Methods of extraction of optical properties from diffuse reflectance measurements of ex-vivo human colon tissue using thin film silicon photodetector arrays

: Spatially resolved diﬀuse reﬂectance spectroscopy (SRDRS) is a promising technique for characterization of colon tissue. Herein, two methods for extracting the reduced scattering and absorption coeﬃcients ( µ (cid:48) s ( λ ) and µ a ( λ ) ) from SRDRS data using lookup tables of simulated diﬀuse reﬂectance are reported. Experimental measurements of liquid tissue phantoms performed with a custom multi-pixel silicon SRDRS sensor spanning the 450 - 750 nm wavelength range were used to evaluate the extraction methods, demonstrating that the combined use of spatial and spectral data reduces extraction error compared to use of spectral data alone. Additionally, SRDRS measurements of normal and tumor ex-vivo human colon tissue are presented along with µ (cid:48) s ( λ ) and µ a ( λ ) extracted from these measurements.


Introduction
Inflammatory bowel diseases (IBD), Crohn's disease and ulcerative colitis, is associated with an increased risk of colorectal cancer. To detect cancer at an earlier and more treatable stage, colonoscopy surveillance is recommended for patients with IBD [1]. The present standard of care is to inspect the colonic lumen surface using white light endoscopy (WLE) and take random biopsies to detect dysplasia (abnormal cellular growth indicative of pre-cancer) and malignancy (cancer). While WLE is effective for the detection of some high-risk tissues such as colon polyps, other types of high-risk tissue, such as flat dysplasia, may not be visually observable to the physician by WLE [2,3]. The limited efficacy of WLE results in reduced adenoma detection rates, unnecessary resection of healthy tissues, incomplete resection of high-risk tissues, and necessitates random sampling of colon in patients known to be at elevated risk for flat dysplasia, such as patients with inflammatory bowel disease [2,3]. Patient outcomes for colon cancer can be improved if the capabilities of WLE can be augmented to readily detect the microstructural and biochemical characteristics of this disease during colonoscopy.
Diffuse reflectance spectroscopy (DRS) is a label free optical technique that has been established as an effective tool for optical characterization of human tissue, both by extraction of tissue optical properties [4][5][6][7], and by determining classifiers based on the spectral signatures of various tissues and conditions [8,9]. Measured DRS signals are sensitive to the concentrations of chromophores such as oxy-hemoglobin and deoxy-hemoglobin in tissue and can quantitatively measure these concentrations through measurement of the tissue absorption coefficient, µ a (λ) [6,10]. Similarly, DRS is sensitive to tissue microstructure and morphology because the difference in the optical refractive index between tissue structures such as cellular nuclei and collagen fibers and the surrounding components of tissue causes tissue to scatter light in a manner that is characteristic of that tissue [11]. The wavelength dependent scattering characteristic of light in tissue can be quantitatively measured with DRS by measurement of the reduced scattering coefficient, µ s (λ) [6,7].
DRS can be used to sense the morphological and biochemical changes that occur when normal colon tissue becomes pre-cancerous or cancerous [4,12,13], and thus, DRS has the potential to augment the performance of traditional WLE. However, the reliance of conventional DRS systems on optical fibers for reflectance collection limits system performance, limits scalability, and constrains the design options. In contrast, custom thin film silicon (Si) photodetectors (PDs) offer a high performance, scalable, and highly customizable alternative to optical fibers for reflectance collection in tissue DRS applications [14][15][16][17][18]. Si PDs improve performance over optical fibers since they have higher numerical apertures (NAs) and collect light from a larger fraction of the probe surface, they are highly scalable due to Si manufacturing technology, they can be geometrically optimized for specific applications, they can be implemented on a variety of substrates, including flexible or conformal, and they can be implemented in the instrument channel or as an attachment to an endoscope. Importantly, arrays of Si PDs can be used to perform spatially resolved DRS (SRDRS), which adds a spatial dimension to DRS by simultaneously measuring the tissue reflectance at multiple illumination-collection distances.
