# Dual-Wavelength Fluorescence Monitoring of Photodynamic Therapy: From Analytical Models to Clinical Studies

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## Abstract

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## Simple Summary

## Abstract

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Analytical Model of Dual-Wavelength Fluorescence Sensing in Biotissues with Different Distributions of Fluorophores

_{ex}at the wavelength λ

_{ex}. It contains a fluorophore which distribution is characterized by a transversely uniform dependence of absorption coefficient µ

_{a,PS}(z, λ

_{ex}) along the longitudinal axis z. In the considered spectral range of 400–800 nm, optical properties of the base biotissue are characterized by spectral dependences of absorption coefficient µ

_{a}(λ), scattering coefficient µ

_{s}(λ), anisotropy factor g(λ) and refractive index n which is assumed to be constant in the abovementioned wavelength range. Supplementary parameters describing diffusive scattering in biotissue are the reduced scattering coefficient ${{\mu}^{\prime}}_{s}\left(\lambda \right)={\mu}_{s}\left(\lambda \right)\left(1-g\left(\lambda \right)\right)$ and transport coefficient ${{\mu}^{\prime}}_{\mathrm{t}}\left(\lambda \right)={\mu}_{\mathrm{a}}\left(\lambda \right)+{{\mu}^{\prime}}_{\mathrm{s}}\left(\lambda \right)$. The absorption of excitation light by the photosensitizer at depth z within the elementary layer of thickness dz results in the emission of fluorescence at the wavelength λ

_{em}with the efficiency characterized by the fluorescence quantum yield ϕ. Propagation of both excitation and fluorescence radiation in the biotissue is governed by their scattering and absorption, and can be described in the framework of the radiative transfer theory (RTT). Assuming a unidirectional incidence of excitation light and an isotropic angular emission of fluorescence, the propagation of excitation light was derived in accordance with the semi-empirical model developed by Jacques [25], while the fluorescence signal was derived within the frames of the diffusion approximation of RTT with the account of the refractive index mismatch at the biotissue–air boundary [22,26,27]. As the result, the outgoing flux of fluorescence radiation F at the biotissue boundary z = 0 normal to its surface can be derived from the expression [22]:

_{ex}and µ

_{em}are the values of the diffusion attenuation coefficient $\mu \left(\lambda \right)=\sqrt{3{\mu}_{a}\left(\lambda \right)\mu {\prime}_{t}\left(\lambda \right)}$ at the corresponding wavelengths λ

_{ex}and λ

_{em}; ${q}_{em}=\frac{2{\mu}_{em}m}{3{{\mu}^{\prime}}_{t}\left({\lambda}_{em}\right)}$, where m is the factor accounting for the total internal reflectance of diffusive fluorescence light determined by formula (2.4.1) in [26]; and m ≅ 2.76 for the predefined refractive index n = 1.37. The value ${k}_{ex}$ is the backscattering factor evaluated in the following form [25]:

_{a,PS}(z, λ

_{ex}) << µ

_{a}(λ

_{ex})).

_{1}and λ

_{2}> λ

_{1}, we introduce the ratio R

_{λ}of fluorescence signals excited at these wavelengths and registered by the same detector, each of them normalized by the excitation intensity at the corresponding wavelength:

_{ex}, and μ

_{ex}) at the corresponding excitation wavelength (λ

_{1}, λ

_{2}).

_{b}, (Section 2.1.3) PS concentration exponentially decreases in-depth with the 1/e decay depth d

_{1/e}, and (Section 2.1.4) a PS layer with an exponentially decaying concentration with the scale d

_{1/e}is covered by a biotissue layer of thickness d

_{b}. Schematics of all of the considered geometries together with the corresponding in-depth PS distributions are shown in Figure 2.

