Model Of Blood Flow In Arteries Research Articles

Mathematical formulation and computation of the dynamics of blood flow, heat and mass transfer during MRI scanning

Computational modeling of arterial blood flow, heat and mass transfer during MRI scanning is studied. The flow is assumed to be unsteady, in-compressible, and asymmetric. Mathematical formulation considers the presence of stenosis, joule heating viscous dissipation and chemical reaction. The explicit finite difference scheme is used to numerically solve the model equations. The MATLAB software was used to plot the graphical results. The study reveals that, during MRI scanning, both radial and axial velocities diminish with increase in the strength of magnetic fields. Besides, the study found that, Eckert number and Hartman number enhance the blood’s temperature and the same, diminishes with increase in Prandtl and Reynolds numbers. Concentration profile is observed to decline with increase in chemical reaction parameter, Schmidt number and Reynolds number. Soret number on the other hand, is observed to positively influence the concentration.

Navigating cardiovascular dynamics through mathematical modeling of arterial blood flow

Blood flow analysis plays an essential role in understanding cardiovascular health and disease. An accurate mathematical modeling is necessary in context of representation of arterial domains and blood flow to learn about the intricate blood dynamics. In this paper we concentrate on the mathematical representation of the geometry of the blood artery and find numerical solutions with mild to severe degree of stenosis. Blood dynamics has steady state, in-compressible and laminar nature. The shear thinning non-viscous effects of blood are assumed to obey Carreau model. Fluid flow is based on coupled Navier-Stokes equation in three dimensions and is simulated with finite volume approach over hexahedral elements. Application of a constant mass flow rate at the inlet of the artery results in a number of observations to analyze. It is found that with increasing the severity of stenosis, blood velocity becomes higher in stenotic region, pressure drop along the arterial domain is increased and shear stresses exerted by blood on walls of artery are increased.

Consequences of blood mediated nano transportation as drug agent to attenuate the atherosclerotic lesions with permeability impacts

This paper is a biomedical theoretical implementation of an arterial blood flow model through the atherosclerotic artery with permeability impacts. The Navier-Stokes equations are used in this analysis as the governing equations for the analysis of blood flow model. Simplified dimensionless model is solved by using appropriate convective and permeability boundary conditions. Propagation of the arterial pressure is discussed through tapering phenomena. To attain effective results flow configurations of hemodynamics are produced. The outcomes obtained in this study are useful in biomedicine literature. At the end, it is achieved from graphical pattern that the use of Ag blood is more suitable to reduce the hemodynamics impacts (i.e. stress on wall and resistance to flow) of the atherosclerotic artery when compared to the case of Ag-Al2O3/blood.

Modelling Blood Pressure in Stenosed Coronary Arteries

In this paper a 1D model is presented for the simulation of blood flow in stenosed coronary arteries. The model was developed by implementing a special boundary counditions in a previously published arterial blood flow model. The stenosis as well as the arterioles were modelled as linear resistances. Using patient-specific parameters, blood flow can be calculated for different inlet flow rates. The model was used to simulate blood pressure waveforms of 5 patients diagnosed with coronary stenosis. Simulation results show good agreement with measurement data.

Abstract TMP103: New Blood Velocity Indices Can Improve the Accuracy of Transcranial Doppler to Detect Vasospasm After Subarachnoid Hemorrhage

