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v

TABLE OF CONTENTS

8.0 OPTIMAL CANNULA DESIGN ........................................................................... 294

8.1 INVESTIGATION OF OBJECTIVE FUNCTIONS DETERMINED

THROUGH FLUID SIMULATION............................................................................... 295

8.1.1 Fluid Dynamic Simulation of a Cannula ................................................ 296

8.1.2 Principal Component Analysis of Objective Functions......................... 299

8.1.2.1 Methods ............................................................................................. 299

8.1.2.2 Results and Discussion ..................................................................... 307

8.1.2.3 Summary ........................................................................................... 312

8.2 SHAPE OPTIMIZATION OF A 2D CANNULA......................................... 312

8.2.1 Methods...................................................................................................... 312

8.2.2 Results and Discussion.............................................................................. 314

8.3 PLATELET MEDIATE THROMBOSIS IN CANNULAE ........................ 320

8.3.1 Cannula Optimization .............................................................................. 320

8.3.1.1 Methods ............................................................................................. 320

8.3.1.2 Results and Discussion ..................................................................... 322

8.3.1.3 Conclusions........................................................................................ 323

8.3.2 Quintessential Ventricular Cannula ....................................................... 324

vi

8.3.2.1 Methods ............................................................................................. 325

8.3.2.2 Results and Discussion ..................................................................... 326

8.4 BIBLIOGRAPHY............................................................................................ 330

vii

LIST OF TABLES

Table 8.1: Optimal parameters and objective function evaluations for the baseline geometry, the

four optimal values, and the anti-optimal values. ....................................................................... 370

viii

ERROR! NO TABLE OF FIGURES ENTRIES FOUND.LIST OF FIGURES

Figure 8.1: The cannulation and anatomical placement of the Streamline VAD. .......................348

Figure 8.2: The geometry of the 2D cannula model showing the control points of the Bezier-

curves and the full range of the walls. Points 1, 4, 5, and 8 were constrained to prevent motion.

Points 2 and 6 were allowed limited horizontal motion. Points 3 and 7 had limited vertical

motion. .........................................................................................................................................349

Figure 8.3: The coarse mesh used for the Cannula CFD study. ..................................................351

Figure 8.4: Mesh convergence diagram for velocity and pressure in the baseline geometry......351

Figure 8.5: The histogram of the element quality for the fine mesh used to simulate flow in the

cannula-CFD study. .....................................................................................................................352

Figure 8.6: Confluence can also be calculated by through observing the velocity and deviation

angles with a small windowed localized about the point of calculation......................................360

Figure 8.7: Comparison of the optimal results when using the mean velocity, a prescribed

velocity field, and the solution to the Stokes flow as predictors of confluence...........................365

Figure 8.8: Statement of the cannula shape optimization problem subject to the geometry in

Figure 8.1. f( apux vvr ,,, ) is the objective function, a is the vector of design parameters, and u and

p are the velocity and pressure predictions from the Navier-Stokes equations. ..........................367

Figure 8.9: Comparison of the final geometry of the four optimal cannula. ...............................370

ix

Figure 8.10: The results of the flow simulation for each of the optimal cannulae. The cannulae

are minimum shear (top left), minimum extension (top right), minimum confluence (bottom left),

and maximum Peclet number (bottom right).. All of the cannula showed a peak velocity at the

outlet of 144 cm/s.........................................................................................................................371

Figure 8.11: Fluid flow through the maximum extension cannula. The contraction results in a

high speed jet, which generates a recirculation region as the domain expands to the exit. .........372

Figure 8.12: The Pareto fronts comparing pairs of the four objective functions: Peclet Number,

Stress, Extension, and Confluence...............................................................................................373

Figure 8.13: Comparison of the MOO optimal cannula, the minimum active platelet cannula, and

the minimum Damkohler cannula................................................................................................377

Figure 8.14: The three traditional geometries for cannulation (Left to Right) the blunt tip, the

beveled tip, and the caged tip. Variations of the cannula tip includes the addition of side ports.379

Figure 8.15: The ventricular geometry used to compare the cannula tips. ..................................380

Figure 8.16: Results depicting the activation of platelets caused by the different cannula tips and

insertion depths. Dark red indicates complete activation of platelets (Color scales not equal)...381

Figure 8.17: Comparison of the flow deviation angle (top) and stagnation area (bottom) for the

cannula insertion study. The color scale for flow deviation in degrees is given in the top right.

Regions of stagnation, i.e. where the velocity less than 5% of the mean inlet velocity, are

indicated by dark red....................................................................................................................382

Figure 8.18: Normalized platelet activation, given by integrating the normalized platelet

concentration over the entire volume of the domain. The baseline value was determined by

integrating the initial activation level (0.05) over the domain.....................................................383

x

Figure 8.19: The formation of a ring thrombus around a standard cannula tip after a PediaFlow

implantation in a sheep. ...............................................................................................................384

xi

ERROR! NO TABLE OF FIGURES ENTRIES FOUND.PREFACE

[It is recommended that acknowledgments, nomenclature used, and similar items should be

included in the Preface.]

[The Preface is optional.]

294

8.0 OPTIMAL CANNULA DESIGN

Cannulae are conduits that connect

two separate regions for the purpose of

transporting a biofluid. Some

examples of cannula include

tracheotomy tubes for feeding

patients, the needles used in blood

donation, and fistula for renal dialysis.

This section focuses on the ventricular

cannula used to connect the apex of

the ventricle to an artificial blood

pump (See Figure 8.1). There are relatively few investigations into the fluid-dynamics of the

ventricular cannula, despite the adverse effects the cannula can have on flow into the blood

pump. It is well known that the flow through curved tubes results in Dean Vortices and the

skewing of the velocity toward the outer-wall of curved tubes. In the collective experience of our

research group, kinks in the cannula tubing and mal-placed insertion into the ventricle can have

deleterious effects on outcomes. The thrombus formed at on the bearing strut of the HMII shown

in Figure 1.2D was initiated by the suck-down of the ventricular wall, which partially obstructed

the flow path resulting in high shear stress and flow disturbances.

Figure 8.1: The cannulation and anatomical placement of the Streamline VAD.

295

8.1 INVESTIGATION OF OBJECTIVE FUNCTIONS DETERMINED

THROUGH FLUID SIMULATION

A multi-objective shape optimization of a cannula flow path was studied in detail in prior

work [1]. The work revolved around four flow parameters, namely Peclet number, shear stress,

extension rate and confluence, which are typically available from numerical fluid packages.

These objectives were calculated by taking

the volume integral of the squared value.

