Directional entropy based model for diffusivity-driven tumor growth
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...
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AIMS Press
2015-11-01
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| Series: | Mathematical Biosciences and Engineering |
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| Online Access: | https://www.aimspress.com/article/doi/10.3934/mbe.2015005 |
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| author | Marcelo E. de Oliveira Luiz M. G. Neto |
| author_facet | Marcelo E. de Oliveira Luiz M. G. Neto |
| author_sort | Marcelo E. de Oliveira |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-09afe4bcbc1549b8b276aa4dcf72176a |
| institution | Kabale University |
| issn | 1551-0018 |
| language | English |
| publishDate | 2015-11-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | Mathematical Biosciences and Engineering |
| spelling | doaj-art-09afe4bcbc1549b8b276aa4dcf72176a2025-01-24T02:35:04ZengAIMS PressMathematical Biosciences and Engineering1551-00182015-11-0113233334110.3934/mbe.2015005Directional entropy based model for diffusivity-driven tumor growthMarcelo E. de Oliveira0Luiz M. G. Neto1Robotic Systems Laboratory, Swiss Federal Institute of Technology (EPFL), Lausanne, CH-1015Department of Mechanical Engineering, Engineering College of Sorocaba (FACENS), São Paulo, 18087-125In 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.https://www.aimspress.com/article/doi/10.3934/mbe.2015005fractal dimension.glioblastomasdiffusivity tensorshannon entropy |
| spellingShingle | Marcelo E. de Oliveira Luiz M. G. Neto Directional entropy based model for diffusivity-driven tumor growth Mathematical Biosciences and Engineering fractal dimension. glioblastomas diffusivity tensor shannon entropy |
| title | Directional entropy based model for diffusivity-driven tumor growth |
| title_full | Directional entropy based model for diffusivity-driven tumor growth |
| title_fullStr | Directional entropy based model for diffusivity-driven tumor growth |
| title_full_unstemmed | Directional entropy based model for diffusivity-driven tumor growth |
| title_short | Directional entropy based model for diffusivity-driven tumor growth |
| title_sort | directional entropy based model for diffusivity driven tumor growth |
| topic | fractal dimension. glioblastomas diffusivity tensor shannon entropy |
| url | https://www.aimspress.com/article/doi/10.3934/mbe.2015005 |
| work_keys_str_mv | AT marceloedeoliveira directionalentropybasedmodelfordiffusivitydriventumorgrowth AT luizmgneto directionalentropybasedmodelfordiffusivitydriventumorgrowth |