Uncertainty quantification and control of kinetic models of tumour growth under clinical uncertainties

TL;DR

This paper develops a kinetic model for tumour growth incorporating clinical uncertainties, demonstrating how control strategies can reduce variability in tumour size despite data scarcity and measurement errors.

Contribution

It introduces a novel kinetic modeling approach for tumour growth under uncertainty and proposes control methods to mitigate variability caused by clinical uncertainties.

Findings

Control strategies effectively reduce tumour size variability.

Uncertainty quantification methods are suitable for kinetic tumour models.

Empirical parameter distributions are calibrated from real glioblastoma cases.

Abstract

In this work, we develop a kinetic model of tumour growth taking into account the effects of clinical uncertainties characterising the tumours' progression. The action of therapeutic protocols trying to steer the tumours' volume towards a target size is then investigated by means of suitable selective-type controls acting at the level of cellular dynamics. By means of classical tools of statistical mechanics for many-agent systems, we are able to prove that it is possible to dampen clinical uncertainties across the scales. To take into account the scarcity of clinical data and the possible source of error in the image segmentation of tumours' evolution, we estimated empirical distributions of relevant parameters that are considered to calibrate the resulting model obtained from real cases of primary glioblastoma. Suitable numerical methods for uncertainty quantification of the resulting kinetic equations are discussed and, in the last part of the paper, we compare the effectiveness of the introduced control approaches in reducing the variability in tumours' size due to the presence of uncertain quantities.