Comparison of three light doses in the photodynamic treatment of actinic keratosis using mathematical modeling

Abstract

Photodynamic therapy (PDT) is an emerging treatment modality for various diseases, especially for cancer therapy. Although high efficacy is demonstrated for PDT using standardized protocols in nonhyperkeratotic actinic keratoses, alternative light doses expected to increase efficiency, to reduce adverse effects or to expand the use of PDT, are still being evaluated and refined. We propose a comparison of the three most common light doses in the treatment of actinic keratosis with 5-aminolevulinic acid PDT through mathematical modeling. The proposed model is based on an iterative procedure that involves determination of the local fluence rate, updating of the local optical properties, and estimation of the local damage induced by the therapy. This model was applied on a simplified skin sample model including an actinic keratosis lesion, with three different light doses (red light dose, 37 J∕cm2, 75 mW∕cm2, 500 s; blue light dose, 10 J∕cm2, 10 mW∕cm2, 1000 s; and daylight dose, 9000 s). Results analysis shows that the three studied light doses, although all efficient, lead to variable local damage. Defining reference damage enables the nonoptimal parameters for the current light doses to be refined and the treatment to be more suitable.

Red light photodynamic therapy for actinic keratosis using 37 J/cm2: Fractionated irradiation with 12.3 mW/cm2 after 30 minutes incubation time compared to standard continuous irradiation with 75 mW/cm2 after 3 hours incubation time using a mathematical modeling

“…A 200 µm thick partial ellipsoid included into a 150 µm thick parallelepiped was used to model a post‐curettage AK in epidermis and an iterative procedure alternating determination of the fluence rate and updating of the optical properties was derived from our previous work to model the PDT process. The determination of the fluence rate involves solving the one‐dimensional diffusion equation (equation 1) while the updating of the optical properties takes the biological clearance of PpIX, the conversion of MAL into PpIX and the PpIX photobleaching into account (equation ).…”

“…Similarly, to Farrell et al , based on a PpIX concentration varying only with depth, , below the irradiated surface (Fig. ), the local total fluence rate at time , depth , and wavelength , denoted by , is given by equation 1 :…”

“…Regarding the photobleaching process, based on our previous work , the number of PpIX molecules eliminated by photobleaching during the time interval , denoted by , can be estimated using equation : …”

“…The integral in the photobleaching term of equation (last part of the right hand side) represents the number of singlet oxygen molecules generated during the time interval in an unit volume, , located at depth in the skin sample model when the PpIX molecules, excited by absorption of photons, return to the ground state . Therefore, the sum of this integral over the time intervals , , ,…, with provides the total cumulative singlet oxygen molecules produced during the time interval .…”

“…In our previous work [21], the conversion of MAL into PpIX was modeled using an exponential growth function resulting in an controversial unlimited increase in time of the number of new PpIX molecules. In this paper, a more realistic model for the conversion of MAL into PpIX also taking into account the biological clearance of PpIX is defined based on clinical data from several studies while the photobleaching model is the same as in our previous work [21]. In order to model the time evolution of the PpIX absorption coefficient when considering only the biological clearance of PpIX and the conversion of MAL into PpIX, we use the fluorescence data reported by Wiegell et al [24].…”