A note on appropriate constraints on the initial input response when applying deconvolution.

Abstract

When deconvolution is employed to estimate cumulative input profiles, nonzero initial values may result unless certain constraints are imposed on the function used to approximate the input response c(t). It is shown that the initial value of the response to a nonimpulse input is zero, i.e., c(t0) = 0, where t0 is the input lag time. If, in addition, the initial value of the impulse response is zero, i.e., c delta (0) = 0, then c'(t0) = 0. Therefore, it is appropriate to impose the constraint c(t0) = 0 in general and c'(t0) = 0 when c delta (0) = 0 if c(t) is the response to a nonimpulse input. The use of such constraints is demonstrated in an example where the cumulative in vivo dissolution profile is estimated by deconvolution.