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Porous Media Tumor Model for Light Penetration and Oxygen Diffusion During Photodynamic Therapy

[+] Author Affiliations
A. Premasiri

Southern Methodist University, Dallas, TX

G. Happawana

California State University, Fresno, CA

A. Rosen

Drexel University, Philadelphia, PA

Paper No. IMECE2008-66480, pp. 505-509; 5 pages
doi:10.1115/IMECE2008-66480
From:
  • ASME 2008 International Mechanical Engineering Congress and Exposition
  • Volume 2: Biomedical and Biotechnology Engineering
  • Boston, Massachusetts, USA, October 31–November 6, 2008
  • Conference Sponsors: ASME
  • ISBN: 978-0-7918-4863-0 | eISBN: 978-0-7918-3840-2
  • Copyright © 2008 by ASME

abstract

Photodynamic therapy (PDT) is an FDA approved, effective, and minimally invasive cancer treatment modality with few side effects. PDT requires three major components; photosensitizing agent, activation light, and molecular oxygen. Optimization of PDT for an individual patient requires good therapeutic selectivity and high efficacy, where the design of such an effective protocol is based on the understanding of the interaction of key therapeutic components with tumor tissue. Tumor models expressive of changes during the growth of tumor along with the behavior of PDT components facilitate the above requirement. In this study we have developed a mathematical model considering tumor as a porous medium of solid of and liquid that enables to express characteristics of a growing tumor. The characteristic lengths and the volumes that can be changed in the model represent the dynamic changes during the growth of the tumor. An energy based light transport model is superimposed with the porous media model to yield an analytical equation of light penetration in turbid media. In addition a molecular diffusion model combined with the porous media tumor model provides a second analytical equation yielding molecular oxygen diffusion during PDT. Experimentally available physiological and photophysical data are used to obtain the results from the developed models. The commonly used wavelength for PDT, 635nm and corresponding photophsical parameters for a healthy tissue are used for the calculations. The modeling results reveal an exponential decay of optical power along the direction of light penetration and the characteristic changes in oxygen diffusion during PDT. Further observations include the time dependent changes in photosensitizer photobleaching and the corresponding increase in oxygen diffusion length. The modeling results in both cases show a promising accordance with the available experimental results in literature. The model calculations also reveal the effect of light penetration on oxygen diffusion in PDT milieu adding to the expression of its usefulness.

Copyright © 2008 by ASME

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