Relevant bibliographies by topics / Blood flow - Mathematical models

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  1. Journal articles
  2. Dissertations / Theses
  3. Books
  4. Book chapters
  5. Conference papers

Academic literature on the topic 'Blood flow - Mathematical models'

Author: Grafiati
Published: 4 June 2021
Last updated: 1 February 2022

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Journal articles on the topic "Blood flow - Mathematical models"

1

Nicosia, Sebastiano, and Giuseppe Pezzinga. "Mathematical models of blood flow in the arterial network." Journal of Hydraulic Research 45, no. 2 (March 2007): 188–201. http://dx.doi.org/10.1080/00221686.2007.9521759.

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Sankar, D. S., and K. Hemalatha. "Non-linear mathematical models for blood flow through tapered tubes." Applied Mathematics and Computation 188, no. 1 (May 2007): 567–82. http://dx.doi.org/10.1016/j.amc.2006.10.013.

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El Khatib, N., O. Kafi, A. Sequeira, S. Simakov, Yu Vassilevski, and V. Volpert. "Mathematical modelling of atherosclerosis." Mathematical Modelling of Natural Phenomena 14, no. 6 (2019): 603. http://dx.doi.org/10.1051/mmnp/2019050.

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The review presents the state of the art in the atherosclerosis modelling. It begins with the biological introduction describing the mechanisms of chronic inflammation of artery walls characterizing the development of atherosclerosis. In particular, we present in more detail models describing this chronic inflammation as a reaction-diffusion wave with regimes of propagation depending on the level of cholesterol (LDL) and models of rolling monocytes initializing the inflammation. Further development of this disease results in the formation of atherosclerotic plaque, vessel remodelling and possible plaque rupture due its interaction with blood flow. We review plaque-flow interaction models as well as reduced models (0D and 1D) of blood flow in atherosclerotic vasculature.
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Rzaev, E. A., S. R. Rasulov, and A. G. Rzaev. "Developing mathematical models for cardiovascular system functional assessments." Kazan medical journal 96, no. 4 (August 15, 2015): 681–85. http://dx.doi.org/10.17750/kmj2015-681.

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Aim. Development of mathematical models of circulation (considering anomaly in hemorheology) allowing to diagnose functional condition of vessels/cardiovascular system. Methods. Echocardiography, mathematical modeling, sedimentation and rheology laws, human mechanics and physiology methods were used for developing mathematical models. Results. The following mathematical models were obtained: for determination of colloid dispersive blood system viscosity, considering concentration of dispersive phase (blood cells) and blood structure formation; velocity of inconvenient blood cells sedimentation depending on flow velocity of sediment and cell concentration; parameters of blood elasticity and viscosity as a connection between the velocity change and blood viscosity, Young`s elasticity and change tension; blood filtration in vessels (modified form of Darcy`s law) considering tension and changes of destroyed and undestroyed colloid blood system structure velocity. It was shown that impairments of blood flow velocity leads to blood cells sedimentation and thrombus structure formation, which is not moving according to Newton’s law. New indicators for diagnosing functional condition of vessels and estimating the severity of vascular insufficiency are introduced. Conclusion. Developed hemorheologic models allow to adequately estimate human cardiovascular bloodflow.
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Farina, Angiolo, Antonio Fasano, and Fabio Rosso. "Mathematical Models for Some Aspects of Blood Microcirculation." Symmetry 13, no. 6 (June 6, 2021): 1020. http://dx.doi.org/10.3390/sym13061020.

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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.
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Namani, Ravi, Yoram Lanir, Lik Chuan Lee, and Ghassan S. Kassab. "Overview of mathematical modeling of myocardial blood flow regulation." American Journal of Physiology-Heart and Circulatory Physiology 318, no. 4 (April 1, 2020): H966—H975. http://dx.doi.org/10.1152/ajpheart.00563.2019.

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The oxygen consumption by the heart and its extraction from the coronary arterial blood are the highest among all organs. Any increase in oxygen demand due to a change in heart metabolic activity requires an increase in coronary blood flow. This functional requirement of adjustment of coronary blood flow is mediated by coronary flow regulation to meet the oxygen demand without any discomfort, even under strenuous exercise conditions. The goal of this article is to provide an overview of the theoretical and computational models of coronary flow regulation and to reveal insights into the functioning of a complex physiological system that affects the perfusion requirements of the myocardium. Models for three major control mechanisms of myogenic, flow, and metabolic control are presented. These explain how the flow regulation mechanisms operating over multiple spatial scales from the precapillaries to the large coronary arteries yield the myocardial perfusion characteristics of flow reserve, autoregulation, flow dispersion, and self-similarity. The review not only introduces concepts of coronary blood flow regulation but also presents state-of-the-art advances and their potential to impact the assessment of coronary microvascular dysfunction (CMD), cardiac-coronary coupling in metabolic diseases, and therapies for angina and heart failure. Experimentalists and modelers not trained in these models will have exposure through this review such that the nonintuitive and highly nonlinear behavior of coronary physiology can be understood from a different perspective. This survey highlights knowledge gaps, key challenges, future research directions, and novel paradigms in the modeling of coronary flow regulation.
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Ellwein, Laura M., Hien T. Tran, Cheryl Zapata, Vera Novak, and Mette S. Olufsen. "Sensitivity Analysis and Model Assessment: Mathematical Models for Arterial Blood Flow and Blood Pressure." Cardiovascular Engineering 8, no. 2 (December 15, 2007): 94–108. http://dx.doi.org/10.1007/s10558-007-9047-3.

