This section deals with the application of advanced numerical techniques to nonlinear mass transport and exchange problems. Mass transport and exchange in the micro circulation are driven by complex nonlinear phenomena. To investigate efficiently these phenomena, quick and accurate numerical solutions to large models are needed. To meet that requirement, we have applied specialized numerical techniques (namely random choice method, Euler-Lagrange method and MacCormack method with and without flux-correction) to a two-region blood-tissue exchange model which include carrier-mediated transport and nonlinear consumptions. The generality of the model has also been extended by allowing for non-uniform distribution of carrier sites and reaction sites along the capillary. To provide investigators with a robust package, stability conditions have been implemented and tested. Extension of the numerical techniques to more complicated models has started.
| Bassingthwaighte, James B; Butterworth, Erik; Jardine, Bartholomew et al. (2012) Compartmental modeling in the analysis of biological systems. Methods Mol Biol 929:391-438 |
| Dash, Ranjan K; Bassingthwaighte, James B (2010) Erratum to: Blood HbO2 and HbCO2 dissociation curves at varied O2, CO2, pH, 2,3-DPG and temperature levels. Ann Biomed Eng 38:1683-701 |
| Bassingthwaighte, James B; Raymond, Gary M; Butterworth, Erik et al. (2010) Multiscale modeling of metabolism, flows, and exchanges in heterogeneous organs. Ann N Y Acad Sci 1188:111-20 |
| Dash, Ranjan K; Bassingthwaighte, James B (2006) Simultaneous blood-tissue exchange of oxygen, carbon dioxide, bicarbonate, and hydrogen ion. Ann Biomed Eng 34:1129-48 |
| Dash, Ranjan K; Bassingthwaighte, James B (2004) Blood HbO2 and HbCO2 dissociation curves at varied O2, CO2, pH, 2,3-DPG and temperature levels. Ann Biomed Eng 32:1676-93 |
| Kellen, Michael R; Bassingthwaighte, James B (2003) Transient transcapillary exchange of water driven by osmotic forces in the heart. Am J Physiol Heart Circ Physiol 285:H1317-31 |
| Kellen, Michael R; Bassingthwaighte, James B (2003) An integrative model of coupled water and solute exchange in the heart. Am J Physiol Heart Circ Physiol 285:H1303-16 |
| Wang, C Y; Bassingthwaighte, J B (2001) Capillary supply regions. Math Biosci 173:103-14 |
| Swanson, K R; True, L D; Lin, D W et al. (2001) A quantitative model for the dynamics of serum prostate-specific antigen as a marker for cancerous growth: an explanation for a medical anomaly. Am J Pathol 158:2195-9 |
| Swanson, K R; Alvord Jr, E C; Murray, J D (2000) A quantitative model for differential motility of gliomas in grey and white matter. Cell Prolif 33:317-29 |
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