A system approach to pharmacodynamics. III: An algorithm and computer program, COLAPS, for pharmacodynamic modeling

Many pharmacodynamic (PD) models may be generalized in the form E(t) = N(L[c(t)]), where E(t) is a recorded effect response, c(t) is a sampled drug level, N is a nonlinear autonomic function, and L is a linear operator that commonly is a convolution operation. The NL class of PD models includes the traditional effect compartment PD models as a subclass, but is not limited to such models. An algorithm and computer program named COLAPS, based on system analysis principles and hysteresis minimization, that enable N and L to be empirically determined for the NL class of models without addressing specific kinetic structure aspects ("model independence") are presented. The kinetic concepts of biophase conduction and transduction functions are used by COLAPS. Such an approach is more general than the effect compartment approaches because it does not assume first-order transport principles. The pitfalls of hysteresis minimization in PD modeling are discussed and the procedures taken by COLAPS to avoid these pitfalls are outlined. A transformation technique prevents improper convergence to a point. A novel reparameterization scheme is introduced that maximizes the flexibility of the kinetic functions and extends the generality of the analysis. Inequality function constraints are maintained without the need for troublesome constrained nonlinear optimization procedures. Usage of the COLAPS program is illustrated in the analysis of the PD of amobarbital. The COLAPS program resulted in an excellent minimization of the effect versus biophase level hysteresis. The biophase conduction function, the biophase drug level (normalized), and the transduction curve were determined. The transduction curve showed clear biphasic behavior.