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Compression OCT-elastography combined with speckle-contrast analysis as an approach to the morphological assessment of breast cancer tissue

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Abstract

Currently, optical biopsy technologies are being developed for rapid and label-free visualization of biological tissue with micrometer-level resolution. They can play an important role in breast-conserving surgery guidance, detection of residual cancer cells, and targeted histological analysis. For solving these problems, compression optical coherence elastography (C-OCE) demonstrated impressive results based on differences in the elasticity of different tissue constituents. However, sometimes straightforward C-OCE-based differentiation is insufficient because of the similar stiffness of certain tissue components. We present a new automated approach to the rapid morphological assessment of human breast cancer based on the combined usage of C-OCE and speckle-contrast (SC) analysis. Using the SC analysis of structural OCT images, the threshold value of the SC coefficient was established to enable the separation of areas of adipose cells from necrotic cancer cells, even if they are highly similar in elastic properties. Consequently, the boundaries of the tumor bed can be reliably identified. The joint analysis of structural and elastographic images enables automated morphological segmentation based on the characteristic ranges of stiffness (Young's modulus) and SC coefficient established for four morphological structures of breast-cancer samples from patients post neoadjuvant chemotherapy (residual cancer cells, cancer stroma, necrotic cancer cells, and mammary adipose cells). This enabled precise automated detection of residual cancer-cell zones within the tumor bed for grading cancer response to chemotherapy. The results of C-OCE/SC morphometry highly correlated with the histology-based results (r =0.96-0.98). The combined C-OCE/SC approach has the potential to be used intraoperatively for achieving clean resection margins in breast cancer surgery and for performing targeted histological analysis of samples, including the evaluation of the efficacy of cancer chemotherapy.

© 2023 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement

1. Introduction

Breast cancer remains the most common global malignancy and the leading cause of cancer deaths [1]. The positive trend of the recent years, however, is that mortality can be reduced due to the use of modern methods of early cancer detection, which allows for timely commencement of cancer treatment based on combinations of surgery with therapeutic approaches. This also opens the possibility to perform breast-conserving surgery which reduces severe side effects of radical mastectomy and at the same time improves the cosmetic effect [2].

Preoperative (neoadjuvant) chemotherapy has been established as an important part of breast cancer treatment contributing to the personalized optimization of subsequent surgical treatment and planning the adjuvant (post-surgery) therapy [3,4]. The chemotherapy efficiency assessment includes two stages: preoperative clinical (mammography, ultrasound, magnetic resonance imaging, etc.) and postoperative pathological (morphological) [5]. In the diagnostic process, clinical imaging modalities allow only to obtain information about the changes in size of the tumor node during chemotherapy and may not fully represent the pathological processes that involve cancer cell. Frequently, a stable size of the clinically imaged tumor might correlate with a sharp decrease of survived (residual) cancer cells and lead to an inadequate evaluation of the degree of response to treatment [6]. Thereby, post-treatment pathological assessment of the presence and biological condition of the residual cancer cells using various response grading systems remains the main approach for evaluation of cancer response to chemotherapy in breast cancer treatment [7]. At the same time, a distinct response of the classical pathological state of cancer that received chemotherapy is the predominance of sclerosis areas represented by stromal fibers that replaced necrotic cancer cells [8,9]. Among the systems used to evaluate the breast cancer response to chemotherapy, the assessment of necrotic areas is secondary or not performed at all [7,10]. However, in such assessment the most time-consuming process is to precisely assess residual cancer cells in the tumor bed (within the tumor node bounding the mammary adipose tissue) after chemotherapy. There are difficulties in identifying the exact location of the tumor bed in the case of pathological complete response (pCR), which requires adequate choice of sampling and assessing methods for examining large volumes of a tumor node [11]. Bearing in mind that histological examination of the entirety of large surgical samples is unacceptably time consuming and laborious, selective examination of a sufficiently large number of small ∼5 mm tumor sites is usually recommended [12]. However, in such cases there is a possibility of missing isolated small clusters of residual cancer cells and making a mistake in the pathological diagnosis of diverse histological patterns in various tumor sites [13], which may lead to incorrect choice of adjuvant therapy [14].

Currently, optical technologies are being widely developed to enable targeted morphological assessment and rapid label free morphometric biological tissue analysis. Optical Coherence Tomography (OCT) is one of such technologies with its new modalities and approaches to numerical analysis of OCT images [15]. Its development to a significant degree has been stimulated by the idea that analysis of OCT images could be used as a kind of optical biopsy to enable a faster and non-invasive (or minimally invasive) alternative to conventional histological examinations [16]. Various approaches to the analysis have been proposed from methods of digital staining [17] of OCT scans to obtain images similar to stained histological slices to methods utilizing machine learning to perform delineation of pathological and normal tissue areas [1820]. In parallel, it was proposed [21] to transfer the elastographic principles from medical ultrasound to OCT. It has been demonstrated in the recent decades [22] that the visualization of differences in elasticity among normal and malignant tissues drastically improves the diagnostic contrast of ultrasound examinations, so that ultrasound elastography has become one of the most promising methods in diagnostics of various diseases, especially breast cancer [23]. By analogy with ultrasound elastography, Compression Optical Coherence Elastography (C-OCE) usage for breast cancer diagnostics and the development of OCT-based optical biopsy approaches also became one of the main trends in OCT development [24]. The key point in realization of C-OCE is the estimation of axial strains created in the soft tissue by an auxiliary quasistatic mechanical loading [25]. The elastography method used in this study is based on phase-resolved OCT, the signal of which is highly sensitive to motions of scatterers in the tissue [26,27]. Appropriate processing of phase-resolved OCT signals makes it possible to quantify and map local strains in the tissue [2831]. Recently, numerous studies in our and other research groups showed the efficiency of C-OCE in breast cancer imaging for identifying cancer progression by high stiffness values [32], differentiating the morphological subtypes of breast cancer [33,34], determining lymph node status [35] and cancer cell detection in the surgical margins during breast-conserving surgery [3639]. Specifically, we previously demonstrated the abilities of C-OCE for in vivo assessment of the cancer response to therapy using murine tumor models [40,41].

