Mathematical Model Of Blood Flow Research Articles

Fluid Flow and Solute Transfer in a Permeable Tube with Influence of Slip Velocity

In this paper, the influence of slip velocity on the fluid flow and solute transfer in a tube with permeable boundary is studied as a mathematical model for blood flow in glomerular capillaries. The viscous incompressible fluid flow across the permeable tube wall, as a result of differences in both hydrostatic and osmotic pressure, is considered. The solutions of differential equations governing the fluid flow and solute transfer are obtained using analytical and Crank-Nicolson type numerical methods. It is observed that the effect of slip on the hydrostatic and osmotic pressures, velocity profiles, concentration profile, solute mass flux and total solute clearance is significant and the results are presented graphically.

The Effect of Stenotic Geometry and Non-newtonian Property of Blood Flow through Arterial Stenosis.

A mathematical model of blood flow is a way to study the blood flow behavior. In this research work, a mathematical model of non-Newtonian blood flow through different stenosis, namely bell shape and cosine shape, is considered. The physiologically important flow quantities of blood flow behavior to describe the blood flow phenomena are obtained such as resistance to flow, skin friction and blood flow rate. Mathematical methods are used to analyze a mathematical model of blood flow through stenosed artery. The resistance to flow, skin friction and blood flow rate were obtained to describe the blood flow in stenosis. The resistance to flow is a relation between pressure and blood flow rate while the skin friction is the friction at the artery membrane. Resutls: The blood flow in cosine geometry exhibits higher resistance to flow and flow rate than in the bell geometry, while the blood flow in bell geometry gives a higher skin friction than in cosine geometry. Not only the effect of stenotic geometry was studied but also the effect of stenosis depth and stenosis height on the flow quantities Moreover, the power law index was adjusted to explore the non-Newtonian behavior. When blood exhibits Newtonian behavior, the resistance to flow and skin friction decrease but the blood flow rate increases. The stenosed artery geometry, the stenosis length, stenosis depth and the power law index (non-Newtonian behavior) are important factors affecting the blood flow through the stenosed artery. This work provides some potential aspects to further study the causes and development of cardiovascular diseases.

A mathematical model of blood flow in a permeable channel: application to flat plate dialyzer

This article presents the theoretical study of the physiological phenomenon brought up by filtration of a non-Newtonian Casson fluid between two parallel permeable membranes. This situation corresponds to blood filtration process in a flat plate hemodialyzer (FPH). Seepage of fluid across the membrane is considered in accordance with the Darcy’s law and the equations of motion governing the flow are modeled. Using the low Reynolds number and long membrane length assumption, equations of motion are solved exactly. Equations describing velocity and pressure filed and various flow variables are derived and effects of wall slip parameter, wall filtration coefficient and the yield stress are presented graphically. A strong influence of these parameters is observed on the flow in an FPH. Theoretical values of the membrane filtration coefficient and mean pressure drop in an FPH are calculated and they are found to be in close agreement with the corresponding available empirical and experimental values in the literature. For certain limiting range of physical parameters, derived solutions reveal that the axial flow rate of Casson fluid in an FPH decays at an exponential rate. This is a physically valid and widely admitted result, used by several researchers in studying the blood filtration process in renal tubules of mammalian kidneys. Since the presented solutions in this article are reduced to their corresponding Newtonian fluid flow solutions between permeable membrane, therefore, it is concluded that a wide range of applications in physiology and engineering can be covered up by the present investigation.

A Mathematical Model of Blood Flow in a Catheterized artery with multiple stenoses

A mathematical model is developed in this investigation for studying the axi-symmetric flow of blood through a catheterized artery with multiple stenoses. Consideration of Newtonian character of blood is described following the report of Young (1968) and Srivastava (2009) with the appropriate constitutive equation governing the flow. The boundary conditions appropriate to the problem under study are the standard no slip conditions at the artery and the catheter wall. Analytical expressions for impedance (flow resistance), the wall stress distribution in the stenotic region and the shear stress at the stenosis throat in their non dimensional form are derived by using the model. The derived expressions are computed numerically and the results are presented graphically for different values of the rheological and other parameters. The study provides an insight into the effects of catheter radius and stenosis height on impedance, wall stress distribution in the stenotic region and the shear stress at the stenotic throat.

