iii course biomedical applications of mathematics elements of cardiocirculatory physiology roberto...

III CourseBiomedical Applications of Mathematics

Elements of cardiocirculatory physiology

Roberto BonmassariS.C. di Cardiologia

APSS-Ospedale Santa Chiara Trento

Preamble

A Course of Biomedical Applications of Mathematics

……when the Hospital goes out and meet the University

I’m not a physiologyst I am a clinician, a cardiologist

Agenda

Three lessons: 7-9-21 october 2015 (five hours)

• Aspects of cardiac anathomy

• The cardiac and circolatory function: phisiologic aspects

• Examples of clinical application of a phisiologic application in a pathologic condition: coronary stenosis and aortic stenosis

The heart is costituted from 4

chambers:

2 atria (right and left)2 ventricles (right and

left)

Atriarecive blood,Ventricleseject blood

POLMONE

CUORE

ORGANI

Piccolo Circolo

Grande Circolo

Scambio Gassoso

Funzione di Pompa

Consumo di Ossigeno

The Heart is a pump

• The cardiac pump is the ground of the circulation

• The are two circulation systems that works in series: systemic and pulmonary circulation

• The cardiac pump has the primary function of insurance an adeguate amount of blood flow through the systemic and the pulmonary vessel bed

• The cardiac pump works with two mechanisms : blood aspiration and pushing

The Heart is a pump

• The cardiac pump produce a mechanical result (the circulation of the bood) due to the contraction and relaxation of the muscolar wall of the cardiac chambers (ventriculi and atria)

• But what is the primum movens of the cardiac function?

• Upstrem the mechanical function is necessary the electric function: the electric excitation

Nodo del seno

Nodo atrio-ventricolare

Fascio di His

Branca destraBranca sinistra

Fibre di Purkinje

The conduction system: Physiology and pathology

The Heart is a pump

• The cardiac electrical activity is an automatic activity

• Is only marginally influenced by nervous system

• These are the basis of the electro-mechanical coupling partneship

The cardiac cycle

4040

Arterial Pressure Curve

IsovolumetricIsovolumetricContractionContraction

IsovolumetricIsovolumetricRelaxationRelaxation

00

120120

100100

6060

Electrocardiogram

Ventricular Pressure

Arterial Pressure

Approx. TimeApprox. Time 00 0.10.1 0.20.2 0.30.3 0.40.4 0.50.5 0.60.6 0.70.7 0.80.8

8080

1010AV ValveAV Valve

OpensOpens

AV ValveAV ValveClosesCloses

Semi-LunarSemi-LunarValve ClosesValve Closes

Semi-LunarSemi-LunarValve OpensValve Opens

Pre

ssu

re (

mm

Hg

)P

ress

ure

(m

m H

g)

VentricularVentricularSystoleSystole

AtrialAtrialSystoleSystole DiastoleDiastole

TTRR

PP

QQ SS

VentricularVentricularFillingFilling

VentricularVentricularEjectionEjectionPhasePhase

AtrialAtrialSystoleSystole

Ciclo di Wiggers 1915 Fasi1 contrazione Vs2 rilasciamento Vs3 riempimento Vs

12

33

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00

120120

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Electrocardiogram


Arterial Pressure

Approx. TimeApprox. Time 00 0.10.1 0.20.2 0.30.3 0.40.4 0.50.5 0.60.6 0.70.7 0.80.8

8080

1010AV ValveAV Valve

OpensOpens




Pre

ss

ure

(m

m H

g)

Pre

ss

ure

(m

m H

g)



DiastoleDiastole

TT

RR

PP

QQ SS


VentricularVentricularEjectionEjectionPhasePhaseAtrialAtrial

SystoleSystole

The cardiac cycle pressure/volume V sin

ratio

Ventricular FillingVentricular Filling

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00

120120

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Electrocardiogram


Arterial Pressure

Approx. TimeApprox. Time 00 0.10.1 0.20.20.30.3 0.40.40.50.5 0.60.60.70.70.80.8

8080

1010AV Valve

Opens




Pre

ss

ure

(m

m H

g)

Pre

ss

ure

(m

m H

g)



