*Article* **VIS-NIR Diffuse Reflectance Spectroscopy System with Self-Calibrating Fiber-Optic Probe: Study of Perturbation Resistance**

**Valeriya Perekatova, Alexey Kostyuk, Mikhail Kirillin \*, Ekaterina Sergeeva, Daria Kurakina, Olga Shemagina, Anna Orlova, Aleksandr Khilov and Ilya Turchin**

> Institute of Applied Physics RAS, 603950 Nizhny Novgorod, Russia **\*** Correspondence: mkirillin@yandex.ru

**Abstract:** We report on the comparative analysis of self-calibrating and single-slope diffuse reflectance spectroscopy in resistance to different measurement perturbations. We developed an experimental setup for diffuse reflectance spectroscopy (DRS) in a wide VIS-NIR range with a fiber-optic probe equipped with two source and two detection fibers capable of providing measurements employing both single- and dual-slope (self-calibrating) approaches. In order to fit the dynamic range of a spectrometer in the wavelength range of 460–1030 nm, different exposure times have been applied for short (2 mm) and long (4 mm) source-detector distances. The stability of the self-calibrating and traditional single-slope approaches to instrumental perturbations were compared in phantom and in vivo studies on human palm, including attenuations in individual channels, fiber curving, and introducing optical inhomogeneities in the probe–tissue interface. The self-calibrating approach demonstrated high resistance to instrumental perturbations introduced in the source and detection channels, while the single-slope approach showed resistance only to perturbations introduced into the source channels.

**Keywords:** diffuse reflectance spectroscopy; diffuse optical spectroscopy; tissue optics; diffuse scattering; oxygenation; tissue chromophores; self-calibrating approach; ratiometric approach

#### **1. Introduction**

Diffuse reflectance spectroscopy (DRS) is an optical technique that allows the evaluation of tissue biochemistry and microstructure for a number of applications including brain hemodynamics [1] also called fNIRS, diagnostics of breast tumor margins [2,3] and treatment monitoring [4], skin cancer diagnostics [5–7], evaluating the scar severity and therapeutic response of keloid [8], and diagnostics of tumor margins in the oral cavity (head and neck cancer) [9], lung [10], liver [11–13], and colon [14,15]. A number of potential applications have also been reported, such as diagnostics of thyroid [16] and adipose tissue [17] and the identification of neurovascular bundles. The DRS principle is based on delivering broadband light to the biotissue and registering the backscattered light at a specified distance. The detected signal contains information about scattering (related to the microstructure of the tissue) and absorption (related to its biomolecular composition). Due to the strong dependence of absorption coefficients of different chromophores (oxyand deoxyhemoglobin, melanin, lipids, water, etc.) on the wavelength, one can reconstruct their concentrations in tissue by analyzing the extinction of the light spectrum between the source and detector.

The DRS probing spectral range is selected depending on the absorption spectra of the studied chromophores and the desired probing volume in tissue. For example, the concentrations of oxy- and deoxyhemoglobin in superficial tissues can be reconstructed using the visible (usually 500–600 nm) spectral range, while for deeper probing it is reasonable to use the range of 700–900 nm due to higher light penetration depth. The NIR range is also

**Citation:** Perekatova, V.; Kostyuk, A.; Kirillin, M.; Sergeeva, E.; Kurakina, D.; Shemagina, O.; Orlova, A.; Khilov, A.; Turchin, I. VIS-NIR Diffuse Reflectance Spectroscopy System with Self-Calibrating Fiber-Optic Probe: Study of Perturbation Resistance. *Diagnostics* **2023**, *13*, 457. https://doi.org/10.3390/ diagnostics13030457

Academic Editor: Viktor Dremin

Received: 15 December 2022 Revised: 24 January 2023 Accepted: 24 January 2023 Published: 26 January 2023

**Copyright:** © 2023 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 (https:// creativecommons.org/licenses/by/ 4.0/).

used to assess water and lipid content [18], while the wider VIS-NIR range can be used for analysis of collagen and elastin content [8]. Currently, VIS-NIR spectroscopy has been applied in several works and has shown higher potential in comparison with VIS or NIR spectroscopy separately [14,19,20], because it allows the reconstruction of concentrations of a larger set of tissue chromophores and/or obtaining a higher accuracy [18,21].

If tissue optical properties vary with depth, DRS in the VIS-NIR range can be applied to assess chromophore concentrations in different tissue layers using differences in sensitivity depths of the VIS and NIR spectrum regions. This approach was successfully applied to assess skin hemoglobin concentrations in the dermis and lower dermis [22].

The results of the reconstruction of tissue chromophores in DRS have the following keys to success: (1) the applied light transport model should be realistic enough to correctly describe light attenuation from source to detector; (2) the reconstruction procedure should have a good convergence; (3) instrumental characteristics, such as source spectral brightness, detector spectral sensitivity, transient characteristics of source and detector fiber channels, and optical contact between the DRS probe and tissue should be taken into account. In the present study we concentrate mainly on the last issue because incorrect consideration of the instrumental characteristics can lead to significant errors in the reconstructed values even with an appropriate light transport model and a valid reconstruction technique. This aspect is especially essential in broadband measurements, in particular VIS-NIR, due to possible light dispersion in the instrumental part and strong differences in light attenuation in tissue in different spectral ranges, and, therefore, a need for adjusted compensation.

Different strategies are applied in DRS to correctly account for the instrumental characteristics depending on the measured data type. For example, investigation of hemodynamics based on the measurement of relative changes in hemoglobin concentrations in time can be implemented using a simple single source-detector distance (SDD) approach with a single source-detector pair. The resulting equation for relative changes in hemoglobin concentrations in time allows for the exclusion of instrumental characteristics [23]. Absolute measurements of chromophore concentrations in a single SDD configuration are usually accompanied by calibration measurements with a tissue phantom with known absorption and scattering characteristics or a reflection standard [24]. However, if instrumental characteristics vary in time (for example, source spectral brightness may significantly vary in lamp sources), a calibration procedure should be applied periodically, which is not convenient or even impossible during continuous biomedical examination. Continuous calibration measurements can be provided with the help of an additional source-detector channel with a reflection standard at the tips of source and detection optical fibers [25].

Two SDDs with a single source and two detectors or a single detector and two sources allow the assessment of effective light attenuation *μeff* in tissue by taking a ratio between the detected signals obtained at different SDDs. In this ratiometric approach, also called single-slope measurement, most of the instrumental characteristics are excluded in the final equation for *μeff*, which yields a more accurate assessment of tissue chromophore content in comparison with the single-distance approach [26]. Multiple sources at a single detector or multiple detectors at a single source are used to increase the precision of the extinction coefficient extraction. However, the effect of instrumental function is not completely eliminated in this approach.

A possible solution to compensate for more instrumental contributions is a selfcalibrating technique suggested in [27]. The idea is based on symmetrical multi-distance measurements; at least four measurements at each wavelength with two sources and two detectors with a symmetrical configuration (Figure 1) should be provided to obtain calibration-free characterization of the studied tissue. This probe demonstrated more reliable data on the optical properties of tissue and higher long-term stability compared to standard DRS configuration due to a reduction in instrumental errors.

**Figure 1.** Schematic of experimental setup with self-calibrating fiber-optic probe. S1,2: the source fibers; D1,2: the detection fibers; areas of effective sensitivities for short (*rS*) and long (*rL*) SDDs are marked with green and red colors, respectively. Bold lines indicate optical fibers, thin lines indicate electrical connections. Elements within the dashed frame are placed in a single housing.

In addition to insensitivity toward instrumental effects, the self-calibrating approach is less sensitive to the changes in optical coupling between the optical probe and tissue. The last advantage is tightly connected with the differences in sensitivity to superficial or deeper chromophores in different approaches: the traditional single-measurement approach has a banana-shaped sensitivity function [28] with maxima near source– and detector–tissue interfaces, while the self-calibrating technique is relatively more sensitive to deeper tissues [29,30]. This finding makes the self-calibrating approach very attractive in its application for studies of brain activity in the NIR spectral region [31]. Single-distance or single-slope approaches register primarily photons backscattered from the scalp and skull masking the brain hemodynamics, and the traditional increase in SDD does not provide any significant benefit, since the maximum sensitivity remains near the source– and detector–tissue contacts. The self-calibrating approach was applied for diagnostics of breast tumors with a more sophisticated probe including 16 continuous-wave (CW) sources at 690 nm and 830 nm and 8 detectors located symmetrically [32]. Multiple sources and detectors allow obtaining a signal averaged over a large tissue volume resulting in more robust data on the oxygenation of tumor tissue [33].

The main drawback of all pure CW optical diffuse measurements is related to the difficulty of separating absorption *μ<sup>a</sup>* and reduced scattering *μ <sup>s</sup>* coefficients which are included in the expression for the effective extinction coefficient of diffuse light as a product:

$$
\mu\_{eff} = \sqrt{3\mu\_a(\mu\_a + \mu\_s')}.\tag{1}
$$

Employing the reduced scattering coefficient values from the literature may cause significant errors in absolute measurements of chromophore concentrations due to tissueto-tissue variations in reduced scattering values [34]. Additional frequency-domain (FD) measurements employing high-frequency modulation of probing light intensity at two or more wavelengths allow assessing reduced scattering directly at these wavelengths. Assuming a power law or a linear wavelength dependence of reduced scattering coefficient (the latter approach is reasonable in NIR where the decrease in *μ <sup>s</sup>*(*λ*) dependence is slow), one can estimate it within the whole spectrum measured by CW DRS, which results in higher precision of chromophores reconstruction [35] (steady-state and frequency-domain

(SSFD) reflectance measurements). SSFD measurements at two wavelengths were also successfully applied in combination with a self-calibrating approach for studying human brain hemodynamics [36,37].

The FD technique is applied successfully for the NIR spectral range for large SDDs that ensure a sufficient phase shift of a photon density wave propagated from source to detector. However, at large SDDs (approx. more than 5 mm), VIS measurements are restricted by high attenuation of light in biotissue. Smaller SDDs (<5 mm) need higher modulation frequency to register the phase shift that is hard to implement technically. In this connection, DRS in VIS range 500–600 nm is usually performed with the CW technique alone [26]. In the joint VIS-NIR range, the reduced scattering spectrum *μ <sup>s</sup>*(*λ*) has a more sophisticated behavior and can be approximated by a sum of Rayleigh-scattering and Mie-scattering components [18], since Rayleigh scattering is assumed to dominate in the UV-blue optical range, while Mie scattering prevails in NIR:

$$\mu\_s'(\lambda) = a \left[ f\left(\frac{\lambda}{\lambda\_0}\right)^{-4} + (1 - f) \left(\frac{\lambda}{\lambda\_0}\right)^{-b} \right] \tag{2}$$

Here the parameter *a* is the reduced scattering coefficient at *λ*<sup>0</sup> = 500 nm, *f* is the fraction of Rayleigh scattering with λ−<sup>4</sup> dependence that is described by the first term in the brackets, and *b* is the power index of Mie scattering wavelength dependence described by the second term. Parameters *a*, *b*, and *f* can be assessed along with unknown tissue chromophores composition from the fitting of an experimentally obtained reflected spectrum by a model function. This approach has been applied in VIS-NIR DRS for a simplified *μ <sup>s</sup>*(*λ*) dependence [38].

