An improved algorithm and its parallel implementation for solving a general blood-tissue transport and metabolism model

JOURNAL OF COMPUTATIONAL PHYSICS

卷:228

Article

Xie, Dexuan¹  Dash, Ranjan K.²  Beard, Daniel A.² 

[1] Univ Wisconsin, Dept Math Sci, Milwaukee, WI 53201 USA

[2] Med Coll Wisconsin, Biotechnol & Bioengn Ctr, Dept Physiol, Milwaukee, WI 53226 USA

关键词: Blood-tissue transport and metabolism;    BTEX algorithm;    Parallel computation;    System of first order semilinear PDEs;    Initial-boundary value problems;   

DOI  :  10.1016/j.jcp.2009.07.024

来源: Elsevier

【 摘 要 】

Fast algorithms for simulating mathematical models of coupled blood-tissue transport and metabolism are critical for the analysis of data on transport and reaction in tissues. Here, by combining the method of characteristics with the standard grid discretization technique, a novel algorithm is introduced for solving a general blood-tissue transport and metabolism model governed by a large system of one-dimensional semilinear first order partial differential equations. The key part of the algorithm is to approximate the model as a group of independent ordinary differential equation (ODE) systems such that each ODE system has the same size as the model and can be integrated independently. Thus the method can be easily implemented in parallel on a large-scale multiprocessor computer. The accuracy of the algorithm is demonstrated for solving a simple blood-tissue exchange model introduced by Sangren and Sheppard [W.C. Sangren, C.W. Sheppard, A mathematical derivation of the exchange of a labeled substance between a liquid flowing in a vessel and an external compartment, Bull. Math. Biophys. 15 (1953) 387-394], which has an analytical solution. Numerical experiments made on a distributed-memory parallel computer (an HP Linux cluster) and a shared-memory parallel computer (a SGI Origin 2000) demonstrate the parallel efficiency of the algorithm. (C) 2009 Elsevier Inc. All rights reserved.

【 授权许可】

Free