DiastoleDiastole

TT

RR

PP

QQ SS



SystoleSystole

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00

120120

100100

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Arterial Pressure


8080

1010AV Valve

Opens




Pre

ss

ure

(m

m H

g)

Pre

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ure

(m

m H

g)



DiastoleDiastole

TT

RR

PP

QQ SS



SystoleSystole

Atrial SystoleAtrial Systole

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00

120120

100100

6060

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Arterial Pressure


8080

1010AV Valve

Opens




Pre

ss

ure

(m

m H

g)

Pre

ss

ure

(m

m H

g)



DiastoleDiastole

TT

RR

PP

QQ SS



SystoleSystole

Isovolumetric ContractionIsovolumetric Contraction

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00

120120

100100

6060

Electrocardiogram


Arterial Pressure


8080

1010AV Valve

Opens




Pre

ss

ure

(m

m H

g)

Pre

ss

ure

(m

m H

g)



DiastoleDiastole

TT

RR

PP

QQ SS



SystoleSystole

Ventricular EjectionVentricular Ejection

4040




00

120120

100100

6060

Electrocardiogram


Arterial Pressure


8080

1010AV Valve

Opens




Pre

ss

ure

(m

m H

g)

Pre

ss

ure

(m

m H

g)



DiastoleDiastole

TT

RR

PP

QQ SS



SystoleSystole

Isovolumetric RelaxationIsovolumetric Relaxation

300300

200200

100100

00

SystoleSystole DiastoleDiastole

Left Left

Right Right

Coronary Coronary Blood Blood Flow Flow

(ml/min(ml/min))

Slide courtesy of A.C. Guyton, MD, Slide courtesy of A.C. Guyton, MD, Textbook of Medical Textbook of Medical Physiology, Physiology, Sixth Edition, 1981 W.B. Saunders CompanySixth Edition, 1981 W.B. Saunders Company

How is the Cardiac function?

Cardiac output and pressure

CO= Pr / R= SV x HR

Legenda

1.Pr = systemic pressure2.R = systemic resistance3.SV = stroke volume (amount of blood eject every beat)4.HR = number of beats per minute

Cardiac function = CODeterminants

• Cardiac rate

• Inotropic condition = contractility

• Venus return (RV): influenced from neuroumoral factors (Frank-Starling law)

• Peripheric resistance

=CARDIAC OUTPUT 4-6 l/min

CARDIAC INDEX 1.6-2.5 l/min/m²

Cardiac output = CO

CO= Pr / R= SV x HRexamples :

1. Increase of FC -> does not increase GC, decrease of the VOLUME SYSTOLE-SV (if Rv does not increase)2. Increase of RV -> increases GC 10-20% (increase of Pa A dx 10 mmHg)3. Increase of FC + increase of RV -> increases GC with = SV4. Stirring adrenergethic -> increases RV + increase of the function of the pump (HR, contract?) = INCREASES GC 5. Important reduction of FC or alteration of V dx -> increase of Pa A dx = barrier for the venous comeback

Organs are able to change their flow working on the oppositions; they are able to regulate the distribution of the CARDIAC RANGE.

Cardiac function: Frank-Starling mechanism

Cardiac function:CO-CI & R ; Conduttance= 1/R

Vascular resistance

The vascular regulation is a local methabolic process in all organs, a part in kidney and skin. In fact even if in a denervation condition these organs are able to matain a adequate vascular tone modificated by methabolic influences. Flow depend closely by the radius

R = L x h8/ x r4

10% in reduction diameter vessel = 50% in increase resistance

sistolica

diastolica

sistolica

Difetto di riempimento

Difetto di espulsione

Cardiac power outputVentricular function index

Cardiac Power output

=MAP x CO

= SW X HR

Cardiac power output

Function of blood circulation

TRANSPORT• substrates and cathabolism products to and from organs and tissues• in a changeable measure and in proportion of her requirements and necessities

GOAL• to maintain an optimal composition of the interstitial fluid necessary for the cellular function