Mathematical model for blood flow through the stenosed channel

In this paper, we investigate the blood flow through a stenoised channel. In current study Cartesian coordinates are contemplated for flow in the channel and in an axisymmetric tube with transfer of heat having cosine shape stenosis. Blood is supposed as Eyring–Powell fluid which is independent of time. Thermal conductivity is determined by temperature. After assimilating these deliberations, dimensional equations are transformed into non-dimensional system of differential equations with the use of similarity transformations and are then solved numerically. A parametric study is executed to depict the impact of various parameters on the velocity and temperature fields of fluid. Heat transfer coefficient and skin friction are also explained through graphs and discussed in tabular form for distinct values of dimensionless parameters. The current investigation tells that velocity field significantly increases by rising the value of M and δ. Temperature field increases for extended value of δ, M, K, B, A and Pr. Nusselt number curve increases due to increase in Pr.

Abstract 146: Glomerular Capillary Hypertrophy is Insufficient to Mitigate Mechanical Stresses in 5/6 Nephrectomy: A Modeling Study

The 5/6-nephrectomy (5/6 Nx) model of renal mass reduction shows an increased glomerular pressure (ΔP) and afferent plasma flow (Q a ) in the remaining glomeruli. These hemodynamic consequences are assumed to increase glomerular capillary wall circumferential hoop stress (HS) and shear stress (SS), respectively. Due to a lack of anatomically-accurate mathematical models of the glomerulus, the actual magnitudes of SS and HS in the entire network of glomerular capillaries remain uncertain in 5/6-Nx. These forces are of significance due to the sensitivity of endothelial cells to SS and podocytes to HS. We developed a mathematical model of blood flow through an anatomically-accurate rat glomerular capillary network to estimate the magnitudes of SS and HS on the glomerular capillary walls in 5/6-Nx. Filtration rates, wall HS and wall SS were calculated for each capillary segment of the network based on parameters obtained from a micropuncture study using normal rats and rats with 5/6-Nx (Kasiske, Bertram L., et al. Circ. Res. 62.2: 367-374. (1988)). In this study, 5/6-Nx increased Q a and ΔP by 174.8% and 19.0%, respectively. To simulate glomerular capillary hypertrophy in 5/6-Nx, the capillary diameters were all increased by 16.1%. Using these data, the Young-Laplace equation was used to calculate HS in each capillary, and SS was calculated assuming Poiseuille flow with blood viscosity scaled based on vessel diameter and hematocrit. Taking into account an increase in diameter of the glomerular capillaries, the model predicted mean SS values of 48.1 dynes/cm 2 in control and 79.4 dynes/cm 2 in 5/6-Nx. The increase in diameter of the glomerular capillaries was not sufficient to prevent the increase in SS, a finding in contrast to the previous experimental analysis which suggested normalization of SS. The increase in glomerular capillary diameter increased mean HS from 144.1 kPa to 199.2 kPa. This study demonstrates that this increase in diameter was not sufficient to mitigate the increased SS in 5/6-Nx and contributes to a significantly increased HS. These increased mechanical stresses on the glomerular capillaries may play a causative role in the progression of glomerular injury in 5/6-Nx thus leading to chronic kidney failure.

