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

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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 δ(0)=0,then c′(t0)=0.Therefore, it is appropriate to impose the constraint c(t0)=0in general and c′(t0)=0when c δ(0)=0if c(t)is the response to a nonimpulse input. The use of such constraints is demonstrated in an example where the cumulative in vivodissolution profile is estimated by deconvolution.