The Peclet Number is an indication of

chemical trauma to blood as it measures

domain washing and clearance of chemical

agonist and active platelets that can

ultimately cause thrombosis. Shear stress is

related to direct mechanical trauma to

blood cells through destruction of the

membrane (hemolysis) or complex

signaling events (SIPA). Confluence is an

indicator of flow perturbations which

results in the transport of cells toward walls and increased residence times. Finally, extension

rate is related to direct mechanical destruction of cells through extensional stresses. The work in

Chapter 5 identified extension rate as an important indicator of blood damage beyond shear

stress. The work reported in Hund[1] was repeated here using a newer, and consequently faster,

version of Femlab and an expanded list of possible parameters.

(x,y)

(x,y) (x,y)

(x,y)(x,y)

(x,y)

(x,y) (x,y)(x,y)

(x,y) (x,y)

(x,y)(x,y)

(x,y)

(x,y) (x,y)

Figure 8.2: The geometry of the 2D cannula model showing the control points of the Bezier-curves and the full range of the walls. Points 1, 4, 5, and 8 were constrained to prevent motion. Points 2 and 6 were allowed limited horizontal motion. Points 3 and 7 had limited vertical motion.

296

8.1.1 Fluid Dynamic Simulation of a Cannula

The cannula design was selected to match the tapered cannula originally selected for use with the

Streamliner VAD. The inlet of the devices had a radius of 0.7 cm and an outlet radius of 0.55 cm

for a resulting area ratio Ao/Ai of 0.617. The cannula was designed to divert flow by a full ninety

degrees from heart to blood pump. The center of the inlet was 4.5 cm above the cannula outlet,

while the centroid of the outlet was 4.3 cm from the inlet, both measured perpendicularly. The

device was designed for a nominal flow rate of 6.0 lpm, although the effect of flow ranges was

also examined to determine off-peak performance.

The ninety degree cannula design was reduced to a 2D problem for four key reasons: 1)

they are much faster than 3D simulation, 2) are more accurate at a given element size 3) have

higher element quality, hence lower numerical error, and 4) have more robust meshing

techniques. Four design parameters were used to describe the shape of the 2D cannula (See

Figure 8.2), where at least 14 parameters were needed to describe the cross-section and

centerline for a 3D cannula. For the sequential quadratic programming (SQP) optimization

technique used here, a single increase in the number of parameters results in the need for

approximately ten times that number in function evaluations due to the finite difference

approximation used for the gradient calculations and line-search algorithms. Finally, the

numerical noise in the 3D simulations was much higher than those of the 2D simulation due to a

coarser mesh for equal degrees of freedom and lower element quality. The noise can result in the

optimizer becoming trapped within local noise minimum or a large gradient approximation

which would slow progress towards a minimum and possibly prohibit finding the global

optimum.

297

The geometry is shown in Figure 8.2.

The sides of the cannula were described by a 3rd

order Bezier curve with weights of 1. The first

and last control points of the curves were

constrained to be the inlet and outlet points for

the cannula. The middle points were constrained

so that the inlet and outlet walls would be

perpendicular to the inlet/outlet surfaces. This

reduced the freedom of motion of the internal

control points to a distance from the inlet or

outlet. An additional non-linear constraint was

placed on the inner wall points to prevent the

geometry from becoming inverted. The constraint prevented the inner wall points from extending

beyond a straight line drawn between the two

free moving outer wall points. Finally, the

free-control points were not allowed to over

lap, i.e. to reduce the line from 3rd order to 2nd

order. This geometry allowed for greater

freedom than previous work by He et. al.[2]

or Abraham et al. [3, 4] despite using less a

third of the design parameters, but showed

reasonable ability to predict channels similar

Figure 8.3: The coarse mesh used for the Cannula CFD study.

Figure 8.4: Mesh convergence diagram for velocity and pressure in the baseline geometry.

298

to those by Gersvirg-Hansen and Haber [5] who used over 2800 design parameters using

topology optimization.

The fluid was assumed to be laminar

with a Reynolds number of 2730 at the inlet,

which is less than the turbulent transition for

blood [6]. The inlet condition was set to be

parabolic with a mean velocity equal to the

average velocity (Q/Ai = 65.0 cm/s) through

the inlet of the Streamliner cannula. The outlet

which extended 3 cm beyond that shown in

Figure 8.2 was set to neutral with pressure set

to 0 at point 5. The walls of the cannula were set to the no-slip velocity conditions. Flow was

simulated using FEMLAB 3.1 using the Navier-Stokes equation, except for one test case using

the MKM viscosity and the generalized Navier-Stokes equations. The geometry was discretized

using a regular-rectangular mesh (See Figure 8.3) The average element quality for the fine mesh,

45 node across the inlet and outlet and 101 nodes along the walls, was 0.63 with a range of 0.53

to .75 (See Figure 8.5).

The accuracy of the simulations was tested using mesh convergence. The simulation did

not reach a grid independent state due to a lack of memory coupled to double digit accuracy of

the flow solver. The L2 norm (Equation 8.13) of velocity showed linear convergence at a rate of

3.5 to 4 which is approximately the theoretical value. The L2 norm of pressure also showed an

estimated convergence rate of 3.5 but was decreased to 2.3 as the mesh became finer. The L2

norm of the differences versus the average element size is shown in Figure 8.4.

Figure 8.5: The histogram of the element quality for the fine mesh used to simulate flow in the cannula-CFD study.

299

8.1.2 Principal Component Analysis of Objective Functions

Principal component analysis is a useful tool from reducing the order of a large subspace, in this

case number of possible objective functions. Although principal component analysis may select

possible objective functions outside of user-feedback, this was avoided because there are

additional mathematical identifiers and user preferences involved in choosing an objective

function. For example, Hund [7] also took into account 1) the first and second variations of

objective function which are directly related to the gradient and Hessian and indirectly to the

convergence of the optimization problem, 2) ease of implementation, and 3) computational time.

8.1.2.1 Methods

The control-points of the Bezier curves were varied parametrically to generate 952 distinct

geometries from a narrow pinch to a bulbous flow path. The range of geometries provided a rich

set of test cases with high and low values of each objective function. The correlation coefficient:

( )ji

jjiiij N

XXXXR

σσ)1()(

−

−−= ∑ , (8.1)

where i and j represent two objective function, X is the value of the objective function for each

design, N is the number of designs, and s is the estimated standard deviation for each objective

function, was calculated for each combination of objective functions. The eigenvalues were

calculated for the correlation matrix and ranked to determine the number of objective properly

selected objective functions were necessary to predict total information of the system.