A four-layered model for flow of non-Newtonian fluid in an artery with mild stenosis

The present article deals with a four-layered mathematical model for blood flow through an artery with mild stenosis. The four-layered model comprises a cell-rich core of suspension of all the erythrocytes described as a non-Newtonian (Jeffrey) fluid, a peripheral zone of cell-free plasma (Newtonian fluid) and the stenosed artery with porous wall consisting of a thin transition (Brinkman) layer followed by Darcy region. Analytical expressions have been obtained for velocity profiles in all the four regions, total volumetric flow rate, wall shear stress and flow impedance. MATLAB software is employed to compute numerical values of the pressure gradient. The influences of different parameters such as variable core fluid viscosity, hematocrit, thickness of the plasma layer, Brinkman and Darcy layer thickness, Darcy number, Jeffrey fluid parameter, and size and shape parameters of stenosis on the physiologically vital flow characteristics, specifically velocity profile, volume flow rate, wall shear stress and flow impedance, have been examined. It is observed that the wall shear stress and resistive impedance decrease with the increase of plasma layer thickness, Jeffrey fluid parameter, Darcy number and Darcy slip parameter, and increase with the rise of hematocrit. The results in the case of variable core viscosity and constant core viscosity are compared to investigate the impact of variable core viscosity in managing the flow of blood.

Glomerular Capillary Hypertrophy in the Diabetic Rat Normalizes Wall Shear Stress: A Modeling Study

Diabetes mellitus (DM) reduces renal hemodynamic autoregulation, leading to increased glomerular pressure (ΔP) and afferent plasma flow (Qa) which is assumed to increase glomerular capillary wall shear stress (SS). However, glomerular capillaries undergo hypertrophy in DM, causing an increase in capillary diameter that would theoretically reduce capillary wall SS (Seyer‐Hansen, Kjartan. Kid. Int. 23.4 (1983): 643–646.). The actual magnitudes of SS in the glomerular capillaries have not been estimated in DM and are of significance because in response to increased SS, endothelial cells increase expression of adhesion molecules and growth factors associated with glomerulopathy.We developed a mathematical model of blood flow through an anatomically‐accurate rat glomerular capillary network to estimate the magnitudes of SS on the glomerular capillary walls in DM and control. Individual filtration rates and wall SS were calculated for each capillary segment of the network based on values of Qa, ΔP and single nephron GFR (SNGFR) obtained from micropuncture studies. To validate mechanical predictions of our model, we compared our calculated SS magnitudes to results from intravital imaging studies of blood flow in rat glomeruli (Ferrell, Nicholas, et al. Am. J. Physiology‐Renal 308.6 (2015): F588‐F593.). To calculate SS magnitudes in the rat glomerulus in control and DM, we performed simulations with parameters obtained from micropuncture studies using normal rats and rats with streptozotocin induced Type I diabetes. In this study, DM increased Qa and ΔP by 74.6% and 33.3%, respectively but reduced the filtration coefficient (Kf) such that filtration fraction (FF) was maintained (Zatz, Roberto, et al. J. clin. Inv. 77.6 (1986): 1925–1930).The model was calibrated using an algorithm previously described (Remuzzi, Andrea, et al. Am. J. Physiology‐Renal 263.3 (1992): F562‐F572). Our model's calculated mean glomerular capillary wall SS was within 10% of the mean SS predicted using intravital imaging, validating our model for use in predicting mechanical aspects of blood flow in the glomerulus. Our simulations demonstrated a wide variance in SS throughout the glomerular capillary network, consistent with previous modeling results. Using parameters from micropuncture experiments and taking into account hypertrophy of the glomerular capillaries, the model predicted mean SS values of 42.1 dynes/cm2 in control and 42.3 dynes/cm2 in DM.We have developed and validated an anatomically‐accurate mathematical model of glomerular filtration for use in predicting functional and mechanical results of varied glomerular pressure, afferent plasma flow and Kf. Using this model, we demonstrated that hypertrophy of the capillaries normalizes capillary wall SS in DM, which may be a protective mechanism limiting the increase in SS and the consequent glomerular injury.Support or Funding InformationThis work was supported by the National Institute of General Medical Sciences IDeA Program (CoBRE P30GM103337) (principal investigator: L. G. Navar) O. Richfield is a graduate student supported by NSF IGERT Grant NSF DGE‐1144646.This abstract is from the Experimental Biology 2019 Meeting. There is no full text article associated with this abstract published in The FASEB Journal.

