Oxygen diffusion and reaction kinetics in the photodynamic therapy of multicell tumour spheroids

Effects of oxygen diffusion and reaction kinetics in photodynamic therapy are considered in the context of a multicell tumour spheroid model. Steady-state measurements of oxygen made with a Clark-style microelectrode (4 microm diameter tip) enable us to determine the rate of metabolic oxygen consumption and the oxygen diffusion coefficient in 500 microm diameter EMT6/Ro spheroids. These values are 5.77 micromol 1(-1) s(-1) and 1460 microm2 s(-1), respectively. Time-dependent electrode measurements of oxygen concentration during laser irradiation of individual Photofrin-sensitized spheroids are fitted to numerical solutions of a pair of diffusion-with-reaction equations. The analysis yields the rate of photodynamic oxygen consumption and a parameter that governs the oxygen sensitivity of photodynamic therapy. These experimentally derived quantities are used to calculate the temporal and spatial distributions of oxygen and the rate of oxygen consumption in a spheroid during irradiation at several fluence rates. The spatial distribution of photodynamic oxygen consumption is strongly fluence rate dependent. Using the experimental and theoretical results developed in this report, previously published survival data are analysed. The analysis indicates that the threshold dose of reacting singlet oxygen in the EMT6/Ro spheroid is 323 +/- 38 micromol 1(-1) (mean +/- SEM).