transient times were spatially correlated with the

regions of elevated WSS. The existence of these flow disturbances suggested

the need for an intervention i.e. enlarging the endoluminal graft diameter by

angioplasty.

Chapter 4 Materials and methods I: experimental

26

CHAPTER 4

MATERIALS AND METHODS I:

EXPERIMENTAL


27

In order to study the hemodynamic of the neo-aorta in patients with surgically

repaired TGA, an experimental approach was chosen because an in-vitro study

can provide controllable and reproducible data.

The complexity of an experimental setup varies according to the problem at

hand and depending on the purposes of the study, influencing the choice of

model (e.g. pure resistance, lumped parameter model, distributed, linear model

or distributed, non-linear model) [Skalak, 1972].

Experimental setups for hydrodynamic testing can take the form of mock

circulatory loops, whereby a network of tubing and lumped resistive and

compliant elements are assembled to reproduce a part or the whole of the

circulatory system. Such mock loops can include a detailed anatomical element

if a specific morphology is deemed important or is being investigated.

Anatomical elements can be either idealised [Vismara et al., 2009] or patient-

specific [Biglino et al., 2012]. An arrangement including a detailed 3D

component and lumped elements representing the remainder of the circulation

can be broadly defined as “multi-scale” [Quarteroni et al., 2001]. This patient-

specific approach was chosen to study the geometry effects in the

hemodynamic combining hydrodynamic data with the imaging potential of 4D

MR flow, previously discussed in 3.1.

4.1 ANATOMICAL MODELS

As the study was carried out at a patient-specific level, a suitable patient with

TGA corrected with ASO was selected (15 years old, 1.7 m2 BSA, male). In

order to appreciate the features of TGA hemodynamics, an age-matched

healthy control case was also selected (15 years old, 1.7 m2

BSA, male). The

control case was identified from a list of subjects screened at Great Ormond

Street Hospital in London for assessment of possible hereditary

cardiomyopathy. Both cases underwent MR examinations of their cardiac

function and their anatomies were reconstructed in 3D from MR data using

commercial software (Mimics, Materialise, Leuven, Belgium).

For the purpose of the reconstructions, the MR images are viewed in 2D, in

three projection planes (transverse, coronal and sagittal) and the software


28

ultimately allows to render a 3D volume ( Figure 4.1). As the study focused on

the aortic region, segmentation of the images was performed selecting the

appropriate region of interest by a thresholding operation and defining the

boundaries of the grayscale in the image. This step was followed by a “region-

growing” operation and detailed refinements to the 3D model were completed

on a pixel by pixel basis. Similar procedures for creating 3D vascular models

have been reported in the literature [Thayyil et al. 2009, Schievano 2007].

Figure 4.1 - Screenshot of the Mimics interface, showing anatomical reconstruction of the

TGA aortic arch. 3D geometry (bottom right panel) is reconstructed from 2D MR images (top

and bottom left panels).

The final model includes the aortic root, the ascending and descending aorta

and the brachiocephalic branches (i.e. innominate, left carotid and left

subclavian arteries). In order to adjust surface irregularities, a smoothing

operation was finally performed using a shrinkage compensation factor.

As the software allows for adding CAD elements to the 3D models by means

of Booleans operations, a small cylinder was positioned in the ascending aorta

(Figure 4.2) as an access port for a pressure catheter, allowing for pressure

measurements in the aortic arch, as further described in 4.2.5.


29

Similarly, the brachiocephalic vessels, the inlet in the aortic root and the outlet

at the descending aorta were all modified using CAD elements in order to

facilitate insertion and connection of the 3D phantom into the mock circulatory

system.

Figure 4.2 - Detail of the port for the pressure catheter. It allows for access the aortic arch in a

very easy way.

The 3D volume can be exported as a Standard Triangle Language (STL) file

compatible with 3D printing. In particular, the rapid prototyping technique

known as PolyJet technology [Ibrahim et al. 2008] was used to manufacture 3D

rigid models suitable for insertion in a mock circulatory loop. A transparent

and robust resin (Watershed 11122; DSM Somos, Elgin, IL) was used for the

printing process. Both the TGA and the control model are shown in Figure 4.3.


30

Figure 4.3 - Control (left) and TGA (right) models manufactured by means of rapid

prototyping. It is possible to appreciate geometries differences among the two models: the

yellow arrow highlights the enlarged aortic root in the TGA model; the red arrows point the

different aortic arches. The green arrow indicates the point of insertion of a pressure catheter

on the ascending aorta (on the TGA model). Finally silicone was used to attach the model to

Tygon tubes, as can also be appreciated from these images.

Rigid models, admittedly not reproducing realistic vessel wall distensibility

and the associated recoil effect, have been used in several studies in the

literature for investigating vascular anatomies [Biglino et al., 2012], providing

valuable hemodynamic data, and it should also be noted that they serve the

purpose of collecting validation data for a computational study where the 3D

models in the CFD study also present rigid walls.

The transparency of the resin allows to see air bubbles in the circuit, thus

facilitating de-airing operations, and to control the correct positioning of the

pressure catheter in the aortic arch.


31

4.2 HYDRAULIC CIRCUIT

In order to understand how the geometric differences between a TGA and a

healthy aorta affect the fluid dynamic in the aortic arch, a hydraulic circuit was

built (Figure 4.4).

It consists of:

I. Pulsatile pump

II. Compliance chambers

III. Resistances

IV. Atrial reservoir.

Figure 4.4 and Figure 4.5 show an image and a schematic representation of the

circuit.

Figure 4.4 - Experimental circuit: II indicates the compliant chambers, III one of the four taps

implementing the resistances, and IV the atrial reservoir.


32

Figure 4.5 - Schematic representation of the circuit. P represents the pulsatile pump, C the

compliant chambers, R the non-linear resistances. The arrow indicates the direction of the flow.

The circuit was built so to be compatible with MR imaging. For this reason,

there is no metal in the components inserted into the scanner. All the

ferromagnetic parts (i.e. the pulsatile pump, consoles of measuring equipment,

laptop, data acquisition system) are located in the adjacent control room.

Tubing, cables and connections are facilitated by a hole in the wall between the

two rooms.

In order to guarantee hygiene and safety of the scanner in the event of

leakages, water was the fluid chosen for performing the experiments, although

other solutions (e.g. mix of water and glycerine) present more similar

properties to blood, especially in terms of viscosity [Gonzalez et al., 2011].

Hydraulic seal between the model, the pipes and the compliant chambers was

ensured using silicon.

4.2.1 PUMP

A Harvard Apparatus pulsatile blood pump (Figure 4.6) was used to simulate

the pumping action of the heart. The pulsatile output closely simulates the


33

ventricular action of the heart thanks to silicone rubber-covered heart-type ball

valves. This action provides physiological advantages in blood flow for

perfusion in cardiovascular and haemodynamic studies.

Figure 4.6 - Harvard Apparatus pulsatile blood pump used for the experiments: A) inlet, B)

outlet. Also indicated, the position of the ball valve that regulates the flow.

This pump has an adjustable stroke volume range between 15 and 100 ml and a

frequency range between 10 and 100 bmp.

The outflow of the pump was connected to the inlet of the model while the

inflow of the pump was connected to the outlet of the reservoir. Sufficiently

long braided pipes, previously filled with water to avoid bubbles, were used to

allow the Harvard Pump sitting in the control room.

The pump heart rate (HR) and stroke volume (SV) were set in accordance to

patient’s data, which was derived from the MR examination report. Patient-

specific settings for the TGA case were: HR = 70 bpm and SV = 90 ml. The

waveform at the inlet of the model, obtained with the settings described, is

shown in Figure 4.7.

.


34

Figure 4.7 - Inflow waveform: it is obtained setting the stroke volume and the heart rate

respectively at 90 ml and 70 bpm.

4.2.2 ARTERIAL COMPLIANCE

Arterial compliance was simulated by using Windkessel (= “air chamber” in

German) elements, according to the theory of compliant air element. Perspex

cylinders (volume = 1324.69 cm3) were thus attached at each outlet of the

model, in order to implement the natural compliant behaviour of the system.

Each chamber has a 3-way valve fitted at the top in order to control the amount

of air, regulating the stiffness of the circuit. Adjustments to the amount of air

can be easily performed to adjust in turn the lumped compliance.

Increasing the stiffness of the whole system rises the amplitude of the pressure

waveform. The range of pressure at the inlet was set between 60 and 115

mmHg according to cuff pressure data measured in the TGA patient.

The 4 compliance values were obtained using the formula:

in which V is the volume of air in each cylinder, Pm is the mean pressure of the

patient (77 mmHg) and Patm the atmospheric pressure (760 mmHg). The values

are shown in Table 4.1, where height refers to the part of each cylinder full of

air.

-10

-5

0

5

10

15

20

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8

Flo

w [

L/m

in]

Time [s]


35

Table 4.1 - Compliance values per each outlet of the model.

Height

[cm]

Diameter

[cm]

Volume

[cm3]

Pm+Patm

[Pa]

C

[m3/Pa]

INNOMINATE 5.5 7.5 242.8 111588.8 2.2 E-09

CAROTID 5.0 7.5 220.8 111588.8 2.0 E-09

DESCENDING AORTA 4.5 7.5 198.7 111588.8 1.8 E-09

SUBCLAVIAN 7.0 7.5 309.1 111588.8 2.8 E-09

4.2.3 VASCULAR RESISTANCE

Metered needle-pinch valves were positioned after each compliance chamber

to simulate the resistance of downstream districts of the circulation. Such taps

have the advantage of being easily adjustable with reproducible settings,

allowing for regulation of the mean pressure in the circuit. However, they are

strongly flow-dependent and thus implement a non-linear resistance.

Resistances were set in order to split the inflow according to the following

physiological indicative proportions: 55% in descending aorta and 45% in the

upper branches (of which 15% innominate, 20% subclavian and 10% carotid).

