Artículos de revistas
Adjoint method for a tumor growth PDE-constrained optimization problem
Fecha
2013-10Registro en:
Knopoff, Damián Alejandro; Fernández Ferreyra, Damián Roberto; Torres, Germán Ariel; Turner, Cristina Vilma; Adjoint method for a tumor growth PDE-constrained optimization problem; Pergamon-elsevier Science Ltd; Computers & Mathematics With Applications (1987); 66; 6; 10-2013; 1104-1119
0898-1221
Autor
Knopoff, Damián Alejandro
Fernández Ferreyra, Damián Roberto
Torres, Germán Ariel
Turner, Cristina Vilma
Resumen
In this paper we present a method for estimating unknown parameters that
appear on an avascular, spheric tumor growth model. The model for the
tumor is based on nutrient driven growth of a continuum of live cells,
whose birth and death generate volume changes described by a velocity
field. The model consists of a coupled system of partial differential
equations whose spatial domain is the tumor, that changes in size over
time. Thus, the situation can be formulated as a free boundary problem.
After solving the direct problem properly, we use the model for the
estimation of parameters by fitting the numerical solution with real
data, obtained via <em>in vitro</em> experiments and medical imaging. We
define an appropriate functional to compare both the real data and the
numerical solution. We use the adjoint method for the minimization of
this functional.