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Mathematical model of endothelial cell proliferation and maturation

Piotr Bajger;  Mariusz Bodzioch — 2018

Mathematica Applicanda

Blood vessel sprouting (angiogenesis) is one of the hallmarks of cancer. Better quantitative understanding of this process would allow more effective antiangiogenic therapies to be developed. It has been hypothesised that not only the number of endothelial cells, but also the quality of the vasculature play an important role in how chemo- and radiotherapies are delivered to tumour site. Hence in this study a minimally-parametrised mathematical model of endothelial cell proliferation and maturation...

Optimal Control in a Model of Chemotherapy-induced Radiosensilisation

Piotr Bajger;  Krzysztof Fujarewicz;  Andrzej Świerniak — 2019

Mathematica Applicanda

  In this work, we consider a simple mathematical model of radiochemotherapy which includes a term responsible for radiosensitization. We focus on finding theoretically optimal controls which maximise tumour cure probability for a finite, fixed therapeutic horizon. We prove that the optimal controls for both therapies are of 0-bang type, a result which is not altered by the inclusion of the radiosensilization term. By means of numerical simulations, we show that optimal control offers a moderate...

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