Significance: Assessment of disease using optical coherence tomography is an actively investigated problem, owing to many unresolved challenges in early disease detection, diagnosis, and treatment response monitoring. The early manifestation of disease or precancer is typically associated with subtle alterations in the tissue dielectric and ultrastructural morphology. In addition, biological tissue is known to have ultrastructural multifractality.
Aim: Detection and characterization of nanosensitive structural morphology and multifractality in the tissue submicron structure. Quantification of nanosensitive multifractality and its alteration in progression of tumor.
Approach: We have developed a label free nanosensitive multifractal detrended fluctuation analysis(nsMFDFA) technique in combination with multifractal analysis and nanosensitive optical coherence tomography (nsOCT). The proposed method deployed for extraction and quantification of nanosensitive multifractal parameters in mammary fat pad (MFP).
Results: Initially, the nsOCT approach is numerically validated on synthetic submicron axial structures. The nsOCT technique was applied to pathologically characterized MFP of murine breast tissue to extract depth-resolved nanosensitive submicron structures. Subsequently, two-dimensional MFDFA were deployed on submicron structural en face images to extract nanosensitive tissue multifractality. We found that nanosensitive multifractality increases in transition from healthy to tumor.
Conclusions: This method for extraction of nanosensitive tissue multifractality promises to provide a noninvasive diagnostic tool for early disease detection and monitoring treatment response. The novel ability to delineate the dominant submicron scale nanosensitive multifractal properties may also prove useful for characterizing a wide variety of complex scattering media of non-biological origin.
Early disease progression in living tissues expected to exhibit nanosensitive structural alteration at the submicron scale. It is highly desirable to develop noninvasive, label-free techniques to detect nanoscale changes in biological tissue for early diagnosis and better treatment. Recently, many optical nanoscopic techniques were developed based on labeling1–6 and are limited to superficial imaging.7–13 It is a challenging task for researchers to develop a diagnostic system that can provide label-free depth-resolved detection. There are few early developments that demonstrated averaged nanosensitive structural detection over a volume- rather than depth-resolved detection.14,15 These methods can identify overall nanosensitive changes rather than depth-resolved alteration, which is crucial to visualize subtle changes of local submicron structure for better diagnosis. In this regard, our research group actively engaged to develop nanosensitive optical coherence tomography (nsOCT) to detect depth-resolved submicron scale structure with few nanometer accuracy.16–18 We have recently demonstrated label-free nsOCT-based imaging technique to visualize few nanometer structural changes19,20 and its application in cornea crosslinking,21 and wound healing study.22 There is a recently demonstrated application of nsOCT for in vivo detection of nanosensitive changes of the human tympanic membrane in otitis media.23 In addition, biological tissue is known to have submicron structural multifractality.24–28 Although, these studies are based on superficial detection and do not provide underlying tissue multifractality. Multifractality is a special class of self-similarity where multiple scaling exponents (generalized Hurst exponents) are extracted to quantify existing multifractality in a complex system.29,30 For both the fundamental study of biological processes and early diagnosis of pathological processes, detection of multifractality in depth-resolved nanosensitive tissue submicron structural morphology is important. Therefore, we have developed a label-free nanosensitive multifractal detrended fluctuation analysis (nsMFDFA) technique in combination with multifractal analysis and nsOCT to extract nanosensitive multifractal parameters in biological tissue. Recently, we have numerically and experimentally validated nsOCT approach on synthetic submicron axial structure with few nanometer accuracy.20 Here we have numerically validated our proposed nanosensitive multifractal analysis approach in combination of nsOCT simulation and multifractal analysis in a tissue-like randomized synthetic phantom. This approach demonstrated its applicability to measure depth-resolved nanosensitive multifractality in submicron structure in biological tissue. After successful validation, we have applied nsOCT method to construct depth-resolved en face images of dominant submicron structure with nanometer scale sensitivity in murine MFP. Subsequently, we have deployed two-dimensional multifractal detrended fluctuation analysis (2D-MFDFA)31–33 approach to extract depth-resolved nanosensitive multifractality in MFP. In an initial ex vivo study on murine tissue, we found interesting change in depth-resolved nanosensitive multifractality in submicron structures after tumor formation in breast tissue samples. This method for extraction of nanosensitive tissue multifractality promises to develop a noninvasive diagnosis tool for the detection of cancer development. This newly developed method offers exciting depth-resolved ultrastructural detection for better treatment and monitoring if there is a tumor response to treatment.