#### 2.1.1. PS Is Distributed Uniformly in the Upper Layer of a Biotissue of Thickness d

_{i}(i = 1, 2):

_{ex}(λ

_{2}) < μ

_{ex}(λ

_{1}) when λ

_{2}> λ

_{1}. At thicknesses exceeding z* = 3/(${\mu}_{ex2}+{\mu}_{em}$), the ratio becomes insensitive to the further increase of d, and saturates at the value

#### 2.1.2. PS Is Distributed Uniformly within the Semispace below the Biotissue Layer of Thickness d_{b}

_{b}, and it is related to the asymptotic value of ${R}_{\lambda ,top}^{\left(\infty \right)}$:

#### 2.1.3. PS Concentration Exponentially Decreases In-depth with the 1/e Decay Scale d_{1/e}

_{i}(i = 1,2), and ${C}_{PS}$ is the concentration of PS at the biotissue surface, which can potentially depend on the PS characteristic decay depth ${d}_{1/\mathrm{e}}$ when a fixed amount of PS is re-distributed in-depth from the top. The ratio (4) for the profile (10) can be calculated by integrating in (4) over a semi-infinite depth range:

_{1/e}is characterized by the slope $\left({\mu}_{ex1}-{\mu}_{ex2}\right)$ which is twice larger than that for ${R}_{\lambda ,top}$.

#### 2.1.4. A Layer with an Exponentially Decaying PS Concentration with the 1/e Scale ${d}_{1/\mathrm{e}}$ Is Located below the PS-Free Biotissue Layer of Thickness ${d}_{b}$

#### 2.1.5. Estimation of the PS Depth from the Ratio ${R}_{\lambda}$

_{λ}), d

_{1/}

_{e}(R

_{λ}), d

_{b}(R

_{λ}) can be constructed, which enables the quantitative estimation of the PS localization depth if the optical properties of the base biotissue and the PS absorption spectrum ${\mu}_{a,PS}\left(\lambda \right)$ are known. We point out that for case (Section 2.1.1) there is no analytical solution for the inverse function $d\left({R}_{\lambda ,top}\right)$, and the problem should be solved numerically. In case (Section 2.1.2), which mimics subcutaneous PS accumulation after intravenous injection, the depth ${d}_{b}$ of the PS upper border can be estimated from the known ratio ${R}_{\lambda ,bottom}$ by following Equation (9):

_{ex}

_{2}/k

_{ex}

_{1}registered from the base medium after illumination at ${\lambda}_{2}$ and ${\lambda}_{1}$.

#### 2.2. Dual-Wavelength Fluorescence Imaging Setup

^{2}at the object surface, correspondingly. The illumination area with the size of 13 cm × 17 cm matched the imaging area. The dark image was captured and subtracted automatically from the fluorescence images for the elimination of ambient light noise. The fluorescence response was calculated for the wavelengths λ

_{ex,}

_{1}= 405 nm and λ

_{ex,}

_{2}= 660 nm as the average signal over the same region of interest (ROI) with the dark level subtracted. As it was proposed earlier [20,21,22], the ratio of fluorescence responses at these two wavelengths can serve as a measure of PS localization depth because it exhibits the proportion of signals coming from deeper and superficial tissue layers.

#### 2.3. Model Experiment on Biotissue Phantoms

_{0}= 0.1% vol.

#### 2.4. Monte Carlo Simulations

_{a,PS}/(μ

_{a,PS}+ μ

_{a, base}) in PS-containing areas yields a map of the light dose absorbed by PS which serves as a distributed fluorescence source. In the second step, the absorption map was treated as the distributed source of fluorescence emission which was assumed to be angularly isotropic. The calculation of the fluorescence emission was performed for the optical properties corresponding to λ

_{em}= 760 nm, while the fluorescence response was calculated as the total weight of fluorescence photons per unit area exiting the tissue via the top boundary. The fluorescence signal ratio was calculated as the ratio of fluorescence responses for probing wavelengths of 660 and 405 nm. Probing irradiation with a planar wave was assumed, which corresponds to the experimental setup configuration and the analytical model. The number of probing photons launched was 10

^{7}.

_{0}(λ

_{i}) is proportional to the PS concentration at the tissue surface and to the PS absorption coefficient at the excitation wavelength λ

_{i}, and ${d}_{1/\mathrm{e}}$ is the characteristic PS decay depth. This distribution was a closer approximation for the case of topical PS administration [28,32]. The biotissue’s optical properties were chosen in accordance with data for the human dermis [23], and are summarized in Table 1. The thickness of the top layer varied from 0.25 mm to 3 mm, while the thickness of the bottom layer was 20 mm; the transversal medium dimensions were 30 mm × 30 mm, in order to diminish edge effects. The values of the PS absorption coefficient corresponded to Revixan Derma concentration of 0.1% vol, which yields the in vivo pure drug concentration of 1 μg/g, as is consistent with the reported values [33,34].

