On the Analysis of Microcontinuum Theory and Morphology for Small Arteries
Date Issued
2007
Date
2007
Author(s)
Kao, Chi-Sen
DOI
en-US
Abstract
On the analysis of the blood flow as the classical Newtonian fluid in small arteries yields a parabolic velocity profile. Experimental observation shows that the blood flow in small arteries does not obey the result. Recently, many studies apply the microcontinuum theory to analyze the blood flow since the theory take red blood cells’ interaction into account in a macroelement.
Literatures denote that cells will be concentrated when the blood flowing into small arteries. But most of the microcontinuum approaches do not consider cells distribution. Hence, a function describing cells distribution is used in our blood model. Accordingly, the model is then reduced into a two-layer flow, a peripheral layer and a core layer. We find the theoretical solutions in the case of both two layers are micromorphic fluids. Later, the core layer is modeled as a micromorphic fluid, and the peripheral layer is made of classical Newtonian fluid based on an effective viscosity formula for dilute fluid then the theoretical solutions are obtained. We also use the solutions to calculate and to create a modified parameter in the micromorphic fluid by experimental results form literatures in order to analyze the problem reasonably.
Numerical results depending on red blood cells distribution, the rotation and velocity fields in small arteries compared with the experimental results from literature are correspondingly. Therefore, red blood cells distribution affects the blood flow properties in small arteries. The results yield higher velocity distribution than the classical Newtonian fluid approach in small arteries. This implies the flow flux is different from the classical analysis.
Since the morphology for small arteries is related to the blood flow flux, we modify the Murray’s law and some morphological analysis for small arteries. The results show that the optimal design of arterial radius in present theory is larger than the classical approach, and the optimal bifurcation angle in small arteries is suggested to be also grater than the classical approximation.
Subjects
微連體理論
微連續體理論
微形流體
Eringen流體
血流
紅血球分布
形態學
血管分叉
Murray定律
microcontinuum theory
micromorphic fluid
Eringen fluid
blood flow
red blood cells distribution
morphology
vascular bifurcation
Type
thesis
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