[Biomathematical aspects of numerical evaluation and mathematical modelling of non-monotonous exponential measuring processes].

Measurements of endocrinological and pharmacological processes often yield courses of time series with exponentially saturated increasing first part followed by an exponentially decreasing part. Such measured courses may be mathematically modelled by the so-called BATEMAN function type, an expression consisting of 2 e-function terms. In this paper, the method of locally adjusted functional approximation for model-free quantitative evaluation of measured time series is sketched. By means of 2 real examples of measured data, it will be demonstrated how the results of the model-free evaluation may serve for internal regression to estimate starting parameter values for an iterative fitting of a BATEMAN function to measured data courses. Furthermore, it is shown that the model-free approach of data evaluation may give substantial hints for the mathematical model building process and for model verification.