Fractional pennes' bioheat equation: Theoretical and numerical studies

Hdl Handle:
http://hdl.handle.net/10034/584009
Title:
Fractional pennes' bioheat equation: Theoretical and numerical studies
Authors:
Ferras, Luis L.; Ford, Neville J.; Morgado, Maria L.; Rebelo, Magda S.; Nobrega, João M.
Abstract:
In this work we provide a new mathematical model for the Pennes’ bioheat equation, assuming a fractional time derivative of single order. Alternative versions of the bioheat equation are studied and discussed, to take into account the temperature-dependent variability in the tissue perfusion, and both finite and infinite speed of heat propagation. The proposed bio heat model is solved numerically using an implicit finite difference scheme that we prove to be convergent and stable. The numerical method proposed can be applied to general reaction diffusion equations, with a variable diffusion coefficient. The results obtained with the single order fractional model, are compared with the original models that use classical derivatives.
Affiliation:
University of Minho & University of Chester, University of Chester, UTAD, UNL Lisboa, University of Minho
Citation:
Ferrás, L., Ford, N., Morgado, M., Rebelo, M. S., & Nobrega, J. M. (2015). Fractional Pennes’ bioheat equation: Theoretical and numerical studies. Fractional Calculus and Applied Analysis, 18(4), pp. 1080-1106. doi:10.1515/fca-2015-0062
Publisher:
de Gruyter
Journal:
Fractional Calculus and Applied Analysis - Fract. Calc. Appl. Anal
Publication Date:
2016
URI:
http://hdl.handle.net/10034/584009
DOI:
10.1515/fca-2015-0062
Additional Links:
http://www.degruyter.com/view/j/fca
Type:
Article
Language:
en
Description:
Accepted for publication in Fractional calculus and applied analysis; Originally published in the journal Fract. Cal. Appl. Anal. Vol. 18 No. 4 / 2015 / pp.1080–1106 / DOI 10.1515/fca-2015-0062. The original publication is available at: http://www.degruyter.com/view/j/fca.2015.18.issue-4/fca-2015-0062/fca-2015-0062.xml?rskey=sWWcn0&result=1
EISSN:
1314-2224
Sponsors:
The authors L.L. Ferras and J. M. Nobrega acknowledge financial funding by FEDER through the COMPETE 2020 Programme and by FCT- Portuguese Foundation for Science and Technology under the projects UID/CTM/50025/2013 and EXPL/CTM-POL/1299/2013. L.L. Ferras acknowledges financial funding by the Portuguese Foundation for Science and Technology through the scholarship SFRH/BPD/100353/2014. M. Rebelo acknowledges financial funding by the Portuguese Foundation for Science and Technology through the project UID/MAT/00297/2013.
Appears in Collections:
Mathematics

Full metadata record

DC FieldValue Language
dc.contributor.authorFerras, Luis L.en
dc.contributor.authorFord, Neville J.en
dc.contributor.authorMorgado, Maria L.en
dc.contributor.authorRebelo, Magda S.en
dc.contributor.authorNobrega, João M.en
dc.date.accessioned2015-12-16T14:40:19Zen
dc.date.available2015-12-16T14:40:19Zen
dc.date.issued2016en
dc.identifier.citationFerrás, L., Ford, N., Morgado, M., Rebelo, M. S., & Nobrega, J. M. (2015). Fractional Pennes’ bioheat equation: Theoretical and numerical studies. Fractional Calculus and Applied Analysis, 18(4), pp. 1080-1106. doi:10.1515/fca-2015-0062en
dc.identifier.doi10.1515/fca-2015-0062en
dc.identifier.urihttp://hdl.handle.net/10034/584009en
dc.descriptionAccepted for publication in Fractional calculus and applied analysisen
dc.descriptionOriginally published in the journal Fract. Cal. Appl. Anal. Vol. 18 No. 4 / 2015 / pp.1080–1106 / DOI 10.1515/fca-2015-0062. The original publication is available at: http://www.degruyter.com/view/j/fca.2015.18.issue-4/fca-2015-0062/fca-2015-0062.xml?rskey=sWWcn0&result=1en
dc.description.abstractIn this work we provide a new mathematical model for the Pennes’ bioheat equation, assuming a fractional time derivative of single order. Alternative versions of the bioheat equation are studied and discussed, to take into account the temperature-dependent variability in the tissue perfusion, and both finite and infinite speed of heat propagation. The proposed bio heat model is solved numerically using an implicit finite difference scheme that we prove to be convergent and stable. The numerical method proposed can be applied to general reaction diffusion equations, with a variable diffusion coefficient. The results obtained with the single order fractional model, are compared with the original models that use classical derivatives.en
dc.description.sponsorshipThe authors L.L. Ferras and J. M. Nobrega acknowledge financial funding by FEDER through the COMPETE 2020 Programme and by FCT- Portuguese Foundation for Science and Technology under the projects UID/CTM/50025/2013 and EXPL/CTM-POL/1299/2013. L.L. Ferras acknowledges financial funding by the Portuguese Foundation for Science and Technology through the scholarship SFRH/BPD/100353/2014. M. Rebelo acknowledges financial funding by the Portuguese Foundation for Science and Technology through the project UID/MAT/00297/2013.en
dc.language.isoenen
dc.publisherde Gruyteren
dc.relation.urlhttp://www.degruyter.com/view/j/fcaen
dc.subjectFractional differential equationsen
dc.subjectCaputo derivativeen
dc.subjectbioheat equation,en
dc.subjectbioheat equation,en
dc.subjectconvergenceen
dc.titleFractional pennes' bioheat equation: Theoretical and numerical studiesen
dc.typeArticleen
dc.identifier.eissn1314-2224en
dc.contributor.departmentUniversity of Minho & University of Chester, University of Chester, UTAD, UNL Lisboa, University of Minhoen
dc.identifier.journalFractional Calculus and Applied Analysis - Fract. Calc. Appl. Analen
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