Previous reports on the development of a custom Si thin film multi-pixel endoscopic optical sensor (MEOS) leveraged the advantages of thin film Si PD based SRDRS systems for endoscopic applications such as colonoscopy [18]. A conceptual diagram of the system used to perform measurements with the MEOS is provided in Fig. 1. The MEOS consists of three concentric semi-annular 10 µm thick Si PDs bonded to a transparent glass substrate. The three Si PDs surround a shared 750 nm diameter illumination aperture, with at increasing mean radii of 450 µm, 540 µm, and 860 µm, for PDs 1, 2, and 3, respectively, and increasing PD widths of 58 µm, 100 µm, and 550 µm, respectively. The geometries of the custom PDs were optimized for measurement of colon tissue, and the MEOS was fabricated using standard Si microfabrication techniques [18]. The tissue (or tissue phantom) measured by the MEOS is interrogated by photons provided by an optical fiber coupled to the backside of the transparent glass substrate. Photons pass through the glass substrate and through the circular illumination aperture at the center of the three concentric PDs before sampling the tissue under measurement. Reflectance data is collected with the PDs in direct contact with the tissue and collected photons that have sampled the tissue are converted to electrical signals by the PDs [18]. Each of the three PDs in the MEOS system measure relative diffuse reflectance, as described by Eq. (1): where I meas (λ) is the photocurrent generated by each PD due to light that has sampled the medium under measurement as a function of wavelength (λ), I ref (λ) is the photocurrent recorded during measurement of a reference phantom or reflectance standard, and both photocurrents have been calibrated to remove background current. Here, we report on the development of extraction of colon tissue optical properties (µ s and µ a ) from SRDRS measurements made using the prototype MEOS system, and demonstrate the extraction of tissue optical properties from MEOS measurements performed on normal and tumor ex-vivo human colon tissue.

Inverse model background
Methods to extract scattering and absorption from DRS spectra generally involve fitting a forward model to DRS measurements [6,7,[19][20][21][22][23][24]. Forward models used for fitting include Monte Carlo (MC) [6], analytical models such as the diffusion approximation [23], and hybrid empirical-analytical models [24]. These approaches entail trade-offs between the computational time and the accuracy of the measured optical properties. Iterative fitting of forward MC models is highly accurate but slow, fitting of analytical models is fast but has undesirable inaccuracy [6], and empirically fit models can be highly accurate but require time consuming experimentation to calibrate each system [21]. Approaches have been taken to minimize the computational time of forward MC models [6], and to minimize the number of calibration measurements needed to implement an empirical model [25], but tradeoffs between accuracy, speed, and experimental overhead are still significant [22]. Another class of inverse models utilizes pre-calculated lookup tables (LUTs) of either MC modeled or experimentally measured reflectance [21,22]. If appropriate values of anisotropy (g) can be estimated for a tissue, and approximations of the spectral dependence of the dominant chromophores and scattering events can be assumed, LUTs offer the advantage of reduced computational time without compromising the accuracy of the modeling method.
Because the MEOS utilizes a multi-pixel PD, it is possible to develop two LUT extraction methods: one that computes the best LUT fit for each PD separately, and a second that computes the LUT fit for all three PDs simultaneously. In the following section these two extraction methods are developed, and then the extraction accuracy of the two methods is evaluated using experimentally measured MEOS data from eight validation tissue phantoms.

Description of LUT optical property extraction methods
Development and evaluation of MC populated LUT inverse models for the extraction of colon optical properties using the MEOS probe were based on the system in Fig. 1, using initial measured phantom and MC forward modeling studies previously reported [18].
The two methods of optical property extraction using LUT based inverse models evaluated herein are: (1) A spatially resolved LUT (SR-LUT), which extracts three pairs of optical properties (µ s and µ a ) at each measured wavelength (one pair for each of the three PDs); and (2) a new spatially constrained LUT (SC-LUT) method, enabled by the multi-pixel PDs, which extracts a single pair of optical properties for each measured wavelength. This SC-LUT method uses the reflectance from all three PDs simultaneously to extract µ s and µ a , treating the sensed volume as homogeneous. Both methods are spectrally constrained by predefined µ s and µ a wavelength-dependence, as described by Eq. (2) and Eq. (3).
