Photodynamic dose does not correlate with long-term tumor response to mTHPC-PDT performed at several drug-light intervals

Abstract

Meso-tetra-hydroxyphenyl-chlorin (mTHPC, Foscan®), a promising photosensitizer for photodynamic therapy (PDT), is approved in Europe for the palliative treatment of head and neck cancer. Based on work in mice that investigated optimal tumor accumulation, clinical protocols with Foscan® typically employ an interval of 96 h between systemic sensitizer administration and irradiation. However, recent studies in mouse tumor models have demonstrated significantly improved long-term tumor response when irradiation is performed at shorter drug-light intervals of 3 and 6 h. Using a previously published theoretical model of microscopic PDT dosimetry and informed by experimentally determined photophysical properties and intratumor sensitizer concentrations and distributions, we calculated photodynamic dose depositions following mTHPC-PDT for drug-light intervals of 3, 6, 24, and 96 h. Our results demonstrate that the singlet oxygen dose to the tumor volume does not track even qualitatively with tumor responses for these four drug-light intervals. Further, microscopic analysis of simulated singlet oxygen deposition shows that in no case do any subpopulations of tumor cells receive a threshold dose. Indeed, under the conditions of these simulations more than 90% of the tumor volume receives a dose that is approximately 20-fold lower than the threshold dose for mTHPC. Thus, in this evaluation of mTHPC-PDT at various drug-light intervals, any PDT dose metric that is proportional to singlet oxygen creation and∕or deposition would fail to predict the tumor response. In situations like this one, other reporters of biological response to therapy would be necessary.

INTRODUCTION

Meso-tetra-hydroxyphenyl-chlorin (mTHPC, Foscan®) is a potent second-generation photosensitizer for photodynamic therapy (PDT). It has been approved for palliative treatment of head and neck cancer in the European Union and has undergone clinical trials for other neoplastic conditions, such as mesothelioma and prostate cancer.¹ The interval between systemic mTHPC administration and irradiation in clinical protocols is typically 96 h.² This interval is based on studies in mice, which demonstrated maximum sensitizer accumulation in squamous epithelium at this time.³

Recently, Cramers et al.⁴ compared plasma and tissue levels of mTHPC at various times after drug administration with the PDT response of normal skin and human mesothelioma xenografts (H-MESO1) implanted subcutaneously in female BALB∕c nude mice. Their results showed that the maximal response of tumor and normal skin occurred when irradiation was performed 1–6 h after i.v. injection. Response was significantly attenuated at longer drug-light intervals. This treatment response did not correlate with H-MESO1 tumor and normal skin mTHPC levels, which increase in the first 24 h after injection and thereafter remain approximately constant for 120 h. Tissue response did exhibit a strong correspondence with plasma drug level, which decreases with time after administration. Triesscheijn et al.⁵ from the same research group expanded this work by further comparing the changes in vascular perfusion and tumor hypoxia induced by mTHPC-PDT at various drug-light intervals with the treatment response of human squamous cell carcinoma xenografts (HNXOE). This study confirmed that PDT using short drug-light intervals of 3 and 6 h leads to marked decrease of vascular perfusion, increase in tumor hypoxia, and the significant degeneration of vascular tissue. These vascular changes were in turn correlated with high plasma drug levels and long-term tumor control. In contrast, treatment at a 48 h drug-light interval, where plasma drug levels were significantly lower, induced a relatively modest response compared to untreated tumors and resulted in rapid tumor regrowth.

