협착된 미세혈관에서 적혈구와 입자의 유변학적 거동에 관한 수치해석 연구

Abstract

Objectives of the present study are to develop a computational framework for high-fidelity prediction of generic fluid-structure interaction in a biological system and to understand complex rheology of blood flow in stenosed microvessels. In the past decades, blood flow in large vessels has been studied using a numerical simulation with a homogeneous Newtonian fluid. However, for studying the rheology of blood flow in a cellular level, an accurate computational methodology for predicting fluid-structure interaction is essentially required. In order to accomplish the objectives, the computational methodology of the present study combines two different immersed boundary (IB) methods which are capable of treating both deformable membranes and complex rigid bodies simultaneously. In the present methodology, fluid flow and structural dynamics are solved by a finite-volume method and a finite-element method, respectively, and their interaction is treated through the present IB methods in a single computational domain by separating a Cartesian grid for a fluid and a Lagrangian grid for structures.

A continuous-forcing IB method with colocated-grid discretization schemes can suffer from the poor capability for volume conservation since an interpolated Lagrangian velocity field is not generally divergence-free. The present IB method overcomes difficulties of the conventional colocated-grid IB methods. Desirable features of staggered-grid IB methods in volume conservation are incorporated into the present colocated-grid IB method through the use of additional variables for the face-centered velocity and the force density along with interpolation techniques. Firstly, a novel and simple method to obtain a Lagrangian velocity field, which satisfies the divergence-free condition, is incorporated into a colocated-grid IB method to reduce the volume error. Secondly, velocity interpolation and force spreading schemes are modified in the manner as in the staggered-grid IB method using the interpolated face-centered velocities and Lagrangian force densities. The superior performance of the present IB method compared to the conventional colocated-grid IB methods for volume conservation is demonstrated in a number of numerical examples.

In order to gain better understanding for rheology of an isolated red blood cell (RBC) and a group of multiple RBCs, new numerical models for describing mechanical properties of cellular structures of an RBC and inter-cellular interactions among multiple RBCs are developed. The viscous property of an RBC membrane, which characterizes dynamic behaviors of an RBC under stress loading and unloading processes, is determined using a generalized Maxwell model. The present model is capable of predicting stress relaxation and stress-strain hysteresis, of which prediction is not possible using the commonly used Kelvin–Voigt model. Nonlinear elasticity of an RBC is determined using the Yeoh hyperelastic material model in a framework of continuum mechanics using finite-element approximation. A novel method to model inter-cellular interactions among multiple adjacent RBCs is also developed. Unlike the previous modeling approaches for aggregation of RBCs, where interaction energy for aggregation is curve-fitted using a Morse-type potential function, the interaction energy is analytically determined. The present aggregation model, therefore, allows us to predict various effects of physical parameters such as the osmotic pressure, thickness of a glycocalyx layer, penetration depth, and permittivity, on the depletion and electrostatic energy among RBCs. Simulations for elongation and recovery deformation of an RBC and for aggregation of multiple RBCs are conducted to evaluate the efficacy of the present RBC modeling.

Lastly, a computational study of flow of deformable RBCs and particles in stenosed microvessels is presented. The influence of varying the hematocrit, area blockage, stenosis shape, and driving force on flow characteristics, and cell and particle behaviors are considered in the present simulation. Distinct flow characteristics are observed in microvessels, which would not occur in the absence of blood cells. The motion of RBCs causes large time-dependent oscillations in flow rates. The root-mean-square of the oscillations increases as the hematocrit or blockage ratio increases, however, it decreases when the stenosis is elongated in the axial direction with a gentle slope. Interestingly, when a hematocrit level increases, downstream particles move closer to the vessel wall due to the enhanced shear-induced lift force from interaction among RBCs and particles. Also, it is observed that geometrical changes of a stenosis affect the axial profile of particle concentration more severely than changes of the hematocrit or the driving force. An asymmetric stenosis results in asymmetric profiles in flow velocity and distribution of cells and particles caused by a geometric focusing effect of the stenosis.