For both methods, LUTs were generated for each PD by MC modeling reflectance for varied absorption and reduced scattering values. A total of 6000 MC simulations implemented in a graphics processing unit (GPU) enabled open-source MC light transport simulator [26,27] were performed to populate LUT reflectance for each of the three PDs with a uniform grid of 30 µ s levels and 200 µ a levels. The light source was modeled as a cone with a divergence angle of 20°and a diameter of 750 µm at the illumination aperture. The refractive index for the modeled phantoms was 1.32 (water), and the refractive index of the detectors was 2.05 (due to the SiN coating on Si PDs). The reduced scattering coefficients (µ s ) ranged from 0.1 mm −1 to 3.1 mm −1 , and the absorption coefficients (µ a ) ranged from 0.00 mm −1 to 3.25 mm −1 , spanning the range of optical properties reported for colon tissue in the wavelength range from 450 nm to 750 nm [5,[28][29][30][31]. All simulations were performed with the Henyey-Greenstein (HG) scattering phase function [32] and an anisotropy value of 0.92, which is close to the reported values of anisotropy for colon tissue for this wavelength range [33], and is also the average anisotropy of 1 µm polystyrene spheres in de-ionized (DI) water (polystyrene spheres were used to prepare liquid validation phantoms for extraction accuracy evaluation). The use of the HG rather than the Mie or another phase function was motivated by the availability of GPU-enhance MC modeling software [26,27], and was justified by previous work forward MC modeling the MEOS system using the HG phase function, where less than 10% MPE was achieved [18]. 2D interpolation was used to define diffuse reflectance surfaces DR LUT (µ s (λ), µ a (λ)) for µ s and µ a values between and including the 6000 forward modeled pairs, using the MATLAB function griddedInterpolant [34]. Generation of the LUTs required approximately 20 minutes running on an Intel i7-8550U CPU with 16 GB of memory and an NVIDIA GeForce MX150 GPU. Comparison of forward modeling of phantom reflectance performed with a 3D as well as 2D simulation space indicated that a 2D model was justified, which permitted the propagation of a small number of photons per run (10 4 ). Figure 2 displays the reflectance surfaces for each of the three PDs. The MC modeled reflectance, which is computed as absolute reflectance, was scaled by a MC modeled reference medium with zero absorption to generate relative reflectance for comparison to experimental results. Likewise, experimental measurements of a single phantom prepared with the reference phantom optical properties were used to scale all experimental results. Measured reflectance spectra are fit to the LUT surfaces using nonlinear least squares minimization implemented with the lsqnonlin function in the MATLAB Optimization toolbox [35]. A commonly used approximation for µ s (λ) was adopted [19,36,37], as described by the following Eq. (2): where A and B are coefficients that describe the power-law wavelength dependence of the reduced scattering coefficient. The absorption coefficient, µ a (λ), was calculated using the wavelength dependent extinction coefficients of oxyhemoglobin and deoxyhemoglobin, ∈ HbO2 (λ) and ∈ Hb (λ) where C and D are the volume averaged total hemoglobin concentration and hemoglobin oxygen saturation, respectively [19,36,37]. Optical property extraction was achieved by fitting measured relative reflectance, DR MEOS (λ), to the LUT by finding values of A, B, C, and D which minimized the sum of squares difference between DR LUT (µ s (λ), µ a (λ)) and DR MEOS (λ), where DR LUT (µ s (λ), µ a (λ)) is the relative diffuse reflectance queried from the MC generated LUT at the values µ s (λ) and µ a (λ). For the fitting process, the diffuse reflectance magnitude was scaled by the light-collecting surface area of each individual PD, A PD . For the SR-LUT method, the minimization occurs for each PD separately, and is described by Eq. (4): (4) where f (A, B, C, D) defines the reduced scattering and absorption coefficients through Eqs. (1) and (2). Minimization using Eq. (4) results in extraction of µ s (λ), and µ a (λ), for each of the three PDs independently, providing spatially resolved optical property extraction. In the case of measurements at N wavelengths, the dimension of the function being minimized is N × 1.