In this study for the first time, we propose the use of C-OCE in combination with speckle-contrast (SC) analysis of the initial OCT images to differentiate tissue components even if their elastic properties may be rather similar. The main focus of this research was to develop an approach to automated morphological assessment of breast tissue based on their elastic and scattering properties using a novel algorithm combining C-OCE with SC analysis of structural OCT images. Firstly, we performed a targeted comparison of OCT and histological images with determining value ranges of stiffness and SC coefficient by each morphological structure for implementing the C-OCE/SC segmentation. The combined C-OCE/SC approach allowed us to solve the problem of differentiation of the adipose cell areas (bounding the tumor bed) from necrotic cancer cell areas, for which high similarity in the elastic properties has been identified. Secondly, we established a correspondence between C-OCE/SC and histological segmentation images to confirm the objectivity of the С-OCE/SC approach to morphological assessment of breast cancer tissue. Finally, we demonstrated the use of С-OCE/SC approach for evaluation of cancer response to chemotherapy by detection of residual cancer-cell areas sizes in tumor bed according to the clinically used response grading system. It can be stated that the use of combined С-OCE/SC approach allows one to avoid large non-informative areas of necrotic cancer cells and select tissue samples with the presence of residual cancer cells for subsequent targeted histological examination for the evaluation of cancer response to therapy.

2. Materials and methods

2.1 Patients and therapy

The study complies with international and ethical standards set out in the World Medical Association Declaration of Helsinki “Ethical principles for medical research involving human subjects” [42]. The present study was approved by the Institutional Review Boards of the Privolzhsky Research Medical University Nizhny Novgorod (protocol#1 of September 28, 2018) and the Nizhny Novgorod Regional Oncologic Hospital (protocol#12 of December 23, 2021). All patients included in the study provided written informed consent prior to enrolment. The patients were treated in the Nizhny Novgorod Regional Oncologic Hospital between 2018-2022 and had been diagnosed with locally advanced breast cancers (T3N0-1M0 stages). All 26 patients had histologically (core biopsy) proven invasive adenocarcinoma without detectable metastatic disease prior to commencing chemotherapy.

The clinical history of the patients included courses of neoadjuvant chemotherapy according to the clinical guidelines (RUSSCO Clinical Practice Guidelines [43], corresponding to generally accepted guidelines [44]). The patients received 4 cycles of AC (Adriamycin * Cytoxan) given at 3 weekly intervals comprising doxorubicin (60 mg/m2) and cyclophosphamide (600 mg/m2), all given by intravenous injection followed by 12 weekly paclitaxel (80 mg/m2) injections.

Following completion of primary chemotherapy before surgical resection, assessments of the responses and tumor bed detection were performed clinically by ultrasound. Patients underwent resection of the residual tumor mass by total mastectomy [n = 9] or breast-conserving surgery [n = 17]. The surgical procedure was carried out between 2- and 6-weeks following the completion of chemotherapy.

2.2 Multimodal OCT device

The studies were performed using a custom-made spectral-domain multimodal OCT device (Institute of Applied Physics of Russian Academy of Sciences, Nizhny Novgorod, Russia) with a central wavelength of 1.3 µm, spectral width of 90 nm, and spectral-fringe rate of 20 kHz [45,46]. This device enables axial resolution of 10 µm, lateral resolution of 15 µm, and scanning depth of 2 mm in air. The one series of initial phase-sensitive structural images was recorded from a 4 mm field in 26 seconds, which made it possible to examine large volumes of tissue in a relatively short time. The OCT system has a flexibly orientable OCT probe based on the use of single-mode isotropic fiber optics with the use of the common path scheme. For phase-sensitive images the developed algorithms of C-OCE, speckle-contrast analysis and subsequent morphological segmentation were applied which will be discussed below.

2.3 Multimodal OCT data collection

Immediately after the completion of surgery, breast samples [n = 26] from tumor node with surrounding tissues (adipose) were excised by cross-section (that includes the largest size of grossly identifiable tumor bed) for subsequent ex vivo multimodal OCT examination. One fresh tissue sample per patient (∼3.0 × 1.0 × 0.5 cm3) was obtained. OCT examination of sample tissue was carried out for 10-25 minutes, which allowed to examine the tissue by the largest size of tumor bed, bounded on both sides by mammary adipose tissue. For spatial positioning of the OCT-probe we used a 3D positioning system – Purelogic R&D PLRA4 (Russia) [38,47]. It performs 3D positioning of the OCT-probe with an accuracy of 10 µm. The use of this setup enabled both high-precision positioning, as well vertical movement of the probe required for performing controlled compression of the studied samples during C-OCE. Immediately after the OCT study, samples were subjected to histological examination. Figure 1 is a schematic representation of the step-by-step study design.

 figure: Fig. 1.

Fig. 1. Schematic step-by-step study design demonstrating the orientation sample and excision line for C-OCE examination, OCT image processing and correspondence of the proposed elasto/speckle-contrast segmentation with histology.

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2.3.1 Compression OCE imaging

The utilized C-OCE technique is based on the compression approach to elastography realization [21,25], but unlike the correlation principles proposed in [21,25] the used variant is based on phase-resolved analysis of a series of phase-sensitive in-depth OCT scans of the examined tissue sample subjected to auxiliary compression loading. This compression is applied by the output window of the OCT probe through the intermediate layer of linearly-elastic translucent silicone which plays the role of optical stress sensor to enable quantitative estimations of the tissue elasticity. The key feature of this approach is that the interframe phase variations enable efficient spatially-resolved estimation of axial strains in the visualized region, so that if the Young’s modulus for the reference silicone is known, it is possible to obtain stress-strain dependences and the tangent Young’s modulus for the studied tissue [24,48,49]. The experimental configuration is schematically shown in Fig. 2(A). Figure 2(B) shows a typical structural image in which both silicone layer and tissue are clearly seen. Figure 2(С) demonstrates an example of a color-coded map of interframe phase variation $\Delta \Phi = {\phi _2} - {\phi _1}$ for a pair of OCT scans subsequently acquired during the tissue compression.

 figure: Fig. 2.

Fig. 2. Schematically shown configuration of the C-OCE-measurements and examples of various stages of C-OCE-visualization. (A) sample compression through the reference layer of precalibrated silicone; (B) is structural OCT image; (C) is an example of interframe phase variation; (D) is the map of cumulative strain found by summation of several tens incremental interframe strains extracted from interframe phase variations; (E) shows the reconstructed stress-strain curves for regions with labels 1 and 2 in panel (D), where thin dotted lines are experiment and solid lines are fitting curves; (F) is the Young’s modulus dependence on tissue strain in regions 1 and 2 obtained by differentiation of the smoothed stress-strain curves; (G) shows the Young’s modulus dependences from (F) replotted as functions of applied stress; panels (H), (I) and (J) show synthesized spatially resolved maps of the tangent Young’s modulus obtained for pre-chosen standardized applied stress 2, 5, and 8 kPa controlled via strain in the reference silicone as described in [53]; bar size vertically and horizontally on all images is 1.0 mm.