In this paper, we present a comparative analysis of the sensitivity of the dual- and single-slope approaches in DRS to various perturbations than can occur in the course of measurements. The analysis is based on the assessment of the changes in the reconstructed effective extinction coefficient spectrum in response to the introduced instrumental distortion. The study is performed using a custom-built experimental setup for VIS-NIR DRS with a fiber-optic probe employing a self-calibrating approach. To the best of our knowledge, this is the first application of a self-calibrating approach for ultra-wideband 460–1030 nm (VIS-NIR) DRS. The problem that arises is the significant difference in absorption coefficients in VIS and NIR spectral regions, leading to difficulties in detecting both regions simultaneously with a single spectrometer at different SDDs with a large enough signal-to-noise ratio. In the proposed experimental setup, we solved this problem by applying individual exposure times for small and large SDDs in order to fit the whole received spectra for both SDDs in the spectrometer dynamic range. The reconstruction of tissue optical parameters is proposed via a minimization in the difference between the effective extinction coefficient *μeff*, which is evaluated from DRS measurements using simplified light diffusion theory, and the expected model coefficient *μeff* calculated with Equation (1). The absorption coefficient in Equation (1) is assumed to be a linear combination of basic biotissue chromophores absorption spectra, while the reduced scattering coefficient is described by Equation (2). The developed experimental setup has been tested for resistance toward different instrumental perturbations including the bending of optical fibers, installing an additional attenuator in an individual channel, and modifying the probe–tissue interface. The results for the self-calibrating approach were compared to those for the single-slope measurements.

#### **2. Materials and Methods**

#### *2.1. Evaluation of Extinction Coefficient with Self-Calibrating Approach Measurements*

Propagation of light between source and detector in biological tissue is well described by the Radiative Transfer Equation (RTE) [39], employing absorption *μ<sup>a</sup>* and scattering *μ<sup>s</sup>* indices and a scattering phase function as tissue optical properties. There exists no general analytical solution to this equation, however, for a number of applications with SDD exceeding several light transport lengths, the RTE can be reduced to the diffuse equation, which has an analytical solution for homogeneously scattering and absorbing media. In the frame of this approach, a photon fluence rate generated by a point light source with unit power in the infinite medium (Green's function) is defined by equation [40]:

$$\phi(r) = \frac{\Im(\mu\_d + \mu\_s')}{4\pi r} \exp\left(-\mu\_{eff}r\right) \tag{3}$$

where *r* is the distance from the source and *μeff* is defined by Equation (1) via the absorption coefficient *μ<sup>a</sup>* and reduced scattering coefficient *μ <sup>s</sup>*. Under certain assumptions (neglecting medium boundary conditions and radiating patterns of source and detection fibers), Equation (3) can be used to characterize light intensity in the detection fiber *Dj* located at distance *rkj* from the source fiber *Sk* (*j*,*k* = 1,2) in the configuration shown in Figure 1. Following these assumptions, the DRS signal registered by a spectrometer at the specific wavelength can be written in the following form:

$$I\_{kj} = \frac{\Im(\mu\_a + \mu\_s') A S\_k A D\_j I\_0 \eta}{4\pi r\_{kj}} E\_{kj} \exp\left(-\mu\_{eff} r\_{kj}\right) \tag{4}$$

where *I*<sup>0</sup> is a light source intensity; *ASk* and *ADj* are the transient characteristics of DRS device parts describing the propagation of light from the light source to a contact of the source fiber *k* with the biotissue and from the biotissue contact with the detection fiber *j* to the spectrometer, respectively; *η* is the spectrometer sensitivity; and *Ekj* is the corresponding spectrometer exposure time.

The ratio of signals received with a common source *k* and two detectors *j* = 1,2 having different SDDs (known as single-slope configuration) carries information about the medium extinction coefficient and excludes most of instrumental characteristics (source transient characteristics, source brightness, and spectrometer sensitivity):

$$\frac{I\_{k1}}{I\_{k2}} = \frac{AD\_1 r\_{k2} E\_{k1}}{AD\_2 r\_{k1} E\_{k2}} \exp\left(-\mu\_{eff} (r\_{k1} - r\_{k2})\right) \tag{5}$$

Typically an assumption is made that both detection channels have equal transient characteristics, i.e., *AD*<sup>1</sup> = *AD*2. In this case, one can evaluate the extinction coefficient following Equation (5) and using the ratio *I*11/*I*<sup>12</sup> of the spectra measured by the system depicted in Figure 1 with source S1 and two detectors D1 and D2 (abbreviated as S1D1D2) as:

$$
\mu\_{eff} = \frac{1}{r\_{12} - r\_{11}} \ln \left[ \left( \frac{I\_{11}}{I\_{12}} \right) \left( \frac{E\_{12}}{E\_{11}} \right) \frac{r\_{11}}{r\_{12}} \right] \tag{6}
$$

and using the ratio *I*22/*I*<sup>21</sup> of the spectra measured with source S2 and two detectors D1 and D2 (abbreviated as S2D1D2) as:

$$
\mu\_{eff} = \frac{1}{r\_{21} - r\_{22}} \ln \left[ \left( \frac{I\_{22}}{I\_{21}} \right) \left( \frac{E\_{21}}{E\_{22}} \right) \frac{r\_{22}}{r\_{21}} \right] \tag{7}
$$

However, if the assumption *AD*<sup>1</sup> = *AD*<sup>2</sup> is incorrect, the extinction spectrum calculated by Equations (6) or (7) contains an error. In this case, for symmetrical measurements when *r*<sup>11</sup> = *r*<sup>22</sup> = *rS* and *r*<sup>21</sup> = *r*<sup>12</sup> = *rL*, Equation (5) yields:

$$\begin{cases} \frac{I\_{11}}{I\_{12}} = \frac{AD\_{1}r\_{L}E\_{11}}{AD\_{2}r\_{S}E\_{12}} \exp\left(\mu\_{eff}(r\_{L} - r\_{S})\right) \\\quad \frac{I\_{21}}{I\_{22}} = \frac{AD\_{1}r\_{S}E\_{21}}{AD\_{2}r\_{L}E\_{22}} \exp\left(-\mu\_{eff}(r\_{L} - r\_{S})\right) \end{cases} \tag{8}$$

and the effective extinction coefficient can be derived in the form that excludes both source and detector transient characteristics:

$$\mu\_{eff} = \frac{1}{2(r\_L - r\_S)} \ln \left[ \left( \frac{I\_{11} I\_{22}}{I\_{12} I\_{21}} \right) \left( \frac{E\_{12} E\_{21}}{E\_{11} E\_{22}} \right) \frac{r\_S^2}{r\_L^2} \right] \tag{9}$$

Equation (9) represents a self-calibrating (or dual-slope) approach, employing four source-detector measurements: S1-D1, S1-D2, S2-D1, S2-D2 (abbreviated as S1D1S2D2). One can note that expression (9) is an average value of the extinction coefficients obtained by Equations (6) and (7).

#### *2.2. Reconstruction of Skin Chromophores and Scattering from μeff Spectrum*

In this study we focus on the characterization of human skin scattering and absorption spectra. Multiplicative combinations of absorption coefficients and reduced scattering coefficients in expression (1) for the extinction coefficient makes their separation from the continuous wave measurements difficult, in contrast to frequency-domain or timedomain techniques. In our study, in order to separate *μ<sup>a</sup>* from *μ <sup>s</sup>* based on Equation (1) and the extinction coefficient spectrum experimentally obtained with Equations (6), (7), or (9), depending on the employed measurement scheme, we make several empirical assumptions.

The absorption coefficient *μ<sup>a</sup>* is considered as a weighted sum of the absorption spectra of basic skin chromophores. In our consideration we limit their set to melanin, blood, water, and "dry matter", assuming that the contribution of other chromophores in the range of 460–1030 nm is negligible:

$$\begin{aligned} \mu\_a(\lambda) &= \mathbb{C}\_{\text{water}} \ast \mu\_a^{\text{water}}(\lambda) + \mathbb{C}\_{\text{mcl}} \ast \mu\_a^{\text{mcl}}(\lambda) + \\ \left[ \mathbb{C}\_{\text{blood}} \ast \left( StO\_2 \ast \mu\_a^{\text{oxy}}(\lambda) + (1 - StO\_2) \ast \mu\_a^{\text{deoxy}}(\lambda) \right) \right] + \mu\_a^{\text{dry}} \end{aligned} \tag{10}$$

where the spectra of *μ HbO*<sup>2</sup> *<sup>a</sup>* , *<sup>μ</sup>Hb <sup>a</sup>* , and *μmel <sup>a</sup>* are taken from [41,42]. Absorption of "dry matter" is taken as a wavelength independent *μdry <sup>a</sup>* . A reduced scattering coefficient spectrum is taken according to Equation (2) with the Rayleigh fraction which approximates scattering at small wavelengths and Mie fraction which dominates in NIR. The contribution of lipids to the absorption coefficient is not considered in this study since the SDD in the described system is limited by 4 mm and the measurements described below have been performed on human palm with low lipid content. The parameters of oxygen saturation *StO*<sup>2</sup> concentration of different chromophores,—*Cwater*, *Cmel*, *Cblood*, *<sup>μ</sup>dry <sup>a</sup>* —together with the scattering parameters *a*, *b*, and *f* from Equation (2), can be determined by fitting the experimentally obtained extinction spectrum *μeff* with a combination of empirical dependencies (10) and (2) substituted into Equation (1). This optimization problem was solved numerically by finding the parameters vector *<sup>K</sup>* = [ *Cblood*, *StO*2, *Cwater*, *<sup>μ</sup>dry <sup>a</sup>* , *a*, *b*, *f* ] using lsqcurvefit MATLAB function within the wavelength range of 460–1030 nm assuming *Cmel* to be a constant equal to 0.005. This solution can be derived using Equation (9) in the case of the self-calibrating approach as:

$$K = \operatorname\*{argmin}\_{K} \sum\_{\lambda} \left( \sqrt{3\mu\_{4}(K)(\mu\_{4}(K) + \mu\_{s}^{\prime}(K))} - \frac{1}{2(r\_{L} - r\_{S})} \ln \left[ \left( \frac{I\_{11}I\_{22}}{I\_{12}I\_{21}} \right) \left( \frac{E\_{12}E\_{21}}{E\_{11}E\_{22}} \right) \frac{r\_{S}^{2}}{r\_{L}^{2}} \right] \right)^{2} \tag{11}$$

or in the case of single-slope approach in S1D1D2 mode using Equation (6) as:

$$K = \operatorname\*{argmin}\_{K} \sum\_{\mathbf{K}} \left( \sqrt{3\mu\_{\mathbf{d}}(\mathbf{K})(\mu\_{\mathbf{d}}(\mathbf{K}) + \mu\_{\mathbf{s}}'(\mathbf{K}))} - \frac{1}{r\_{L} - r\_{S}} \ln \left[ \left( \frac{I\_{11}}{I\_{12}} \right) \left( \frac{E\_{12}}{E\_{11}} \right) \frac{r\_{S}}{r\_{L}} \right] \right)^{2}, \tag{12}$$

or in S2D1D2 mode using Equation (7) as:

$$K = \operatorname\*{argmin}\_{K} \sum\_{\Lambda} \left( \sqrt{3\mu\_{a}(K)(\mu\_{a}(K) + \mu\_{s}^{\prime}(K))} - \frac{1}{r\_{L} - r\_{S}} \ln \left[ \left( \frac{I\_{22}}{I\_{21}} \right) \left( \frac{E\_{21}}{E\_{22}} \right) \frac{r\_{S}}{r\_{L}} \right] \right)^{2}. \tag{13}$$

