Line-scan chromatic confocal microscopy for multi-depth imaging of skin tissue using deconvolution

Abstract

In this paper, we present a line-scan chromatic confocal microscopy for rapid, multi-depth imaging of non-transparent skin tissue. Leveraging spectral dispersion encoding, this system enables the simultaneous acquisition of reflectance data across a depth range exceeding 180 $\mu$ m in skin tissue, effectively eliminating mechanical axial scanning and minimizing associated artifacts. With a lateral effective field of view (FOV) of 13.2 mm, the system provides a wide-field perspective for comprehensive tissue analysis. Furthermore, to overcome the typical limitations of lateral resolution in line-scan systems, we employ pre-calibrated deconvolution using an empirically determined point spread function obtained with a micro-spot mirror. We demonstrate deep-tissue tomography with ex vivo bovine skin tissue, achieving an increase in resolution from 45.25 lp/mm to 50.79 lp/mm post-deconvolution, as quantified using a USAF 1951 target. These results highlight the potential of line-scan chromatic confocal microscopy with pre-calibrated deconvolution as a powerful platform for multi-depth biomedical imaging applications requiring enhanced lateral resolution and contrast.

1. Introduction

The visualization of biological tissues has significantly advanced the biomedical community’s understanding of these complex structures and their intrinsic properties [1–3]. Notably, anomalies often reside within the tissue volume, rather than being readily apparent at the surface. In such cases, three-dimensional (3D) imaging techniques for skin tissue are crucial for facilitating early and accurate disease diagnosis. A variety of 3D imaging modalities, including optical coherence tomography (OCT) [4],confocal microscopy [5], chromatic confocal microscopy (CCM) [6],and light sheet microscopy [7], have been developed to address this need. While optical coherence tomography (OCT) can maintain high resolution within the focal plane, its resolution degrades substantially with increasing distance from the focal point [8].Light sheet microscopy can provide high-contrast sample images from a focal plane, but owing to its complex architecture,it has limited in vivo applications [9]. Confocal microscopy is a well-established technique in biological imaging; however, its application is inherently limited to a restricted focal plane, typically defined by the objective lens’s depth of field [10]. This limitation stems from the technique’s reliance on spatial filtering, which rejects out-of-focus light, thereby enhancing image contrast and resolution within the focal plane. Volumetric imaging with conventional confocal microscopy necessitates mechanical scanning along the Z-axis, a process achieved by physically moving either the objective lens or the sample stage [11]. This mechanical scanning is susceptible to introducing motion artifacts, such as blurring or distortions, particularly when imaging dynamic or delicate samples, thereby compromising overall image quality and potentially leading to inaccurate interpretations [12].

Chromatic confocal microscopy offers a distinct advantage by enabling the simultaneous acquisition of reflectance signals from all points along the axial range defined by dispersion encoding [13,14]. This approach utilizes a broadband light source and a dispersive element to create a spectrally encoded axial gradient, effectively mapping each wavelength to a unique focal position along the optical axis. As a result, a single acquisition captures reflectance information from a range of depths, significantly accelerating volumetric image acquisition while obviating the need for mechanical axial scanning and, consequently, minimizing the risk of motion artifacts. Furthermore, leveraging its non-destructive and non-contact characteristics, stemming from the use of light as the primary probe, chromatic confocal microscopy has found widespread applications in diverse fields, including 3D metrology for surface profilometry and bio-imaging for tissue analysis [15,16]. Nevertheless, conventional chromatic confocal microscopy based on point-scanning principles requires X-Y raster scanning to reconstruct complete tomographic information [17,18]. This raster scanning process involves serially acquiring data points across the sample surface, which substantially increases the overall measurement time, especially when imaging large areas or volumes. This prolonged acquisition time can be a significant limitation in applications requiring high-throughput imaging or real-time monitoring of dynamic processes. Hu et al [19] proposed a line-scan chromatic confocal microscopy, which greatly improved the scanning efficiency, but the crosstalk between lateral pixels led to a decrease in the lateral resolution of the line-scan chromatic confocal microscopy [20].

In this paper, a line-scan chromatic confocal microscopy(LSCCM) is built for multi-depth imaging of skin tissue to a depth exceeding 180 $\mu$ m was achieved using this system and a pre-calibrated deconvolution method is proposed to improve the lateral resolution of LSCCM to overcome the typical limitations of lateral resolution in line-scan systems.