The objective functions, 109 in total, were broken down into four categories, 1)

mechanical trauma due to shear, 2) mechanical trauma due to extensional flow, 3) chemical

clearance, and 4) flow deviation.

300

Stress is the most common indicator of blood trauma from viscometric studies, but for

more-complex flows stress is a tonsorial quantity. Therefore it is necessary to calculate a norm

that reduces the tensor to a scalar quantity. Four methods are used to such, the first being:

τττ :21

= (8.2)

which is the standard definition by the Society of Rheology [8]. The second is the maximum

principal shear stress calculated from Mohr’s circle, which for 2D flows can be calculated as:

( ) 22 2/ xyyyxxττττ +−= . (8.3)

The third norm is the von Mises stress or octahedral stress modified to be consistent with

viscometric flows:

( ) ( ) ( )( )231

232

2216

1 σσσσσστ −+−+−= , (8.4)

where σ1, σ2, and σ3 are the principal components of the stress tensor [9]. Finally, the Tresca

criterion is:

),,max( 313221 σσσσσστ −−−= . (8.5)

The infinity norm, which is calculated from the maximum absolute matrix element, was not used

in this study. The magnitude of the vorticity, or curl of the velocity vector:

)(ucurl r=ω , (8.6)

and viscous dissipation:

2γη &=VD , (8.7)

have been suggestion as relating to shear induced blood trauma [2, 10, 11]. In other flow

situations, the stress and strain are studied through the invariants of the gradient of velocity

tensor L, the symmetric portion of L, and the skew-symmetric portion of L. First:

301

uL v∇≡ (8.8)

It then follows that:

( )TuuD vv ∇+∇=21 (8.9)

and

[ ]TuuW vv ∇−∇=21 . (8.10)

The first invariant of a matrix is its trace, therefore the 1st invariant of L and D reduce to the

divergence of velocity which is zero for all incompressible fluids. The first invariant of any

skew-symmetric tensor is zero as well. The second invariant of a matrix is the trace of the square

of the matrix, hence:

)(:)( 2XtraceXXXII == . (8.11)

Finally, the third invariant is the determinant of the matrix, which in 2D is:

2)det()( xyyyxx XXXXXIII −== (8.12)

All of these quantities can be evaluated using the norms: 1) L2:

∫Ω

Ω= dxx 22

, (8.13)

the average norm:

Ω= 2

xx

a (8.14)

and the infinity norm:

Ω∨=∞

)max( xx . (8.15)

The most common method for evaluating shear-induced blood trauma is the power-law

model:

302

βατ tAD = . (8.16)

The power-law model was evaluated using several methods: 1) local estimation:

βατ ⎟

⎠⎞

⎜⎝⎛=UhAD , (8.17)

where h is the local element diameter and U is the average velocity over the element, 2) method

of Garon et al. describe by Equations 6.2 – 6.4, 3) full Eulerian simulation (Equations 6.6), and

4) the Lagrangian method. The local estimation was evaluated using the L2, average, and infinity

norms. Lagrangian damage was also calculated using the model of Yeleswarapu et al. from

Equation 582. Sharp has developed a threshold model for blood damage that takes the form:

500,106.0τrest

D = . (8.18)

It is also possible to study sub-lethal blood trauma through the strain energy of the RBC.

Three strain energy models have been used for the simulation of RBCs on a micro-scale: 1)

⎟⎟⎠

⎞⎜⎜⎝

⎛+

+−=1

116 2

1 λλτE , (8.19)

where E is the strain energy, and λ1 and λ2 are the planar deformation of the membrane, 2)

( )22 )1log(5.)12log(1

6+++−= λλλτE , (8.20)

and 3)

⎟⎠

⎞⎜⎝

⎛ +−+=8

)5(.41 2

2121

λλλλτ

CE . (8.21)

The planar strain was estimated using the elongational index fit to the data of Lee et al. [12],

having the form:

( ) )()exp(1 bmAEI +−−= ττ , (8.22)

303

where A, m, and b are the empirical constants 0.0397 dyn-1, 3.64e-4 dyn-1, and 0.508

respectively. Now, if it is assumed that the RBCs have a constant volume, given by the equation:

abcV π43

= , (8.23)

where V is volume, and a, b, c are the radii of the semi-axes. It has been shown for RBCs that the

semi-minor axes are almost equal, therefore:

2

43 acV π= . (8.24)

The elongational index, identical to the Taylor index, is defined as:

cacaEI

+−

≡ . (8.25)

If an aspect ratio is defined as:

caAR = , (8.26)

then the elongational index can be transformed into:

11

+−

=ARAREI , (8.27)

and the aspect ratio can be determined from:

EIEIAR

+−

=11 . (8.28)

Combining the aspect ratio and the volume, the semi-minor axis can be found from:

3

43

ARVc = . (8.29)

The strain approximation are defined as:

micronsa

8.51 =λ , (8.30)

304

and

micronsb

1.22 =λ . (8.31)

Two functions have been used to represent damage caused by pure extension of RBCs,

namely extension rate and acceleration. The magnitude of the acceleration is calculated from:

uuuuaaA vvvvrv ∇⋅∇=⋅= (8.32)

Extensional rate can be calculated in several ways. The simplest is:

sU∂∂

=ε& . (8.33)

Another approximation is to take the square root of the sum of the diagonal components of the

stress tensor squared. An improvement to this method is to rotate the stress tensor into the local

velocity frame and taking the square root of sum of the diagonal components squared. The final

method is to decompose the field into extensional and simple shear. The elongational index and

acceleration were evaluated through the L2, average, and infinity norms.

Flow deviation can be determined through two general methods, confluence and the

inversion of the wall shear stress. The confluence is the angle between the velocity vector of the

simulation and a reference vector:

)vfuf,vf-atan2(uf yxxy +=φ . (8.34)

The reference velocity can be prescribed [7], set to the mean-flow velocity[13-16], set to the

Stokes flow solution, or parallel to the nearest wall location. The Stokes solution can be obtained

for free by setting the initial velocity to the zero vector, thus the first iteration of the non-linear

solver is the Stokes solution. The confluence can also be calculated using windowing function,

namely local evaluations (See). The windowing function calculated confluence at a position x, y

305

through several methods. The first method uses the velocity at x, y as the reference velocity, and

then calculates the deviation as:

∫Ω

Ω= dyxuwyxw )),((),( φφ , (8.35)

where w was 1 within 0.1/π cm of x and y and zero outside or 1 throughout the entire domain.

