Premium
A comprehensive mathematical model of microscopic dose deposition in photodynamic therapy
Author(s) -
KangHsin Wang Ken,
Mitra Soumya,
Foster Thomas H.
Publication year - 2007
Publication title -
medical physics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.473
H-Index - 180
eISSN - 2473-4209
pISSN - 0094-2405
DOI - 10.1118/1.2401041
Subject(s) - photodynamic therapy , photobleaching , photosensitizer , singlet oxygen , deposition (geology) , irradiation , biophysics , chemistry , biomedical engineering , dosimetry , materials science , biological system , optics , oxygen , fluorescence , physics , photochemistry , nuclear medicine , medicine , paleontology , organic chemistry , sediment , nuclear physics , biology
We have developed a comprehensive theoretical model for rigorously describing the spatial and temporal dynamics of oxygen ( O 23 ) consumption and transport and microscopic photodynamic dose deposition during photodynamic therapy (PDT) in vivo . Previously published models have been improved by considering perfused vessels as a time‐dependentO 23source and linking theO 23concentration in the vessel to that within the tissue through the Hill equation. The time‐dependent photochemicalO 23consumption rate incorporates sensitizer photobleaching effects and an experimentally determined initially nonuniform photosensitizer distribution. The axial transport ofO 23is provided for in the capillaries and in the surrounding tissue. A self‐sensitized singlet oxygen ( O 21 ) ‐mediated bleaching mechanism and the measured, initially nonuniform distribution of meso ‐tetrahydroxyphenyl chlorin at 3 h after intravascular administration were used to demonstrate the capabilities of the model. Time‐evolved distributions ofO 23concentration were obtained by numerically solving two‐dimensional diffusion‐with‐reaction equations both in the capillary and the adjacent tissue. Using experimentally established physiological and photophysical parameters, the mathematical model allows computation of the dynamic variation of hemoglobin‐ O 23saturation ( SO 2 ) within the vessels, irreversible sensitizer degradation due to photobleaching, and the microscopic distributions ofO 23 , sensitizer concentration, andO 21dose deposition under various irradiation conditions. The simulations reveal severe axial gradients inO 23and in photodynamic dose deposition in response to a wide range of clinically relevant treatment parameters. Thus, unlike former Krogh cylinder‐based models, which assume a constantO 23concentration at the vessel, this new model identifies conditions in whichO 23depletion and minimal deposition of reactingO 21exist near the end of axial segments of vessels and shows that treatment‐limitingO 23depletion is induced at fluence rates as low as 10 mWcm − 2. These calculations also demonstrate that intercapillary heterogeneity of photosensitizer contributes significantly to the distribution of photodynamic dose. This more rigorous mathematical model enables comparison with experimentally observable, volume‐averaged quantities such asSO 2and the loss of sensitizer fluorescence through bleaching that have not been included in previous analyses. Further, it establishes some of the intrinsic limitations of such measurements. Specifically, our simulations demonstrate that tissue measurements ofSO 2and of photobleaching are necessarily insensitive to microscopic heterogeneity of photodynamic dose deposition and are sensitive to intercapillary spacing. Because prior knowledge of intercapillary distances in tumors is generally unavailable, these measurements must be interpreted with caution. We anticipate that this model will make useful dosimetry predictions that should inform optimal treatment conditions and improve current clinical protocols.