# A Comparison of Singlet Oxygen Explicit Dosimetry (SOED) and Singlet Oxygen Luminescence Dosimetry (SOLD) for Photofrin-Mediated Photodynamic Therapy

^{1}

^{2}

^{3}

^{4}

^{5}

^{*}

## Abstract

**:**

^{3}O

_{2}])—to calculate the amount of reacted singlet oxygen ([

^{1}O

_{2}]

_{rx}), the main cytotoxic component in type II PDT. Experiments were performed in phantoms with the photosensitizer Photofrin and in solution using phosphorescence-based singlet oxygen luminescence dosimetry (SOLD) to validate the SOED model. Oxygen concentration and photosensitizer photobleaching versus time were measured during PDT, along with direct SOLD measurements of singlet oxygen and triplet state lifetime (τ

_{Δ}and τ

_{t}), for various photosensitizer concentrations to determine necessary photophysical parameters. SOLD-determined cumulative [

^{1}O

_{2}]

_{rx}was compared to SOED-calculated [

^{1}O

_{2}]

_{rx}for various photosensitizer concentrations to show a clear correlation between the two methods. This illustrates that explicit dosimetry can be used when phosphorescence-based dosimetry is not feasible. Using SOED modeling, we have also shown evidence that SOLD-measured [

^{1}O

_{2}]

_{rx}using a 523 nm pulsed laser can be used to correlate to singlet oxygen generated by a 630 nm laser during a clinical malignant pleural mesothelioma (MPM) PDT protocol by using a conversion formula.

## 1. Introduction

^{3}O

_{2}]) [3]. In a typical photodynamic process, the photosensitizer is excited by the treatment light and enters the excited singlet state. This singlet state undergoes intersystem crossing to the triplet state. This triplet state can react directly with molecular substrates or transfer a hydrogen atom or an electron to

^{3}O

_{2}to produce radicals or radical ions in a type I process [4]. Most clinically relevant photosensitizers undergo type II processes in which the triplet state transfers energy to ground-state oxygen,

^{3}O

_{2}, to produce singlet oxygen,

^{1}O

_{2}[4], which is the main photocytotoxic agent leading to cell death and therapeutic response [5,6].

^{1}O

_{2}but also the tissue optical properties [9,10]. In turn, the penetration of light is dependent on the tissue optical properties [11]. Simplistically, PDT dose may be defined as the time integral of the photosensitizer concentration and the light fluence. However, this does not take into account the effect of tissue hypoxia. In a hypoxic environment, the production of

^{1}O

_{2}will be lower than expected and treatment outcome will not be predictable [7,8].

^{1}O

_{2}] as the dosimetric measure has been suggested. Direct measurement of

^{1}O

_{2}by its near-infrared luminescence emission is technically challenging in vivo due to the weakness of the signal and the short lifetime of

^{1}O

_{2}, ~30–180 ns [12,13]. Hence, a macroscopic singlet oxygen explicit dosimetry (SOED) model has been previously developed and studied for various sensitizers in vivo [8,14,15,16]. In the present work, SOED was compared in solutions to direct singlet oxygen luminescence dosimetry (SOLD) [17,18]. The relevant photophysical parameters for the macroscopic model were verified by performing explicit dosimetry of oxygen concentration and photosensitizer concentration. In performing a direct comparison between SOED- and SOLD-measured

^{1}O

_{2}, the use of SOED in scenarios where direct luminescence detection is difficult is validated. Furthermore, an analysis is provided to show that SOLD measured using a 523 nm pulsed laser (currently required by the availability of lasers with suitable pulse length, repetition frequency, and energy) is well-correlated to singlet oxygen generated by Photofrin by a CW 630 nm laser during PDT, by correcting for the tissue optical properties at the two wavelengths.

