METAMATS_CORE

This code is devoted to the simulation of a partial differential equation (PDE) based model for the time development of a population of secondary tumors (metastases) [1, 2].

Features

• Size-structured transport PDE for metastatic development
• Customizable growth and dissemination laws
• Metastases from metastases (or not)
• Multiple characteristic traits for tumors (e.g. vascular capacity and angiogenic development) [3, 4]
• Effect of therapy (cytotoxics and/or anti-angiogenics) on metastatic growth [5, 6]
• Systemic interactions between tumors (possibly from angiogenic inhibition) [7, 8]

Languages

• Matlab: fully developed version
• Python: only minimal version

References:

[1] Iwata, K., Kawasaki, K., & Shigesada, N. (2000). A Dynamical Model for the Growth and Size Distribution of Multiple Metastatic Tumors. Journal of Theoretical Biology, 203(2), 177–186. http://doi.org/10.1006/jtbi.2000.1075

[2] Benzekry, S., Tracz, A., Mastri, M., Corbelli, R., Barbolosi, D., & Ebos, J. M. L. (2016). Modeling Spontaneous Metastasis following Surgery: An In Vivo-In Silico Approach. Cancer Research, 76(3), 535–547. http://doi.org/10.1158/0008-5472.CAN-15-1389

[3] Benzekry, S. (2011). Mathematical analysis of a two-dimensional population model of metastatic growth including angiogenesis. Journal of Evolution Equations, 11(1), 187–213.

[4] Benzekry, S. (2012). Passing to the limit 2D–1D in a model for metastatic growth. J Biol Dynam, 6(sup1), 19–30.

[5] Benzekry, S. (2012). Mathematical and numerical analysis of a model for anti-angiogenic therapy in metastatic cancers. ESAIM: Mathematical Modelling and Numerical Analysis, 46(2), 207–237.

[6] Benzekry, S., André, N., Benabdallah, A., Ciccolini, J., Faivre, C., Hubert, F., & Barbolosi, D. (2012). Modelling the impact of anticancer agents on metastatic spreading. Mathematical Modelling of Natural Phenomena, 7(1), 306–336.

[7] Benzekry, S., Gandolfi, A., & Hahnfeldt, P. (2014). Global Dormancy of Metastases Due to Systemic Inhibition of Angiogenesis. PLoS ONE, 9(1), e84249–11. http://doi.org/10.1371/journal.pone.0084249

[8] Benzekry, S., Gandolfi, A., & Hahnfeldt, P. (2014). A mathematical model of systemic inhibition of angiogenesis in metastatic development. ESAIM: Proceedings and Surveys, 45, 75–87. http://doi.org/10.1051/proc/201445008