Realistic simulation of the 3-D growth of brain tumors in MR images coupling diffusion with biomechanical deformation

Abstract

We propose a new model to simulate the 3D growth of glioblastomas multiforma (GBMs), the most aggressive glial tumors. The GBM speed of growth depends on the invaded tissue: faster in white than in gray matter, it is stopped by the dura or the ventricles. These different structures are introduced into the model using an atlas matching technique. The atlas includes both the segmentations of anatomical structures and diffusion information in white matter fibers.We use the finite element method (FEM) to simulate the invasion of the GBM in the brain parenchyma and its mechanical interaction with the invaded structures (mass effect). Depending on the considered tissue, the former effect is modeled with a reaction-diffusion or a Gompertz equation, while the latter is based on a linear elastic brain constitutive equation. In addition, we propose a new coupling equation taking into account the mechanical influence of the tumor cells on the invaded tissues. The tumor growth simulation is assessed by comparing the in-silico GBM growth with the real growth observed on two magnetic resonance images (MRIs) of a patient acquired with six months difference. Results show the feasibility of this new conceptual approach and justifies its further evaluation.

Tumor Growth Modeling in Oncological Image Analysis

“…Extending the idea of Swanson et al regarding the differential motility of tumor cells on different tissues, Clatz et al and later Jbabdi et al included anisotropy to the invasion mechanism of tumor cells, [6] and [7]. They modelled the diffusivity of tumor cells through an anisotropic-nonhomogeneous diffusion.…”

“…Although some of these features are not well observable in medical images they model them based on assumptions coming from biological experiments. As First two columns show the initial image and initial state of the model respectively, while the third column shows the tumor after 6 months and the fourth column shows the evolved tumor using the model given in [6].…”

“…Clatz et. al combined two approaches of the macroscopic modelling in [6] in creating a formulation for glioblastoma multiforme (GBM). They have formulated the invasive nature of the tumor growth, besides proliferation, and the deformation this causes on the brain tissue.…”

“…They have adopted the growth model proposed by Clatz et al [6]. In addition to this model, in their formulation they took into account the displacement and destruction of white matter fibers using image warping and nonlinear interpolation, based on the observations of Lu et al [22].…”

“…For macroscopic models the comparison is done with observed medical images, which are not able to visualize the whole tumor. Although some quantitative validation methods was proposed by some authors, [6,11], the field still lacks a golden standard in validation methodology.…”