#### 2.5. Photosensitizers

#### 2.6. Animal Studies

#### 2.6.1. Intact Tissue Study

^{2}of the tissue surface; 30 min after the application, the rest of the PS was removed from the tissue surface, also with a cotton swab. Prior to the PDT procedure, all of the surrounding tissues except the treated area were covered by a reflecting tape to avoid their direct irradiation. The irradiation was performed with the PDT device “Harmonia” (Laser MedCenter Ltd., Moscow, Russia), equipped with LED arrays with wavelengths of 405 and 660 nm; the fluence rate at the tissue surface was 200 mW/cm

^{2}for each wavelength. The irradiation spot size was 9 mm in diameter. The accumulated light doses included in the analysis were limited by 50 J/cm

^{2}.

#### 2.6.2. Tumor Study

^{5}in 100 μL PBS, were injected subcutaneously into the outer side of the left shin. The developed tumor model was subject to treatment 7 days after inoculation, when its linear size reached 3–5 mm. Prior to the PDT procedure, the animals were narcotized with the intramuscular injection of a mixture of 40 mg/kg Zoletil (Valdepharm, Val-de-Reuil, France) and 10 mg/kg XylaVet (Alpha-Vet Veterinary Ltd., Szekesfehervar, Hungary). The studied PDT regimes included doses of 250 J/cm

^{2}delivered with red light (λ = 660 nm), 200 J/cm

^{2}delivered with blue light (λ = 405 nm), and 250 J/cm

^{2}delivered with a combination of red and blue light in equal doses (125 J/cm

^{2}at 660 nm followed by 125 J/cm

^{2}at 405 nm). In the protocols with intravenous injection, Fotolon PS (Belmedpreparaty, Minsk, Belarus) was administered intravenously in the amount of 5 mg/kg two hours prior to the PDT procedure [41]. In the protocols with topical application, Revixan Derma gel was applied topically in the amount of ~0.1 mL, and was distributed evenly with a cotton swab to cover all of the tumor surface (approx. 2 cm

^{2}); 30 min after the application, the rest of the PS was removed from the tumor surface, also with a cotton swab. Prior to the PDT procedure, all of the surrounding tissues except the treated area were covered by a reflecting tape to avoid their direct irradiation. During the application period and after the PDT procedure, the mice were kept in darkened cages. Irradiation was performed with the above-mentioned PDT device “Harmonia” (Laser MedCenter Ltd., Moscow, Russia); the fluence rate at the tissue surface was 200 and 100 mW/cm

^{2}for wavelengths of 660 and 405 nm, respectively. The irradiation spot size was 9 mm in diameter.

#### 2.7. In Vivo Experiment on Volunteers

^{2}. Fluorescence images of these areas were obtained consequently both for the wavelengths of 405 nm and 660 nm, 200, 400, 600 and 900 s after the PS application. Prior to the fluorescence imaging, an excessive amount of PS was removed from the skin surface in order to ensure that only PS penetrated into the skin contributed to the fluorescence response. The studies were approved by the Ethics Committee of Privolzhsky Research Medical University (Protocol #13, 4 July 2019).

#### 2.8. Clinical Studies

#### 2.8.1. Actinic Keratosis Study

^{2}(the intensity on the tissue surface was I = 200 mW/cm

^{2}). The total number of patients enrolled in the study was 4, with the total number of nodes amounting 14.

#### 2.8.2. Basal Cell Carcinoma Study

^{2}, with intensity on the tissue surface of 300 mW/cm

^{2}.