Materials and Methods
Nanosensitive Optical Coherence Tomography
Flowchart of nsOCT is shown in Fig. 1. Recorded interference spectra divided into number of windows before applying Fourier transform for nsOCT construction. Then identifying spatial frequency corresponding to maximum contributed spectral window at different depths of constructed A-line. Subsequently, identified maximum spatial periods map as nsOCT at different depths. In nsOCT approach, detectable spatial period (; = refractive index of the medium) depends on wavelength range of the broadband source ( to 1413 nm).18 Therefore, in case of biological tissue, we can detect axial structure range from 420 to 504 nm with few nanometer accuracy.18 It is worth mentioning here that biological tissue may have axial structures ranging from 0 to (or 0 to tissue physical size). However, our nsOCT approach has a limitation of detection from 420 to 504 nm, which is limited by wavelength range and finding tissue structural differences based on this specified axial scale range only. There may be other axial structures that also exist in biological tissue beyond our detection range that need further study with a much more sophisticated system having a higher wavelength band. In this direction, our research group developing new ultra-high wavelength band nsOCT system.
Numerical Simulations for Nanosensitive Multifractal Detrended Fluctuation Analysis in Randomized Submicron Structure
In our recent publications,20,34 we have experimentally and numerically demonstrated the implementation of nsOCT to image a commercially fabricated sample with 431.56 nm axial periodic structures. In Ref. 34, we have demonstrated that we can detect random submicron dominant structures at different depths with accuracy. In this study, we have numerically synthesized randomized 3D structure with submicron scale axial structure varies from 445 to 485 nm. The dimension of synthetic volume is . We have followed standard Fourier domain OCT theory and simulation strategy35,36 to construct nsOCT. The MATLAB 2019b (MathWorks®) has been used for implementation of simulation. The OCT signal was constructed as an interference spectrum of the reflected light from different layers of synthetic sample with the reflected light from a gold mirror. We have also added suitable noise in detector and source spectra to mimic experimental reality. The signal-to-noise ratio was 86 dB in this simulation. The inverse Fourier transform was performed to form A-lines nsOCT of a synthetic volume as each lateral position of . Then we have performed 2D-MFDFA on synthetic and nsOCT constructed en face images to compare.
Multifractal Analysis on Nanosensitive Submicron Structural En Face Images
We have followed our established nsOCT methodology to construct depth-resolved dominant structures of synthetic and tissue volume. Flowchart of nsOCT processing displayed in Fig. 1. Subsequently, we have applied 2D-MFDFA on nsOCT constructed en face images to extract nanosensitive multifractal parameters namely, Hurst exponent [ or correlation and width of singularity spectra () or strength of multifractality. To study the hidden nanosensitive multifractal properties in the submicron scale surface morphology, a 2D-MFDFA31–33 is implemented here. This method is simple yet innovative and has easy computer implementation. This proposed method is the modification of one-dimensional MFDFA, which is implemented to study the multiple scaling exponents of one-dimensional signals and for identification of long-range correlations in non-stationary time series.30 The detailed 2D-MFDFA approach can be found in Ref. 31. We have briefly discussed about 2D-MFDFA steps here.
Step 1: The two-dimensional en face nsOCT image [size: divided into non-overlapping square subsurface of equal length , where and are positive integers. Each square segment denoted by , where and . Here size of square subsurface varies from 4 to 32.
Step 2: Each square segment is cropped and denoted as , where, .
