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12 June 2023
Abstract:Dynamical systems are often expressed in either continuous or discrete time. Some biomedical processes are however more suitably modeled as impulsive systems, which combine continuous dynamics with abrupt changes of the state of the system. This thesis concerns two such systems: the pharmacokinetics of the anti-Parkinson's drug levodopa, and the testosterone regulation in the human male. Despite the differences between these systems, they can be modeled in similar ways. Modeling entails not only the model, but also the methods used to estimate its parameters. Impulsive dynamics can enable simpler representations compared with using continuous dynamics alone, but may also complicate the estimation procedure, since standard techniques often cannot be used. The contributions of this thesis are therefore both in model development and parameter estimation.
Model development is the topic of Paper I. It presents a model of the multi-peaking phenomenon in levodopa pharmacokinetics, which is manifested by secondary concentration peaks in the blood concentration profile of the drug. The remaining papers focus on estimation, in a setup where a sequence of impulses is fed to a linear plant, whose output is measured. Two estimation techniques are considered. The first is presented in Paper II and uses a Laguerre domain representation to estimate the timing and weights of the impulses. The second combines estimation of the impulsive input with estimation of the plant parameters, which represent the elimination rates of testosterone-regulating hormones. This problem is particularly challenging since increasing the estimated elimination rates and the number of impulses generally improves the model fit, but only models with sparse input signals are practically useful. Paper III addresses this issue through a novel regularization method. The uncertainties in model and measurements encountered when working with clinical hormone data add another layer of complexity to the problem; methods for handling such issues are described in Paper IV.
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