EFFICIENT NUMERICAL-METHODS FOR NONLINEAR-FACILITATED TRANSPORT AND EXCHANGE IN A BLOOD-TISSUE EXCHANGE UNIT

The analysis of experimental data obtained by the multiple-indicator m ethod requires complex mathematical models for which capillary brood-t issue exchange (BTEX) units are the building blocks. This study presen ts 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 convecti on-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 an d Euler-Lagrange methods are preferred over the MacCormack method beca use they allow for the derivation of a heuristic criterion that makes the numerical methods stable without degrading their efficiency. Numer ical 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.