These two tumor response studies are supported by detailed tissue drug pharmacokinetics measurements. Further, the intratumor distribution of mTHPC relative to capillaries has been imaged over this range of drug-light intervals,⁶ and the photophysical properties of mTHPC have been well characterized.⁷ These factors combine to create a favorable opportunity to study the deposition of photodynamic dose using a recently published, comprehensive mathematical model.⁸ This model enables the incorporation of all of the relevant photophysical phenomena, including photobleaching, and accommodates experimentally determined initially nonuniform sensitizer distributions and concentrations. Results from simulations performed with this model indicate that at all drug-light intervals a large fraction of the tumor volume received a photodynamic dose that was significantly below an experimentally determined threshold for mTHPC-PDT.⁹ Significant heterogeneities in dose distributions were particularly evident for the 3 and 6 h drug-light intervals, where tumor response was most durable. Finally, the trend in the calculated volume-averaged singlet oxygen (¹O₂) dose for the various drug-light intervals did not track with the corresponding trend in tumor response, indicating that any dose metric proportional to ¹O₂ would not be successful in predicting the treatment outcome in this situation.

METHODS

Theoretical model

The theoretical model and numerical methods used in this study were described in detail by Wang et al.⁸ Briefly, a cylindrical geometry and solutions to time-dependent oxygen (³O₂) transport-with-reaction equations were adopted to simulate the spatial distribution of ³O₂ within and near a capillary, the reacted ¹O₂ within the surrounding tissue region, and the irreversible degradation of the photosensitizer via photobleaching. Capillaries at defined intercapillary spacings are the ³O₂ sources to the immediately surrounding tumor tissue. Each capillary is a cylinder with a finite length L. As blood flows downstream from the arterial (z=0) to the venous (z=L) end of the capillary, ³O₂ is transported within the capillary and into the adjacent tumor tissue in both the radial, r, and axial, z, directions. Incorporating the above transport mechanisms and the Hill equation,

$$\mathrm{S}{\mathrm{O}}_2=\frac{C_{\mathrm{cap}}^n}{C_{50}^n+C_{\mathrm{cap}}^n},$$ (1)

where SO₂ is the hemoglobin oxygen saturation, C_cap is the oxygen concentration dissolved in the vessel, n is the Hill coefficient, and C₅₀ is the dissolved vessel oxygen concentration corresponding to 50% hemoglobin saturation, we can derive the two-dimensional, time-dependent ³O₂ diffusion equations within the capillary and tissue by mass balance. The equation in the capillary is written

$$(1+C_{\mathrm{sat}}\frac{\partial \mathrm{S}{\mathrm{O}}_2}{\partial C_{\mathrm{cap}}})\frac{\partial C_{\mathrm{cap}}}{\partial t}=D_{\mathrm{cap}}\left(\frac{1}{r}\frac{\partial }{\partial r}\left(r\frac{\partial C_{\mathrm{cap}}}{\partial r}\right)\right)+D_{\mathrm{cap}}\frac{{\partial }^2{C}_{\mathrm{cap}}}{\partial z^2}-V(1+C_{\mathrm{sat}}\frac{\partial \mathrm{S}{\mathrm{O}}_2}{\partial C_{\mathrm{cap}}})\frac{\partial C_{\mathrm{cap}}}{\partial z},0⩽r⩽R_c,$$ (2)

where

$$C_{\mathrm{sat}}\frac{\partial \mathrm{S}{\mathrm{O}}_2}{\partial C_{\mathrm{cap}}}=C_{\mathrm{sat}}n{C}_{50}^n\frac{C_{\mathrm{cap}}^{n-1}}{{(C_{50}^n+C_{\mathrm{cap}}^n)}^2}$$ (3)

and the equation in the tissue is

$$\frac{\partial C_{\mathrm{tiss}}}{\partial t}=D_{\mathrm{tiss}}\left(\frac{1}{r}\frac{\partial }{\partial r}\left(r\frac{\partial C_{\mathrm{tiss}}}{\partial r}\right)\right)+D_{\mathrm{tiss}}\frac{{\partial }^2{C}_{\mathrm{tiss}}}{\partial z^2}-\Gamma ,R_c⩽r⩽b.$$ (4)

