Computational Fluid Dynamic Analysis Of The Effect Of Kink Conduit In Microvascular Vein Grafting

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Computational Fluid Dynamic Analysis Of The

Effect Of Kink Conduit In Microvascular Vein

Grafting

M. N. Rahman Y.

a,

*, Shahriman A.B.

a,

**, SK Za‘aba

a

, SA Roohi

b

, Khairunizam WAN

a

,

M. Nasir Ayob

a

, A.H. Ismail

a

School of Mechatronic Engineering, Universiti Malaysia Perlis, Main Campus Pauh Putra, Perlis, Malaysia, 02600

b

Orthopedics Department, Faculty of Medicine and Health Sciences, Universiti Putra Malaysia, Serdang, Selangor, Malaysia, 43400

*[email protected],**[email protected]

Abstract— Arterial disease of the upper extremity is an uncommon occurance, most commonly caused by atherosclerosis.In some patients with arterial disease, surgical bypass by vein grafting or vein interposition may be performed. However, due to the length kink between the existing artery and applied vein graft or more of the length of the applied vein graft may get blocked or severely narrowed. The objective of this study is to investigate the influence of blood flow on a failed vein graft due to length kink. The 3-D computational fluid dynamic method was employed to determine pulsatile flow velocity, pulsatile pressure gradient, and wall shear stress impact on the mismatched diameter of artery-vein graft model. We expect that pulsatile flow velocity, pulsatile pressure gradient and wall shear stress impact on mismatched diameter of artery-vein graft model to behave non-hydraulically compared to an ideal length model.

Index Term-- vein graft survival; digital artery disease; upper extremity; computational fluid dynamic; numerical method

I. INT RODUCT ION

Atherosclerosis formation in upper e xt re mity is uncommon compared to vascular disease in lower e xt re mity [1, 2]. It causes a narrowing of the lu men of the blood vessel and also an increase in the blood vessel wa ll stiffness or decrease in compliance of the blood vessel. In some patients who suffer with arterial d isease, surgical vein bypass or interposition vein grafting is performed to overcome the block especially in digital a rtery [1, 3-5]. In 1906, Ca rre l and Guthrie have performed the first successful application of blood vessel repair [6]. In the surgerica l technique, the thro mbosed artery segment is e xc ised, and the harvested saphenous vein graft is inserted reversed [7, 8].Su itable veins are available on the volar aspect of the forearm or on the dorsum of the foot and ankle [8, 9].

One of the require ments is that the vein graft should have approximately the same dia meter and the sa me length as the previously exc ised artery segment [9].Thus saphenous vein have been proposed as an ideal vein for gra fting [ 8-14]. There are several reasons for this. First, because of its relative ly large dia meter and wall characteristics, it is technically easy to use; second, it is plentiful, and therefore can be used to perform mu lt iple gra fts; third, it is long and can reach any artery; and fourth, it is easily harvested [15]. However, despite the initial success of procedure performed

by surgeon, its durability and longevity are still unpredictable, and many vein graft failure cases that have still been reported [1, 7, 8, 15]. Most defected finger was cool and pale [1-3, 16-17]. Furthermore, it is depending on surgeon‘s skill and meticulous surgical technique to ensure clean and matching vein graft stitching [8, 12, 15].

Based on previous study, a kinking of the vein [9,14,18] as well as mis matched internal dia meter of end-to end vein graft [9,13,19, 20] causes vein graft failure. In fact, the length and internal d ia meters of the vein are strongly related to the vein graft lifespan [21, 22]. He modyna mics including blood flow pattern, velocity, pressure gradient, strain rate, and shear stress impact on vessel wall has been believed to affect the development and progression of arterial stenosis but previous studies lack of realistic physiological considerations such as irregular vein geo metry formation, flow pulsatility, especially in the mic rovascular vein grafting. The objective of this study to investigate the relationships between kink ve in graft and thro mbosis in microvessels with low Reynolds blood flows.

The three dimensional CFD (co mputational flu id dynamic ) analysis were applied to calculate blood flow ve locity, pressure gradient in blood flow along the vein gra ft model, resistance of blood flow through vein graft model and wa ll shear stress impact on vein graft wall consist of the searching of flow patterns in a given ideal and kink vein model and applying the boundary conditions for flow variables. The co mputational fluid dyna mic techniques were also used previously to investigate the hemodynamic factors such as deformat ion erythrocytes [15-19], blood viscosity [20, 22], wall shear stress impact on vessel wall [20,21], and blood flow ve locity [20,21,24,25] in the comp le x three-dimensional blood mic rovessels. Those studies demonstrated that the computational fluid dyna mic approach can provide the motion informat ion of blood flow flowing in the microvessel models.

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straight vein graft model (0°) a lso have been proposed as an ideal vein graft for co mparison with the kink vein graft model since any flu id flows in straight tube provided very accurate fluidic properties [10,13,14,36-38].

