Mathematical models of arterial transmural transport

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Abstract
A finite-element model (FEM) and corresponding 5-parameter analytical model (AM) were derived to study the 1-dimensional transport of chemically reactive macromolecules across (x) arterial tissue. Derivations emphasize chemical activity [a(x)], its gradient and water flux as driving forces for chemical reactions and transport. The AM was fitted to 28 measured 125I-albumin transmural concentration [c(x)] curves giving parameter estimates of diffusivity (DA), convective velocity (.nu.A) and so on as functions of pressure (P), location (z) along the vessel, etc. The FEM was used to study intimal-medial .alpha.(x) associated with molecular sieving and medial edema, reversible binding and errors of AM in analysis of c(x). Average relative error for the 28 AM fits was 5.3%. Only estimates of DA and .nu.A had acceptable coefficients of variation. DA (.apprx. 0.10 .times. 10-7 cm2 .cntdot. s-1) decreased with P, increased with z to a maximum, and then decreased; .nu.A was approximately proportional to P (.apprx. 0.12 .times. 10-7 cm .cntdot. s-1 .cntdot. mmHg-1) and decreased slightly with z; distribution coefficient (.epsilon.F) decreased with z and was smaller for serum than for simple albumin reagent. Assumed boundary conditions for AM were associated with .apprx. 1.4% error in AM c(x). Parameter estimates were sensitive to wall inhomogeneity, e.g., .apprx. 15% error. The AM and FEM stimulated measured c(x) well; the FEM is useful for study of mechanisms, experimental designs and AM errors; trends of AM parameter estimates suggest dependence on P, z and composition of reagent for further FEM and experimental study.

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