Modeling of a Type II Photofrin‐mediated Photodynamic Therapy Process in a Heterogeneous Tissue Phantom

Abstract

We present a quantitative framework to model a Type II photodynamic therapy (PDT) process in the time domain in which a set of rate equations are solved to describe molecular reactions. Calculation of steady-state light distributions using a Monte Carlo method in a heterogeneous tissue phantom model demonstrates that the photon density differs significantly in a superficial tumor of only 3 mm thickness. The time dependences of the photosensitizer, oxygen and intracellular unoxidized receptor concentrations were obtained and monotonic decreases in the concentrations of the ground-state photosensitizer and receptor were observed. By defining respective decay times, we quantitatively studied the effects of photon density, drug dose and oxygen concentration on photobleaching and cytotoxicity of a photofrin-mediated PDT process. Comparison of the dependences of the receptor decay time on photon density and drug dose at different concentrations of oxygen clearly shows an oxygen threshold under which the receptor concentration remains constant or PDT exhibits no cytotoxicity. Furthermore, the dependence of the photosensitizer and receptor decay times on the drug dose and photon density suggests the possibility of PDT improvement by maximizing cytotoxicity in a tumor with optimized light and drug doses. We also discuss the utility of this model toward the understanding of clinical PDT treatment of chest wall recurrence of breast carcinoma.

Explicit dosimetry for 2-(1-hexyloxyethyl)-2-devinyl pyropheophorbide-a-mediated photodynamic therapy: macroscopic singlet oxygen modeling

“…(3) Tissue and blood oxygenation is a central component for PDT and also affects the tissue optical properties. 13,14,[26][27][28][29][30] (4) If the tissue is hypoxic, or becomes hypoxic as a result of the PDT treatment, the yield of 1 O 2 will be lower than expected. 6,7,24,31 To complicate matters further, all these parameters can change during treatment and each of the parameters can also influence the others.…”

“…(1), based on the diffusion approximation. Spatial and temporal distribution of the ground state photosensitizer (S 0 ) and 3 O 2 and 1 O 2 concentrations are obtained by solving a set of coupled time-dependent differential equations initially proposed by Foster et al 12,13 and later expanded by Hu et al 14 and our group 7,10,15 for macroscopic modeling. As the singlet and triplet state photosensitizers (½S 1 and ½T) as well as 1 O 2 decay or react with cellular targets immediately after they are created, their lifetimes are very short (nanoseconds to microseconds).…”

The role of photodynamic therapy (PDT) physics

“…21 A second, macroscopic model has also been developed. 22,23 This is an empirical model that does not take into account the actual oxygen and photosensitizer diffusion processes microscopically but instead approximates them with simpler functions. It does, however, explicitly account for the larger-scale spatial variation in fluence rate based on the diffusion approximation.…”

“…This model provides a quantity ͑reacted singlet oxygen͒ that can be used directly for clinical PDT dosimetry, and that relates directly to the threedimensional distribution of photosensitizers, light fluence rate, and a mean tissue oxygenation distribution. 22,23 …”

Macroscopic modeling of the singlet oxygen production during PDT

“…We adopted the rate equation approach first proposed by Foster et al 10 and later refined by Hu et al 11 to describe the PDT kinetics process. We use k i (i = 0, 1, …, 7) to designate the reaction rate.…”