Here, C_tiss is the oxygen concentration in the tissue, t is time, V is the blood flow velocity, C_sat is the maximum saturated concentration of oxygen bound to hemoglobin, and R_c and b are the capillary radius and half the distance between two adjacent capillaries, respectively. Γ is the sum of the metabolic, Γ_met, and photodynamic, Γ_PDT, rates of ³O₂ consumption. Michaelis–Menten kinetics¹⁰ are used to describe the ³O₂ dependence of metabolic ³O₂ consumption and avoid the production of nonphysiological negative ³O₂ concentrations. The specific form of Γ_PDT used in this study incorporates the self-sensitized ¹O₂-mediated bleaching mechanism developed by Georgakoudi et al.¹¹ and a low photosensitizer concentration correction proposed by Finlay¹² and by Dysartet al.¹³ The photobleaching of mTHPC has been shown to be consistent with this mechanism.^{7, 14, 15} The expression for Γ_PDT is written

$${\Gamma }_{\mathrm{PDT}}(r,z,t)={\Gamma }_0\left(\frac{C_{\mathrm{tiss}}(r,z,t)}{C_{\mathrm{tiss}}(r,z,t)+k_p∕k_{\mathrm{ot}}}\right)(1-\xi )\exp \{-\frac{k_{\mathrm{os}}}{k_{\mathrm{oa}}\left[A\right]}\int {\Gamma }_{\mathrm{PDT}}(r,z,t)dt\},$$ (5)

where

$$\xi =\frac{\delta k_{\mathrm{os}}}{\left[S_0\right]\left(0\right)k_{\mathrm{oa}}\left[A\right]}\int {\Gamma }_{\mathrm{PDT}}(r,z,t)\exp \{\frac{k_{\mathrm{os}}}{k_{\mathrm{oa}}\left[A\right]}\int {\Gamma }_{\mathrm{PDT}}(r,z,t)dt\}dt$$ (6)

and Γ₀=β_PDTψ. Γ₀ is the initial, maximal rate of photochemical oxygen consumption prior to photobleaching under conditions where oxygen is not rate limiting, [S₀](0) is the initial ground-state photosensitizer concentration prior to irradiation, β_PDT is the proportionality constant between Γ₀ and fluence rate ψ. The time integration of Eq. 5 for a given irradiation period yields the corresponding photodynamic dose, defined as the local amount of reacted ¹O₂ per unit volume of tissue. The definitions of the model parameters are given in the nomenclature.

Using a whole-mount fluorescence imaging technique, Mitra et al.⁶ measured the spatially nonuniform sensitizer distributions near perfused vessels at 3, 6, 24, and 96 h following i.v. injection of 5 mg kg⁻¹ mTHPC. This concentration was higher than that used in the tumor control studies of Cramers et al.⁴ and Triesscheijn et al.⁵ (0.3 mg kg⁻¹), but it was necessary in order to image at adequate signal to noise ratio. We then mapped volume averaged mTHPC concentrations measured by Jones et al.¹⁶ following an injected concentration of 0.3 mg kg⁻¹ into the experimentally measured mTHPC distributions and incorporated these into the simulations as initial conditions. In the presence of a nonuniform sensitizer distribution, the initial ground-state photosensitizer concentration, [S₀](0), becomes a function of the radial distance from the capillary wall. Thus, the expression for [S₀] takes the form

$$\left[S_0\right]\left(r\right)=\left[S_0\right](R_c,0)\times F\left(r\right),$$ (7)

where r is the radial distance from the vessel wall to the midpoint between two adjacent capillaries, [S₀](R_c,0) is the initial mTHPC concentration at capillary wall, and F(r) is the initial sensitizer distribution at the four different drug-light intervals, which is obtained by interpolating the experimental data along the radial direction.

The two diffusion equations for the capillary (Eq. 2) and the tissue regions (Eq. 4) are solved numerically using a finite difference method, subject to the appropriate boundary and initial conditions.⁸ We consider the case of a 5.5 μm capillary radius, a 350 μm capillary length, an intercapillary distance of 170 μm, and a 100 μm s⁻¹ blood flow velocity. The value of the other physiological parameters can be found in our previous publication.⁸ The photophysical parameters and the physiological parameters related to the Hill Equation used for this study are listed in Table 1. These parameters are experimentally determined, and their origins are previously described.⁸ The specific choice of physiological parameters such as the rate of metabolic oxygen consumption, intercapillary spacing, capillary radius, and capillary length, will change the details of the computed dose deposition. However, we have tested that within a reasonable range of these parameters, the perturbation induced by the choice of parameters is not able to change the qualitative features of the results presented in this study.