PLACCA ATEROSCLEROTICA

VASO ARTERIOSO

TONACA MEDIA

TONACA INTIMA = ENDOTELIO

TONACA AVVENTIZIA

Distribution of blood flow

• It is necessary to give at any time to organs and tissues

a blood flow distribution based on requirements

• There are two control mechanisms in a close correlation

• Central Autoregulation

• Local Autoregulation

Distribuzion of blood flow

Central Autoregulation GOAL: TO MAINTAIN COSTANT

perfusion pressure of the organs (independently from the flow: Fl= P/R)

Mechanism: neuro-ormonal central control on R e Fl

Local Autoregulation GOAL: TO MAINTAIN ADEQUATE

flow for each organ for the metabolic erquirements

(independently from systemic pressure)Mechanism: regulation of local vascular resistance

due to metabolism activity

Circulation modelling

• • ORGANS in parallelo if we consider AORTA with different metabolic, vascular, anathomic characteristics (f.e. heart, abdominal argans, muscols, brain…)

• VASCULAR SYSTEM: determinate from a segments sequence in serie similar in each organ

Arterie – arteriole – capillari – venule – vene

The Vascular System: segments

1) Aorta e great proximal arteries

• Elastic matrix tessue prevalent HISTOLOGY

• Improve distention of vascular wall during sistole PHISIOLOGY

• cinetic energy of stroke volume (during systole ) is storaged as elastic

energy released during diastole (partecipate at the diastolic value of BP)

• modulation of suddenly variations of BP : dynamic sistolic reserve • pressure wave downstream is delayed

• Riduction of elastic properties PATHOLOGY

• reduction of dynamic sistolic reserve• increase differential blood pressure even if a costant stroke volume• increase of afterload of left ventricle• increase of the rate of propagation of the pressure wave


2) Muscolar small arteries• Arteries with a thick muscolar medium tonaca: are the junction betweengreat arteries and organs and tessues

– Thick medium muscolar tonaca ( high thickness/lumen ratio )– COSTANT STRESS of the wall (PR x radius/ thickness)– COSTANT DIAMETER with variations due to neuro-horrmonal control– Regulatory mechanims : metabolics production and myogenic control

• Play a central role in the vascular resistance control = control and persistance of an adequate flow to organs and tessues FL= P / R

– Is the principal location of the flow resistance (aortic pressure 100 mmHg, small arteries pressure 30 mmHg, vein pressure 15 mmHg)

• The pressure gradient between small arteries and veins (about 15 mmHg) permits

– The capillar filtration – The distal reabsorbtion

The Vascular System: segments 3) Capillars

• In this segments is present the most importanti function of circulation = SUBSTRATES AND OXIGEN EXCHANGE BETWEEN BLOOD/TESSUES WIT H AN FOUDAMENTAL ROLE IN OMEOSTASIS OF THE INTERSTITIAL FLUID

– The walls are very smooth , sometimes in certein organs fenestrates – Little diameter = little transmural stress (Stress= D x P/spessore) with a better tolerance of the transmural pressure – There is a significant flow resistance with a fall of pressure (from 30 mmHg to 15 mmHg)– At the arteriolar portion happen THE FILTRATION at the venular portion THE REABSORBTION– In any time not in all THE CAPILLARS there is perfusion: the density of the perfused capillars is important in terms of exchange between the tessues– The exchange happen due to:

•Pressure gradients (FLUIDS): hydrostatic pressure (proximal side) and colloido osmotic pressure (distal side)•Diffusion: liposoluble gas and yhdrosoluble substances

– The amount of not reabsorbed fluids returns to the systemic circulation through an alternative circulation : THE LINFATIC SYSTEM = 4-5/L in a day-> 1/4 -1/2 TOTAL PLASMATIC ALBUMIN

The Vascular System: segments 3) Capillars

CAUSES OF INCREASE OF FILTRATION

1.Increase of the exchanges surface (due to the increase of number of the perfused capillars)

2.Increase of the pre-capillar pressure (more diffusion)

3.Increase of the postcapillar pressure (less reabsorbtion))

4.Increase of the permeability per surface unit (increase of holes)

INTERCAPILLAR DISTANCE =

less distance = more opend capillars = more fast the exchange


4) Venule and veins

• EMODYNAMIC: – Pressure = 15 mmHg in orizzontal position– Prefusion pressure for the veins heart return

