Stability of finite difference deconvolution I: theoretical analysis

Analysis of the stability of finite difference deconvolution (FDD) shows that it is dependent on the characteristics of the unit impulse response function and the sampling schedule of the input response function, and that stability properties are improved when the cumulative amount function is directly estimated rather than the rate function. The estimated input rate for an intravenous (iv) unit impulse response function and the release rate for an oral solution unit impulse response function are unstable for any sampling schedule of the input response function. However, for an iv unit impulse response function, the estimated cumulative amount absorbed is stable for any sampling schedule of the response function. For an oral unit impulse response function, the estimated cumulative amount released is unstable for all the sampling points of the input response function located before the time of the maximum of the oral unit impulse response function, but it can be made stable if an appropriately designed sampling schedule of the input response function is used. In addition, the theoretical basis for choosing a sampling schedule to overcome the instability of FDD has been established.