Computer modeling in mechanics of circulation

Some cardiovascular pathology connected with variations in geometry, wall properties and microcirculatory disorders can be studied by computer simulations. The mathematical model that allows to calculate the parameters of blood circulation – velocities of blood and pressure, displacements of the artery walls - for a complex vascular tree in real time is proposed.The geometrical model is based on the detailed postmortem measurements on the systemic arterial trees (more than 1000 arterial segments). The aortic model consists of 32 aortic segments and 59 side branches of the aorta including the larger and medium vessels. Mathematical model of blood flow in the system is described by Womersley model of the pulsatile viscous flow in the viscoelastic tube using the pressure and volumetric rate continuity conditions at the bifurcations of arteries. The Windkessel and structured tree outflow boundary conditions at the outlets of the branches have been used. The solution has been found as superposition of the forward and backward running waves. Based on the model, blood circulation parameters were calculated in the aortic model (91 tubes). The calculation results correspond to in vivo measurements. It was shown most of the branches have zero wave reflection coefficients but the large branches like celiac, renal and iliac arteries could produce noticeable wave reflections. The smaller branches possess negative wave reflection coefficient and, thus, contribute to the blood suction effect and lower aortic resistance to the blood flow. It is shown, the individual geometry plays an essential role in the location of the positive and negative wave reflection sites along the aorta and, thus, in the pressure and flow patterns and blood distribution into the branches. The influence of occlusion of the iliac arteries, low/high wall rigidity, and total length of aorta are studied on different individual geometries. The model can be used for determination of the individual parameters for patient-specific cardiovascular models and further modeling of the outcomes of the surgical and therapeutic procedures.

Современные методы математического моделирования кровотока c помощью осредненных моделей

Изучение физиологических и патофизиологических процессов, связанных с системой кровообращения, является на сегодняшний день актуальной темой многих исследований. В данной работе рассматривается ряд подходов к математическому моделированию кровотока, основанных на пространственном осреднении и/или использующих стационарное приближение. Обсуждаются допущения и предположения, ограничивающие область применения моделей такого рода. Приводятся наиболее распространенные математические постановки задач и кратко описываются методы их численного решения. В первой части обсуждаются модели, основанные на полном пространственном осреднении и/или использующие стационарное приближение. Один из наиболее распространенных на сегодняшний день подходов состоит в проведении аналогий между течением вязкой несжимаемой жидкости в эластичных трубках и электрическим током в цепи. Такие модели используются не только сами по себе, но и как способ постановки граничных условий в моделях, учитывающих одномерную или трехмерную пространственную зависимость переменных. Динамические, полностью осредненные по пространству модели позволяют описывать динамику кровотока на достаточно больших временных интервалах, равных длительности десятков сердечных циклов и более. Далее рассмотрены стационарные модели основанные как на полностью осредненном, так и на двухмерном подходе. Такие модели могут быть использованы для моделирования кровотока в микроциркуляторном русле. Во второй части обсуждаются модели, основанные на одномерном осреднении параметров кровотока. Преимущество данного подхода также состоит в невысоких, по сравнению с трехмерным моделированием, требованиях к вычислительным ресурсам и возможности охвата всех достаточно крупных кровеносных сосудов в организме. Модели данного типа позволяют рассчитывать параметры кровотока в каждом сосуде сосудистой сети, включенной в модель. Структура и параметры такой сети могут быть заданы как на основе данных литературы, так и с помощью методов сегментации медицинских данных. Основными и весьма существенными предположениями при выводе одномерных уравнений из уравнений Навье – Стокса с помощью асимптотического анализа или их интегрирования по объему являются радиальная симметрия течения и постоянство формы профиля скорости в поперечном сечении. Существующие в настоящее время работы, посвященные валидации одномерных моделей, их сравнению между собой и с данными клинических исследований, позволяют говорить об успешности данного подхода и подтверждают возможность его использования в медицинской практике. Одномерные модели позволяют описывать такие динамические явления, как распространение пульсовой волны и звуки Короткова. В этом приближении могут быть учтены такие факторы, как действие на кровоток силы тяжести, действие на стенки сосудов силы сжатия мышц, регуляторные и ауторегуляторные эффекты.

