PC simulation of photobleaching

It is possible to simulate the decrease in the concentrations o f ground state

photosensitisers using a numerical iterative model on a PC. The model used is based on the equations described in figure 5-1 and uses a com puter program which was originally

designed to model the concentrations involved in complex gaseous chain reactions and

was obtained from Dr. Adrian W hitwood (Departm ent o f Chemistry, University o f York,

York, UK). It must be noted that the model presented here does not consider vascular constriction which reduces the oxygen concentration in the treated tissue. To simplify

the modelling the oxygen level was held constant during each simulation.

Specifying initial concentrations o f photosensitiser and oxygen together with com posite rate constants for the reactions it is possible to calculate the concentration o f the ground

state photosensitiser as a function o f time The program can then display a graph

illustrating these changes. The figure below dem onstrates a typical output graph

showing depletion o f So through photobleaching induced by PDT.

10 9.59 n 7.67 - 5.76 - 3.84 - 1.92 - -^*10% 10.00 .0 0 .00 2 .0 0 4.00 6.00 8.00

Using the simulation software it is possible to vary the initial concentrations o f both the photosensitiser and the oxygen and study the change this has on the half-life (time taken to reach 1/e o f the initial value) o f the photosensitiser concentration (i.e. fluorescence intensity). The initial concentrations and rate constants are listed below together with the relevant references:

So=lxlO'^M, concentration o f photosensitiser in vivo (i.e. IpM , Chatlani et al 1993)

8h u = lxlO ’^ s '\ rate o f excitiation ki & q, =1x10* s'% (if~5ns (|)f=<|)t=0.5) kz = 1x10* s'% (Oschner, 1997)

ks=lxlO^ s'^ M"\ (for porphyrins - Borland et al, 1987) k4’=lxlO^ s'% (1(^0 2) ~ 0.1|is, Oschner, 1997)

ks’=2xl0^ s'^

ké=2xl0^ s'% (triplet state lifetime o f ~500|is, Oschner, 1997)

These values are typical for PDT photosensitisers, although kg would not apply to phthalocyanines - singlet oxygen reaction with the ground state. The values IC4’ & ks’ are

estimated pseudo first order rate constants. The value for the lifetime o f singlet oxygen at 0.1 ps is an estimate for a biological system. In simple solvents the lifetime is generally several microseconds whereas singlet oxygen is rapidly consumed through reactions with biolmolecules and thus has a shorter lifetime. The value o f k2 is typical for photosensitisers bound to proteins and is slower than values measured in solution (typically 2x10* NT^ s'^) where a higher rate o f oxygen diffusion applies. The rate o f excitation is calculated as 8hu=Iep, where I is the fluence rate and r is the molar conversion factor (3.8x10'^^ M cm"^). A value o f 10'^ corresponds to an intensity o f lOmW cm'^ s'^ with 8 at 3x10^ cm"\ The oxygen concentration w as held constant

for each simulation by inputting a pseudo first order rate constant k2’ = k2[0 2]. The figure below demonstrates the effect o f changing the rate o f excitation using a constant oxygen concentration o f lOpM.

Photobleaching 155 700 6 0 0 — in 50 0 H if) 2: 4 0 0 H O

S

o

0.01

0.02

Figure 5-28 Changes rate o f photobleaching %vith intensity o f incident light

Figure 5-28 shows change in the half-life o f the photosensitiser during photobleaching as a function o f the rate o f excitation. Over the selected intensity range the half-life decreases from 600s i.e. 10 minutes to about a minute. The rate o f excitation depends on the extinction coefficient and the irradiation intensity. Therefore for a constant irradiation intensity the rate o f photobleaching is increased for higher extinction coefficients. Estimation o f the value o f ks’ is admittedly arbitrary but increasing the value o f k f as expected resulted in an accelerated rate o f bleaching. The effect o f changing the oxygen levels was then simulated.

1100

1000

8

S

4

1e-8

O xygen concentration /M

1e-5

Figure 5-29 Effect on the half-life dependence o f S,, with various oxygen levels.

Figure 5-29 shows the half-life dependence on the initial oxygen concentration using a fixed rate o f excitiation at 10'^ s \ It is clearly seen from the above graph that the half- life o f the ground state photosensitiser is shorter at lower oxygen concentrations., i.e. photobleaching is faster at lower oxygen concentrations. This can be explained by the fact that the triplet state lifetime is longer at low oxygen levels, i.e. there is less quenching back to the ground state (ks dominates), and since the lifetime is longer there is a higher probability o f the triplet state reacting with the biomolecules, resulting in photobleaching.