Flow measurements at each outlet for quantifying flow distribution were

performed using the ultrasonic flow probe described in 4.2.6. The resistances

were characterized using a simple continuous flow circuit (as in Figure 4.8).


36

Figure 4.8 - Schematic representation of the circuit using for characterising the resistances.

The red and the blue arrow indicate the position of the pressure catheters to measure pressure

values before and after the tap.

Imposing known flows with a continuous pump (Q) the pressure drop across

the tap (R) was measured with two pressure catheters (Table 4.2).

Table 4.2a - Pressure drop in carotid.

Flow

[L/min]

Pbefore

[mmHg]

Pafter

[mmHg]

0.31 15.30 13.14

0.33 15.54 13.03

0.55 25.56 13.76

0.66 32.12 13.91

0.95 53.91 14.87

1.25 84.30 16.63

1.42 104.35 17.37

1.46 108.85 17.66

1.99 189.87 21.93


37

Table 4.2b- Pressure drop in innominate and subclavian.

Flow

[L/min]

Pbefore

[mmHg]

Pafter

[mmHg]

0.46 15.54 13.61

0.80 25.60 14.65

1.07 37.42 15.90

1.38 55.25 18.03

1.84 89.13 22.08

1.89 91.90 22.96

2.07 109.24 25.39

2.60 161.87 30.17

2.78 180.73 30.61

Table 4.2c – Pressure drop in descending aorta.

Flow

[L/min]

Pbefore

[mmHg]

Pafter

[mmHg]

0.23 9.47 12.58

0.45 10.38 13.11

1.42 16.69 16.48

1.48 17.37 17.07

2.40 30.14 24.51

2.60 34.32 27.08

3.25 42.19 29.95

4.09 60.16 32.45

4.50 70.35 45.26

.


38

Using these data to produce pressure drop-flow curves, interpolating them with

a second order polynomial, it was possible to obtain the characteristic curves of

each resistance (Figure 4.9).

Figure 4.9 - Characteristic curves, with the respective equations, of the resistances: carotid

(blue), innominate and subclavian (red), descending aorta (green).

4.2.4 ATRIAL RESERVOIR

All outlets of the 3D model drain to a reservoir representing an ‘atrial

reservoir’, positioned between the outlet of the model and the pump, and

implementing atrial pressure. This chamber is filled with water and the level of

water was set to guarantee a pressure of 9 mmHg, given by the hydraulic head.

4.2.5 PRESSURE MEASURING EQUIPMENT

Pressure in the aortic arch was measured by means of a high-fidelity factory-

calibrated fiber optic catheter (Samba Preclin Samba sensors AB; Vastra

Frolunda, Sweden). The transducer technology is based on a pressure sensitive

optical interferometer (Fabry-Perot manufactured in silicon). The sensor

element (0.36-0.42 mm of diameter) is mounted at tip of an optical fiber (0.25-

0.40 mm of diameter) (Figure 4.10).

y = 42.913x2 - 0.621x

y = 1.6396x2 - 1.71x

y = 19.886x2 - 0.9766x

0

20

40

60

80

100

120

140

160

180

0 1 2 3 4 5

Pre

ssu

re d

rop

[m

mH

g]

Flow [L/min]

carotid

descending aorta

innominate and subclavian


39

Figure 4.10 - Catheter tip dimension compared with a match.

Calibration of the pressure catheter was carried out prior the experiments with

the methods of ‘column of water’, associating the console’s read-out in Volts

with known heights of water implementing known hydrostatic pressure values

(1 mmHg = 1.36 cmH2O). Thus, a correlation between pressure read in Volts

by the catheter and the corresponding mmHg value was established (Figure

4.11).

Figure 4.11 – Pressure catheter manual calibration: on the ‘x’ axis the output of the console in

Volts (V) and on the ‘y’ axis the associated pressure in mmHg.

y = 84.445x - 121.16 R2 = 0.9999

-20

0

20

40

60

80

100

120

1 1.2 1.4 1.6 1.8 2 2.2 2.4 2.6 2.8

Pre

ssu

re [

mm

Hg]

Output [V]


40

The catheter was positioned in the ascending aorta, as shown in Figure 4.12,

through the appropriate port created in Mimics.

Figure 4.12 - Catheter position: the yellow arrow indicates the dedicated port for the pressure

catheter. It is possible to see the light blue little pipe, fixed to the model with silicone, along

which the catheter is guided into the model.

4.2.6 FLOW MEASURING EQUIPMENT

Flow at the inlet of the model was evaluated with an ultrasonic flow probe

(Transonic 400-Series Multi-Channel Flowmeter Consoles & Modules for

Laboratory Research).

Four transducers (piezoelectric crystals) within the flow probe alternately emit

sound rays to form an ultrasound beam. As the beam transverses a vessel, each

ray undergoes a phase shift in transit time proportional to the average velocity

of the liquid times the path length over which this velocity is encountered.

With wide-beam ultrasonic illumination the receiving transducers integrate

these velocity and yields volume flow (Figure 4.13).


41

Figure 4.13 - Transit time ultrasound theory of operation: a schematic representation. On the

left: cross-talk between the crystals mounted inside the probe. On the right: position of the

probe, snugly clumped to the Tygon tube.

Calibration of the flow probe was performed prior the experiments with the

method of ‘timed collection’. This was performed by setting increasing flows

with a continuous pump (Sicce Multifunction Pump 2500) and measuring the

amount of water (mL) per minute gathered with a measuring cylinder and

comparing these values with the respective Volts measured by the probe

(Figure 4.14).

Figure 4.14 - Flow-probe calibration: on the ‘x’ axis the output of the flow-meter in Volts (V)

and on the ‘y’ axis the associated flow in L/min.

y = 2.0044x - 0.0097 R² = 0.9998

-1

0

1

2

3

4

5

6

0 0.5 1 1.5 2 2.5 3

Flo

w [

L/m

in ]

Output [V]


42

The probe was positioned at the inlet of the model, in order to verify the

stability of the inflow during the experiment (Figure 4.15). A thin layer of

Vaseline was used to improve acoustic coupling.

Figure 4.15 - The yellow arrow points at the flow-probe position, which is the inlet of the

phantom.

This specific flow probe was designed by the manufacturer to be MR

compatible, thus including special connectors and cables. This should have

allowed simultaneous flow acquisitions during MR scanning. However,

preliminary testing highlighted that the presence of the probe was still causing

image artefacts, as in Figure 4.16.


43

Figure 4.16 - The yellow arrow underlines the flow-probe artefact in MR scan, visible in the

aortic root.

For this reason, the protocol of the experiment was changed, such that the flow

waveform was acquired with the probe with the model already mounted on the

table but only before inserting it into the scanner.

4.2.7 DATA ACQUISITION AND DATA ANALYSIS

During the experiments a data acquisition system (BIOPAC System Inc.,

Goleta, California) was used to record pressure and flow output data gathered

from the catheter and the probe (Figure 4.17). Data was acquired at 250 Hz

(AcqKnowledge 4.1.1, BIOPAC System Inc., Goleta, California).


44

Figure 4.17 - AcqKnowledge interface: pressure curve is shown in purple, flow curve in red.

Data was saved as Microsoft Excel files for later off line analysis. Values are

reported as mean ± standard deviation.

4.3 MAGNETIC RESONANCE (MR)

4.3.1 ACQUISITION

All MR examinations were performed with a 1.5 T scanner (Avanto; Siemens

Medical Systems, Erlangen, Germany).

The TGA geometry was first tested in the scanner. After having checked with

the flow probe that the flow split corresponded with the one in the patient (see

4.2.3) and having verified there were no leaks in the circuit, it was inserted into

the MR scanner. Due to its dimension, the bucket representing the atrium was

positioned right outside the scanner at the same level of the rest of the circuit.

Once the phantom was correctly positioned in the centre of the scanner, the

pump was turned on to set appropriate pressure and flow waveforms.

Acquisitions were gated to the pump’s external trigger, via a BNC connection

cable.

Firstly, phase contrast data was acquired for 2D quantification of flow-velocity.

Imaging parameters were:


45

Venc: 250 cm/s for the outlets, 500 cm/s for the inlet;

Repetition time/echo time: 29.9/2.18 ms;

Pixel spacing: 1.17 mm;

Section thickness: 5 mm;

Flip angle: 30°.

From the phase contrast MR scan two sets of images are extracted: the

magnitude and the phase, the latter encoding the velocity information.

According to the direction of the flow, increasing values of velocity are shown

in increasing grades of black or white.

The images were taken in 4 different planes, always planned as perpendicular

to the flow: inlet, descending aorta, innominate and subclavian arteries.

Moreover, the 4D (3 spatial dimension and time) acquisitions were performed.

During each scan two different sequences were tested: a standard sequence

(Siemens) and a higher temporal and spatial resolution sequence, lasting 15

minutes and 1 hour and 10 minutes, respectively.

Imaging parameters for the standard 4D sequence were:

Venc: 200 cm/s;



Section thickness: 2.2 mm;

Flip angle: 5°.

Imaging parameters for the high resolution sequence were:

Venc: 200 cm/s;



Section thickness: 1.2 mm;

Flip angle: 5°.

The same imaging protocols were adopted for the control geometry. It is

important to stress that the values of the compliances and the resistances used

to test the control model were the same as for the TGA model.


46

4.3.2 DATA EXTRACTION

OsiriX Imaging Software (Pixmeo; Geneva, Switzerland) is a DICOM viewer

specifically designed for navigation and visualization of multimodality and

multidimensional images: 2D Viewer, 3D Viewer, 4D Viewer (3D series with

temporal dimension, i.e. Cardiac-CT) and 5D Viewer (3D series with temporal

and functional dimensions, i.e. Cardiac-PET-CT).

The 3D Viewer offers all modern rendering modes: multiplanar reconstruction

(MPR), surface rendering, volume rendering and maximum intensity projection

(MIP). All these modes support 4D data and are able to produce image

fusion between two different series (PET-CT and SPECT-CT display support).