The second method is to calculate a local mean velocity:

∫

∫

Ω

Ω

Ω

Ω=

wd

duwyxuw

v

v ),( (8.36)

and consequently:

∫Ω

Ω= dyxuwyx ww )),((),( φφ . (8.37)

Finally, the windowed confluence can be calculated through:

( ) windowe within th)),((max),( yxuyxw φφ = . (8.38)

Another method for mathematically quantifying flow reversal is to calculate the wall stress

which reverses sign when flow reverses itself. The wall shear stress, as calculated in Femlab, is

positive in forward flow and negative for reverse flow. Thus the indicator can be calculated as:

∫Γ

Γ<=Γwall

dwallrev )0(τ . (8.39)

The final set of functions is used to predict clearance and flow stagnation. Flow

stagnation, i.e. low velocity, is indicated by either the magnitude of the velocity, the Peclet

Number, or the Damkohler number. In addition, stagnation time is indicated by long residence

times, which can be estimated from:

Uht =exp (8.40)

306

These four indicators were evaluated using the L2, average, and infinity norms. Stagnation can

also be quantified using the stagnation area which can be calculated through:

∫Ω

Ω<= dUUSA ref )( . (8.41)

Another factor in the build up of chemical agonists is the surface-to-volume ratio:

ΩΓ

=VS . (8.42)

Finally, stagnation velocities results in low-wall shear stresses.

Figure 8.6: Confluence can also be calculated by through observing the velocity and deviation angles with a small windowed localized about the point of calculation.

307

8.1.2.2 Results and Discussion

The PCA showed that four objective functions represent 93.1% of the information that can be

calculated from the full set of objective function, where seven objective functions are required to

predict over 99% of the information. The functions in the class of clearance were anti-correlated

(R ranging from -0.4 to -0.23) with functions representing extensional deformation. Since there

were no strong anti-correlations (<-0.8), multi-objective optimization can be effectively

employed to find a compromise between opposing functions. The average and L2 norm were

well correlated with each other (R > 0.92) and correlated to the infinity norm (R > 0.87). The

infinity norm is not ideal for optimization because it only reflects a single point in the flow,

hence may produce designs that are sub-optimal. The infinity norm may also produce a

discontinuous objective function if the variation of the parameter causes the maximum value to

jump from one spatial location to another. The L2 and averaging norm show similar behaviors,

yet may bias the results. Since the L2 norm ignores area, it could be biased toward designs with

small area, and conversely the average norm is biased toward designs with higher areas. The

underlying problem should be well understood before selecting particular norm to reduce area

artifacts.

The various methods for calculating shear stress, viscous dissipation, the second

invariants of L, W, and D, and vorticity were all highly correlated (R > 0.999), despite varying

mathematical forms. This agrees with the work of Garon et al. who showed that blood damage

prediction using power-law models were not greatly altered by choice of norm [17]. Of the

various norms for reducing the tensor to a scalar, the one in Equation 10.2, has the greatest utility

because it is directly calculated from the components of the stress tensor. The principal stress,

the modified octahedral stress or von Mises stress, and Tresca criterion all rely on principal stress

308

values which require the determination of the eigenvalues of the stress tensor for 3D flows. The

calculation must be done for every node and can quickly become costly. As expected, the

invariants of L, D, and W were also well correlated with the stresses. The 2nd invariant of D is

proportional to the stress norm given by Equation 10.2. Vorticity also correlates well with the

shear stress, despite the different mathematical forms. It is difficult to explain shear induced

blood damage through vorticity. For example, pure solid body rotation shows a vorticity of half

the rotational speed but in this case RBCs would not deform and consequently be exposed to

damage. One possible reason for the correlation is that near walls vorticity can be approximated

by:

tu

nu nt

∂∂

−∂∂

=ω , (8.43)

and stress as:

tu

nu nt

∂∂

+∂∂

=ητ , (8.44)

where ut is the velocity tangential to the wall, un is the velocity normal to the wall, t is the

coordinate along the wall, and n is the coordinate perpendicular to the wall. Two consequences

of no-slip conditions are that the normal velocity is small and does not change considerably

along the tangential direction; hence both vorticity and stress are dominated by the derivative of

the tangential velocity in the normal direction. Another contraindication for the use of vorticity is

that the curl of the velocity vector is not frame invariant. The norm of stress given in 10.2 and

viscous dissipation (Equation 10.7) have desirable mathematical qualities and can readily be

calculated from the flow information. Viscous dissipation has the further advantage that most

turbulent models provide the energy dissipation, where an acceptable surrogate for the turbulent

stress has not been found.

309

The shear stresses were weakly correlated (R > 0.78) to the various damage models

irregardless of method of calculation, the 3rd invariants of L, W, and D, the elongational index,

and the strain energy equations. For the damage models, the reduced correlation was caused by

the value of α resulting in the Giersiepen model having a correlation of 0.97 and the PSF had a

correlation of 0.8 when compared to the norm of stress squared. The Richardson model, also

involving stress squared had a correlation coefficient of 0.999. Garon et al. [17] showed that the

accumulation of damage was approximately equation to the integral of the source term

(Equations 5.2 and 5.3) which is almost identical to the L2 norm of the scalar stress. In

optimization, it can be shown that for a quantity that is greater than zero over for the entire

domain the optimal value is the same irregardless of the power. Hence, the minimization of

hemolysis or SIPA can be done by simply minimizing the stress using the L2 norm. It should

also be noted that computers use approximate solutions when dealing with non-integer powers,

hence there is a higher numerical error when using the Giersiepen or Antaki coefficients. The

method for calculating blood damage also affected the correlation with shear stress, with the

Lagrangian method having the lowest correlations (0.78) and the method of Garon having the

highest (>0.999). This, combined with the additional time required to calculate the path-lines,

indicates that the Eulerian method would be preferred in this case. The 3rd invariants were also

weakly correlated with shear stress, but there have been no studies to date that implicate the 3rd

invariant in blood damage. The elongational index and strain energy calculations enrich the

objective function space, but required numerous assumptions and approximations, and hence are

not as accurate as the calculation of shear stress or dissipation.

The class of functions for extension were well correlated (R>0.9) with the stress group.

Of the various methods for determining extension rate, Equation 10.33 was the most accurate

310

outside of flow decomposition. Pressure gradient was another likely surrogate from this class (R

> 0.999) of functions and is far simpler to calculate than extension rate. The elongation index

was not well correlated with the extension rate (Equation 10.33, R = 0.913), but it should be

understood that cell elongation or extension is not the same as flow extension rate. Experiments

in simple shear cases, such as Couette and Poiseuille flow, show cell elongation despite no fluid

extension. Conversely, Lee et al. [18] showed that the elongation index is greater in extensional

flow than in simple shear flow.

