# American Institute of Mathematical Sciences

2016, 13(2): 333-341. doi: 10.3934/mbe.2015005

## Directional entropy based model for diffusivity-driven tumor growth

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

Received  June 2015 Revised  October 2015 Published  November 2015

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.
Citation: Marcelo E. de Oliveira, Luiz M. G. Neto. Directional entropy based model for diffusivity-driven tumor growth. Mathematical Biosciences & Engineering, 2016, 13 (2) : 333-341. doi: 10.3934/mbe.2015005
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