## 2. Materials and Methods

#### 2.1. SOED Model In Vitro and In Vivo

^{1}O

_{2}], photosensitizer concentration, [S

_{0}], the ground-state oxygen concentration, [

^{3}O

_{2}], and the reacted singlet oxygen concentration, [

^{1}O

_{2}]

_{rx}for the in vitro scenario with parameters (and k

_{i}) defined in Table 1 (and its footnote) [19]:

_{1}/(k

_{6}+ k

_{7}[A]), ξ = Φ

_{Δ}(ε/hν), τ

_{Δ}

^{−1}= k

_{6}+ k

_{7}[A], and β = k

_{4}/k

_{2}. Here, Φ

_{Δ}is the singlet oxygen quantum yield in the aqueous Intralipid medium. The parameters used for the calculation for each phantom are summarized in Table 1. For studies without NaN

_{3}, the

^{1}O

_{2}quencher used in solutions, [A] = 0. For the in vivo scenario, Equations (2) and (3) can be rewritten as [8,14,15,16,20]:

_{0}] + δ) << 1. Here we have added an oxygen perfusion term to account for vasculature in vivo, and the value of g = 0.7 μM/s for Photofrin.

_{0}](t) gives the values of δ and σ used in Table 1. The photobleaching rate (−d[S

_{0}]/dt) was determined at each time point, along with the values of φ, [

^{3}O

_{2}], [S

_{0}], and β for the calculation of the left-hand side of Equation (7). A linear fit to the data yields a value for the intercept and slope, and the intercept divided by the slope gives δ and the slope divided by ξ gives σ. A recent review lists known values for in vivo photophysical parameters for many photosensitizers used clinically [19]. The SOED-calculated solutions were compared with the oxygen and [S

_{0}](t) concentrations. All calculations were performed using Matlab 2014b (MathWorks, Natick, MA, USA).

#### 2.2. SOLD Instrumentation

^{1}O

_{2}] signal as a function of time following a short illumination pulse.

_{R}[23].

_{A}is the PS absorption cross-section (σ

_{A}= (ε/N

_{A}) × 10

^{9}), N

_{A}is Avogadro’s constant (6.022 × 10

^{23}), ε is the extinction coefficient, and τ

_{R}is the

^{1}O

_{2}phosphorescence lifetime (k

_{6}

^{−1}). A fit of the background-subtracted histograms was performed to Equation (8) (with a y-axis offset as a free parameter to account for any change in the background level) using Origin software with a Levenberg–Marquardt algorithm to iterate the parameter values.

#### 2.3. Measurements in Tissue-Simulating Phantoms

#### 2.4. Comparison of 630 nm and 523 nm SOED

_{0}] and [

^{3}O

_{2}], the information of φ distribution, the magnitude of the Photofrin-specific reaction-rate parameters, and the measured photosensitizer concentrations [33] were passed to the time (t)-dependent differential Equations (5) and (6) for a given treatment time point, which were then used to calculate [

^{1}O

_{2}]

_{rx}using Equation (4).

## 3. Results

#### 3.1. SOED Photophysical Parameters

^{1}O

_{2}]

_{rx}. These parameters are listed in Table 1. Figure 2 shows the SOLD measurement of singlet oxygen lifetime as a function of the concentration of added sodium azide (NaN

_{3}), which is a potent singlet oxygen-specific quencher, for Photofrin in MeOH solution. The intercept of the linear fit (solid line in Figure 2) corresponds to k

_{6}and the slope corresponds to the value for k

_{7}.

#### 3.2. SOED in Phantom

^{3}O

_{2}] and PS concentration, [S

_{0}], under CW 630 nm laser excitation. [

^{3}O

_{2}](t) was measured using an oxygen phosphorescence probe and the photophysical parameters taken from Table 1.

^{3}O

_{2}] and [S

_{0}] at just below the surface (d = 0) versus time in an Intralipid phantom (with μ

_{s}’ = 0.2 cm

^{−1}) for three different initial Photofrin concentrations (27, 50, 167 mM). The symbols are measured values and the lines are SOED-calculated results. Figure 3c shows the PS photobleaching rate per PDT dose, $-\frac{d[{S}_{0}]}{dt}\frac{1}{[{S}_{0}]\varphi [{}^{3}O_{2}]/([{}^{3}O_{2}]+\beta )}$ versus [S

_{0}]. The symbols are calculated values using Equation (7), and the line is the best linear fit. Figure 3d shows the expected SOED-calculated cumulative reacted singlet oxygen concentration, [

^{1}O

_{2}]

_{rx}, during illumination.

