Computational modelling of metastasis development in renal cell carcinoma 

Etienne Baratchart 1, 2 Sébastien Benzekry 1, 2, * Andreas Bikfalvi 3, * Thierry Colin 1, 4, 2, * Lindsay S. Cooley 3 Raphäel Pineau 3 Emeline Ribot 5 Olivier Saut 1, 2 Wilfried Souleyreau 3 

* Corresponding author

1 MONC - Modélisation Mathématique pour l'Oncologie 

IMB - Institut de Mathématiques de Bordeaux, INRIA Bordeaux - Sud-Ouest, Institut Bergonié - CRLCC Bordeaux

2 IMB - Institut de Mathématiques de Bordeaux 

3 LAMC - Laboratoire Angiogenèse et Micro-environnement des Cancers 

4 UB - Université de Bordeaux 

5 RMSB - Résonance magnétique des systèmes biologiques 

Abstract : To improve our understanding of the biology of the metastatic colonization process, we conducted a modelling study based on multi-modal data from an orthotopic murine experimental system of metastatic renal cell carcinoma. The standard theory of metastatic colonization usually assumes that secondary tumours, once established at a distant site, grow independently from each other and from the primary tumour. Using a mathematical model describing the metastatic population dynamics under this assumption, we challenged the theory against our data that included: 1) dynamics of primary tumour cells in the kidney and metastatic cells in the lungs, retrieved by green fluorescent protein tracking, and 2) magnetic resonance images (MRI) informing on the number and size of macroscopic lesions. While the model could fit the primary tumour and total metastatic burden, the predicted size distribution was not in agreement with the MRI observations. Moreover, the model was incompatible with the growth rates of individual metastatic tumours. To explain the observed metastatic patterns, we hypothesised that metastatic foci derived from one or a few cells could aggregate, resulting in a similar total mass but a smaller number of metastases. This was indeed observed in our data and led us to investigate the effect of spatial interactions on the dynamics of the global metastatic burden. We derived a novel mathematical model for spatial tumour growth, where the intra-tumour increase in pressure is responsible for the slowdown of the growth rate. The model could fit the growth of lung metastasis visualized by magnetic resonance imaging. As a non-trivial outcome from this analysis, the model predicted that the net growth of two neighbouring tumour lesions that enter in contact is considerably impaired (of 31% ± 1.5%, mean ± standard deviation), as compared to the growth of two independent tumours. Together, our results have implications for theories of metastatic development and suggest that global dynamics of metastasis development is dependent on spatial interactions between metastatic lesions.

https://hal.inria.fr/hal-01164834