Table 1.

Photophysical and physiological parameters used in the simulation.

Symbol	Value
aβPDT (μM s−1 mW−1 cm2)	0.063
	0.045
	0.021
	0.006
δ	33 μM
kp∕kot	8.7 μM
kos∕koa[A]	29.7 M−1
n	2.46
Csat	8722 μM
C50	35 μM
SO2(t=0)	0.58

^aOn the basis of published reports (see Refs. ⁴, ⁵, ¹⁶), we estimate that the mTHPC concentrations in murine tumors at 3, 6, 24 and 96 h following i.v. injection (0.3 mg kg⁻¹) are 0.3, 0.42, 0.54, and 0.18 μg ml⁻¹, assuming a tissue density of 1 g cm⁻³. Using these data and methods described in Wang et al. (Ref. ⁸), we calculate β_PDT at 650 nm at the capillary wall to be 0.063, 0.045, 0.021, and 0.006 for the cases of nonuniform mTHPC distribution at 3, 6, 24 and 96 h drug-light intervals, respectively.

In vivo confocal imaging of mTHPC

As noted above, the mathematical model uses experimentally determined intratumor distributions of mTHPC as an initial condition, and it was therefore important to ensure that our intratumor distributions of mTHPC were not perturbed by irradiation in vivo. Using in vivo confocal fluorescence imaging, Mitra and Foster¹⁷ found that following a 1 h drug-light interval, a fluence of 10 J cm⁻² resulted in significant extravasation of mono-L-aspartylchlorin-e6 (NPe6) in an intradermal mouse EMT6 tumor model. We used the same in vivo imaging method and tumor model to investigate possible mTHPC intratumor redistribution upon irradiation at short drug-light intervals. mTHPC was obtained from Biolitec AG (Jena, Germany) and dissolved in 30% polyethylene glycol 400, 20% ethanol, and 50% water according to the manufacturer’s recommendations. Tumors were initiated by injection of 2×10⁵ EMT6 cells into the intradermal space of the ear pinna of 4–6 week old female BALB∕c mice. PDT irradiation and imaging were performed when the tumors reached a diameter 3–5 mm. In vivo imaging of anaesthetized, live mice was performed using a custom, inverted laser scanning confocal microscope.¹⁸ To render the vasculature fluorescent, a 20 μl solution of 0.05 mg ml⁻¹ AlexaFluor488-conjugated anti-mouse CD31 antibodies (clone MEC13.3, Biolegend, San Diego, CA) was injected intradermally 6 h before imaging.¹⁷ 5 mg kg⁻¹ mTHPC was intravenously injected via the tail vein 3 or 6 h prior to PDT. The anesthetized mouse was positioned with the tumor in contact with a coverslip mounted on the stage of the microscope. Hair overlying the tumor was removed using a depilatory cream (Nair, Princeton, New Jersey) prior to imaging. The tumors were subjected to 658 nm irradiation using a diode laser (Power Technology Inc., Alexander, AR), with an irradiance of 100 mW cm⁻². The mTHPC fluorescence was imaged prior to PDT and after delivery of specific fluences up to 30 J cm⁻². Sequential two-color excitation (488 nm for AlexaFluor488; 639 nm for mTHPC) provided fluorescence images of CD31-labeled vasculature and mTHPC distributions, respectively, in identical fields of view.

RESULTS

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 Figs. 1a, 1b, 1c, 1d. 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 Triesscheijnet 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 [Fig. 1a, 1b]. In contrast, Figs. 1c, 1d 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.

Figure 1.

