1. Opto CANADA 9-10 May 2002CAo6-515 Model calculation on the efficiency of PDT by pulsed laser application Hans-Georg Fercher, Dirk Meyer, and Hans-Jochen Foth, Dept. of Physics, University of Kaiserslautern Germany

2. Problem: Cw-irradiation causes hypoxic regions between microvessels  PDT becomes ineffective J.P. Henning et al. 1995 T.H. Foster et al. 1991 Solution: Light fractionation (on/off intervalls with  t = 5 s to 60 s, T.H. Foster et al. 1992) Pulsed systems (pulsed flashlamp pumped dye laser with 15µs long pulses)

5. Conditions for transient calculation Laser parameters   = 15 ms  E P = 50 mJ  = 635 nm Distance between the capillaries  L = 100  m Time dependent values of the concentrations are shown for the centre between the capillaries

6. Numerical solution of the system of coupled differential equations on a personal computer

7. Used constants TransitionSymbolValue S 0  S 1 B S0S1 2 – 2,6 10 -3 m 2 /J S 1  S 0 k + A = U S0S1 1 – 30 10 6 s -1 M 1  M 0 k M1M0 0 – 3 10 5 s -1 T 1  S 0 k T1S0 1 – 40 10 3 s -1 S 1  T 1 k S1T1 1 – 80 10 6 s -1 M 1  A k M1A 1 10 6 s -1 Triplet Quench-RateQ1,5 – 2 10 -6 m 3 /(mol s) Ratio of collisions T 1  S 0 which generate M 1 SASA 0,4 – 0,6 Oxygen-diffusion rateD2 10 -5 s -1 cm 2 /s Metabolic O 2 decay rate  1,7 – 3,5 10 -3 mol/(m 2 s)

8. Results for transient calculation

10. Decrease of oxygen

13. Results using the responce function

14. Optimal treatment duration Goal: Treatment duration should be as short as possible Depletion of oxygen leads to low repetition rates which is in contrast to The treatment threshold is faster reached under high repetition rates

15. Number of pulses to reach the threshold = N = Therapeutic threshold [O 2 ] x pulse energy Treatment duration = t = N Repetition rate Decreases with increasing repetition rate

17. Conclusion Experimental finding: Efficiency of PDT is under pulsed laser exposure higher than under cw irradiation Results of this model calculations: The depletion of oxygen leads to a lower level of phototoxic compounds: Diffusion of oxygen is the bottle neck. Overlap of the efficiency and the mean power leads to a repetition rate around 5 Hz for the shortest treatment duration This value depends on the rate constants

18. Result for transient calculations