An algorithm for constrained deconvolution based on reparameterization.

The method of deconvolution is the most general method of evaluating drug absorption. Deconvolution does not normally subscribe to a particular structured model for the input function that would ensure non-negativity of the calculated input rate. Unfortunately, the increased flexibility gained by this "model independence" sometimes results in a calculated input rate that becomes negative in the late absorption phase. A method for constrained deconvolution is proposed to overcome this deficiency. The method is based on a reparameterization of the input function in a "model-free" context. The reparameterization schemes proposed are optimal in the sense that they give the input function its maximum flexibility possible while at the same time ensuring non-negativity. The method makes use of "deconvolution through convolution." The basic procedure of this technique is, during the curve fitting, to iteratively adjust the input function so that when it is convolved with the unit impulse response function it results in a curve that best fits the data from the extravascular administration. Cimetidine data from oral and iv administrations are deconvolved by the proposed method to demonstrate the basic procedures involved. The proposed method is easy to implement since it relies on simple curve-fitting procedures as routinely performed in pharmacokinetics. The procedure can be carried out using any of the many curve-fitting programs available that allow the user to supply the function to be fitted and allow simple bounds to be specified for the fitted parameters. The convolution required by the method can be done analytically using a previously published computer program.