Alternatively, for the SC-LUT method, all three of the PDs are evaluated simultaneously: the radial dependence of the reflectance is included in the modeling to increase the dimension of the minimization function to N × 3. In this case, DR LUT , and DR MEOS (λ) are N × 3 matrices, A PD is a vector of all three PD areas, and the minimization is described by Eq.
where the minimization across the three PDs is included by the term PD . A result of using the SC-LUT method of Eq. (5) is that the extracted optical properties are volume averaged over the entire sensed volume.

Experimental evaluation of the inverse method of optical property extraction
To evaluate the performance of the SR-LUT and SC-LUT for optical property extraction, eight liquid phantoms for validation were prepared with 1 µm diameter polystyrene spheres (Polysciences, Inc.) as the scattering agent, powdered hemoglobin (Sigma-Aldrich Co. LLC.) as the absorbing agent, and deionized (DI) water as the solvent. Optical absorption coefficients for the phantoms were calculated by measuring the absorption coefficient for concentrations of hemoglobin powder dissolved in DI water by a spectrophotometer (Shimadzu UV-3600) and calculating the extinction coefficient for the purchased hemoglobin chromophore. Based on the spectrophotometer resolution of measured extinction coefficients and precision of the microbalance used to prepare phantom solutions, the error in the theoretical value of µ a was estimated to be approximately 1%. Reduced scattering coefficients for the solutions were calculated using an open-source program for calculating scattering from Mie theory [39]. The optical properties of the eight validation phantoms, as well as the reference phantom used for scaling in the wavelength range 450-750 nm at 10 nm wavelength intervals are shown in Fig. 3. The accuracy of the theoretical values of µ s calculated by Mie theory was primarily limited by the 3% coefficient of variance for the polystyrene scatterers [40]. The values of µ s (λ) shown in Fig. 3 and calculated by Mie theory for 1 µm diameter polystyrene spheres can be fit by Eq. (2) with 1.1% root-mean-square error, averaged across the 31 wavelengths used for validation. Phantoms were measured with the probe surface placed into the liquid phantom solution such that the entire front face of each PD in the array was immersed. Illumination for all DRS measurements was provided by a 1 mm diameter optical fiber with a 0.39 NA (Thorlabs FT1000UMT). A 300 W Xenon lamp coupled to a Newport CS130 monochromator (TLS-300XU, Newport Corp.) provided the optical input to the 1 mm fiber and thus, to the MEOS probe. The PD photocurrents were measured using transimpedance amplifier (TIA) arrays. The TIA system used Texas Instruments TI IVC102 TIA chips for current integration, Adafruit ADS1015 chips for analog-to-digital conversion, and an Arduino Mega 2560 microcontroller to control integration times and data acquisition. All measurements with the TIA system were performed with a 100 ms integration time. For the phantom measurements performed between 450 nm and 750 nm, 4 minutes was required to acquire data at these 31 wavelengths. The TIA system and the monochromator were controlled using LabView. Repeated measurements of the same phantom without removing the MEOS device did not alter the measured reflectance more than 1% on average, thus settling of the phantoms was not considered to be a problem.
