Photoacoustic (PA) imaging has become invaluable in preclinical and clinical research. Endoscopic PA imaging in particular has been explored as a noninvasive imaging modality to view vasculature and diagnose cancers in the digestive system. However, these feasibility studies are still limited to rodents or rabbits. Here, we develop a fully synchronized simultaneous ultrasound and photoacoustic microscopy system using two spectral bands (i.e., the visible and near-infrared) in both optical- and acoustic-resolution modes. We investigate the feasibility of imaging gastric vasculature in an ex vivo porcine model. The entire gastric wall, including the mucosa, submucosa, muscularis propria, and serosa, was excised from fresh porcine stomachs immediately followed by ultrasound and PA imaging being performed within a few hours of sacrifice. PA images of the mucosal vasculature were obtained at depths of 1.90 mm, which is a clinically significant accomplishment considering that the average thickness of the human mucosa is 1.26 mm. The layer structure of the stomach wall could be clearly distinguished in the overlaid PA and US images. Because gastric cancer starts from the mucosal surface and infiltrates into the submucosa, PA imaging can cover a clinically relevant depth in early gastric cancer diagnosis. We were able to detect mucosal vasculature in the entire mucosal layer, suggesting the potential utility of combined PA/US imaging in gastroenterology.
© 2021 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
Stomach cancer is the fourth most common cancer and the third-highest cause of cancer death in the world . With the development of early gastric cancer (EGC) detection devices and associated medical technology, the mortality from gastric cancer has decreased every year , but it is still one of the main causes of death worldwide.
According to the American Joint Committee on Cancer (AJCC), the most common method of diagnosing the severity of stomach cancer is based on the tumor-node-metastasis (TNM) staging system . In particular, the tumor (T) indicator, ranging from Tis to T2 in EGC, indicates the degree of tumor penetration into each layer of the stomach wall (Fig. 1). Accurate local staging of gastric cancer is important because it helps to determine if the cancerous lesion can be removed endoscopically by endoscopic submucosal dissection (ESD) or requires surgical resection. Current guidelines state that some T1a and T1b (with <500 µm depth of submucosal invasion) lesions can be resected by ESD . However, current imaging methods are poor at identifying depth of invasion. Initial endoscopic examination is performed with high-definition white light endoscopy (HD-WLE). Since HD-WLE provides the same image as the naked eye, it allows for rapid identification of gastric cancers; however, HD-WLE is poor at assessing depth of invasion. To overcome these limitations, both narrow-band imaging (NBI) using a xenon light source and chromoendoscopy using dyes (e.g., indigo carmine, Lugol, or methylene blue) with and without magnification are often used. However, they can only directly evaluate the surface, revealing little about the morphology of deep tissues [5,6]. Therefore, to see deeply, endoscopic ultrasound (EUS) has been widely used to assess for depth of invasion. An EUS probe can be inserted into the channel of a conventional endoscope or an echoendoscope can be advanced into the stomach to provide tomographic images of relatively deep regions (several millimeters to centimeters) of the gastrointestinal (GI) tract [7,8]. However, EUS-based staging is often not sufficient to differentiate between T1a and T1b tumors because of the limited resolution of ultrasound used for endoscopic imaging (5-20 MHz) [9,10].
Photoacoustic imaging (PAI) is a biomedical imaging modality that detects ultrasonic waves (or photoacoustic (PA) waves) generated via thermal expansion by irradiating a sample with pulsed light. It has become widely used in biomedical research imaging [11–14], and clinical field  because it is radiation-free, noninvasive, and multiparametric (i.e., different contrast agents can provide structural, physiological, and molecular information) with high resolution [16–18]and high speed imaging [19–21].Over the last decade, many research studies have been performed to develop miniaturized photoacoustic endoscopic (PAE) probes which apply PAI technology to the existing EUS [22–28]. However, despite the advances offered by these endoscope developments, animal imaging research is still limited to relatively small animals, such as rodents and rabbits. PAI imaging results for the mucosa of large animals and blood vessels inside the submucosa are insufficient, hindering potential clinical translation. Using indocyanine green, Wang et al. created a tumor-mimicking phantom on an excised porcine stomach and imaging the model ex vivo with acoustic-resolution photoacoustic microscopy (AR-PAM). However, microvessel structures were not clearly visualized due to the modality’s low spatial resolution . Lin et al. used an array-based PA imaging system to image artificial tumors in an excised porcine stomach ex vivo. Again, the PA image qualities were poor due to the low spatial resolution, and it was not possible to demonstrate the potential for clinical translation .