## 3. Results

#### 3.1. Comparison of the Analytical Model and Numerical Simulations

_{λ}for the cases of topical and systemic PS administration. The dual-wavelength FI was modeled for the fluorescence excitation at the two wavelengths corresponding to the peaks of the Soret band (λ

_{1}= 405 nm, “blue excitation”) and Q band (λ

_{2}= 660 nm, “red excitation”) in the absorption spectrum of chlorin e6–based PS, with emission detection at λ

_{em}= 760 nm. Figure 4a–c demonstrate the numerically simulated and analytically calculated dependencies of the fluorescence responses at the two probing wavelengths and their ratio for the described cases (Section 2.1.1, Section 2.1.2 and Section 2.1.3), respectively, on the corresponding PS distribution parameters d (Figure 4a,d), d

_{b}(Figure 4b,e) and d

_{1/e}(Figure 4c,f). Uniform (Figure 4a,d) and exponentially decaying (Figure 4c,f) distributions of PS within the top layer of biotissue imitate topical PS application, while the PS localization below the slab of non-fluorescing biotissue (Figure 4b,e) mimics systemic administration of PS by intravenous injection. For the case (Section 2.1.3), the total amount of PS is considered to be constant for different d

_{1/e}values, such that the surface PS concentration C

_{PS}~1/d

_{1/e}. The optical properties used in analytical model and the Monte Carlo simulations are shown in Table 1, and meet the assumption of a small effect of PS on the overall medium optical properties in the analytical model. Quantum yields ϕ

_{1}and ϕ

_{2}were taken to be equal to 1.

_{1/e}is considered as the characteristic PS accumulation depth. Because the total amount of PS in the medium is assumed to be constant, and because it is redistributed in the tissue with the increase of d

_{1/e}, the dependencies for both blue-light and red-light excitation demonstrate a monotonous decrease.

_{λ,top}for case (Section 2.1.1) (Figure 4d) monotonously increases, reaching a constant asymptotic value. Approaching the asymptotic level means that the measurement volumes for both red and blue light are within the PS-containing layer. These results are in agreement with the previously reported studies of the top PS-containing layer [22]. Similar result is observed for the exponential PS in-depth profile, which is a more realistic model of topical PS administration (Figure 4f).

_{b}is observed for both wavelengths (Figure 4b) due to the decay of the amount of probing light which reaches the PS-containing region. The ratio of the fluorescence signals (Figure 4e), on the contrary, demonstrates a monotonous increase, because blue-light-excited fluorescence attenuates faster compared to red-light-excited fluorescence. As the theory predicts, this dependence has a growing exponential trend as the function of the top layer thickness with the rate determined by the difference in attenuation coefficients at two probing wavelengths (see Equation (9)). The sensitivity to the PS localization depth in this case is higher than that in the previously described case of topical PS administration.

_{λ}values in Figure 4d,f at large thicknesses of the PS layer do not exceed 3%, and are, presumably, due to the accumulated inaccuracy of the diffusion approximation taken as the basis of the theoretical model.

#### 3.2. Phantom Experiments

_{λ}value for the test object contains the information of the source intensities, quantum yields and PS absorption coefficients at two probing wavelengths:

_{λ}were normalized for the calibration coefficient ${R}_{\lambda ,ref}$, which allowed us to obtain the characteristic ${R}_{\lambda}^{c}$ independent of the parameters of the measurement setup and unknown PS properties:

_{λ}

^{c}on the thickness d of the phantom top layer containing PS obtained in the experiment, as simulated by MC and calculated using the developed analytical model. The MC data and analytical solution demonstrate a good quantitative agreement with the results of the phantom experiments, although discrepancy for a small thickness of the PS-containing layer may originate from inaccuracies in the optical properties reconstruction, the phantom layer thickness measurement, and the inhomogeneity of the phantom optical properties caused by its fabrication technique. Note that the absolute values of R

_{λ}

^{c}in the experimental studies are different from those for R

_{λ}

^{c}demonstrated for the numerical simulations (Figure 4) due to the introduction of calibration, and from the difference in the optical properties, although both dependencies on d have the same trend. Figure 5b demonstrates the comparison of the results of the phantom experiment with the developed analytical model and MC data for case (Section 2.1.2). The observed trend exhibits a theoretically predicted exponential dependence of the R

_{λ}value on the thickness of the top PS-free layer (see Equation (9)).

#### 3.3. Reconstruction of the Fluorophore Localization Depth from Dual-Wavelength Measurements

_{λ}obtained from the Monte Carlo simulations were used to extract the PS localization depth using the base medium optical properties, and with the scattering and/or absorption coefficients varied by 30% in value, assuming the uncertainty in the published biotissue optical properties typically used for the interpretation of the in vivo measurements [44]. The analysis of the reconstruction accuracy was performed for the cases of the exponential in-depth decay of the PS concentration (case (Section 2.1.3) mimicking topical PS application) and a two-layer model with the bottom layer containing uniformly distributed PS (case (Section 2.1.2) mimicking intravenous PS injection) using the inverse analytical relations (16) and (15), respectively.

