Automatic smoothing can be overridden by manually setting the smoothing parameter or smoothing can be turned off. In this case, the input rate function consists of the precursor function alone.
Besides controlling the degree of smoothing, the initial behavior of the estimated input time course can be influenced. In particular, the initial input rate can be constrained to zero (f(0)=0) and/or the initial change in the input rate can be constrained to zero (f'(0)=0). By default, Phoenix does not constrain either initial condition. Leaving f(0) unconstrained permits better characterization of formulations with rapid initial “burst release,” that is, extended release dosage forms with an immediate release shell. This is done by optionally introducing a bolus component or “integral boundary condition” for the precursor function so the input function becomes:
where the fp(t)*fd(t) is defined as before.
The difference here is the superposition of the extra term xd fd(t) that represents a particularly smooth component of the input. The magnitude of this component is determined by the scaling parameter xd, which is determined in the same way as the other wavelet scaling parameters previously described.
The estimation procedure is not constrained with respect to the relative magnitude of the two terms of the composite input function given above. Accordingly, the input can “collapse” to the “bolus component” xd fd(t) and thus accommodate the simple first-order input commonly experienced when dealing with drug solutions or rapid release dosage forms. A drug suspension in which a significant fraction of the drug may exist in solution should be well described by the composite input function option given above. The same may be the case for dual release formulations designed to rapidly release a portion of the drug initially and then release the remaining drug in a prolonged fashion. The prolonged release component will probably be more erratic and would be described better by the more flexible wavelet-based component fp(t)*fd(t) of the above dual input function.
Constraining the initial rate of change to zero (f'(0)=0) introduces an initial lag in the increase of the input rate that is more continuous in behavior than the usual abrupt lag time. This constraint is obtained by constraining the initial value of the precursor function to zero (fp(0)=0). When such a constrained precursor is convolved with the dispersion function, the resulting input function has the desired constraint.