Parameter Optimization for FEM based modeling of singlet oxygen during PDT using COMSOL

Transcription

1 Presented at the COMSOL Conference 21 Boston COMSOL Conference, Boston, 1/8/21 Parameter Optimization for FEM based modeling of singlet oxygen during PDT using COMSOL Xing Liang, Ken Kang-Hsin Wang, and Timothy C. Zhu Department of Radiation Oncology, School of Medicine, University of Pennsylvania

2 Outline Introduction Theory for PDT dosimetry model Optimization results PDT dosimetry quantity prediction for prostate using COMSOL Conclusions

3 Outline Introduction Theory for PDT dosimetry model and optimization Optimization results PDT dosimetry quantity prediction for prostate using COMSOL Conclusions

4 Introduction Photodynamic therapy (PDT) is an important treatment modality for cancer and other localized diseases. In PDT, photosensitizers excited by light react with ground state oxygen, which leads to generation of singlet oxygen - the major cytotoxic agent - to kill the surrounding tissues and cells. Compared with other treatment modalities, PDT has advantages including non-ionizing, localized photon delivery and better cosmetic outcome.

5 Introduction Jablonski Diagram for Type II PDT interaction S 1 Intersystem crossing k 7, Reaction with targets [A] k 5 Energy transfer to O 2 k, absorption T 1 O 2 k 2 k 3,fluorescence k 4, phosphorescence k 6, phosphorescence, l = 126 nm S k 1, photobleaching 3 O 2 Sensitizer Oxygen Sensitizer (PS) + light + oxygen ( 3 O 2 ) singlet oxygen ( 1 O 2 )

6 Introduction Apparent reacted singlet oxygen [ 1 O 2 ] rx was introduced as a PDT dosimetry quantity to better predict the PDT treatment outcome than PDT dose Light Distribution Optimal Parameters Geometry Parameters Experimental Necrosis Radius Geometry From Ultrasound Image By COMSOL By COMSOL + MATLAB Predicted [ 1 O 2 ] rx distribution Flow chart for PDT photophysiological parameter optimization and dosimetry prediction

7 Outline Introduction Theory for PDT dosimetry model and optimization Optimization results PDT dosimetry quantity prediction for prostate using COMSOL Conclusions

8 Theory for PDT dosimetry model Light diffusion equation 1 a 3 s ' S COMSOL Photo chemical equations S 3 ds [ ] [ ] [ O2] [ S 3 ] dt [ O2 ] 3 3 d[ O2] [ S] 3 [ O2] [ 3 O2 ] g1 3 dt [ O2] [ O2]( t ) MATLAB 1 3 d[ O2 ] rx [ S][ O2 ] 3 dt [ O2 ] φ Light fluence rate [S ] Ground sensitizer concentration [ 3 O 2 ] Ground triplet oxygen concentration [ 1 O 2 ] rx Reacted singlet oxygen concentration

9 Theory for optimization model Initial guess of [ ξ, σ, β, g] Differential equations Solution for [ 1 O 2 ] rx In vivo mice study Necrosis radius Minimize deviation of 1 O 2 MAX 1 1 O 2 rx ( r ) n rx, sd [ 1 O 2 ] rx (r n ) [ 1 O 2 ] rx,sd Fitting results [ ξ, σ, β, g] and [ 1 O 2 ] rx

10 Outline Introduction Theory for PDT dosimetry model and optimization Optimization results PDT dosimetry quantity prediction for prostate using COMSOL Conclusions

11 Optimization results LS source strength (mw/cm) Aug Nov Apr Treatment time (s) Necrotic Dis. (mm) 4 2 fluence rate at nec. rad. (mw/cm 2 ) mice index mice index

12 Optimization results Parameters Final fit Apr Fit Apr and Aug Fit Previous fit [1] Published values ξ (cm 2 /s/mw) u i [2] σ (1/M) β (M) g (M/s) [2] [3] _ [ 1 O 2 ] rx,sh (mm) _ [1] Wang et al., J. Biophoton, 21. [2] Mitra et al., Photochem. Photobiol, 25. [3] Georgakoudi et al., Photochem. Photobiol

13 Optimization results Final fitting results including experimental data from All data [ 1 O 2 ] rx (mm) Aug M1 no PDT effect Aug M2 w/ PDT effect Aug M3 w/ PDT effect Aug M4 w/ PDT effect Apr M5 no PDT effect Apr M6 no PDT effect Apr M7 w/ PDT effect Apr M8 no PDT effect Apr M9 w/ PDT effect Nov M1 w/ PDT effect Nov M11 w/ PDT effect Nov M12 w/ PDT effect Oxygen (μm) (um) Sensitizer concentration (um) (μm) r (mm) Apparent reacted singlet oxygen concentration r (mm) Oxygen concentration r (mm) Photosensitizer concentration

14 Optimization results Fitting results: apparent reacted singlet oxygen concentration All data April data April and August data [ 1 O 2 ] rx (mm) Aug M1 no PDT effect Aug M2 w/ PDT effect Aug M3 w/ PDT effect Aug M4 w/ PDT effect Apr M5 no PDT effect Apr M6 no PDT effect Apr M7 w/ PDT effect Apr M8 no PDT effect Apr M9 w/ PDT effect Nov M1 w/ PDT effect Nov M11 w/ PDT effect Nov M12 w/ PDT effect [ 1 O 2 ] rx (mm) [ 1 O 2 ] rx (mm) r (mm) g =.8 M/s = 2. x 1-3 cm 2 mw -1 s -1 = 11.2 x 1-5 M -1 [ 1 O 2 ] rx,sh =.41 mm r (mm) g =.62 M/s = 5. x 1-3 cm 2 mw -1 s -1 = 6.6 x 1-5 M -1 [ 1 O 2 ] rx,sh =.46 mm r (mm) g =.56 M/s = 3.9 x 1-3 cm 2 mw -1 s -1 = 11.5 x 1-5 M -1 [ 1 O 2 ] rx,sh =.41 mm

15 Outline Introduction Theory for PDT dosimetry model and optimization Optimization results PDT dosimetry quantity prediction for prostate using COMSOL Conclusions

16 [ 1 O 2 ] rx prediction using COMSOL Prostate geometry for prediction model Geometry Meshing

17 [ 1 O 2 ] rx prediction using COMSOL PDT dosimetry quantities for treatment up to 3 s in a homogeneous prostate mm Slide view of [ 1 O 2 ] rx Isosurface of [ 1 O 2 ] rx at.41 mm Isosurface of light flucence

18 [ 1 O 2 ] rx,sh prediction using COMSOL Top view of isosurface of [ 1 O 2 ] rx at.41 mm 2 s 5 s 1 s Top view of isosurface of light flucence 3 J/cm 2 75 J/cm 2 15 J/cm 2

19 Conclusions PDT model including light diffusion and PDT kinetics equations Optimized photo-chemical parameters in the PDT model PDT prostate model with homogeneous properties Prediction of PDT dosimetry quantities for treatment

20 Thank you!