A Mathematical Model of Blood Flow in Narrow Blood Vessels in Presence of Magnetic Field

This paper discuss the biomagnetic fluid aspect of blood flow through narrow tubes with mild stenosis. The blood flow in narrow arteries is treated as two-fluid model with non-Newtonian Jeffrey fluid in the core region and in peripheral region as Newtonian fluid. An analytical solution is obtained for the velocity, volume flow rate, and wall shear stress. The effect of Hartmann number, Jeffrey fluid parameter, shape and size of the stenosis on the velocity, volume flow rate and wall shear stress is discussed.

EFFECT OF COUPLE STRESSES ON ELECTROKINETIC OSCILLATORY FLOW OF BLOOD IN THE MICROCIRCULATORY SYSTEM

Of concern in the paper is the development of a mathematical model of blood flow in the microcirculatory system. The study pertains to a situation, where the system is subject to the action of an external AC electric field and the flow is oscillatory. The general case when the frequency of the electric field is different from that of the flow has been studied. Blood is treated as a couple stress fluid. The flow is supposed to take place between two oscillatory plates and is considered to be of electro-osmotic type. Our study is aimed at examining the effect of couple stress at different frequencies of the capillary wall and the applied AC electric field on electroosmotic flow of blood. The computational results indicate very clearly that the electrokinetic velocity of blood reduces as the couple stress effect increases and that the velocity reduces, when the Reynolds number rises. The results of the present study will serve as a reasonably good estimate for electro-osmotic transport of blood in small blood vessels.

Insights into cerebral haemodynamics and oxygenation utilising in vivo mural cell imaging and mathematical modelling

The neurovascular mechanisms underpinning the local regulation of cerebral blood flow (CBF) and oxygen transport remain elusive. In this study we have combined novel in vivo imaging of cortical microvascular and mural cell architecture with mathematical modelling of blood flow and oxygen transport, to provide new insights into CBF regulation that would be inaccessible in a conventional experimental context. Our study indicates that vasoconstriction of smooth muscle actin-covered vessels, rather than pericyte-covered capillaries, induces stable reductions in downstream intravascular capillary and tissue oxygenation. We also propose that seemingly paradoxical observations in the literature around reduced blood velocity in response to arteriolar constrictions might be caused by a propagation of constrictions to upstream penetrating arterioles. We provide support for pericytes acting as signalling conduits for upstream smooth muscle activation, and erythrocyte deformation as a complementary regulatory mechanism. Finally, we caution against the use of blood velocity as a proxy measurement for flow. Our combined imaging-modelling platform complements conventional experimentation allowing cerebrovascular physiology to be probed in unprecedented detail.

Subject-specific pulse wave propagation modeling: Towards enhancement of cardiovascular assessment methods.