Background and Objectives: Early diagnosis of vasospasm after subarachnoid hemorrhage (SAH) can prompt aggressive treatment and improve neurological outcomes. Transcranial Doppler (TCD) is the only diagnosis modality that is noninvasive and available bedside. The purpose of this study was to numerically evaluate the relevance of various blood velocity indices in detection of unbalanced cerebral blood flow due to vasospasm, and to improve the accuracy of diagnosis using TCD. Methods: We employed a well-validated numerical model of arterial blood flow coupled with a sophisticated intracranial model to generate a cerebral blood flow database. Anterior (MCA and/or ACA) and posterior (PCA and/or basilar arteries) vasospasms were considered under normal and impaired cerebral autoregulation conditions. For each case, mean blood velocities and their ratios between ipsilateral and contralateral, downstream and upstream, and anterior and posterior arteries were monitored during the progress of vasospasm. Results: Blood velocities at vasospastic arterial segments demonstrated non-monotonic behavior, i.e. the velocities increased initially with mild and moderate vasospasm, however further vasospasm leads to decreasing values. This may lead to false-negative decisions clinically. Blood flow rates, however, decreased monotonically at the affected arteries. Blood velocities upstream of the vasospastic artery decreased in proportion to the blood flow rates (e.g. for MCA vasospasm, 30% and 20% reduction at ICA and CCA). For all vasospasm locations considered, normalization of velocities by upstream and contralateral velocities provided more robust detection. Moreover, the improvements were most compelling in cases with impaired cerebral autoregulation. Conclusions: The velocity indices and diagnosis strategy proposed in this study can improve the accuracy of TCD diagnosis for cerebral vasospasm. These indices are particularly effective in cases of severe vasospasm where traditional indices (e.g. absolute velocities, Lindegaard index) become problematic.

Numerical reproduction of hemodynamics change by acupuncture on Taichong (LR-3) based on the lumped-parameter approximation model of the systemic arteries

BackgroundThe aim of this study was to develop a mathematical model of blood flow in the systemic circulation to emulate the change in hemodynamics by acupuncture therapy to elucidate the mechanism of the therapy. For this purpose, as a first step, a simple model of arterial blood flow was presented to reproduce previously reported change in the blood flow volume by the acupuncture needle stimulation of Taichong (LR-3). MethodsThis model was based on the lumped-parameter approximation of arterial blood flow together with linear resistance of peripheral circulation. It has been reported that blood flow in the left arm was enhanced after the stimulation, yielding the peripheral vascular resistance-regulated blood flow dominated by the sympathetic nervous system. In addition to the peripheral resistance, another parameter that possibly regulates the blood flow is the cross-sectional area of the vessel. These two factors were changed to numerically examine their contributions to the blood flow based on the hypothesis that they could be changed by the stimulation. The numerical result was compared with the experimental result to confirm the validity of the hypothesis that the blood flow in the arm is regulated by the peripheral resistance. ResultsThis model is extremely simple and the physical parameters introduced for the simulation were gleaned from different reports in the literature. It was demonstrated, however, that regulation of the peripheral resistance rather than of the cross-sectional area could reproduce the experimentally observed change in the blood flow. Moreover, the relationship between the changes in the flow volume and the systemic vascular resistance quantitatively matched the experimental data. ConclusionThe present model has a potential to emulate hemodynamic change by acupuncture therapy by incorporating physiological correlation of stimulation of an acupoint and regulation of parameters that affect the hemodynamics.

Numerical Analysis of One-dimensional Mathematical Model of Blood Flow to Reproduce Fundamental Pulse Wave Measurement for Scientific Verification of Pulse Diagnosis

Pulse diagnosis in traditional Chinese medicine is said to be able to detect not only illness but also decline of health in the patients from tactile sense of the pulse in the radial artery at the wrists. This diagnosis, however, is not supported by concrete scientific evidence. The authors have proposed a non-linear spring model of subcutaneous tissue on the radial artery and one-dimensional arterial blood flow model in an arm for the purpose of scientific verification of the pulse diagnosis. They performed, in the former study, a numerical experiment with this mathematical model in which the radial artery was indented in a stepwise manner by a pressure sensor, which extract the fundamental mechanism of the pulse diagnosis, to validate the subcutaneous tissue model and to find the appropriate coefficient to fit the experimental result. They investigated, in this research, contribution of parameters of supply pressure of the blood and tube law of the artery on the change in the pressure pulse waves with the indentation steps with respect to mean value Poav and amplitude ΔPo of the pressure. It was shown that mean supply pressure affects both Poav and ΔPo, while amplitude of the supply pressure affects ΔPo. It was also shown that profile of ΔPo vs. distance of the indentation changes drastically as the artery becomes hard. Lastly, it was examined to reproduce the experimentally obtained pressure pulse waves during the indentation in their former work with the mathematical model by adjusting the parameters. The result showed better agreement than the former result, but it implied that ulnar artery had to be taken into consideration for quantitative fitting of the pulse waves to the range where the radial artery was nearly flattened by the indentation.