2. Methods

Chromatic confocal microscopy simultaneously focuses different wavelengths of light into different depths using a highly-chromatic lens, and records the reflected light using a spectrometer in a confocal manner, in which depth information is encoded in the spectra.Based on this principle, a line-scan chromatic confocal microscopy can realize the multi-depth imaging of skin tissue while its line scanning design greatly improves the imaging efficiency.

2.1. Setup of the LSCCM

As shown in Fig. 1,a line-scan chromatic confocal system was built where the pathways for illumination and detection are mutually independent.A light source(Led,XLamp XD16, Cree LED,380-780nm) emits a broadband collimated light through a slit (length $\times$ width: 10mm $\times$ 25 $\mu$ m) and collimator lens. A collimated light beam is dispersed by a transmission grating (GT25-08, 830 lines/mm, Thorlabs), and a custom linear dispersion component then focuses the resulting wavelengths onto the sample surface, creating an illumination beam with a linear distribution of wavelengths along its vertical height. An extra lens assembly, which includes a linear dispersion element, a transmission grating, and a collimator lens, gathers the reflected beam. This assembly is arranged symmetrically relative to the illumination setup.The angle between the illumination and detection light paths is ${\mathrm{120}}^{\circ }$ . The reflected light establishes a confocal configuration through the slit (length $\times$ width: 10 mm $\times$ 25 $\mu$ m). Consequently, it is only permitted to accept a specific wavelength that is in focus at surface of the specimen. Furthermore, different wavelengths are separated through an imaging component that includes a collimator lens, a reflective grating(1200 Grooves, 1200 lines/mm, Edmund Optics)and an imaging lens, forming a linear profile of the sample. All the spectral images are captured by the camera(1088 $\times$ 2048 pixels, Daheng VC-2MC-M 150 ). The linear dispersion element is a critical component of the system, designed to provide a precisely controlled angular dispersion as a function of wavelength. Over the 545-640 nm wavelength range, the foci span a depth range of 3000 $\mu$ m, which corresponds well with our optical model.The axial point spread functions at different positions are shown in Fig. 1.(b).The axial response function demonstrates that the axial resolution of this system is approximately 20 $\mu$ m.The chromatic focal shift of the dispersion component of the LSCCM is obtained by finding the peak intensity wavelength for each axial position.Experimental data showing the relationship between focus depth and wavelength in Fig. 1.(c).The CMOS camera is used as a spectrum signal receiver; the lateral FOV is 13.2 mm; the axial range is 3 mm; the working distance is more than 28.3 mm. The resolution of the area CMOS sensor in the spread spectrum direction (1088 pixels) determines the spectrum analysis precision, while the resolution in the measurement line direction (2048 pixels) determines the number and distribution of points along the scanning line.

Fig. 1.

(a) Setup of the LSCCM.(b) The axial point spread functions in different positions.(c) Experimental data results between focus depth and wavelength.

To acquire a complete three-dimensional image of the sample, a precise scanning mechanism, consisting of a high-resolution translation stage, is employed to move the sample laterally relative to the illumination line focus. The translation stage is controlled by custom-written software running on a computer, allowing for precise control of the scanning speed and step size. At each lateral position, the camera captures a spectral image of the sample’s cross-sectional images. The camera is synchronized with the translation stage to ensure accurate spatial registration of the acquired data. The camera data are then transferred to a computer for post-processing, which involves background subtraction, flat-field correction, and spectral calibration to accurately determine the cross-sectional images at each lateral position. Subsequently, these cross-sectional images are computationally processed to create a three-dimensional tomographic image of the sample.

2.2. Point spread function and de-convolution method

For an optical imaging system, its output image g(x,y) can be thought of as the result of the convolution of the point spread function h(x,y) of its system and the input image f(x,y) [21].The convolution procedure explains how the resultant signal emerges from the interaction between light and the sample. Similarly, the interface optics of line scan chromatic confocal microscopy can be considered as an imaging instrument with point spread function(PSF) described by h(x,y) and the output image g(x,y) captured by the camera of the line scan chromatic confocal microscopy system can be expressed by the convolution of input image with PSF

$$g(x,y)=f(x,y)\otimes h(x,y),$$ (1)

where $\otimes$ represents the convolution operation.