During the optimization procedure the following limitations were set on the extracted variables: *StO*<sup>2</sup> varies in the physiological range of [0, 1], *a* varies in the range of [0.5, 10] mm<sup>−</sup>1, *b* varies in the range of [0, 3], *f* varies in the range of [0, 1], volume fractions *Cblood* and *Cwater* vary within [0, 1], and *<sup>μ</sup>dry <sup>a</sup>* varies within [0, ∞]. Lower and upper limits for the parameters *a* and *b* are determined according to the reported data on the range of the skin reduced scattering coefficient at *λ*<sup>0</sup> = 500 nm and the corresponding power index values [18,43]. Since *μmel <sup>a</sup>* (*λ*) and *μ <sup>s</sup>*(*λ*) both monotonously decrease with the wavelength, high uncertainty arises in the joint reconstruction of the parameters of *Cmel*, *a*, *b*, and *f*; therefore, *Cmel* was chosen as a constant value.

#### *2.3. Experimental DRS Setup*

An experimental DRS setup with a self-calibrating fiber-optic probe was constructed in accordance with the scheme shown in Figure 1. Radiation from Fiber-Coupled Xenon (SLS205, Thorlabs, Newton, NJ, USA) broadband 240–1200 nm light source was used for tissue probing. The source has a mechanical shutter driven by a TTL pulse from the Control unit Arduino Uno (Arduino, Scarmagno, Italy). It has rather high spectral radiance both in VIS and NIR spectral regions in comparison with those traditionally applied in VIS-NIR spectroscopy tungsten halogen lamps which have low spectral radiance at wavelengths below 600 nm. Probing light passes through BS-8 (Zapad Pribor, Moscow, Russia) absorption filter cutting UV light below 380 nm placed in the fiber-optic FOFMS/M (Thorlabs Inc., Newton, NJ, USA) filter holder. A UV filter is used to prevent possible negative effects on biological tissue and solarization of the probe and switch optical fibers. Spectrally corrected light passes through 1 × 2 fiber-optical switch 1 (Piezosystem Jena GmbH, Jena, Germany) which selects the *S*1 or *S*2 source fiber of the probe to illuminate biological tissue. Diffusively scattered light is detected by detection fibers *D*1 and *D*2, one of which is selected by a 1 × 4 switch 2 (Piezosystem Jena GmbH, Jena, Germany) to deliver light to spectrometer Maya 2000 PRO (Ocean Optics, Orlando, FL, USA). Switch 2 uses only two outputs for the applied optical probe which has only two detection fibers. Both switches are driven by the control unit. The Maya spectrometer has rather high sensitivity in NIR up to 1100 nm which covers water and lipid absorption bands near 980 nm and has high linearity due to the applied calibration which is essential for the application of a self-calibrating approach. The spectrometer exposure times are set individually for small and large SDDs to fit the spectrometer dynamic range. In the current in vivo and phantom studies, the exposure times were set equal to *E*<sup>21</sup> = *E*<sup>12</sup> = 80 ms for long SDD *rL*= 4 mm and *E*<sup>11</sup> = *E*<sup>22</sup> = 15 ms for short SDD *rS*=2 mm. For each source–detector pair, the detected signal is averaged over several subsequent measurements in order to increase signal-to-noise ratio with the following subtraction of a dark signal obtained at the closed source shutter with the same exposure time and averaging. For the in vivo studies, the averaging number is taken from the ratio T/*E*<sup>21</sup> or T/*E*<sup>11</sup> where T is a heartbeat period. The resulting spectra *I*11, *I*12, *I*21, and *I*<sup>22</sup> are stored at PC for further analysis described below in Section 2.3.

Domestically designed probe housing is made of black photopolymer resin Anycubic Basic (HONGKONG Anycubic Technology Co., Limited, Hong Kong, China) by 3D printing on a Phrozen Shuffle 2019 (Hsinchu City, Taiwan) printer and has 6 × 8 mm2 area of the probe–tissue interface. Two 400 μm source fibers and two 200 μm detection fibers with 0.22 NA (Thorlabs, Newton, NJ, USA) were placed in line inside the probe housing at a 2 mm distance between neighboring fibers, which results in short and long SDDs of *rS* = 2 mm and *rL* = 4 mm, respectively.

The fiber-optic probe is equipped with a mechanical pressure control unit. The pressure was set equal to 12.7 kPa in all studies.

The DRS system is fully automated by a JAVA code operated with a source shutter, spectrometer, and fiber switches with the help of a control unit. Full acquisition time was about 6 s for the abovementioned exposure times and a heartbeat period of 1 s.

#### *2.4. Instrumental Perturbations in Phantom and In Vivo DRS Studies*

The developed experimental setup was tested on a silicone-based biotissue phantom employed as a reference standard for DRS measurements in [26] and on a palm of a healthy volunteer from the group of the researchers. In both series of experiments, various types of instrumental perturbations were applied to a developed DRS setup in order to compare the stability of the self-calibrating and single-slope approaches, including installing an additional attenuator in an individual channel, bending the optical fiber, and modifying the probe–tissue interface (Table 1).

**Table 1.** Description of instrumental perturbations used in phantom and in vivo experiments.


Installing additional fibers (labeled as D1L and S1L in Table 1) with a smaller core diameter of 105 μm (compared to 200 and 400 μm fibers used in the setup) in an individual channel simulates possible losses in fiber-optic contacts between different instrumental parts: the light source, detector, optical switches, and fiber-optic probe. Curving a probe fiber (labeled as D1C and S1C in Table 1) into a 50 mm radius ring simulates the fiber curvature occurring in the course of a medical procedure when a fiber-optic probe examines different tissue localizations and fibers are randomly bent. Modification of the probe–tissue interface with plastic page stickers (series NEON, BRAUBERG, Frankfurt, Germany) with different colors (blue, green, and pink labeled as D1B and S1B, D1" and S1G, and D1P and S1P, respectively) simulates random biotissue surface inhomogeneities that are always present in biological tissue examinations.

In order to quantify the spectral effects of all the studied perturbations, we measured the spectral transfer functions of the introduced perturbation (the ratio of the measured spectrum with the perturbation introduced to that in the absence of the perturbation). The measurement results are shown in Figure 2 and demonstrate that most of the considered perturbations lead to spectrum shape distortion which may potentially lead to errors in reconstruction of physiological properties from the DRS measurements.

**Figure 2.** Transfer functions of the studied perturbations (the ratio of the measured spectrum with the perturbation introduced to that in the absence of the perturbation). Perturbations are indicated in accordance with Table 1.

The colored stickers naturally feature transmission bands corresponding to their visible colors. Note a significant difference in the transmittance coefficient for perturbations S1L and D1L consisting in the insertion of an additional fiber to the source or the detection channel, respectively, that originates from the different mismatch between the diameters of the original fibers and the inserted fiber. For each perturbation, DRS measurements were repeated 3 times; before each measurement the position of a probe was slightly changed by removing and then replacing the probe. Unperturbed measurements were repeated 6 times: 3 times before applying perturbations and 3 times after.

The perturbations applied to source S2 and detector D2 are not listed in Table 1 because they provide similar results to the perturbations applied to S1 and D1 for reasons of symmetry (Figure 1).

#### *2.5. Calculation of Extinction Spectra Variations*

Various instrumental perturbations listed in Table 1 result in different deviations in the extinction spectrum calculated by Equations (6), (7), or (9). These deviations are quantified as a root mean square deviation (RMSE) of the extinction spectrum values *μP*,*<sup>m</sup> eff* (*λ*) evaluated under particular perturbation in a single experiment from the initial *μINIT eff* extinction spectrum measured without perturbations:

$$
\Delta\mu\_{eff}^{P\_{\rm m}} = \sqrt{\frac{\sum\_{i=1}^{N\_{\lambda}} \left(\mu\_{eff}^{P\_{\rm m}}(\lambda\_i) - \mu\_{eff}^{INIT}(\lambda\_i)\right)^2}{N\_{\lambda}}} \tag{14}
$$

where *λ<sup>i</sup>* is the *i*-th wavelength, *i* = 1 ... *N*; *P* is the perturbation index listed in Table 1, and *m* is the measurement number with the particular perturbation *m* = 1 ... *NP*. For perturbed measurements, *NP*=*INIT* = 3, and for unperturbed measurements, *NP*=*INIT* = 6. The initial extinction spectrum *μINIT eff* (*λi*) is calculated as an average value for each wavelength over 6 measurements provided without any perturbations. To quantify deviations caused by perturbations of type *P*, an average value over Δ*μP*,*<sup>m</sup> eff* is calculated:

$$
\Delta\mu\_{eff}^P = \frac{\sum\_{m=1}^{Np} \Delta\mu\_{eff}^{P,m}}{N\_P} \tag{15}
$$

Variations of reconstructed tissue chromophore concentrations and scattering properties obtained for in vivo measurements were calculated in the same way.

#### **3. Results**

#### *3.1. Phantom DRS Measurements*

Several DRS phantom measurements have been performed with and without the instrumental perturbations indicated in Table 1.

