Hemodynamics: Macroscopic and Microscopic Modeling (original) (raw)

Mathematical Models for Some Aspects of Blood Microcirculation

Symmetry

Blood rheology is a challenging subject owing to the fact that blood is a mixture of a fluid (plasma) and of cells, among which red blood cells make about 50% of the total volume. It is precisely this circumstance that originates the peculiar behavior of blood flow in small vessels (i.e., roughly speaking, vessel with a diameter less than half a millimeter). In this class we find arterioles, venules, and capillaries. The phenomena taking place in microcirculation are very important in supporting life. Everybody knows the importance of blood filtration in kidneys, but other phenomena, of not less importance, are known only to a small class of physicians. Overviewing such subjects reveals the fascinating complexity of microcirculation.

Microcirculatory model relating geometrical variation to changes in pressure and flow rate

Annals of Biomedical Engineering, 1981

A primary first step in defining the functional capabilities of a given microcirculatory bed is to describe the distribution of intravascular pressure and flow throughout the network using an idealized geometrical model By applying an approach developed by the geomorphological sciences, changes in vessel lengths, numbers, and diameters were systematically related to order number by applying three mathematical relationships. From measurements of a number of vascular modules, generalized relationships were obtained which applied to the microcirculation as a whole. An idealized model was developed by the computergeneration of node-node connections based on their probabilities of occurrence, and by generation of lengths and diameters, based on equations relating diameter and length to branching order number. Networks of this type were readily analyzable in terms of pressure-flow characteristics, using linear network analysis techniques. The current study focused on two specific microvascular beds:

A review on the requirements of modelling of blood flow

2015 2nd International Conference on Biomedical Engineering (ICoBE), 2015

The critical issue to model blood flow in mesoscale or microscale is impossible to consider all blood constituents. First, we clarify blood flow which consisting of different constituents. Platelets are the most influential constituent to affect thrombosis process after comparison of all blood constituents. Consequently, critical issue can be solved by selecting platelets as the only constituent to model in mesoscale or microscale. Some numerical techniques to solve blood flow modelling in biomechanics are reviewed. In conclusion, the review shows that multiscale modelling of blood flow is required because combining the advantages of macroscale-mesoscale enable sufficient computational efficiency with high accuracy. Therefore, multiscale modelling of platelets is highly recommended.

Two-phase blood-flow model

In blood flows in small vessels (smaller than 200 µm in diameter), the rheological properties of blood depend on the vessel diameter. In small vessels, it is necessary to take into account near-wall effects and aggregation of erythrocytes. Such flows are described by discrete-continuum or two-layer models of the flow. In this paper, a unified two-phase model of blood is proposed, which can describe the blood flow in both large and small blood vessels. The model describes the integral characteristics of the flow, such as the hematocrit (packed cell volume), viscosity, and velocity of blood. Based on this model, the well-known specific features (effects) of the blood flow in blood vessesl are explained: hematocrit dependence on the vessel diameter, existence of a cell-free (erythrocyte-free) layer of the plasma near the vessel wall, obtuse profile of the blood velocity (as compared to the Poiseuille flow profile), and dependence of the blood viscosity on the vessel diameter. Analytica...

Methods of Blood Flow Modelling

Mathematical Modelling of Natural Phenomena, 2015

This review is devoted to recent developments in blood flow modelling. It begins with the discussion of blood rheology and its non-Newtonian properties. After that we will present some modelling methods where blood is considered as a heterogeneous fluid composed of plasma and blood cells. Namely, we will describe the method of Dissipative Particle Dynamics and will present some results of blood flow modelling. The last part of this paper deals with onedimensional global models of blood circulation. We will explain the main ideas of this approach and will present some examples of its application.

A Simple Model for the Arterial System

Journal of Theoretical Biology, 2003

We present a simple model for the arterial part of the cardiovascular system, based on Poiseuille flow constrained by the power dissipated into the cells lining the vessels. This, together with the assumption of a volume-filling network, leads to correct predictions for the evolution of vessel radii, vessel lengths and blood pressure in the human arterial system. The model can also be used to find exponents for allometric scaling, and gives good agreement with data on mammals.

Blood pressure distribution in microvascular networks

2014

Abstract: Blood rheology is complex and nonlinear. The effective viscosity variations are important due to red blood cells packing inside capillaries, the socalled FåhræusLindquist effect, whilst concomitantly phase segregation appears in bifurcations. We have performed direct numerical simulations of different nonlinear rheological models of the blood on realistic threedimensional microvascular networks. These simulations point out two significant results. First, various rheological models lead to very similar pressure distributions over the whole range of physiologically relevant hematocrits. Secondly, different models for phase segregation lead to very distinct hematocrit distributions in the microvascular network. Moreover, for all the investigated rheological models, the hematocrit distribution very weakly affects the pressure distribution, when prescribing uniform pressure boundary conditions.

Blood flow in microvascular networks. Experiments and simulation

Circulation Research, 1990

A theoretical model has been developed to simulate blood flow through large microcirculatory networks. The model takes into account the dependence of apparent viscosity of blood on vessel diameter and hematocrit (the Fahraeus-Lindqvist effect), the reduction of intravascular hematocrit relative to the inflow hematocrit of a vessel (the Fahraeus effect), and the disproportionate distribution of red blood cells and plasma at arteriolar bifurcations (phase separation). The model was used to simulate flow in three microvascular networks in the rat mesentery with 436,583, and 913 vessel segments, respectively, using experimental data (length, diameter, and topological organization) obtained from the same networks. Measurements of hematocrit and flow direction in all vessel segments of these networks tested the validity of model results. These tests demonstrate that the prediction of parameters for individual vessel segments in large networks exhibits a high degree of uncertainty; for exa...