Intratumor mTHPC distributions relative to the capillary wall (r=5.5 μm) prior to the onset of PDT at (a) 3 h, (b) 6 h, (c) 24 h, and (d) 96 h following i.v. injection (see Ref. 6). The initial volume averaged mTHPC concentrations corresponding to the 3, 6, 24 and 96 h drug-light intervals are 0.3, 0.42, 0.54 and 0.18 μg ml⁻¹, respectively (see Refs. ⁴, ⁵, ¹⁶).

Recently, Mitra and Foster¹⁷ 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).

Figure 2 illustrates the computed cumulative spatially resolved ¹O₂ 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 ¹O₂ 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 [Figs. 1c, 1d], 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 [Figs. 2a, 2b vs. Figs. 2c, 2d]. 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 [Fig. 2a].

Figure 2.

Computed spatial distribution of ¹O₂ dose, [¹O₂] (r,z), deposited during mTHPC-PDT at an irradiance of 100 mW cm⁻² for a fluence of 30 J cm⁻², assuming initial 3 h (a), 6 h (b), 24 h (c) and 96 h (d) mTHPC distributions.

In Fig. 3, we present for each of the four drug-light intervals the simulated volume-averaged reacted ¹O₂ concentrations, ⟨[¹O₂]⟩, vs. fluence [Fig. 3a] and the irreversible loss of mTHPC via photobleaching after 30 J cm⁻² [Fig. 3b] 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 Fig. 2, and they represent quantities proportional to those that would be measured experimentally by ¹O₂ luminescence or photobleaching, respectively. For a given fluence, the amount of ¹O₂ 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 article⁸ and the current results, we note that the macroscopic deposition of reacted ¹O₂ is more sensitive to the initial sensitizer concentration than to the pattern of the initially nonuniform distributions. Figure 3c plots the loss of sensitizer vs. the reacted ⟨[¹O₂]⟩ following a fluence of 30 J cm⁻² for all four of the drug-light intervals. Consistent with expectations for a self-sensitized ¹O₂-mediated reaction process, for a given fluence, the extent of photosensitizer degradation correlates well with the amount of ¹O₂ dose deposited. These results may be compared with the summary of tumor responses to mTHPC-PDT presented in Table 2, 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.

Figure 3.

(a) Simulated volume-averaged reacted ¹O₂ concentration, ⟨[¹O₂]⟩, vs fluence (J cm⁻²) for a fluence rate of 100 mW cm⁻² and four drug-light interval intervals, 3, 6, 24, and 96 h, corresponding to the initial mTHPC concentrations of 0.3, 0.42, 0.54 and 0.18 μg ml⁻¹, respectively. (b) Volume-averaged loss of mTHPC mediated by a ¹O₂-mediated bleaching mechanism vs four drug light intervals and PDT irradiation conditions of 100 mW cm⁻² and a fluence of 30 J cm⁻². (c) PDT-induced loss of mTHPC vs. the reacted ⟨[¹O₂]⟩ at 30 J cm⁻² for four drug light intervals.

Table 2.

Mean recurrence-free survival of mTHPC—PDT-treated tumors illuminated with 100 mW cm⁻² and 30 J cm⁻² reproduced from Fig. 3 of Cramers et al. (see Ref. 4) and Fig. 2(A) of Triesscheijn et al. (see Ref. 5). The recurrence-free interval is defined by the time taken for a tumor diameter to increase 2 mm from its treatment size. Tumors that had not regrown within 120 days were defined as cured.

Drugh-light interval (h)	Recurrence-free survival (days)
	Cramers et al. (see Ref. 4)	Triesscheijn et al. (see Ref. 5)
Control	16	10
0.08	33	40
0.33	63	67
1	100	100
3	120	120
6	104	117
24	40	84
48	24	30
72	22	NA

The plots of Fig. 4 show differential dose volume histograms depicting the percentage of the tumor volume that receives increments of reacted [¹O₂] 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. 23. Each individual column in the histograms represents an increment of 0.01 mM of [¹O₂]. These histograms demonstrate that for all cases, cells throughout the entire tumor volume receive a dose of ¹O₂ that is low relative to the 8 mM threshold of reacting ¹O₂ 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 ¹O₂ 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.

