Diagnose and treat cancer as a mathematical error

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A cancer is always an error in the formulation of cells when they suffer an alteration in their genetic material and end up causing mutations. A process that can be understood by mathematical algorithms because it represents an anomaly compared to the normal functioning of the tissues of the organism that leads to cells that multiply at a higher speed.

To understand these reformulations and equations that generate the cancer processes has become one of the objectives of the Laboratory of Oncology Mathematics (Mathematical Oncology Laboratory or MôLAB) of the Institute of Applied Mathematics to Science and Engineering, University of Castilla-La Mancha, whose director, Víctor M. Pérez-García, describes which your team applies the Mathematics to describe, understand, and cure cancer, both looking to improve on existing treatments as create new ones.

From mathematical tools such as differential equations, numerical methods, geometry optimization and statistics, MôLAB has been investigating, since 2009, different types of cancer such as leukemia, although its focus is on brain tumors and glioblastomas.

After these ten years of cancer research, the team led by Pérez-García already has clinical trials, based on real patients that have made it possible to create alternatives to oncological treatments based on mathematical concepts, such as combinations of drugs proposed based on the results of their models. A way to develop personalized medications for each tumor.

“We work by uniting mathematics and medicine, and with applied mathematical tools we try to solve useful questions for medicine. How can we define measures that inform us about the status and prognosis of a cancer? Can we better customize therapies for each patient? We seek to respond to the challenges with the available data and with mathematical modelling,” said Pérez-García, who participated yesterday in the International Congress of industrial and Applied Mathematics (Iciam) held this week in Valencia.

Another MôLAB project focuses on rare brain pathologies. With the help of computer simulators they complete the few clinical analyses that can be done: they parameterize real patients, obtain their ranges of variables and generate virtual patients. This way, without risk, tests can be experimented and done computational.

MôLAB receives a large number of requests for collaboration in applying mathematics in other areas of Health. Members of this group of researchers have recently taken part in a study to quantify brain tissue from medical imaging in patients suspected of Alzheimer’s disease. This quantification study will be able to make an early diagnosis and begin treatments before the cerebral cortex is damaged. They also work to monitor response times to diabetes treatments.

The president of the Organizing Committee of the Congress, Tomás Chacón, urged that society should know about these improvements in order to understand why it is important to research in Mathematics. Investment in research is a long-term social investment. “There is that awareness of the industry, the company and the society of the relevance of mathematics to consider as a resource that they have at their disposal.”

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