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The elastographic processing utilizes the well known relationship between the axial interframe displacement $\Delta U$ of scatterers and the resultant variation $\Delta \Phi = {\phi _2} - {\phi _1}$ in the OCT-signal phase:

$$\Delta U = \frac{{{\lambda _0}\Delta \Phi }}{{4\pi n}}$$
where ${\lambda _0}$ is the central wavelength of the illuminating OCT signal in vacuum, and n is the refractive index of the examined tissue. The interframe axial strain $\Delta \varepsilon$ (along-the-depth gradient) is evidently proportional to the axial gradient of interframe phase variation:
$$\Delta \varepsilon \equiv \partial (\Delta U)/\partial z = ({\lambda _0}/4\pi n)\partial (\Delta \Phi )/\partial z$$

Usually, the maximal measurable interframe strains are of the order of ${10^{ - 2}}$, but much larger strains $\varepsilon$ can be measured by finding the cumulative strain $\varepsilon = \sum {\Delta \varepsilon }$ for a series of consequently acquired OCT-scans of the deformed sample [50].

For estimating interframe strains, a robust and computationally efficient vector algorithm can be used, in which complex-valued OCT signals $a = A\,\exp (i\phi ) = A\cos (\phi ) + iA\sin (\phi )$ with amplitude A and phase $\phi$ are treated as vectors in the complex plane [30,51]. The strain estimation is made with a processing window of adjustable size to obtain a reasonable compromise between the reduction of measurement noises and strain-map resolution. Real examples of a structural OCT image, interframe phase variations and the corresponding map of interframe strains are shown in Figs. 2(B), (C), (D).

When the compressed reference silicone layer with the Young’s modulus ${E_s}$ and studied tissue are not confined in the lateral directions, the incremental interframe strain $\Delta {\varepsilon _s}$ in the reference silicone defines the incremental stress $\Delta \sigma = {E_s}\Delta {\varepsilon _s}$ applied through the silicone to the tissue. Special attention was paid to the verification of the fact that the Young’s modulus ${E_s}$ of silicones does not depend on the initial pre-straining of the silicone layer [50,52]. Then by summing the interframe strains of the tissue and incremental stresses one can obtain spatially resolved stress-strain dependences for the studied tissue (Fig. 2(E)). By finding the slope of such stress-strain dependences, tangent Young’s modulus can be estimated and represented as a function of either current strain or applied stress as shown in Figs. 2(F), (G). The usage of the cumulative values enables much better robustness and tolerance to measurement errors of the Young’s modulus estimation in comparison with its direct estimation as the ratio $E = \Delta \sigma /\Delta \varepsilon$ of interframe stresses and strains.

Another important remark is that usually, for real tissues, the stress-strain dependences are pronouncedly nonlinear as illustrated in Fig. 2(E), which means that the tangent Young’s modulus may strongly (several times and even greater) vary depending on the applied stress. At the same time, the stress created in the examined region is usually spatially inhomogeneous due to multiple uncontrollable factors (surface irregularities, own inhomogeneity of the tissue, etc.); this statement is illustrated by inhomogeneity of strain distribution in the reference silicone layer in Fig. 2(D). For this reason, the interframe (apparent) deformability of the nonlinearly-elastic tissue is caused by very different loading conditions even for a single scan and for different measurements the uncertainty is even much greater. To exclude the influence of this uncertainty, special procedures of “standardization” of the applied stress to a preselected stress level can be applied using the reference silicone as the distributed stress sensor [52,53]. The corresponding examples of the Young’s modulus distribution obtained from the initial strain map shown in Fig. 2(C) are shown in Figs. 2(H), (I), (J) for different values of the standardized stress. These examples demonstrate that depending on the applied stress the apparent distribution of the tissue stiffness may vary significantly, therefore for quantitative elastographic segmentation of the tissue structures it is necessary to specify the used stress level. Concerning detection of tumor zones, it is important to note that the maximal contrast between the cancerous tissue (cancer cell areas with high stiffness values and stroma areas with medium stiffness values) and the peritumoral zone (mammary adipose areas with low stiffness values) is usually observed at an intermediate (neither very low, nor too high) stress level, usually in the 1-4 kPa range [39]. The elastographic maps discussed in the following sections correspond to the stress-standardization level of 4 kPa. In the resultant 2D С-OCE image, the resolution (on the order of 1/2 of the processing-window size that was used to estimate gradients of interframe phase variations) was about 4 times lower than in the initial OCT images, i.e., ∼40–50 µm in both directions. Such an averaging-window size still enabled a decent accuracy of morphological segmentation (with a resolution corresponding to the size of ∼10 cells) and at the same time strongly enhanced the signal-to-noise ratio, which is known to be very important in analyzing signal phase in OCT [54]. The sizes of such sliding averaging areas around each pixel are exemplified by rectangles with labels 1 and 2 in Fig. 2(D).

2.3.2 Speckle-contrast analysis of the structural OCT images

Interferometric OCT principle determines a rather specific speckle structure of the OCT scans. In general, its physical origin was understood quite long ago (e.g. [55]) and was explained by random interference of sub-resolution scatterers located within the sample volume, for which the lateral size is determined by the diameter of the illuminating beam and the axial size corresponds to the coherence length of the light source. When each sample volume contains sufficiently large number of sub-resolution scatterers, the speckle structure is termed “fully developed” and the probability function $P(a)$ for the speckle amplitudes a in OCT images exhibits the Rayleigh distribution [55]:

$$P(a) = (a/{\sigma ^2})\exp ( - {a^2}/2{\sigma ^2})$$
with a single parameter $\sigma$. In practice, even for two scatterers in the sample volume, the speckle-amplitude statistics is already fairly close to Rayleigh distribution [56]. Notice that parameter $\sigma$ determines both the width of the Rayleigh distribution and the mean value of speckle amplitude. In real OCT scans, the usage of absolute amplitudes is inconvenient because they depend on the sensitivity of the OCT system, brightness of scatterers, etc., so that utilization of a more universal amplitude-independent characteristic is preferable. Such a convenient characteristic is the speckle contrast ($SC$) defined for the signal amplitude as
$$S{C_{amp}} = {\{ M[{(a - M(a)]^2})\} ^{1/2}}/M(a)$$
where $M(..)$ denotes the mean value (expectation) of the corresponding quantity. For a Rayleigh probability function, the speckle contrast for speckle amplitudes is expected to be $S{C_{amp}} \approx 0.52$ independently of parameter $\sigma$. In practice it is also convenient to reformulate the speckle probability distribution in terms of speckle intensities $I = {a^2}$, for which the probability distribution $P(I)$ acquires a simple exponential form
$$P(I) = \exp ( - I/2{\sigma ^2})/2{\sigma ^2}$$
where parameter $\sigma$ is the same as in Eq. (3). The speckle contrast for the intensity distribution given by Eq. (5) then is
$$S{C_{{\mathop{\rm int}} }} = {\{ M[{(I - M(I)]^2})\} ^{1/2}}/M(I)$$