#### 3.3. SOED/SOLD Comparison in Solution

^{1}O

_{2}. The latter was correlated with the amount of

^{1}O

_{2}produced instantaneously and cumulatively. Instantaneous [

^{1}O

_{2}] accounts for the singlet oxygen generated for each pulse of laser excitation, while cumulative [

^{1}O

_{2}]

_{rx}is the integral of all singlet oxygen produced during the entire illumination time over the entire illumination volume. The agreement between the two methods (SOED and SOLD) is shown in Figure 4: (a) shows SOLD counts per accumulation time (in seconds, t = 300 s before and after PDT) and (b) shows cumulative SOLD counts over the entire treatment time of 900 s. Photofrin was dissolved in MeOH solution.

## 4. Discussion

#### 4.1. SOED and SOLD Intercomparison

^{1}O

_{2}] value in solution in Figure 4a corresponded to the volumetric averaged instantaneous singlet oxygen concentration over a volume of 1 cm depth and 1 cm

^{2}area. SOED-calculated [

^{1}O

_{2}]

_{rx}in Figure 4b corresponded to the volumetric average reacted singlet oxygen concentration of the same 1 cm

^{3}volume. In these solutions, the light fluence was calculated by introducing attenuation that was only due to the photosensitizer absorption, since no scatterer was added and solutions were of pure Photofrin: φ = φ

_{0}exp(−μ

_{a}× d), where φ

_{0}is the light fluence rate (mW/cm

^{2}) measured directly in the back of the front wall of the solution facing the laser. Absorption coefficients (μ

_{a}) were 0.15, 0.45, and 0.74 cm

^{−1}for Photofrin concentrations of 17, 50, and 83 mM, respectively, at 523 nm.

^{1}O

_{2}to

^{3}O

_{2}(k

_{6}) and the bimolecular reaction rate of

^{1}O

_{2}with the substrate (k

_{7}) in Photofrin phantoms, photosensitizer triplet-state and singlet oxygen lifetime measurements were obtained using the SOLD system. Varying amounts of the singlet oxygen quencher, sodium azide (NaN

_{3}), were added to the Photofrin–MeOH solutions. The resulting fits to obtain k

_{6}and k

_{7}are shown in Figure 2. For Photofrin with NaN

_{3}, k

_{6}was found to be 1.14 × 10

^{5}s

^{−1}(the intercept of the line of best fit in Figure 2) and k

_{7}was found to be 235 μM

^{−1}·s

^{−1}(the slope of the line of best fit in Figure 2). k

_{7}is pH-dependent, but is in the range of the reported value of 300–400 μM

^{−1}·s

^{−1}for the quenching rate constant in water [38]. These values were used to calculate τ

_{∆}for the in vitro condition (without NaN

_{3}) and the in vivo condition (taken from the literature for biological tissue [34]). Assuming that k

_{7}for NaN

_{3}is greater than or equal to that of in vivo conditions (assuming biological tissue is less efficient than NaN

_{3}in quenching

^{1}O

_{2}), it can be estimated that in vivo acceptor concentration [A] ≥ 10

^{7}(s

^{−1})/235 mM

^{−1}·s

^{−1}= 42 mM. This value is much higher than [A] = 0.83 mM in the literature [10], but we feel that it is more reasonable since the singlet oxygen lifetime in vivo, τ

_{∆}, does not change for reacted singlet oxygen concentrations [

^{1}O

_{2}]

_{rx}as high as 12 mM [16], indicating there are still plenty of acceptors in vivo at this level.