A 1D arterial blood flow model incorporating ventricular pressure, aortic valve and regional coronary flow using the locally conservative Galerkin (LCG) method

AbstractThere is an important interaction between the pumping performance of the ventricle, arterial haemodynamics and coronary blood flow. While previous non‐linear 1D models have focused only on one of these components, the model presented in this study includes coronary and systemic arterial circulations, as well as ventricular pressure and an aortic valve that opens and closes ‘independently’ and based on local haemodynamics. The systemic circulation is modelled as a branching network of elastic tapering vessels. The terminal element applied at the extremities of the network is a single tapering vessel which is shown to adequately represent the input characteristics of the downstream vasculature. The coronary model consists of left and right coronary arteries which both branch into two ‘equivalent’ vessels that account for the lumped characteristics of subendocardial and subepicardial flows. As contracting heart muscle causes significant compression of the subendocardial vessels, a time‐varying external pressure proportional to ventricular pressure is applied to the distal part of the equivalent subendocardial vessel. The aortic valve is modelled using a variable reflection coefficient with respect to backward‐running aortic waves, and a variable transmission coefficient with respect to forward‐running ventricular waves. A realistic ventricular pressure is the input to the system; however, an afterload‐corrected ventricular pressure is calculated and results in pressure gradients between the ventricle and aorta that are similar to those observed in vivo. The 1D equations of fluid flow are solved using the locally conservative Galerkin method, which provides explicit element‐wise conservation, and can naturally incorporate vessel branching. Each component of the model is verified using a number of tests to ensure accuracy and reveal the underlying processes that give rise to complex pressure and flow waveforms. The complete model is then implemented, and simulations are performed with input parameters representing ‘at rest’ and exercise states for a normal adult. The resulting waveforms contain all of the important features seen in vivo, and standard measures of haemodynamic state are found to be normal. In addition, one or several characteristics of some common diseases are imposed on the model and are found to produce haemodynamic changes that agree with experimental observations in the published literature. Using a patient‐specific carotid bifurcation geometry, 1D velocity waveforms are also compared with waveforms obtained from a three‐dimensional model. The 1D and 3D results show good agreement. Copyright © 2008 John Wiley & Sons, Ltd.

Blood Flow in Major Blood Vessels—Modeling and Experiments

Although primarily motivated by an interest in atherosclerosis, modeling of arterial blood flow is also important to an understanding of congenital effects and to improvements in therapeutics. A variety of methods are available to estimate the flow field in living arteries, each with its own advantages and limitations. Tradeoffs must be made among the realism of the technique, spatial resolution, geometric fidelity, and the reliability of assumed wall mechanical properties. Once the velocity field is obtained, each differentiation, to obtain wall shear or its spatial or temporal derivatives, adds additional uncertainty into the results, demanding cautious interpretation. A distinction is made between "macro" and "micro" levels of flow structure detail: macro level structure is relatively coarse and more descriptive of the flow field, pressure, and shear distribution than the cellular response; the micro approach tries to relate a more local hemodynamic description to vascular pathology. The applications of each, and the interactions between them, are described. Issues related to these approaches, including the use of clinical data, animal experimentation, the role of cell and organ culture, and in vivo flow measurement, are briefly discussed. The summary closes with a list of recommendations for future developments in this area.

Mathematical modeling of arterial blood flow and correlation to atherosclerosis

The importance of arterial flow phenomena with regard to atherosclerosis motivates detailed studies of local cardiovascular flow dynamics. The quantitative analysis of flow characteristics can contribute to the understanding of fluid dynamic induced and favored mechanisms in atherogenesis. Numerical methods are very useful in supporting experimental methods and often enable the determination of flow variables which are difficult to obtain in experiments. Due to the development of improved numerical procedures for the blood specific flow equations and due to the application of modern computer technology, the calculations can be carried out under conditions describing the physiological situation in a realistic manner including essential effects. Here various aspects of arterial flow simulation are presented and discussed. The possibilities and difficulties of numerical simulation of arterial flow using finite element approximations are illustrated with the aid of the human carotid artery bifurcation and a distal end-to-side anastomosis model. Further convective-diffusive mass transport in a curved tube model is considered.

A finite-element model of blood flow in arteries including taper, branches, and obstructions.