Confluence and negative wall shear stress were well correlated (> .98). The various

methods for calculating confluence were highly correlated (>0.999). Figure 8.7 shows the

optimal cannula using each method to prescribe the desired flow field. The easiest method to

implement mathematically is that which prescribes desired velocity field. This method is

practical when the flow field is simple, such as the cannula used here, but may not be practical

for more complex flow situations such as ventricular assist device and dialysis machines. Also,

the optimal solution may be biased toward the prescribed flow field as shown in Figure 8.7. The

Figure 8.7: Comparison of the optimal results when using the mean velocity, a prescribed velocity field, and the solution to the Stokes flow as predictors of confluence.

311

use of the Stokes solution can be applied to any flow domain, but may require an additional

simulation, particularly when using CFD software, such as ADINA, CFX, or FLUENT, that use

the SIMPLE solver and alternate between pressure and velocity solves. For more general solver,

the Stokes solution can be obtained for “free” by setting the initial condition for velocity to zero,

thus obtaining the Stokes solution on the first iteration of the non-linear solver. However, the

non-linear solver may not converge from this initial condition, particularly in highly non-linear

flow situations. The mean velocity is readily obtained during post processing, but may

unnecessarily bias the flow as seen in Figure 8.7. Three optimal solutions were obtained for flow

deviation each avoiding recirculation. However, the optimal result was drastically different when

the reference velocity is the mean velocity in the domain as compared to the other two methods.

The window functions were correlated with the confluence methods (>0.72) but required

considerable computational time, 35.1 minutes or 7.44 times the clock time for the simulation.

When the using the window to determine the local mean had a higher correlation than the

windowed function that did all calculations locally (0.999 vs. 0.72). The difference in

performance of these functions can be attributed to the fact that the second set (R < 0.8) only

picked up the boundary between the recirculating and forward flow region. The windowed

functions produced the same optimal cannula as that using the mean velocity.

The clearance variables were also strongly correlated with each other (R= 0.999). The

magnitude of velocity and Peclet number are directly related, particularly when using a constant

diffusivity. The Damkohler Number gave the best physical representation of chemically induced

blood trauma, but required an additional simulation to estimate the reaction rate for platelet

activation. The residence time is another physically tangible estimator that is difficult to

calculate. The method described in 10.40 depends on the size of the mesh and works best when

312

the mesh is topologically consistent. Another method, required and additional simulation of the

convection-diffusion equation (Equation 4.10) with S = 1, could produce results that are mesh

independent but would require an additional simulation. Stagnation area is determined from an

arbitrary threshold value which is undesirable. It also penalized the near wall layer where the

velocity is low due to the wall.

8.1.2.3 Summary

Various objective functions were analyzed within a four class framework, stress,

extension, recirculation, and clearance. It was determined that the best indicator of stress is either

the norm of the stress tensor (Equation 10.2) or viscous dissipation (Equation 10.7). The best

indicator of extension rate was found to be the pressure gradient. The best indicator of flow

deviation is confluence as indicated by the Stokes flow. The best indicator of clearance is either

the magnitude of velocity or Peclet number.

8.2 SHAPE OPTIMIZATION OF A 2D CANNULA

8.2.1 Methods

The statement of the optimization problem is in Figure 8.8. The optimal design was determine

using the SQP method built into the fmincon function available through the MATLAB

optimization toolbox. This method, a gradient based approach, was chosen over gradient-free

methods (GFM) such as genetic algorithms or ant-hill models for several reasons. The GFM

methods require a large number of iterations compared to the expected number for a gradient

313

outlet andinlet thelar toperpendicu are wallscannula that thesoyrepectivel xand ,y , x,y todconstraine are xand ,y , x,y and

geometry VAD theand sconstraint anatomicalby fixed are y and , x,y , x,y , x,y , xwhere

solution a toEquations Stokes-Navier theof econvergenc :2geometry inverted none i.e. geometry, valida :1

:of tsrequiremennolinear with

:by boundEquations StokesNavier

:subject to],,,[:respect towith

),,,(min

85417632

88554411

7632

highlow aaa

yxyxaapuxf

vvv

v

vvr

≤≤−

=

Figure 8.8: Statement of the cannula shape optimization problem subject to the geometry in Figure 8.1. f( apux vvr ,,, ) is the objective function, a is the vector of design parameters, and u and p are the velocity and pressure predictions from the Navier-Stokes equations.

based method. Secondly, all of the shape

parameters are continuous and would

have to be discretized for the GFM. The

derivatives were calculated using the

finite difference approach while the

Hessian was approximated using the

BFGS method proposed independently

by Broyden [19], Fletcher [20], Goldfarb

[21], and Shanno [22] to guarantee that

it remained positive definite and led to

the minimum. The finite difference method was used to calculate the derivatives as other

methods, such as the adjoined method, require information on the variation of the mesh with

respect to the design variables. The BFGS method was used to update the Hessian matrix

because it only requires the gradient approximations and will remain positive definite if the

initial guess, here the identity matrix, is positive definite. A positive definite Hessian guarantees

that the optimization routine will converge to a solution and is indicative of a rapid solution. The

line search algorithm used a quadratic/cubic approximation to determine the step size. The

optimal point was validated from 5 different design starting points to ensure convergence to the

global optimum and not a local optima. This was also compared to the study of the optimal field

done in Hund [1]. The objective functions were normalized using the method suggested by Koski

[23, 24] to remove the effect of variance and magnitude for multi-objective optimization. In

essence they were normalized so that the optimal point was 0 and the worst case scenario became

314

1. The Pareto optimal front was calculated for various pairs of objective functions by determine

the optimal values for the objective:

jiijobj FaFF )1( −+= α , (8.45)

and varying the parameter alpha from 0 to 1. The clock-time of the Pareto calculation was

decreased by starting the optimization run using the initial condition of the previous alpha value.

The unbiased MOO function was simply the sum of the four transformed objectives:

)( extensionshearConfluencePecletMOO FFFFF +++= β , (8.46)

where the penalty coefficient β was set to 0.1. The unbiased approach gives use a design that

minimizes the total percent deviation of all objectives from their optimal point. This method

allows for a single optimal design to be determined without direct intervention of an engineer;

however the Pareto front can provide greater information that the engineer can use to determine

the best design choice.