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Sankar, D. S., and Yazariah Yatim. "Comparative Analysis of Mathematical Models for Blood Flow in Tapered Constricted Arteries." Abstract and Applied Analysis 2012 (2012): 1–34. http://dx.doi.org/10.1155/2012/235960.

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Pulsatile flow of blood in narrow tapered arteries with mild overlapping stenosis in the presence of periodic body acceleration is analyzed mathematically, treating it as two-fluid model with the suspension of all the erythrocytes in the core region as non-Newtonian fluid with yield stress and the plasma in the peripheral layer region as Newtonian. The non-Newtonian fluid with yield stress in the core region is assumed as (i) Herschel-Bulkley fluid and (ii) Casson fluid. The expressions for the shear stress, velocity, flow rate, wall shear stress, plug core radius, and longitudinal impedance to flow obtained by Sankar (2010) for two-fluid Herschel-Bulkley model and Sankar and Lee (2011) for two-fluid Casson model are used to compute the data for comparing these fluid models. It is observed that the plug core radius, wall shear stress, and longitudinal impedance to flow are lower for the two-fluid H-B model compared to the corresponding flow quantities of the two-fluid Casson model. It is noted that the plug core radius and longitudinal impedance to flow increases with the increase of the maximum depth of the stenosis. The mean velocity and mean flow rate of two-fluid H-B model are higher than those of the two-fluid Casson model.
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Balazs, ALBERT, and PETRILA Titus. "Mathematical Models and Numerical Simulations for the Blood Flow in Large Vessels." INCAS BULLETIN 4, no. 4 (December 10, 2012): 3–10. http://dx.doi.org/10.13111/2066-8201.2012.4.4.1.

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ZAMAN, GUL, YONG HAN KANG, and IL HYO JUNG. "ORIENTATIONAL STRESS TENSOR OF POLYMER SOLUTION WITH APPLICATIONS TO BLOOD FLOW." Modern Physics Letters B 25, no. 12n13 (May 30, 2011): 1157–66. http://dx.doi.org/10.1142/s0217984911026875.

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Blood circulating efficiently inside the veins and arteries, provides essential nutrients and oxygen to tissues and organs in the entire body. To highlight the fundamental properties of blood and gain insight into the regularizing effect of various formulations, we need to develop mathematical models. In order to do this, first we present the polymer dynamics in terms of an ensemble of Hookean dumbbells with Brownian configuration fields to derive the orientation stress tensor. Then, we describe the continuity and the momentum equations for time-dependent incompressible flow and the Oldroyd-B model. Finally, we present our numerical analysis of the model and give the effect of the orientation stress tensor in a blood vessel. The development of mathematical models and numerical procedures for the approximation of the blood specific flow equations have enabled us to understand the complex behaviors of blood flows inside the vessel.
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Dissertations / Theses on the topic "Blood flow - Mathematical models"

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Pincombe, Brandon. "A study of non-Newtonian behaviour of blood flow through stenosed arteries /." Title page, contents and summary only, 1999. http://web4.library.adelaide.edu.au/theses/09PH/09php6469.pdf.

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Healy, Timothy M. "Multi-block and overset-block domain decomposition techniques for cardiovascular flow simulation." Diss., Georgia Institute of Technology, 2001. http://hdl.handle.net/1853/15622.

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Carrig, Pauline Elize. "The effect of blood chemistry on the rheological properties of the fluid." Thesis, Virginia Polytechnic Institute and State University, 1986. http://hdl.handle.net/10919/94451.