Step 3: The local fit for each is calculated by fitting it with a bivariate polynomial function as
Step 4: The detrended fluctuation function for the segment is defined as
The ’th order fluctuation function for a nsOCT mapped en face image at each depth is
Step 5: The generalized Hurst exponents  can be extracted for multiple order of moments () by considering long-range power law behavior of this calculated fluctuation function as
From this above equation, the scaling exponent is obtained by calculating slopes of linear fitting on versus plots. The is known as the generalized Hurst exponents and is called the Hurst index of the en face nsOCT surface.
The classical multifractal scaling exponent corresponding to every value is given by
The two-scaling exponent and along with singularity spectrum can completely characterize any multifractal surface. The singularity spectrum , which characterizes the singularity strength or multifractality of en face nsOCT surface is related to via a Legendre transformation as the Holder exponents,
In this study, we have characterized (a) Hurst exponent  and (b) width of the singularity spectrum , () to measure correlation and multifractality, respectively, on detected nanosensitive submicron scale en face images.
Tissue Sample Preparation
All animal procedures were performed in accordance with the Guidelines for Care and Use of Laboratory Animals of the “Animal Care Research Ethics Committee (ACREC), National University of Ireland Galway (NUIG)” and approved by the “Health Product Regularity Authority (HPRA), Ireland”.
Female BALB/c mice (Charles River Laboratories Ltd.) aged between 6 and 8 weeks were employed. A mouse received a mammary fat pad (MFP, 4th inguinal) injection of 4T1 breast cancer cells suspended in RPMI medium. The early stage tumor was detected by palpation after seven days of injection and was visually inspected. Tumor growth was monitored using calipers measurement. The tumor size was . Animals were sacrificed by inhalation. Tumor tissue and healthy portion were harvested and placed in PBS solution for transfer to the OCT imaging facility for ex vivo analysis. Harvested samples were taken out from PBS and mounted on a glass slide to bring them under the objective of spectral domain OCT system (Telesto III, Thorlabs Inc.) to record OCT images.
Results and Discussion
Numerical Validation of Nanosensitive Multifractal Detrended Fluctuation Analysis in Synthetic Submicron Scale Volume Structures
We have recently demonstrated an experimental and numerical approach for nsOCT validation and detection of submicron structure with few nanometer accuracy.19 Here we have simulated nsOCT in synthesized volume () phantom composed of randomized submicron structures throughout the volume. Figure 2(a) displays synthesized en face map of submicron structure at depth. Figure 2(b) displays corresponding nsOCT detected en face map of submicron structure. Figure 2(b) demonstrates that nsOCT can detect submicron scale dominant structure with 5-nm accuracy (comparing scale bar of synthetic submicron structure: 448 to 482 nm and nsOCT constructed scale bar: 443 to 482 nm). To check multifractality and correlation in synthesized en face and in nsOCT detected en face, we have applied state of the art 2D-MFDFA on each en face images throughout the depth. Figure 2(c) shows plots of generalized Hurst exponents [ versus ] calculated from synthetic en face in Fig. 2(a) (blue color) and from nsOCT constructed en face in Fig. 2(b) (red color). Variation of versus in Fig. 2(c) indicates that synthetic submicron structural en face has a multifractality (blue color plot) and can be detected with almost no error (red color plot). In addition, Hurst exponent  in synthetic and nsOCT constructed en face is almost equal in values confirms our capability to detect submicron scale structural correlation within a complex tissue sample. Similarly, Fig. 2(d) shows plots of singularity spectrum [ versus ] calculated from synthetic en face in Fig. 2(a) (blue color) and from nsOCT constructed en face in Fig. 2(b) (red color). The width of singularity spectrum () is a measure of multifractality is almost equal in synthetic and nsOCT extracted en face image proved our capability to detect submicron scale structural multifractality within a complex tissue sample.
