James D. Murray
Applied & Computational Mathematics, Princeton University
Wolfson Centre for Mathematical Biology, University of Oxford
Applied Mathematics, University of Washington
On the Virtues of Simple Models: From Resolving a Prostate Cancer Diagnostic Anomaly to Quantifying the Efficacy of Brain Tumour Therapies
The recent US government agencies’ guidelines for prostate cancer screening is controversial. I shall describe a simple, medically realistic, model which resolves the anomaly associated with PSA (prostate specific antigen) screening and, along with recent trials, shows why the guidelines are wrong. The prognosis for patients with high grade brain tumors (gliomablatomas) is grim and the various current treatment protocols cannot effect a cure. I shall describe a surprisingly informative simple quantitative model, now used clinically, for quantifying the spatio-temporal growth of such tumours, enhancing imaging techniques and quantifying individual patient treatment protocols prior to their use. Analysis of the model shows how difficult it is to decide on the tumor volume to be treated and clearly shows why such treatments have so little success. The model simulations can estimate life expectancy for individual patients and suggests why some patients can live longer than others with similar treatments. Finally with possible future clinical studies associated with long term cell phone use, it will of use to estimate when and where a tumor started.