In this study, we develop a switchable optical- and acoustic-resolution photoacoustic microscopy system with a simultaneous ultrasound imaging capability (USPAM). Two visible and near-infrared optical wavelength bands are employed. In the visible band, the wavelength of 532 nm, which is frequently used for vascular PA imaging, was selected because it has high absorption in hemoglobin and oxyhemoglobin. In the near-infrared band, a wavelength of 760 nm having a small scattering in the tissue and a local peak point in the absorption spectrum for hemoglobin is selected . We demonstrate the feasibility of PAI of the gastric mucosa in ex vivo porcine stomachs with anatomical and physiological similarities to human stomachs. High-resolution PAI blood vessels and tissue images were obtained from the dissected porcine stomach wall. Whereas the thickness of the mucosa is 1.50∼1.87 mm, PA images of the mucosal vessels were obtained at depths as deep as 1.90 mm, and the results were validated by histology. Considering these vascular imaging and depth analysis capabilities, this study discusses the potential usefulness of PA/US imaging in establishing important T indicators for cancer diagnosis.
2. Materials and methods
2.1 High-speed ultrasound/photoacoustic microscopy (USPAM) system based on a waterproof MEMS scanner
Figure 2(a) is a schematic of our simultaneous USPAM system. The system is an upgraded version of a commercial PAM (OptichoM, Opticho, Republic of Korea) with the added capability of US imaging . The USPAM system utilizes Nd:YAG (532 nm) and Ti:sapphire (700–900 nm) pulsed lasers (AWAVE 532-1W-10 K and AWAVE-Ti:S-700–900, respectively, Advanced Optowave, NY, USA). The optical beams from the two lasers are separately collimated using two lenses (LD2297 and LA1508, Thorlabs, NJ, USA) respectively. The collimated beams are combined using flat mirrors and a dichroic beam splitter (BB1-E02 and DMSP550R, Thorlabs, NJ, USA), and then coupled to a 50-μm core multi-mode fiber (M42L05, Thorlabs, NJ, USA) or a 400-μm core multi-mode fiber (M74L05, Thorlabs, NJ, USA) using a reflective coupler (RC04FC-P01, Thorlabs, NJ, USA). In the main body of the system, the beam spread from the fiber is collimated using a reflective collimator (RC08FC-P01, Thorlabs, NJ, USA). To prevent wavelength-dependent chromatic aberration due to different refractive indices, reflective fiber-optic components are used. The collimated beam is focused on the imaging targets by a focusing lens (AC127-050-A, Thorlabs, NJ, USA) and a microelectromechanical systems (MEMS) scanning module (OptichoM-MS, Opticho, Republic of Korea). In the scanning module, the optical beam is reflected onto an opto-ultrasonic combiner and the MEMS scanner, from where it irradiates the targets, generating PA waves. The PA waves are returned to the US transducer (V214-BC-RM, Olympus NDT, MA, USA), passing through the opto-ultrasonic combiner. An acoustic lens (#45-010, Edmund Optics, NJ, USA) with 6 mm diameter and -18 mm focal length maximally collects the PA waves from the focused spot, and a correction lens compensates for the change in the optical path by the acoustic lens. For US generation, a US pulser-receiver (DPR500-S, Imaginant, NY, USA) is connected to the US transducer. The generated and returned US waves propagate along the same path as the PA waves. The US and PA signals acquired by the US transducer are amplified by an input-protected 40-dB amplifier (PE15A63001, Pasternack, CA, USA), digitized on a high-speed data acquisition (DAQ) device (ATS9350, Alazar technologies, QC, Canada), and transferred to LabVIEW (National Instruments, TX, USA) on a personal computer. The MEMS scanner rapidly swings the optical and acoustic beams while maintaining coaxial alignment, enabling high-speed imaging with high-signal-to-noise ratios (SNRs). To expand the field of view, the body is installed on two linear stages (L-509, Physik Instrumente, Germany). Another DAQ device (PCIe-6321, National Instruments, TX, USA) is programmed for precisely timed operation of the above parts, (Fig. 2(b)). To prevent the PA and US signals from overlapping, the second DAQ triggers the lasers and pulser-receiver using a single pulse repetition frequency with time intervals. Each device is triggered before triggering the high-speed DAQ with different delays to make up for the times of flight of the US and PA waves and the device-dependent offset delay, defined as the time delay from the triggering to the light irradiation or US generation. Although the MEMS scanner can acquire up to 25 frames per second (fps), the pulse repetition frequency (PRF) limit of the Ti:sapphire pulsed laser is 2 kHz, resulting in a B-mode imaging rate of 2.5 fps. The entire volume data consists of four single volume data concatenated in the x-direction. The imaging time for each single volume data is 160 s (0.4 s/frame x 400 frames) and it takes 640 s to acquire the entire volume (4 volumes) data. The field of view (FOV) of each single data is 2 mm x 8 mm along the x and y axes, respectively, (reference directions are shown in Fig. 2(a)) and the total FOV measures 8 mm x 8 mm along the x and y axes, respectively.