OsiriX is at the same time a DICOM PACS workstation for imaging and image

processing software for medical research (radiology and nuclear imaging),

functional imaging, 3D imaging, confocal microscopy and molecular imaging.

In particular, it allows quantification of flow from phase-contrast data using an

in-house written plugin (Figure 4.18), validated in a separate study [Odille

2011].

The identification of the ROI, where the flow data is acquired, is performed

manually on one frame, preferably at peak systole when most visible and when

the edges are crisp, then, using a non-rigid registration algorithm previously

validated [Odille et al., 2011], the ROI is propagated in all frames. Using a

plug-in developed at Great Ormond Street Hospital it was possible to calculate

the instantaneous flow volume at any time in the cardiac cycle. The mean

velocity was obtained dividing the flow by the ROI area.

The difference between the inlet and the other three measured flows provides a

measure of carotid flow, as data in the carotid were not acquired.


47

Figure 4.18 - Data extraction via Osirix : magnitude (right) and phase (left). The enlightened

circles in the left image are the inlet (top) and the descending aorta (bottom), while the two big

grey circles are the two bottles full of water positioned in the scanner to simplify the

identification of the model.

Four-D data were later analysed by means of the Siemens 4D Flow software.

A 3D mask of the region of interest of the model was drawn by a combination

of thresholding and segmentation operations. This region defines the volume in

which the fluid dynamics are investigated, as shown in Figure 4.19.


48

Figure 4.19 - 3D mask and planes in the TGA model. The numbers indicate the planes for the

velocity analysis: 1-2 inlet, 3 aortic roots, 4 ascending aorta, 5-6 descending aorta.

Once the mask was created the velocity were computed by drawing some

planes of interest. We took 6 planes of interest: two at the inlet of the model

(planes 1 and 2), one in the aortic root (planes 3), one before and one after the

upper branches (planes 4 and 5) and one in the descending aorta (plane 6). For

each of these planes, it is possible to save a corresponding Excel file containing

the information on flow, velocity and area.

Finally we used the tools provided by the software to place particle seed on

useful planes of the geometry, as shown in Figure 4.20. Particles are seeded on

the XYZ plane on the mask with a brush function allowing manual control.


49

Figure 4.20 - Particle seeds at different locations along the 3D model then used to generate

streamlines and pathlines.

The evolution of particle traces and streamlines, originated by these particle

seeds, was recorded in order to obtain temporal information. It is possible to

choose different density of the seeds and width of streamlines and particle

traces in order to have a clear and complete visualisation of the results. It is

also possible to assign a specific colour to each seed or group of seeds to

follow their path and better understand complex flow patterns or mixing of

flows of different origins.

4.4 ASSESSING THE EFFECT OF COMPLIANCE:

COMPLIANT TGA MODEL

As previously acknowledged, the models tested in the MR scanner were

printed with a robust resin, thus obtaining a rigid geometry.

The main shortcoming of using a rigid model is that the compliant behaviour of

blood vessels is not taken into consideration. An interesting addition to the

study is to account for this compliant behaviour and evaluate how local fluid

dynamics are affected, and in particular if the compliant model resembles

closer the physiological scenario than the rigid one.


50

For this purpose, a compliant TGA phantom was also manufactured and

included in the study. The material chosen to replicate the compliance of the

vessels is a commercially available rubber-like material, which can be used for

PolyJet rapid prototyping, called TangoPlus FullCure 930 [Biglino et al.,

2013], suggested as suitable for manufacturing arterial phantoms. In Figure

4.21 a picture of the TangoPlus TGA model is shown.

Figure 4.21 - Compliant TGA geometry. Clearly the new model was printed starting from the

same STL file used for the rigid one. Thus the only differences are the properties of the two

different materials.

With respect to the rigid model, this material is not transparent. As a

consequence, it is more difficult to positioning the pressure catheter inside the

aortic arch, through the pressure port. To avoid this problem the little tube used

as guide to insert the catheter was cut at a length measured corresponding to

the length necessary for the tip to be inside the arch.

The new compliant TGA geometry was connected to the same hydraulic circuit

described in Chapter 4.2, with the same flow and pressure values used before


51

and described in paragraphs 4.2.2 and 4.2.3. Therefore, the only overall

difference in the circuit is represented by the material of the phantom.

Chapter 5 Materials and methods II: computational

52

CHAPTER 5

MATERIALS AND METHODS II :

COMPUTATIONAL


53

5.1 ANATOMICAL MODELS

The two geometries used for the CFD simulations are the same as the ones

printed for the in-vitro study described in Chapter 4.1. The computational part

of the study includes an additional model, described in detail in the following

paragraph, together with the rationale for its inclusion in the study.

5.1.1 AN ADDICTIONAL CASE

In order to better understand how the geometric differences could affect the

hemodynamics in the aortic arch, with all the problems described in paragraph

1.3 arising after ASO, and to better evaluate the effect of the Lecompte

maneuver, a patient with a slightly different surgical operation was taken into

consideration in our study.

The additional patient is not age-matched with the other two. He is, a 25 year

old male with a BSA of 1.9 m2. Nevertheless, this patient was indicated by the

cardiologists at Great Ormond Street Hospital as a case of interest, warranting

inclusion in the study, and suitable for comparing aortic geomtries. In fact, this

patient had TGA repaired with ASO but a Lecompte maneuver was not

performed in this instance. This results in a different anatomical arrangement,

with the aorta preserving a more spiral curvature, albeit this cannot be striclty

considered a case of spiral surgery as described in paragraph 1.4. This case

presents an enlarged aortic root, typical of TGA patients, but the aortic arch is

more similar to the control geometry, and will be hereby referred to as “spiral”

geometry. In Figure 5.1 a comparison between the two different arterial switch

operations geometries and the control are shown including the pulmonary

arteries, and it is possible to appreciate the differences both in spatial

arrangement as well as in aortic arch morphology.


54

Figure 5.1 - Comparison of three different geometries: TGA, control and “spiral”. Images at

the bottom represent the 3D volumes recostructed in Mimics. The aorta is shown in red and the

pulmonary arteries are shown in blue.

5.2 MESH AND SENSITIVITY ANALYSIS

The STL files of the geometries obtained from Mimics were imported in ICEM

(Ansys Inc., Canonsburg, PA), in order to build the finite volume mesh. Given

the complex patient-specific geometries, tetrahedral elements were chosen.

Also, a wall mesh inflation (5 layers of prisms, 1.2 grow ratio, 1 mm maximum

height) was applied in order to efficiently resolve boundary layer flows, in

which viscous effects are significant (Figure 5.2).


55

Figure 5.2 - Mesh example at the inlet of the model: it is possible to notice the 5 layers of

prisms.

To be sure that the numerical solutions were not influenced by the chosen grid,

sensitivity analysis was undertaken. A compromise must be reached between

computational time and accuracy of results: coarse mesh could lead to

inappropriate results, while a fine mesh could require excessive time for the

simulations to converge.

Using the TGA geometry, five different element dimensions, resulting in five

different meshes of 400000, 500000, 700000, 900000 and 1200000 volumes

respectively were tested with steady CFD simulations. A constant velocity

value of 0.13 m/s was imposed at the inlet and the flow split obtained

experimentally during the tuning of the taps (55% descending aorta, 20%

subclavian, 15% innominate and 10% carotid) was set at the outlets.

The influence of the mesh was evaluated by analysing the power dissipation

index W’dissip defined as difference between the power entering and the power

exiting the 3D volume [Pennati et al., 2011; Dubini et al., 1996; Low et al.,

1993]:

W diss ∑ i

(pi

1

2vi

2ρ) ∑

(p

1

2v

2 ρ)


56

where the first summation is calculated at the inlet face (i), while the second

summation is evaluated at the outlet faces (o); is the density of the fluid

(water, 1000 kg/ ), Q, v and p are respectively the averaged face flows,

velocities and pressures computed during the simulations.

As it is possible to appreciate from

Figure 5.3, there is a negligible difference of 1.4% ( corresponding to W’diss=

0.10∙105 W) between the 900000 elements mesh and the 1200000 elements

mesh. For this reason the mesh with 900000 volumes was chosen for our

models.

Figure 5.3 - Sensitivity analysis: variation of the power dissipation index with the number of

elements in the mesh. There is no significant difference between 900000 elements mesh and

1200000 element mesh.

Figure 5.4 shows the control (left), the TGA (central) and the spiral (right)

geometries with the chosen tetrahedral meshes.

5.00E-05

5.50E-05

6.00E-05

6.50E-05

7.00E-05

7.50E-05

8.00E-05

300000 500000 700000 900000 1100000

W' d

iss

[W]

Number of elements


57

Figure 5.4 - Control (right), TGA (central) and spiral (left) geometries meshed with tetrahedral

elements. The different colours represent different portions of the models separated by planes

used to evaluate the fluid dynamics at 1)aortic root, 2)ascending aorta, 3)descending aorta.

5.3 CFD SIMULATION

All the CFD simulations in this work were run using the commercial finite

volumes software Fluent (Ansys Fluent 14, Fluent Inc. ©, Lebanon, NH). The

method used for the solution of the NS momentum equations is a second order

upwind scheme, with a standard spatial discretization for the pressure, and an

implicit “least square cell based” discretization for the gradient. A SIMPLE

(Semi-Implicit Method for Pressure Linked Equations) pressure-velocity

coupling algorithm was exploited.

Furthermore the under-relaxation factors were set, as default, to 0.3 for the

pressure and 0.7 for the momentum. In all the simulations, the absolute

convergence criterion was the residuals of mass and momentum conservation

equations to be less than 10-4

.


58

5.3.1 WORKING HYPOTHESIS

As for the in-vitro experiment, the fluid chosen for the simulations is water

(density ρ=1000 kg/m3, viscosity μ=1 cP), considered completely

incompressible and Newtonian.

The simulations were run under the following working hypotheses:

laminar flow conditions

isotherm conditions

no gravitational effects

rigid-wall with no-slip condition.