Deconvolution is widely employed to address coupling issues. This is facilitated by the Fourier transform,which elegantly converts the convolution operation in the time domain into a point-wise multiplication in the frequency domain, simplifying the deconvolution process, Eq. (1) can be transformed into

$$G(u,v)=F(u,v)H\left(u,v\right),$$ (2)

where $G\left(u,v\right)$ , $H\left(u,v\right)$ , $F\left(u,v\right)$ are the Fourier transformations of the the input image, the final image and the PSF of the system.And $(u,v)$ represent the spatial frequency coordinates.

Once the PSF is determined, the undistorted signal can be retrieved via an iterative Wiener deconvolution process, as detailed below

$$F{(u,v)}_n=F{(u,v)}_{n-1}+\frac{H^{\ast }(u,v)G(u,v)}{|H(u,v){|}^2+\xi },$$ (3)

where $\xi$ is noise factor, and n is the the number of iterations.

A critical challenge lies in the accurate identification of the PSF that precisely corresponds to the underlying LSCCM characterization. Precise PSF estimation is crucial for minimizing the number of iterations required in the deconvolution algorithm and ensuring the accurate recovery of the original image f(x,y).

According to confocal microscopy method described in [22], the PSF of the confocal microscopy can be expressed as the product of the illumination and detection optical paths

$$h(z,x,y)=h_{ill}(z_i,x_i,y_i)h_{dec}(z_d,x_d,y_d),$$ (4)

where $h_{ill}(z_i,x_i,y_i)$ and $h_{dec}(z_d,x_d,y_d)$ represent the PSF of the illumination and detection light paths, respectively.

Assuming the angle between the illumination light path and the detection light path is $\theta$ ; $z_d$ , $z_i$ , $z$ denotes the axial coordinate of the illumination light path, the axial coordinate of the detection light path, and the axial coordinate of the line-scan chromatic confocal system;where X-direction is the scanning direction, and the Y-direction is the focusing linear direction(lateral direction along the slit scan line).

According to spatial coordinate transformation, Eq. (5) is achievable.

$$\begin{array}{l}\{\begin{array}{c}{x}_i=x\cos \theta -z\sin \theta \\ y_i=y\\ z_i=x\sin \theta +z\cos \theta \end{array}\\ \{\begin{array}{c}{x}_d=x\cos \theta +z\sin \theta \\ y_d=y\\ z_d=-x\sin \theta +z\cos \theta \end{array}\end{array}$$ (5)

Substituting Eq. (4) into Eq. (5), we obtain

$$h_D(z,x,y)=h(z\cos \theta +x\sin \theta ,-z\sin \theta +x\cos \theta ,y)\times h(-x\sin \theta +z\cos \theta ,x\cos \theta +z\sin \theta ,y),$$ (6)

The PSF of the illumination path can be further expressed as

$$h_{ill}\left(x_i,y_i,z_i\right)={\int }_{-\mathrm{\infty }}^{+\mathrm{\infty }}P\left(x_{\rho },y_{\rho }\right)\exp [\frac{i{u}_i}{2}(x_{\rho }^2+y_{\rho }^2)]\exp \left\{i\left[v_{ix}{x}_{\rho }+v_{iy}{y}_{\rho }\right]\right\}d{x}_{\rho }d{y}_{\rho },$$ (7)

Meanwhile,the PSF of the detection path can be further expressed as

$$h_{dec}\left(x_d,y_d,z_d\right)={\int }_{-\mathrm{\infty }}^{+\mathrm{\infty }}P\left(x_{\rho },y_{\rho }\right)\exp [\frac{i{u}_d}{2}(x_{\rho }^2+y_{\rho }^2)]\exp \left\{i\left[v_{dx}{x}_{\rho }+v_{dy}{y}_{\rho }\right]\right\}d{x}_{\rho }d{y}_{\rho },$$ (8)

where $v_{ix}=\frac{2\pi x_i\sin \alpha }{\lambda }$ , $v_{iy}=\frac{2\pi y_i\sin \alpha }{\lambda }$ ,and $u_i=8\pi x{z}_i{\sin }^2(\alpha /\lambda )$ are the normalized coordinates of the illumination path; $v_{dx}=\frac{2\pi x_d\sin \alpha }{\lambda }$ , $v_{dy}=\frac{2\pi y_d\sin \alpha }{\lambda }$ ,and $u_d=8\pi x{z}_d{\sin }^2(\alpha /\lambda )$ are the normalized coordinates of the detection path;and $P(x_{\rho },y_{\rho })$ represents the pupil function.

