Singlet Oxygen Modeling of BPD Mediated-PDT Using COMSOL

Transcription

1 Singlet Oxygen Modeling of BPD Mediated-PDT Using COMSOL Timothy C. Zhu, Baochang Liu, Xing Liang COMSOL Boston, October -5, 01 Excerpt from the Proceedings of the 01 COMSOL Conference in Boston

2 Outline Introduction Theory for PDT dosimetry model Experiments and Optimization results Comparison between Photochemical parameters between photofrin and BPD Conclusions

3 Introduction

4 Mechanics of Action Photosensitizer (BPD or Photofrin) Light Activated Photosensitizer Type I (Substrate) Type II (O ) Free Radicals Cytotoxic Oxyproducts Cellular Destruction 4

5 Motivation why? PDT efficacy depends on three parameters: light, drug, and oxygen Current state of art for human PDT trial: PDT dose, the product of drug concentration and light fluence, is quantified. The effect of light fluence rate is not accounted for. Apparent reacted singlet oxygen, 1 O rx, can be introduced for clinical PDT to account for all three components including light fluence rate effect. However, sensitizer-specific photochemical parameters are unknown. 5

6 Introduction S 1 k 0, absorption k 5 Intersystem crossing Energy transfer to O T 1 O k k 7, Reaction with targets A S 0 k,fluorescence k 4, phosphorescence Sensitizer k 1, photobleaching k 6, phosphorescence, l = 160 nm O Oxygen Jablonski Diagram Type II PDT interaction Sensitizer (PS) + light + oxygen ( O ) singlet oxygen ( 1 O ) 6

7 Introduction Apparent reacted singlet oxygen 1 O rx was introduced as a PDT dosimetry quantity to better predict the PDT treatment outcome than PDT dose 1 O rx T 0 S0 O O dt 7

8 Introduction Apparent reacted singlet oxygen 1 O rx was introduced as a PDT dosimetry quantity to better predict the PDT treatment outcome than PDT dose By COMSOL By COMSOL + MATLAB Light Distribution Optimal Parameters Geometry Parameters Predicted 1 O rx distribution Experimental Necrosis Radius Geometry From Anatomic Image Flow chart for PDT photophysiological parameter optimization and PDT dosimetry 8

9 Theory for PDT dosimetry model 9

10 10 Theory for PDT dosimetry model g is the maximum oxygen perfusion rate where there is no oxygen gradient = k4/k can be treated as constant. =S D k5/(k+k5)e/hn/(k6/k7a1) s = k1/(k7a) S s a ' 1 ( ) S O O S dt S d s 0 0) ( 1 0 t O O g O O S dt O d O O S dt O d rx S: source term, Fluence rate: S 0 (t), O (t), and 1 O rx (t) Equs. are function of, s,, and g, and initial conditions of O and S 0.

11 Theory for optimization model Initial guess of ξ, σ, β, g Differential equations Solution for 1 O rx In vivo mice study Necrosis radius Minimize deviation of 1 O MAX 1 1 O rx ( rn ) rx, sd 1 O rx (r n ) 1 O rx,sd Fitting results ξ, σ, β, g and 1 O rx 11

12 Experiments and Optimization Results 1

13 Experimental details Interstitial treatment is designed to induce the necrosis distance which is expected to be related with the computed 1 O rx profile. BPD, 1 mg/kg, hours, 690 nm light RIF tumor grown on mouse shoulder Linear light source Catheters Isotropic detector Necrosis distance can be detected by H&E staining 1

14 Results on BPD data Necrosis not approaching boundary (Necrosis approaching boundary) 14

15 Results on BPD data Mouse # BPD concentration (um) LS strength (mw/cm) Treatment time (s) μ a (cm -1 ) μ s (cm -1 ) Ф at necrosis radius (mw/cm ) Necrosis radius (mm) (5) (6) (8) (9) (10) (1)

16 Results on selected BPD data Parameters BPD (A) BPD (B) BPD (All) Photofrin (cm /s/mw) 0.6 x x x x 10 - s (1/M).5 x x x x10-5 (M) g (M/s) O rx,sh (mm) 0.5± ± ± ±0.6 16

17 Results on selected BPD A 1 O rx (mm) predicted necrotic radius (mm) O rx true necrotic rad r (mm) measured necrotic radius (mm) 17

18 Results on selected BPD B 1 O rx (mm) predicted necrotic radius (mm) O rx true necrotic rad r (mm) measured necrotic radius (mm) 5 18

19 Comparison between photochemical parameters between Photofrin and BPD 19

20 Results on BPD data Photosensitizer BPD Photofrin Incubation time hr 4 hr Drug concentration 1 mg/kg 5 mg/kg Light wavelength 690 nm 60 nm 0

21 Comparison PS (cm /s/mw) s (1/M) k 5 /(k +k 5 ) e (M -1 cm -1 ) k 7 A/k 6 Photofrin (60nm).9 x x BPD (690nm) 0.6 x x References 1, 1, 1. Mitra and Foster, Photochem & Photobiol 81, (005).. Hu et al, Photochem & Photobiol, 81, (005).. Aveline B, Hasan T, et al, Photochem & Potobiol, 59, 8-5 (1994) 1

22 Comparison PS Media Threshold dose Reference 1 Photofrin spheroid 1.1±1. mm I. Georgakoudi, M. G. Nichols, and T. H. Foster, Photochem. Photobiol. 65(1), (1997). mthpc Mice in vivo 0.4 mm K. K. Wang, S. Mitra, and T. H. Foster, Med. Phys. 5(8), (008). Photofrin Mice in vivo 0.74 mm Wang K et al, J Biophoton, (010), 4 mthpc spheroid 7.9 ±. mm S. Coutier, S. Mitra, L. N. Bezdetnaya, R. M. Parache, I. Georgakoudi, T. H. Foster, and F. Guillemin, Photochem. Photobiol. 7, 97 0 (001).

23 Conclusions PDT model including light diffusion and PDT kinetics equations PS-specific photochemical parameters can be obtained in the in-vivo PDT model using COMSOL Photochemical parameters for BPD is reasonable based on previous results for Photofrin. Apparent singlet oxygen can be used directly for clinical PDT treatment to correlate better with efficacy than PDT dose.

24 Acknowledgements Lab technicians Joann Miller, Shannon Gallagher-Colombo, Carmen Rodriguez Physicists Jarod C. Finlay, Michele M Kim, Dayton McMillan, Daniel Chen Biologists Theresa Busch Physicians Keith Cengel, Chuck Simon, Stephen M Hahn, Eli Glatstein Grant support NIH R01 CA and P01 CA

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