For the exponential intensity distribution (5) which is equivalent to Rayleigh distribution (3) the speckle unity value of $S{C_{{\mathop{\rm int}} }}$ in Eq. (6) [57] means that speckle amplitude obey the Rayleigh distribution that is expected for the spatially uniform distribution of scatterers with a sufficiently large density (>2 scatterers in the sample volume). For inhomogeneous spatial distribution of speckle intensities in the analyzed region the value of the speckle contrast $S{C_{{\mathop{\rm int}} }}$ is expected to deviate from the unity value. This deviation may be caused, in particular, by the mean in-depth attenuation of the OCT signal if the size of the area, over which the speckle contrast is estimated, is comparable or larger than the characteristic decay length [58]. Also, for sufficiently small density of scatterers, when there are intermittent regions of clusters of scatterers located within a sample volume and dark regions among such clusters, where scatterers are absent, the speckle contrast value should also deviate from the unit value. More specifically, a higher speckle contrast is expected in regions where scatterers are spatially-inhomogeneously distributed with intermediate almost non-scattering zones. Such inhomogeneous distribution is typical of adipose regions characterized by specific honeycomb texture in OCT images as demonstrated by real examples below. Thus, in addition to differentiation of tissue structures based on the differences in the elastic modulus, segmentation based on calculation of SC coefficient within a sliding window (typically 16 × 16 px in size similarly to the processing window used for OCE processing) can be efficiently used to differentiate the regions of adipose from other tissue structures which may have similar low values of the elastic modulus.

2.4. Morphological assessment

2.4.1 Histological study and evaluation of cancer response grades by therapy

After imaging, all the samples were forwarded to histological study. For co-location, the positions of the C-OCE scans were marked on the surface of the studied samples using the histological ink. Samples were fixed in 10% formalin for 48 hours. Then several (3-6) serial sections with a thickness of 7 µm were made along the direction coinciding with the C-OCE-scan position. Histological sections were stained according to the standard technique with hematoxylin and eosin (H&E), which made it possible to assess the tissue structure and the pathomorphological changes caused by chemotherapy. In this study, histological sections of post-therapy breast cancer samples were assessed by a pathologist (S.S.K.) with the highlighting of typical morphological structures (residual cancer cells, cancer stroma, necrotic cancer cells and mammary adipose cells, which bounded the tumor bed) for studied tissue [59,60]. To calculate the areas of each morphological structure and defining / marking the boundaries in the histology images, the QuPath software v0.4.1 (Belfast, Northern Ireland, UK) for histological segmentation and image morphometric analysis was used [61].

To assess the cancer response to chemotherapy, Miller-Payne (MP) histological grading system was used. MP grading system focuses on the principal manifestation of chemotherapeutic effect, namely, the reduction of the areas occupied by residual cancer cells in the tumor bed in histological images [62]. Among the 26 samples of breast cancer tissue, 5 grades of pathological response were identified according to the MP grading system: grade 5 was a pathological complete response (pCR) [n = 4] and other cases are categorized as a pathological partial response, where: grade 4 – only single small clusters of residual cancer cells are detected (more than 90% loss) [n = 5], grade 3 – between an estimated 30% and 90% reduction in cancer cells [n = 9], grade 1-2 – a minor loss of cancer cells but overall cellularity still high (up to 30% loss) [n = 8].

2.4.2 Determining C-OCE-based and SC-based criteria for morphological segmentation of OCT images

C-OCE and structural OCT images were juxtaposed with histological images of the post-therapy breast samples, where topology and borders of all the analyzed morphological structures were identified. The comparison made it possible to establish specific ranges of the stiffness (Young’s modulus) and the SC coefficient for the four studied morphological structures (residual cancer cells, cancer stromal fibers, necrotic cancer cells and mammary adipose cells) of breast cancer tissue, so that the elastographic and structural OCT images could be segmented according to these ranges by analogy with the previous studies [33,40,63]. In particular, we evaluated percentages of areas for each segmented morphological structure in the histological images and in the corresponding C-OCE and SC images to identify the best correspondence between the histological and OCT-based segmentation (described in section 3.1).

2.5. Statistical analysis

The variable for statistical inter-group comparison was the values of stiffness (Young’s modulus) and SC coefficient calculated from C-OCE and SC images, respectively. Descriptive statistics results are expressed as mean ± SD. The independent-samples Kruskal-Wallis test with Bonferroni correction were used to significant stiffness/speckle-contrast value differences between the four groups of morphological structure: residual cancer cells, cancer stroma, necrotic cancer cells and mammary adipose cells. For verification of the degree of correspondence between the areas of morphological structures delineated in histological images and the corresponding automatically segmented areas in C-OCE images and SC maps, we performed paired Student's t-tests, with P less than 0.05 indicating statistical significance. Besides the t-tests, the Pearson correlation coefficient r was calculated between the OCT-based and histology-based segmented areas for each morphological structure.

Statistical analysis was performed in the GraphPad Prism 8.0 (San Diego, CA, USA) and the Statistical Package for Social Sciences 26.0 (Chicago, IL, USA).

3. Results

The presented below results comprise the following aspects: (1) development of C-OCE/SC approach for morphological assessment of breast tissue that allows to use segmentation of phase-sensitive structural OCT images by the combined usage of characteristic stiffness and SC coefficient ranges for four morphological structures typical of post-therapy breast cancer, and (2) identification of the ability of C-OCE/SC approach to evaluate the degree of cancer response to chemotherapy by detecting the presence of residual cancer cells in the primary tumor bed. Concerning the latter issue, it should be emphasized that although C-OCE images do not directly enable cellular resolution, the presence of even scarce amounts of cancer cells can be detected through the changes in the Young’s modulus of the tissue where these cells are embedded.

