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

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)

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

S 0

S 1

T 1

M 0

M 1A

D iffu s io n

SensitizerO xygen

Reaction partnerof O1

2

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

Numerical solution of the system of coupled differential equations

on a personal computer

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)

Results for transient calculation

Results for transient calculation

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

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

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

Results using the responce function

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

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

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

Result for transient calculations