Computational Modelling of Metastasis Development in Renal Cell Carcinoma

The biology of the metastatic colonization process remains a poorly understood phenomenon. To improve our knowledge of its dynamics, 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 that translates this assumption into equations, we challenged this 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. Critically, when calibrated on the growth of the primary tumour and total metastatic burden, the predicted theoretical size distributions were not in agreement with the MRI observations. Moreover, tumour expansion only based on proliferation was not able to explain the volume increase of the metastatic lesions. These findings strongly suggested rejection of the standard theory, demonstrating that the time development of the size distribution of metastases could not be explained by independent growth of metastatic foci. This led us to investigate the effect of spatial interactions between merging metastatic tumours on the dynamics of the global metastatic burden. We derived a mathematical model of spatial tumour growth, confronted it with experimental data of single metastatic tumour growth, and used it to provide insights on the dynamics of multiple tumours growing in close vicinity. Together, our results have implications for theories of the metastatic process and suggest that global dynamics of metastasis development is dependent on spatial interactions between metastatic lesions.Author Summary: We used mathematical modelling to formalize the standard theory of metastatic initiation, under which secondary tumours, after establishment in a distant organ, grow independently from each other and from the primary tumour. When calibrated on the experimental data of primary tumour and total metastatic burden in the lungs in an animal model of renal cell carcinoma, the initial model predicted a size distribution of metastatic foci that did not fit with observations obtained experimentally using magnetic resonance imaging (which provided size and number of macro-metastases). The model predicted an increase in the number of lesions, but of smaller size when compared to the data. This led us to revise the standard theory and to propose two hypotheses in order to explain the observations: 1) small metastatic foci merge into larger ones and/or 2) circulating tumour cells may join already established tumours. We then derived a spatial model of tumour growth in order to explore the quantitative implications of tumours merging on global tumour growth and estimated the numbers of required metastatic foci to obtain the observed metastatic volumes.