• HISTOLOGY: –Thin wall– Very strechable–Muscolar portion very thin

•FUNCTION: – Return of blood from tissue sto the heart– Storage of blood able to control the return to the heart– Influence to the capillar pressure

• LEGS: superficial and deep veins– Muscolar wall more thick– Unidirectional valves (distribution of the Hydrostatic pressure in orthostatisms)

Vascular resistance

• Not uniform distribution a long the segments of circulation1. Arteries 5%2. Small arteries 60%3. Capillars 20%4. Veins 15%

• Medium vascular resistence-> integrated values of organs and tissues in parallelo respect the aorta

Vascular resistance

The vascular regulation is a local methabolic process in all organs, a part in kidney and skin. In fact even if in a denervation condition these organs are able to matain a adequate vascular tone modificated by methabolic influences. Flow depend closely by the radius

R = L x h8/ x r4

10% reduction diameter vessel = 50% increase resistance

Peripheric distribution ofCO and oxygen consumption

Myocardial ischemiaFractional Flow Reserve –

FFR

Coronary circulation:anatomic aspects

• Coronary tree = vascular system with dicotomyc regular ramification with a diameter progressively smaller

• 2 distinct section in term of anatomic and functional characteristics

- 1 Epicardic portion - 2 Microcirculation section

Epicardial segment

Microcirculation)

Coronary Circulation: segments

Coronary circulation:anatomic aspects

• Epicardic portion (diameter 4-5 - 0.5 mm) - “Conduttance” vessel : not able to influence the

vascular resistance - are visible using contrast media

• Microcirculation (diameter < 0.5 mm) - “ Resistance” vessel site of autoregulation

process - Are able to modify vascular resistance up to 6

times - Incompletely visible with contrast media (cause of

“myocardial blush”)

Coronary Circulationphysiologyc aspects

• Coronary Flow = Pressure/Resistance = 300-600 ml/min

• 5-10% of cardiac output (4-6 l/m)• Can increase up to 5-6 times (Resistance can change

up to 6 times)• Pulsed flow (not continue) with a prevalent diastolic

component• Cardiac methabolism: exclusively aerobic - O2

dependent with a very high O2 extraction from the arterial blood (10 ml/100gr/min vs 0.5 ml/100gr/min in the skelectric muscle) and with 30% O2 saturation the blood of coronary sinus

= more oxigen demand request more oxigen supply

it is mandatory an increase of coronary flow it is not possible more oxigen extraction

300300

200200

100100

00

SystoleSystole DiastoleDiastole

Left Left

Right Right

Coronary Coronary Blood Blood Flow Flow (ml/min(ml/min))

Slide courtesy of A.C. Guyton, MD, Slide courtesy of A.C. Guyton, MD, Textbook of Medical Textbook of Medical Physiology, Physiology, Sixth Edition, 1981 W.B. Saunders CompanySixth Edition, 1981 W.B. Saunders Company

PLACCA ATEROSCLEROTICA

Physiopathology ischemia

MVO2

SupplySupply Demand Demand

Supply: stenosi spasmo riserva coronaricaDemand: FC PAO e contrattilità, ipertrofia

Coronary stenosis: physiopathology

concept of coronary flow reserve

• A coronary stenosis (> 40%) determine a reduction in perfusion pressure without a concomitant flow reduction due to contemporary microcirculation resistance reduction FL= P/R, if decrease P and R contemporary = FL remain stable

• Stenosis upper a limit level (80-85% diameter) run out the dilatation possibilities of the microcirculation: in this condition every other reduction of pressure means reduction of flow because the incapacity of reduction of resistance = ischemia

RUN OUT OF THE CORONARY FLOW RESERVE

IVUS - INTERMEDIATE LESION RCAIVUS - INTERMEDIATE LESION RCA

FFR

CFR (E TEST NON INVASIVI)

FFR and CFR: What Do They Investigate?

