{"title":"Monotonicity functional for a transient mathematical model of oxygen depletion during Photodynamic therapy","authors":"I. Gkigkitzis","doi":"10.1109/BIBMW.2012.6470263","DOIUrl":null,"url":null,"abstract":"Accurate and computationally inexpensive energy density functional are highly desirable in the simulation of biochemical systems. A molecular \"energy\" integral functional for the reaction diffusion equation of the triplet oxygen [3O2] in the pseudo state equilibrium during treatment with Photodynamic therapy (PDT) is defined, and its monotonicity is analyzed. When the functional is evaluated on the solution of an existing mathematical model of a spheroid that represents the real physical system of a cell during PDT treatment, it gives a time dependent monotonically decreasing expression energy.","PeriodicalId":6392,"journal":{"name":"2012 IEEE International Conference on Bioinformatics and Biomedicine Workshops","volume":null,"pages":null},"PeriodicalIF":0.0000,"publicationDate":"2012-10-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"2012 IEEE International Conference on Bioinformatics and Biomedicine Workshops","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1109/BIBMW.2012.6470263","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
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Abstract
Accurate and computationally inexpensive energy density functional are highly desirable in the simulation of biochemical systems. A molecular "energy" integral functional for the reaction diffusion equation of the triplet oxygen [3O2] in the pseudo state equilibrium during treatment with Photodynamic therapy (PDT) is defined, and its monotonicity is analyzed. When the functional is evaluated on the solution of an existing mathematical model of a spheroid that represents the real physical system of a cell during PDT treatment, it gives a time dependent monotonically decreasing expression energy.
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