3.1 Development of C-OCE/SC approach for morphological assessment of breast cancer tissue

The obtained structural OCT and C-OCE images were compared with segmented histological images (Fig. 3). High stiffness values of residual cancer cells were established – 829 ± 173 kPa (Fig. 3(A), (B)). For the cancer stroma (connective tissue fibers), medium stiffness values 214 ± 81 kPa, and low stiffness values of mammary adipose cells surrounding the tumor bed 49 ± 16 kPa were found. Quantitative analysis confirmed that the revealed differences in the stiffness values for the described above morphological structures (regions with residual cancer cells, cancer stroma and mammary adipose cells) are statistically significant (p < 0.001). Also, areas of necrotic cancer cells were found in seven post-therapy tissue samples (Fig. 3(E)). According to the results of C-OCE examination, necrotic cancer-cell areas exhibited low stiffness values 78 ± 22 kPa (Fig. 3(F)), which were not statistically significantly different from the stiffness values for adipose areas (p = 0.0614) (Fig. 3(I)). Such similarity in the stiffness values does not allow for clear distinction between the areas of necrotic cancer cells areas and adipose cells in C-OCE scans of post-therapy samples of breast cancer.

 figure: Fig. 3.

Fig. 3. C-OCE and SC findings for post-therapy breast cancer tissue: representative histological (A,E), C-OCE (B,F), structural OCT (C,G) and SC (D,H) images of detectable morphological structures and pathological changes, with designations as: C – residual cancer cells (topological boundaries on histological images are marked with blue lines), S – cancer stroma, A – adipose-cell area (contoured by green lines), N – necrotic cancer cells (red lines); bar size vertically and horizontally on all images – 0.5 mm; the diagrams of stiffness (I) and SC (J) values distributions for the studied morphological structures; for each box plot, the center line represents mean value of the analyzed parameter, box plot limits indicate standard deviations, whiskers are minimum/maximum values (Kruskal-Wallis test with Bonferroni correction).

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In search of additional optical differences between necrotic cancer cell areas and adipose areas, we paid attention to a specific structural feature of adipose cells – a distinctive porous mesh structure in OCT images (zones labeled “A” in Fig. 3(C) and Fig. 4(A)). This structure is characterized by high difference in intensity values between neighboring speckles in structural OCT images, which is not observed for other morphological structures of breast cancer tissue (see regions of cancer cells, stroma and necrotic cancer cells in Fig. 3(C), (G) and Fig. 4(A)). This visual distinction of adipose from other regions suggested that quantitatively the difference of adipose from all other morphological structures may be expressed in terms of SC which is discussed in detail in “Materials and Methods”, section 2.3.2. As a result of SC calculation, maps of SC coefficient distribution (SC images) were obtained, where the SC coefficient values for adipose cell areas pronouncedly exceeded values for all other morphological structures (Fig. 3(D), (H)). Quantitative analysis demonstrated a statistically significant (p < 0.001) difference in SC coefficient values of adipose cell areas – 2.53 ± 0.46, compared with residual cancer cells areas – 1.39 ± 0.21, cancer stroma areas – 1.38 ± 0.22, and necrotic cancer cells areas – 1.39 ± 0.23 (Fig. 3(J)). No statistically significant differences were found between SC coefficient values of residual cancer cells, cancer stroma, and necrotic cancer cells (p > 0.05). The established differences in SC coefficient values of adipose cells areas from other morphological structures make it possible to perform rather reliable morphological segmentation using combination of the established differences among all the cancer morphological structures in C-OCE-scans and the additional difference in SC between adipose and cancer regions in structural OCT images.

 figure: Fig. 4.

Fig. 4. Implementation of C-OCE/SC segmentation, qualitative and quantitative comparison of C-OCE/SC and histological segmentation of breast cancer tissue, where obtained by conventional stitching wide-field structural OCT images (A), C-OCE images (B), synthesized from them segmented C-OCE/SC images (C), and corresponding to them segmented histological images (D) are presented; designations: C – residual cancer cells (topological boundaries on histological images are marked with blue lines), S – cancer stroma, A – adipose cells (green lines), N – necrotic cancer cells (red lines); bar size vertically and horizontally on all images – 0.5 mm; (E) – relationship between the amount of space occupied by each allocated morphological zone and the percentage of the areas on the C-OCE/SC images with a value in the range of this morphological zone. A strong and direct correlation is visible (Pearson correlation coefficient for adipose cells r =0.98, for necrotic cancer cells r =0.96, for cancer stroma r =0.97, for residual cancer cells r =0.98; p < 0.001).

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Then the optimal value ranges of Young’s elastic modulus and SC coefficient of each morphological structures were selected for joint C-OCE/SC morphological segmentation and comparison of the obtained C-OCE/SC and histological images. In the obtained structural OCT images of breast cancer tissue, only adipose cells areas with a peculiar mesh cellular architectonics were clearly visually different from other morphological structures (zone labeled “A” in Fig. 4(A)), which made it possible to readily segment adipose regions by their SC coefficient values. Next, in the C-OCE images, residual cancer cells areas were distinguished by high stiffness values, cancer stroma – by medium stiffness values, and adipose cells areas and necrotic cancer cells areas – by low stiffness values (Fig. 4(B)), which was consistent with our previous studies [33,64]. In Fig. 4(B) we use the red-blue colormap to be consistent with the palette conventionally used in ultrasound elastography. Differentiation of adipose regions from zones of necrotic cancer cells was performed using SC calculated from structural OCT scans. As a threshold, SC coefficient values >1.94 between adipose cells and other morphological structures were chosen. This value enabled the highest correspondence of adipose areas detection in OCT and histological images. In order to differentiate regions of residual cancer cells from stroma, the optimal stiffness threshold for differentiation of all cancer cells >420 kPa from other types of breast tissue was chosen based on results of this and our earlier studies on the evaluation of breast cancer cell stiffness without preoperative treatment [33]. A stiffness value range of 80-420 kPa was established to differentiate regions of cancer stroma by highest correspondence of C-OCE and histological images. Along with necrotic cancer cell regions, adipose regions also fall in the elasticity range <80 kPa, although using only differences in the elasticity necrotic regions cannot be reliably distinguished from adipose. However, as pointed above, adipose can be readily distinguished from necrotic regions using the increased SC coefficient value. Therefore, the combined usage of differences in the Young’s modulus and SC coefficient enables fairly clear differentiation of all four discussed tissue components.

Figure 4(C) demonstrates an example of the result of such combined morphological segmentation obtained using the determined stiffness ranges (for necrotic cancer cells, cancer stroma and residual cancer cells) on C-OCE images and SC coefficient range (for mammary adipose cells) on SC images. Each segmented component in Fig. 4(C) is shown by its own color, such that the segmented C-OCE/SC image qualitatively demonstrates a high degree of similarity with the morphologically segmented histological images (Fig. 4(D)). To quantitatively confirm the adequacy of resulting segmented images, we compared the results of the morphometric analysis for C-OCE/SC and histological images for 26 studied tissue samples. It should be emphasized that the shapes of the segmented zones in OCT scans and histological images cannot fully coincide in principle: during OCT examinations the shape of the sample is changed due to compression and the procedures of histological slide preparation produce additional shape distortions. For this reason, only percentages of the areas corresponding to each of the segmented structures for C-OCE/SC images and histological images can be meaningfully compared. Figure 4(E) shows the graphs representing the results of such comparison.