A major improvement in this system is the fully synchronized operation of the parts. To realize this, the motif is taken from the design of a digital circuit that uses a clock signal to synchronize many digital signals. To obtain high-resolution images, we used a quasi-optical-resolution PAM (qOR-PAM) mode, in which a 50-μm core multimode fiber was utilized to a conventional optical-resolution PAM (OR-PAM) system . The penetration depth of qOR-PAM was approximately 1 mm. Further, an AR-PAM mode was implemented by replacing the optical fiber in the same system with a 400-μm core multimode optical fiber to improve the penetration depth . In order to quantify SNRs and spatial resolutions, we imaged a carbon fiber with a diameter of 7 μm. The SNRs were calculated by dividing the magnitude of the peak amplitude pixel by the standard deviation of the noise. The PA SNR with the qOR-PAM system was 54 dB at 532 nm and 55 dB at 760 nm. The US SNR was 25 dB. The PA SNR with the AR-PAM system was 53 dB at 532 nm. The spatial resolution was measured by calculating the full-width at half-maximum (FWHM) of the line spread functions (Fig. 2(c)). The axial resolution was around 44 μm in all modes, determined by the bandwidth of the US transducer. The PA lateral resolutions in the qOR-PAM mode were 21 μm and 26 μm at 532 and 760 nm, respectively. The PA lateral resolution in the AR-PAM mode was 60 μm. The US lateral resolution was 54 μm.
The laser pulse repetition frequency for qOR-PAM imaging was 2 kHz and the output power was 3.4 mW (1.7 μJ/pulse) for 532 nm light and 9.4 mW (4.7 μJ/pulse) for 760 nm light. The calculated light exposure on the surface was 0.26 mJ/cm2 for 532 nm pulses and 0.72 mJ/cm2 for 760 nm pulses. The PRF for AR-PAM was 10 kHz, and the power was 73 mW (7.3 μJ/pulse, 532 nm). The calculated light exposure on the surface was 0.65 mJ/cm2. In all cases, the illuminated light pulse energies were much lower than maximum permissible exposure (20 mJ/cm2 at 532 nm and 26.3 mJ/cm2 at 760 nm), which is stipulated by the American National Standards Institute.
2.2 Sample preparation
A fresh porcine stomach was obtained from a certified abattoir immediately after sacrifice, and the imaging experiments were performed within a few hours. To remove residual impurities, the inside of the stomach was washed with water. Then, the less curvature area was carefully cut away from the stomach, taking care to minimize blood leakage. Initially, the dissected gastric wall including whole layers (i.e., the mucosa, submucosa, muscularis propria and serosa) was photoacoustically and ultrasonically imaged from the inside of the stomach (i.e., from the mucosal surface) to acquire a mucosal image (Fig. 3(a)) mimicking the result of imaging endoscopy. Then, the mucosa, including muscularis mucosae, was removed to image the submucosa, and the sample was also imaged from the lumen side (Fig. 3(b)). Finally, the opposite side of the submucosal sample was imaged (Fig. 3(c)). After the imaging experiments, the samples were fixed with 10% formalin solution (approx. 4% formaldehyde) and stained with hematoxylin & eosin (H&E) for histology to validate the imaging results.