_{a}) of 0.09, 0.18, and 0.58 cm

^{−1}, and reduced scattering coefficient (μ

_{s}’) of 0.2 cm

^{−1}. The resulting φ/φ

_{0}is shown in Figure 5 along with an exponential fit based on μ

_{a}. For the tissue-simulating phantoms with Photofrin shown in Figure 3, φ

_{0}is the measured local fluence rate at the front inner surface of the phantom facing the laser and d is the depth from surface. At 630 nm, μ

_{a}= 0.09, 0.18, and 0.58 cm

^{−1}for Photofrin concentrations of 27, 50, and 167 mM, respectively. It is clear that the function e

^{−μad}, while working well for the broad beam, does not work very well for the 0.8 cm diameter beam at the deepest depths investigated. As a result, MC-generated light fluence rate φ/φ

_{0}was used directly for the SOED calculations in phantom.

^{3}O

_{2}] and [S

_{0}]. In particular, the consumption rate of [S

_{0}] per PDT dose was used to determine a more accurate value of σ (slope/ξ) and δ (intercept/slope) for the experimental setup used (Figure 3c and Equation (7)). This was used to determine δ and σ using a method from Reference [40] that is also described in Section 2.1. Photosensitizer concentration was measured over time to determine the photobleaching rate (−d[S

_{0}]/dt) and [S

_{0}]. Along with the measured [

^{3}O

_{2}], the PS photobleaching rate per PDT dose can be calculated and plotted as in Figure 3c. The slope and intercept of the fit to the data are used to calculate δ and σ. The value for ξ in vitro was calculated by the definition of ξ provided in Table 1. The resulting values were δ = 25 ± 4.3 μM and σ = (6.6 ± 7) × 10

^{−5}μM

^{−1}. The value of β was set to be 11.9 μM for this set of experiments [34]. Figure 3a,b show the SOED calculations using Equations (2) and (3), which agree with [

^{3}O

_{2}](t) and [S

_{0}](t) measurements at surface (d = 0 cm) of the Intralipid phantom. Figure 3d shows the magnitude of SOED-calculated [

^{1}O

_{2}]

_{rx}using Equation (4) for Photofrin to be in the mM range.

^{1}O

_{2}] counts, [SOLD], and SOED-calculated [

^{1}O

_{2}]

_{rx}values track each other very well (R

^{2}= 0.98) for Photofrin, with a conversion factor of the following form:

^{−6}s, which is consistent with the value of τ

_{Δ}obtained (9.4 × 10

^{−6}s). The reason for the intercept is not known, and a linear fit without intercept reduces the correlation (R

^{2}= 0.86). The good correlation of SOED-calculated [

^{1}O

_{2}] and [SOLD] demonstrates that SOED can be utilized in scenarios where direct phosphorescence measurement of

^{1}O

_{2}is difficult.

#### 4.2. Feasibility of Using SOLD at 523 nm for Predicting [^{1}O_{2}]_{rx} at 630 nm

^{1}O

_{2}] is not the same as that of the 630 nm treatment light used clinically with Photofrin. Figure 6 shows the measured values μ

_{a}and μ

_{s}’ in various sites measured in vivo in patients, including the anterior chest wall, apex of the heart (apex), posterior chest wall, diaphragm (diaph), serratus (ser), anterior sulcus, posterior sulcus, pericardium (peri), and normal (norm) tissue. Patients were undergoing an institutional review board (IRB)-approved pleural mesothelioma Photofrin-PDT clinical protocol at the University of Pennsylvania. These optical properties were measured using a custom-built multifiber contact probe for absorption spectroscopy [27]. The measured optical properties include μ

_{a}and μ

_{s}’ for tissue as well as Photofrin.

_{air}) versus tumor depth for (a) 523 nm and (b) 630 nm. The gray area shows the region of φ/φ

_{air}with the upper and lower bounds of the tissue optical properties obtained in vivo as dark blue and light blue, respectively. The dashed black lines show the calculated light fluence distribution using the mean optical properties of μ

_{a}= 5.52 cm

^{−1}and μ

_{s}’ = 17.61 cm

^{−1}for 523 nm and μ

_{a}= 0.58 cm

^{−1}and μ

_{s}’ = 15.61 cm

^{−1}for 630 nm. As expected, the optical penetration is much deeper at 630 nm than at 523 nm in in vivo malignant pleural mesothelioma (MPM) patients.

