Wolfram Computation Meets Knowledge

Wolfram Summer School


Enrique Barrajon

Summer School

Class of 2010


Enrique Barrajon is a 50-year-old Spanish and European certificate in medical oncology. He holds a PhD in medicine from the Universidad de Navarra and a master’s degree in statistics and research design from the Universidad Autònoma de Barcelona. He is Head of Medical Oncology at the Hospital Clinica Benidorm in Spain, and a member of several national and international medical societies.

He is interested in mathematical modeling of cell growth, differentiation, mutagenesis, carcinogenesis, tumor development, immunology, clonal evolution, drug resistance, pharmacokinetics and pharmakodynamics. Other interests are painting, mountain biking, and swimming.

Project: Tumor Growth: An Aggregation Model Approach

Cancer is a genetic desease characterized by the progressive growth of some cells in an organism. Tumor growth is assumed to follow a Gompertzian curve, a special case of the Richard’s family of curves.

The Gompertz model, though based on only two mathematical parameters, has been useful at suggesting the effectiveness of adjuvant treatments and of dose-dense chemotherapy schedules, but does not explain why and how some tumors may be cured, while others are incurable. A Gompertzian growth based on more “biological” parameters may allow more theoretical interactions with the model, and the consequent design of more rational treatments. This goal can be achieved with cellular automata programming using Mathematica.

In this project, a search of the 2D totalistic cellular automaton is done, starting from generalized aggregation models, looking for Gompertzian growth. Model rules stability are studied by applying mutations and external interactions. The search is upgraded to different values of colors k and radius r, to hexagonal grids, and to 3D spaces. In a further step, rules should be interpreted as interactions between units in a weighted network, susceptible to manipulation.

Favorite Four-Color Totalistic Cellular Automaton

Rule 100664