Mathematical Models for Optimisation of Drug Administration in Intensive Care Units

Finazzi, Stefano (2019). Mathematical Models for Optimisation of Drug Administration in Intensive Care Units. PhD thesis The Open University.



Clinical status of critically ill patients is often extreme and rapidly evolving. Hence, pharmacological therapies must be tailored to patients' characteristics and adapted according to the evolution of their clinical pictures. To identify optimal personalized treatments, possible scenarios produced by different therapeutic choices must be predicted and compared. This process requires complex analyses involving the development of appropriate mathematical models.

In this Thesis, I focused on two important aspects of the pharmacological treatment of critically ill patients: the administration of antimicrobial drugs and the control of their glycaemic level. Although these problems are clinically very different, the modelling of their pathophysiological mechanisms can be addressed with similar tools.

I performed analyses based on retrospective clinical data collected with MargheritaTre, an electronic health record developed by GiViTI. The software to synchronize databases from hospitals to our laboratory and to preprocess data for analyses was written for the purpose of this Thesis.

Starting from the study of the physiological mechanisms at the basis of vancomycin pharmacokinetics I constructed a model to describe the evolution of the plasma concentration of this drug in critically ill patients. Compartment models were fitted on a sample of 141 patients, testing about 30 patient covariates and several functional dependencies for each variable.

Glucose dynamics were described through a system of delay differential equations reproducing intake, uptake and endogenous production of glucose, and organ-organ interactions mediated by hormones. Existing models, describing only the dynamics of glucose and insulin, fail to reproduce the correct evolution when glucose concentrations vary too rapidly. I improved these models, by introducing an equation describing glucagon dynamics and taking into account its effect on glucose metabolism. I investigated the dynamical properties of my model with analytical analyses, numerical simulations and fitting it to observed data.

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