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A four variable constitutive equation was developed utilizing the method first presented by Schneck and Walburn. Spearman rank correlation coefficients were calculated on whole blood samples within a narrow range of hematocrit to investigate further the effect of the various plasma constituents on whole blood viscosity. Viscosity measurements were made on one hundred anticoagulated blood samples of known hematocrit and chemical composition. The constitutive equation was developed using a power law functional form similar to that employed by Schneck and Walburn. This equation contains two parameters, the consistency index and the non-Newtonian index. A computerized multiple regression technique with apparent viscosity as the dependent variable was used to determine the particular form of these parameters. The one, two and three variable models developed confirmed the results of the previous work of Schneck and Walburn. The four variable model included the total lipids in combination with the concentration of total protein minus albumin and hematocrit. Spearman rank correlation coefficients showed the highest correlations between whole blood viscosity and the plasma constituents to be those of the globulins, total protein and fibrinogen. The constitutive equation developed did not show as high a correlation between experimental data and theory as did the Schneck-Walburn three variable model. The addition of a fourth variable did produce a statistically significant increase over the best three variable model of the present study.
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Hong, Say Yenh. "Fluid structure interaction modeling of pulsatile blood flow in serial pulmonary artery stenoses." Thesis, McGill University, 2007. http://digitool.Library.McGill.CA:80/R/?func=dbin-jump-full&object_id=112571.

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Motivated by the physiological phenomena of collapse and flow limitation for a serial pulmonary artery stenosis, we investigated the three-dimensional influence of spatial configuration on the wall motion and hemodynamic. Our numerical study focused on the effect of two geometrical parameters: the relative distance and the angular orientation between the two stenoses. The collapse of a compliant arterial stenosis may cause flow choking, which would limit the flow reserve to major vital vascular beds such as the lungs, potentially leading to a lethal ventilation-perfusion mismatch. Flow through a stenotic vessel is known to produce flow separation downstream of the throat. The eccentricity of a stenosis leads to asymmetric flow where the high velocity jets impinge on the sidewall, thereby inducing significant dissipation. The additional viscous dissipation causes a higher pressure drop for a flow through a stenotic vessel, than in a straight compliant vessel. It is likely that some particular morphology would have a higher vulnerability to the fluid induced instability of buckling (divergence), under physiological pulsatile flow. It was found that fluid pressure distribution have substantial implication for the downstream wall motion, under conditions of strong coupling between nonlinear vessel geometries, and their corresponding asymmetric flow. The three-dimensional fluid structure interaction problem is solved numerically by a finite element method based on the Arbitrary Lagrangian Eulerian formulation, a natural approach to deal with the moving interface between the flow and vessel. The findings of this investigation reveal that the closeness between stenoses is a substantial indication of wall collapse at the downstream end. Moreover, the results suggest a close link between the initial angular orientation of the distal stenosis (i.e. the constriction direction) and the subsequent wall motion at the downstream end. For cases showing evidence of preferential direction of wall motion, it was found that the constricted side underwent greater cumulative displacement than the straight side, suggestive of significant wall collapse.
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Ang, Keng Cheng. "A computational fluid dynamic study of blood flow through stenosed arteries /." Title page, table of contents and summary only, 1996. http://web4.library.adelaide.edu.au/theses/09PH/09pha5808.pdf.

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Fry, Brendan. "Theoretical Models for Blood Flow Regulation in Heterogeneous Microvascular Networks." Diss., The University of Arizona, 2013. http://hdl.handle.net/10150/293413.

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Proper distribution of blood flow in the microcirculation is necessary to match changing oxygen demands in various tissues. How this coordination of perfusion and consumption occurs in heterogeneous microvascular networks remains incompletely understood. Theoretical models are powerful tools that can help bridge this knowledge gap by simulating a range of conditions difficult to obtain experimentally. Here, an algorithm is first developed to estimate blood flow rates in large microvascular networks. Then, a theoretical model is presented for metabolic blood flow regulation in a realistic heterogeneous network structure, derived from experimental results from hamster cremaster muscle in control and dilated states. The model is based on modulation of arteriolar diameters according to the length-tension characteristics of vascular smooth muscle. Responses of smooth muscle cell tone to myogenic, shear-dependent, and metabolic stimuli are included. Blood flow is simulated including unequal hematocrit partition at diverging vessel bifurcations. Convective and diffusive oxygen transport in the network is simulated, and oxygen-dependent metabolic signals are assumed to be conducted upstream from distal vessels to arterioles. Simulations are carried out over a range of tissue oxygen demand. With increasing demand, arterioles dilate, blood flow increases, and the numbers of flowing arterioles and capillaries, as defined by red-blood-cell flux above a small threshold value, increase. Unequal hematocrit partition at diverging bifurcations contributes to capillary recruitment and enhances tissue oxygenation. The results imply that microvessel recruitment can occur as a consequence of local control of arteriolar tone. The effectiveness of red-blood-cell-dependent and independent mechanisms for the metabolic response of local blood flow regulation is examined over a range of tissue oxygen demands. Model results suggest that although a red-blood-cell-independent mechanism is most effective in increasing flow and preventing hypoxia, the addition of a red-blood-cell-dependent mechanism leads to a higher median tissue oxygen level, indicating distinct roles for the two mechanisms. In summary, flow rates in large microvessel networks can be estimated with the proposed algorithm, and the theoretical model for flow regulation predicts a mechanism for capillary recruitment, as well as roles for red-blood-cell-dependent and independent mechanisms in the metabolic regulation of blood flow in heterogeneous microvascular networks.
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Alirezaye-Davatgar, Mohammad Taghi Graduate School of Biomedical Engineering Faculty of Engineering UNSW. "Numerical simulation of blood flow in the systemic vasculature incorporating gravitational force with application to the cerebral circulation." Awarded by:University of New South Wales. Graduate School of Biomedical Engineering, 2006. http://handle.unsw.edu.au/1959.4/26177.