The lower part of Fig. 2(e) displays 2D-MFDFA extracted depth-resolved Hurst exponent  from synthetic (black color plot) and from nsOCT detected (blue color plot) submicron scale en face structures. The upper part of Fig. 2(e) displays 2D-MFDFA extracted depth-resolved width of singularity spectrum () from synthetic (green color plot) and from nsOCT detected (red color plot) submicron scale en face structures. Detected depth-dependent Hurst exponent  and strength of multifractality () from synthetic and nsOCT simulated en face structure is very close to each other. These results validated our capability to detect submicron scale structural multifractality through the proposed nsMFDFA methodology from a tissue-like complex submicron scale multifractal structure with greater accuracy.
Application of Validated Nanosensitive Multifractal Analysis Technique on Pathologically Characterized MFP Tissue Samples
After successful validation of nsMFDFA approach, we have applied this technique on ex vivo tissue with healthy MFP and tumor portion. Figures 3(a) and 3(d) display hematoxylin and eosin (H&E) stained microscopic images of healthy MFP and tumor tissue, respectively. Figures 3(b) and 3(e) represent conventional OCT images from healthy MFP and tumor tissue, respectively. Note that average intensity values are 32.04 and 33.32, respectively, in healthy MFP and tumor tissue volume. Therefore, it is very difficult to differentiate OCT of healthy MFP and tumor tissue. Figures 3(c) and 3(f) display volume nsOCT where dominant axial submicron structure mapped onto healthy MFP and tumor tissue, respectively. Measured overall average maximum spatial period for healthy MFP is 447.5 nm and tumor tissue is around 454.6 nm. Although, we can see a difference in healthy and tumor tissue based on this overall volume average nanosensitive measurement, but they may not have differences at different depths. Figure 3(g) displays depth-resolved nanosensitive structural averages at each en face for healthy [blue plot extracted from volume in Fig. 3(c)] and tumor [red plot extracted from volume in Fig. 3(f)]. It shows that at 0.35 mm depth, the average value of dominant structure is almost the same for healthy and tumor tissue. Here it is difficult to differentiate tumor from healthy tissue based on local nsOCT measurement only. It is also unable to provide quantitative and depth-specific nanosensitive submicron scale tissue morphological complexities.
In these regards, it is known that tissues have multifractality in submicron structure. Therefore, it is always interesting to have depth-resolved quantitative submicron scale multifractal parameters for better understanding. Quantitative submicron scale multifractal parameters can also help to develop computer-assisted automated differentiation of tumor tissue from healthy tissue. In this direction, we have performed 2D-MFDFA on depth-resolved nsOCT constructed en face images to find nanosensitive multifractal parameters.
In Figs. 4(a) and 4(e), we have displayed maximum spatial period en face images at depth corresponding to volume images in Figs. 3(c) and 3(f). Figures 4(b) and 4(f) represent submicron structural histogram corresponding to Figs. 4(a) and 4(e). Figures 4(c) and 4(g) represent local nanoscale variation after subtracting local trends with detrending scaling window [see Eqs. (3) and (4)]. Figure 4(d) displays generalized Hurst exponent versus for healthy (blue color) en face and tumor (red color) en face image. Figure 4(h) displays singularity spectrum versus Holder exponent, for healthy MFP (blue color) en face, and tumor (red color) en face image. Variation of in Fig. 4(d) indicates multifractality and greater variation of indicates larger multifractality in tumor tissue [red color plot in Fig. 4(d)]. This multifractality reflected in singularity spectrum plots with larger width of singularity spectrum in case of tumor tissue [red color plot in Fig. 4(h)].
