Uncertainty quantification and control of kinetic models of tumour growth under clinical uncertainties. (May 2022) - Medaglia, A.; Colelli, G.; Farina, L.; Bacila, A.; Bini, P.; Marchioni, E.; Figini, S.; Pichiecchio, A.; Zanella, M.
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. Highlights: New kinetic model for tumour growth with clinical uncertainties. The action of therapeutic protocols steers the tumours' volume towards a target size. The introduced therapies reduce the variability due to uncertain quantities. Calibration of the model based on MRI scans. Examples based on UQ methods for kinetic equations.