Mathematical-numerical modeling of glioma evolution

SUÁREZ CECILIA; TURJANSKI PABLO; MARSHALL GUILLERMO

Córdoba

Congreso; 2do Congreso Argentino de Bioinformática y Biología Computacional; 2011

Asociación Argentina de Bioinformática y Biología Computacional

Gliomas, derived from glial cells or their precursors, are the most common primary brain tumors. Up to now, they are almost incurable, mainly due to their great invasiveness capacity. Most of present imaging technology used in brain tumor detection (nuclear magnetic resonance and computed tomography), is not yet able to detect the real extension of tumor infiltration. This is one of the causes of the high recurrence of tumor growth observed after surgery and the final treatment failure. Here we present a mathematical model, based in a previous one from Swanson, that describes the three dimensional growth and invasiveness of a glioma inside a human brain and its possible reduction/elimination by an eventual treatment (figure 1). The model considers a net proliferation rate, described by a logistic equation, and a net invasion rate, described by the Fick?s law, differing for grey and white matter. An initial state with only cellular proliferation (benign tumor) and an advanced state where cellular infiltration begins (malignization) are considered. The survival time is estimated on the basis of tumor size and the type of brain structures affected. The mathematical model was approximated with finite differences and implemented in Matlab. The domain is based on a series of digitized images of brain slices developed by the Neurological Institute of Montreal, covering the whole human brain with a spatial resolution of 1 mm3. At present we are concerned with the clinic validation of the model with the aim of employing it as a predictive tool, complementary with other techniques, when determining the risk/benefit relationship of a given treatment in a patient-specific manner.