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Background. Extensive studies have been conducted to simulate blood flow in the human vasculature using nonlinear equations of pulsatile flow in collapsible tube plus a network of vessels to represent the whole vasculature and the cerebral circulation. For non-linear models numerical solutions are obtained for the fluid flow equations. Methods. Equations of fluid motion in collapsible tubes were developed in the presence of gravitational force (Gforce). The Lax-Wendroff and MacCormack methods were used to solve the governing equations and compared both in terms of accuracy, convergence, and computer processing (CPU) time. A modified vasculature of the whole body and the cerebral circulation was developed to obtain a realistic simulation of blood flow under different conditions. The whole body vasculature was used to validate the simulation in terms of input impedance and wave transmission. The cerebral vasculature was used to simulate conditions such as presence of G-force, blockage of Internal Carotid Artery (ICA), and the effects on cerebral blood flow of changes in mean and pulse pressure. Results. The simulation results for zero G-force were in very good agreement with published experimental data as was the simulation of cerebral blood flow. Both numerical methods for solutions of governing equations gave similar results for blood flow simulations but differed in calculation performance and stability depending on levels of G-force. Simulation results for uniform and sinusoidal G-force are also in good agreement with published experimental results, Blood flow was simulated in the presence of a single (left) carotid artery obstruction with varying morphological structures of the Circle of Willis (CoW). This simulation showed significant differences in contralateral blood flow in the presence or absence of communicating arteries in the CoW. It also was able to simulate the decreases in blood flow in the cerebral circulation compartment corresponding to the visual cortex in the presence of G-force. This is consistent with the known loss of vision under increased acceleration. Conclusions. This study has shown that under conditions of gravitational forces physiological changes in blood flow in the systemic and cerebral vasculature can be simulated realistically by solving the one-dimentional fluid flow equations and non-linear vascular properties numerically. The simulation was able to predict changes in blood flow with different configurations and properties of the vascular network.
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Bouchnita, Anass. "Mathematical modelling of blood coagulation and thrombus formation under flow in normal and pathological conditions." Thesis, Lyon, 2017. http://www.theses.fr/2017LYSE1300/document.