Figure 3 shows the examples of extinction spectra *μP*,*<sup>m</sup> eff* of a silicone phantom calculated using the single-slope approach in S1D1D2 and S2D1D2 configurations and the calibrationfree approach in S1S2D1D2 configuration for different kinds of source (S1L, S1C, S1B) and detector (S1L, S1C, S1B) perturbations, as well as for unperturbed data. As one can see from Figure 3a,b,f, all extinction spectrum curves calculated using the self-calibrating approach are close to each other, which indicates a high resistance to instrumental perturbations introduced to source or detector channels (Figure 3a,b). In contrast, the single-slope approach demonstrates resistance only to source perturbations (Figure 3(d)), while perturbations introduced to the detector channel lead to significant variations in *μeff* (Figure 3c,e). It can be seen from Figure 3c,e that if a perturbation *P* results in an increase in *μ<sup>P</sup> eff* values calculated by S1D1D2 data, the value of *μP*,*<sup>m</sup> eff* calculated by S2D1D2 data decreases. For example, the absorption band of the blue sticker (see Figure 2) employed in perturbation D1B manifests by the deformation of the *μeff* spectrum reconstructed by single-slope measurements in S1D1D2 and S2D1D2 configurations in opposite ways (Figure 3(c) and 3(e), respectively) according to Equations (6) and (7). The introduction of loss perturbation D1L appears as a negative (Figure 3c) or positive (Figure 3e) shift in the reconstructed *μeff* spectrum together with a variation around 950 nm which is determined by the transmission peak in the transfer function of this perturbation (Figure 2). The fiber curving perturbation D1C provides minimal variations in *μeff* spectrum since it has a transmittance close to 100% (Figure 2). The increase in the noise level in Figure 3b,d for S1L perturbation is caused by a drop in light intensity, while the shape of the extinction spectra does not change in both S1D1D2 and S1S2D1D2 cases.

Figure 3f demonstrates variations in the extinction spectra of the uniform silicone phantom for repeated unperturbed measurements. Variations for the single-slope configurations are higher than those for the self-calibrating approach. It should also be noted that red and blue curves corresponding to *μeff* calculated by the single-slope approach in the two configurations S1D1D2 and S2D1D2, respectively, are positioned above and below the gray curve for *μeff* recovered by the self-calibrating approach, which is associated with non-identical transient characteristics of the detection channels D1 and D2.

**Figure 3.** Spectra of *μP*,*<sup>m</sup> eff* of a biotissue phantom calculated with self-calibrating approach S1S2D1D2 (**a**,**b**) and single-slope approach in configurations S1D1D2 (**c**,**d**) and S2D1D2 (**e**) for different kinds of detector (left column) and source (right column) perturbations listed in Table 1. Index m indicates individual measurement under particular perturbation P. Comparison of *μINIT eff* spectra (**f**) obtained by three approaches S1S2D1D2 (gray), S1D1D2 (red), and S2D1D2 (blue) for unperturbed measurements shown as mean with confidence bounds.

#### *3.2. In Vivo DRS Measurements of Human Skin*

In vivo DRS measurements demonstrate almost similar results to the phantom studies (Figure 4). High resistance of the self-calibrating approach to both source (Figure 4b) and detector (Figure 4a) instrumental perturbations is observed for this case, whereas the singleslope approach has resistance only to source perturbations (Figure 4d), while detector perturbations can lead to a significant corruption of the reconstructed extinction spectrum (Figure 4c,e) such as those observed for the silicone phantom measurements (Figure 3c,e).

**Figure 4.** Examples of *μP*,*<sup>m</sup> eff* spectra of a human palm calculated with self-calibrating approach S1S2D1D2 (**a**,**b**), and single-slope configurations S1D1D2 (**c**,**d**), and S2D1D2 (**e**) for different kinds of detector (left column) and source (right column) perturbations described in Table 1. Index m indicates individual measurements under particular perturbation P. Comparison of *μINIT eff* spectra (**f**) obtained by three approaches S1S2D1D2 (gray), S1D1D2 (red), and S2D1D2 (blue) for unperturbed measurements shown as mean with confidence bounds.

In contrast to the results of phantom studies, the extinction coefficient in in vivo studies calculated for unperturbed (INIT) measurements (Figure 4f) demonstrate similar variations in self-calibrating and the single-slope approaches. This can be explained by the spatial variations of palm biotissue optical properties that are much higher than the variations of a homogeneous tissue phantom.

Figure 5 provides the comparison of the average deviations in the extinction coefficient Δ*μ<sup>P</sup> eff* for different types of perturbations in the studies of a biotissue phantom and a human palm. In Figure 5a the deviations in reconstructed extinction coefficient Δ*μ<sup>P</sup> eff* for all types of perturbations in phantom studies are summarized. It can be seen from the diagram that deviations in the extinction coefficient calculated by the self-calibration approach are smaller than those calculated by the single-slope approach for all types of perturbations.

**Figure 5.** Deviations in extinction coefficient Δ*μ<sup>P</sup> eff* spectra calculated for different types of perturbations by Equation (15) using single-slope approach in configurations S1D1D2 and S2D1D2 and self-calibrating approach S1S2D1D2 in phantom (**a**) and in vivo (**b**) studies. Error bars show deviations in Δ*μP*,*<sup>m</sup> eff* values.

For unperturbed measurements, deviations in the extinction coefficient are 0.003 mm−<sup>1</sup> for the self-calibration approach, and 0.007 and 0.011 mm−<sup>1</sup> for the single-slope technique in two configurations, respectively. For all types of perturbations, the deviation of the extinction coefficient calculated by the self-calibration approach does not exceed 0.013 mm<sup>−</sup>1, while deviations in this value calculated using the single-slope approach exceed 0.6 mm−<sup>1</sup> for the loss perturbations in detection channels. It also can be seen from this plot that the deviations in the extinction coefficient caused by perturbations in the source channel are smaller than those applied to the detection channel. Figure 5b shows the values of the deviations for the in vivo measurements. Similar to Figure 5a, detector perturbations (D1L, D1C, D1B, D1G, D1P) lead to large values of deviations in the extinction coefficient calculated using the single-slope approach, and this effect is significantly lower for the self-calibrating approach. Larger error values in Figure 5b compared to Figure 5a can be explained by a smaller level of the DRS signals detected in vivo owing to higher extinction.

#### *3.3. Reconstruction of Skin Chromophores and Scattering Properties*

Examples of fitting the extinction spectra of the in vivo human palm calculated using the self-calibrating and single-slope approaches for unperturbed DRS data with expressions given by Equations (1), (2), and (10) using Equations (11)–(13) are shown in Figure 6. The fitting curve tracks the most pronounced visible features of the extinction spectrum: oxyhemoglobin peaks in the visible spectral range at 540 and 576 nm, deoxyhemoglobin peak at 756 nm, water absorption peak at 975 nm, and an overall decrease in the extinction coefficient from short to long wavelengths due to a decrease in absorption and scattering. However, there is some discrepancy between the reconstructed and experimentally obtained extinction spectra caused by the significant simplification of the applied model of light transfer in a human palm.

**Figure 6.** Fitting the extinction spectra of the in vivo human palm obtained from unperturbed measurements using (**a**) S1S2D1D2, (**b**) S1D1D2, and (**c**) S2D1D2 approaches with the reconstructed extinction spectra using Equations (11)–(13).

Figure 7 shows the values of blood *Cblood* and water *Cwater* content, tissue oxygenation *StO*2, and scattering properties *a*, *b*, and *f* of human palm reconstructed from fitting the experimental extinction spectra which were obtained using different measurement approaches (self-calibrating S1S2D1D2 and single-slope S1D1D2, S2D1D2) from DRS data measured under different instrumental perturbations listed in Table 1. The reconstructed values obtained for unperturbed (INIT) data are in agreement with typical skin physiological parameters [18,43]: *StO*<sup>2</sup> is about 0.8 and *Cblood* and *Cwater* are around 0.002 and 0.4, respectively. The reconstructed values of *a*, *b*, and *f* yield the *μ <sup>s</sup>*(*λ*) dependence, which is in agreement with the reduced scattering spectra reported in [43]: the short wave range of the reconstructed spectrum tends to the typical values reported for epidermis owing to a smaller probing depth in this range, while in the NIR range the recovered spectrum corresponds well to the *μ <sup>s</sup>* spectrum reported for dermis.

As follows from the analysis of extinction coefficient deviations, skin optical parameters reconstructed from S1S2D1D2 extinction spectra demonstrate high stability for all DRS data obtained under all possible perturbations in which the deviation does not exceed 16%. In contrast, the parameters reconstructed from the single-slope data S1D1D2 and S2D1D2 demonstrate stability only for source perturbations and unperturbed data. These results are summarized in Figure 8, showing relative deviations in different skin characteristics obtained with all source (S1L, S1C, S1B, S1G, S1P) and all detector (D1L, D1C, D1B, D1G, D1P) perturbations. These plots demonstrate low average variations (less than 16%) of the parameters reconstructed from self-calibrating data for all types of perturbations, while detector perturbations may result in high variations (up to several times for particular perturbations) of reconstructed values from single-slope data (Figure 8a).

**Figure 7.** Values of *Cblood* (**a**), *StO*<sup>2</sup> (**b**), *Cwater* (**c**), *a* in mm−<sup>1</sup> (**d**), *b* (**e**), and *f* (**f**) reconstructed from the experimental extinction spectra using S1S2D1D2, S1D1D2, and S2D1D2 approaches and averaged over 3 measurements for each of the 10 perturbations (Table 1) and over 6 measurements for INIT data. Error bars show deviations in the corresponding reconstructed values in the series of the experiment. All values of *b* are below 10−8, except the two corresponding to the perturbations D1B and D1L, which lead to largest deviations in the reconstructed extinction spectra from the unperturbed one (see Figure 4c,e).

**Figure 8.** Relative deviations in *Cblood*, *StO*2, *Cwater* , *a*, and *f* values reconstructed using selfcalibrating (S1S2D1D2) and single-slope (S1D1D2 and S2D1D2) approaches from the unperturbed measurement values. Relative deviations are averaged over different types of detector (**a**) and source (**b**) perturbations for each reconstructed value. Note that the plot (**b**) does not contain S2D1D2 data since perturbations introduced to the S1 channel provide no impact on these measurements.

#### **4. Discussion**

In this study we compared the capabilities of single- and dual-slope approaches in DRS to resist different perturbations that may occur during measurements. An experimental setup for wide-band DRS with a fiber-optic contact probe capable of employing a selfcalibrating approach was constructed. This system contains a broadband fiber-optic source allowing for diffuse reflectance measurements in a wide VIS-NIR band (460–1030 nm). The upper wavelength range boundary is limited by the detector sensitivity curve, while detection in the short wavelength range is limited by strong probing light attenuation in biotissue. The self-calibrating scheme is based on symmetrical source-detector measurements performed through two fiber-optic switches for two source and two detection fibers of the probe (Figure 1). In order to fit the spectrometer dynamic range for the whole wavelength range for short (2 mm) and long (4 mm) SDDs, we applied different exposure times of 15 and 80 ms, respectively.