Apart for the mesh sensitivity analysis, where steady-state simulations were

performed, an unsteady flow regime was used for all the simulations. The time-

step for the unsteady simulations was set at 10-4

s. In order to reach asymptotic

behaviour in the results, 5 cardiac cycles per simulation were replicated for a

total of 400000 time-steps.

Monitors at the inlet and outlets of each model were set in order to collect flow

and pressure data for quantitative analysis. Also, planes were created in the

aortic arches in correspondance of the location of the pressure catheter ports of

the physical 3D models used in the mock circuit. Other two planes, one in the

aortic root and one in the middle of the descending aorta, were created in each

model in order to further investigate the fluid dynamics in these positions

(Figure 5.4).

5.3.2 BOUNDARY CONDITIONS

Each of the 3 aortic arch modelled (TGA, control and spiral) presents 5

boundary faces: one aortic inlet, three brachio-cephalic outlets (Innominate,

Carotid, Subclavian), and one descending aorta outlet, as shown in Figure 5.5.

Velocity inlet and pressure outlets boundary conditions were imposed as

described below.


59

Figure 5.5 - TGA geometry: inlet (A) and outlets (B, C, D, E).

5.3.2.1 INLET

The TGA and the control inlet velocity information imposed during the

experimental tests were extracted from MR measurement, through the software

OsiriX as a discrete set of data, since MR scans were segmented in 30 temporal

frames per cardiac cycle (T=0.8 s). These data were then interpolated in order

to obtain continuous functions through a Fourier series with eleven

coefficients. The two resulting velocity curves (Figure 5.6), both with a mean

velocity of 0.9 m/s and minimum and maximum values of -0.8 m/s and 2.8 m/s,

were imposed at the inlets of the TGA and control CFD models respectively.

These inflow conditions were used to replicate computationally the

experimental tests performed using the two different phantoms (TGA and

control).

Moreover, taking advantage of the computational capability of conducting

parametric studies, in order to analyse how different surgical approaches could

influence the fluid dynamics in the aortic arch of these patients, additional

simulations were run imposing the same inflow condition at the three patient-

specific models. In particular, the TGA inflow velocity was chosen as inlet

boundary condition also for the control and spiral reconstructed anatomies.

The time-varying velocity functions were imposed at the inlet through a script

written in the computer language C, and read by Fluent under the name of UDF

(user defined function).


60

Figure 5.6 - TGA (top) and control (bottom) velocities imposed at the inlet of the 3D

geometries during the CFD simulation.

5.3.2.2 OUTLETS

A lumped parameter network (Figure 5.7) representing the experimental circuit

was developed and coupled with the 3D geometry as shown in Figure 5.7. In

particular, the coupling was implemented through pressures and flows

information exchanged between the 0D network and the 3D domain in

correspondance of the boundary faces.

Figure 5.7 - 3D geometry of the TGA patient coupled with the LPN.

-2

-1

0

1

2

3

4

0 0.2 0.4 0.6 0.8Ve

loci

ty [

m/s

]

Time [s]

-2

-1

0

1

2

3

4

0 0.2 0.4 0.6 0.8Ve

loci

ty [

m/s

]

Time [s]


61

Figure 5.8 shows the details of the lumped parameter network implemented at

each of the outlet branch. All the outlet branches share the same network

typology, but the values of the parameters are characteristics for eah branch.

The variables involved are:

Qin : flow value read and averaged by Fluent on each outlet face and

imposed as inlet to the LPN at every iteration;

P : pressure calculated by the UDF and imposed at each volume of the

outlet face;

Qin2 : flow, dumped by the compliance C, going through the resistances

R1 and R2;

Qx : flows coming from the other branches;

Qt : flow resulting from the sum of all the branches entering the final

part of the LPN, common to all branches;

Pt: pressure at the junction of all the branches;

Qt2: flow, dumped by the compliance Ct, going through the common

resistance Rt;

Patrium: pressure of the right atrium, set to 9 mmHg as measured from

the experimental tests.

Figure 5.8 - LPN implemented at each of the outlet branch: Qin, Qin2, Qt, Qx represent the

flows, P, Pt, Patrium the pressures; R2 and Rt are linear resistances, while R1 is flow-

dependant; C and Ct are compliances.

The parameter values were chosen in order to replicate the experimental

circuit.


62

The non-linear resistance R1 corresponds to the taps of the mock circuit, and is

characterised through the pressure drop-flow relationship obtained during the

tap experimental calibration (Table 5.1).

Table 5.1 - Pressure drop (ΔP) across each non-linear resistance. Q indicates flow-rate.

polynomial

INNOMINATE ΔP=1∙1013

∙Q2-8∙10

6∙Q

CAROTID ΔP=2∙1013

∙Q2-5∙10

6∙Q

DESCENDING AORTA ΔP=8∙1011

∙Q2-1∙10

7∙Q

SUBCLAVIAN ΔP=1∙1013

∙Q2-8∙10

6∙Q

R2 is the linear resistance representing the pressure drop contribution along the

tube connecting the considered branch to the connection point with the other

branches’ extensions. Rt lumpes the final common tube connecting the outlets’

junction to the right atrium. These resistances take into account the distributed

(equation 5.2) and the concentrated (equation 5.3) pressure drops, due to the

length of the pipes, the pipes’ connections, the sudden variations of section,

etc..

where μ is the viscosity of the fluid, L and D are the length and the diameter of

the pipes, v the velocity of the fluid and k a constant depending on the kind of

concentrated drop. In Table 5.2 the values of these resistances are reported.


63

Table 5.2 - Linear resistances of the LPN.

R

[Pa∙s/m3]

INNOMINATE Ri=5∙107

CAROTID Rc=1∙108

DESCENDING AORTA Rd=2.5∙107

SUBCLAVIAN Rs=1∙107

COMMON SECTION Rt=8∙107

C is the compliance representing the compliant chambers of the experimental

circuit. Ct is a numerical trick necessary to stabilise the variations of the

pressure Pt, and was set to a value which do not influence pressure and flow

results. Table 5.3 shows the values chosen for the compliances.

Table 5.3 - Compliances of the LPN.

C

[ m3/Pa ]

INNOMINATE Ci=1.88∙10-9

CAROTID Cc=1.98∙10-9

DESCENDING AORTA Cs=1.48∙10-9

SUBCLAVIAN Cd=3.06∙10-9

COMMON SECTION Ct=0.36∙10-11

The linear equation (equation 5.4), the ordinary differential equations (ODE)

(equations 5.5 and 5.7), and the second order equation (equation 5.6) solving

the LPN are reported below:

( )


64

{ √[ ( )] }

where the apex “old” refers to the value assumed by the variable at the

previous time step; a and b are the coefficients of the pressure drop-flow

second order equation charachterising the non linear resistance R1.

The ODE are resolved through explicit Eulero numerical method (equation 5.8)

with a time-step of 10-4

s.

( ) ( ) ( )

where f*(t) is the approximation of the function at the current time-step.

As for the inlet boundary condition, the LPN equations were written in the

computer language C and included in the UDF. The UDF compiled by the

software Fluent realises the 0D-3D coupling at the boundary faces by reading

the flow value computed from the CFD simulation, by calculating the pressure

P as results of the LPN equations, and by finally imposing it at each of the

outlet faces.

Chapter 6 Results

65

CHAPTER 6

RESULTS

Chapter 6 Results

66

6.1 EXPERIMENTAL RESULTS

All hydrodynamic experiments and data acquisition were accomplished

successfully. The mock circuit proved to be suitable for the representation of

the downstream districts of the circulatory system, and pressure and flow

values are in the physiological range. Moreover, it is important to underline

that it is possible to easily substitute one 3D model to another in order to repeat

scans with different geometries. The system ran successfully for 2-3 hours

inside the MR scanner during each acquisition.

6.1.1 CONSIDERATIONS ON TEMPORAL RESOLUTION

FOR 4D FLOW ACQUISITIONS

As previously mentioned in 4.3.1, two different 4D flow sequences were

exploited during the experiments: a Standard sequence from Siemens and a

High Resolution (HighRes) sequence.

In Figure 6.1 is possible to appreciate that there are no substantial differences

between the flows acquired with the two sequences. In both cases the mean

flow (OsiriX Qmean = 5.5 L/min, Standard Qmean = 5.5 L/min, HighRes Qmean = 7

L/min) and the amplitude of the signals (OsiriX Qpeak = 17 L/min, Standard

Qpeak = 15 L/min, HighRes Qpeak = 20 L/min) are comparable with the ones

measured with OsiriX from traditional 2D Cartesian phase-contrast flow

acquisitions, which represented our reference. The high resolution sequence

was noisier, and it slightly overestimated the systolic peak.

Chapter 6 Results

67

Figure 6.1 – Flows at the inlet of the model acquired with the Standard (blue) and High

Resolution (red) 4D Flow sequences, compared with the OsiriX 2D acquisition (green).

From a qualitative point of view, the images extracted from the high resolution

sequence do not provide any additional information compared to the standard

one. Figure 6.2 shows the differences in the streamlines obtained with the two

sequences. The high resolution sequence exhibits a noisier background, likely

due to compromised signal to noise ratio (SNR), preventing a good

thresholding, as well as a smaller number of streamlines, which could not

represent adequately the fluid dynamics in the arch.

-10

-5

0

5

10

15

20

25

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8

Flo

w [

m3 /

s]

Time [s]

OsiriX 2D

4D Standard

4D HighResolution

Chapter 6 Results

68

Figure 6.2 – Qualitative comparison of the streamlines of the High Resolution (left) and the

Standard (right) 4D flow sequences. The first image shows a noisier background and visibly

less number of streamlines than the Standard one.

As the differences between the two sequences are negligible, the high

resolution was performed only on the TGA case depicted in Figure 6.2. During

all other experiments only the considerably quicker (15 minutes vs. 1 hour 10

minutes) standard sequence was acquired.

6.1.2 4D FLOW RESULTS: TGA AND CONTROL

GEOMETRIES

Siemens 4D flow software’s tools, in particular streamlines and particle traces,

represent a quick and effective method to visualise qualitative fluid dynamics

differences between the different geometries.

