Monotonicity functional for a transient mathematical model of oxygen depletion during Photodynamic therapy

Author

Gkigkitzis, I.

Author_Institution

Dept. of Math., East Carolina Univ., Greenville, NC, USA

fYear

2012

fDate

4-7 Oct. 2012

Firstpage

914

Lastpage

916

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.

Keywords

biochemistry; biodiffusion; oxygen; photodynamic therapy; physiological models; O₂; PDT treatment; biochemical system simulation; computational inexpensive energy density functionals; expression energy; functional monotonicity; molecular energy integral functional; photodynamic therapy; physical system; pseudostate equilibrium; reaction diffusion equation; spheroid mathematical model; transient mathematical model; triplet oxygen depletion; Biological system modeling; Equations; Integral equations; Kinetic theory; Mathematical model; Medical treatment; Numerical models; formatting; insert; style; styling;

fLanguage

English

Publisher

ieee

Conference_Titel

Bioinformatics and Biomedicine Workshops (BIBMW), 2012 IEEE International Conference on

Conference_Location

Philadelphia, PA

Print_ISBN

978-1-4673-2746-6

Electronic_ISBN

978-1-4673-2744-2

Type

conf

DOI

10.1109/BIBMW.2012.6470263

Filename

6470263