However, in practical line-scan chromatic confocal systems, some of the defocused light will still reach the detector through the slit [23].This allows for multi-point entry along the slit, accompanied by spectral dispersion causing wavelength-dependent focal variations. Consequently, the predictive capabilities of the mathematical model regarding the PSF of the LSCCM system are compromised. The actual PSF is formed by the superposition of diffracted contributions from both focused and defocused light. Therefore, empirical determination of the PSF through direct measurement provides a more reliable representation compared to relying solely on a mathematically derived model.

2.3. Line-scan chromatic confocal microscopy using pre-calibrated PSF deconvolution

We propose a deconvolution method, utilizing a pre-calibrated PSF, to mitigate the lateral resolution degradation induced by crosstalk in line-scan chromatic confocal microscopy. The flowchart of this method is presented in Fig. 2. In order to minimize potential inaccuracies arising from mathematically modeled PSF functions, we pre-calibrated the line-scanning chromatic confocal microscope by experimentally measuring its PSFs at various axial positions prior to conducting practical measurements.

Fig. 2.

Flowchart of the proposed pre-calibrated deconvolution method.

A specialized micro-spot mirror, as shown in Fig. 3, was designed and fabricated to enable PSF extraction for our line-scan chromatic confocal microscopy system, allowing for accurate PSF characterization of the LSCCM.

Fig. 3.

Micro-spot mirror.(a)schematic diagram of micro-spot mirror.(b)image of the micro-spot mirror.

The mirror consists of a silver coating applied to a transparent window substrate. The fabrication protocol involved the deposition of a reflective silver film onto a 1-inch diameter window.Specifically, a 1-inch diameter circular window was first cleaned using a rigorous multi-step solvent process involving ultrasonic baths of acetone, isopropyl alcohol, and deionized water to remove any surface contaminants. Following the cleaning procedure, a thin adhesion layer of chromium was deposited onto the window surface using electron beam evaporation to enhance the adhesion of the subsequent silver layer. Subsequently, the window was placed in a DC magnetron sputtering system, and a 30 $\mu$ m-diameter shadow mask was positioned in close proximity to the window surface. A 100nm-thick layer of silver was then deposited through the mask, with the sputtering parameters (argon pressure, sputtering power, substrate temperature) carefully optimized to achieve a smooth, uniform, and highly reflective film. The deposition rate and film thickness were carefully monitored using a quartz crystal microbalance to ensure uniformity and the desired thickness of the silver micro-spot.

3. Results

3.1. Multi-depth imaging of skin tissue using LSCCM

Utilizing our custom-built line-scanning chromatic confocal microscopy system, we successfully achieved tomographic imaging of bovine skin tissue, demonstrating an imaging depth exceeding 180 $\mu$ m. A key advantage of our system is its ability to acquire a cross-sectional profile of the sample in a single measurement. This is achieved through the spectral encoding of depth information along the illumination line. By carefully optimizing the system parameters, including the linear dispersion element and the spectral bandwidth of the light source, we were able to maximize both the axial resolution and the penetration depth. Along the lateral direction, a 13.2-mm lateral field of the tissue was mapped to 2048 pixels of the CMOS sensor. Therefore, each pixel along the lateral direction represented average 6.445 $\mu$ m on the tissue and the x-axis and y-axis represent the same scale in the presented tissue images in this paper.The current system allows us to acquire full volumetric data (2048 $\times$ 1088 $\times$ 2048 $\mathrm{p}\mathrm{i}\mathrm{x}\mathrm{e}{\mathrm{l}}^3$ ) in 2.56s which can be improved further using a fast scanner and camera combination.

Consequently, complete tomographic imaging of the bovine skin tissue could be accomplished with only a single lateral scan, significantly reducing the acquisition time compared to traditional point-scanning chromatic confocal microscopy. Representative cross-sectional (x-z plane, single acquisition) and tomographic (x-y plane, after lateral scan) images derived from the bovine skin tissue are presented in Fig. 4. These images clearly reveal the epidermis, demonstrating the system’s ability to capture detailed structural information from deep within the tissue.

Fig. 4.