Chapter 6 Results

69


geometry (right) at t= 0.2 s (systolic peak). The range of velocity goes from 0 to 1.38 m/s for

both images. The yellow arrow indicates the jet impinging the aortic root.


geometry (right) at t= 0.6 s (diastole). The range of velocity goes from 0 to 1.38 m/s for both

images.

Chapter 6 Results

70

During systole, in the TGA model, a flow jet (1.38 m/s), impinging on the

enlarged aortic root and indicated by a yellow arrow in Figure 6.3 was clearly

visible. Nearby this jet, velocities are significantly lower (about 0.3 m/s) and

with a whirling or even chaotic trend.

In the control case it is not possible to identify a single flow jet hitting the

aortic wall within the streamlines, and their path is more uniform, especially in

the aortic root, compared with the TGA patient. In this case, water flows

smoothly toward the upper branches.

During the diastolic phase, the absence of a valve in the model led to

noticeable reverse flow, as it is possible to see in Figure 6.4. Once again,

during diastole the flow in the TGA model is more chaotic and whirling than in

the control one.

As the flow inlet waveforms of the two models are comparable (see paragraph

5.3.2.1), the difference in the intensity of the colours representing the velocity

values is ascribable to the enlarged root in the TGA geometry, which presents a

significantly difference in the root diameter compared with the control’s one

(DTGA=43-46 mm; Dcontrol=27-30 mm).

6.1.3 THE EFFECT OF COMPLIANCE: DISTENSIBLE

PHANTOM

While the pump was brought to the set point working condition, important

geometric changes were observed in the compliant model. In particular, at the

same flow values as per the rigid model, the shape differences between the

compliant and the rigid geometry are relevant: because of the viscoelastic

properties of Tango Plus and its highly distensible nature, the geometry visibly

dilated, not retaining its original shape. As the aim of the work is to study the

effect of a specific geometry on the fluid dynamics, this material is not suitable

for our experiments.

In Figure 6.5 and Figure 6.6 a comparison between the two models (prior to

and during pulsatile flow) is provided.

Chapter 6 Results

71

Figure 6.5 - TGA compliant model (left) and TGA rigid model (right). As expected there are

no shape differences between the two phantoms. The only difference is represented by the

material used for the rapid prototyping process.

Figure 6.6 – The compliant TGA model (left) is connected with the pulsatile pump. The

pressure effect is clearly visible, as the model did not retain its original shape, especially in the

aortic root. The TGA rigid model (right) was placed next to the compliant one in order to

better appreciate the geometric differences.

Chapter 6 Results

72

One additional problem detected, before putting the model inside the scanner

for the images acquisition, was the structural failure of the material in

correspondence of the aortic arch.

The material resulted to be not suitable for working in this range of pressure.

For these reasons, it was not possible to accomplish the image acquisition

inside the scanner.

Despite the problems described before, it was possible to acquire pressure data

in the compliant model. As expected, the compliance of the material being the

only difference, the pressure waveform is more damped than in the rigid

phantom, as shown in Figure 6.7.

Figure 6.7 - Pressure waveform comparison between the rigid TGA model (red) and the

compliant one (blue). As expected the second one in more damped than the first one, as a result

of the additional proximal compliance implemented by the distensible phantom.

6.2 COMPUTATIONAL RESULTS

All simulations converged and were compared with experimental data for

validation purposes.

50

70

90

110

0 0.4 0.8 1.2 1.6 2 2.4 2.8 3.2 3.6 4

Pre

ssu

re [

mm

Hg]

Time [s]

Rigid model

Compliant model

Chapter 6 Results

73

For both the quantitative and qualitative analysis, the fourth cardiac cycle out

of the five cycles simulated in Fluent was selected.

6.2.1 MODEL VALIDATION

In order to verify that the lumped parameters network implemented in the UDF

reproduces the experimental circuit described in Chapter 4.2, a quantitative

comparison between flow and pressure values collected in the mock circuit and

the ones resulting from CFD simulations is necessary. For this purpose, two

CFD simulations were considered: a) TGA geometry with TGA inflow, and b)

control geometry with control inflow, in order to exactly replicate the

experimental conditions.

With regard to the flows, three comparisons were performed: mean flow, flow

distribution at the different outlets, and the flow waveforms.

Table 6.1and Table 6.2 report the mean flow comparisons at every outlet of the

TGA and the control model, respectively.


every outlet for the TGA model.

Osirix

[L/min]

CFD

[L/min]

INNOMINATE 0.92 0.86

CAROTID 0.54 0.56

DESCENDING AORTA 2.92 3.02

SUBCLAVIAN 1.17 0.98

Chapter 6 Results

74


every outlet for the control model.

OsiriX

[L/min]

CFD

[L/min]


CAROTID 0.59 0.58



The results show very good agreement and the computational model replicated

appropriately the experimental hydrodynamic environment.

Table 6.3 and Table 6.4 show the flow split at every outlet respectively in the

TGA and control model. They were calculated as percentage values relatively

to the inlet flow.

Table 6.3 - Flow split calculated by OsiriX software (left) and Fluent simulation (right) at

every outlet for the TGA model. The following percentages are computed relatively to the inlet

flow.

Osirix

[%]

CFD

[%]


CAROTID 9.9 10.3



Chapter 6 Results

75

Table 6.4 - Flow split calculated by OsiriX software (left) and Fluent simulation (right) at

every outlet for the control model. The following percentages are computed relatively to the

inlet flow.

OsiriX

[%]

CFD

[%]


CAROTID 10.2 11.1



Flow distribution results are in excellent agreement, with a maximum

difference in the flow split in the TGA’s subclavian of 3.5%. The overall

distributions in the computational models are comparable with the ones

registered in the experiments.

Finally, Figures 6.8-6.11 and 6.12-6.15 report respectively the TGA and

control flow waveforms at every outlet, with a comparison between the real

data measured in OsiriX (blue) and the simulated results (red).


TGA’s subclavian for a cardiac cycle (T=0.8 s).

-4

-2

0

2

4

6

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8

Flo

w [

L/m

in]

Time [s]

OsiriX

CFD

Chapter 6 Results

76


TGA’s innominate for a cardiac cycle (T=0.8 s).


TGA’s carotid for a cardiac cycle (T=0.8 s).

-4

-2

0

2

4

6

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8Flo

w [

L/m

in]

Time [s]

OsiriX

CFD

-4

-2

0

2

4

6

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8

Flo

w [

L/m

in]

Time [s]

OsiriX

CFD

Chapter 6 Results

77


TGA’s descending aorta for a cardiac cycle (T=0.8 s).


control’s subclavian for a cardiac cycle (T=0.8 s).

0

2

4

6

8

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8

Flo

w [

L/m

in]

Time [s]

OsiriX

CFD

-4

-2

0

2

4

6

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8

Flo

w [

L/m

in]

Time [s]

OsiriX

CFD

Chapter 6 Results

78


control’s innominate for a cardiac cycle (T=0.8 s).


control’s carotid for a cardiac cycle (T=0.8 s).

-4

-2

0

2

4

6

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8

Flo

w [

L/m

in]

Time [s]

OsiriX

CFD

-4

-2

0

2

4

6

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8Flo

w [

L/m

in]

Time [s]

OsiriX

CFD

Chapter 6 Results

79


control’s descending aorta for a cardiac cycle (T=0.8 s).

Also in terms of flow tracings, results show that the computational simulations

reproduce in a satisfactory way the flowing conditions of the experimental

setup.

With regard to pressure measurement, experimentally it was measured only in

the aortic arch. For this reason the only possible comparison is with pressure

values measured by Fluent in a plane, specifically created in the geometry, at

the same level of the dedicated port for the pressure catheter.

Figures 6.16 and 6.17 show the comparison between the experimentally (blue)

and computationally (red) obtained pressures for the TGA and the control

model, respectively.

0

2

4

6

8

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8

Flo

w [

L/m

in]

Time [s]

OsiriX

CFD

Chapter 6 Results

80


TGA’s aortic arch for a cardiac cycle (T=0.8 s).


control’s aortic arch for a cardiac cycle (T=0.8 s).

Satisfactory agreement was noted in terms of pressure tracings and pressure

values. In particular, the TGA mean pressure value for the experimental curve

40

60

80

100

120

0 0.2 0.4 0.6 0.8

Pre

ssu

re [

mm

Hg]

Time [s]

Catheter

CFD

40

60

80

100

120

0 0.2 0.4 0.6 0.8

Pre

ssu

re [

mm

Hg]

Time [s]

Catheter

CFD

Chapter 6 Results

81

is 84.6 mmHg and for the computational one is 85.7 mmHg. The control model

exhibits an experimental mean pressure of 87 mmHg and a computational one

of 83.2 mmHg.

6.2.2 QUALITATIVE COMPARISON BETWEEN 4D FLOW

AND CDF SIMULATIONS

Both 4D flow Siemens software and Fluent allow visualisation of the velocity

streamlines. For a qualitative comparison of the fluid dynamics in the different

geometries, four temporal instants (Figure 6.18) out of the entire cardiac cycle

(T= 0.8 s) were considered: t1= 0.1 s (early systole), t2= 0.2 s (systolic peak),

t3= 0.4 s (late systole) and t4= 0.6 s (diastole).

Figure 6.18 - Temporal instants considered for the comparison displayed in the cardiac cycle. :

t1 represents the early systole, t2 the systolic peak, t3 the late systole and t4 the diastole.

Figure 6.19-6.22 show velocity streamlines for the TGA geometry.

-10

-5

0

5

10

15

20

0 0.2 0.4 0.6 0.8

Flo

w [

L/m

in]

Time [s]

t1

t2

t3

t4

Chapter 6 Results

82


(early systole) in the TGA model. The range of velocity is the same for both images.


(peak systole), in the TGA model. The range of velocity is the same for both images. It is

clearly visible in both of them the flow jet hitting the wall.