Figure 4.

Differential dose volume histograms depicting the percent of the tumor volume receiving various concentrations of reacted ¹O₂ [¹O₂] for four drug-light intervals, (a) 3 h, (b) 6 h, (c) 24 h, and (d) 96 h. The histograms are computed from the spatial dose distributions of Fig. 2. Each individual column in the histograms represents 0.01 mM of [¹O₂]. The maximum deposited dose decreases with increasing drug-light interval.

Plotted in Fig. 5a, 5b is the percentage of the tumor volume receiving doses within the ranges [¹O₂]<0.4 mM and [¹O₂]⩾0.8 mM for the various drug-light intervals. Figures 5c, 5d illustrate 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. Figure 5a 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 Fig. 5c, even when the analysis is restricted to the volume close to a perfused vessel, large fractions of the cells receive doses within this range. Figures 5b, 5d 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 [Fig. 5d], 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.

Figure 5.

(a,b) Histograms depicting the percent of the tumor volume receiving reacted [¹O₂] within two dose ranges, [¹O₂]<0.4, and [¹O₂]⩾0.8 mM. (c-d) The corresponding histograms for the tumor volume within a 25 μm radial distance of the capillary wall. The maximum deposited dose for drug-light intervals of 24 and 96 h is less than 0.8 mM. As shown in (a), more than 90% of the tumor volume receives a dose lower than 0.4 mM at all of the drug-light intervals. Panel (b) shows that less than 1% of the tumor volume receives a dose within an order of magnitude of the threshold dose for mTHPC-PDT.

DISCUSSION

Several experimental methods, including ¹O₂ luminescence and photosensitizer fluorescence photobleaching^{19, 20, 21} have been proposed and are being evaluated as means to monitor the deposition of PDT dose in vivo. These measurements have and will continue to have an important role to play in clinical and preclinical dosimetry. They are, however, necessarily limited to sampling relatively large tissue volumes and are therefore inherently unable to monitor the accumulated ¹O₂ dose distributions over distances corresponding to intercapillary spacings. In this respect, theoretical analysis provides a useful complementary approach to accessing and understanding these potentially important microscopic heterogeneities. Although results obtained from mathematical modeling will always be vulnerable to assumptions regarding the complex physiology of solid tumors, simulations that are well informed by experiment can provide insights into phenomena that may not be accessible via direct experiment. It is in this spirit that we undertook the modeling of the tumor responses to mTHPC-mediated PDT reported by Cramers et al.⁴ and Triesscheijn et al.⁵

The results of our simulations revealed low concentrations of ¹O₂ deposition at all of the drug-light intervals. The microscopic distributions of these concentrations of reacted ¹O₂, depicted in the plots of Fig. 2 and summarized in the histograms of Figs. 45, show that large volumes of the tumor, including volumes close to the vessels, receive minimal photodynamic dose under these treatment conditions. At none of the drug-light intervals does any subpopulation anywhere in the tumor receive a dose that is equal to the 8 mM threshold dose of reacting ¹O₂ determined by Coutier et al.⁹ using a combination of oxygen consumption measurements in mTHPC-sensitized spheroids and clonogenic cell survival. More strikingly, at all of the drug-light intervals more than 90% of the tumor volume receives a photodynamic dose that is 20-fold lower than this threshold, and fewer than 1% of the cells throughout the tumor receive a dose that is within an order of magnitude of the threshold. Thus, our simulations underscore the importance of vascular and host responses^{4, 22, 23, 24, 25} in determining tumor response to PDT. One interesting consequence of these findings is that molecular signaling and gene expression responses to PDT,^{26, 27, 28} which require at least short-term cell viability, are likely to be favored in those abundant tumor cell populations that receive relatively low photodynamic doses. At higher doses that are immediately lethal, these responses are attenuated significantly.²⁹