Cardiovascular diseases are the leading cause of death worldwide. Pulse wave analysis (PWA) technique, which reconstructs and analyses aortic pressure waveform based on non-invasive peripheral pressure recording, became an important bioassay for cardiovascular assessment in a general population. The aim of our study was to establish a pulse wave propagation modeling framework capable of matching clinical PWA data from healthy individuals on a per-subject basis. Radial pressure profiles from 20 healthy individuals (10 males, 10 females), with mean age of 42 ± 10 years, were recorded using applanation tonometry (SphygmoCor, AtCor Medical, Australia) and used to estimate subject-specific parameters of mathematical model of blood flow in the system of fifty-five arteries. The model was able to describe recorded pressure profiles with high accuracy (mean absolute percentage error of 1.87 ± 0.75%) when estimating only 6 parameters for each subject. Cardiac output (CO) and stroke volume (SV) have been correctly identified by the model as lower in females than males (CO of 3.57 ± 0.54 vs. 4.18 ± 0.72 L/min with p-value < 0.05; SV of 49.5 ± 10.1 vs. 64.2 ± 16.8 ml with p-value = 0.076). Moreover, the model identified age related changes in the heart function, i.e. that the cardiac output at rest is maintained with age (r = 0.23; p-value = 0.32) despite the decreasing heart rate (r = −0.49; p-value < 0.05), because of the increase in stroke volume (r = 0.46; p-value < 0.05). Central PWA indices derived from recorded waveforms strongly correlated with those obtained using corresponding model-predicted radial waves (r > 0.99 and r > 0.97 for systolic (SP) and diastolic (DP) pressures, respectively; r > 0.77 for augmentation index (AI); all p—values < 0.01). Model-predicted central waveforms, however, had higher SP than those reconstructed by PWA using recorded radial waves (5.6 ± 3.3 mmHg on average). From all estimated subject-specific parameters only the time to the peak of heart ejection profile correlated with clinically measured AI. Our study suggests that the proposed model may serve as a tool to computationally investigate virtual patient scenarios mimicking different cardiovascular abnormalities. Such a framework can augment our understanding and help with the interpretation of PWA results.

About computer modeling of blood flow in the arteries of the legs

Used in medical practice, schemes of assessment of the arterial bed and prediction of treatment outcomes is ambiguous in its objectivity. Development of new methods for assessment of the arterial bed, of predicting the course of atherosclerosis of the arteries of the lower extremities, to select the optimal method of revascularisation of the arterial bed of the legs is a topical task of science and practice. On the basis of parameters obtained from the analysis of data, an instrumental examination of 10 employees (computer tomography, ultrasonic research of vessels of lower extremities) created a mathematical model of blood flow in the arteries of the legs at different localizations of their occlusive-stenotic lesions. The degree of stenotic changes are standardized: 20 %, 50 % and 75 %, occlusion of the artery. Changes in blood flow that occur with isolated and combined lesions of the arteries were estimated. It was demonstrated that the speed of blood flow in the stenosis of arteries of legs is increased; narrowing of the arteries lower leg > 65 % significantly reduces blood flow, and stenosis of vessels >75 % blood flow practically ceases; when combined occlusive-stenotic lesions of several arteries significant disruption of blood flow is observed with stenosis > 50 %. Occlusive-stenotic lesions not only affects the blood flow in the arteries, but also affects the hemodynamics in other vessels of the lower extremities. Modeling disorders of blood vessels in the feet can be an effective technology for the examination and treatment of patients with failure of blood supply of the lower extremities.

Modelling of Newtonian blood flow through a bifurcated artery with the presence of an overlapping stenosis

Mathematical modelling of blood flow is developed by treating the blood as a Newtonian fluid. In this study, stenosis has been accounted as an overlapping shaped in two-dimensional Cartesian coordinate system. Blood are assumed as steady laminar flow, fully developed and incompressible which flowing through an arterial bifurcation where the wall considered rigid with no-slip condition. Galerkin weighted residual method is performed and a Matlab code is developed to solve the problem. To validate the code, comparison has been made with the results obtained by COMSOL Multiphysics. Results on the velocity profiles and the streamlines pattern are observed and discussed in details.