II. RESEARCH MET HODOLOGY

The basic concept in modeling vein graft blood flow is by applying the diffe rent e xisting artery dia meter that attached with the same dia meter of vein graft. The three dimensional Navier-stokes equation is used in the three dimensional vein graft geo metry model. The energy equation was ignored in this study since we were only concentrating our study blood flow in vein graft model.

The blood flow in microvessels has been modeled as three dimension flow in a rigid wall, and governing equations, the

incompressible Navier-Stokes equations, are expressed as :

(

)

( )

(1)

(

)

( )

(2)

(

)

(

) (3)

Where t is time, ρ is the density, p is the pressure, μ is the viscosity. The blood velocity components in x, y and z

directions are denoted as u, v and w. The components of gravity effect in these directions are denoted by gx, gy, and gz respectively. Each node from meshing cell of three dimensional meshing of the three dimensional vein g raft geometry imp le mented the above differentia l equations. In this study, the gravity effect was a lso ignored.All analysis simu lation works we re done by ANSYS Fluent Inc. comme rcia l co mputational fluid dynamic software application.

A. Kink model

The dimension of the conduits, namely the saphenous vein graft was obtained from [9, 34]. The three-dimensional geometry of the saphenous vein graph model (Fig. 1) was constructed using the commerc ial fluid dynamic software GAM BIT. The graft length and diameter is provided in Table I

TABLE I

Ve in Graft Model

Pro xi ma l and Distal Internal Dia meter, cm

Amplit ude, cm

Curva ture Degree, °

Ve in Length, cm

Ideal 0.1 0 0 10

Case

1 0.1 0.05 9 10.01

Case

2 0.1 0.1 18 10.04

Case

3 0.1 0.15 27 10.10

Proximal (Inlet) Vessel Wall Distal(Outlet)

(a) Ideal

(b) Case 1 (c) Case 2

(d) Case 3

Fig. 1. Figure of geometry of vein graft model (a) Ideal; (b) Case 1; (c) Case 2; (d) Case 3

B. Meshing Grid and Boundary Condition

To nume rica lly ca lculate b lood flow through the each vein graft model, a simulat ion and every boundary condition need to be set for each reg ion. All meshing grid in vein g raft geometry models are divided into a number of finite computational volu mes or cells. The equations are non-linear, unsteady and comple x, several iteration of the solution loops were needed before a solution result was fully converged. Once calculation was converged after some iteration, the co mputed solution provides flow -variab le values at the each cell in the grid.

By applying this approach, the resultant algebraic equations for the dependent variables (the blood flow velocit ies) in each control volume we re solved by a Least Squares Cell Based for linear equation solver and discretizations method. The calculat ion was ca rried out by setting the convergence criteria as 10-6.

The governing equations were calculated rap idly until calculations of all flow variables were converged on a HP workstation Z600 desktop (Intel Xeon, 4 GB RAM). The number of ma ximu m over iterations was set as 40. The size time steps were 1 and the size steps were set as 10s.

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Fig. 2. Figure of location of boundary conditions on the vein graft model

C. Proximal Boundary Condition

As a blood flow is a laminar flow at the inlet of vein graft geometry models; that is, the blood is at all point moving parallel to the walls of the vessel, so that:

( )

Where u is the velocity, do is the internal dia meter of the whole vein graft model (0.1 c m) and d is the diameter location as measured from the center of the boundary wall surface.

The inlet velocity boundary conditions to the model of pulsatile flo w where they were 6.25c m/s as dias tolic phase, 12.50c m/s as mean velocity and 18.75c m/s as systolic phase and were set as a velocity-inlet zone.

D. Distal Boundary Condition

The zone for the outlet boundary conditions to the model were set as a pressure-outlet.

E. Vessel Wall Boundary Condition and Assumption

The vessel wa ll is long, cylindrica l shape, rigid body; the dia meter does not vary with the internal blood pressure and were set as a wall zone.

F. Blood Density and Viscosity

The blood is ho mogenous and its viscosity is the same at a ll rates of shear and does not slip at the wall. For mode ling purpose, a constant density of blood is 1050 kg/ m3 and viscosity is 0.0035 kg/ms.

III. RESULT AND DISCUSSION

As blood flow in d igita l arteries is not steady, t≠0, one of the

basic assumptions of deriving the Poiseuille equation is breached. Thus it is to be anticipated that the velocity profile will not be the same parabolic form that is found in steady la minar flo w, t=0 [32].The equation for the motion of a viscous liquid in la minar flow in a tube of circular c ross section, radius R, was derived earlie r for steady flow, t=0 [32]. In its general form for an inco mpressible liquid, we can write

(Wome rsley,1955a ,b, 1957a) [32]. Following co mmon convention, the axis of the vein gra ft is taken as x a xis and the blood velocity in the direction of that is u m/s (the velocities in the y and z a xis for a rig id body of vein g raft will both be zero [32]. In this study, we observed the blood flow characteristic in the vein g raft models after calcu lations were co mpleted. For b lood flow ve locity observation, we chose the computed velocity at pro ximal (inlet ) and distal (outet) of every case, Ideal, Case 1, Case 2 and Case 3.