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Cette thèse est consacrée à la modélisation mathématique de la coagulation sanguine et de la formation de thrombus dans des conditions normales et pathologiques. La coagulation sanguine est un mécanisme défensif qui empêche la perte de sang suite à la rupture des tissus endothéliaux. C'est un processus complexe qui est règlementé par différents mécanismes mécaniques et biochimiques. La formation du caillot sanguin a lieu dans l'écoulement sanguin. Dans ce contexte, l'écoulement à faible taux de cisaillement stimule la croissance du caillot tandis que la circulation sanguine à fort taux de cisaillement la limite. Les désordres qui affectent le système de coagulation du sang peuvent provoquer différentes anomalies telles que la thrombose (coagulation exagérée) ou les saignements (insuffisance de coagulation). Dans la première partie de la thèse, nous présentons un modèle mathématique de coagulation sanguine. Le modèle capture la dynamique essentielle de la croissance du caillot dans le plasma et le flux sanguin quiescent. Ce modèle peut être réduit à un modèle qui consiste en une équation de génération de thrombine et qui donne approximativement les mêmes résultats. Nous avons utilisé des simulations numériques en plus de l'analyse mathématique pour montrer l'existence de différents régimes de coagulation sanguine. Nous spécifions les conditions pour ces régimes sur différents paramètres pathophysiologiques du modèle. Ensuite, nous quantifions les effets de divers mécanismes sur la croissance du caillot comme le flux sanguin et l'agrégation plaquettaire. La partie suivante de la thèse étudie certaines des anomalies du système de coagulation sanguine. Nous commençons par étudier le développement de la thrombose chez les patients présentant une carence en antihrombine ou l'une des maladies inflammatoires. Nous déterminons le seuil de l'antithrombine qui provoque la thrombose et nous quantifions l'effet des cytokines inflammatoires sur le processus de coagulation. Puis, nous étudions la compensation de la perte du sang après un saignement en utilisant un modèle multi-échelles qui décrit en particulier l'érythropoïèse et la production de l'hémoglobine. Ensuite, nous évaluons le risque de thrombose chez les patients atteints de cancer (le myélome multiple en particulier) et le VIH en combinant les résultats du modèle de coagulation sanguine avec les produits des modèles hybrides (discret-continues) multi-échelles des systèmes physiologiques correspondants. Finalement, quelques applications cliniques possibles de la modélisation de la coagulation sanguine sont présentées. En combinant le modèle de formation du caillot avec les modèles pharmacocinétiques pharmacodynamiques (PK-PD) des médicaments anticoagulants, nous quantifions l'action de ces traitements et nous prédisons leur effet sur des patients individuels
This thesis is devoted to the mathematical modelling of blood coagulation and clot formation under flow in normal and pathological conditions. Blood coagulation is a defensive mechanism that prevents the loss of blood upon the rupture of endothelial tissues. It is a complex process that is regulated by different mechanical and biochemical mechanisms. The formation of the blood clot takes place in blood flow. In this context, low-shear flow stimulates clot growth while high-shear blood circulation limits it. The disorders that affect the blood clotting system can provoke different abnormalities such thrombosis (exaggerated clotting) or bleeding (insufficient clotting). In the first part of the thesis, we introduce a mathematical model of blood coagulation. The model captures the essential dynamics of clot growth in quiescent plasma and blood flow. The model can be reduced to a one equation model of thrombin generation that gives approximately the same results. We used both numerical simulations and mathematical investigation to show the existence of different regimes of blood coagulation. We specify the conditions of these regimes on various pathophysiological parameters of the model. Then, we quantify the effects of various mechanisms on clot growth such as blood flow and platelet aggregation. The next part of the thesis studies some of the abnormalities of the blood clotting system. We begin by investigating the development of thrombosis in patients with antihrombin deficiency and inflammatory diseases. We determine the thrombosis threshold on antithrombin and quantify the effect of inflammatory cytokines on the coagulation process. Next, we study the recovery from blood loss following bleeding using a multiscale model which focuses on erythropoiesis and hemoglobin production. Then, we evaluate the risk of thrombosis in patients with cancer (multiple myeloma in particular) and HIV by combining the blood coagulation model results with the output of hybrid multiscale models of the corresponding physiological system. Finally, possible clinical applications of the blood coagulation modelling are provided. By combining clot formation model with pharmacokinetics-pharmacodynamics (PK-PD) models of anticoagulant drugs, we quantify the action of these treatments and predict their effect on individual patients
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Lucas, Claire. "An anatomical model of the cerebral vasculature and blood flow." Thesis, University of Oxford, 2013. http://ora.ox.ac.uk/objects/uuid:37d408b6-b804-4085-b420-a9704aeb97eb.

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The brain accounts for around 2 % of human adult bodyweight but consumes 20 % of the resting oxygen available to the whole body. The brain is dependent on a constant supply of oxygen to tissue, transported from the heart via the vasculature and carried in blood. An interruption to flow can lead to ischaemia (a reduced oxygen supply) and prolonged interruption may result in tissue death, and permanent brain damage. The cerebral vasculature consists of many, densely packed, micro-vessels with a very large total surface area. Oxygen dissolved in blood enters tissue by passive diffusion through the micro-vessel walls. Imaging shows bursts of metabolic activity and flow in localised brain areas coordinated with brain activity (such as raising a hand). An appropriate level of oxygenation, according to physiological demand, is maintained via autoregulation; a set of response pathways in the brain which cause upstream or downstream vessels to expand or contract in diameter as necessary to provide sufficient oxygen to every region of the brain. Further, autoregulation is also evident in the response to pressure changes in the vasculature: the perfusing pressure can vary over a wide range from the basal-state with only a small effect on flow due to the constriction or dilation of vessels. Presented here is a new vasculature model where diameter and length are calculated in order to match the data available for flow velocity and blood pressure in different sized vessels. These vessels are arranged in a network of 6 generations each of bifurcating arterioles and venules, and a set of capillary beds. The input pressure and number of generations are the only specifications required to describe the network. The number of vessels, and therefore vessel geometry, is governed by how many generations are chosen and this can be altered in order to create more simple or complex networks. The flow, geometry and oxygen concentrations are calculated based on the vessel resistance due to flow from geometry based on Kirchoff circuit laws. The passive and active length-tension characteristics of the vasculature are established using an approximation of the network at upper and lower autoregulation limits. An activation model is described with an activation factor which governs the contributions of elastic andmuscle tension to the total vessel tension. This tension balances with the circumferential tension due to pressure and diameter and the change in activation sets the vessel diameter. The mass transport equation for oxygen is used to calculate the concentration of oxygen at every point in the network using data for oxygen saturation to establish a relationship between the permeability of the vessel wall to oxygen and the geometry and flow in individual vessels. A tissue compartment is introduced which enables the modelling of metabolic control. There is evidence for a coordinated response by surrounding vessels to local changes. A signal is proposed based on oxygen demand which can be conducted upstream. This signal decays exponentially with vessel length but also accumulates with the signal added from other vessels. The activation factor is therefore set by weighted signals proportional to changes in tissue concentration, circumferential tension, shear stress and conducted oxygen demand. The model is able to reproduce the autoregulation curve whereby a change in pressure has only a small effect on flow. The model is also able to replicate experimental results of diameter and tissue concentration following an increase in oxygen demand.
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Bevan, Rhodri L. T. "A locally conservative Galerkin approach for subject-specific biofluid dynamics." Thesis, Swansea University, 2010. https://cronfa.swan.ac.uk/Record/cronfa42314.