2.3 Image acquisition and processing
The entire 3D volume data measured 8 mm x 8 mm x 3 mm in the x, y, and z axes, respectively, and it was constructed by concatenating four single volume data of 2 mm x 8 mm x 3 mm along the x, y, and z axes, respectively. When combining the four single volume data, we used 3D PHOVIS to adjust the phase change of the scanner for the operating voltage, the offset distance between the imaging starting point and the scanner, and the scanning angle of the scanner . We also adjusted the azimuth, elevation, and zenith tilt of each volume to compensate for minor angular errors that occurred when the scanner was attached to the system. Each segmented volume data was apodized into the x-direction with a Hanning window to mitigate the edge distortion caused by the phase error of the MEMS scanner. To analyze the imaging depth, the surface of the stomach lining was estimated using the 3D PHOVIS software. To superimpose the PA images on the US images, the PA data were linearly interpolated by inserting the mean value between each pixel to compensate for the one-way reception of PA waves in PA imaging, as distinguished from the round-trip of US waves in US imaging. The cross-sectional overlaid PA and US images are all log-compressed. In the depth-encoded image, the colors are labeled according to their estimated distance from the surface, and the brightness is proportional to the amplitude of the PA signal.
Figure 4 shows PA and US images obtained from all the stomach samples in Fig. 3. The field of view of each image is 8 mm x 8 mm along the x and y axes, respectively, and the step sizes along the x and y axes are 10 and 20 μm, respectively. Each image is the result of a maximum amplitude projection (MAP, for PA) or maximum intensity projection (MIP, for US) along the axial direction after removal of the DC components, which is occurred during the analog-to-digital conversion process, and envelope detection processes. From left to right, the images in each row represent the experimental results for a mucosal sample (Figs. 4(a)–(d)), a submucosal sample (Figs. 4(e)–(h)), and a serosal sample (Figs. 4(i)–(l)). Each column shows the corresponding photographs, PA images at 532 nm, PA images at 760 nm, and US images in order. Although the opaque epithelium (red arrow in Fig. 4(a)) obscures the vasculature of the lamina propria in the photograph of the mucosal sample, the vascular networks are clearly distinguished in the PA image (red arrows in Figs. 4(b) and (c)). Notably, microvessels with diameters <∼30 μm are invisible in the photographs (white arrow in Figs. 4(a)), but they are clearly visualized in the PA images (white arrows in Figs. 4(b) and (c)). In the photograph of the submucosal sample, some blood vessels can be seen, but micro-capillaries are not identifiable (red arrow in Fig. 4(e)). The PA images, on the other hand, show the overall vasculature and tortuosity of the capillaries (red arrows in Figs. 4(f) and (g)). In the mucosal (Figs. 4(b) and (c)) and submucosal (Figs. 4(f) and (g)) PA images obtained at 532 nm and 760 nm, the vascular patterns match well with the photographs. Although the vessels are not directly distinguished in the US images (Figs. 4(d) and (h)), the acoustic shadows (red dashed lines) closely correlate with the vessel patterns. In the serosal sample images, although there appears to be some livor mortis caused by gravitational settling of blood during the mucosal and submucosal imaging (Fig. 4(i)), dense superficial capillaries are seen in the PA images and match well with the photograph (Figs. 4(j) and (k)).
