A detailed numerical treatment of the boundary conditions imposed by the skull on a diffusion-reaction model of glioma tumor growth. Clinical validation aspects

Giatili, SG; Stamatakos, GS

dc.contributor.author	Giatili, SG	en
dc.contributor.author	Stamatakos, GS	en
dc.date.accessioned	2014-03-01T02:07:15Z
dc.date.available	2014-03-01T02:07:15Z
dc.date.issued	2012	en
dc.identifier.issn	00963003	en
dc.identifier.uri	https://dspace.lib.ntua.gr/xmlui/handle/123456789/29533
dc.subject	Boundary conditions	en
dc.subject	Diffusion	en
dc.subject	Glioblastoma multiforme	en
dc.subject	Glioma	en
dc.subject	In silico oncology	en
dc.subject	Multiscale cancer modeling	en
dc.subject.other	Active field	en
dc.subject.other	Biological phenomena	en
dc.subject.other	Biological problems	en
dc.subject.other	Biomedical research	en
dc.subject.other	Boundary geometry	en
dc.subject.other	Brain-imaging data	en
dc.subject.other	Computational problem	en
dc.subject.other	Conjugate gradient	en
dc.subject.other	Crank-Nicolson	en
dc.subject.other	Diffusion-reaction	en
dc.subject.other	Diffusion-reaction model	en
dc.subject.other	Diffusive behavior	en
dc.subject.other	Diffusive growth	en
dc.subject.other	Glioblastoma multiforme	en
dc.subject.other	Glioma	en
dc.subject.other	Macroscopic behaviors	en
dc.subject.other	Mathematical treatments	en
dc.subject.other	Multiscales	en
dc.subject.other	Neumann boundary condition	en
dc.subject.other	Numerical experimentations	en
dc.subject.other	Numerical formulation	en
dc.subject.other	Numerical solution	en
dc.subject.other	Numerical treatments	en
dc.subject.other	Tumor growth	en
dc.subject.other	Boundary conditions	en
dc.subject.other	Conjugate gradient method	en
dc.subject.other	Diffusion	en
dc.subject.other	Tumors	en
dc.title	A detailed numerical treatment of the boundary conditions imposed by the skull on a diffusion-reaction model of glioma tumor growth. Clinical validation aspects	en
heal.type	journalArticle	en
heal.identifier.primary	10.1016/j.amc.2012.02.036	en
heal.identifier.secondary	http://dx.doi.org/10.1016/j.amc.2012.02.036	en
heal.publicationDate	2012	en
heal.abstract	The study of the diffusive behavior of glioma tumor growth is an active field of biomedical research with considerable therapeutic implications. An important aspect of the corresponding computational problem is the mathematical handling of boundary conditions. This paper aims at providing an explicit and thorough numerical formulation of the adiabatic Neumann boundary conditions imposed by the skull on the diffusive growth of gliomas and in particular on glioblastoma multiforme (GBM). Additionally, a detailed exposition of the numerical solution process for a homogeneous approximation of glioma invasion using the Crank-Nicolson technique in conjunction with the Conjugate Gradient system solver is provided. The entire mathematical and numerical treatment is also in principle applicable to mathematically similar physical, chemical and biological phenomena. A comparison of the numerical solution for the special case of pure diffusion in the absence of boundary conditions or equivalently in the presence of adiabatic boundaries placed in infinity with its analytical counterpart is presented. Numerical simulations for various adiabatic boundary geometries and non zero net tumor growth rate support the validity of the corresponding mathematical treatment. Through numerical experimentation on a set of real brain imaging data, a simulated tumor has shown to satisfy the expected macroscopic behavior of glioblastoma multiforme including the adiabatic behavior of the skull. The paper concludes with a number of remarks pertaining to both the biological problem addressed and the more generic diffusion-reaction context. © 2011 Elsevier Inc. All rights reserved.	en
heal.journalName	Applied Mathematics and Computation	en
dc.identifier.doi	10.1016/j.amc.2012.02.036	en
dc.identifier.volume	218	en
dc.identifier.issue	17	en
dc.identifier.spage	8779	en
dc.identifier.epage	8799	en