Arteriosclerosis is a frequent cardiovascular disease and has become one of the most leading causes of death in the modern society. Arteriosclerosis causes the deposition of lowdensity lipoprotein, atheroma, and cholesterol [
In this paper, a model composed of three arterial segments with different wall stiffness was constructed. Furthermore, a fluidwall interaction was introduced to investigate blood flow and mechanical characteristics. In the model, the same walls at two ends were stiffer than the wall in the middle. This model was employed to simulate arterial compliance mismatch. The aim of this paper is to study the effects of arterial compliance mismatch on flow distributions, wall stresses, and deformations and find out the stiffnessinduced differences of mechanical properties in the model. This study is helpful in making a detailed understanding of biomechanical effects of compliance mismatch. The understanding may be important in the selection of arterial grafts and in designing artificial blood vessels.
Figure
The geometry of the model.
For the fluid model, the NavierStokes equations were used as the governing equations. Blood was modeled as an incompressible and Newtonian fluid, with a density of 1050 kg/m^{3} and a dynamic viscosity of 0.0035 Pa·s.
For the wall model, the linear elastic constitutive equations were used as the governing equations. The material constants used in the linear elastic relationship were Young’s modulus and Poisson’s ratio. Here, we made a compliance difference according to different values of Young’s modulus. Young’s modulus of the middle artery was 5 MPa and the moduli of the arteries at two ends were 200 MPa [
Timedependent flow condition measured by Gijsen et al. [
The map of velocity at the inlet.
This fluidstructure interaction technique allows studying the arterial fluid mechanics by accounting for both the instantaneous fluid forces acting on the wall and the effects of the wall motion on the fluid dynamic field. Fluid forces, wall displacements, and velocities are transferred across the fluidstructure interface.
The fluidwall interaction scheme was constructed using the finite element method [
Figure
The velocity contours at different time. (a)
It can be seen that the velocity distributions at different locations are almost identical at the same time. The maximum velocity values at
Here, the maximum wall shear stresses at three locations are presented (Figure
The distributions of timedependent wall shear stresses.
The distributions of timedependent pressures.
As we know, the increasing residence time of atherogenic particles, such as platelets, leukocytes, and macrophages, could increase the probability of deposition or adhesion of blood particles with the arterial wall. The residence time is correlated with wall shear stress. Low wall shear stress is prone to increase the residence time and it can promote plaques formation and intimal thickening [
The stresses and strains in an arterial wall are caused by both blood pressure and wall shear. It is known that circumferential stresses and strains are directly related to the remodeling of arterial walls and affect the structure and physiological function of arterial walls. Therefore, the circumferential stresses and strains of the inner walls at three locations are concerned in this study. The time dependence of the circumferential stresses is the same as that of the pressures (Figure
The distributions of timedependent circumferential stresses.
The distributions of timedependent circumferential strains.
The absolute maximum and minimum values of the circumferential stresses at
The maximum and minimum circumferential stresses at three locations.

Maximum stress (Pa)  Minimum stress (Pa) 

70  2088.38 

100  760.663 

140  919.78 

The absolute maximum and minimum values of the circumferential strains at
The maximum and minimum circumferential strains at three locations.

Maximum strain  Minimum strain 

70 


100 


140 


Cyclic strain may play a role in atherosclerosis. It is possible that there exists a correlation between high cyclic strain levels and enhanced macromolecular permeability, in turn leading to atherosclerotic inflammation [
Several simplifying assumptions were made in the current analysis, which ignored anisotropy, nonlinear elastic properties of the arterial wall, nonNewtonian blood, and so forth. All these higher order effects can be considered in future studies.
A computational model for biomechanical effects of arterial compliance mismatch on blood flow and mechanical characteristics has been constructed. The flow distributions and wall stresses and deformations based on the model have been performed numerically. The results indicate that the arterial compliance mismatch could induce the differences of mechanical characteristics between different locations. The differences promote the probability of intimal thickening at some locations. Compliance mismatch is a negative factor and it needs to be considered cautiously in arterial bypass grafting. Consequently, the avoidance of compliance mismatch could enhance graft patency. The constructed model in this paper gives satisfactory results and may be better in expressing biomechanical properties of arterial compliance mismatch. The computational model is effective and could be extended to all kinds of arteries with complicated geometrical and material factors.
The authors declare that there is no conflict of interests regarding the publication of this paper.
The authors thank National Natural Science Foundation of China (81401492) and the Science and Technology Project of Beijing Municipal Commission of Education (KM201510016012) for financially supporting this research. The work is also supported by the Foundation of Research and Innovation Team (PXM 2013_014210_000173) and the Academic Innovation Team of Beijing University of Civil Engineering and Architecture (21221214111).