8.2.2 Results and Discussion

The choice of objective was found to drastically affect the optimal design. Figure 8.9 shows an

over-lay view of the four optimal geometries. Table 8.1 quantifies the optimal parameters and

evaluates the various objective functions in each of the optimal cannulae. The minimum shear

stress (optimal) and Peclet number cannula (non-optimal) and the maximum confluence cannula

(non-optimal) were identical. None of the optimal, meaning highest quality, cannulae were the

same. The design improvement was evaluated through the use of an optimality index (OI),

computed as the percent difference from the baseline (one of the initial conditions for the

optimization algorithm):

315

%100base

baseopt

ObjObjObj

OI−

= . (10.47)

The optimal stress cannula showed reduced the shear stress 81.1% over the baseline value, and

also improved in extension rate of 48.0%. Confluence and Peclet number deteriorated by 941%

and 11.0% respectively. The optimal extension cannula reduced the extension rate by 48.4% and

the shear stress by 46.2%, with an increase in confluence of 700% and a decrease in clearance of

10.5%. The optimal confluence cannula improved confluence, shear stress, and extension rate by

99.8%, 29.2%, and 16.7% respectively, while decreasing clearance by 7.67%. The optimal

clearance cannula (Peclet number) improved the clearance, stress, and extension by 0.162%,

3.33%, and 13.7% respectively, but worsened confluence by 47.2%. The objective function for

the worst-case stress cannula was 1,500 times that of the optimal design. The objective function

for the maximum extension rate cannula was 2,860 times the optimal value. The cannula

exhibiting the highest recirculation had a

confluence of 5,030 times the optimal

cannula. Finally, the optimal clearance

cannula was only 12.8% higher than the

anti-optimal cannula.

Figure 8.9: Comparison of the final geometry of the four optimal cannula.

316

The optimal confluence was the only cannula that did not exhibit recirculation. (See

Figure 8.10). The optimal stress and extension cannulae presented large recirculating regions on

the inner wall and a smaller recirculation region on the outer wall. The optimal clearance cannula

resulted in a small recirculation region on the outer wall.

Optimization

was able to improve

each design when

compared to the initial

design. The greatest

improvement was seen

in confluence where the

optimal results were

0.2% of the baseline

value. The design was

least sensitive to Peclet

number with an overall

Figure 8.10: The results of the flow simulation for each of the optimal cannulae. The cannulae are minimum shear (top left), minimum extension (top right), minimum confluence (bottom left), and maximum Peclet number (bottom right).. All of the cannula showed a peak velocity at the outlet of 144 cm/s.

Table 8.1: Optimal parameters and objective function evaluations for the baseline geometry, the four optimal values, and the anti-optimal values.

Objective X1 Y1 X2 Y2 Stress Extension Confluence Pe #(cm) (cm) (cm) (cm) (dyn2/cm2) (cm2/s2) (cm2deg2) (cm2)

Baseline 3 3 4 4 1231 84,100 9,170 99,000

Stress 0.275 0.35 4.03 4.15 233 43,700 95,500 88,300Extension 1.7 0.35 4.03 4.15 662 43,400 73,300 88,600Confluence 2.35 1.76 2.43 3.54 871 70,100 19 91,400Peclet Number 2.91 3.03 4.03 4.15 1190 72,600 13,500 99,600

Max Shear 3.6 3.6 2.2 2.25 3.50E+05 4.21E+07 26,700 97,700Max Extension 1.75 1.76 0.7 0.55 57,000 1.24E+08 16,200 97,300Max Confluence 0.275 0.383 4.03 4.15 233 43,700 95,500 88,300Min Peclet 0.275 0.383 4.03 4.15 233 43,700 95,500 88,300

Optimal Parameters Function Evaluation

317

variability of 1.12%, where the other three objectives offered improvements of three orders of

magnitude. Clearance was a weak indicator of recirculation, as shown in Figure 8.11 where a

sufficient recirculation area counteracts the high velocity jet. However, clearance is not as

effective of an indicator of recirculation as confluence.

One might be inclined to select the optimal confluence cannula as the best design since it

successfully reduced recirculation, shear, and extension rate with minimum impact on the

clearance when compared to the base-line model. However, this is dependent on the choice of

initial design and may vary depending on that choice. Therefore, biocompatibility has numerous

facets and lends itself to multi-objective optimization (MOO). MOO optimization offers tools to

assist the designer in determining the best overall design. Figure 8.12 shows six Pareto fronts

showing the trade-offs between the various objective functions. All of the fronts are either

strongly linear or concave up, indicating that a compromise can be reached irregardless of the

chosen objective functions. The Pareto fronts also indicate that the stress and extension rate more

susceptible to trade-offs, meaning Peclet

number and confluence can be improved

by a large amount, without a large increase

in stress or extension.

Another approach to multi objective

optimization is to weight each objective

function and thus obtaining a single

optimal design. Two methods were used

here: 1) an unbiased optimization and 2) a

biased optimization. The unbiased

Figure 8.11: Fluid flow through the maximum extension cannula. The contraction results in a high speed jet, which generates a recirculation region as the domain expands to the exit.

318

Figure 8.12: The Pareto fronts comparing pairs of the four objective functions: Peclet Number, Stress, Extension, and Confluence.

319

optimization treats all weights as one and therefore minimizes the percent error. Since

mechanical blood trauma is low in a cannula, shear stress and extension rate, are weighted

(b=0.1) as a penalty function. The optimal results for the multi-objective cannula are shown in

Figure 8.13. There may be considerable error in the simulation when the domain contracts to a

small cross-sectional area, as seen in Figure 8.11. The fluid is rapidly accelerated as the area

decreases, hence increasing the flow velocity by a factor of 7.55 over the mean inlet velocity.

The Reynolds number increases to 4,400 indicative of a transition to a turbulent jet. The effect of

this error on an individual simulation is large, but since the optimal results remain within the

non-turbulent regime, this error can be neglected.

It should also be acknowledged that the 2D simulation misses several key flow features

observed in thee-dimensional flow through curved tubes. Several of these features, including

Dean vortices and a skewing of the velocity profile, require the full 3D geometry in order to

predict. The cannula evaluation here is primarily aimed and better understanding the

performance of various objective function and not at producing a functional device for real world

applications; therefore these effects are of secondary concern.

There are no guarantees that the optimal results are a global optimal although the initial

geometry was varied several times for each objective function. Future work should involve

global optimization routines such as genetic algorithms, pattern search, and simulated annealing.

