A mathematical method for parameter estimation in a tumor growth model

In this paper, we present a methodology for estimating the effectiveness of a drug, an unknown parameter that appears on an avascular, spheric tumor growth model formulated in terms of a coupled system of partial differential equations (PDEs). This model is formulated considering a continuum of live cells that grow by the action of a nutrient. Volume changes occur due to cell birth and death, describing a velocity field. The model assumes that when the drug is applied externally, it diffuses and kills cells. The effectiveness of the drug is obtained by solving an inverse problem which is a PDE-constrained optimization problem. We define suitable objective functions by fitting the modeled and the observed tumor radius and the inverse problem is solved numerically using a Pattern Search method. It is observed that the effectiveness of the drug is retrieved with a reasonable accuracy. Experiments with noised data are also considered and the results are compared and contrasted.