Optimal design of experiments to estimate LDL transport parameters in arterial wall

Abstract

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 optimized 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.