Figure 5 shows cross-sectional PA and US images cut along lines #1 and #2 in Fig. 4(b). Figures 5(a)–(c) are images along line #1: a cross-sectional US image, an overlaid 532 nm PA and US image, and an overlaid 760 nm PA at and US image, respectively. Figures 5(d)–(f) are the corresponding images along line #2. In the US images (Figs. 5(a) and (d)), we can clearly distinguish the mucosal surface and the boundary between the epithelium and the lamina propria (blue dashed line). In addition, the cross-sections of a gastric gland (green dashed circles) and blood vessels (red dashed circles) are minimally discernable. The calculated thickness of the epithelium is 250 μm. In the PA images (Figs. 5(b), (c), and f), strong signals are observed at the top of the lamina propria along the epithelial boundary. As a result of simultaneous PA and US imaging, the stratified tissue structure and vasculature are complementarily acquired. In particular, the blood vessels (red dashed circles) and gastric glands (blue dashed circle), which are difficult to distinguished using US imaging alone, are clearly differentiated in the combined images. In this qOR-PAM mode, PA signals could be obtained from as deep as 0.95 mm at both 532 and 760 nm. Note that the penetration depth of PA imaging at 760 nm is not improved over that at 532 nm. The expected PA signal amplitudes at 532 nm are about 20 to 30 times higher than those at 760 nm, assuming that the oxygen saturation (SO2) of the blood is 80 to 90% based on their optical absorption coefficients . However, as mentioned above, the incident light pulse energy at 760 nm is 0.72 mJ/ cm2, the maximum output of the laser, but this value is only three times higher than that at 532 nm (0.26 mJ/ cm2). Since for normal tissue the reduced optical scattering coefficient at 760 nm is 1.49 times lower than at 532 nm , more laser pulse energy at 760 nm is certainly preferable for deeper penetration. Considering all these factors, the penetration depth of PA imaging at 760 nm could be improved. However, more laser pulse energy at 760 nm may still be preferable for deep penetration
To analyze the depth information of the blood vessels according to their depths from the mucosal surface, color-encoded depth image processing was applied to the 3D PA volume data in Fig. 4(f) (Fig. 6). First, the 2D surface profile was extracted from the 3D US data (yellow dashed line in Fig. 6(a)). After applying the same surface profile to the 3D PA volume data, each PA signal was labeled according to the distance from the surface (Fig. 6(b)). A color-encoded PA depth image covering the entire depth (e.g., 0–1 mm) is shown in Fig. 6(c). Branch vessels were located at a depth of about 0.4 mm from the surface (blue region indicated by blue arrow in Fig. 6(c)), and large vessels were found at a relatively deep depth of 0.6 mm (yellow region indicated by yellow arrow in Fig. 6(c)). In order to visualize the more detailed vascular networks, the color encoding process was compartmentalized according to the depth, (Fig. 6(d) and (e)). Figure 6(d) is the result of compartmentalizing the PA signals from 0 to 0.5 mm deep. After the compartmentalization, the microvasculature originating from the upper lamina propria is clearly distinguishable, which otherwise would be overwhelmed by the strong deep PA signals (red dashed circle in Fig. 6(d)). The compartmentalization from 0.5 to 1 mm is shown in Fig. 6(e). Depth encoding may be helpful in discriminating adenocarcinomas by detecting the angiogenesis caused by the tumor in the epithelial layer. Moreover, tumor infiltration to the basement membrane (the boundary between the epithelium and lamina propria) can accelerate metastasis and cancer progression, detecting such infiltration via compartmentalized images becomes even more useful.
The results above demonstrate that high-resolution imaging of the lamina propria is possible. However, because the average thickness of the mucosal layer is 1.26 mm in humans  (the thickness of the pig’s mucosal layer was 1.50∼1.87 mm in this experiments), the penetration depth of the qOR-PAM system is limited in distinguishing the T1b index indicating submucosal penetration. Therefore, deep tissue imaging experiments were performed using the AR-PAM system, where the optical fibers with 50 μm cores were replaced by fibers with 400 μm cores. We validated the overlaid PA/US image with the histological results (Fig. 7). Figure 7(a) is the cross-sectional overlaid PA and US image. In the US image, a strong US signal is generated in the epithelium, with a thickness of about 250 μm, indicating the boundary between the epithelium and the lamina propria (blue dashed line). Further, the boundary between the lamina propria and the muscularis mucosae (red dashed line) and the boundary between the muscularis mucosae and submucosa (yellow dashed line) are weakly discernable. The boundary between the submucosa and muscularis propria was also confirmed (green dashed line) by its strong US intensity. Various-sized blood vessels were photoacoustically identified in the muscularis mucosae (#1, #7), lamina propria (#2–#5), and submucosa (#6). Figure 7(b) shows the histological confirmation. The epithelium and lamina propria were stained purple, the muscle tissue was stained pink, and the red blood cells in the blood were stained red. The submucosa was distinguished by a loose connective tissue structure. The slight discrepancy in boundaries compared to the overlaid PA and US image is due to sample distortion (e.g., from dehydration) during tissue processing for histology and to the loosely connective nature of the submucosa, which is easily compressed and has an irregular thickness. Among previous clinical gastrointestinal endoscopic ultrasonography studies, there was a consensus that the mucosa-lining interface, the submucosa, and the submucosa-muscularis propria interface are hyperechoic, whereas the deep mucosa, muscularis mucosae, and deep muscularis are hypoechoic [38,39]. Hyperechoic US signals are visible above the blue dashed line and around the yellow and green dashed lines, in agreement with previous studies. Moreover, the blood vessels acquired in the PA images are clearly resolved up to the submucosal layer representing high correlation with the histological result. In the overlaid PA and US image, clearly verifiable vascular signals confirmed with the histology are obtained up to 1.9 mm from the mucosal surface. It can be inferred that the complementation of PA/US imaging can provide a stratified tissue structure and mucosal/submucosal vasculature, which is expected to be helpful in diagnosing the degree of tumor infiltration and angiogenesis in the corresponding layers.