^{1}O

_{2}]

_{rx}at 630 nm. MPM PDT is currently performed at 630 nm. Correlation between the calculated [

^{1}O

_{2}]

_{rx}for 630 and 523 nm is shown in Figure 8. μ

_{a}ranges from 0.66 to 23.1 cm

^{−1}at 523 nm and 0.17 to 1.35 cm

^{−1}at 630 nm, while μ

_{s}’ ranges from 2.80 to 73.7 cm

^{−1}at 523 nm and 2.55 to 30.5 cm

^{−1}at 630 nm (Figure 6). In order to investigate the effects of different φ on the [

^{1}O

_{2}]

_{rx}, the SOED calculations were repeated for φ = 5, 25, 50, 75, and 150 mW/cm

^{2}. Different colors of symbols represent different φ. The black solid lines are the best fits in Figure 8b. At 523 nm, the range of [

^{1}O

_{2}]

_{rx}changed from 0–0.1, 0–0.63, and 0–5.6 mM for PS concentrations of 0.21, 2.1, and 21 µM, respectively, while the range of [

^{1}O

_{2}]

_{rx}at 630 nm changed from 0–0.25, 0–2.5, and 0–20 mM, respectively, for the same PS concentrations.

^{2}[33] can be expressed as:

^{2}). We thus conclude that SOLD measurement at 532 nm can be used to monitor [

^{1}O

_{2}]

_{rx}at 630 nm if a conversion formula (Equations (11)–(13)) is used to convert the measured SOLD signal.

## 5. Conclusions

^{−5}μM

^{−1}in vitro). Using lifetime measurements obtained with the SOLD system, photophysical parameters k

_{6}(1.14 × 10

^{−5}s

^{−1}) and k

_{7}(235 μM

^{−1}·s

^{−1}) were found for in vitro solutions with NaN

_{3}. A linear relationship between SOLD singlet oxygen photon counts at 1270 nm and SOED-calculated reacted singlet oxygen (Equation (10)) was established for Photofrin for 523 nm light excitation. Based on our SOED calculations, a formula (Equations (11)–(13)) for converting cumulative SOLD signal measured at 523 nm to the corresponding [

^{1}O

_{2}]

_{rx}at 630 nm was established using the optical properties at the two wavelengths in an ongoing MPM clinical protocol.

## Acknowledgments

## Author Contributions

## Conflicts of Interest

## Abbreviations

PS | Photosensitizer |

SOED | Singlet Oxygen Explicit Dosimetry |

SOLD | Singlet Oxygen Luminescence Dosimetry |

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**Figure 1.**Singlet oxygen luminescence dosimetry (SOLD) instrumentation setup (

**a**) on an optical bench; and (

**b**) schematic diagram of the experimental arrangement. PPG—pulse pattern generator; SPAD—single photon avalanche diode; TCSPC—time-correlated single-photon counting.

**Figure 2.**Singlet oxygen lifetime (τ

_{Δ}) changes due to quenching with various concentrations of sodium azide (NaN

_{3}) for Photofrin (50 μM) in MeOH, τ

_{Δ}

^{−1}= k

_{6}+ k

_{7}[A]. Symbols represent measured data and the solid line is the best linear fit.

**Figure 3.**Comparison of measured and singlet oxygen explicit dosimetry (SOED)-calculated values of (

**a**) [

^{3}O

_{2}](t) and (

**b**) [S

_{0}](t) at d = 0 for three initial photosensitizer concentrations, [S

_{0}]

_{0}= 27, 50, 167 μM. Measurements of ground-state oxygen were made at 5–30 s intervals, while photosensitizer spectra were obtained every 10 s. The average initial [

^{3}O

_{2}]

_{0}value was 160.4 μM. (

**c**) The left-hand side of Equation (7) versus the Photofrin concentration, with the line of best fit. The slope of the fit was (6.86 ± 0.6) × 10

^{−7}mM·s

^{−1}·mW

^{−1}·cm

^{2}and the intercept was (1.78 ± 0.25) × 10

^{−5}s

^{−1}·mW

^{−1}·cm

^{2}, resulting in a value of δ = 25 ± 4.3 μM. (

**d**) Calculated volume-averaged [

^{1}O

_{2}]

_{rx}over time. The light fluence rates used in the experiment were φ

_{0}= 45, 38, and 42 mW/cm

^{2}for each sensitizer concentration. The symbols are measured values in Figure 3a,b and are calculated values using Equation (7) for Figure 3c. The lines are SOED-calculated results for Figure 3a,b,d, and the line of best fit for Figure 3c.