Different instrumental perturbations have been introduced into source and detector channels including attenuation, fiber bending, and corrupting probe–tissue interface in order to compare resistance to them of self-calibrating and single-slope approaches in phantom and in vivo studies. Both approaches have been applied to analyze the corresponding extinction spectrum deviations originating from the applied perturbation during DRS measurements. The results of phantom and in vivo studies have shown (Figures 3 and 4) that both approaches have resistance to instrumental perturbations introduced into the source channel (S1L, S1C, S1B, S1G, S1P). At the same time, perturbations introduced into the detection channel (D1L, D1C, D1B, D1G, D1P) may lead to significant deviations in the extinction spectra calculated by the single-slope approach (S1D1D2 or S2D1D2), while the self-calibrating approach (S1S2D1D2) demonstrated much higher resistance. This can be explained by the fact that Equation (5) for single slopes contains the ratio of detector transient characteristics and excludes source transient characteristics. However, Equations (6) and (7) are written under the assumption that the transient characteristics of both detectors are equal, therefore, perturbations introduced into one of the detector channels lead to the corruption of the evaluated extinction spectra. In contrast to this, in Equation (9) for the extinction spectrum calculated using self-calibrating approach, the transient functions for both sources and detectors are reduced. Figure 5a also demonstrates higher variations of extinction spectra calculated by the single-slope approach in comparison with the self-calibrating approach even for unperturbed data and all source perturbations. This effect is explained by residual instrumental perturbations (residual fiber bending, variations in SMA-connectors, etc.) that remained after perturbations introduced into source and detector channels during phantom studies. Figures 3f and 4f also demonstrate the imperfections in the detection channels of the designed DRS system seen by the discrepancies in the opposite sign between the values of *μeff* reconstructed from the unperturbed spectra in self-calibrating mode versus those for single-slope configurations S1D1D2 and S2D1D2.

Reconstruction of the biotissue properties from the obtained extinction coefficient spectra demonstrated that the self-calibrating approach provides reliable values with average deviations not exceeding 16% for all the considered perturbations. In this connection, if the spectral changes induced by instrumental perturbations in clinical conditions are similar to those we employed in this study, one can expect approximately the same accuracy of the self-calibrating technique. However, it should be noted that the DRS measurements in subcutaneous tissues are sensitive to the applied pressure of a DRS probe. Excessive pressure of a DRS probe may result in a significant change in tissue optical properties, while a loose probe–tissue contact may lead to a slight probe shift during the measurement procedure. Both effects may result in errors in the reconstructed physiological parameters. To avoid these effects, in the designed system, the DRS probe was equipped with a pressure control unit allowing it to keep the optimal pressure during measurements.

In the present study we applied the simplest reconstruction technique of skin optical properties based on a standard MATLAB minimization function, and the model of DRS spectra was taken from the diffusion approximation of radiation transfer theory for infinite and homogeneously scattering and absorbing medium. This model was applied to assess the instability of reconstructed tissue property values caused by instrumental variations; however, the reconstructed *μeff* spectrum has noticeable discrepancy with the experimental extinction spectrum obtained from the unperturbed measurements (Figure 6). We also limited the number of chromophores that contribute to the absorption spectrum in the described wavelength range and did not consider lipids because we focused on characterizing the chromophores of human palm, where the content of lipids is typically moderate and located mainly in hypodermis. Since our DRS system has SDDs of units in millimeters, it is mostly sensitive to superficial chromophores of skin such as water, blood, and melanin and to a lesser extent, to lipids in hypodermis at depths exceeding 1–2 mm. For a more precise reconstruction, the presence of the biotissue boundary and the skin layered structure should be taken into account, and more sophisticated algorithms of reconstruction should be used. It is essential for broadband DRS measurements in which light in the VIS and NIR spectral ranges penetrates to different depths in tissue. Monte-Carlo modeling of light transport can be used to take into account layered skin structure [44,45], and tissue properties can be derived using machine learning based on advanced theoretical and numerical models of light transport [46–49].

#### **5. Conclusions**

A comparative analysis of the sensitivity of single- and dual-slope (self-calibrating) approaches in DRS was performed using a custom-built wideband 460–1030 nm DRS setup in phantom and in vivo studies. Different instrumental perturbations have been introduced into source and detector channels in order to compare the stability of self-calibrating and single-slope approaches toward uncontrolled attenuations in individual channels, optical fiber bending, and optical inhomogeneities at the probe–tissue interface. Both singleslope and self-calibrating approaches have demonstrated high stability to perturbations introduced into the source channels. Perturbation in the detection channels may lead to significant deviations in the extinction spectra recovered from the measured backreflectance spectra by the single-slope approach, however, the self-calibrating approach has demonstrated high stability for all types of perturbations. Reconstruction of the biotissue properties from the obtained extinction coefficient spectra demonstrated that the self-calibrating approach provides reliable values with average deviations not exceeding 16% for all the considered perturbations. Thus, we can conclude that the self-calibrating approach can be applied to DRS to provide robust measurements insensitive to instrumental perturbations in a wide VIS-NIR spectral band.

**Author Contributions:** Conceptualization, I.T., M.K. and E.S.; methodology, I.T., D.K. and E.S; software, O.S., V.P. and A.K. (Aleksandr Khilov); validation, E.S., M.K. and D.K.; formal analysis, E.S., M.K., I.T.; investigation, A.K. (Alexey Kostyuk), A.K. (Aleksandr Khilov), D.K., A.O.; resources, A.K. (Alexey Kostyuk) and I.T.; data curation, I.T., V.P, M.K. and E.S.; writing—original draft preparation, I.T. and V.P.; writing—review and editing, I.T., V.P., M.K. and E.S.; visualization, I.T., V.P. and A.K. (Aleksandr Khilov). project administration, I.T.; All authors have read and agreed to the published version of the manuscript.

**Funding:** The authors acknowledge the support by Center of Excellence «Center of Photonics» funded by The Ministry of Science and Higher Education of the Russian Federation, Contract No. 075-15-2022-316.

**Institutional Review Board Statement:** Not applicable.

**Informed Consent Statement:** Informed consent was obtained from all subjects involved in the study.

**Data Availability Statement:** The data presented in this study are available on a reasonable request from the corresponding author.

**Acknowledgments:** The authors thank Vladimir Vorobjev and Sergey Pozhidaev for the electrical and mechanical engineering of the developed DRS setup; we also thank Mikhail Kleshnin for valuable recommendations during discussion about probe design.

**Conflicts of Interest:** The authors declare no conflict of interest.

#### **References**


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## *Article* **The Glycerol-Induced Perfusion-Kinetics of the Cat Ovaries in the Follicular and Luteal Phases of the Cycle**

**Alexey A. Selifonov 1,\*, Andrey S. Rykhlov <sup>2</sup> and Valery V. Tuchin <sup>3</sup>**


**Abstract:** The method of immersion optical clearing reduces light scattering in tissues, which improves the use of optical technologies in the practice of clinicians. In this work, we studied the optical and molecular diffusion properties of cat ovarian tissues in the follicular (F-ph) and luteal (L-ph) phases under the influence of glycerol using reflectance spectroscopy in a broad wavelength range from 200 to 800 nm. It was found that the reflectance and transmittance of the ovaries are significantly lower in the range from 200 to 600 nm than for longer wavelengths from 600 to 800 nm, and the efficiency of optical clearing is much lower for the ovaries in the luteal phase compared to the follicular phase. For shorter wavelengths, the following tissue transparency windows were observed: centered at 350 nm and wide (46 ± 5) nm, centered at 500 nm and wide (25 ± 7) nm for the F-ph state and with a center of 500 nm and a width of (21 ± 6) nm for the L-ph state. Using the free diffusion model, Fick's law of molecular diffusion and the Bouguer–Beer–Lambert radiation attenuation law, the glycerol/tissue water diffusion coefficient was estimated as *<sup>D</sup>* = (1.9 <sup>±</sup> 0.2)10−<sup>6</sup> cm2/s for ovaries at F-ph state and *<sup>D</sup>* = (2.4 <sup>±</sup> 0.2)10−<sup>6</sup> cm2/s—in L-ph state, and the time of complete dehydration of ovarian samples, 0.8 mm thick, as 22.3 min in F-ph state and 17.7 min in L-ph state. The ability to determine the phase in which the ovaries are stated, follicular or luteal, is also important in cryopreservation, new reproductive technologies and ovarian implantation.

**Keywords:** ovarian tissues; follicular phase; luteal phase; glycerol; tissue water; total transmittance spectra; diffuse reflectance spectra; diffusion coefficient; optical clearing efficiency

#### **1. Introduction**

Every year, around the world, there is an increase in the number of diagnosed oncological diseases, including among patients of reproductive age [1]. For example, in the United States, about 70,000 cancer patients under the age of 45 are diagnosed annually [2]. Patients with malignant neoplasms, according to existing modern medical standards, undergo complex chemotherapy and radiation therapy. As a result of such treatment, there is a high probability of partial or complete loss of fertility in women, due to the high cytotoxicity of antitumor treatment [3–6]. A large group of patients is young women and girls, whose treatment requires bone marrow transplantation, before which alkylating drugs are used in high concentrations, which in most cases leads to sterilization. Currently, it is possible to preserve the reproductive function of women with cancer, with impaired reproductive function or with premature ovarian failure; this is the cryopreservation (freezing) of healthy ovarian tissue with subsequent transplantation or autotransplantation after recovery [7–10].

One of the most informative and reliable methods for examining ovarian tissue is laparoscopy, which is widely used in gynecology for both diagnostic and surgical purposes [11,12]. The laparoscope is inserted into the abdominal cavity through a small incision, which allows one to directly examine the organs of the small pelvis and abdominal

**Citation:** Selifonov, A.A.; Rykhlov, A.S.; Tuchin, V.V. The Glycerol-Induced Perfusion-Kinetics of the Cat Ovaries in the Follicular and Luteal Phases of the Cycle. *Diagnostics* **2023**, *13*, 490. https://doi.org/10.3390/ diagnostics13030490

Academic Editor: Viktor Dremin

Received: 23 December 2022 Revised: 25 January 2023 Accepted: 26 January 2023 Published: 29 January 2023

**Copyright:** © 2023 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 (https:// creativecommons.org/licenses/by/ 4.0/).

cavity or, by connecting a video camera, transmit the image to the monitor. However, such an image is formed only by light reflection from the surface of the organ under study; the internal structure of the organ is hidden from observation due to strong light scattering by the tissues of this organ. Using the immersion optical clearing of tissue, it is possible to suppress scattering and observe previously hidden pathological changes in tissues for some time [13–17]. Typical times for the optical clearing of the upper layers of the tissue are 20–40 min. It is important that radiocontrast and MRI contrast agents can act as optical clearing agents. This opens the way to multimodal diagnostics and the support of laparoscopic surgery. It should be noted that hysterosalpingography and hysteroscopy [11,12,18] can be combined in one study with the possibility of obtaining high-quality optical images using laparoscopically compatible optical imaging techniques, as radiopaque and MRI agents are good optical clearing agents [13–17].