For further verification and confirmation, we have applied this extraction method of nanosensitive multifractality on 10 healthy MFP and 10 tumor volume images in different areas of a tissue sample. We found consistence differences of nanosensitive correlation and strength of multifractality over different depths of tissue. Figures 5(a) and 5(b) represent mean Hurst exponent [ using Eq. (5)] and strength of multifractality [ using Eq. (9)] over 10 healthy MFP (blue line plot) and tumor (red line plot) tissue on en face images at different depths. Vertical lines at each depth represent standard deviation from mean trends over 10 samples. In Fig. 5(a), reduction trends of nanosensitive Hurst exponent indicate decrease of correlation of dominant submicron structural distribution over en face images as tumor progress. In Fig. 5(b), increase of nanosensitive multifractality indicates increase of strength of multifractality or distortedness of dominant submicron structural distribution over en face images as tumor progress.
A novel approach to quantify submicron scale nanosensitive multifractality in combination with nsOCT and multifractal analysis has been demonstrated. We validated the nsOCT technique numerically on synthetic submicron scale axial structures. We developed a novel nanosensitive submicron scale multifractal analysis technique to characterize tissue depth-resolved ultrastructural morphology. Reduction of the Hurst exponent  from healthy MFP to tumor indicates reduction of correlation or self-similarity in dominant submicron structures. Increase of width of singularity spectrum () from healthy MFP to tumor indicates increase of multifractality or roughness in dominant nanosensitive submicron scale tissue structures. This newly developed method promises early disease detection for better treatment guidance and monitoring response to treatment in cancer patients. Results promise to detect nanosensitive multifractality in the submicron scale structural distribution and its alteration in deep tissue as tumor progress. This ability to delineate nanosensitive self-similarity may provide a noninvasive measuring tool for characterization of biological tissue and nonbiological media. Observed differences in the submicron scale nanosensitive multifractality between healthy and tumor tissue show considerable promise as potential biomarkers for cancer detection. The ability to probe and quantify nanosensitive self-similarity and change of multifractality related to development of cancer using backscattering mode FD-OCT bodes well for in vivo deployment. Exploiting the interference spectra recorded from tissue depths with the reference mirror, in vivo applications of this approach should be realized with a fiber optic-based handheld probe assisted with scanning lens and galvo mirror. Finally, the developed nsMFDFA method represents as a novel approach with much potential for in vivo detection of cancer initiation and other non-biological application remain to be rigorously evaluated.
The authors have no other relevant financial interest in this article and no other potential conflicts of interest to disclose.
This project received funding from Irish Research Council (IRC), under Government of Ireland postdoctoral fellowship with project ID: GOIPD/2017/837. Nandan Das acknowledge National University of Ireland Galway (NUIG) for research facilities. He would also like to acknowledge the Knut and Alice Wallenberg Foundation support through the Wallenberg Centre for Molecular Medicine (WCMM) at Linköping University (LiU), Sweden. Also, this project has received funding from the European Union’s Horizon 2020 research and innovation program under Grant Agreement Nos. 761214 and 779960. The materials presented and views expressed here are the responsibility of the author(s) only. The EU Commission takes no responsibility for any use made of the information set out.
All animal procedures were performed in accordance with the Guidelines for Care and Use of Laboratory Animals of the Animal Care Research Ethics Committee (ACREC), National University of Ireland Galway (NUIG), and approved by the Health Product Regularity Authority (HPRA) of Ireland.
Nandan Das is a postdoctoral researcher at Linköping University (LiU), Sweden. His main research interest is in biomedical optics and biophotonics. He has vast experience in optical system design and numerical modeling to explore subtle tissue structural and functional parameters for biological tissue diagnosis. He has expertise in fluorescence spectroscopy, Muller matrix polarimetry, photoacoustic microscopy, optical coherence tomography, spatial frequency domain imaging (SFDI), multifractal analysis, nano sensitive study, correlation mapping imaging etc.
Sergey Alexandrov is a senior research fellow at NUI Galway. His main area of research is the development of new optical methods and tools, such as imaging and measuring techniques (holographic, interference, polarization, super-resolution microscopy, OCT, spectral, etc.) for biomedical and other applications. His contributions have resulted in the creation of new highly sensitive and super-resolution optical methods and techniques for study of different samples, including biomedical samples and human beings in vivo.