Model calculation on the efficiency of PDT by pulsed laser a pplication
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Opto CANADA 9-10 May 2002 CAo6-515
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
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Problem:
Cw-irradiation causes hypoxic regions between microvessels PDT becomes ineffective
J.P. Henning et al. 1995T.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)
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A rte ry
Ve in
C ap illa ry
T issu e C y lin d e r
Tissu e m o d e lK ro g h 's cy lin d e r
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S 0
S 1
T 1
M 0
M 1A
D iffu s io n
SensitizerO xygen
Reaction partnerof O1
2
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Conditions for transient calculation
Laser parameters = 15 ms EP = 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
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Numerical solution of the system of coupled differential equations
on a personal computer
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Used constants
Transition Symbol Value
S0 S1 BS0S1 2 – 2,6 10-3 m2/J
S1 S0 k + A = US0S1 1 – 30 106 s-1
M1 M0 kM1M0 0 – 3 105 s-1
T1 S0 kT1S0 1 – 40 103 s-1
S1 T1 kS1T1 1 – 80 106 s-1
M1 A kM1A 1 106 s-1
Triplet Quench-Rate Q 1,5 – 2 10-6 m3/(mol s)
Ratio of collisions T1 S0
which generate M1
SA 0,4 – 0,6
Oxygen-diffusion rate D 2 10-5 s-1 cm2/s
Metabolic O2 decay rate 1,7 – 3,5 10-3 mol/(m2 s)
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Results for transient calculation
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Results for transient calculation
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Decrease of oxygen
0 .0 0 .1 0 .2 0 .3 0 .4 0 .5 0 .6 0 .7
4 .9 0
4 .9 5
5 .0 0
5 .0 5
5 .1 0
5 .1 5
5 .2 0
5 .2 5
CM 0(x1 00,t)
T im e [m s]
Con
cent
ratio
n [1
0 m
ol/m
]-3
3
=30 s, E =50 m Jp
=30 s, E =100 m Jp
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0 1 00 2 00 3 00 4 00 5 000
1
2
3
4
5
5Hz 10Hz 20Hz 30Hz 50Hz 100Hz 200Hz
C o n c e n tra tio n o f A u n d e r v a r io u s re p e titio n ra te s
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0 2 0 4 0 6 0 8 0 1 0 0 1 2 0 1 4 0 1 6 0 1 8 0 2 0 0
4 .2
4 ,4
4 ,6
4 ,8
5 ,0
5 ,2
5 ,4
a fte r 3 5 0 p u lse s w ith 5 0 m J
50H z
30H z
D is tan ce [ m ]
C o n ce n tra tio n o f re ac tio n p ro d u c ts
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Results using the responce function
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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
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Number of pulses to reach the threshold = N =
Therapeutic threshold
[O2] x pulse energy
Treatment duration = t = N
Repetition rate
Decreases with increasing repetition rate
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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
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Result for transient calculations