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Numerical investigation and identification of susceptible sites of atherosclerotic lesion formation in a complete coronary artery bypass model

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Abstract

As hemodynamics is widely believed to correlate with anastomotic stenosis in coronary bypass surgery, this paper investigates the flow characteristics and distributions of the hemodynamic parameters (HPs) in a coronary bypass model (which includes both proximal and distal anastomoses), under physiological flow conditions. Disturbed flows (flow separation/reattachment, vortical and secondary flows) as well as regions of high oscillatory shear index (OSI) with low wall shear stress (WSS), i.e., high-OSI-and-low-WSS and low-OSI-and-high-WSS were found in the proximal and distal anastomoses, especially at the toe and heel regions of distal anastomosis, which indicate highly suspected sites for the onset of the atherosclerotic lesions. The flow patterns found in the graft and distal anastomoses of our model at deceleration phases are different from those of the isolated distal anastomosis model. In addition, a huge significant difference in segmental averages of HPs was found between the distal and proximal anastomoses. These findings further suggest that intimal hyperplasia would be more prone to form in the distal anastomosis than in the proximal anastomosis, particularly along the suture line at the toe and heel of distal anastomosis.

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Abbreviations

B n :

Fourier coefficients

D G :

diameter of graft (4 mm)

f :

frequency in Hz

i :

\( {\sqrt { - 1} }, \) unit imaginary number

J 0 :

the first kind of Bessel function of order 0

J 1 :

the first kind of Bessel function of order 1

N :

the total number of Fourier transform terms

OSI:

oscillatory shear index, defined as \( {\text{OSI}} = \frac{1} {2}{\left( {1 - \frac{{{\left| {{\int\limits_0^T {\tau _{{\text{w}}} {\text{d}}t} }} \right|}}} {{{\int\limits_0^T {{\left| {\tau _{{\text{w}}} } \right|}{\text{d}}t} }}}} \right)} \)

p :

static pressure (Pa)

Q G :

mean flow rate in the graft during the pulsatile flow cycle (m3/s)

Q(t) :

flow rate at time t (m3/s)

r :

radial location (m)

R :

radius of the aorta (12.5 mm)

Re :

Reynolds number of aorta, defined as Re = 2ρuR/μ

t :

time (s)

T :

time of a period (s)

u i :

velocity in i direction (m/s), i = 1, 2, 3 for x, y, z directions in Cartesian coordinate respectively

u(r, t) :

the distribution of axial velocity (m/s) at different radial location (r) and time (t)

WSS:

time-averaged wall shear stress (Pa), defined as \( {\text{WSS}} = \frac{1} {T}{\int\limits_0^T {{\left| {\tau _{{\text{w}}} } \right|}} }{\text{d}}t \)

WSSG:

normalized time-averaged spatial wall shear stress gradient, defined as \( {\text{WSSG}} = \frac{1} {T}\frac{{D_{{\text{G}}} }} {{\tau _{{\text{G}}} }}{\int\limits_0^T {{\sqrt {{\left( {\frac{{\partial \tau _{x} }} {{\partial x}}} \right)}^{2} + {\left( {\frac{{\partial \tau _{y} }} {{\partial y}}} \right)}^{2} + {\left( {\frac{{\partial \tau _{z} }} {{\partial z}}} \right)}^{2} } }} }{\text{d}}t \)

x i :

location in Cartesian coordinate (m), i = 1, 2, 3 for x, y, z directions, respectively

α :

Womersley number, defined as \( \alpha = R{\sqrt {\omega /\upsilon } } \)

μ :

dynamic viscosity of the working fluid (Pa s)

ρ :

density of the working fluid (kg/m3)

τ G :

Poiseuille type wall shear stress at the graft corresponding to the mean flow rate in the graft (Pa), defined as \( \tau _{{\text{G}}} = \frac{{32\mu Q_{{\text{G}}} }} {{\pi D^{{\text{3}}}_{{\text{G}}} }} \)

τ i :

wall shear stress in Cartesian coordinate (Pa), i = x, y, z for x, y, z directions, respectively

τ w :

wall shear stress (Pa), defined as \( \tau _{{\text{w}}} = \left. {\mu (\partial u/\partial n)} \right|_{{{\text{wall}}}} , \) where ∂u/∂n| wall is the normal velocity gradient at the wall

υ :

kinematic viscosity of the working fluid (m2/s)

ω :

angular frequency in radian per second of the oscillatory motion, defined as ω = 2πf

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Acknowledgments

The financial support of A*STAR Project 0221010023 is gratefully acknowledged.

Author information

Author notes

  1. Jun-Mei Zhang

    Present address: Temasek Laboratories, National University of Singapore, 5 Sports Drive 2, Singapore, 117508, Singapore

  2. Dhanjoo N. Ghista

    Present address: Parkway Academy, Singapore, 238164, Singapore

Authors and Affiliations

  1. Thermal and Fluids Engineering Division, School of Mechanical and Aerospace Engineering, Nanyang Technological University, Singapore, 639798, Singapore

    Jun-Mei Zhang, Leok Poh Chua, Dhanjoo N. Ghista & Simon Ching Man Yu

  2. National Heart Centre, Singapore, 17 Third Hospital Avenue, Singapore, 168752, Singapore

    Yong Seng Tan

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  1. Jun-Mei Zhang
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Correspondence to Leok Poh Chua.

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Zhang, JM., Chua, L.P., Ghista, D.N. et al. Numerical investigation and identification of susceptible sites of atherosclerotic lesion formation in a complete coronary artery bypass model. Med Biol Eng Comput 46, 689–699 (2008). https://doi.org/10.1007/s11517-008-0320-4

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  • DOI: https://doi.org/10.1007/s11517-008-0320-4

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