PC-based differential model fitting as a support for clinical research

A PC-based minimisation software written in C-language is described, which solves numerically both simple non-linear regression problems and problems expressed as systems of (unsolved) initial-value ordinary or partial differential equations. The software uses second-order iterated Runge-Kutta algorithm to approximate numerically the solution curves. It uses a quasi-Newton algorithm to minimize either sums of squares (weighted or unweighted) or NONMEM loss functions. Inverse Hessian approximation to the parameter dispersion and Monte Carlo generation of artificial samples are offered to test the robustness of the parameter values obtained. A real test problem is described, involving the hydrolysation of plasma Medium Chain Triglycerides to Free Fatty Acids and the uptake of these from plasma. Two competing models were evaluated, one involving linear terms for each transfer and one involving carrier-mediated, rate-limited hydrolysis and tissue absorption steps. The simpler linear model was found to be more robust and eventually used to describe the experimental data.