Confocal images of ex vivo bovine skin tissue acquired with LSCCM.(a) Cross-sectional images at different scanning positions.(b-d)En face images at different depths

Pig skin tissue, a turbid biological sample, was used to further demonstrate the capabilities of the LSCCM. The cross-sectional images of the tissue (Fig. 5(a)) at different scanning positions and images acquired at various depths from 60 to 180 $\mu$ m (Fig. 5(b-d)) clearly show resolved follicle structures, indicating the effectiveness of the system in different skin samples.

Fig. 5.

Confocal images of ex vivo pig skin tissue acquired with LSCCM.(a) Cross-sectional images at different scanning positions.(b-d)En face images at different depths

3.2. PSF estimation of the chromatic line confocal microscopy system

To investigate the imaging performance at varying depths within the micro-spot mirror, C-scan images were acquired at three distinct depths: 140 $\mu$ m, 150 $\mu$ m, and 160 $\mu$ m, measured relative to the micro-spot mirror’s surface using a precision depth control mechanism. At each specified depth, 10 independent C-scan images were collected sequentially, ensuring minimal temporal separation between acquisitions to minimize potential variations in the sample. These multiple acquisitions were performed to enable subsequent averaging, a common technique employed to mitigate the influence of speckle noise, a prevalent artifact in confocal imaging modalities. Specifically, for each depth, 10 acquired C-scan images were registered and then averaged pixel-wise to produce a single, composite image with reduced speckle noise. The averaging process was implemented using a custom-written algorithm in MATLAB, which incorporated outlier rejection to further minimize the impact of any spurious data points. The primary objective of this data processing pipeline was to enhance the image quality, particularly in terms of signal-to-noise ratio and image clarity, of the averaged C-scan obtained at the central depth of 150 $\mu$ m.

Our empirical PSF measurement involved acquiring C-scan images of the micro-spot mirror, the resulting 3D data contains information about the PSF variation in all three dimensions within the calibrated volume. For the deconvolution presented, we generated an average PSF based on images around the central depth (150 $\mu$ m) and across the relevant lateral region used for imaging. During the calibration, the axial position was maintained at a fixed value of 150 $\mu$ m. As shown in Fig. 6, the recorded data exhibits C-scan image obtained from the micro-spot mirror and the enlarged view of the micro-spot mirror.At each specific axial position, 10 C-scan images were acquired. The average PSF was then calculated and used as the PSF corresponding to that position.

Fig. 6.

Estimation of PSF.(a) C-scan image obtained from the micro-spot mirror.(b) the enlarged view of the micro-spot mirror.

3.3. Resolution enhancement of chromatic line confocal microscopy images via deconvolution

During actual measurements, Wiener deconvolution, employing a pre-calibrated PSF, is applied to the acquired image data to generate higher-resolution tomographic images. This deconvolution process aims to computationally reverse the blurring effects introduced by the optical system, thereby sharpening fine details and improving the overall clarity of the reconstructed tomographic volumes. The pre-calibrated PSF, obtained through independent measurements as described in Section 3.2, accurately characterizes the system’s lateral resolution limitations. By utilizing this pre-calibrated PSF within the Wiener deconvolution algorithm, we effectively minimize artifacts and noise amplification that can arise from inaccurate PSF estimations. The resulting higher-resolution tomographic images are expected to exhibit improved contrast, enhanced lateral resolution, and increased visibility of subtle structural features within the sample, ultimately facilitating more accurate and detailed analysis of the imaged tissue.

To validate the efficacy of the proposed deconvolution method, we performed experiments on ex vivo bovine skin tissue.LSCCM imaging was conducted on ex vivo bovine skin tissue before and after the application of deconvolution. The resulting images are shown in Fig. 7(a) and 7(b), respectively. A qualitative assessment indicates a noticeable enhancement in image quality after deconvolution. To further quantify this improvement, we analyzed the intensity histograms of the original and deconvolved images (Fig. 7(c) and 7(d)). The histograms reveal a broader intensity distribution in the deconvolved image, suggesting an increase in image contrast.

Fig. 7.

