Efficient numerical methods for nonlinear-facilitated transport and exchange in a blood-tissue exchange unit

• Published in: Annals of biomedical engineering Vol. 25; no. 3; pp. 547 - 564
• Main Authors: POULAIN, C. A, FINLAYSON, B. A, BASSINGTHWAIGHTE, J. B
• Format: Journal Article
• Language: English
• Published: New York, NY Springer 01.05.1997; Springer Nature B.V
• Subjects: Algorithms; Biological and medical sciences; Blood; Blood vessels and receptors; Capillary Permeability - physiology; Diffusion; Experimental data; Fundamental and applied biological sciences. Psychology; Intracellular Fluid - physiology; Mass transfer; Mathematical models; Mathematics; Methods; Nonlinear Dynamics; Numerical Analysis, Computer-Assisted; Plasma - physiology; Studies; Vertebrates: cardiovascular system; Data analysis; Experimental data; Euler Lagrange equation; Numerical method; Exchange reaction; Blood; Mass transfer; Transport process; Tissue; Non linear process; Non linear model; Blood capillary; Circulatory system; Mathematical model
• ISSN: 0090-6964; 1573-9686; 1521-6047
• DOI: 10.1007/bf02684194

The analysis of experimental data obtained by the multiple-indicator method requires complex mathematical models for which capillary blood-tissue exchange (BTEX) units are the building blocks. This study presents a new, nonlinear, two-region, axially distributed, single capillary, BTEX model. A facilitated transporter model is used to describe mass transfer between plasma and intracellular spaces. To provide fast and accurate solutions, numerical techniques suited to nonlinear convection-dominated problems are implemented. These techniques are the random choice method, an explicit Euler-Lagrange scheme, and the MacCormack method with and without flux correction. The accuracy of the numerical techniques is demonstrated, and their efficiencies are compared. The random choice, Euler-Lagrange and plain MacCormack method are the best numerical techniques for BTEX modeling. However, the random choice and Euler-Lagrange methods are preferred over the MacCormack method because they allow for the derivation of a heuristic criterion that makes the numerical methods stable without degrading their efficiency. Numerical solutions are also used to illustrate some nonlinear behaviors of the model and to show how the new BTEX model can be used to estimate parameters from experimental data.