Dynamic models with quantized output for modeling patient response to pharmacotherapy

This article presents a way of modeling patient response to a pharmacotherapy by means of dynamic models with quantized output. The proposed modeling technique is exemplified by treatment of Parkinson´s disease with Duodopa ^®, where the drug is continuously administered via duodenal infusion. Titration of Duodopa ^® is currently performed manually by a nurse judging the patient´s motor symptoms on a quantized scale and adjusting the drug flow provided by a portable computer-controlled infusion pump. The optimal drug flow value is subject to significant inter-individual variation and the titration process might take up to two weeks for some patients. In order to expedite the titration procedure via automation, as well as to find optimal dosing strategies, a mathematical model of this system is sought. The proposed model is of Wiener type with a linear dynamic block, cascaded with a static nonlinearity in the form of a non-uniform quantizer where the quantizer levels are to be identified. An identification procedure based on the prediction error method and the Gauss-Newton algorithm is suggested. The datasets available from titration sessions are scarce so that finding a parsimonious model is essential. A few different model parameterizations and identification algorithms were initially evaluated. The results showed that models with four parameters giving accurate predictions can be identified for some of the available datasets.