Figure 4(E) demonstrates that the areas occupied by morphological structures in C-OCE/SC and histological images demonstrate not only linear proportionality, but a very good correspondence with the proportionality coefficient equal to unity. The difference between the fractional areas segmented using C-OCE/SC images and histological slides was evaluated using Student’s t-test for every of the four morphological structures. The performed tests indicated with a 95% confidence level that there is no difference between the morphometric analysis results of conventional histology-based segmentation and the proposed approach of C-OCE/SC segmentation. This correspondence indicates that the value ranges of stiffness and SC coefficient are correctly chosen for separating the segmented morphological structures. Otherwise, the areas of the segmented zones based on C-OCE/SC images would demonstrate either underestimation or overestimation in comparison with the histological results. The good correspondence between the results of histological and C-OCE/SC segmentation is confirmed by the high values of the Pierson correlation coefficient: r = 0.98 (p < 0.001) for adipose cells areas, r = 0.96 (p < 0.001) for necrotic cancer cells areas, r = 0.97 (p < 0.001) for cancer stroma areas, and r = 0.98 (p < 0.001) for residual cancer cells areas (Fig. 4(E)). This high correlation between the morphometric analysis results based on histological and C-OCE/SC images confirms the adequacy and accuracy of the proposed OCT-based segmentation approach. Accurate detection of adipose cell areas along the edges of the studied tissue samples allows one to precisely identify the boundaries of tumor bed for morphometric analysis. In the next section, an attempt will be made to evaluate the breast cancer response to chemotherapy according to the results of morphometric analysis of segmented C-OCE/SC images.

3.2 Applying the C-OCE/SC approach to the evaluation of breast cancer response to therapy

Before performing a morphometric analysis of residual sizes of cancer-cell areas in the studied tissue samples, the projection of the tumor bed was determined by subtracting areas of breast adipose cells from the analysis (Fig. 5). This analysis, which involves counting residual cancer cells in tumor bed, is the main clinically used approach to the pathological assessment of cancer response to therapy [6,7,10,62].

 figure: Fig. 5.

Fig. 5. Comparison of morphometric analysis based on histological and C-OCE/SC segmented images of breast cancer, including: (A) – identification of tumor bed boundaries among adipose cells for morphometric analysis of histological (A1), structural OCT (A2) and C-OCE/SC (A3) images; (B) – representative examples for each degree of cancer response to chemotherapy according to the MP system in histological (B1) and C-OCE/SC (B2) images; (C) – quantitative comparison of morphometric analysis results represented by sizes of residual cancer-cell areas identified in histological and C-OCE/SC images for each tissue sample studied. Designations: C – residual cancer cells (topological boundaries on (A1) images are marked with blue lines), S – cancer stroma, A – adipose cells (green lines); bar size vertically and horizontally on (A1), (A2), (A3) images – 0.5 mm, on (B1), (B2) images – 50 µm.

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In the standard morphometric analysis of cancer response to therapy, the calculations of percentage of residual cancer-cell areas were performed in the tumor bed, excluding adipose cells areas at the edges of the histological image of the examined sample (Fig. 5(A1)). The tumor bed is detected using the proposed speck-contrast method to exclude adipose surrounding the tumor based on specific honey-comb structure of adipose in structural OCT images (Fig. 5(A2)). Similarly, a morphometric analysis of segmented C-OCE/SC images of the same sample was made, where only the tumor bed area was analyzed (marked in yellow on Fig. 5(A3)) and percentage of residual cancer-cell areas there (marked blue on Fig. 5(A3)) was also calculated.

According to the MP pathological gradation system of cancer response to therapy, among the examined samples (see examples in Fig. 5(B)) we identified the pairs of histological and C-OCE/SC segmented images, for which the morphometric analysis corresponded to various MP grades: grade 5 – four cases, grade 4 – five cases, grade 3 – nine cases, grade 1-2 – eight cases. Figure 5(C) shows the corresponding estimated percentages of the residual cancer-cell areas based on histology and C-OCE/SC segmentation, respectively. It is worth emphasizing again the good topological consistency of the C-OCE/SC segmentation (Fig. 5(B2)) with histological images (Fig. 5(B1)) for the discussed response groups to breast cancer therapy. However, in the quantitative analysis of the segmented C-OCE/SC images aimed as assessing the cancer response to chemotherapy, two cases of discrepancies in grading were found (between grades 1-2 and 3, and also between grades 3 and 4). This discrepancy is primarily caused by the closeness of the estimated percentages of the residual cancer-cell areas to the threshold percentage values separating the grades. In the first case, the residual cancer cell areas were estimated to be 73% by histology and 68.3% by C-OCE/SC, whereas 70% is the borderline. In the second case, it was 9.3% by histology and 12.4% by C-OCE/SC, whereas 10% is the borderline (see the areas of these borderlines in Fig. 5(C)). It is worth noting the absence of erroneous results in differentiating cases of pCR [n = 4] from pathological partial response [n = 22] by C-OCE/SC.

4. Discussion

In this study we present a new approach to automated morphological segmentation of OCT-scans based on the combined use of C-OCE with speckle-contrast analysis of structural OCT images. This could be used for a reliable intraoperation identification of residual cancer cells at the background of typical morphological structures of post-therapy breast cancer (necrotic cancer cells, cancer stroma and mammary adipose cells). This study confirms earlier results [33] demonstrating that C-OCE imaging allows for high contrast differentiation of cancer-cell clusters by their high stiffness (both after treatment or without treatment) from the surrounding stroma and fibrous tissue with lower stiffness values. The established high stiffness values of the residual cancer cells (829 ± 173 kPa), are somewhat higher than the observed stiffness values (>420 kPa) of breast cancer samples established in previous studies [33,63] for patients who did not receive therapy. Some increase in stiffness values of residual cancer cells areas may be associated with reorganization of collagen in tumor bulk due to chemical drug therapy, which was demonstrated by multiphoton imaging [65].