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In this thesis, a parallel solver was developed for the modelling of blood flow through a number of patient-specific geometries. A locally conservative Galerkin (LCG) spatial discretisation was applied along with an artificial compressibility and characteristic based split (CBS) scheme to solve the 3D incompressible Navier-Stokes equations. The Spalart-Allmaras one equation turbulence model was also optionally employed. The solver was constructed using FORTRAN and the Message Passing Interface (MPI). Parallel testing demonstrated linear or better than linear speedup on hybrid patient-specific meshes. These meshes were unstructured with structured boundary layers. From the parallel testing it is clear that the significance of inter-processor communication is negligible in a three dimensional case. Preliminary tests on a short patient-specific carotid geometry demonstrated the need for ten or more boundary layer meshes in order to sufficiently resolve the peak wall shear stress (WSS) along with the peak time-averaged WSS. A time sensitivity study was also undertaken along with the assessment of the order of the real time step term. Three backward difference formulae (BDF) were tested and no significant difference between them was detected. Significant speedup was possible as the order of time discretisation increased however, making the choice of BDF important in producing a timely solution. Followed by the preliminary investigation, four more carotid geometries were investigated in detail. A total of six haemodynamic wall parameters have been brought together to analyse the regions of possible atherogenesis within each carotid. The investigations revealed that geometry plays an overriding influence on the wall parameter distribution. Each carotid artery displayed high time-averaged WSS at the apex, although the value increased significantly with a proximal stenosis. Two out of four meshes contained a region of low time-averaged WSS distal to the flow divider and within the largest connecting artery (internal or external carotid artery), indicating a potential region of atherosclerosis plaque formation. The remaining two meshes already had a stenosis in the corresponding region. This is in excellent agreement with other established works. From the investigations, it is apparent that a classification system of stenosis severity may be possible with potential application as a clinical diagnosis aid. Finally, the flow within a thoracic aortic aneurysm was investigated in order to assess the influence of a proximal folded neck. The folded neck had a significant effect on the wall shear stress, increasing by up to 250% over an artificially smoothed neck. High wall shear stresses may be linked to aneurysm rupture. Being proximal to the aneurysm, this indicated that local geometry should be taken into account when assessing the rupture potential of an aneurysm.
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Books on the topic "Blood flow - Mathematical models"

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NATO Advanced Study Institute on Cerebral Blood Flow: Mathematical Models, Instrumentation, and Imaging Techniques for the Study of CBF (1986 L'Aquila, Italy). Cerebral blood flow: Mathematical models, instrumentation, and imaging techniques. New York: Plenum Press, 1988.

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ASME/JSME Fluids Engineering and Laser Anemometry Conference and Exhibition (1995 Hilton Head, S.C.). Bio-medical fluids engineering: Presented at the 1995 ASME/JSME Fluids Engineering and Laser Anemometry Conference and Exhibition, August 13-18, 1995, Hilton Head, South Carolina. New York, N.Y: American Society of Mechanical Engineers, 1995.

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Computational hydrodynamics of capsules and biological cells. Boca Raton: Chapman & Hall/CRC, 2010.

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Multicomponent flow modeling. Boston: Birkhäuser, 1999.

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As, S. C. van. Traffic flow theory. 3rd ed. [Pretoria]: SARB Chair in Transportation Engineering, Dept. of Civil Engineering, University of Pretoria, 1990.

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Kolev, Nikolay Ivanov. Multiphase flow dynamics. Berlin: Springer, 2002.

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Integrated flow modeling. Amsterdam: Elsevier Science B.V., 2000.

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Traffic flow fundamentals. Englewood Cliffs, N.J: Prentice Hall, 1990.

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Multiphase flow dynamics. 2nd ed. Berlin: Springer, 2005.

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Kolev, Nikolay Ivanov. Multiphase flow dynamics. 4th ed. Berlin: Springer, 2011.

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Book chapters on the topic "Blood flow - Mathematical models"

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de Moura, Alexandra Bugalho. "1D Models for Blood Flow in Arteries." In Mathematics in Industry, 17–33. Cham: Springer International Publishing, 2020. http://dx.doi.org/10.1007/978-3-030-50388-8_2.