_{1/e}for the exponential decay of the PS concentration are shown in Figure 6a for the base optical properties employed for the reconstruction, and for cases when the scattering and/or absorption coefficients are known with an error of 30%. The inverse estimation of d

_{1/e}by the formula (16) provides the accuracy within 10% for the characteristic depth up to 0.75 mm, given that the optical properties are exactly known. Variations in the scattering coefficient of ±30% with respect to the basic value almost do not influence the reconstruction accuracy of d

_{1/e}. On the contrary, the error in the absorption coefficient value results in a large error in the determination of the fluorophore localization, especially when µ

_{a,base}is underestimated. Note that all of the acquired dependencies are close to linear ones.

_{b}values, while the underestimation of the optical properties’ values causes the overestimation of the localization depth, and vice versa. The simultaneous overestimation of the absorption and scattering by 30% results in about a 25% underestimation of the reconstructed value, while their simultaneous underestimation by 30% results in about a 50% overestimation of the reconstructed value.

#### 3.4. In Vivo Estimations of the PS Accumulation Depth

_{λ}

^{c}registered upon dual-wavelength fluorescence monitoring in vivo in laboratory animals, human volunteers, and patients for both cases of the topical application and the intravenous injection, while Figure 7b demonstrates the ranges of the reconstructed PS localization depths obtained from Equation (16) for the topical application and Equation (15) for the intravenous injection of PSs. The groups with the topical application of PS (human skin, rabbit ear, CT26 tumor model in mice, actinic keratosis) demonstrated typical values of R

_{λ}

^{c}in the range of 1.0–3.0. Reconstruction of the typical PS localization depths for human skin using optical properties adopted from Salomatina et al. [23] resulted in the mean value of the PS penetration depth of 0.12 mm, with a maximum value of 0.29 mm, which is consistent with the typical values of human epidermis thickness varying in the range of 0.05–0.64 mm, depending on the location [45]. Note that the fluorescence measurements in the group of actinic keratosis characterized by morphological alterations in the epidermis layer and hyperkeratosis [46,47] provide higher estimations of the PS penetration depths, with the d

_{1/e}mean value being equal to 0.27 mm and the maximum value of 0.54 mm, which is in accordance with the morphological data. Moreover, follicular extension typical for actinic keratosis [48] also stimulates deeper PS penetration. Estimations for the PS accumulation depth in CT-26 tumor-bearing mice after topical administration using the optical properties for murine tissues from Sabino et al. [49] demonstrated the mean accumulation depth of 0.17 mm, with a maximal detected value of 0.45 mm for the measured R

_{λ}

^{c}values. This is in agreement with the results of our previous study [24], which demonstrated partial response of tumors to PDT treatment after topical PS administration, indicating that PS penetration through the skin to the tumor tissue occurs. Evaluation of the PS penetration depth in the rabbit ear was performed using the optical properties of human skin (because we failed to find optical properties for rabbit ear tissues), which yields the estimated penetration depth in the range of 0.06–0.24 mm, which is comparable with the human skin observations.

#### 3.5. Monitoring of PDT in Animal Studies

_{λ}

^{c}from the fluorescence measurements prior to and after the PDT procedure delivered with either red (λ = 660 nm) or blue (λ = 405 nm) light to both normal and tumor tissue in the animal experiments.

_{λ}

^{c}detected prior to and after the PDT procedures with topical PS administration observed in the rabbit ear inner surface, treated with the total dose of 50 J/cm

^{2}delivered with red or blue light, or their combination in equal parts, and in the CT26 tumor model in Balb/c mice with the total dose of 200 or 250 J/cm

^{2}, delivered with red or blue light, or their combination in equal parts. The data for the rabbit ear do not demonstrate a significant change in the R

_{λ}

^{c}value as a result of a PDT procedure. However, the red light procedure demonstrates an insignificant decrease in the R

_{λ}

^{c}value opposite the blue light procedure yielding an insignificant increase in R

_{λ}

^{c}. The latter is presumably owing to the primarily superficial photobleaching leading to the deepening of PS-containing volume. Similar effect with a smaller magnitude is observed for the PDT protocol with the combination of red and blue light exposure.