Chapter 6 Results

83


(late systole), in the TGA model. The range of velocity is the same for both images. Once

again in both of them it is possible to appreciate a flow jet impinging on the aortic wall.


(diastole), in the TGA model. The range of velocity is the same for both images.

Chapter 6 Results

84

Considering these results, we could verify a good agreement between the 4D

flow and CFD simulations for the TGA geometry. In particular, the CFD is

able to show the same flow jet impinging at the top of the aortic root wall, and

the surrounding whirl visible in 4D flow images. The ranges of velocities are

comparable in terms of magnitude and distributions. The correspondence is

excellent both in systole and in diastole.

In Figure 6.23-6.26 the same 4D flow and CFD velocity streamlines

comparison is repeated for the control geometry at the same time points as for

the TGA model.


(early systole) in the control model. The range of velocity is the same for both images.

Chapter 6 Results

85


(peak systole), in the control model. The range of velocity is the same for both images. It is

clearly visible in both of them the flow jet flowing smoothly towards the upper branches.


(late systole), in the control model. The range of velocity is the same for both images. Once

again in both of them it is possible to appreciate a flow jet flowing towards the subclavian

artery.

Chapter 6 Results

86


(diastole), in the control model. The range of velocity is the same for both images

The results of CFD and 4D flow simulations show an excellent agreement for

the control geometry. The CFD exhibits streamlines comparable with 4D flow

in terms of magnitude and distribution, both in systole and diastole. In

particular, is it possible to observe the same flow jet, uniform throughout the

whole aortic root and smoothly reaching the upper branches, as in the 4D flow

data.

6.2.3 THE EFFECT OF THE AORTIC ARCH GEOMETRY:

CFD COMPARISON BETWEEN TGA, CONTROL

AND SPIRAL GEOMETRIES

For the CFD comparison, the simulations considered the three different

geometries with the same inflow and outflow boundary conditions (the TGA

inflow was chosen), as the aim was to analyse only the effects of the geometry

on the fluid dynamics.

Chapter 6 Results

87

Table 6.5 shows the mean flows of the TGA, control and spiral obtained at

each outlet face.

Table 6.5 - Mean flows calculated by Fluent at every outlet of the TGA (left), control (central)

and spiral (right) models.

TGA

[L/min]

CONTROL

[L/min]

SPIRAL

[L/min]

INNOMINATE 0.92 0.86 0.87

CAROTID 0.57 0.57 0.54

DESCENDING AORTA 3.02 2.83 2.80

SUBCLAVIAN 0.99 0.87 0.89

The differences between these values are negligible and the mean flows in the

three geometries are comparable.

Table 6.6 displays the flow split at every outlet in the three geometries.

Percentage values are computed relatively to the inlet flow.

Table 6.6 - Flow split calculated by Fluent at every outlet of the TGA (left), control (central)

and Spiral (right) models. The following percentages are computed relatively to the inlet flow.

TGA

%

CONTROL

%

SPIRAL

%

INNOMINATE 16.70 16.77 17.05

CAROTID 10.42 11.20 10.64


SUBCLAVIAN 17.99 16.87 17.42

Since the aortic arch geometry was the only different variable between these

three simulations, it is possible to deduce that the less spiral arch of the TGA

patient (with the indentation typically resulting from the Lecompte maneuver)

and the enlarged root of both TGA and spiral models do not affect the flow

Chapter 6 Results

88

split, that is instead mainly governed by the downstream resistances. The

difference in the flow-split is around 1%, with a maximum of 1.12% in the

subclavian arteries of the TGA and control models.

Figure 6.27-Figure 6.30 report the flow waveforms at each outlet, comparing

TGA (red), control (blue) and spiral geometry (green).

Figure 6.27 - CFD innominate flow waveforms comparison between TGA (red), control (blue)

and spiral (green) geometries for a cardiac cycle (T=0.8 s).

Innominate flow waveforms are really similar in the three geometries, ranging

between -1.96±0.02 and 4.47±0.2 L/min.

-3

-2

-1

0

1

2

3

4

5

6

0 0.2 0.4 0.6 0.8

Flo

w [

L/m

in]

Time [s]

TGA

CONTROL

SPIRAL

Chapter 6 Results

89

Figure 6.28 - CFD carotid flow waveforms comparison between TGA (red), control (blue) and

spiral (green) geometries for a cardiac cycle (T=0.8 s).

The flows in the carotid arteries exhibit values between -1.74±0.17 and

3.32±0.27 L/min. The differences between the geometries are negligible.

Figure 6.29 - CFD subclavian flow waveforms comparison between TGA (red), control (blue)

and spiral (green) geometries for a cardiac cycle (T=0.8 s).

-3

-2

-1

0

1

2

3

4

5

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8

Flo

w [

L/m

in]

Time [s]

TGA

CONTROL

SPIRAL

-4

-3

-2

-1

0

1

2

3

4

5

6

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8

Flo

w [

L/m

in]

Time [s]

TGA

CONTROL

SPIRAL

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90

In subclavian arteries the values range from -2.32±0.5 and 4.14±0.45 L/min,

with a very similar trend between TGA, control and spiral.

Figure 6.30 - CFD descending aorta flow waveforms comparison between TGA (red), control

(blue) and spiral (green) geometries for a cardiac cycle (T=0.8 s).

Finally, the waveforms in the descending aorta, waving between 0.61±0.2 and

5.63±0.12 L/min, show no differences linked with the geometry.

A comparison between velocity streamlines in the three different geometries

(with the same inlet flow and outlet LPN) at four different temporal instants

(t=0.1s, t=0.2s, t=0.4s and t=0.8s as for Figure 6.19) is shown in Figure 6.31-

Figure 6.34.

0

1

2

3

4

5

6

7

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8

Flo

w [

L/m

in]

Time [s]

TGA

CONTROL

SPIRAL

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91

Figure 6.31 - Control (left), TGA (central) and spiral (right) velocity streamlines at t=0.1 s.

In early systole (t=0.1s) the velocities are increasing at the inlet but they are

still low in the rest of the geometry. In the control geometry the majority of the

streamlines has a straight path following the geometric shape, while in the

TGA and spiral geometries the streamlines follow chaotic paths in the enlarged

roots, while they recover a more regular trend after the aortic arch, in the

descending aorta.

Chapter 6 Results

92


At peak systole (t=0,2 s) the three geometries show three different behaviours.

In the control model, once again, the streamlines path follows the geometry.

The velocity magnitude remains high up to the level of the upper branches.

In the TGA the flow jet is clearly visible, and, being not directed as the

curvature of the geometry, it hits the wall of the enlarged root, losing velocity

before reaching the upper branches.

Finally, in the spiral geometry, the flow jet, once again clearly visible, is

directed as the curvature, but where the enlarged root shrinks, the flow jet hits

the wall causing a chaotic trend in the streamlines. In TGA and spiral

geometries whirling streamlines, characterised by lower velocity modulus,

surround the main flow jet.

Chapter 6 Results

93


At late systole (t=0.4 s) what described for the systolic peak is still visible. In

particular, the difference between the TGA and the spiral geometries is due to

the different orientation of the inlet: in the TGA it points towards the external

curvature of the wall, directing the flow in this way, while in the spiral the flow

jet hits the wall when the area shrinks. The reduced area increases the velocity

of the water if compared with the velocity in the enlarged root.

Chapter 6 Results

94

Figure 6.34 – Control (left), TGA (central) and spiral (right) velocity streamlines at t=0.6 s.

The image above (Figure 6.34) reports the diastole (t=0.6 s) in the three

geometries. As expected the velocities are lower than in the systolic phase. As

observed in Figures 6.27-6.30, it should be noted that the inlet face and all

outlets except for the descending aorta are characterised by retrograde flow at

this time point. Also, the more chaotic streamlines trend in the enlarged roots

of both the TGA and spiral geometries if compared to the control one should be

highlighted.

Another interesting parameter to be evaluated in this study is the wall shear

stress (WSS). Figure 6.35-Figure 6.36 report WSS distributions at systolic peak

for control, TGA and spiral geometries, respectively.

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95

Figure 6.35 - Front view of the WSS in control (left), TGA (central), spiral (right) models.

The range of wall shear stress goes from 0 to 35 Pa.

Figure 6.36 - Lateral view of the WSS in control (left), TGA (central), spiral (right) models.

The range of wall shear stress goes from 0 to 35 Pa.

Chapter 6 Results

96

The first difference to be noticed between the control and the other two

geometries is the area interested by a WSS higher than 25 Pa (green/yellow

colour): it is very extended in the two pathological situations, rather than in the

physiological one. In both the TGA and the spiral WSS reaches values around

35 Pa (red) at different points. In the spiral model higher values correspond to

the narrowing of the root, in a portion corresponding to the ascending aorta. In

the TGA this shrinkage is less marked, but the area interested by a high WSS is

wider.

Table 6.7 reports the values of mean pressure at each outlet of the control,

TGA and spiral geometries.

Table 6.7 – Mean pressure calculated at each outlet of the control (left), TGA (central) and

spiral (righ) models.

TGA

[mmHg]

CONTROL

[mmHg]

SPIRAL

[mmHg]

ASCENDING AORTA 85.18 86.41 84.52

INNOMINATE 85.80 87.19 85.66

CAROTID 86.33 85.31 84.17


SUBCLAVIAN 81.99 85.04 82.04

As for the flow split, the outlet mean pressure is not affected by the changes in

geometry. Pressures in the TGA model are really similar to the control ones,

with a maximum variance in subclavian artery (3.7%). Comparing the spiral

and the control geometry, the difference is around 1%, with the biggest

variation in carotid (2.5%).

In Figure 6.37-6.39 velocity vectors in the aortic arch at peak systole (t=0.2s)

are shown.

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97

Figure 6.37 –Velocity vectors at peak systole (t=0.2s) in the control model .

Figure 6.38 - Velocity vectors at peak systole (t=0.2s) in the TGA model .

Chapter 6 Results

98

Figure 6.39 - Velocity vectors at peak systole (t=0.2s) in the spiral model.