Cryopreservation is a new method that is successfully used in clinical practice. By 2020, about 85 transplantations of cryopreserved ovarian tissue have been performed, and cases of birth of 30 children have been described, although a longer follow-up of patients is required [19,20]. The standard method for cryopreservation of ovarian tissue is slow freezing using a medium with the addition of cryoprotectants: dimethyl sulfoxide (DMSO), ethylene glycol and 1,2-propanediol (PrOH), which are able to penetrate cell membranes and provide their protection. Slow freezing is carried out with liquid nitrogen for several hours [14,21,22]. However, with slow freezing, there is a risk of damage to cells by ice crystals [8,23,24]. Therefore, penetrating cryoprotectants are often used in combination with non-penetrating ones such as sucrose, glycerol, or human serum albumin [22]. They protect cells through dehydration and stabilization of the lipid layer and proteins. The use of glycerol during the cryopreservation of ovarian tissue can be useful for maintaining the viability of follicles, as glycerol causes the dehydration of cells and, when mixed with water, reduces the freezing point (the temperature of ice formation in cells and solutions) and increases the viscosity of aqueous solutions. After preparing the biological material by soaking it in cryogenic liquids, the vitrification procedure is used, which consists of immersing the material in liquid nitrogen. This method effectively preserves the morphology and viability of the follicles [25–27].

The method of the cryopreservation of ovarian tissue is new and requires further comprehensive study. Many researchers estimate the recovery of ovarian function after cryopreserved tissue transplantation as short-term. Ischemia that occurs in the first hours after transplantation can lead to the death of more than a third of primordial follicles and, therefore, is the main reason for the decrease in the functional activity of the ovary [28]. To restore the reproductive potential, it is extremely important to reduce the time interval of ischemia and accelerate the revascularization of grafts. In this regard, the transplantation of whole ovarian tissue on a vascular pedicle has been proposed as the most acceptable approach compared to the transplantation of the ovarian cortex alone [29,30]. As shown in animals, the transplantation of an intact whole ovary with microsurgical vascular anastomosis, despite the technical complexity of this procedure, is the only solution to the problem, as it provides a direct blood supply to the ovarian tissue after transplantation, minimizing the risk of ischemia. Therefore, the whole ovary cryopreservation method requires development and further research. The determination of the kinetic parameters of ovarian perfusion with cryoprotectants in different phases of the cycle, including the rate of diffusion of glycerol and the flow of tissue water induced by it, as well as changes in the optical properties of ovarian tissue, is a necessary condition for creating personalized clinical protocols for cryopreservation.

The aim of this work was to study the perfusion-kinetic properties of cat ovaries in the follicular (F-ph) and luteal (L-ph) phases of the cycle by optical clearing method under the influence of glycerol and using diffuse reflectance spectroscopy.

#### **2. Materials and Methods**

#### *2.1. The Structure of the Ovaries and the Cycle*

The ovaries are a paired organ located on the sides of the uterus, next to the ampullar sections of the fallopian tubes, their size in women ranges from 1.5 to 5 cm [31] and in cats, from 0.5 to 1.5 cm [32]. From above, the ovaries are covered with a layer of the epithelium; the next layer consists of connective tissue and contains many elastic fibers (Figure 1). The medulla contains many blood vessels and nerve endings. In the cortical layer, there are follicles in which eggs are formed and mature.

**Figure 1.** Schematic representation of the ovarian cycle. Adopted from Ref. [31].

The female cycle normally lasts from 21 to 35 days. The main phases can be distinguished: 1: follicular (F-ph), in this phase of the cycle, there are many growing and primary follicles in the ovaries (Figure 1); 2: ovulation is a hormone-dependent process of the rupture of the wall of the tertiary (preovulatory) follicle and the release of the female germ cell, and a peak level of hormones is observed: follitropin and lutropin; and 3: luteal phase (L-ph). The corpus luteum has a size of 1.0 to 2.7 cm. A gland of temporary secretion contains lutein and produces a large amount of progesterone, the dominant hormone of the luteal phase, which is important for the safety and proper development of a potential embryo [33].

When studying the blood supply to the ovaries of cows, it was found that the uterine branch of the ovarian artery and especially its anastomosis with the uterine artery were larger on the side of the ovary containing the corpus luteum [34]. The blood supply of the mature corpus luteum is the highest of all body organs per unit volume of tissue. An increase in blood supply is an integral part of the development of the corpus luteum. This important process, mediated by angiogenic growth factors, includes the destruction of the basement membrane of the follicles, the proliferation and migration of endothelial cells, and the development of a large network of capillaries [35]. The corpus luteum functions for only a few (4–7) days and then undergoes involution. A white body (scar) appears in its place [36] (Figure 1).

#### *2.2. Histological Examination*

Normal ovarian tissue was taken from outbred cats aged 1 to 12 years with a diagnosis of "clinically healthy". The ovaries were collected after laparoscopic oophorectomy and ovariohysterectomy from 10 cats. Animals were administered general anesthesia: premedication—meditin (0.1%); intravenous anesthesia—zoletil 100; and alpha 2—antagonist antiemetic for withdrawal from anesthesia. According to visual inspection, all ovaries planned for the study were divided into two groups: "light" and "dark" (Figure 2). Ten light and ten dark tissue samples from different individuals were used for histological examination.

**Figure 2.** Photos of the studied clinically healthy cat ovaries: (**a**) light; (**b**) dark.

In vitro histological studies were carried out using halves of each ovary, which were manually cut with a scalpel and fixed. The other halves of the ovaries without fixation were kept frozen for ex vivo optical measurements. The material for histological examination was prepared after no more than 48 h had passed after oophorectomy and ovariohysterectomy; 10% buffered formalin was used for tissue fixation. The thickness of tissue sections was 2–3 μm. The hematoxylin–eosin staining method was used for the histological examination of all samples.

To obtain histological scans, an Aperio AT2 digital slide converter (on-screen diagnostic scanner) equipped with an LED light source and calibration tools was used. According to the results of the histological studies, it was proved that normal, pathologically unchanged tissues were selected for research, that dark samples contain the corpus luteum and correspond to the luteal phase, and light samples contain multiple follicles, which corresponds to the follicular phase.

#### *2.3. Optical Measurements*

Measurements of the optical properties of cat ovarian tissue were performed ex vivo without tissue fixation. The thickness of sections (samples) of tissue was measured with an electronic micrometer (Union Source CO., Ltd., Ningbo, China). The measurements were carried out at several points of the sample and averaged. The accuracy of each measurement was ±0.1 mm. The thickness of the tissue section of both dark and light ovaries averaged (0.8 ± 0.1) mm. To measure the diffuse reflectance spectra (DRS) and the total transmittance spectra (TTS) of the tissue samples in the spectral range of 200–800 nm, a Shimadzu UV-2550 double-beam spectrophotometer (Tokyo, Japan) with an integrating sphere was used (Figure 2). A total of 20 ovaries, 10 light and 10 dark, were examined for optical measurements. To study the kinetics of the DRS, ten sections were taken from every five light and five dark samples. Similarly, ten sections from the other five + five ovaries were used to measure the TTS.

The radiation source was a halogen lamp with radiation filtering in the studied spectral range. The limiting resolution of the spectrometer was 0.1 nm. Prior to measurements, the spectra were normalized using a BaSO4 reference reflector with a suitable reflectivity for the entire spectral range, including UV. All measurements were carried out at room temperature (~25 ◦C) and normal atmospheric pressure. Each sample of the studied tissue was fixed with a double-sided adhesive tape in a special frame with a window of 0.5 × 0.5 cm in a quartz cuvette so that the tissue sample was pressed against the wall of the cuvette and subjected to optical measurement of DRS or TTS as shown in Figure 3. To measure the TTS, a quartz cuvette with a tissue sample was placed directly in front of the integrating sphere, collecting all the radiation transmitted through the tissue sample. The diameter of the light beam incident on the sample was 3 mm. The initial DRS or TTS spectrum was taken from the ovarian tissue sample pressed against the cuvette wall. Then, glycerol was added into

the space between the sample surface and the cuvette wall, after which, measurements were carried out for 100 min until the time dependence was saturated due to the completion of the glycerol/interstitial water diffusion process. The measurement of the DRS kinetics was used for the determination of the diffusion coefficient of the molecular flux induced by the topical application of glycerol to a tissue sample. In the study, a chemically pure 99.5%-glycerol was used (Akrihimfarm LLC., Moscow, Russia).

**Figure 3.** Scheme of the experimental setup for measuring the DRS and TTS of ex vivo samples of cat ovarian tissue.

It is important to note that, in the wavelength range from 150 to 800 nm, the absorption of glycerol is negligible [37]. However, to determine the effectiveness of optical clearing after the clearing process was completed, the frame with the sample was transferred to a similar, but dry, clean cuvette. Then, the final values of the DRS and TTS of the sample were measured and compared with the initial values before clearing, which were also obtained in a cuvette without glycerol.

#### **3. Calculations**

The determination of the diffusion coefficient of glycerol/interstitial water in tissue is based on measuring the kinetics of the DRS. Figure 4 illustrates this schematically. The process of glycerol/interstitial water transport in a sample can be described in terms of the model of free diffusion [13–17,38–40]. Geometrically, a sample of tissue can be represented as a plane-parallel plate of finite thickness. Using the second Fick's law and performing transformations based on the use of the modified Bouguer–Beer–Lambert law, described in detail in refs. [16,38], we obtain an expression for the difference Δ*A*(*t*, λ) between the effective optical density at the current time *A*(*t*, λ) and at the initial time *A*(*t* = 0, λ):

$$\Delta A(t,\ \lambda) = A(t,\ \lambda) - A(t=0,\ \lambda) = \Delta \mu\_{\rm eff}(t,\ \lambda)L \quad \sim \mathbb{C}\_0 \{1 - \exp(-t/\tau)\}L \tag{1}$$

$$I = I\_0 \exp[-\mu\_{\rm eff} \mathcal{L}],\ \mu\_{\rm eff}(t,\ \lambda) = \sqrt{3\mu\_{\rm a}(\mu\_{\rm a} + \mu\_{\rm s}')} \to \Delta \mu\_{\rm eff}(t,\ \lambda)$$

where the effective optical density is determined from the measurements of DRS:

$$A = -\log \mathcal{R}(t, \lambda),\tag{2}$$

**Figure 4.** Diagram showing the interaction of a hyperosmotic agent (glycerol) with ovarian tissue.

*t* is the time in seconds during which the diffusion occurs, λ is the wavelength in nm, Δμeff (*t*, λ) is the difference between the effective coefficient of attenuation of light in the tissue μeff(*t*, λ) at the current time and at the initial time, 1/cm; *L* is the average path length of photons, which in the backscattering mode is *L* ∼= 2*l*d, (*l*d) <sup>−</sup><sup>1</sup> <sup>=</sup> <sup>μ</sup>eff; <sup>μ</sup>'s <sup>=</sup> <sup>μ</sup>s(1 − *g*), 1/cm; *g* is the scattering anisotropy factor (varies from 0 to 1, for many tissues, *g* ∼= 0.93) [16,39]; and for transmission mode *L* ∼= *l*, *l* is the thickness of the sample, cm; *D* is the diffusion coefficient of the glycerol/interstitial water molecules, cm2/s; and C0 is the initial concentration of the glycerol, mol/L.

