New Mexico Supercomputing Challenge

Modeling the Metastatic Process

Team: 43

School: Las Cruces YWiC

Area of Science: Biology


Interim: Mathematical and computational models of metastasis promise to make predictions in regards to tumor stage and movement through the body where imaging fails, hopefully increasing the quality of care for cancer patients. We aim to create such a model.


Aside from extensive background research familiarizing ourselves with the basis of cancer and metastasis on the molecular level, we investigated several possible models for the problem we aimed to solve ,ultimately deciding to work with a partial differential equation model of tumor growth and adding a stochastic approach to determine likeliness of cancer spread to various parts of the body, as evaluated by relative interconnection (through blood vessels, lymph, etc.) and correcting for error using experimental data on sites of metastasis for various types of cancer. Work on the project thus far has gone towards the challenge of solving ordinary and partial differential equations in python, a primary challenge in our project, which has not so far proven to be very friendly. We are achieving our solution by mixing several mature libraries and packages such as Instant (allows us to utilize C) and Swiginac (which will help with symbolic mathematics in the code), which we hope will make our code cleaner and more efficient in its utilization of numerical methods to evaluate these equations with respect to time. Variables are defined within the mathematical model that we are utilizing. Our continuing work will deal with the coding and utilization of Markov chains for the stochastic portion of the model.


References

Anderson, A. R., & Chaplain, M. A. J. (1998). Continuous and discrete mathematical models of tumor-induced angiogenesis. Bulletin of mathematical biology, 60(5), 857-899.

Araujo, R. P., & McElwain, D. L. S. (2004). A history of the study of solid tumour growth: the contribution of mathematical modelling. Bulletin of mathematical biology, 66(5), 1039-1091.

Guyer, J. E., Wheeler, D., & Warren, J. A. (2009). FiPy: partial differential equations with Python. Computing in Science & Engineering, 11(3), 6-15.

Jones, D. S., Plank, M., & Sleeman, B. D. (2011). Differential equations and mathematical biology. CRC press.

Liotta, L. A., Steeg, P. S., & Stetler-Stevenson, W. G. (1991). Cancer metastasis and angiogenesis: an imbalance of positive and negative regulation. Cell, 64(2), 327-336.

Mardal, K. A., Skavhaug, O., Lines, G. T., Staff, G. A., & Ødegård, Å. (2007). Using Python to solve partial differential equations. Computing in Science & Engineering, 9(3), 48-51.

Quaranta, V., Weaver, A. M., Cummings, P. T., & Anderson, A. R. (2005). Mathematical modeling of cancer: the future of prognosis and treatment. Clinica Chimica Acta, 357(2), 173-179.


Team Members:

  Sophia Sánchez-Maes
  Mireya Sánchez-Maes

Sponsoring Teacher: Rebecca Galves

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