Theory and modeling for cancer biology

Participants: Thierry Colin, Olivier Saut, Clair Poignard, Sébastien Benzekry, Etienne Baratchart.

Biology labs involved:
Center of Cancer Systems Biology, TUFTS University School of Medicine, Boston, directed by Lynn Hlatky
Angiogenesis and cancer microenvironment laboratory, Inserm, Bordeaux, directed by the Pr Andreas Bikfalvi.

In order to gain biological understanding of complex phenomena, we develop theoretical mathematical models for various processes of cancer biology such as avascular and vascular tumor growth but also development of a cancer disease at the organism level, integrating the metastatic process, which represents the major cause of death in a cancer disease (90%). These models yield insights about various topics including anti-angiogenic therapies, metastatic dormancy or post-surgery metastatic acceleration.


Theoretical models of tumor growth
In a series of work together with B. Ribba and E. Grenier we have introduced a generic PDE (partial differential equations) model for tumor growth. The models were designed for both vascular and avascular stages. The model is based on the description of the development of populations of cells. We consider proliferative cells, quiescent cells and healthy tissues. The proliferative cells undergo a cell cycle that is regulated by various biological processes such as hypoxia or overcrowding. The distribution of oxygen depends on a vascular network that is obtained through an angiogenesis model that describes proliferation and migration of endothelial cells according to chemotaxis phenomena regulated by secretion of several pro- and anti-angiogenic factors (VEGF, PDGF, angiostatin, angiopoietin,…). Interaction with the extracellular matrix and influence of metalloproteinases are also considered. Several mechanical aspects have been investigated (visco-elasticity, elasticity of membranes, Darcy's law, …). Eventually, we have also tested the influence of several treatments (radiotherapy, chemotherapy, anti-angiogenic drugs, inhibitors of MMP...). The model has been implemented in a 3D framework in C++ in the platform developed by O. Saut. More details can be found in the following publications:

F. Lignet, S. Benzekry, S. Wilson, F. Billy, O. Saut, M. Tod, B. You, A. Adda Berkane, S. Kassour, M.X. Wei, E. Grenier, B. Ribba, Theoretical investigation of the efficacy of antiangiogenic drugs combined to chemotherapy in xenografted mice, Journal of Theoretical Biology, Volume 320, pp. 86-99, 2013
D. Bresch, T. Colin, E. Grenier, B. Ribba, O. Saut A viscoelastic model for avascular tumor growth, DCDS Supplements, 101-108, Volume 2009, Issue : Special, september 2009.
F. Billy, B. Ribba, O. Saut, H. Morre-Trouilhet, Th. Colin, D. Bresch, J.-P. Boissel, E. Grenier, J.-P. Flandrois, A pharmacologically-based multiscale mathematical model of angiogenesis, and its use in analysing the efficacy of a new anti-cancer treatment strategy. Journal of Theoretical Biology, vol. 260, Issue 4, 21 October 2009, Pages 545-562.
Billy F., Saut O., Morre-Trouilhet H., Colin T., Bresch D., Ribba B., Grenier E. Modèle mathématique multi-échelle de l'angiogenèse tumorale et application à l'analyse de l'efficacité de traitements anti-angiogéniques. Bull Cancer, mars 2008 ; vol.95, numéro spécial : 65.
D. Bresch, T. Colin, E. Grenier, B. Ribba, O. Saut, Computational modeling of solid tumor growth: the avascular stage, SIAM J. SCI. COMPUT. Vol. 32, No. 4, pp. 2321–2344, 2010.
B. Ribba, Th. Colin, S. Schnell, A multi-scale mathematical model of cancer growth and radiotherapy efficacy: The role of cell cycle regulation in response to irradiation, Theoretical Biology and Medical Modeling 2006, 3:7 (10 Feb 2006).
B. Ribba, O. Saut, T. Colin, D. Bresch, E. Grenier, J.P. Boissel, A multi-scale mathematical model of avascular tumor growth to investigate the therapeutic benefit of anti-invasive agents, Journal of Theoretical Biology 243 (2006) 532–541.
D. Bresch, Th. Colin, E. Grenier, B. Ribba, O. Saut, O. Singh and C. Verdier, Quelques méthodes de paramètre d'ordre avec applications à la modélisation de processus cancéreux, ESAIM:proc, vol. 18, 2007.


Metastatic dynamics and tumor-tumor interactions
In collaboration with the Center of Cancer and Systems Biology in Boston (in particular with Philip Hahnfeldt), we study angiogenic tumor-tumor interactions and the implications for global dynamics of a cancer disease combining biological experiments and quantitative modeling. Indeed, tumors are known to relase in the circulation anti-angiogenic molecules that provoke Systemic Inhibition of Angiogenesis (SIA) and collectively suppresses the growth of all lesions. Models are written at the organism scale, taking into account both primary and secondary tumors (metastases). Clinical and biological implications of the SIA theory for metastatic global dormancy ("Cancer without disease") and possible acceleration of metastatic growth after removal of a primary lesion are derived.

Model for systemic inhibition of angiogenesis and simulation reproducing an experiment with resection or not of primary tumor when it reaches 1500 mm3. Size distribution of the metastases at the end shows growth acceleration of preexisting metastases.

Pre-metastatic niche
Based on biological experiments performed in the Angiogenesis and cancer microenvironment laboratory, we try to formalize into a mathematical model the theory of the pre-metastatic and metastatic niche. These are newly discovered biological processes by which a pre-established primary tumor prepares the soil in distant organs for seeding of migratory cells that develop into metastases. Activation of distant stroma such as fibroblast cells is thought to be mediated by bone-marrow derived cells recruited by cytokines emitted by the primary tumor. By establishing and validating a mathematical model, we want to identify critical players in this phenomenon in order to help to develop anti-metastatic strategies.

Left: Schematic representation of pre-metastatic nich formation. From Peinado, Lavotshkin and Lyden, The secreted factors responsible for pre-metastatic niche formation: old sayings and new thoughts, Seminars in Cancer Biology, 2011.
Right: Microscopy image of stained lung tissue. Blue fluorescence stains for cells nuclei (DAPI) and green fluorescence for granulocytes.