_{λ}

^{c}as a result of the procedure were smaller than those observed in PDT of CT26 tumors where the delivered light doses were significantly higher. For the combination of two exposure wavelengths delivered in equal doses, the observed increase was smaller than that for the blue light case, owing to smaller exposure dose of the latter.

_{λ}

^{c}as a result of a PDT procedure. However, the effect of the blue light PDT is manifested by the significant ratio increase owing to the much stronger sensitivity of this parameter to the PS localization depth in the case of intravenous injection (see Figure 4e and Figure 5b). This increase is governed by both the higher concentration of PS in the underlying tissue layer where major blood vessel plexuses are located, and the primary photobleaching of the PS in the superficial layers owing to the comparatively low blue light penetration depth. The blue light PDT procedure with a dose of 200 J/cm

^{2}demonstrated a higher increase in R

_{λ}

^{c}compared to that with red and blue light doses delivered in equal parts (125 + 125 J/cm

^{2}) owing to the smaller dose of blue light delivered in the latter case.

#### 3.6. Clinical PDT Monitoring

^{2}, while the BCC studies included a standard protocol with the total dose of 150 J/cm

^{2}delivered with red light. Typical results of the dual-wavelength fluorescence monitoring of the PDT treatment of BCC are shown in Figure 9.

_{λ}

^{c}measurement prior to and after PDT both for actinic keratosis and the BCC treatment are shown in Figure 10.

_{λ}

^{c}as a result of the procedure, indicating that photobleaching is quite uniform in depth because typical impact depth of the red light procedure is comparable or higher than typical depth of the PS penetration upon topical administration. The blue light procedure demonstrates a jump in R

_{λ}

^{c}associated with the photobleaching of PS primarily in the superficial tissues [28,32]. The protocol involving the combination of red and blue light illumination also demonstrates an increase in R

_{λ}

^{c}, which is in line with the observations in animal studies with dual-wavelength protocols. The BCC treatment monitoring demonstrates an insignificant decrease of the R

_{λ}

^{c}as a result of the PDT procedure. This observation is consistent with animal study observations for a red light antitumor regime with intravenous injection.

#### 3.7. Estimation of the PS Localization Depth Variation as a Result of a PDT Procedure

_{1/e}(Equation (14)). As a result, for both cases, the change in the PS embedding depth can be evaluated by the corresponding R

_{λ}values before (${R}_{\lambda}^{before}$) and after (${R}_{\lambda}^{after}$) PDT from the relation similar to Equation (17):

#### 3.8. Fluorescence Signal Ratio: Overview

_{λ}

^{c}registered in vivo in laboratory animals, human volunteers and patients for the cases of topical application and intravenous injection prior to and after the PDT procedures delivered with different wavelength combinations. This figure allows us to estimate typical ranges of R

_{λ}

^{c}detected in vivo. The topical application groups demonstrate typical values of R

_{λ}in the range of 0.5–4.0, which is in line with the predictions of the analytical and numerical studies. Note that a redistribution of PS may occur as a result of a PDT procedure because the photobleaching primarily affects the superficial tissue layer, thus “shifting” the R

_{λ}

^{c}values to those typical for the intravenous injection case where the superficial layer contains a small amount of fluorophore, or none. The systemic administration groups demonstrate the R

_{λ}

^{c}values in the range of 3.0–20.0, which is also in line with the results of the model predictions for a PS localization depth of up to 0.5 mm.

## 4. Discussion

_{λ}and its changes during the PDT procedure related to the PS redistribution in biotissue may have the potential to become one of the predictive factors of the PDT procedure outcome, together with the photobleaching efficiency [63], though this requires further studies. We also consider dual-wavelength FI as a promising diagnostic component of theranostic PDT modality which can be applied not only during treatment but also at the stage of PS accumulation after intravenous administration. Tracking of dual-wavelength fluorescence excited by low-intensity light sources during PS accumulation will provide additional information about its distribution in the area of interest: the amount of the accumulated PS is related to the intensity of individual fluorescence signals, while the change in its spatial organization influences the measured ratio R

_{λ}. Moreover, the reported approach is not limited by chlorin e6-based PSs only, but can also be applied for other types of widely employed PSs with pronounced absorption in two different bands of the visible spectrum, e.g., in 5-ALA-based [64] or benzoporphyrin derivative-mediated [65] PDT. Thus, the discussed modality of dual-wavelength FI for monitoring the fluorophore distribution in biotissues is a feasible concept of diagnostic enhancement by biophotonics tools.

