Optimal design of experiments to estimate LDL transport parameters in arterial wall EVAN D. MORRIS, GERALD M. SAIDEL, AND GUY M. CHISOLM III Department of Biomedical Engineering, Case Western Reserve University, and Department of Vascular Cell Biology and Atherosclerosis Research, Cleveland Clinic Foundation, Cleveland, Ohio 44195 MORRIS, EVAN D., GERALD M. SAIDEL, AND GUY M. CHISOLM III. Optimal design of experiments to estimate LDL transport parameters in arterial wall Am. J. Physiol. 261 (Heart Circ. Physiol. 30): H929-H949, 1991.-To quantify transport processes in atherosclerosis, the arterial wall is often exposed to labeled lipoproteins. In vivo experiments are desirable for estimation of transport parameters, but they are technically difficult. A dynamic mass transfer model has been developed to describe experimental transmural profiles of lipoprotein accumulation as a function of luminal permeability, diffusion, convection, and degradation. To avoid extraneous experiments and to assure successful parameter estimation, an optimal design of experiments is needed. For our purposes a design was considered optimal when it maximized the sensitivity of the model output to changes in parameter values as indicated by the determinant of the Hessian matrix of the objective function. A comparison was made between two designs: dual-time designs prescribing unequal circulation times for two distinguishable injections of labeled low-density lipoprotein (LDL) and dual- species designs requiring simultaneous circulation of LDL and tyramine-cellobiose-modified LDL. Circulation time was opti- mized for both designs. Although both were heavily dependent on the circulation times, dual-time designs required better preliminary knowledge of parameter values. Because labeled degradation products of the modified tracer become anchored in the arterial tissue, information about the degradation process is retained in the dual-species study. For this reason, dual- species designs were generally superior to dual-time designs. low-density lipoprotein; tyramine-cellobiose; mathematical model; spatial distribution; parameter estimation; sensitivity analysis; optimal experiment design ATHEROSCLEROSIS is accompanied by an excessive ac- cumulation of plasma low-density lipoprotein (LDL) in the extracellular spaces of major arteries (20). Arteries are lined on the luminal surface of the intima by the one- cell-thick endothelium and are bounded on the abluminal side of the media by vascularized adventitia (Fig. 1). The accumulation of LDL, which accompanies atherosclero- sis, occurs primarily in the intima and inner media of the vessels (34). To examine events related to athero- sclerosis, investigators have studied the uptake and dis- tribution of injected tracer macromolecules (e.g., LDL) by the arteries of experimental animals. Analysis of data from such experiments requires the use of mathematical models of the processes governing transport of macro- molecules in arterial tissue. Mathematical models have been developed and applied to data from tracer studies performed on arteries both in vivo and in vitro (6, 13, 39, 43). To describe and analyze data from in vivo experiments, compartmental models have been used (7) that quantify exchange rates of tracers between plasma and tissue compartments without regard to transport processes within the compartments. An inherent assumption in these models is that the com- partments are well mixed (17). To describe transport processes affecting tracer behavior within the tissue, investigators have used spatially distributed models (16). Models have included such mechanisms as filtration of large molecules by the internal elastic lamina (14) or infrequent “holes” in the endothelium (41,43) to explain the pathological accumulation of LDL in the subendo- thelial space. The spatially distributed model used in the present study is an extension of models proposed previ- ously by us (21, 30) and by others (6, 16, 39, 40). An eventual objective of these studies is to estimate the parameters of interest depicted in our model and to evaluate the relative significance of the corresponding processes. In a mechanistic mass transport model, parameters characterize physiological processes. Parameters are evaluated by estimation algorithms that give the best fit of model-predicted simulations to experimental data. In our system, the data consist of concentration profiles of the tracer across the wall of the rabbit aorta from lumen to adventitia. They are obtained after intravenous injec- tion and circulation of the tracer in the plasma for a specified time. The profile of radioactivity across the artery wall that results from an injection of LDL labeled with radioactive iodine (“I-LDL) consists of the intact, undegraded *I-LDL at each point in the tissue. A com- mon limitation of this approach is that the data are not sufficient to assure precise estimates of all important parameters (13, 40). Factors that reduce precision are variability of biological tissue samples, small signal-to- noise ratio of the lower tracer concentrations, and overly 0363-6135/91 $1.50 Copyright 0 1991 the American Physiological Society H929