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JSim models of two‐dimensional concentrations in capillary‐tissue systems relating center‐of‐mass of retained tracer to washout kinetics
Author(s) -
Raymond Gary M.,
Bassingthwaighte James B.
Publication year - 2012
Publication title -
the faseb journal
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.709
H-Index - 277
eISSN - 1530-6860
pISSN - 0892-6638
DOI - 10.1096/fasebj.26.1_supplement.905.17
Subject(s) - concentric , capillary action , cylindrical coordinate system , mechanics , diffusion , washout , physics , geometry , flux (metallurgy) , chemistry , mathematical analysis , mathematics , thermodynamics , organic chemistry , meteorology
The transport of a metabolite from a capillary into tissue surrounding it and subsequent back flux and washout is modeled. The system is radially symmetric. It is solved using JSim's Mathematical Modeling Language (MML) by subdividing the tissue into equally spaced concentric rings surrounding a cylindrical capillary. The capillary and concentric rings are modeled as partial differential equations in the axial direction. In the radial direction they are mathematically connected by second order accurate finite difference equations where the permeability‐surface area parameters are calculated from the radial diffusion coefficient. Solutions from the capillary and tissue rings are assembled into an array and contoured. The center of mass of material as a function of axial distance and absolute radial distance is calculated. Animated visualizations are constructing by linking the solutions to MatlabTM through a JSim procedure written in Java. The model was generated using the Modular Program Constructor allowing us to prototype a system where the governing equations repeat patterns of information.(Supported by NIH grants T15‐HL088516 and R01‐EB08407)