In both TGA and spiral roots the vectors show a more complex fluid dynamics

rather than in the control model, with presence of secondary flows. While

higher velocities in the control model are clustered in the centre of the surface,

in the other two they have a random distribution.

In ascending aorta the effect of the geometry is clearly visible in the spiral

model. Here, the vectors are the result of the sudden shrinking of the section in

proximity of the plane considered. In the TGA ascending aorta, as the section

variance is smaller, this effect is reduced.

.

Chapter 7 Discussion

99

CHAPTER 7

DISCUSSION


100

This study successfully applied a modelling paradigm involving both

experimental and computational tools to tackle a complex case of congenital

heart disease. Specifically, Transposition of the Great Arteries (TGA) is a

congenital condition presenting a wide range of complications, such as aortic

root dilation [Ntsinjana et al.,2002], reduced aortic distensibility [Grotenhuis et

al., 2008] and compromised ventricular-vascular coupling [Biglino et al., 2013]

on the aortic side, and unilater pulmonary artery stenosis on the pulmonary side

[Shrivastava et al., 1976]. The full consequences and effects of TGA repaired

with the Arterial Switch Operation (ASO) are not fully appreciated yet, due to

the relatively young age of the patients. In fact, ASO was introduced in the

1980s and TGA was previously palliated with an atrial switch approach

[Jatene, 1982]. The variety of approaches shows, in itself, the complexity of

this disease and the extent to which surgeons have gone to improve the

physiology of patients born with TGA.

This work focused solely on the aortic side of the problem, using modelling

techniques to evaluate the effect of the shape of the neo-aorta in this group of

patients. Overall, a patient-specific approach was chosen. Also, a validation

study was carried out to demonstrate the reliability of the computational model,

which was later used to gather additional information on the fluid dynamics of

TGA repaired with ASO.

Following from the results presented in Chapter 6, a relatively simple and

compact mock circuit proved to be an excellent tool to study TGA

experimentally. By setting adequate R and C boundary conditions, the mock

circuit is able to accurately reproduce the pathological scenario of interest, at a

patient-specific level, according to cuff pressure measurements. The boundary

conditions in fact can be easily tuned manually adjusting the stroke volume and

the heart rate of the pulsatile pump, the volume of air in the compliant

chambers and the extent of closure of the taps used to implement vascular

resistance. Moreover, using the manufacturing technique known as rapid

prototyping, patient-specific geometries are obtained, and these can be easily

mounted into the circuit, implementing patient-specific 3D information. This is


101

important not only because it allows to take into account the variety in aortic

morphology between different patients (by testing multiple models), but also

because the study focused specifically on the hemodynamics within the neo-

aorta.

Such hemodynamic features can be appreciated experimentally by taking

advantage of the imaging technique known as 4D MR flow [Meierhofer er al.,

2012]]. This requires first of all to construct an MR-compatible mock circuit,

which was successfully achieved in this work.

Four-D MR flow can be very informative in the field of congenital defects, as

in cases of Fontan circulation [Valverde et al., 2012] as well as bicuspid aortic

valve [Barker at al., 2012]. The advantage of using this technique, instead of

standard 2D acquisitions, is that there is no need to plan flow acquisition prior

to acquiring the data, which is collected over a volume of interest. As a result,

this can make the technique time-efficient, especially in those cases where

multiple flows need to be planned and acquired [Nordmeyer et al., 2010], albeit

acquisition time remains a concerns for clinical application of 4D MR flow,

especially in children.

Furthermore the post-processing of a 4D flow dataset gives access to exquisite

flow visualisation, including streamlines and particle tracing, over the 3D

volume of interest.

Only one study recently applied 4D MR flow to the study of TGA in humans

[Hsiao et al., 2012], however there are several advantages linked to using an

experimental approach. Firstly, the use of a hydraulic circuit solves problems

related to patient’s motion, which are of particular concern especially in

younger patients and over a long acquisition (15-20 minutes, or more).

Moreover, the circuit can be kept inside the scanner for as long as required, and

this is useful if multiple acquisitions are necessary. For example, in this study a

1 hour and 10 minute long high spatial and high temporal resolution sequence

was performed on the model. The reason to perform this additional scan was to

evaluate whether increased resolution provided access to meaningful additional


102

fluid dynamic details, especially in complex geometries, such as TGA. In this

work, because of the compromised SNR, it was not possible to get more

information than from the standard sequence. This point could be tackled in the

future from an MR physics perspective, trying to acquire high resolution

sequences without compromising SNR and ongoing work in the MR unit at

Great Ormond Street Hospital is evaluating the complexities of 4D flow

acquisition. However, as the results of the ‘standard’ (15 minute) sequence

were satisfactorily informative for the hemodynamic problem under

investigation, further work in this context was deemed not necessary.

Full datasets were ultimately acquired experimentally for the TGA anatomy

and the age-matched healthy control model. In both cases, pressure values were

in agreement with cuff pressure readings obtained at the time of the clinical

MR scan (Pmean = 80 mmHg). On the other hand, flow distribution between

upper and lower body and in the different head and neck vessels was ensured to

be realistic but was not set to patient-specific values, as flow data is not

acquired in each brachiocephalic vessel in routine clinical scans, so these data

were not available.

All the experimental acquisitions of this work were carried out using rigid

models. Rigid models are easy to mount and robust. Also, transparency

associated with some of the rigid resins used for printing rigid models are

important for some visualisation studies (e.g. particle image velocimetry, PIV

[Ibrahim et al., 2009]), albeit not necessary for MR imaging. The disadvantage

of using a rigid material, on the other hand, is that it does not take into account

the compliant behaviour of the human vessels and the associated recoiling

effect in diastole. For this reason, an additional model was printed using a

commercially available compliant compound i.e. Tango Plus, as discussed in

paragraph 4.4. This material allowed to print a complex TGA geometry and

was chosen because it is compatible with PolyJet printing technique,

guaranteeing fine printing resolution (16 μm), and based on previous evidence

of realistic distensibility [Biglino, 2013]. However, the model failed to


103

withstand the range of aortic pressures that were required for the patient-

specific runs, and was also prone to tear, resulting in the model being damaged

prior to completing a full acquisition. The lack of data gathered in the

compliant model, nevertheless, did not impinge on the validation study: as the

CFD models have rigid walls, validation data was successfully provided from

the models printed in rigid resin.

As shown in the results, presented in Chapter 6, the CFD simulations are in

overall good agreement with the experiments, which allowed to proceed with

the analysis just from a computational point of view. Although it is possible to

properly set the boundary conditions also with an experimental approach, a

computational approach guarantees their stability. In fact, minor leaks can

occur while gathering experimental data, especially over long acquisitions (i.e.

multiple scans in the MR). Also, other changes are not straightforward to

monitor, e.g. if a solution of water and glycerine were used, its content is prone

to changes in viscosity with small changes in temperature.

Computationally, it is also possible to easily undertake parametric studies,

simply changing one parameter at a time in order to understand its influence on

the fluid dynamics. The only concern in this case is the computational cost of

each additional simulation, rather the time associated with re-assembling an

experimental rig. It is also possible to extract retrospectively other parameters

and values of interest at different locations in the model, not necessarily

planned beforehand, while this is not possible in an experimental study.

In this study we performed three different simulations, the only difference

among them being the 3D element in the multi-scale network. This approach is

suitable to understand how geometry alone affects the fluid dynamics,

effectively isolating one variable in a complex clinical problem. Again, the

only cost associated with this procedure is computational.

Another advantage of the CFD is the amount of information that is possible to

gather during the post-processing. Indeed, in addition to streamlines and flows,

the software can provide values and 3D visualization of several other

parameters, such as pressure distribution and wall shear stress. The values of


104

the parameters of interest can be easily obtained at every point of the geometry,

without planning it before the simulation.

In the three geometries included in this study, the shape differences, clearly

visible in the enlargement of the root and on the different aortic arch

angulation, are ascribable to the different surgical operation (Figure 7.1). The

enlarged aortic root in both the ‘TGA’ and ‘spiral’ model is a common feature

related to their diagnosis and consequent surgery, whereas the indentation on

the ascending aorta and the more acute angle of the aortic arch observed solely

in the ‘TGA’ model are to be ascribed to the Lecompte maneuvre, which was

not performed in the ‘spiral’ model.

Figure 7.1 - Control (right), TGA (central) and spiral (left) geometries.

Analysing streamlines and WSS it is possible to understand how this affects the

fluid dynamics and, consequently, which are the potential clinical implications.

First of all it is important to underline, as shown in Chapter 6, how flow split

and overall pressure distribution are not dependent on the 3D geometry but


105

only on the downstream network. On the other hand, the local fluid dynamics

are strongly affected by anatomical changes.

The influence of the enlarged root is a point of great interest as it is evident by

analysing the velocity streamlines. In the TGA and spiral geometries the result

of this shape is a high velocity flow jet, surrounded by lower velocity flows

that follow a whirling path. This fluid dynamic feature, characterised by low

velocities and recirculation areas, could be critical from a clinical point of

view, since it can promote particle deposition and consequently thrombus,

clotting and plaques formation, thus increasing the risk of atherosclerosis

[Meierhofer et al., 2012].

Moreover, in the spiral geometry, in correspondence of the shrinking after the

enlarged root, the velocity increases considerably and the fluid dynamics result

to be very chaotic, while in the TGA model the arch angulation and the overall

geometric arrangement address the flow jet to hit the aortic wall. For this

reason in the TGA ascending aorta, the velocity is quite low.

These portions of aorta of the models resulted, in our study, to show a high

WSS (Figure 7.2).

Figure 7.2 - WSS in control (left), TGA (central), spiral (right) models.


106

The risk of having high WSS is potential mechanical damage of the inner wall

of the vessel [Chien et al., 1998; Shyyy ,2001], which could in turn weaken the

vessel and possibly initiate a lesion. TGA and spiral models are subjected to

considerably higher values of WSS. In addition the interested area in which it

has a value higher than 25 Pa is more extended in the pathological scenarios

than in the physiological one.

