Title :
Monotonicity functional for a transient mathematical model of oxygen depletion during Photodynamic therapy
Author_Institution :
Dept. of Math., East Carolina Univ., Greenville, NC, USA
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;
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
DOI :
10.1109/BIBMW.2012.6470263
