Reparameterization to implementing kinetic constraints in pharmacokinetics.

Polyexponential expressions are widely used in pharmacokinetic system analysis to represent various functions and pharmacokinetic responses. It is often necessary to impose simple constraints (e.g., non-negativity, monotonicity, etc.) to make such expressions agree with obvious kinetic conditions or general assumptions made. Enforcement of such constraints is typically obtained by specifying upper and/or lower limits for the polyexponential parameters in the curve fitting procedure. However, this method often limits the search to only a subset of all possible polyexponentials expressions which satisfy the specified constraints. A less restricted search may be performed by not specifying a lower or upper limit on some polyexponential parameters, but this may occasionally result in violations of the constraints. A reparameterization approach is presented to overcome the above problems. Various schemes are presented that allow a completely unrestricted search to be done among all possible polyexponential expressions which satisfy various constraint configurations. The practical significance of this approach is discussed and demonstrated with some examples. It is pointed out that evaluation of various pharmacokinetic processes in the context of specific models or families of models may intrinsically impose certain constraints that may not be justified when the kinetics is analyzed in a more general system analysis context. The application of system analysis principles in conjuction with an enforcement of functional constraints in a "model-free" context by reparameterization appears to be a rational alternative to current methods.