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The mathematical path to develop a heterogeneous, anisotropic and 3-dimensional glioma model using finite differences

Marias Kostas, Zervakis Michail, Sakkalis, Vangelis, Roniotis Alexandros, Karatzanis Ioannis

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URIhttp://purl.tuc.gr/dl/dias/C143B02B-6F99-4887-8B3B-16A37778AC64-
Identifierhttps://doi.org/10.1109/ITAB.2009.5394336-
Identifierhttps://ieeexplore.ieee.org/document/5394336/?section=abstract-
Languageen-
Extent4 pagesen
TitleThe mathematical path to develop a heterogeneous, anisotropic and 3-dimensional glioma model using finite differencesen
CreatorMarias Kostasen
CreatorZervakis Michailen
CreatorΖερβακης Μιχαηλel
CreatorSakkalis, Vangelisen
CreatorRoniotis Alexandrosen
CreatorΡονιωτης Αλεξανδροςel
CreatorKaratzanis Ioannisen
PublisherInstitute of Electrical and Electronics Engineersen
Content SummarySeveral mathematical models have been developed to express glioma growth behavior. The most successful models have used the diffusion-reaction equation, with the most recent ones taking into account spatial heterogeneity and anisotropy. However, to the best of our knowledge, there hasn't been any work studying in detail the mathematical solution and implementation of the 3D diffusion model, addressing all related heterogeneity and anisotropy issues. This paper presents a complete mathematical framework on how to derive the solution of the equation using different numerical schemes of finite differences. Moreover, the derived mathematics can be customized to incorporate various cell proliferation schemes. Lastly, a comparative study of the numerical scheme helps us select the best of them and then apply it to real clinical data.en
Type of ItemΠλήρης Δημοσίευση σε Συνέδριοel
Type of ItemConference Full Paperen
Licensehttp://creativecommons.org/licenses/by/4.0/en
Date of Item2015-10-25-
Date of Publication2009-
SubjectBasic medical sciencesen
SubjectBasic sciences, Medicalen
SubjectBiomedical sciencesen
SubjectHealth sciencesen
SubjectPreclinical sciencesen
SubjectSciences, Medicalen
Subjectmedical sciencesen
Subjectbasic medical sciencesen
Subjectbasic sciences medicalen
Subjectbiomedical sciencesen
Subjecthealth sciencesen
Subjectpreclinical sciencesen
Subjectsciences medicalen
SubjectAnisotropic magnetoresistanceen
SubjectMathematical modelen
SubjectFinite difference methodsen
SubjectNeoplasmsen
SubjectLinear systemsen
SubjectDifferential equationsen
SubjectBrain modelingen
SubjectTensile stressen
SubjectPartial differential equationsen
SubjectInformation technologyen
Bibliographic CitationA. Roniotis, K. Marias, V. Sakkalis, I. Karatzanis and M. Zervakis,"The mathematical path to develop a heterogeneous, anisotropic and 3-dimensional glioma model using finite differences," in 9th International Conference on Information Technology and Applications in Biomedicine, 2009, pp. 1-4. doi: 10.1109/ITAB.2009.5394336en

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