Directional entropy based model for diffusivity-driven tumor growth

Marcelo E. de  Oliveira; Luiz M. G.  Neto

doi:10.3934/mbe.2015005

Article Contents

2016, Volume 13, Issue 2: 333-341. Doi: 10.3934/mbe.2015005

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Directional entropy based model for diffusivity-driven tumor growth

Marcelo E. de Oliveira^1, and
Luiz M. G. Neto^2,

1.
Robotic Systems Laboratory, Swiss Federal Institute of Technology (EPFL), Lausanne, CH-1015
2.
Department of Mechanical Engineering, Engineering College of Sorocaba (FACENS), São Paulo, 18087-125

Received: May 31, 2015

Revised: September 30, 2015

Published: November 2015

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Abstract

In this work, we present and investigate a multiscale model to simulate 3D growth of glioblastomas (GBMs) that incorporates features of the tumor microenvironment and derives macroscopic growth laws from microscopic tissue structure information. We propose a normalized version of the Shannon entropy as an alternative measure of the directional anisotropy for an estimation of the diffusivity tensor in cases where the latter is unknown. In our formulation, the tumor aggressiveness and morphological behavior is tissue-type dependent, i.e. alterations in white and gray matter regions (which can e.g. be induced by normal aging in healthy individuals or neurodegenerative diseases) affect both tumor growth rates and their morphology. The feasibility of this new conceptual approach is supported by previous observations that the fractal dimension, which correlates with the Shannon entropy we calculate, is a quantitative parameter that characterizes the variability of brain tissue, thus, justifying the further evaluation of this new conceptual approach.

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Mathematics Subject Classification: Primary: 94A17, 62P10, 68U10; Secondary: 65M06, 37M10.

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