The combination of these two factors may have an impact in long-term

pathologies, in particular the development of aortic dilatation [Poltem, 2012].

This effect, added to the already enlarged root because of the surgical

operation, may leads to structural failure of the vessels.

Another aspect of particular interest is the comparison between the different

geometries resulting from two different surgical operations. The difference in

our case is the lack of the Lecompte maneuver for the spiral geometry. The

idea in this case is to evaluate if, reproducing a more physiological

arrangement of the vessels, it is possible to obtain a positive influence on the

fluid dynamics.

Both the information collected by streamlines and WSS do not show an

improvement with respect to the TGA scenario with Lecompte maneuver. The

enlarged root of the spiral case presents vorticity as for the TGA case, but the

direction of the high velocity flow jet has a different orientation. While in the

TGA it impinges the inner wall of the aortic root, in the spiral it hits the first

section of the ascending aorta, just after the shrinkage. The WSS is

significantly high in that area (around 35 Pa) extending for a considerable

portion of the ascending aorta, and the hemodynamics result to be very

whirling. This suggests that this particular case does not show any obvious

hemodynamic improvement with respect to the TGA case.

In comparing these two models, it should be considered that they are not age-

matched. The TGA and the control models are 15 years old with a BSA of 1.7

m2, while the spiral model is reconstructed from a 25-year-old patient. The

main difference related to the age mismatch is the distensibility of the vessels.

Since the study considers rigid models, this difference does not affect the work.

Despite this difference in age, the BSA is 1.9 m2, which is not substantially


107

different from the previous two. Moreover, as this study is focused on the

effects of geometrical changes, this case is particularly interesting because

of the different approach undertaken during the surgical operation. Finally, the

compliant behaviour of the wall was not taken into account in this study,

neither experimentally nor computationally. CFD simulations assumed rigid

vessel walls, so different distensibility was not an issue. Admittedly, such

variations in vessel compliance have been reported also at young ages [Voges

et al., 2012], but these are not as meaningful as much more significant changes

in distensibility occurring later on in life.

From a methodological point of view, all simulations were performed using

water as the flowing medium. This was set to replicate the experimental part of

the study, in which water was chosen for hygiene and safety reasons related to

operating the mock loop inside the MR scanner, rather than a solution of water

and glycerol or other accepted blood analogues. This could potentially

underestimate viscous effects that may occur in the model, although no

significant narrowing is present in the three geometries that were modelled.

This could also reflect on the magnitude of the WSS, but would not affect

considerations on different WSS distribution between different anatomies

Chapter 8 Conclusions and future works

108

CHAPTER 8

CONCLUSIONS AND FUTURE

WORK


109

The aim of this thesis was to model the fluid dynamics of patients who

underwent treatment for transposition of great arteries (TGA). Specifically, the

focus was on TGA repaired by arterial switch operation (ASO). ASO is

nowadays the most common and successful procedure for patients affected by

TGA and aims to resolve the underlying issue of insufficient oxygen supply to

the tissues and excessive ventricular workload.

Two cases of ASO were modelled in this thesis, i.e. with and without

Lecompte maneuver. The latter indicates a specific arrangement following

ASO with the pulmonary arteries effectively positioned anterior to the aorta

and the pulmonary branches embracing the aorta itself, resulting also in an

indentation of the ascending aorta. These are anatomical features typical of

repaired TGA and by including a case without Lecompte manoeuvre it was

possible to appreciate the influence of the changes in aortic morphology and

anatomical arrangement.

The other main features to be addressed in a study of the neo-aorta following

ASO are mainly a) the dilated aortic root and b) the modified aortic arch

angulation. Both have been suggested to negatively affect the physiology of

these patients [Ntsinjana et al., 2012].

In order to take into account all these realistic anatomical features, patient-

specific geometries were reconstructed from MRI data and employed both in

the experimental and computational model.

Three cases were ultimately studied in detail:

i) a TGA patient who underwent the standard ASO procedure,

ii) a TGA patient who underwent the ASO procedure without the

Lecompte maneuver, also referred to as “spiral”, with reference to

the novel spiral surgery for TGA repair [Chiu et al., 2012]

iii) a healthy individual with normal aortic geometry, referred to as

“control case”, which was matched to (i) for age and BSA.

In order to tackle this congenital scenario, we proposed a methodology

involving different tools, such as hydrodynamic experiments, 4D MR flow and


110

CFD, in order to describe patient-specific hemodynamics. We used a mock

circulatory system, which included a rapid prototyped patient-specific 3D

element for both the TGA and the control cases, and tuned according to clinical

data. Four-D MR flow was acquired in these models and highlighted the

influence of changes in geometry on the hemodynamics, especially

appreciating differences in the streamlines in the aortic root and ascending

aorta.

Two CFD simulations, coupled with a LPN properly tuned in order to exactly

replicate the conditions of the experiments, were performed, thus using the

experimental data to validate the computational models. Computational results

were in excellent agreement with their experimental counterpart.

Once the computational model is validated, we could study the effect of

changing aortic geometry alone by varying the 3D element in the multi-scale

simulations and imposing the same boundary conditions to the three cases.

From our results we could conclude that aortic geometry does not affect overall

pressure and flow values, which are regulated by the whole vasculature,

especially since abrupt changes (e.g. aortic coarctation) were not present in the

models under investigation. On the other hand, the anatomy typical of repaired

TGA results in unfavourable hemodynamics. This was indicated by high values

of wall shear stress on the ascending aortic wall, with a jet impinging on the

posterior ascending aorta, as well as by noticeable areas of flow recirculation in

the dilated aortic root. Interestingly, the “spiral” case behaved more like the

TGA case, also exhibiting substantially higher WSS than the control model and

similar flow features in the dilated aortic root, albeit the angulation of the aortic

arch resembled more that of the control case. This may suggest that features

inherent to TGA (i.e. the main vessels being repositioned with the resulting

wall abnormalities) are not improved, from a hemodynamic point of view, by

retaining a more spiral geometry of the aortic arch. However, this observation

was performed only on one patient. Furthermore, this was a case of ASO

without Lecompte manoeuvre and not a case of spiral surgery as defined by

Chiu et al. [Chiu et al., 2012]. Our conclusions thus refer to the effect of the


111

anatomy alone, without drawing considerations on the actual surgical

procedure.

Nevertheless, making use of a validated methodology, it would be possible to

suggest changes in order to advice the clinicians on potential ways to improve

the surgical technique. For example, by virtually creating a range of different

surgical outcomes, it would be possible to evaluate the potential hemodynamic

benefit of each and indicating differences in the fluid dynamics.

In conclusion, this study provides a reliable methodology for hemodynamics

evaluations in patient-specific models. Experimental data were in agreement

with clinical values. A novel imaging technique (i.e. 4D MR flow) was

employed and provided insight into hemodynamic differences between the

neo-aorta post-ASO and the healthy aorta. These considerations were expanded

using CFD simulations, validated against experimental data, which proved to

be a useful tool to study complex geometries and to potentially inform

clinicians on different surgical options for a same patient.

FUTURE WORK

1.Statistics. This study included three patient-specific models, which

effectively could be considered as three cases studies. Both the experimental

and the computational results highlighted differences between the three

scenarios, however in order to comment on the statistical significance of the

results more models need to be included in the study, for each scenario. This

can be conveniently done by making use of the validated CFD model. A range

of patient-specific models could be inserted into the validated (i.e. reliable)

multi-scale model, thus running a larger amount of simulations. This study,

which would be more computationally expensive, would provide a larger

amount of data for statistical analysis comparing different patients populations.

This could strengthen considerations on the potential long-term effects of

different morphologies.


112

2.Compliant models. Certainly, one aspect to take into consideration for further

studies is the compliant behaviour of the physiological vessels. A compliant

model, reproducing closely realistic distensible behaviour, would be helpful to

further understand the fluid dynamics. While gross differences in flow split or

aortic pressure are not expected, local hemodynamics, especially in the aortic

root, could be described in greater detail. This was attempted in this study,

however the material chosen for manufacturing the compliant TGA model did

not withstand physiological pressures for the whole time needed for a full MR

acquisition and was prone to tear. The material (i.e. TangoPlus) suffered

structural failure, so different materials should be evaluated. Silicone-based

compounds may represent a valid alternative in this regard.

If significant difference were observed experimentally between a rigid and a

compliant model, it is possible to simulate such compliant behaviour also

computationally, by means of fluid-structural interaction (FSI) simulations.

One problem typically related with this tool is the lack of information of elastic

characteristic of natural vessels. It is possible to avoid this issue by using an

artificial material which experimentally reproduces the compliant behaviour of

the vessel considered. In this way the elastic characteristic would be known,

facilitating the FSI simulations.

3.Decomposing the velocity inlet. 4D MR flow is a novel imaging technique

and in this work we have suggested that it could be used not only to validate

the computational model, but also to set it. In fact, it is possible to extract from

MR data the values of the velocity in time in each of the voxels of the inlet, in

the x, y and z components. Imposing these values to each corresponding

element of the mesh at the inlet of the computational model, instead of the

spatial average as typically done, could allow to obtain a more detailed

characterisation of the complex fluid dynamics. Clearly, the time necessary for

the simulations is considerably increased, while the flow split and overall

pressure distribution would not be affected by this different approach,

potentially providing more detail on the local fluid dynamics, e.g. whirling and

recirculation in the root. A first attempt was performed in this study, making


113

use of 2D Cartesian flow acquisitions, in order to explore the methodological

aspects related to this point. In order to reduce the high computational cost a

coarsen mesh (300000 elements), shown in Figure 8.1, was considered.

However, the mesh was not fine enough for this complex simulation. Therefore

the convergence was not reached. This warrants further study.

Figure 8.1 - Coarsen mesh on the inlet face of the TGA model, used for the pixel by pixel

imposition of the velocity.

References

114

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Websites

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the neoaorta in patients with transposition … · figure 1.3 - schematic representation of the...

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