A. Velocity Profile Observation Of Pulsatile Blood Flow

(a)

(b)

(c)

0 0.05 0.1 0.15 0.2

0 5 10 15

Ve locity, m/s

Time , s

Velocity Profile In Ideal

Proximal

Distal

0 0.05 0.1 0.15 0.2

0 5 10 15

Ve locity, m/s

Time , s

Velocity Profile In Case 1

Proximal

Distal

0 0.05 0.1 0.15 0.2

0 5 10 15

Ve locity, m/s

Time , s

Proximal

Distal

Proximal

Vessel Wall

Distal

Vessel Wall

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(d)

Fig. 3. Figure of velocity profile of vein graft model (a) Ideal; (b) Case 1; (c) Case 2; (d) Case 3

Fro m our observation on velocity profile at pro xima l and distal position, we can see that velocities profile at in a ll three cases are same.

B. Pressure Gradient Observation Of Pulsatle Blood Flow

Flow pressure gradient is the how the flow pressure change with e levation meaning the flow pressure decreases as it move forward or upward.

In this study, we observed the pulsatile flo w pressure gradient in the ve in gra ft models a fter ca lculations we re completed. Fo r the pulsatile flow pressure gradient observation, we chose the computed pulsatile pressure at proxima l (in let) and distal (outet) of every case, Ideal, Case 1, Case 2 and Case 3.

(a)

(b)

(c)

(d)

Fig. 4. Figure of pulsatile pressure gradient of vein graft model (a) Ideal; (b) Case 1; (c) Case 2; (d) Case 3

Fro m our observation on pulsatile pressures at pro xima l and distal positions, we can see that the highest

reduction in the amplitude of flow wave is for Case 1, Case 2 and Case 3 as co mpare to the Ideal. This is due to the blood being pushed (force through) at higher speed fro m the arteria l vessels to the curved vein grafted vesselscausinga high reduction in the a mplitude of flo w waves [32]. Alterations of pulsatile pressure gradient also can be related to vein graft life span [21].

C. Shear Stress Observation Of Vessel Wall

Wall shear stress influences vascular bio logy in many ways. We continue our study by the observation of wall shear stress impact on vein graft wa ll by observation in all vein graft model. We can see that the highest wall shear stress impact occurs in the ideal case only.

(a)

0 0.05 0.1 0.15 0.2

0 5 10 15

Ve locity, m/s

Time , s

Proximal

Distal

-50000 -30000 -10000 10000 30000 50000

0 5 10 15

Static Pre ssure, Pa

Time , s

Pulsatile Pressure Gradient In Ideal

Proximal

Distal

-50000 -30000 -10000 10000 30000 50000

0 5 10 15

Time , s

Pulsatile Pressure Gradient In Case 1

Proximal

Distal

-50000 -30000 -10000 10000 30000 50000

0 5 10 15

Time , s

Proximal Distal

-50000 -30000 -10000 10000 30000 50000

0 5 10 15

Time , s

Proximal

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(b)

Fig. 5. Figure of wall shear stress of vein graft model (a) Ideal at diastolic phase; (b) Ideal at systolic phase

(a)

(b)

Fig. 6. Figure of wall shear stress of vein graft model (a) Case 1 at diastolic phase; (b) Case 1 at systolic phase

(a)

(b) (b)

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(b)

The mechanism whereby wall shear influences the occurrence of atherosclerosis has not been exp lained yet however, it has been suggested that it involves the regulation of the release by the Endothelium-De rived Re la xing Factor (EDRF), which is believed to be nitric oxide [32]. The modulation of EDRF re leased by the wall shear stress also influences the development of atherosclerosis via another mechanis m and reduces the vein graft life span.

IV. CONCLUSION

The computed results have revealed that the length kin k between artery-vein graft model behave non-hydraulically like an ideal case. As a conclusion the only straight or 0° curvature vein graft has a high potential in prolonging vein graft survival. We decided to do a pulsatile flow simu lation in a straight tube in o rder to validate vein geo metry meshing and input user defined functions. In future, we propose to investigate pulsatile b lood flo w on an actual vein g raft model so as to closely simulate the in-vivo condition of a vein graft. After that, co mparison in longitudinal impedance between simulation result and clinical result will be studied, perhaps in a local environ ment of a saphenous vein graft. The long-term survivals of vein grafts are strongly dependent on the size (conduit dia meter and length) and quality of the venous conduit. As stated before, the blood flow velocity, pulsatile p ressure gradient and wall shear stress impact on vein grafts also has a predictive value for vein graft survival.

V. ACKNOWLEDGEMENT

Special thanks to all me mbe rs of UNIMAP Advanced Intelligent Co mputing and Sustainability Research Group and School Of Mechatronics Engineering, Universit i Malaysia Perlis (UNIMAP), 02600 A rau, Perlis, Malaysia for providing the research equip ment and internal foundation. This work is also supported by the fundamental research grant scheme (FRGS) a warded by the Min istry of Higher Education to Un iversiti Malaysia Perlis (FRGS 9003-00313).

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