**Figure 4.**(

**a**) Comparison of SOLD-obtained

^{1}O

_{2}counts (Equation (8)) per accumulation time (in seconds) at 523 nm and SOED-calculated instantaneous [

^{1}O

_{2}] (Equation (1)) for Photofrin concentrations in MeOH of 17, 50, and 83 μM, and light fluence φ

_{0}= 30 mW/cm

^{2}. The initial oxygen concentration was measured as 175 ± 6 μM. (

**b**) Comparison of SOLD cumulative

^{1}O

_{2}counts (Equation (9)) and reacted singlet oxygen concentration ([

^{1}O

_{2}]

_{rx}) calculated with SOED (Equation (4)) for Photofrin concentration of 17, 50, and 83 μM. PDT was performed with 523 nm light at φ

_{0}= 30 mW/cm

^{2}for 900 s.

**Figure 5.**Monte Carlo (MC) simulation of fluence rate distribution by a circular beam of radius (

**a**) 0.4 cm and (

**b**) 8 cm incident on a semi-infinite liquid surface as a function of depth (d) for μ

_{a}= 0.09, 0.18, and 0.58 cm

^{−1}and μ

_{s}’ = 0.2 cm

^{−1}. Fits of exponential forms are shown along with the MC data. The exponential form of e

^{−μad}fits the simulation well up to a depth of 0.4 cm, while overestimating φ/φ

_{0}at larger depths. Broad-beam simulations agree with the simple exponential form up to a depth of 1.3 cm.

**Figure 6.**(

**a**) Tissue μ

_{a}’ and (

**b**) μ

_{s}’ at 523 (hollow symbols) and 630 (filled symbols) nm measured in vivo in malignant pleural mesothelioma (MPM) patients.

**Figure 8.**(

**a**) [

^{1}O

_{2}]

_{rx}calculated at 630 nm and 523 nm for different total fluence (φ = 10, 60, 120 J/cm

^{2}) for mean Photofrin concentrations (c) of (from left to right) 0.21, 2.1, and 21 μM. Absorption and scattering coefficients were obtained at the two wavelengths from Figure 6. SOED calculation of [

^{1}O

_{2}]

_{rx}used Equations (5) and (6) and averaged over a 1 cm depth and 1 cm

^{3}volume using photophysical parameters listed in Table 1 for the in vivo conditions; (

**b**) Slope and intercept of the correlation of [

^{1}O

_{2}]

_{rx}at 630 nm and 523 nm as a function of fluence and PS concentration.

Parameter | Definition | In Vitro | In Vivo |
---|---|---|---|

ε (cm^{−1}·μM^{−1}) | Photosensitizer extinction coefficient | 0.0035 at 632 nm ^{(1)}0.0089 at 523 nm ^{(1)} | |

β (μM) | Oxygen-quenching threshold concentration $\frac{{k}_{4}}{{k}_{2}}$ * | 11.9 [34] | |

δ (μM) | Low-concentration correction | 25 ± 4.3 ^{(2)} | 33 [15] |

ξ (cm^{2}·mW^{−1}·s^{−1}) | Specific oxygen consumption rate $\xi ={\Phi}_{\mathrm{\Delta}}\frac{\epsilon}{h\nu}$ | 10.3 × 10^{−3 (3)}at 632 nm 24.8 × 10 ^{−3 (4)}at 523 nm | 3.7 × 10^{−3} [34]at 632 nm 8.99 × 10 ^{−3 (5)}at 523 nm |

σ (μM^{−1}) | Specific photobleaching ratio where σ = k_{1}τ_{Δ} * | (6.6 ± 7) × 10^{−5 (2)} | 7.6 × 10^{−5} [8,34] |