## 5. Conclusions

_{λ}and the PS localization depth in several particular cases mimicking topical PS administration and intravenous injection. The model is in good agreement with the results of the Monte Carlo simulations and phantom experiments. The inverse formulae reveal the opportunity to estimate the fluorophore localization depth based on the fluorescence signal ratio, given that the optical properties of the tissue are known.

_{λ}value allows to noninvasively evaluate the effect of a PDT procedure that can be performed either at 660 nm or 405 nm corresponding to the absorption peaks of chlorin e6. Red light has higher penetration depth compared to blue light, thus providing deeper PDT action, while blue light primarily activates the PS accumulated in superficial tissue layers. In this connection, red light procedures feature weak variation in R

_{λ}as a result of the irradiation, while blue light therapeutic exposure does not reach deep-seated PS which still can be sensed by fluorescence imaging, thus resulting in an increase in the R

_{λ}value. The effect was demonstrated in laboratory animals and in patients with actinic keratosis.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

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**Figure 1.**Dual-wavelength fluorescence imaging with chlorin e6 based photosensitizers. (

**a**) Absorption and fluorescence spectra of chlorin e6-based PS and typical spectra of scattering and absorption coefficients of human dermis (*adopted from Salomatina et al. [23]); arrows show fluorescence excitation wavelengths employed in the proposed dual-wavelength imaging; (

**b**) principles of FI with dual-wavelength excitation for topical PS administration (left) and intravenous PS injection (right).

**Figure 2.**Schematics of the considered cases of PS distribution in the tissue mimicking basic examples of topical or systemic PS administration: (

**a**) PS is distributed uniformly in the upper layer of biotissue of thickness d; (

**b**) PS is distributed uniformly within the semispace below the biotissue layer of thickness d

_{b}; (

**c**) PS concentration exponentially decreases in depth with the 1/e decay depth d

_{1/e}; and (

**d**) a PS layer with an exponentially decaying concentration with the scale d

_{1/e}is covered by the biotissue layer of thickness d

_{b}. The dependence C

_{PS}(z) illustrates the PS concentration in-depth profile.

**Figure 3.**Reconstructed spectra of the reduced scattering (

**a**) and absorption (

**b**) coefficients of the base tissue phantom and the phantom with PS, and the absorption spectrum of the water-based photosensitizer gel Revixan Derma dissolved in purified water (

**c**). Dashed lines show the fluorescence excitation (405 nm, 660 nm) and emission detection (760 nm) wavelengths.

**Figure 4.**Analytical (theory) and numerically simulated (MC) dependencies of the fluorescence signals at different excitation wavelengths (

**a**–

**c**) and signal ratios R

_{λ}(

**d**–

**f**) on the characteristic PS localization depth within human dermis mimicking biotissue, which model different methods of PS administration: (

**a**,

**d**) topical PS administration—uniform PS distribution within the top layer; (

**b**,

**e**) systemic PS injection—uniform PS distribution in the bottom layer; (

**c**,

**f**) topical PS administration—exponential PS concentration in-depth profile.

**Figure 5.**Experimentally measured fluorescence signal ratio for the agarose biotissue phantoms with (

**a**) a PS-containing top layer and (

**b**) a PS-containing bottom layer versus the PS localization depth, corresponding analytical dependencies and results of the Monte Carlo simulations.

**Figure 6.**Reconstructed values of the fluorophore localization depth versus the true localization depth, depending on the medium optical properties employed for the reconstruction for cases of topical PS administration (

**a**) and intravenous injection (

**b**).

**Figure 7.**Normalized fluorescence signal ratio values of R

_{λ}

^{c}detected after the PS accumulation (

**a**) and the corresponding PS localization depths (

**b**) for topical application (TA) and intravenous injection (SA) in laboratory animals (CT26 tumor model in Balb/c mice, inner surface of the rabbit ear), human volunteers (normal human skin) and in patients (actinic keratosis, BCC). In the brackets, total number of time points, treatment sites and independent species in the group is shown.

