A MATHEMATICAL-MODEL OF GLIOMA GROWTH - THE EFFECT OF CHEMOTHERAPY ONSPATIOTEMPORAL GROWTH

During the past two decades computerized tomography (CT) and magnetic resonance imaging (MRI) have permitted the detection of tumours at muc h earlier stages in their development than was previously possible. In spite of this earlier diagnosis the effects of earlier and more exten sive treatments have been difficult to document. This failure has led to an increasing awareness of the importance of infiltration of glioma cells into surrounding grossly normal brain tissue such that recurren ce still occurs. In this paper a simple mathematical model for the pro liferation and infiltration of such tumours is introduced, based in pa rt on quantitative image analysis of histological sections of a human brain glioma and especially on cross-sectional area/volume measurement s of serial CT images while the patient was undergoing chemotherapy. T he model parameters were estimated using optimization techniques to gi ve the best fit of the simulated tumour area to the CT scan data. Nume rical solution of the model on a two-dimensional domain, which took in to account the geometry of the brain and its natural barriers to diffu sion, was used to determine the effect of chemotherapy on the spatiote mporal growth of the tumour.