The additional SC analysis is required because in this study we demonstrate that in the C-OCE images it is difficult to distinguish necrotic cancer cells from mammary adipose cells areas, for which significantly overlapping low stiffness values <80 kPa are found. Necrotic cancer cell areas can develop due to the preoperative therapeutic procedures (such as neoadjuvant chemotherapy), and also may be a marker of high malignancy and aggressive/destructive biology of cancer [66]. To differentiate low stiffness value areas of necrotic cancer cells from zones of mammary adipose cells we focused on the specific “honeycomb” architectonics of adipose region in structural OCT images. The additional evaluation of speckle contrast in structural OCT images was used as a simple and rather reliable method for differentiating adipose from zones of necrosis despite the high similarity of these morphological components in terms of their elastic modulus. The principle of SC-based differentiation was based on the expectation that specific honey-comb structure of adipose with intermittent bright/dark sub-regions should lead to an increased level of speckle contrast in comparison with SC ∼0.52 typical of fully developed speckles with Rayleigh distributions of amplitudes in regions of fairly dense and uniform distribution of scatterers [5658]. It can be noted that usually a reduced (rather than increased) speckle-contrasts level is used for detection of regions of moving scatterers in images obtained using sufficiently long acquisition time (e.g. [67]). In some publications (e.g. [19]), speckle variance and mean speckle intensity closely related to speckle contrast were used for performing segmentation of OCT images of motionless tissue along with some other signal features using machine-learning-based analysis of OCT scans. This study demonstrated that a straightforward use of elevated speckle contrast parameter with duly chosen threshold based on comparison with histological images can be efficiently used for differentiation of adipose in breast-tissue samples. In the present study, a threshold value for the SC coefficient was established, so that areas with SC coefficient >1.94 in structural OCT images are identified as mammary adipose-cell areas. Thus, the C-OCE and SC-based methods complement each other and, in combination, promise good results for assessing various breast tissues and evaluating cancer response to therapy, including detecting the tumor bed boundaries.

For the first time, we used joint C-OCE/SC analysis to perform automated morphometric segmentation of breast tissue samples post-therapy (see section 3.1). The stiffness values range >420 kPa was chosen for separating residual cancer-cell areas from cancer stroma (80-420 kPa). The stiffness values <80 kPa were used to differentiate necrotic cancer-cell areas from cancer stroma. Identification of adipose as areas with SC coefficient >1.94 made is possible to differentiate adipose from necrotic cancer-cell areas despite overlapping stiffness ranges. The established specific ranges of stiffness and SC coefficient were tested by correlating the results of morphometric analysis for histological and C-OCE/SC images. High correlation for the results of histological and C-OCE/SC morphometry were obtained – r = 0.96-0.98 (p < 0.001), which indicates the high objectivity of results of C-OCE/SC segmentation and possible applicability of this approach to morphometric analysis of breast cancer tissue. It is worth noting that the obtained results are in good agreement with previous studies [33,34,63,64], which suggests the potential of the use of C-OCE/SC for other cancer types in evaluation of response to therapy.

The most important clinical result of our study is an infallible differentiation of pCR cases from pathological partial response cases with the detection of residual cancer cells by C-OCE/SC (see section 3.2). Such analysis of post-therapy cancer structure makes it possible to predict efficiency of adjuvant therapy and the likelihood of cancer recurrence [68]. Particularly important for the subsequent selection of the adjuvant therapy approach is the differentiation of pCR from other response variants [69,70]. Erroneous conclusions based on clinical examination at this stage and missed individual small clusters of residual cancer cells during histology often take place due to the large volume of tumor bed [59]. In detection of single clusters of residual cancer cells, C-OCE allows one to identify their localization and then conduct a targeted histological study of a sample region of interest to precisely identify the degree of cancer response to therapy. Four cases of a pCR and twenty-two cases of a pathological partial response (with residual cancer) were accurately identified. According to the obtained results, a high efficiency of adjuvant therapy and high overall survival for pCR cases [71] and the adjustment of approaches to adjuvant therapy for pathological partial response cases [72] can be suggested for further clinical supervision of patients. Two cases of discrepancy with histology in assessing the grade of pathological partial response are related to the closeness of the residual cancer-cell percentage to the boundary values for the used MP grading system. The other twenty-four (92.3%) cases are correctly identified by the MP system. Morphometric analysis of the tumor bed is required to correctly calculate the percentage of residual cancer-cell areas and for evaluating the degree of cancer response to therapy. Thus, the described technique of the combined C-OCE/SC assessment of tissue samples makes it possible to scan large volumes of breast tissue, completely covering the tumor bed in the largest size.

At present, another optical technology used for identification of breast cancer response to neoadjuvant chemotherapy is multiphoton imaging. For example, study [73] demonstrated that multiphoton microscopy (based on two-photon excitation fluorescence and second-harmonic generation) can differentiate different degrees of cancer response (slight, significant, or complete) and detect morphological alteration associated with extracellular matrix during the progression of breast carcinoma following preoperative chemotherapy. Cellular resolution and detection of individual collagen fibers can contribute to an in-depth study of cancer processes occurring during chemotherapy. The advantage of multiphoton imaging over conventional histological examination is the absence of the need to stain histological sections. However, in comparison with C-OCE/SC, a significant disadvantage of multiphoton imaging is the much stronger limited scanning depth and a small scanning field. In fact, C-OCE/SC, compared to multiphoton imaging, is characterized by classical advantages over microscopy – a high speed of obtaining images from a fairly large area of tissue under study. As for the biological object studied in this research, the lower resolution (a few tens of microns in elastographic scans) of C-OCE/SC allows for detecting individual small clusters of cancer cells, as has been demonstrated in this paper (see Fig. 5(B)) and earlier [39,40,47]. Based on the current understanding of the cancer response to chemotherapy, the new С-OCE/SC approach can accurately detect clinically important pCR cases of post-therapy breast cancers and distinguish them from cases of residual cancer. The results of fairly rapid and biologically non-destructive OCT-based procedures are important for guidance of the subsequent targeted histological examination and optimization of the mandatory morphometric analysis of the breast tissue based on conventional laborious and time-consuming histology.

In the future, we plan to collect more surgical material to establish standard clinical diagnostic parameters in evaluation of different breast cancer response grades to therapy by C-OCE/SC. In addition, further study of the application of this approach both for breast tissues and for other types of tissues will allow us to establish the diagnostic significance (sensitivity and specificity) of this approach.

To summarize, the proposed combined С-OCE/SC approach is a promising tool for clinical rapid morphological assessment of breast cancer tissue, including evaluation of response to neoadjuvant chemotherapy and intraoperative evaluation of the cleanliness of the resection margin during breast-conserving surgery. C-OCE/SC has already proven its ability for label-free visualization of large tissue areas in a short time, which gives the pathologist the necessary preliminary information about the localization of residual cancer cells and even about the degree of breast cancer response to therapy.