Analysis of blood flow with nanoparticles induced by uniform magnetic field through a circular cylinder with fractional Caputo derivatives

The magneto hydrodynamic blood flow in the presence of magnetic particles through a circular cylinder is investigated. To calculate the impact of externally applied uniform magnetic field, the blood is electrically charged. Initially the fluid and circular cylinder is at rest but at time t=0+, the cylinder starts to oscillate along its axis with velocity fsin(Ωt). To obtain the mathematical model of blood flow with fractional derivatives Caputo fractional operator is employed. The solutions for the velocities of blood and magnetic particles are procured semi analytically by using Laplace transformation method. The inverse Laplace transform has been calculated numerically by using MATHCAD computer software. The obtained results of velocities are presented in Laplace domain in terms of modified Bessel function I0(·). The obtained results satisfied all imposed initial and boundary conditions. The hybrid technique that is employed here less computational effort and time cost as compared to other techniques used in literature. As the limiting cases of our results the solutions of the flow model with ordinary derivatives has been procured. Finally, the impact of Reynolds number Re, fractional parameter α and Hartmann number Ha is analyzed and portrayed through graphs. It is worthy to pointing out that fractional derivatives brings remarkable differences as compared to ordinary derivatives. It also has been observed that velocity of blood and magnetic particles is weaker under the effect of transverse magnetic field.

A Two-Layer Mathematical Model of Blood Flow in Porous Constricted Blood Vessels

In this paper, we discussed a mathematical model for two-layered non-Newtonian blood flow through porous constricted blood vessels. The core region of blood flow contains the suspension of erythrocytes as non-Newtonian Casson fluid and the peripheral region contains the plasma flow as Newtonian fluid. The wall of porous constricted blood vessel configured as thin transition Brinkman layer over layered by Darcy region. The boundary of fluid layer is defined as stress jump condition of Ocha-Tapiya and Beavers–Joseph. In this paper, we obtained an analytic expression for velocity, flow rate, wall shear stress. The effect of permeability, plasma layer thickness, yield stress and shape of the constriction on velocity in core & peripheral region, wall shear stress and flow rate is discussed graphically. This is found throughout the discussion that permeability and plasma layer thickness have accountable effect on various flow parameters which gives an important observation for diseased blood vessels.

A computational study of the Fontan circulation with fenestration or hepatic vein exclusion

Fontan patients may undergo additional surgical modifications to mitigate complications like protein–losing enteropathy, liver cirrhosis, and other issues in their splanchnic circulation. Recent case reports show promise for several types of modifications, but the subtle effects of these surgeries on the circulation are not well understood. In this paper, we employ mathematical modeling of blood flow to systematically quantify the impact of these surgical changes on extracardiac Fontan hemodynamics. We investigate two modifications: (1) the fenestrated Fontan and (2) the Fontan with hepatic vein exclusion. Closed–loop hemodynamic models are used, which consist of one–dimensional networks for the major vessels and zero–dimensional models for the heart and organ beds. Numerical results suggest the hepatic vein exclusion has the greatest overall impact on the hemodynamics, followed by the largest sized fenestration. In particular, the hepatic vein exclusion drastically lowers portal venous pressure while the fenestration decreases pulmonary artery pressure. Both modifications increase flow to the intestines, a finding consistent with their utility in clinical practice for combating complications in the splanchnic circulation.

Modeling of Blood Flow Through a Bifurcated Artery Using Nanofluid

A mathematical model for blood flow through a bifurcated artery with mild stenosis in its parent artery is presented by taking blood as a copper suspended nanofluid with water as base fluid. The boundary of bifurcated artery is converted into a well-organized boundary using suitable transformations. The numerical solutions for temperature profiles, flow rate, impedance, and shear stress are found by using the finite difference method. The influence of admissible parameters on physical quantities on both sides of the apex is discussed graphically. It has been noticed that flow rate and impedance have been changed suddenly with the pertinent parameters on both sides of the apex. This occurs because of the backflow of the streaming blood at the onset of the lateral junction and secondary flow near the apex. All these observations on blood flow through bifurcated artery are of medical interest.