KNOPOFF Damian Alejandro
A mathematical method for parameter estimation in a tumor growth model
DAMIAN KNOPOFF; FERNANDEZ FERREYRA DAMIAN; TORRES GERMAN; TURNER CRISTINA
COMPUTATIONAL AND APPLIED MATHEMATICS
Año: 2017 vol. 36 p. 733 - 748
In this paper we present a methodology for estimating the effectivenessof 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 definesuitable 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.