**Figure 8.**Normalized fluorescence signal ratios prior to and after PDT procedures obtained in animal studies (inner surface of rabbit ear in norm and CT26 tumor model in Balb/c mice) for topical application (

**a**) and intravenous injection (

**b**). The PDT regimes’ abbreviations below the bars indicate the therapeutic wavelength (‘r’ = 660 nm, ‘b’ = 405 nm, ‘rb’ = 660 nm + 405 nm) and dose in J/cm

^{2}.

**Figure 9.**Typical fluorescence images of the BCC node site prior to (

**a**,

**c**) and after (

**b**,

**d**) the PDT procedure delivered at λ = 660 nm, with a dose of 150 J/cm

^{2}acquired at probing wavelengths of 405 (

**a**,

**b**) and 660 (

**c**,

**d**) nm.

**Figure 10.**Fluorescence signal ratio prior to and after the PDT procedures obtained in the treatment of actinic keratosis (AK) with topical PS administration and basal cell carcinoma (BCC) with intravenous PS injection. The PDT regimes’ abbreviations below the bars show the therapeutic wavelength (‘r’ = 660 nm, ‘b’ = 405 nm, ‘rb’ = 660 nm + 405 nm) and dose in Joules.

**Figure 11.**PS localization depth changes, Δd

_{b}measured in laboratory animals and in patients as a result of the PDT procedure (TA—topical application; SA—systemic administration). In the brackets, total number of procedures, treatment sites and independent species in the group is shown.

**Figure 12.**Normalized fluorescence signal ratio, R

_{λ}

^{c}, summarized over all of the measurements in laboratory animals, human volunteers and patients upon PS administration or/and in the course of a PDT procedure (TA—topical application; SA—systemic administration). In the brackets, total number of time points, treatment sites and independent species in the group is shown.

**Table 1.**Optical properties of biotissue layers at the fluorescence excitation and emission wavelengths employed in the Monte Carlo simulations (BT = base tissue).

λ(nm) | μ_{a PS}, mm^{−1} | M_{0} | μ_{a BT}, mm^{−1} | μ_{s BT}, mm^{−1} | g_{BT} | μ_{s}‘_{BT}, mm^{−1} |
---|---|---|---|---|---|---|

405 | 0.1 | 0.02 | 0.96 | 38 | 0.8 | 7.6 |

660 | 0.02 | 0.004 | 0.15 | 14 | 0.8 | 2.8 |

760 | 0 | 0 | 0.13 | 12 | 0.8 | 2.4 |

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Kirillin, M.; Khilov, A.; Kurakina, D.; Orlova, A.; Perekatova, V.; Shishkova, V.; Malygina, A.; Mironycheva, A.; Shlivko, I.; Gamayunov, S.; Turchin, I.; Sergeeva, E. Dual-Wavelength Fluorescence Monitoring of Photodynamic Therapy: From Analytical Models to Clinical Studies. *Cancers* **2021**, *13*, 5807.
https://doi.org/10.3390/cancers13225807

**AMA Style**

Kirillin M, Khilov A, Kurakina D, Orlova A, Perekatova V, Shishkova V, Malygina A, Mironycheva A, Shlivko I, Gamayunov S, Turchin I, Sergeeva E. Dual-Wavelength Fluorescence Monitoring of Photodynamic Therapy: From Analytical Models to Clinical Studies. *Cancers*. 2021; 13(22):5807.
https://doi.org/10.3390/cancers13225807

**Chicago/Turabian Style**

Kirillin, Mikhail, Aleksandr Khilov, Daria Kurakina, Anna Orlova, Valeriya Perekatova, Veronika Shishkova, Alfia Malygina, Anna Mironycheva, Irena Shlivko, Sergey Gamayunov, Ilya Turchin, and Ekaterina Sergeeva. 2021. "Dual-Wavelength Fluorescence Monitoring of Photodynamic Therapy: From Analytical Models to Clinical Studies" *Cancers* 13, no. 22: 5807.
https://doi.org/10.3390/cancers13225807