A method for computing the derivative of noisy time-activity curves and its application to radioisotope dynamic analysis.

A method for computing the slope or the derivative of time-activity curves containing statistical fluctuations is described. The algorithm presented employs digital differentiation as a digital filter. In designing an effective differentiating filter the Chebyshev-type min-max method and Remez exchange algorithm are used to minimise the weighted Chebyshev error. The validity of this method has been investigated using computer-based Monte Carlo simulation. Renogram curve analysis is presented as an example of an application of this method to radioisotope dynamic analysis. The ratio of the bilateral slopes of the renogram's second segments estimated using this method correlated well with the renal plasma flow ratio (r = 0.97, n = 16). The functional images of the slope of the renogram's second segments have been constructed and ascertained to be clinically useful. This method is considered to provide a powerful tool for extraction of quantitative information both in research and in routine nuclear medicine clinical work, and may be useful in various other fields.