Spatial modelling of tumour drug resistance: the case of GIST liver metastases Mathematical Medicine and Biology Advance

Guillaume Lefebvre 1, 2 François Cornelis 3, 1 Patricio Cumsille 4, 5, 6 Thierry Colin 1, 2 Clair Poignard 1, 2 Olivier Saut 1, 2
1 IMB - Institut de Mathématiques de Bordeaux
2 MONC - Modélisation Mathématique pour l'Oncologie
IMB - Institut de Mathématiques de Bordeaux, Inria Bordeaux - Sud-Ouest, Institut Bergonié - CRLCC Bordeaux
3 CHU de Bordeaux Pellegrin [Bordeaux]
4 CeBiB - Centre for Biotechnology and Bioengineering [Santiago]
5 GIANT - Group of investigation in tumor angiogenesis [Concepción]
Department of Basic Sciences [Concepción]
6 GMA - Group of applied mathematics [Concepción]
Department of Basic Sciences [Concepción]
Abstract : This work is devoted to modelling gastrointestinal stromal tumour metastases to the liver, their growth and resistance to therapies. More precisely, resistance to two standard treatments based on tyrosine kinase inhibitors (imatinib and sunitinib) is observed clinically. Using observations from medical images (CT scans), we build a spatial model consisting in a set of non-linear partial differential equations. After calibration of its parameters with clinical data, this model reproduces qualitatively and quantitatively the spatial tumour evolution of one specific patient. Important features of the growth such as the appearance of spatial heterogeneities and the therapeutical failures may be explained by our model. We then investigate numerically the possibility of optimizing the treatment in terms of progression-free survival time and minimum tumour size reachable by varying the dose of the first treatment. We find that according to our model, the progression-free survival time reaches a plateau with respect to this dose. We also demonstrate numerically that the spatial structure of the tumour may provide much more insights on the cancer cell activities than the standard RECIST criteria, which only consists in the measurement of the tumour diameter. Finally, we discuss on the non-predictivity of the model using only CT scans, in the sense that the early behaviour of the lesion is not sufficient to predict the response to the treatment.
Keywords : tumour growth modelling partial differential equations cancer drug resistance tumour heterogeneity
Type de document :
Article dans une revue
Mathematical Medicine and Biology, Oxford University Press (OUP), 2016, 00, pp.1 - 26. 〈10.1093/imammb/dqw002〉
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Guillaume Lefebvre, François Cornelis, Patricio Cumsille, Thierry Colin, Clair Poignard, et al.. Spatial modelling of tumour drug resistance: the case of GIST liver metastases Mathematical Medicine and Biology Advance. Mathematical Medicine and Biology, Oxford University Press (OUP), 2016, 00, pp.1 - 26. 〈10.1093/imammb/dqw002〉. 〈hal-01380292〉

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