A mathematical modelling tool for predicting survival of individual patients following resection of glioblastoma: a proof of principle

The prediction of the outcome of individual patients with glioblastoma would be of great significance for monitoring responses to therapy. We hypothesise that, although a large number of genetic-metabolic abnormalities occur upstream, there are two 'final common pathways' dominating glioblastoma growth - net rates of proliferation ( rho) and dispersal ( D). These rates can be estimated from features of pretreatment MR images and can be applied in a mathematical model to predict tumour growth, impact of extent of tumour resection and patient survival. Only the pre-operative gadolinium-enhanced T1-weighted ( T1-Gd) and T2-weighted ( T2) volume data from 70 patients with previously untreated glioblastoma were used to derive a ratio D/rho for each patient. We developed a 'virtual control' for each patient with the same size tumour at the time of diagnosis, the same ratio of net invasion to proliferation ( D/rho) and the same extent of resection. The median durations of survival and the shapes of the survival curves of actual and 'virtual' patients subjected to biopsy or subtotal resection ( STR) superimpose exactly. For those actually receiving gross total resection ( GTR), as shown by post-operative CT, the actual survival curve lies between the 'virtual' results predicted for 100 and 125% resection of the T1-Gd volume. The concordance between predicted ( virtual) and actual survivals suggests that the mathematical model is realistic enough to allow precise definition of the effectiveness of individualised treatments and their site( s) of action on proliferation ( rho) and/or dispersal ( D) of the tumour cells without knowledge of any other clinical or pathological information.