τ_{Δ} (s) | Singlet oxygen lifetime $\frac{1}{{k}_{6}+{k}_{7}[A]}$ * | (9.4 ± 0.2) × 10^{−6 (6)} | 1.6 × 10^{−7} [35] |

τ_{t} (s) | Triplet state lifetime $\frac{1}{{k}_{4}+{k}_{2}[{}^{3}O_{2}]}$ * | (0.43 ± 0.03) × 10^{−6 (7)} | 1.5 × 10^{−6 (7)} |

Φ_{Δ} | Singlet oxygen quantum yield | 0.56 [36,37] | 0.20 [19] |

^{(1)}Measured from absorption spectroscopy;

^{(2)}Obtained from fitting shown in Figure 3c using Equation (7);

^{(3)}Calculated using Φ

_{Δ}= 0.56 in water, ε = 0.0035 cm

^{−1}·μM

^{−1}, and hν = 3.2 × 10

^{−16}mWs at 632 nm;

^{(4)}Calculated using Φ

_{Δ}= 0.64 in MeOH, ε = 0.0089 cm

^{−1}·μM

^{−1}, and hν = 3.8 × 10

^{−16}mWs at 523 nm;

^{(5)}Scaled in vivo value at 632 nm by ε(at 523 nm)/ε(at 632 nm);

^{(6)}Measured values from SOLD experiment when [A] = 0 (i.e., without NaN

_{3}in MeOH solution);

^{(7)}Calculated from measured data using [

^{3}O

_{2}] = 40 μM for in vivo conditions and [

^{3}O

_{2}] = 169 μM for in vitro conditions. Thereby, τ

_{t}in vivo was estimated by determining k

_{2}in vitro (1.3 × 10

^{4}μM

^{−1}·s

^{−1}) and using β = k

_{4}/k

_{2}= 11.9 μM and 1/τ

_{t}= k

_{2}(β + [

^{3}O

_{2}]); * The definition of the photophysical parameters are [19]: k

_{1}= rate of photosensitizer (PS) photobleaching; k

_{2}= rate of triplet PS quenching by

^{3}O

_{2}; k

_{4}= decay rate of triplet PS without

^{3}O

_{2}; k

_{6}= rate of

^{1}O

_{2}phosphorescence decay; k

_{7}= rate of

^{1}O

_{2}quenching by substrate.

© 2016 by the authors; licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC-BY) license (http://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Kim, M.M.; Penjweini, R.; Gemmell, N.R.; Veilleux, I.; McCarthy, A.; Buller, G.S.; Hadfield, R.H.; Wilson, B.C.; Zhu, T.C.
A Comparison of Singlet Oxygen Explicit Dosimetry (SOED) and Singlet Oxygen Luminescence Dosimetry (SOLD) for Photofrin-Mediated Photodynamic Therapy. *Cancers* **2016**, *8*, 109.
https://doi.org/10.3390/cancers8120109

**AMA Style**

Kim MM, Penjweini R, Gemmell NR, Veilleux I, McCarthy A, Buller GS, Hadfield RH, Wilson BC, Zhu TC.
A Comparison of Singlet Oxygen Explicit Dosimetry (SOED) and Singlet Oxygen Luminescence Dosimetry (SOLD) for Photofrin-Mediated Photodynamic Therapy. *Cancers*. 2016; 8(12):109.
https://doi.org/10.3390/cancers8120109

**Chicago/Turabian Style**

Kim, Michele M., Rozhin Penjweini, Nathan R. Gemmell, Israel Veilleux, Aongus McCarthy, Gerald S. Buller, Robert H. Hadfield, Brian C. Wilson, and Timothy C. Zhu.
2016. "A Comparison of Singlet Oxygen Explicit Dosimetry (SOED) and Singlet Oxygen Luminescence Dosimetry (SOLD) for Photofrin-Mediated Photodynamic Therapy" *Cancers* 8, no. 12: 109.
https://doi.org/10.3390/cancers8120109