As noted above, the microscopic heterogeneities apparent in our simulations are not accessible via currently available experimental methods. Direct connection with experiment is accomplished by collapsing the spatially resolved simulations of reacting ¹O₂ and photosensitizer concentration into volume-averaged quantities, such as those shown in Fig. 3. From these simulations, a second general finding emerged from this study. Neither the volume-averaged ¹O₂ reactions nor the corresponding loss of mTHPC concentration tracks even in a qualitative way with the long-term tumor recurrence. The largest concentration of reacting ¹O₂ is observed for the 24 h drug-light interval; tumor responses are most durable at 3 and 6 h intervals. Thus, in these studies, which examined tumor responses to mTHPC-PDT at various drug-light intervals, a dosimetry that tracks ¹O₂ creation directly or indirectly would not predict clinical outcome. In cases like this one, it is likely that techniques sensitive to some measure of biological response, such as tumor perfusion, would be more useful. Imaging and spectroscopy methods to monitor tumor blood flow and hemoglobin oxygen saturation are undergoing intense evaluation by several groups.^{30, 31, 32, 33, 34}

In several respects, the findings reported here should be interpreted cautiously. First, some of these simulation results may be specific to mTHPC-PDT, where the sensitizer distribution undergoes dramatic changes with time post administration. Thus, certain predictions, including the details of the dose distributions in Fig. 2, may not be generalized to other photosensitizers. Second, although the spatial resolution of the radial grid used for the tissue region in these simulations, 0.33 μm, is fine enough to enable us to record dose deposited to the endothelial cells lining the vessels, we do not and indeed cannot at this time estimate effects that may arise from ¹O₂ reactions with blood borne elements. These effects would be most likely to occur when plasma levels of mTHPC are highest, but there is simply not enough known about either the dose deposited directly to circulating cells or the biological consequences to enable even a rough estimate regarding their contribution to the “vascular” response to PDT. Third, although the preclinical tumor responses reported by Cramers et al.⁴ and Triesscheijn et al.⁵ were more robust at shorter drug-light intervals, other considerations, such as normal tissue toxicity, are important factors in determining clinical protocols. In situations where vascular targeting is deemed essential, careful real-time optical dosimetry will be critical in protecting sensitive normal tissue adjacent to the target volume.^{35, 36} Finally, although a ¹O₂-based dosimetry did not provide a correct rank ordering of tumor responses to mTHPC-PDT performed at different drug-light intervals, there are no doubt many important situations in which direct or indirect monitoring of ¹O₂ will be very useful. PDT dosimetry is complex, and it is certain that no single prescription will find universal applicability.

Nomenclature

n

Hill coefficient

D_cap

³O₂ diffusion constant within capillary μm² s⁻¹

D_tiss

³O₂ diffusion constant within tissue μm² s⁻¹

C_sat

maximum saturated concentration of ³O₂ bound to hemoglobin μM

C₅₀

dissolved ³O₂ concentration in the vessel corresponding to 50% hemoglobin saturation μM

k_p

the rate of monomolecular decay of the sensitizer triplet state s⁻¹

k_ot

the bimolecular rate of triplet sensitizer quenching by ³O₂ μM⁻¹ s⁻¹

k_os

the bimolecular rate for ¹O₂ reaction with ground-state sensitizer μM⁻¹ s⁻¹

k_oa

the bimolecular rate of reaction of ¹O₂ with biological substrate [A] μM⁻¹ s⁻¹

δ

a characteristic sensitizer concentration at and below which ¹O₂-mediated bleaching becomes independent of sensitizer concentration μM

[S₀]

sensitizer ground state μM

[A]

concentration of cellular targets for singlet oxygen reactions μM

Γ_met

rate of metabolic oxygen consumption μM s⁻¹

Γ_PDT

rate of photodynamic oxygen consumption μM s⁻¹

V

blood flow velocity μm s⁻¹

R_c

capillary radius μm

b

half the distance between two adjacent capillaries μm

ψ

fluence rate mW cm⁻²