Based on the whole mount imaging study of Mitra *et al.*^{6}, we simulated the initial spatial distributions of mTHPC as a function of radial distance from a perfused vessel in the tumor tissue at 3, 6, 24 and 96 h following *i.v.* injection as shown in . Immediately prior to irradiation, we estimated the volume-averaged mTHPC concentrations corresponding to these four drug-light intervals as 0.3, 0.42, 0.54, and 0.18 μg ml^{-1}, respectively^{16}, which are consistent with those reported by Cramers *et al.*^{4} and Triesscheijn *et al.*^{5}. Thus, in the simulations these average concentrations were distributed according to the measured intratumor distributions, which exhibited radial but no axial concentration gradient. As reported by Mitra *et al.*^{6}, at the short drug-light intervals of 3 and 6 h, the mTHPC concentration is higher in the vicinity of perfused vessels and decreases significantly with radial distance (). In contrast, show a dramatic reversal of the relative drug distributions at the 24 and 96 h time-points, with higher mTHPC concentrations remote from the nearest perfused vessels. In our mathematical simulations, these measured concentrations and intratumor distributions were explicitly incorporated as initial conditions.

Recently, Mitra and Foster^{17} evaluated the intratumor distribution of the photosensitizer NPe6 in an intradermal mouse EMT6 tumor model using *in vivo* confocal fluorescence imaging. They found that following a 1 h drug-light interval, PDT irradiation resulted in significant sensitizer extravasation. Thus, the sensitizer distribution that existed immediately prior to the onset of irradiation was modified by the treatment. Because such a redistribution would influence the simulations of photodynamic dose deposition, we used the same *in vivo* imaging method and intradermal tumor model to investigate the possibility that mTHPC might similarly extravasate upon irradiation at short drug-light intervals when drug is abundant in circulation. The intradermal tumors in anesthetized mice were irradiated on the stage of the confocal microscope using PDT treatment conditions (100 mW cm^{-2}, 30 J cm^{-2}) that were informed by those used by Cramers *et al.*^{4} and Triesscheijn *et al.*^{5}, and the drug-light intervals were 3 and 6 h. Unlike the case of NPe6-PDT, we observed no irradiation-induced redistribution of mTHPC from tumor vessels at either of these time points (not shown).

illustrates the computed cumulative spatially-resolved ^{1}O_{2} dose deposition within tumor tissue regions at the four drug-light intervals, calculated for mTHPC-PDT performed at an irradiance of 100 mW cm^{-2} and a fluence of 30 J cm^{-2}. Significant radial gradients in ^{1}O_{2} deposition are present in the 3 and 6 h cases for all axial locations. Because of the combination of oxygen diffusion from vessels and the reversal of the initial spatial mTHPC distributions at 24 and 96 h (), the dose distributions for these two drug-light intervals are more uniform in the radial direction than at the 3 and 6 h time-points (). The maximum dose deposition at any location among all the treatment conditions is approximately 1.1 mM, which occurs at the capillary wall and *z* = 0, for the 3 h case ().

In , we present for each of the four drug-light intervals the simulated volume-averaged reacted ^{1}O_{2} concentrations, < [^{1}O_{2}] >, vs. fluence () and the irreversible loss of mTHPC via photobleaching after 30 J cm^{-2} () for PDT delivered at an irradiance of 100 mW cm^{-2}. The volume averages are computed from the spatially resolved distributions like those shown in , and they represent quantities proportional to those that would be measured experimentally by ^{1}O_{2} luminescence or photobleaching, respectively. For a given fluence, the amount of ^{1}O_{2} deposited in the tumor is greatest for the 24 h interval. At 30 J cm^{-2}, the deposited dose for the 24 h case is 1.6-fold greater than that at 3 h. Based on our previous report^{8} and the current results, we note that the macroscopic deposition of reacted ^{1}O_{2} is more sensitive to the initial sensitizer concentration than to the pattern of the initially nonuniform distributions. plots the loss of sensitizer vs. the reacted < [^{1}O_{2}] > following a fluence of 30 J cm^{-2} for all four of the drug-light intervals. Consistent with expectations for a self-sensitized ^{1}O_{2}-mediated reaction process, for a given fluence, the extent of photosensitizer degradation correlates well with the amount of ^{1}O_{2} dose deposited. These results may be compared with the summary of tumor responses to mTHPC-PDT presented in , which were collected from the reports of Cramers *et al.*^{4} and Triesscheijn *et al.*^{5}. It is apparent that neither of the volume-averaged dose metrics predicts the rank ordering of recurrence free survival measured for these PDT treatment conditions.

The plots of show differential dose volume histograms depicting the percentage of the tumor volume that receives increments of reacted [^{1}O_{2}] from a minimum of 0.06 to a maximum of 1.12 mM for the four drug-light intervals and the same irradiation protocol as used for the simulations of Figs. and . Each individual column in the histograms represents an increment of 0.01 mM of [^{1}O_{2}]. These histograms demonstrate that for all cases, cells throughout the entire tumor volume receive a dose of ^{1}O_{2} that is low relative to the 8 mM threshold of reacting ^{1}O_{2} determined by Coutier *et al.*^{9} for mTHPC-PDT in multicell tumor spheroids. The maximum deposited dose decreases with increasing drug-light interval. Although subpopulations of tumor cells receive higher ^{1}O_{2} doses at the 3 and 6 h vs. 24 and 96 h drug-light intervals, the tumor volume receiving these comparatively higher doses is extremely small. For example, the maximum dose deposited anywhere in the tumor for the 24 h case is 0.42 mM, and at 3 and 6 h drug-light intervals this maximum increases to 1.12 and 0.81 mM, respectively. At these shorter intervals, however, the percentages of the tumor volume receiving doses greater than 0.42 mM are only 2.5% and 6.6%, respectively.

Plotted in is the percentage of the tumor volume receiving doses within the ranges [^{1}O_{2}] < 0.4 mM and [^{1}O_{2}] ≥ 0.8 mM for the various drug-light intervals. illustrates the percentage of tumor volume within a 25 μm radial distance of the capillary wall, which is the tumor region containing the endothelial cells and proliferating tumor cells, for the same dose ranges and drug-light intervals. demonstrates that for all cases, more than 90% of the whole tumor volume receives a dose which is less than 0.4 mM, which is 20-fold below the 8 mM threshold. As shown in , even when the analysis is restricted to the volume close to a perfused vessel, large fractions of the cells receive doses within this range. illustrate that a dose greater than or equal to 0.8 mM, which represents a dose within an order of magnitude of the experimentally determined threshold, is deposited to cells only at the shorter drug-light intervals of 3 and 6 h. The tumor volumes receiving these maximum doses are however extremely small. Thus, even within 25 μm of the capillary (), at the 3 h drug-light interval only approximately 5% of the cells receive a dose within an order of magnitude of the threshold. At the 6 h interval, the fraction is significantly less.