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Sequeira, Adélia. "Hemorheology: Non-Newtonian Constitutive Models for Blood Flow Simulations." In Lecture Notes in Mathematics, 1–44. Cham: Springer International Publishing, 2018. http://dx.doi.org/10.1007/978-3-319-74796-5_1.

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Kumar, Anil. "Mathematical Model of Blood Flow in Arteries with Porous Effects." In IFMBE Proceedings, 18–21. Berlin, Heidelberg: Springer Berlin Heidelberg, 2010. http://dx.doi.org/10.1007/978-3-642-14515-5_5.

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Hadjinicolaou, Maria, and Eleftherios Protopapas. "A Microscale Mathematical Blood Flow Model for Understanding Cardiovascular Diseases." In Advances in Experimental Medicine and Biology, 373–87. Cham: Springer International Publishing, 2020. http://dx.doi.org/10.1007/978-3-030-32622-7_35.

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Hadjinicolaou, Maria. "A Mathematical Model for the Blood Plasma Flow Around Two Aggregated Low-Density Lipoproteins." In Advances in Experimental Medicine and Biology, 173–84. Cham: Springer International Publishing, 2014. http://dx.doi.org/10.1007/978-3-319-09012-2_11.

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Kiseleva, Anna A., Petr V. Luzhnov, and Dmitry M. Shamaev. "Verification of Mathematical Model for Bioimpedance Diagnostics of the Blood Flow in Cerebral Vessels." In Advances in Artificial Systems for Medicine and Education II, 251–59. Cham: Springer International Publishing, 2019. http://dx.doi.org/10.1007/978-3-030-12082-5_23.

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Bodnár, Tomáš, Antonio Fasano, and Adélia Sequeira. "Mathematical Models for Blood Coagulation." In Fluid-Structure Interaction and Biomedical Applications, 483–569. Basel: Springer Basel, 2014. http://dx.doi.org/10.1007/978-3-0348-0822-4_7.

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Elefteriadou, Lily. "Mathematical and Empirical Models." In An Introduction to Traffic Flow Theory, 129–35. New York, NY: Springer New York, 2013. http://dx.doi.org/10.1007/978-1-4614-8435-6_6.

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Kovarik, Karel. "Mathematical Models of Groundwater Flow." In Numerical Models in Groundwater Pollution, 61–108. Berlin, Heidelberg: Springer Berlin Heidelberg, 2000. http://dx.doi.org/10.1007/978-3-642-56982-1_5.

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Holstein-Rathlou, N. H., K. H. Chon, D. J. Marsh, and V. Z. Marmarelis. "Models of Renal Blood Flow Autoregulation." In Springer Series in Synergetics, 167–85. Berlin, Heidelberg: Springer Berlin Heidelberg, 1995. http://dx.doi.org/10.1007/978-3-642-79290-8_9.

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Conference papers on the topic "Blood flow - Mathematical models"

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Isaac, Abdalla W., and Mikhial Mathuieu. "A Mathematical Model for Blood Flow under Periodic Acceleration." In Biomedical Engineering. Calgary,AB,Canada: ACTAPRESS, 2011. http://dx.doi.org/10.2316/p.2011.723-022.

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Isaac, Abdalla Wassf, and Mikhial Maher Mathuieu. "A MATHEMATICAL MODEL FOR BLOOD FLOW UNDER PERIODIC ACCELERATION." In Biomedical Engineering. Calgary,AB,Canada: ACTAPRESS, 2010. http://dx.doi.org/10.2316/p.2010.723-022.

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Alnussairy, Esam A., and Ahmed Bakheet. "MHD micropolar blood flow model through a multiple stenosed artery." In THIRD INTERNATIONAL CONFERENCE OF MATHEMATICAL SCIENCES (ICMS 2019). AIP Publishing, 2019. http://dx.doi.org/10.1063/1.5136202.

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Sankar, D. S., Usik Lee, Atulya K. Nagar, and Maziri Morsidi. "Mathematical analysis of Carreau fluid model for blood flow in tapered constricted arteries." In PROCEEDINGS OF THE 3RD INTERNATIONAL CONFERENCE ON APPLIED SCIENCE AND TECHNOLOGY (ICAST’18). Author(s), 2018. http://dx.doi.org/10.1063/1.5055530.

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Hossain, Md Shahadat, Bhavin Dalal, Ian S. Fischer, Pushpendra Singh, and Nadine Aubry. "Modeling of Blood Flow in the Human Brain." In ASME 2010 3rd Joint US-European Fluids Engineering Summer Meeting collocated with 8th International Conference on Nanochannels, Microchannels, and Minichannels. ASMEDC, 2010. http://dx.doi.org/10.1115/fedsm-icnmm2010-30554.