5. Conclusions

In this study, we introduce a novel OCT-based approach combining detection of the Young's modulus and SC coefficient for rapid and label-free morphological assessment of cancer tissue. The additional SC analysis helped us to differentiate between areas of mammary adipose cells (49 ± 16 kPa) and necrotic cancer cells (78 ± 22 kPa), for which a significant overlap in terms of their elastic properties was found, whereas their SC coefficient was clearly different. The established threshold value of SC coefficient (>1.94) for detection of adipose tissue made it possible to clearly identify the boundaries of the tumor bed for subsequent morphometric analysis and, consequently, exclude non-informative necrotic areas and detect suspected residual cancer zones for subsequent histological study. Detection within the tumor bed of residual cancer cells using threshold value of stiffness >420 kPa made it possible to reliably differentiate cases of pathological partial and complete responses of a breast cancer to therapy. For the first time, joint segmentation of C-OCE/SC according to elastic properties (for residual cancer cells, cancer stroma and necrotic cancer cells) and SC (for mammary adipose cells) was used, where the results of C-OCE/SC morphometric analysis were highly consistent with histology (r =0.96-0.98, p < 0.001). In addition, C-OCE/SC approach showed high efficiency in evaluation of the degree of breast cancer response to chemotherapy (correct in 91.3% by MP grading system). The proposed approach may optimize the process of assessing a large volume of tumor node both for a preliminary evaluation of cancer response to therapy, and for performing a targeted histological analysis of samples to evaluate residual cancer.

Funding

Russian Science Foundation (18-75-10068, 22-12-00295).

Acknowledgments

Patients study on evaluation of breast cancer response to neoadjuvant chemotherapy by C-OCE/SC approach was funded by the Russian Science Foundation under grant No. 18-75-10068. Development of combined C-OCE/SC approach was funded by the Russian Science Foundation under grant No. 22-12-00295.

Disclosures

The authors declare no conflict of interest.

Data Availability

The datasets generated and/or analyzed during the current study are available from the corresponding author upon request.

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Data Availability

The datasets generated and/or analyzed during the current study are available from the corresponding author upon request.

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Figures (5)

Fig. 1.
Fig. 1. Schematic step-by-step study design demonstrating the orientation sample and excision line for C-OCE examination, OCT image processing and correspondence of the proposed elasto/speckle-contrast segmentation with histology.
Fig. 2.
Fig. 2. Schematically shown configuration of the C-OCE-measurements and examples of various stages of C-OCE-visualization. (A) sample compression through the reference layer of precalibrated silicone; (B) is structural OCT image; (C) is an example of interframe phase variation; (D) is the map of cumulative strain found by summation of several tens incremental interframe strains extracted from interframe phase variations; (E) shows the reconstructed stress-strain curves for regions with labels 1 and 2 in panel (D), where thin dotted lines are experiment and solid lines are fitting curves; (F) is the Young’s modulus dependence on tissue strain in regions 1 and 2 obtained by differentiation of the smoothed stress-strain curves; (G) shows the Young’s modulus dependences from (F) replotted as functions of applied stress; panels (H), (I) and (J) show synthesized spatially resolved maps of the tangent Young’s modulus obtained for pre-chosen standardized applied stress 2, 5, and 8 kPa controlled via strain in the reference silicone as described in [53]; bar size vertically and horizontally on all images is 1.0 mm.
Fig. 3.
Fig. 3. C-OCE and SC findings for post-therapy breast cancer tissue: representative histological (A,E), C-OCE (B,F), structural OCT (C,G) and SC (D,H) images of detectable morphological structures and pathological changes, with designations as: C – residual cancer cells (topological boundaries on histological images are marked with blue lines), S – cancer stroma, A – adipose-cell area (contoured by green lines), N – necrotic cancer cells (red lines); bar size vertically and horizontally on all images – 0.5 mm; the diagrams of stiffness (I) and SC (J) values distributions for the studied morphological structures; for each box plot, the center line represents mean value of the analyzed parameter, box plot limits indicate standard deviations, whiskers are minimum/maximum values (Kruskal-Wallis test with Bonferroni correction).
Fig. 4.
Fig. 4. Implementation of C-OCE/SC segmentation, qualitative and quantitative comparison of C-OCE/SC and histological segmentation of breast cancer tissue, where obtained by conventional stitching wide-field structural OCT images (A), C-OCE images (B), synthesized from them segmented C-OCE/SC images (C), and corresponding to them segmented histological images (D) are presented; designations: C – residual cancer cells (topological boundaries on histological images are marked with blue lines), S – cancer stroma, A – adipose cells (green lines), N – necrotic cancer cells (red lines); bar size vertically and horizontally on all images – 0.5 mm; (E) – relationship between the amount of space occupied by each allocated morphological zone and the percentage of the areas on the C-OCE/SC images with a value in the range of this morphological zone. A strong and direct correlation is visible (Pearson correlation coefficient for adipose cells r =0.98, for necrotic cancer cells r =0.96, for cancer stroma r =0.97, for residual cancer cells r =0.98; p < 0.001).
Fig. 5.
Fig. 5. Comparison of morphometric analysis based on histological and C-OCE/SC segmented images of breast cancer, including: (A) – identification of tumor bed boundaries among adipose cells for morphometric analysis of histological (A1), structural OCT (A2) and C-OCE/SC (A3) images; (B) – representative examples for each degree of cancer response to chemotherapy according to the MP system in histological (B1) and C-OCE/SC (B2) images; (C) – quantitative comparison of morphometric analysis results represented by sizes of residual cancer-cell areas identified in histological and C-OCE/SC images for each tissue sample studied. Designations: C – residual cancer cells (topological boundaries on (A1) images are marked with blue lines), S – cancer stroma, A – adipose cells (green lines); bar size vertically and horizontally on (A1), (A2), (A3) images – 0.5 mm, on (B1), (B2) images – 50 µm.

Equations (6)

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Δ U = λ 0 Δ Φ 4 π n
Δ ε ( Δ U ) / z = ( λ 0 / 4 π n ) ( Δ Φ ) / z
P ( a ) = ( a / σ 2 ) exp ( a 2 / 2 σ 2 )
S C a m p = { M [ ( a M ( a ) ] 2 ) } 1 / 2 / M ( a )
P ( I ) = exp ( I / 2 σ 2 ) / 2 σ 2
S C int = { M [ ( I M ( I ) ] 2 ) } 1 / 2 / M ( I )
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