Photobleaching 157

This may seem a surprising result but it appears to be in accord with some o f the experimental results e.g. the rate o f photobleaching o f AlS2Pc appeared to be faster when the blood supply to the organ was clamped, i.e. low oxygen levels. Likewise in the case o f PpIX the model predicts a faster rate o f bleaching at lower oxygen concentrations. A further important point to check however, was the contribution o f pathway f (i.e. reaction o f the ground state with singlet oxygen). For the above simulation a value o f k3=lxlO^ was selected but it was found that even if this value was increased to 1x10^® s'^ that the half-life remains unaffected at both low and high oxygen concentrations. The reason for this discrepancy compared to solution phase results is that in biological systems the half-life o f singlet oxygen is very much shorter and therefore its steady state concentration is much lower compared to a solution using the same oxygen and sensitiser concentrations. Therefore in this model using an initial photosensitiser concentration o f IpM the dominant photobleaching process even for PpIX is pathway h (photoreaction o f the triplet state photosensitiser with biolmolecular substrates). A deficiency in this model is that the local intracellular sensitiser concentration may be much higher so the contribution o f this reaction cannot necessarily be excluded in cells containing porphyrins.

Moreover in the case o f PpIX there is a further possible photobleaching mechanism to be considered which has been identified by Kreig & Whitten, (1984). They studied the mechanism o f PpIX photobleaching in erythrocyte ghosts and microemulsions with added amino acids (e.g. methionine). They proposed the following mechanism in which singlet oxygen firstly reacts with a biomolecular substrate to produce an intermediate peroxide which can then oxidise the porphyrin, resulting in photobleaching:

* O2 + B B + physical quenching (Icj)

+ A -> A O2 oxidation (k?)

+ A O2 photoproduct photobleaching (kg)

These equations were then added to the computer model described above. The values for the pseudo first order rate constant k? was selected as 1x10* s'^ which is an order o f

magnitude smaller than that for physical quenching; the value o f the rate constant kg was arbitrarily selected as 1x10^ M'^s'\ Inclusion o f these equations modified significantly the photobleaching kinetics as a function o f the oxygen concentration. Instead o f the rate o f photobleaching being faster at lower oxygen levels the rate o f bleaching was slightly slower at lower oxygen levels e.g. a half-life o f 520s was found at an oxygen concentration o f lOpM compared to a half-life o f 600s at 0.1 pM. Without this additional photobleaching mechanism the rate o f PpIX bleaching would be significantly faster at low oxygen levels which conflicts with previous experimental data on cells. The slightly slower rate o f photobleaching at low oxygen levels is in fact in reasonable agreement with cell studies carried out by Moan et al, (1997) where the oxygen concentration in the incubation medium was varied from air equilibrated levels to anoxic conditions (nitrogen purging). The cells were incubated with various concentrations o f ALA and then the fluorescence intensity o f PpIX was measured during irradiation. They found that the rate o f bleaching was about 50% slower at low oxygen levels. Another interesting result from the simulation was that the rate o f bleaching was now dependent on the initial photosensitiser concentration with a faster rate observed at higher concentrations, i.e. a second order dependence: increasing the initial sensitiser concentration to lOpM from IpM doubled the rate o f decay. Again this in agreement with the results o f Moan et al (1997) on cellular photobleaching. Whilst this simulation can be used to fit experimental data in incubated cells where the concentration o f oxygen is fairly constant it does have a limitation in the modelling photobleaching in tissue where the oxygen concentration will change during treatment. The comparison between the model and the dynamics in biological media is o f course somewhat qualitiative since the values o f the rate constants are estimates and in a cellular system would depend on localisation o f the photosensitiser. However, this modelling simulation does show that the photobleaching dynamics can at least explain differences observed between biological media and simple cuvette solvent studies.

Photobleaching 159

5 .8 Di s c u s s i o n

The change in the photosensitiser concentration during PDT has been monitored through diffuse reflectance spectroscopy, fluorescence emission spectroscopy and fluorescence imaging. Since the work concentrated on tw o photosensitisers in particular this section will be split to deal which each individually.

5.8.1 Photobleaching: Aluminium disulphonated phthalocyanine