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The non-Newtonian properties of blood, i.e., shear thinning and viscoelasticity, can have a significant influence on the distribution of Cerebral Blood Flow (CBF) in the human brain. The aim of this work is to quantify the role played by the non-Newtonian nature of blood. Under normal conditions, CBF is autoregulated to maintain baseline levels of flow and oxygen to the brain. However, in patients suffering from heart failure (HF), Stroke, or Arteriovenous malformation (AVM), the pressure in afferent vessels varies from the normal range within which the regulatory mechanisms can ensure a constant cerebral flow rate, leading to impaired cerebration in patients. It has been reported that the change in the flow rate is more significant in certain regions of the brain than others, and that this might be relevant to the pathophysiological symptoms exhibited in these patients. We have developed mathematical models of CBF under normal and the above disease conditions that use direct numerical simulations (DNS) for the individual capillaries along with the experimental data in a one-dimensional model to determine the flow rate and the methods for regulating CBF. The model also allows us to determine which regions of the brain would be affected relatively more severely under these conditions.
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Hossain, Md Shahadat, Shriram B. Pillapakkam, Bhavin Dalal, Ian S. Fischer, Nadine Aubry, and Pushpendra Singh. "Modeling of Blood Flow in the Human Brain." In ASME 2011 International Mechanical Engineering Congress and Exposition. ASMEDC, 2011. http://dx.doi.org/10.1115/imece2011-64525.

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Under normal conditions, Cerebral Blood Flow (CBF) is related to the metabolism of the cerebral tissue. Three factors that contribute significantly to the regulation of CBF include the carbon dioxide and hydrogen ion concentration, oxygen deficiency and the level of cerebral activity. These regulatory mechanisms ensure a constant CBF of 50 to 55 ml per 100g of brain per minute for mean arterial blood pressure between 60–180 mm Hg. Under severe conditions when the autoregulatory mechanism fails to compensate, sympathetic nervous system constricts the large and intermediate sized arteries and prevents very high pressure from ever reaching the smaller blood vessels, preventing the occurrence of vascular hemorrhage. Several invasive and non-invasive techniques such as pressure and thermoelectric effect sensors to Positron Emission Tomography (PET) and magnetic resonance imaging (MRI) based profusion techniques have been used to quantify CBF. However, the effects of the non-Newtonian properties of blood, i.e., shear thinning and viscoelasticity, can have a significant influence on the distribution of CBF in the human brain and are poorly understood. The aim of this work is to quantify the role played by the non-Newtonian nature of blood on CBF. We have developed mathematical models of CBF that use direct numerical simulations (DNS) for the individual capillaries along with the experimental data in a one-dimensional model to determine the flow rate and the methods for regulating CBF. The model also allows us to determine which regions of the brain would be affected more severely under these conditions.
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Shakeri, Mostafa, Iman Khodarahmi, and M. Keith Sharp. "Preliminary Imaging of Red Blood Cells in Turbulent Flow." In ASME 2012 Summer Bioengineering Conference. American Society of Mechanical Engineers, 2012. http://dx.doi.org/10.1115/sbc2012-80416.

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Considerable uncertainty exists about how momentum and energy are transferred to cells in turbulent flow, which has been shown to cause six times more damage to red blood cells (RBC’s) than laminar flow with the same mean wall shear stress [Kameneva, et al. 2004]. Though it is a purely mathematical construct to yield closure of the time-averaged Navier-Stokes equation for a continuum fluid, which is not valid at the scale of the cell, Reynolds stress has been used as an empirical indicator for damage potential [Sallam & Hwang 1984]. Other scales, including local viscous stress [Jones 1995], flow of plasma around inertia cells [Quinlan & Dooley 2007], shear within eddies [Quinlan & Dooley 2007] and shear between rigid cells within an eddy [Antiga & Steinman 2009], have been forwarded. To provide data to validate these models, an imaging system was assembled to directly observe RBC’s in turbulent flow under a microscope.
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Bakheet, Ahmed, Esam A. Alnussairy, Zuhaila Ismail, and Norsarahaida Amin. "The effect of body acceleration on the generalized power law model of blood flow in a stenosed artery." In THE 4TH INTERNATIONAL CONFERENCE ON MATHEMATICAL SCIENCES: Mathematical Sciences: Championing the Way in a Problem Based and Data Driven Society. Author(s), 2017. http://dx.doi.org/10.1063/1.4980893.

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Sindeev, S. V., S. V. Frolov, and A. Yu Potlov. "Mathematical Modeling of Blood Flow in a Patientspecific Model of the Middle Cerebral Artery Taking into Account Non-Newtonian Blood Behavior." In 2019 International Science and Technology Conference "EastConf". IEEE, 2019. http://dx.doi.org/10.1109/eastconf.2019.8725318.

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Sankar, D. S., and M. F. Karim. "Influence of body acceleration in blood flow through narrow arteries with multiple constrictions - a mathematical model." In 5th Brunei International Conference on Engineering and Technology (BICET 2014). Institution of Engineering and Technology, 2014. http://dx.doi.org/10.1049/cp.2014.1068.

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