Mathematical models of arterial transmural transport

Abstract

A finite-element model (FEM) and corresponding five-parameter analytical model (AM) were derived to study the one-dimensional transport of chemically reactive macro-molecules 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 1) intimal-medial a(x) associated with molecular sieving and medial edema, 2) reversible binding, and 3) errors of AM in analysis of c(x). Results are as follows. Average relative error for the 28 AM fits was 5.3%. Only estimates of DA and nu A had acceptable coefficients of variation. DA (approximately 0.10 X 10(-7) cm2 X s-1) decreased with P, increased with z to a maximum, and then decreased; nu A was approximately proportional to P (approximately 0.12 X 10(-7) cm X s-1 X 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 approximately 1.4% error in AM c(x). Parameter estimates were sensitive to wall inhomogeneity, e.g., approximately 15% error. In conclusion, the AM and FEM simulated 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.