It should also be acknowledged that this work only examined two methods for performing

multi-objective optimization and is far from complete in this analysis. Marler and Arora [25], in

their review on MOO, include two additional methods for normalizing the individual objective

functions and additional methods for optimization. The method used here falls into the class of

weighted sums with a priori statement of preference. Other methods that involve a priori

320

statement of preference include the lexicographical method with a ranked preference, the

weighted Tchebycheff method, exponential weighted sums which improve the calculation of

Pareto front, and product weighting. There are also methods for determining preference a

posteriori or without stating preference.

8.3 PLATELET MEDIATE THROMBOSIS IN CANNULAE

Despite the uncertainty in surface reactivities and RBC-induced migration, the platelet mediated

thrombosis model provides more information toward defining a biocompatible device than fluid

dynamic parameters alone. For example, the platelet activation model can elegantly combine

SIPA with chemically induced activation. In section 8.2, these two factors were taken into

account through minimizing shear stress and maximizing Peclet number, but can be uniquely

determined through kpa. Furthermore, platelet activation occurs based on a threshold which

indicates that shear stresses does not necessarily be minimized but only reduced to a level

sufficiently below that which could cause activation. In order to investigate the effectiveness of

the platelet model in predicting biocompatibility, the model was incorporated into the design of

both the 2D cannula presented in sections 8.1 and 8.2.

8.3.1 Cannula Optimization

8.3.1.1 Methods

The cannula simulation, described in detail in section 8.1.2.1 and 8.2.1, was augmented

with the platelet mediated thrombosis model described in Chapter 4. Since the reaction rates, krs,

321

kas, and kaa have yet to be calibrated to materials used in cannula the effects of platelet

deposition was neglected. The reactive wall conditions were replaced by zero flux conditions.

Since the scale of the model is much higher than the scales at which RBC induced margination is

significant, hematocrit was assumed to be uniform through-out the domain. Furthermore, platelet

activation was assumed to have reached steady-state since ventricular cannulae are long-term

devices. Several objective functions were used for the optimization of the cannula: 1) the

effluence of active platelets:

∫Γ

Γ⋅= dAPunF ][ˆ v , (8.48)

2) the rate of activation:

∫Ω

Ω= dkF pa , (8.49)

3) the area of activation:

( )∫Ω

Ω≥= dkpaF 1 , (8.50)

4) the production of TAT:

∫Γ

Γ= dPTF ][ , (8.51)

5) the accumulation of agonists:

∫ ∑Ω

Ω⎟⎟⎠

⎞⎜⎜⎝

⎛= d

AgonistAgonistF

N *, (8.52)

6) active platelets:

∫Ω

Ω= dAPF 2][ , (8.53)

and 7) Damkohler number:

322

MOO OptimalMinimum APMinimum Damkohler Number

MOO OptimalMinimum APMinimum Damkohler Number

Figure 8.13: Comparison of the MOO optimal cannula, the minimum active platelet cannula, and the minimum Damkohler cannula.

Ω⋅++

= ∫Ω

dRuu

kRF

inrbcb

pain

22

2

)( vvκκ. (8.54)

To further investigate the relationship between the functions estimated by the model and the

parameters obtained through fluid flow simulations, a design-space study similar to 8.1 was

performed. Since the thrombus model requires more computational time (a factor of 15.2) than

the a simple fluid simulation, only 117 different geometries were analyzed. The results model

results including SIPA were correlated with shear stress, confluence, Peclet number, and

stagnation area.

8.3.1.2 Results and Discussion

Figure 8.13 shows the optimal

cannulae for active platelets and

Damkohler number. The other objective

functions led to cannulae similar to that

for active platelets and were close to the

optimal confluence and MOO objective

cannula. This is an encouraging result

since platelet mediated thrombosis model

adds significant computation coast and

complexity due to eight highly-nonlinear,

coupled equations in addition to the fluid simulation. The Damkohler cannula was unique in its

shape resulting in a decisive pinch compared to that of any other objective function. This is most

likely due to the balance between the reaction rate in the numerator and the transport in the

denominator. The high transport or clearance, results in an increase in the RBC enhanced

323

diffusivity and the convective transport. The width of the flow path of the cannula is decreased

until the effect of shear-induced activation becomes significant.

The study of the design space showed several functions that were well correlated (r > .8).

The confluence, Peclet Number, and Stagnation were correlated to the platelet activation

functions represented by Equations 10.48-53. The correlations to the Damkohler number (8.54)

were between 0.6 to 0.75. These functions were also weakly anti-correlated to SIPA (-0.4 < r < -

0.3). However, shear stress was highly-correlated to SIPA (r = 0.97).

8.3.1.3 Conclusions

Despite the apparent need for two objective function (SIPA and one from Equation

10.48-53), the activation threshold included either directly (functions involving kpa) or indirectly

(functions involving active platelets or thrombin) and gives a more accurate picture of

thrombogenicity and biocompatibility. However, the multi-objective approach may be more

desirable as it avoids the high computation cost associated with platelet mediated model.

Furthermore, the functions directly using the activation term are non-differentiable using the

discontinuous model, meaning they can predict infinite or large gradients under the right

conditions. Even the continuous version, although being smooth, can result in a large gradient at

the point were activation occurs. The discontinuous and continuous activation rate also lack

curvature below the activation threshold leading to an infinite number of “optimal solutions”.

Other functions, such as the Damkohler number and power-law models, do not produce positive

definite Hessian matrices. A positive definite Hessian guarantees rapid convergence to the

optimal point, but if the Hessian is not positive definite convergence depends on how close the

initial guess is to the optimal point.

324

8.3.2 Quintessential Ventricular Cannula

Despite a nearly-nonstop effort to improve the performance and biocompatibility of

Ventricular Assist devices, very little effort has been placed on the cannula connection. One

revolutionary device, known as the Quintessential Ventricular Cannula (QVC), promises to

reduce the thrombogenicity of the ventricular connection. The QVC has a novel flanged tip that

fits flush against the ventricular wall as opposed to projecting into the ventricular cavity as done

with caged type, beveled, and blunt cannula. Figure 8.1shows the various cannula tips that have

had historical use. This study seeks to examine the flow improvements and biocompatibility of

the blunt tipped cannula and the QVC.

Figure 8.14: The three traditional geometries for cannulation (Left to Right) the blunt tip, the beveled tip, and the caged tip. Variations of the cannula tip includes the addition of side ports.