The performance of each of the two LUT inverse models described herein was quantified by the mean absolute value percent error between the values of µ s (λ) and µ a (λ) calculated for each phantom based on their concentrations of hemoglobin and polystyrene spheres, and the corresponding values extracted from the measured reflectance using the SR-LUT and SC-LUT inverse models. The values of µ s (λ) and µ a (λ) calculated from the phantom hemoglobin and polystyrene spheres are referred to herein as the theoretical values. For µ s (λ), the overall average error (averaged across all wavelengths and all three PDs) decreased from 13.25% to 6.38% going from the SR-LUT model to the SC-LUT model, and for µ a (λ) the overall average error decreased from 31.42% to 8.38%. The time required to extract µ s (λ) and µ a (λ) for each phantom was about 10 seconds for either the SR-LUT or the SC-LUT, but the extraction algorithm was not optimized for extraction speed. The MPE on for each of the three PDs for the SR-LUT model for µ s is 12.9%, 7.0%, and 19.9% for PDs 1, 2, and 3, respectively. For µ a , the MPE is 16.5%, 11.9%, and 65.9% for PDs 1, 2, and 3, respectively. While the error for µ a on PD 3 is higher than the error on the other two PDs, and the error on µ s for PD3 is higher than for the other PDs, differences in error on PD1 and PD2 are less pronounced. The difference may be due to lower signal magnitudes incident on PD3, which is furthest from the illumination source for low albedo phantoms. Additionally, some  amount of variation of reflectance agreement with modeling results could arise from sub-diffuse reflectance components. Researchers [41,42] have recently indicated that at short radial distances, higher order moments of the photon scattering phase-function may influence reflectance by as much as 10% [41], suggesting that in order to achieve the lowest possible discrepancy between experimental measurements and modeling, a higher order function than the Henyey-Greenstein phase function may be more desirable, and should be investigated in future studies of the MEOS system. Additionally, while prior researchers [6,43,44] have demonstrated that µ s may be used to accurately characterize scattering well beyond the 'diffusion approximation' [45], future work should investigate whether higher dimension LUTs could be implemented to improve extraction accuracy by accounting for sub-diffuse effects. However, for the purposes of achieving sufficient agreement between modeled and experimental reflectance for our system (<10% MPE) to enable comparison of optical property extraction methods, we believe that the Henyey-Greenstein phase function employed in this work is valid [18].
A clear improvement in extraction accuracy is achieved by extracting reduced scattering and absorption coefficients with the SC-LUT method compared to the SR-LUT method. This result is consistent with the findings of Tseng et al. [19], who found a similar improvement in optical property extraction accuracy by using both the spatial and spectral components of the diffuse reflectance collected by a fiber-based system, although the inverse model of Tseng et al. was based on iterative MC simulation rather than on LUTs. Using all three PDs together decreases the average extraction error to less than any individual PD would be able to achieve alone, as summarized by Table 1. A disadvantage of the SC-LUT method is that the output data loses possible depth information for each individual wavelength, since the tissue volume sampled by all three PDs is different and larger than for any single PD. Thus, the extracted optical properties from the SC-LUT are averaged over a larger volume than the properties extracted by the SR-LUT. For application to layered tissue (e.g. colon), the volume-averaged nature of optical properties measured with DRS should always be considered when analyzing experimental results and is especially important when comparing measurements with a different resolution of volume-averaging. While averaging over a larger volume with the SC-LUT compared to the SR-LUT is disadvantageous because it reduces the volume resolution of each probe measurement, it may also be advantageous because by averaging tissue measurements over a larger area, volume inhomogeneities, such as blood vessels, may be less likely to distort the measurements. Distortion of DRS measurements by blood vessel packaging of hemoglobin has been a criticism of DRS as a tissue diagnostic tool [46].

Human tissue measurement experimental procedure
Measurements of human colon tissue have been conducted, and the preliminary results described herein. The procedure for the human tissue study was developed to collect MEOS measurement data from excised human colon specimens within 30 min after resection from patients undergoing colectomy, where the colon was expected to have locations of tumor as well as normal tissue. This approach facilitated measurements on normal and tumor human colon tissue in as near as possible a biological condition to in-vivo tissue, but with minimized patient risk. The primary aim of the study was to determine the ability of the MEOS to quantitatively characterize absorption and scattering characteristics of different types of human colon tissue. To enable evaluation of measured tissue spectra with known histology, MEOS measurement locations were co-registered to a surgical biopsy by triangulating each MEOS measurement location using three sutures, which enabled tissue sections to be taken at each location for histopathologic analysis. For each wavelength measured at each location, the MEOS system recorded 30 consecutive TIA current readings with an integration time of 100 ms for each TIA measurement. For measurements on human tissue, reflectance at 24 total wavelengths from 450 nm to 680 nm were recorded, requiring 3 minutes total acquisition time. Tissue optical properties are sensitive to applied pressure due to changes in blood perfusion as well as cellular crowding [47,48]. To ensure that a consistent force was applied by the sensor to the tissue being measured, the approach of Nichols et al. [49] was followed, where a custom pressure sensitive stage was developed consisting of an aluminum plate resting on four 5 lbf load cells. Prior to and following each set of human tissue measurements, the MEOS was measured on a reflectance standard (puck).