Fractional Flow Reserve (FFR)

FFR = Qmax

Qmax

S

N

Pd

Pa

=

During maximal hyperemia

Pa

Pd

FFR = the ratio of maximal myocardial flow in the stenotic territory to maximal myocardial flow in that same territory

if the stenosis were absent

FFR = Q Pd

Q Pa

=

sten

N

FFR: a Flow Index Derived from Pressures

Normal Value of Myocardial Fractional Flow Reserve

Normal FFR = 1

Pa Pd

FFR = Pa

Pd

Myocardial Fractional Flow Reserve: Definition

Qmax

S

Qmax

N= FFR

FFR =Pd / R myo

Pa / R myo

=Pd

Pa

Pa Pd Pv

Pa

100 Pd

70 Pv

0

Pa

100 Pv

0

During Maximal Vasodilatation

FFR = Pd

Pa = 0.70

Q

P10070

Q100

Q70

R.E. 50-y-old man. Aborted sudden death.

LV angiogram: mild hypokinesia of the anterior wall.

Pa Pd

FFR = Pd /Pa = 56/80 = 0.70

HYPEREMIA

Coronary Pressure Measurements 1979 2001

Coronary Pressure Measurements: Prerequisits

1. Pressure Measuring Guide Wire

2. Maximal Hyperemia

3. FFR instead of P

0.014”

3 cm

Pressure Monitoring Guide Wires

0

100

50

Pa = Guiding Catheter

Pd = Pressure Wire




3. FFR instead of P

Hyperemia - administration• Hyperemic stimuli

– Intravenous Adenosine 140-160 g/kg/min

– Intracoronary Adenosine LCA: 20-40 g

RCA:15-30 g

– Intracoronary Papaverine LCA: 15 mg

RCA: 10 mg

– Adenosine Triphosphate (ATP) (ic. or iv) (same dosages as for Adenosine)

0

100

50

ADENOSINE

200

100

0

200

100

0

Aortic Pressure = 122 mm Hg Aortic Pressure = 89 mm Hg

Coronary Pressure = 52 mm Hg Coronary Pressure = 40 mm Hg

P = 70 mmHG P = 49 mmHG

FFR = 52/122 = 0.43 FFR = 40/89 = 0.45

Influence of Systemic Pressure on Transstenotic Gradient




3. FFR instead of P

Pa

Pd

FFR = Pd /Pa (during hyperemia) = 58/79 = 0.730

Pa

Pd

Baseline HyperemiaAdenosine IC

100

80

60

40

20

Fractional Flow Reserve in Clinical Practice

REST HYPEREMIA

FFR=58/112=0.52

150

50

0

100

Proximal to the lesion

Distal to the lesion

Crossing the lesion

58

112

Fractional Flow Reserve in Clinical Practice

Coronary Pressure Measurements

Clinical Applications1. Diagnostic Setting:

Is this lesion responsible for patient’s complaints?

Should this lesion be revascularized?

2. Interventional Setting:

Is a stent needed after balloon angioplasty?

Is the stent well deployed?

BDB 98/029

Clinical Applications of FFR

1. Before PTCA:

when FFR > 0.75 the prognosis is at

least as good without than with an angioplasty.

when FFR < 0.75 an angioplasty is

justified by a marked symptomatic

improvement following

revascularization.


2. After balloon:

when FFR > 0.90 and angio is OK, the long-term outcome after POBA is similar than

what can be expected after additional stent implantation.


3. After stent:

pullback maneuver : No pressure drop during hyperemia.

A B C D

FFR = 91 / 107 = 0.85FFR = 75 / 101 = 0.74 FFR = 90 / 106 = 0.85 FFR = 98 / 100 = 0.98

represents the true fraction of maximum flowwhich can still be maintained in spite of the

presence of a stenosis.

FFRmyo Myocardial Fractional Flow Reserve

Myocardial Fractional Flow Reserve

It is exactly that index which tells to what extent a patient is limited by his coronary disease.

FFRmyo

FFRmyo

=Max. myocardial blood flow in the presence of a stenosis

normal maximum blood flow

FFRmyo Myocardial Fractional Flow Reserve

is a lesion specific index

is independent of hemodynamic parameters

has a normal value of 1.0

takes into account collateral flow

has no need for a normal control artery

can be easily obtained: FFRmyo = Pd / Pa

In summary

FFRmyo ...

Courtesy of Charles Chan, M.D.