The recorded DRSs [*R*(λ), %] are converted using the standard Kubelka–Munk algorithm to *A*(λ) extinction spectra (Shimadzu UV-2550 spectrophotometer software).

Glycerol is a well-known effective hyperosmotic agent and is often used for the optical clearing of tissues [13–17,38,39,41,42]. To evaluate the efficiency of optical clearing of ex vivo tissue samples, TTS measurements are usually used, and the efficiency parameter Q is calculated:

$$\mathbb{Q}\left(\%\right) = \left\{ T(t,\lambda) - T(t=0,\ \lambda) \right\} / T(t=0,\ \lambda),\tag{4}$$

where *T*(*t* = 0, λ) is the transmittance of the tissue sample for a specific wavelength λ at the initial time, and *T*(*t*, λ) is the same at the current time.

The bars on the DRS and TTS charts represent the boundaries of the confidence interval, found as:

$$
\sigma = (t\_{\text{sSD}}) / \left(\sqrt{n}\right) \tag{5}
$$

where *t*s is Student's coefficient; SD, standard deviation, *n* = 5, *p* = 0.95.

#### **4. Results and Discussion**

#### *4.1. Histological Examination*

Histological examination of a tissue sample from the light ovaries revealed cortical and medulla (Figure 5a); an ovarian capsule was also found for the dark ovaries, including the germinal epithelium (single-layered cuboidal epithelium) and the tunica albuginea (subepithelium) (Figure 5b). However, these structural elements are present in both phases.

**Figure 5.** Histology of clinically healthy cat ovaries: (**a**) cortex (1) and medulla (2) in the light ovary (follicular phase); (**b**) the structure of the membrane of the dark ovary (luteal phase): single layer cuboidal epithelium (1) and subepithelial albuginea (2).

In the structure of the ovaries, a clear division into the medullary vascular, fibrous cortical layers is determined. In the latter, numerous groups of primordial follicles are noted subcapsularly (Figure 6a) with nearby primary and secondary follicles. Primordial follicles consist of a primary oocyte surrounded by a single layer of flattened follicular cells. Primary follicles include a larger oocyte and a layer or layers of cuboidal granulosa cells and the shiny sheath of the follicle formed around it (Figure 6b). Secondary follicles have a cavity that separates the oocyte with adjacent granulosa cells (crown radiata) from the layers of granulosa cells lining the follicle from the inside of the basement membrane. Outside of such follicles, layers of theca cells are poorly visualized (Figure 6c). The follicles of the cortical layer are located in hypercellular lean fibrous connective tissue, among which, there are single scar-like structures (Figure 6d).

**Figure 6.** Histology of clinically healthy cat ovaries in the follicular phase: (**a**) primordial follicles; (**b**) primary follicle (1): granulosa of the follicle (2), shiny sheath of the follicle (3); (**c**) oocyte (1): granulosa of the oocyte (2), the shiny coat of the oocyte (3); (**d**) flattened follicular cells surrounding the oocyte.

In dark specimens, the cortical substance is well developed and dominates over the stroma, and the corpus luteum is well visualized (Figure 7a). Some specimens show corpus luteum hyperplasia without atypia. The stroma is represented by a typical theca tissue without edema. It is moderately developed, the capillary network is multiple and smallfocal fresh hemorrhages are noted, in some samples multiple. Vessels are thick-walled and unevenly plethoric in some samples with perivascular fibrosis and hyalinosis. Scattered atretic follicles are visualized (Figure 7b) with internal and external follicular theca with an abundance of blood vessels (Figure 7c) and interstitial connective tissue (Figure 7d).

**Figure 7.** Histology of clinically healthy cat ovaries in the luteal phase: (**a**) corpus luteum; (**b**) atretic follicle; (**c**) follicular theca with an abundance of blood vessels: 1—internal, 2—external; (**d**) interstitial connective tissue.

The results of histological studies made it possible to conclude that all the samples of light and dark ovaries taken to study the optical and molecular diffusion properties under the action of glycerol can be attributed to clinically healthy. It was found that light ovaries belong to the follicular phase, and dark ovaries belong to the luteal phase, as the corpus luteum is clearly visualized. Most of the samples showed that the ovaries have a histologically typical structure; in two samples, the histological picture of the ovary with involutive changes was revealed. Necrotic foci, inflammatory infiltrate and atypical growth were not found for all the studied material.

#### *4.2. Spectrophotometric Studies*

DRSs of the studied samples of cat ovaries in the follicular phase (light ovarian tissue) (F-ph) and in the luteal phase (dark ovarian tissue) (L-ph), initially and after interaction with glycerol, averaged for five samples of each phase of cat ovaries, are shown in Figure 8a,b. It can be seen that the DRSs of both types of samples are almost identical both before and after the diffusion of glycerol. In the UV range, the initial DRSs of the ovarian samples have obvious dips characteristic of the absorption bands of amino acid residues of connective tissue proteins in the form of collagen and reticular fibers, hemoglobin, and porphyrins. In the region of about 415–420 nm and 540–580 nm, the observed dips correspond to

the absorption bands of oxyhemoglobin (415, 542 and 576 nm). Water absorption in the measured range of 200–800 nm is insignificant. The main absorption bands in the UV range for common tissue components are located at: 200 nm (proteins), 260 nm (DNA and RNA) and 375 nm (Hb) [16,39]. As a result, tissues are very opaque in the UV range due to the absorption and very strong scattering of light.

**Figure 8.** DRC spectra in the range from 200 to 800 nm of cat ovary tissue before and after immersion in 99.5% glycerol during 100 min: (**a**) F-ph (light ovarian tissue); (**b**) L-ph (dark ovarian tissue).

The diffusion coefficient of glycerol/interstitial water in the samples was determined from a least squares analysis of a section of the experimental curve characterizing the change in optical density from the time of glycerol action at selected wavelengths. Figure 9a shows the kinetics of DRS during glycerol interaction for 100 min for one of the light samples of cat ovaries. Calculations for each sample were performed for three wavelengths at 600, 700 and 800 nm (Figure 9b).

**Figure 9.** DRSs of cat ovarian tissue samples during 99.5% glycerol immersion. The corresponding kinetics of the difference in effective optical densities at the current and initial time Δ*A*(*t*, λ) were recorded at 600, 700 and 800 nm and then averaged (see Equation (1)) of the studied ovarian samples during the application of glycerol. The symbols represent the experimental data, and the solid curves represent the corresponding approximation of the experimental data within the framework of the free diffusion model; (**a**,**b**) F-ph; (**c**,**d**) L-ph.

Figure 9c shows the kinetics of DRSs with glycerol action for 100 min on one of the dark cat ovary samples. In both types of tissues (F-ph) and (L-ph) under study, the slowing down and termination of the diffusion process occurred within about 30 min. It can be seen that the interaction of glycerol with the samples leads to a gradual decrease in the reflectance over the entire wavelength range under study. As highly concentrated glycerol was used, it can be assumed that the main outflow of interstitial water from the sample and, consequently, the dehydration of tissues due to the release of water from the sample determine the temporal behavior of the DRS, which indicates a decrease in light scattering and, accordingly, makes it possible to unambiguously relate the rate of diffusion of water molecules to the rate of change in the DRS.

Using Equation (1), we find τ (diffusion time), which was 22.3 ± 0.6 min for a light sample of ovarian tissue (F-ph), and 17.7 ± 0.7 min for a dark sample of ovarian tissue (L-ph). The average diffusion coefficient for ovarian samples (*n* = 5) in F-ph was *<sup>D</sup>* = (1.9 ± 0.2)·10−<sup>6</sup> cm2/s, and in the L-ph *<sup>D</sup>* = (2.4 ± 0.2)·10−<sup>6</sup> cm2/s. The diffusion coefficients of glycerol/interstitial water fluxes in the studied samples determined from the experimental data (Figure 7) according to Equations (1)–(3) and the least squares method are presented in Table 1.

**Table 1.** Kinetic parameters of molecular diffusion in the sections of cat ovaries of the initial thickness *l* = 0.8 ± 0.1 mm and whole ovary (dehydration time *t*deh calculated using diffusion coefficient) at the application of 99.5% glycerol.


The data obtained can be compared with the values of the diffusion coefficients of molecular flows, which are caused by the topical application of highly concentrated glycerol. The molecular diffusion coefficient measured in human gingival tissue at the action of 99.5% glycerol was found as (1.78 ± 0.22) × <sup>10</sup>−<sup>6</sup> cm2/s (*<sup>n</sup>* = 5; *<sup>l</sup>* = 0.59 ± 0.06 mm) [41,42], which correlates well with the data received in this paper (Table 1) and the literature data for other tissues [13–17,38–42] taking into account the structural features of tissues and mostly related to tissue water diffusion due to osmotic pressure. As we assume that under the influence of glycerol mainly water migrates in the tissue, the upper limit for the diffusion coefficient should be the rate of water diffusion in the tissue. Based on data for water self-diffusion (*D*<sup>w</sup> = 3 × <sup>10</sup>−<sup>5</sup> cm2/s [43]), and considering that soft tissues contain up to 75% water, we can estimate the rate of water diffusion in a typical tissue, taking into account the effect of hidden diffusion, which is quantified by the ratio of the path length of the molecular flow between two points in a tissue to the direct distance between these points, named tortuosity [17,44]:

$$\text{Tortuosity} = \sqrt{{}^{D\_w/D}} \tag{6}$$

The tortuosity was estimated at 3.9 for the gingival lamina propria (LP) layer [44] and at 3.5 for the skin dermis [17], which allows to obtain *<sup>D</sup>*LP = 1.9 × <sup>10</sup>−<sup>6</sup> cm2/s and *<sup>D</sup>*dermis = 2.4 × <sup>10</sup>−<sup>6</sup> cm2/s that is in excellent agreement with the measured values of the diffusion coefficient for light ovarian (F-ph) and dark ovarian (L-ph) tissues, with the tortuosity of 3.9 and 3.5, respectively.

Of course, in reality, there is not one flux, but two opposite fluxes: water flux from the tissue and glycerol flux into the tissue. However, at a high concentration of glycerol, the rate of its diffusion in water is low [45]. The diffusion coefficient of glycerol in water at its mass fraction of 84% at room temperature is 2 × <sup>10</sup>−<sup>7</sup> cm2/s, which is an order of magnitude lower than the diffusion rate that we obtained experimentally in this study and

which is in good agreement with the water diffusion model in the tissue accounting for the phenomenon of tortuosity.