Original (a) and deconvolved (b) LSCCM en face images of an ex vivo bovine skin tissue at the depth of 150 $\mu$ m. The corresponding intensity histograms (c, d) are also shown. Scale bar:200 $\mu$ m

With the system’s resolution performance a key metric for evaluating overall system effectiveness, a USAF 1951 resolution target was employed to quantify the difference between system resolution with and without deconvolution. Specifically, images of the USAF 1951 target were acquired both before and after the application of the deconvolution algorithm, ensuring that all other imaging parameters remained constant. The smallest resolvable element on the target was then identified in both the original and deconvolved images, and the corresponding lateral resolution was calculated based on the target’s known dimensions. This allowed for a quantitative comparison of the system’s resolution, directly demonstrating the impact of the deconvolution process on improving image clarity and detail.The resulting images are shown in Fig. 8(a) and 8 (b), respectively.

Fig. 8.

Original (a) and deconvolved (b) LSCCM en face image of the USAF target located at the depth of 150 $\mu$ m.The corresponding intensity profile (c, d) are also shown.

Evaluation of the imaging results obtained using the USAF 1951 resolution target revealed that the system was capable of resolving Group 5 Element 4 prior to the application of deconvolution. This corresponds to a lateral resolution of 45.25 line pairs per millimeter (lp/mm). Following the implementation of the deconvolution algorithm, the system’s resolving capability was enhanced, enabling it to resolve Group 6 Element 4 on the resolution target. This represents a significant improvement, corresponding to a lateral resolution of 50.79 lp/mm.Crucially, analysis of the line pair profile within the red rectangle area on the resolution target reveals a marked sharpening and increased contrast of the line pairs after deconvolution. This improved line pair profile directly confirms the increase in resolvable line pairs and demonstrates the effectiveness of the deconvolution process in mitigating optical blurring and enhancing the system’s ability to discern fine details.

4. Discussion and conclusion

This study introduced a line-scan chromatic confocal microscope designed for multi-depth imaging of skin tissues. The core innovation lies in the integration of pre-calibrated deconvolution to mitigate the inherent lateral resolution limitations of line-scan confocal architectures. By employing spectral dispersion encoding, the LSCCM achieves simultaneous acquisition of reflectance data across a significant depth range (demonstrated up to 180 $\mu$ m in ex vivo skin tissue), effectively eliminating the need for time-consuming mechanical axial scanning and its associated motion artifacts.

The empirical determination of the system’s PSF using a custom-fabricated micro-spot mirror is a crucial aspect of this work. This approach contrasts with relying solely on theoretical PSF models, which often fail to fully capture the complexities of real-world optical systems, particularly those involving spectral dispersion and multi-point illumination. The pre-calibrated PSF enables a more accurate implementation of the Wiener deconvolution algorithm, minimizing the introduction of artifacts and maximizing the enhancement in lateral resolution and image contrast.

The quantitative results, obtained using a USAF 1951 resolution target, clearly demonstrate the efficacy of the deconvolution process. The improvement in resolving power, from 45.25 lp/mm to 50.79 lp/mm, represents a substantial enhancement in the system’s ability to discern fine structural details within the imaged tissue. This improvement is visually evident in the ex vivo bovine skin tissue images, where the deconvolved images exhibit sharper delineation of tissue layers.

While the current study focused on ex vivo tissue, the LSCCM’s design and performance characteristics suggest its potential for a wide range of in vivo applications. The non-invasive nature of the technique, coupled with its high acquisition speed and improved resolution, makes it particularly well-suited for applications such as early skin tissue cancer detection, wound healing monitoring, and intraoperative tissue assessment. Future work will focus on adapting the system for in vivo imaging, including addressing challenges related to tissue motion and optimizing imaging parameters for specific clinical applications. The integration of advanced image processing techniques, such as adaptive optics and computational clearing, could further enhance the system’s performance and penetration depth.

In conclusion, the developed LSCCM system, incorporating pre-calibrated deconvolution, represents a significant advancement in confocal microscopy for multi-depth tissue imaging. The system’s ability to acquire high-resolution, three-dimensional images rapidly and without mechanical axial scanning offers considerable advantages over conventional point-scanning confocal microscopes. The demonstrated performance and potential for in vivo adaptation suggest that this technology could have a significant impact on biomedical research and clinical diagnostics.

Funding

National Key Research and Development Program of China 10.13039/501100012166 ( 2022YFB3206000); Wuhan Science and Technology Project 10.13039/501100018583 ( 2024010702020024).

Disclosures

The authors declare no conflicts of interest.

Data availability

Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.