Human tissue measurement results and discussion
Preliminary MEOS measurements were performed on a single excised human colon, including two measurements performed at a single normal tissue location, and two measurements performed at a single tumor location to assess repeatability. During these repeated measurements, the MEOS probe was removed from contact with the tissue between measurements at the same location. The average percent difference between repeated measurements was 7.7%. The DRS spectra from these four measurements are displayed in Fig. 6, with a separate subplot for each of the three PDs, and error bars representing the standard deviation of the reflectance at each wavelength. The optical absorption and reduced scattering coefficients, µ a and µ s , were extracted from the DRS data shown in Fig. 6 using the SC-LUT inverse method detailed in Section 2, using the same LUTs generated for evaluation of the two inverse methods. The values of µ a and µ s extracted from these human colon tissue measurements are plotted in Fig. 7. Error bars on the data points plotted in Fig. 7 represent the average error observed at each wavelength for extraction of µ a and µ s from the eight validation phantoms shown in Fig. 3. Although the optical properties plotted in Fig. 7 represent only a single site of each type of tissue for a single patient, they are still an interesting contribution to the literature because they were measured on ex-vivo tissue which was freshly excised and underwent minimal sample preparation (not frozen). The majority of reported optical properties for human colon tissue have been performed on tissue samples that have undergone freezing and thawing [5,29,30,50], which can significantly alter tissue optical properties [51]. Fig. 7. Tissue absorption and reduced scattering coefficients extracted from the spectra provided in Fig. 7, with error bars, using the SC-LUT method. One the right, H&E-stained tissue sections of the two measured locations are displayed (both photomicrographs at 4x magnification, bar = 500 µm).
Values of µ a and µ s for human colon tissue reported in the literature span a broad range. For example, at 500 nm, the value of µ a for normal tissue ranges from 0.22 mm −1 [5] to 0.84 mm −1 [52], and for precancerous tissue from 0.37 mm −1 [31] to 0.60 mm −1 [5]. For µ s , previously reported values for normal tissue range from 0.79 mm −1 [5,52] to 2.1 mm −1 [31], and for precancerous tissue from 0.55 mm −1 [5] to 2.36 mm −1 [31]. While the µ a and µ s values for normal and tumor presented in Fig. 7 are not completely bracketed by previously reported values, the values are consistent given the large span of values reported. It is important to emphasize however, that the results presented here are representative for only one patient, and that the intention of including these results is to demonstrate the potential for applying the MEOS system to colon tissue optical property extraction, rather than validation of this technique's viability as a diagnostic tool.

Summary and conclusions
This paper describes and evaluates two inverse methods for extracting the reduced scattering and absorption coefficients, µ s (λ) and µ a (λ), from reflectance measurements using the MEOS probe. Both extraction methods rely on lookup tables of Monte Carlo simulated diffuse reflectance. The first method, the SR-LUT method, extracts µ s (λ) and µ a (λ) for each MEOS PD independently, yielding spatially resolved information. The second approach, the SC-LUT method, spatially constrains the extracted µ s (λ) and µ a (λ) to the same values for each of the three MEOS PDs, yielding less error between the theoretical (true) and extracted absorption and reduced scattering coefficients. Eight liquid phantoms composed of polystyrene spheres and hemoglobin in deionized water were measured to experimentally evaluate the performance of these inverse methods on values of µ s (λ) and µ a (λ) that spanned the range of reported values for colon in the 450-750 nm wavelength range. The SC-LUT was found to decrease the average extraction error of µ s (λ) and µ a (λ) from 13.25% and 31.42%, respectively, to 6.38% and 8.38%, respectively. Additionally, preliminary measurements of ex-vivo human colon tissue were presented, and the optical properties µ a and µ s were extracted from human tissue MEOS measurements that had less than 10% variation between repeated measurements. The MEOS multi-pixel custom Si PD probe extracts both spatial and spectral information with each measurement, and the use of the SC-LUT is able to leverage both spatial and spectral information together to yield lower tissue absorption and scattering coefficient extraction error compared to the use of the similar SR-LUT extraction method, which relies on spectral information alone.