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M. Kozek, N. Jovanovic:
"Parameter-Linear Modeling of Non-Linear Pharmacodynamics";
Talk: 3rd Conference on Modeling and Simulation in Biology, Medicine and Biomedical Engineering, Balamand, Lebanon; 2003-05-28 - 2003-05-30; in: "Proceedings of the 3rd Conference on Modeling and Simulation in Biology, Medicine and Biomedical Engineering", (2003), 6 pages.

Pharmacodynamics are often modeled by a sigmoid dose-response
curve which in turn is described by the Hill-equation. Although
this equation uses only two non-linear parameters, for the purpose
of parameter estimation a parameter-linear model is desirable to
ensure convergence and global optimality. In this work several
realizations of non-linear, mixed, and purely linear models are
discussed, and a simple and versatile piece-wise linear static map
is proposed as a good compromise between computational effort of
parameter estimation and prediction accuracy. Without using
algebraic constraints this linear description is tailored to fit
sigmoid dose-response curves and the performance is compared to
nonlinear or mixed methods.