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Mathematical Model of Blood Flow in an Anatomically Detailed Arterial Network of the Arm

Sansuke M. Watanabe, Pablo J. Blanco, Raúl A. Feijóo (2013)

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

A distributed-parameter (one-dimensional) anatomically detailed model for the arterial network of the arm is developed in order to carry out hemodynamics simulations. This work focuses on the specific aspects related to the model set-up. In this regard, stringent anatomical and physiological considerations have been pursued in order to construct the arterial topology and to provide a systematic estimation of the involved parameters. The model comprises 108 arterial segments, with 64 main arteries...

Mathematical Models of Dividing Cell Populations: Application to CFSE Data

H.T. Banks, W. Clayton Thompson (2012)

Mathematical Modelling of Natural Phenomena

Flow cytometric analysis using intracellular dyes such as CFSE is a powerful experimental tool which can be used in conjunction with mathematical modeling to quantify the dynamic behavior of a population of lymphocytes. In this survey we begin by providing an overview of the mathematically relevant aspects of the data collection procedure. We then present an overview of the large body of mathematical models, along with their assumptions and uses,...

Microscale Complexity in the Ocean: Turbulence, Intermittency and Plankton Life

L. Seuront (2008)

Mathematical Modelling of Natural Phenomena

This contribution reviews the nonlinear stochastic properties of turbulent velocity and passive scalar intermittent fluctuations in Eulerian and Lagrangian turbulence. These properties are illustrated with original data sets of (i) velocity fluctuations collected in the field and in the laboratory, and (ii) temperature, salinity and in vivo fluorescence (a proxy of phytoplankton biomass, i.e. unicelled vegetals passively advected by turbulence) sampled from highly turbulent coastal waters. The strength...

Microscopic Modelling of Active Bacterial Suspensions

A. Decoene, S. Martin, B. Maury (2011)

Mathematical Modelling of Natural Phenomena

We present two-dimensional simulations of chemotactic self-propelled bacteria swimming in a viscous fluid. Self-propulsion is modelled by a couple of forces of same intensity and opposite direction applied on the rigid bacterial body and on an associated region in the fluid representing the flagellar bundle. The method for solving the fluid flow and the motion of the bacteria is based on a variational formulation written on the whole domain, strongly...

Modeling of the oxygen transfer in the respiratory process

Sébastien Martin, Bertrand Maury (2013)

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

In this article, we propose an integrated model for oxygen transfer into the blood, coupled with a lumped mechanical model for the ventilation process. Objectives. We aim at investigating oxygen transfer into the blood at rest or exercise. The first task consists in describing nonlinear effects of the oxygen transfer under normal conditions. We also include the possible diffusion limitation in oxygen transfer observed in extreme regimes involving parameters such as alveolar and venous blood oxygen...

Modeling the Dynamics of the Cardiovascular-respiratory System (CVRS) in Humans, a Survey

F. Kappel (2012)

Mathematical Modelling of Natural Phenomena

In this paper we give a survey on modeling efforts concerning the CVRS. The material we discuss is organized in accordance with modeling goals and stresses control and transport issues. We also address basic modeling approaches and discuss some of the challenges for mathematical modeling methodologies in the context of parameter estimation and model validation.

Modelling the Impact of Pericyte Migration and Coverage of Vessels on the Efficacy of Vascular Disrupting Agents

S. R. McDougall, M. A.J. Chaplain, A. Stéphanou, A. R.A. Anderson (2010)

Mathematical Modelling of Natural Phenomena

Over the past decade or so, there have been a large number of modelling approaches aimed at elucidating the most important mechanisms affecting the formation of new capillaries from parent blood vessels — a process known as angiogenesis. Most studies have focussed upon the way in which capillary sprouts are initiated and migrate in response to diffusible chemical stimuli supplied by hypoxic stromal cells and leukocytes in the contexts of solid tumour...

Numerical modelling of flow in lower urinary tract using high-resolution methods

Brandner, Marek, Egermaier, Jiří, Kopincová, Hana, Rosenberg, Josef (2013)

Programs and Algorithms of Numerical Mathematics

We propose a new numerical scheme based on the finite volumes to simulate the urethra flow based on hyperbolic balance law. Our approach is based on the Riemann solver designed for the augmented quasilinear homogeneous formulation. The scheme has general semidiscrete wave–propagation form and can be extended to arbitrary high order accuracy. The first goal is to construct the scheme, which is well balanced, i.e. maintains not only some special steady states but all steady states which can occur....

Numerical simulation of blood flows through a porous interface

Miguel A. Fernández, Jean-Frédéric Gerbeau, Vincent Martin (2008)

ESAIM: Mathematical Modelling and Numerical Analysis

We propose a model for a medical device, called a stent, designed for the treatment of cerebral aneurysms. The stent consists of a grid, immersed in the blood flow and located at the inlet of the aneurysm. It aims at promoting a clot within the aneurysm. The blood flow is modelled by the incompressible Navier-Stokes equations and the stent by a dissipative surface term. We propose a stabilized finite element method for this model and we analyse its convergence in the case of the Stokes...

On a constrained minimization problem arising in hemodynamics

João Janela, Adélia Sequeira (2008)

Banach Center Publications

Experimental evidence collected over the years shows that blood exhibits non-Newtonian characteristics such as shear-thinning, viscoelasticity, yield stress and thixotropic behaviour. Under certain conditions these characteristics become relevant and must be taken into consideration when modelling blood flow. In this work we deal with incompressible generalized Newtonian fluids, that account for the non-constant viscosity of blood, and present a new numerical method to handle fluid-rigid body interaction...

On the stability of the coupling of 3D and 1D fluid-structure interaction models for blood flow simulations

Luca Formaggia, Alexandra Moura, Fabio Nobile (2007)

ESAIM: Mathematical Modelling and Numerical Analysis

We consider the coupling between three-dimensional (3D) and one-dimensional (1D) fluid-structure interaction (FSI) models describing blood flow inside compliant vessels. The 1D model is a hyperbolic system of partial differential equations. The 3D model consists of the Navier-Stokes equations for incompressible Newtonian fluids coupled with a model for the vessel wall dynamics. A non standard formulation for the Navier-Stokes equations is adopted to have suitable boundary conditions for the...

Particle Dynamics Methods of Blood Flow Simulations

A. Tosenberger, V. Salnikov, N. Bessonov, E. Babushkina, V. Volpert (2011)

Mathematical Modelling of Natural Phenomena

Various particle methods are widely used to model dynamics of complex media. In this work molecular dynamics and dissipative particles dynamics are applied to model blood flows composed of plasma and erythrocytes. The properties of the homogeneous particle fluid are studied. Capillary flows with erythrocytes are investigated.

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