The diffusion time (τ, min) found from the experimental data for the dark ovary in L-ph turned out to be shorter than for the F-ph (light) samples. This may be because L-ph ovaries contain a larger network of capillaries and are therefore more porous and permeable to migrating molecules. Taking into account the thickness of the whole ovary of *l* = 5 mm and using experimentally determined diffusion coefficients from Table 1 and equation (3), we calculated the dehydration time *t*deh of the whole ovary under the action of highly concentrated glycerol. The ovary in the luteal phase is dehydrated after (2.1 ± 0.1) hours, and in the follicular phase, a little longer—after (2.3 ± 0.1) hours.

The TTS kinetics for typical samples is shown in Figure 10. In contrast to the DRS, the TTS of the two types of ovarian tissue samples have noticeable differences. The transmittance of both types of samples in the UV is close to zero. The TTSs of light samples (F-ph) show absorption bands of blood hemoglobin, which correlate with the DRSs (Figure 9a). For the TTSs of the dark samples (L-ph), the transmittance is practically zero from 200 to 450 nm and then at 540–590 nm. Obviously, this is due to the fact that this type of ovarian tissue is largely supplied with a capillary network filled with blood. The initial (0 min) and final (100 min) average TTS for all five samples for each type of ovary are shown in Figure 11.

After the complete immersion of the samples, it can be seen that the optical clearing of tissues occurred with the formation of transparency windows. In samples of ovaries in F-ph, the formation of two transparency windows is observed: one in the UV region with a center 350 nm wide (46 ± 5) nm and with a center 500 nm wide (25 ± 7) nm (Figure 11a,b). In the ovary sample in L-ph, the formation of one transparency window in the visible region of the spectrum with a center of 500 and a width of (21 ± 6) nm is observed, and the UV region does not become more transparent (Figure 11c,d).

**Figure 10.** TTSs of cat ovarian tissue samples during 99.5% glycerol immersion: (**a**,**b**) F-ph; (**c**,**d**) L-ph.

**Figure 11.** Averaged TTS of 5 samples of cat ovarian tissue sections when immersed in 99.5% glycerol: (**a**,**b**) F-ph; (**c**,**d**) L-ph.

The method of immersion optical clearing using hyperosmotic agents, in particular, highly concentrated glycerol, is based on the following mechanisms for suppressing light scattering in tissues. Glycerol induces a partial exchange of tissue water in the interstitial fluid and in the cell cytoplasm and causes tissue dehydration, which, in turn, leads to the matching of the refractive indices of scatterers with the environment (interstitial fluid) and their better packing [13–17,38,39,41,42]. Glycerol has a higher refractive index than interstitial fluid, so when it penetrates the tissues, it also provides refractive index matching, which also causes a decrease in light scattering. As the concentration of glycerol in the tissue becomes sufficiently high, a third mechanism associated with protein dissociation arises [46,47]. However, it is well known that all these mechanisms are reversible and are important for different stages of the optical clearing process [13–17,44,46–50].

The kinetics of change in transmittance for different wavelengths are shown in Figure 12. When a more blood-filled ovary in the luteal phase interacts with glycerol, hemoglobin is rapidly washed out, which goes quickly, as the erythrocytes burst due to osmosis and, together with tissue water, hemoglobin goes into a larger volume of the surrounding solution. Thus, transmission is increased not only by decreasing scattering but also by decreasing the absorption of hemoglobin and its forms, which is a much faster process (see Figure 12d) [50].

**Figure 12.** The kinetics of the total optical transmittance *T*(*t*) of cat ovarian tissue samples for different wavelengths λ when exposed to 99.5% glycerol: (**a**,**b**) F-ph; (**c**,**d**) L-ph.

The efficiency of optical clearing under the influence of 99.5% glycerol (*Q*, %), determined by Equation (4), was calculated using experimental data presented in Figure 9a–d for ovarian tissue in different phases of the cycle (Table 2).



Figure 13 shows visual changes in the studied tissue samples before and after optical clearing with 99.5% glycerol. The images were taken using the camera of a Samsung Galaxy A51 smartphone with a resolution of 48 MP. To obtain the photos, the samples were placed on a sheet of white paper with white light falling from above.

In the UV range, the efficiency of optical clearing of cat ovarian tissue with 99.5% glycerol is high and reaches 370% for the F-ph samples and 411% for the L-ph samples. The absolute optical transmittance is not high and reaches 3.5% at 350 nm for F-ph samples (Figure 10b) and only 0.2% for L-ph samples because of strong light scattering combined with strong absorption by the endogenous chromophores, including blood hemoglobin. At 500 nm, the optical clearing efficiency reaches 946% for the F-ph samples and 2074% for the L-ph samples, with the total transmittance up to 16% for the F-ph samples and 4% for the L-ph samples. At 600 nm, the optical clearing efficiency reaches 306% for the F-ph samples and 529% for the L-ph samples, with the total transmittance up to 5% for the F-ph samples and 0.3% for the L-ph samples.

In the so-called "first therapeutic/diagnostic window" at 650–800 nm [16], the efficiency of optical clearing is not the highest and reaches 213% for the F-ph samples and 405% for the L-ph samples. However, due to the absence of strong absorption bands of endogenous chromophores in this region, the absolute transmittance is quite large and amounts to 70% (Figure 10a,c).

Similar results were obtained when using highly concentrated glycerol for the optical clearing of colorectal tissues in normal conditions and in polyposis pathologies, as well as healthy gingival tissue [44]. For the colonic mucosa, two windows of dynamic transparency were identified in the UV range from 200 to 260 nm and from 260 to 418 nm, and a lower efficiency of optical clearing was shown in the long-wave visible/NIR region with a high level of absolute transmittance.

#### **5. Conclusions**

Two groups of cat ovarian samples were studied. The histological examination of these samples revealed a difference between these groups. It was determined that the light ovaries are in the follicular phase and do not contain a corpus luteum. In the darker ovaries, corpora luteal of various stages were found, which corresponds to the luteal phase of the cycle. The diffuse reflectance and total transmittance of samples in the pre-luteal and luteal phases of the cycle were determined by diffuse spectroscopy. Using the optical kinetics of ovarian tissue samples at glycerol action, glycerol/tissue water diffusion coefficient was estimated, *<sup>D</sup>* = (1.9 ± 0.2) × <sup>10</sup>−<sup>6</sup> cm2/s for ovaries in the follicular stage of the cycle and *<sup>D</sup>* = (2.4 ± 0.2) × <sup>10</sup>−<sup>6</sup> cm2/s for ovaries in the luteal phase of the cycle. Using the obtained diffusion coefficients, it was possible to obtain the time for the complete dehydration of the whole ovary at glycerol action. The time of the complete dehydration of the ovary sections 0.8 mm-thick in the follicular phase was estimated as 22.3 min, and in the luteal phase, 17.7 min. These data can be used to evaluate total ovarian dehydration at concentrated glycerol applications. In general, the data received in this study can be used for designing the protocols for drug delivery and the cryopreservation of organs.

The total optical transmittance of the ovaries in the follicular phase is much higher than in the luteal phase, which is associated with an anastomosis of an extensive network of capillaries and abundant blood supply to the ovary during this phase of the cycle. Thus, using diffuse spectroscopy, it is possible to fix a fairly short period of formation of the corpus luteum, which is an extremely dynamic temporary organ—a gland that produces progesterone and plays a central role in the reproductive process. The emergence and development of the corpus luteum are extremely rapid with a high cell turnover and a strong blood supply that is primarily regulated by angiogenic growth factors. This ability to accurately determine the timing of lutein formation is extremely important in the study of infertility of unknown origin and when using assisted reproductive technologies.

Optical clearing technology using hyperosmotic agents, in particular glycerol, reduces light scattering and, as a result, improves the penetration depth of light. When ovarian tissue was immersed in glycerol, the efficiency of optical clearing reached 370% in the wavelength range from 280 to 410 nm and up to 946% in the range of 430–550 nm. This effect can be used in therapeutic and diagnostic clinical applications to study molecular structures deep in the tissue.

The optical clearing technology presented in this study also improves tissue transparency in the UV range and may be useful for the effective application of existing and future UV biomedical spectroscopies and therapies, in particular, to study the structure and dynamics of proteins using UV resonance Raman spectroscopy [51], for the general use of deep UV Raman spectroscopy [52], the detection of pathologies such as gliomas with UV fluorescence excitation [53], or the use of deep UV fluorescence microscopy in cell biology and tissue histology [54] and for other biomedical optical technologies, where UV excitation is fundamentally important.

The optical clearing and diffusion–kinetic properties of a number of other, more common cryopreservatives, such as DMSO, ethylene glycol and PrOH, have been studied for muscle and skin tissues [13–16,48]. It seems important to carry out similar quantitative studies for animal ovaries in the follicular and luteal phases of the cycle.

The studied glycerol-induced perfusion kinetics of ovarian tissues is of great importance both for the development of clinical protocols for optical tissue clearing in laparoscopic diagnostic or surgical applications and for the cryopreservation of ovarian tissues. Moreover, the technology can potentially be used for the optical monitoring of changes in tissue structure during the storage of a cryopreserved organ.

An in-depth interdisciplinary study is needed to reduce side effects and preserve fertility in women with cancer [3–6,10], including those complicated by diabetes mellitus [55], using new technologies for ovarian cryopreservation, including surgical procedures for ovarian transplantation and new reproductive technologies. The successful cryopreservation and subsequent thawing of the transplanted ovary largely depend on the knowledge of the quantitative characteristics of the perfusion–kinetic processes during the freezing and thawing of the organ.

**Author Contributions:** Conceptualization, V.V.T.; Methodology, A.A.S.; Formal analysis, A.A.S. and V.V.T.; Investigation A.A.S. and A.S.R.; Resources, A.A.S. and V.V.T.; Writing—original draft preparation, A.A.S.; Writing—review and editing, V.V.T.; Project administration, A.A.S. and V.V.T.; Funding acquisition, A.A.S. and V.V.T. All authors have read and agreed to the published version of the manuscript.

**Funding:** Russian Science Foundation Grant No. 22-75-00021 (A.A.S.); Ministry of Science and Higher Education of the Russian Federation within the framework of a state assignment (project No. FSRR-2023-0007) (V.V.T.).

**Institutional Review Board Statement:** The study was conducted in accordance with the Declaration of Helsinki, and approved by the Ethics Committee of Saratov State Medical University named after V. I. Razumovsky (No. 4 dated 1 November 2022).

**Informed Consent Statement:** Not applicable.

**Data Availability Statement:** Data are available from the authors.

**Acknowledgments:** A.A.S. was supported by the Russian Science Foundation Grant No. 22-75-00021. V.V.T. was supported by the Ministry of Science and Higher Education of the Russian Federation within the framework of a state assignment (project No. FSRR-2023-0007).

**Conflicts of Interest:** The authors declare no conflict of interest. The funders had no role in the design of the study; in the collection, analyses, or interpretation of data; in the writing of the manuscript; or in the decision to publish the results.

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