325

Cannula Insertion Point(Normal Outflow, p=0)

Ventricular Wall(No-slip and insulation)Li

ne o

f Sym

met

ry(v

=0, z

ero

flux,

du/

dn=0

) VentricularRadius

Cannula Insertion Point(Normal Outflow, p=0)

Ventricular Wall(No-slip and insulation)Li

ne o

f Sym

met

ry(v

=0, z

ero

flux,

du/

dn=0

) VentricularRadius

Figure 8.15: The ventricular geometry used to compare the cannula tips.

8.3.2.1 Methods

The insertion of a blunt tipped

cannula and the QVC can readily be

represented by a 2D flow domain or an

axisymmetric domain. 2D domains allow

for denser meshes and better element

quality resulting in greater accuracy of

the numerical method. Secondly, the

reduction into 2D results in fewer

degrees of freedom and a reduction of

non-linear equations by one. Only the

lower portion of the ventricle was

simulated. (See Figure 8.15) The diameter of the heart was assumed to be 8 cm representing a

dilated heart which also indicated that the flow was laminar. Furthermore, blood was assumed to

be Newtonian with a density of 1.05 g/cm3 and viscosity of 3.5cP. The depth of the heart was

approximately 3.5 cm, assuming that the significant dilation occurs in the radial direction. The

flow rate was set to 6 lpm, effectively modeling a completely non-function ventricle. Due to the

complexity of simulating fluid-structure interactions, particularly for such a flaccid material firm

as a failed ventricle, the outer walls were considered immobile. The blunt tip cannula was

simulated at insertion depths of 0.5 cm and 1cm to show the effect of insertion depth on the flow

and thrombogenicity. Furthermore, the effect of insertion angle was simulated over a range of

zero to ten degrees. The QVC was design to fit flush against the ventricle wall thus resisting the

problem of over-insertion and preliminary studies proved that the QVC was not as sensitive to

326

insertion angle as blunt tipped cannulae [26], therefore the effect of insertion angle was not

studied. Thrombogenicity was determined through evaluation of the fluid dynamic parameters of

confluence and stagnation area and by simulation of the platelet activation as described in section

8.3.1.1. A finally measurement was a simulated dye-washout study in which an initially uniform

concentration (set to 1 U/cm3 for convenience) was allowed to wash out of the domain for 5

second indicating regions of poor washing.

8.3.2.2 Results and Discussion

Figure 8.16 shows the steady-state platelet activation caused by the three different insertions.

The 100% activation, indicated by red, is pronounced in the regions between the cannula and the

ventricular wall of both blunt cannula. The deeper the insertion depth, the greater the area of

platelet activation becomes and subsequent thrombogenicity was is increased. When the cannula

is only slightly inserted (the far right case) shows that some of the fluid impinges into the region

below the lip of the cannula. The QVC only shows a small amount of platelet activation near

Blunt Tip QVC Blunt TipBlunt Tip QVC Blunt Tip

Figure 8.16: Results depicting the activation of platelets caused by the different cannula tips and insertion depths. Dark red indicates complete activation of platelets (Color scales not equal)

327

φφ

Figure 8.17: Comparison of the flow deviation angle (top) and stagnation area (bottom) for the cannula insertion study. The color scale for flow deviation in degrees is given in the top right. Regions of stagnation, i.e. where the velocity less than 5% of the mean inlet velocity, are indicated by dark red.

where the flange contacts the ventricle wall. The thrombogenicity of this region can be reduced

by tapering the flange down as the distance from the insertion point increases. The effluence of

active platelets, when compared to the influx, showed a 375% increase, 40% increase, and 215%

increase for the deeply inserted blunt tip cannula, the QVC, and the well placed blunt tip

cannula.

328

0.070.060.050.040.030.020.010.0

0o 5o 10o

Nor

mal

ized

Act

ivat

ion

Baseline

Figure 8.18: Normalized platelet activation, given by integrating the normalized platelet concentration over the entire volume of the domain. The baseline value was determined by integrating the initial activation level (0.05) over the domain.

Figure 8.17 shows the confluence or flow deviation angle (top) and the stagnation area

(bottom). Both of these fluid dynamic parameters and the dye washout experiment indicate the

same regions of concern as the platelet activation model, namely the region between the cannula

tip and the ventricular wall and the end of the QVC flange. However, these region reveal an

additional recirculation region within the entrance of the cannula. This region did not show

activation, but shows recirculation and stagnation. A single numerical value quantifying the flow

deviation angle was evaluated using the L2 norm. The flow deviation index was 14,500, 2,640,

and 5,910 for the three cannula tips respectively. This index implies that the well placed cannula

is only twice as thrombogenic as the QVC, where the improperly placed blunt tip cannula was

5.5 times as thrombogenic as the QVC. After 1 second of flow, the forward flow regions were

entirely evacuated of dye leaving only the region between the cannula and the ventricular wall

for the blunt tipped cannulae with dye. The dye persists in that region even after the five second

simulation time. The dye was almost completely washed from the QVC after one second. Slight

amount of dye, less than 15%, remained near the regions of concern and on the inside of the

cannula. The total amount of dye remain in the

ventricles was 1.59 U, 0.0351 U, and 0.119 U

for the respective cannula.

Figure 8.18 shows the effect of insertion

angle on platelet activation with the blunt tipped

cannula. The platelet activation was lowest (I =

0.0482) at the ten degree deviation and peaked

at two degrees (0.0622) before decreasing to

0.0600 at zero degrees. An initial assessment

329

Figure 8.19: The formation of a ring thrombus around a standard cannula tip after a PediaFlow implantation in a sheep.

would imply that the cannula should be inserted at an angle and near the wall. However, the

cannula entrance located near the wall results in a higher risk of suck down [26]. Furthermore,

assessing the insertion angle inside the heart is difficult to do during actual surgery.

Irregardless of the method used to

evaluate the thrombogenicity of the

cannula tip, the QVC outperformed the

blunt tipped cannula. It was also shown

that the depth of insertion is a critical issue

when placing the cannula within a patient,

as over-insertion considerably increases

the thrombogenicity at the insertion point.

The danger is further augment due to the

trauma caused to the surrounding tissue

and blood as the cannula is inserted. The

QVC shows a reduction in predicted

thrombogenicity when compared to the

blunt tipped cannula. Figure xxx shows a ring of thrombus forming around a caged tip cannula

used during a PediaFlow animal study. The thrombus can pre-activate platelets or sensitize them

to shear activation before entering the ventricular assist device. Furthermore, the thrombus can

detach and releasing emboli into the arterial blood flow. Conversely, the QVC showed superior

performance irregardless of the selection criterion. These results are further corroborated by

experimental studies of Bachman, where micro-beads were shown to accumulate around the

blunt tip but not around the QVC [26].

330

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