Compared to the vigorous development of PAE research for preclinical GI tract applications, imaging study has been limited to small animals, such as rodents and rabbits. Although there have been attempts to image the porcine stomach with PAI, they suffered from low spatial resolutions, and consequently it was difficult to clearly identify the vasculature. Therefore, to investigate the feasibility of PA/US imaging of gastric stomach, we have developed a simultaneous multispectral PA and US microscopic imaging system which can image both acoustic and optical structures. Using this system, high-resolution PA/US 3D volume data was obtained in a single imaging procedure from the ex vivo porcine stomach layer. The gastric layers were clearly delineated in the US image, as are the microvasculature in the PA images, and the combinational imaging results were histologically validated. In this study, blood vessels were imaged as deep as 1.9 mm from the mucosal surface, supporting the feasibility of imaging to the submucosal layer. Considering the average thickness of the human mucosal layer (∼1.26 mm) , it is expected that the mucosa and submucosa could be fully visualized, which would allow for differentiation of Tis, T1a, and T1b tumors. Differentiation of T1a from T1b is clinically invaluable because it is an important index in determining whether to proceed with ESD or surgical resection. In addition, since there is a high correlation between angiogenesis in the submucosa and metastasis of cancer to lymph nodes, it may be useful to also determine if there is lymphovascular involvement through submucosal vascular imaging. Following this study, several experiments may be proposed to extend the work. First, we acquired PA signals only from an endogenous chromophore (i.e., hemoglobin). However, PAI with exogenous contrast agents could detect lymphovascular invasion. This improvement can be achieved by employing multi-wavelength laser sources and spectral analysis. In addition, the 1064 nm with high pulse energy would be a great option for deep penetration. Second, because our Ti:Sapphire laser is able to provide various optical wavelengths in the NIR band, SO2 in the microvessels can be potentially estimated. Third, in order for a feasibility study using PAM to have clinical significance for PAE, it should be able to translate the advantages of PAM into PAE. PAM has two main advantages over PAE. The first is optical and acoustic coaxial focusing through any size optical and acoustic lens and a beam combiner. Through this, PAM can obtain a high SNR. The second is the wide FOV through the raster scanning of the motor. For the first point, it is necessary to coaxially align the optical beam and the acoustic beam by applying a miniature beam combiner or a ring transducer or a transparent transducer to the PAE. For the second point, a MEMS or fiber scanner can be inserted to perform raster scanning of the x-y coordinate system at high speed. Further, since EGC is defined as cancer confined to the mucosa or submucosal layer, a qOR- or an AR-PA/US endoscope capable of imaging at least the entire submucosal layer must be developed.
In conclusion, we developed a system that can simultaneously acquire PA images and US images in the visible and near-infrared bands. In addition, by providing combined images of PA and US, for the first time, high-resolution vascular images and layered ultrasound images of the stomach wall of large animals are provided by superimposing them. This is expected to have a clinical impact by helping the differentiation of T-indicators and helping to diagnose EGC and ESD.
Ministry of Education (NRF-2020R1A6A1A03047902); Ministry of Science and ICT, South Korea (NRF-2019R1A2C2006269); Ministry of Health and Welfare (HI15C1817); Ministry of Science and ICT, South Korea (2020M3H2A1078045); BK21 FOUR project.
We would like to express our gratitude to the CEO Daeho Choi of Changsung livestock for helping us with the supply of experimental materials. Further, this research is performed based on the cooperation with POSTECH-LIG Nex1 Cooperation.
Chulhong Kim has financial interests in Opticho, which, however, did not support this work.
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.
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