Modeling Long-term Response to Drugs (on the Gene Expression and Population Dynamic Levels) in Oncology Therapies
My primary research topic is the modeling of long term development of cancer tumors. The concerning problem is the activity of drugs over cancer tumors, since right now its effectiveness is reduced. Cancer affects more people every year, and there is still no cure or treatment that guaranties healing.
We work in one part of a Medsys project, which involves other universities and private companies. Our part of the project considers the modeling of long-term response to drugs on the gene expression and population dynamic levels for cancer tumors. During the first 6 months of research I have been focused on acquiring background knowledge on the specific field, reviewing the known models and coding model problems that allow a better understanding of the mathematical bases, and of course a deeper knowledge on the development of combined and more complex models. To this point I have reviewed the main trends in cancer modeling, drug response modeling and tumor development. Komarova and Wodarz [ref] work in the field is much respected and is used as base in several different models. Simple models consider cancer and normal tissue in population dynamics models, using PDEs to reproduce tumor growth (Fig1). From these simple models, several variables are included, like drug therapies, drug resistance, differentiation between steam cells and regular cells, compartments, metastasis, etc.
These models transform into predator prey models, game theory models, and even 3D models, where the tumor growth is measured by size instead of by number of cancer cells. The objectives for this year involve the choosing of a working model, or several working models, and the use of real data on these models to evaluate prediction effectiveness and model accuracy. To accomplish so, a “state of the art” document will be developed, and several statistical proofs will be done over these models. One of the problems in the field is the need to work with several assumptions due to the computational costs a more realistic model implies. In the choosing of a model we must consider the possibility of improve the accuracy of the model, by taking it closer to the reality.