A nonlinear mathematical model of arterial blood flow, which can account for tapering, branching, and the presence of stenosed segments, is presented. With the finite-element method, the model equations are transformed into a system of algebraic equations that can be solved on a high-speed digital computer to yield values of pressure and volume rate of flow as functions of time and arterial position. A model of the human femoral artery is used to compare the effects of linear and nonlinear modeling. During periods of rapid alternations in pressure or flow, the nonlinear model shows significantly different results than the linear model. The effect of a stenosis on pressure and flow waveforms is also simulated, and the results indicate that these waveforms are significantly altered by moderate and severe stenoses.

Energy dissipation in mammalian arteries—An assessment of the distribution of energy dissipation between the blood and the vessel wall

The non-linear, one-dimensional numberical model of arterial blood flow has been used to examine the distribution of energy dissipation between viscous shear in the blood and viscous damping in the vessel wall. Neglecting additional losses due to taper and oscillatory flow, the energy dissipated in the wall was ca. 1 8 , for the femoral artery and 1 15 , for the upper thoracic aorta, of that dissipated by the blood. When the taper and oscillatory flow effects were included for the femoral artery, the energy dissipated by the blood was approximately doubled and the ratio of wall to blood dissipation halved, to 1 16 .

Prediction Of Human Arterial Pulse Wave ShapeChanges In Aging And Hypertension

A folly nonlinear model of arterial blood flow and pressure pulse propagation which can account for tapering, branching, variable thickness and nonlinear elastic properties of the arterial wall is presented. The model can accommodate different elastic modulus for Collagen and Elastin fibbers, with a recruitment function for the former. One dimensional momentum and continuity equations coupled with a pressure-area relationship yields a system of nonlinear hyperbolic partial differential equations. The system is reduced to the canonic form and solved by a Hartree like Finite Difference Method over the characteristics. A complete model of the human arterial system is implemented, giving geometrical and physical data for the major vessels and, appropriate inlet and outlet boundary conditions, using a windkessel approximation for peripheral vascular resistance and compliance. An experiment of vasodilatation and vasoconstriction is simulated, exhibiting features of the natural pulses along the arm's arteries and comparison is made with clinical data reported in the literature . Resulting pressure and diameter waves, show similar changes to those that occurs in aging and moderate hypertension.

A generalized approach to the modeling of arterial blood flow.

Arterial blood flow may be described as the almost periodic, unsteady-state flow of a non-Newtonian fluid through a flexible-walled, tapered, branching conduit. A generalized approach to the development of a realistic mathematical model is described. All assumptions involved in the analysis are evaluated critically in terms of their quantitative effect on the validity of the model. As a result some of the traditional assumptions are avoided. A numerical integration routine for obtaining solutions to the resulting nonlinear partial differential equations comprising the model is outlined. The possible application of the model to compute localized arterial wall elasticity is discussed. Successful implementation of this procedure could lead to a significant clinical diagnostic tool for vascular disease.

Wave Propagation through a Newtonian Fluid Contained within a Thick-Walled, Viscoelastic Tube

The propagation of harmonic pressure waves through a Newtonian fluid contained within a thick-walled, viscoelastic tube is considered as a model of arterial blood flow. The fluid is assumed to be homogeneous and Newtonian, and its motion to be laminar and axisymmetric. The wall is assumed to be isotropic, incompressible, linear, and viscoelastic. It is also assumed that the motion is such that the convective acceleration is negligible. The motion of the fluid is described by the linearized form of the Navier-Stokes equations and the motion of the wall by classical elasticity theory. The frequency dependence of the wall mechanical properties are represented by a three parameter, relaxation-type model. Using boundary conditions describing the continuity of stress and velocity components in the fluid and the wall, explicit solutions for the system of equations of the model have been obtained. The longitudinal fluid impedance has been expressed in terms of frequency and the system parameters. The frequency equation has been solved and the propagation constant also expressed in terms of frequency and system parameters. The results indicate that the fluid impedance is smaller than predicted by the rigid tube model or by Womersley's constrained elastic tube model. Also, the velocity of propagation is generally slower and the transmission per wavelength less than predicted by Womersley's elastic tube model. The propagation constant is very sensitive to changes in the degree of wall viscoelasticity.