Numerical simulation of a stroke: numerical problems and methodology

The numerical simulation of an ischemic stroke is a challenging problem: a complicated geometry, and a very stiff large system of reaction-diffusion equations. This paper, intended for mathematicians as well as for biologist, gives a survey and an introduction to the numerical methods used and some results.

[1]  Jean-Pierre Boissel,et al.  A mathematical model of ion movements in grey matter during a stroke. , 2006, Journal of theoretical biology.

[2]  Marc Massot,et al.  Operator splitting for nonlinear reaction-diffusion systems with an entropic structure : singular perturbation and order reduction , 2004, Numerische Mathematik.

[3]  F. Krogh,et al.  Solving Ordinary Differential Equations , 2019, Programming for Computations - Python.

[4]  Stéphane Descombes,et al.  Convergence of a splitting method of high order for reaction-diffusion systems , 2001, Math. Comput..

[5]  John N. Shadid,et al.  Stability of operator splitting methods for systems with indefinite operators: reaction-diffusion systems , 2005 .

[6]  L. Halpern Absorbing boundary conditions and optimized Schwarz waveform relaxation , 2006 .

[7]  N. Rashevsky,et al.  Mathematical biology , 1961, Connecticut medicine.

[8]  Thierry Dumont,et al.  Role of astrocytes in grey matter during stroke: A modelling approach , 2007, Brain Research.

[9]  Charalambos Makridakis,et al.  Implicit-explicit multistep methods for quasilinear parabolic equations , 1999, Numerische Mathematik.

[10]  G. Strang On the Construction and Comparison of Difference Schemes , 1968 .

[11]  James Demmel,et al.  A Supernodal Approach to Sparse Partial Pivoting , 1999, SIAM J. Matrix Anal. Appl..

[12]  G. Marchuk Splitting and alternating direction methods , 1990 .

[13]  Bruce E. Shapiro,et al.  Osmotic Forces and Gap Junctions in Spreading Depression: A Computational Model , 2004, Journal of Computational Neuroscience.