National Heart Center, Singapore

Aortic stenosis

AORTIC VALVE: tricuspid

Valvola normale Valvola stenotica

Aortic stenosis: pathology

AORTIC STENOSIS: imaging

Aortic stenosis: pressure curves

Acquiring Hemodynamic DataAcquiring Hemodynamic Data

• O2 consumption measured from metabolic hood or Douglas bag; it can also be estimated as 3 ml/min/kg or 125 ml/min/m2.

• AVo2 difference calculated from arterial – mixed venous (pulmonary artery) O2 content, where O2 content = saturation x 1.36 x Hg

• O2 consumption measured from metabolic hood or Douglas bag; it can also be estimated as 3 ml/min/kg or 125 ml/min/m2.

• AVo2 difference calculated from arterial – mixed venous (pulmonary artery) O2 content, where O2 content = saturation x 1.36 x Hg

*Accurate method of measuring CO, especially in patients with low cardiac output.

CO/(SEP)(HR)Area in cm² = ---------------------------------------- 44.3(C)(sq rt of pressure gradient)

Where C = empirical constant For MV, C = 0.85 (Derived from comparative data)

For AV, TV, and PV, C = 1.0 (Not derived, is assumed based on MV data)

Aortic stenosis hemodynamic evaluation Gorlin equation

Alternative to the Gorlin FormulaAlternative to the Gorlin Formula

*A simplified formula for the calculation of stenotic cardiac valves proposed by Hakki et al…Circulation 1981. Tested 100 patients with either AS or MS.

*Based on the observation that the product of HR, SEP or DFP, and the Gorlin equation constant was nearly the same for all patients measured in the resting

state (pt. not tachycardic). Values of this product were close to 1.0.

*Calculations somewhat comparable………

*A simplified formula for the calculation of stenotic cardiac valves proposed by Hakki et al…Circulation 1981. Tested 100 patients with either AS or MS.

*Based on the observation that the product of HR, SEP or DFP, and the Gorlin equation constant was nearly the same for all patients measured in the resting

state (pt. not tachycardic). Values of this product were close to 1.0.

*Calculations somewhat comparable………

How measure stenosis severty?

Echocardiography

Pressure gradients

VTI LVOT

VTI AO

LV

LA

Ao

Continuity equation: equal istantaneal flow through left ventricular outflow tract (LVOT) and the aortic valve Flow LVOT = Flow Ao V

Aortic Stenosis: valvular area with continuity equation

Flow = area (3.14 x (D/2)² x Integral time velocity Doppler (ITV)

Area LVOT (3.14 x (D/2)² x Integral time velocity Doppler (ITV LVOT) = Area Ao V (3.14 x (D/2)² x Integral time velocity Doppler (ITV Ao V)

Aortic Valve area = 3.14 x (D/2)² x (ITV LVOT / ITV Ao V)

Classification of severty of Valve Disease in Adults

Prognostic Importance of Quantitative Ex DopplerEchocardiography in Asymptomatic Valvular

Aortic Stenosis

Prognostic Importance of Quantitative Ex DopplerEchocardiography in Asymptomatic Valvular

Aortic Stenosis

All patients who displayed hard events (D or HF) had an AVA 0.75 cm2, an abnormal exercisetest, and a significant exercise-induced increase in mean transaortic pressure

gradientLancellotti et al. Circulation, 2005; 112: I-377 Lancellotti et al. Circulation, 2005; 112: I-377

Relationship between CO and Aortic Pressure Gradient over a range of values for AV area (Based on Gorlin formula)

A

Discrepancies between Gorlin and continuity-calculated effective orifice areas

Discrepancies between Gorlin and continuity-calculated effective orifice areas

JACC 2006; 47: 1241JACC 2006; 47: 1241

Since recommended cut-off values for the severity of aortic stenosis are largely based on the clinical experience with Gorlin-calculated areas, the use of the inherently lower continuity calculated effective orifice areas will

lead to a systematic overestimation of stenosis severity.

Since recommended cut-off values for the severity of aortic stenosis are largely based on the clinical experience with Gorlin-calculated areas, the use of the inherently lower continuity calculated effective orifice areas will

lead to a systematic overestimation of stenosis severity.

PRESSURE RECOVERY PHENOMENON

iii course biomedical applications of mathematics elements of cardiocirculatory physiology roberto...

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