1. Introduction

Cancer is a severe threat to human health. Currently, 25% of all deaths in the United States come from cancer[1]. Early detection of cancer is considered the best way to increase the chance for survival. However, the traditional technique for the detection, biopsy, is invasive. Diagnostic optical spectroscopy, a minimally invasive approach, can detect biochemical and morphological changes indicative of neoplastic progression [2]. This technique has a potential to revolutionize the clinical management of cancer by facilitating the localization of biopsies or, eventually, eliminating their need altogether.

Biomedical spectroscopy typically involves delivery of light, and collection of reflected light or fluorescence remitted from the tissue. In most cases, both incident and collected light are within the ultraviolet A (UVA, 320–400 nm) and visible (VIS, 400–750 nm) spectral regions. Biochemical constituents such as collagen, elastin, keratin, NADH, flavin adenine dinucleotide and porphyrin contribute to detected fluorescence spectra. Both fluorescence and reflectance are also influenced by chromophores such as hemoglobin and water as well as scatterers such as cell constituents, tissue fibers and the interfaces between structural components. The transport of light in a tissue is dominated by the fundamental optical properties (OP) of the tissue-the absorption coefficient (μ_a), the scattering coefficient (μ_s), the anisotropy coefficient (g), and the index of refraction of the tissue (n). To reduce complexity, μ_s and g are often lumped into a reduced scattering coefficient [μ_s′=μ_s (1-g)].

Since many diagnoses, especially fluorescence-based detections of neoplastic lesions, are carried out within UVA-VIS wavelength range, establishment of an efficient and robust model to elucidate light-tissue interaction effects and extract μ_a and μ_s′ of the tissue in these ranges are necessary. In recent years, significant progress has been made in the development of fiberoptic techniques for measuring tissue optical properties within the UVA-VIS wavelength range. These approaches make it possible to characterize internal tissues in situ, including via endoscopic delivery. They also enable measurements of intact ex vivo tissues, as opposed to prior ex vivo techniques which involved freezing, sectioning or homogenization, which may change the tissue optical properties. Amelink, et al., [3] demonstrated the capability of differential path-length spectroscopy which consisted of two bifurcated optical fibers to determine the local optical properties of a tissue. Moffitt, et al., [4] constructed a sized-fiber spectroscopy system consisting of two fibers with diameters of 200 and 600 µm and tested the system in the μ_a range of 0.1-2.0 cm^-1 and μ_s′ range of 5-50cm^-1. Each fiber emitted and collected its own backscattered light. Sun, et al., [5] developed a diffusion-theory-based inversion method for the extraction of tissue optical properties from in vivo spectral measurement ranging from 350 nm to 650 nm with a cylindrical optical fiber probe. The probe was composed of a central collection fiber surrounded by six hexagononally close-packed illumination fibers. The tissue optical properties used in their study were μ_s=40–100 cm^-1, μ_a=0.1-2.5 mm^-1, and g=0.84. Thueler, et al., [6] described a fast spectroscopic system for superficial and local determination of the absorption and scattering properties of a tissue with a probe composed of eleven linearly arranged optical fibers, one for illumination and ten for detection. Palmer, et al., [7] identified an optimal probe geometry which consisted of a single illumination and two collection fibers. They found that μ_a ranging from 0 to 80 cm^-1 and μ_s′ ranging from 3 to 40 cm^-1 could be extracted from reflectance with root-mean-square (RMS) errors of 0.30 cm^-1 and 0.41 cm^-1 respectively using this probe geometry in conjunction with a neural network algorithm. This was only a purely theoretical study without any experiments.

In prior studies by our group, Pfefer, et al., [8] developed a neural network algorithm for the extraction of μ_a and μ_s′ from spatially resolved diffuse reflectance. Reflectance datasets for development of the neural network were generated by direct measurement of Intralipid-dye tissue phantoms at 675 nm and Monte Carlo simulation of light propagation with μ_a 1–25 cm^-1 and μ_s′ 5–25 cm^-1. The algorithm was able to extract μ_a and μ_s′ of the phantoms to within RMS errors of ±2 and ±3 cm^-1, respectively. Sharma, et al., [9] improved on this system by implementing an imaging spectrograph, high sensitivity CCD camera and in-line neutral density filters to maximize dynamic range and signal to noise ratio. With a similar algorithm the new system estimated μ_a and μ_s′ values with average errors of 4.0% and 5.5%, respectively.

Fiberoptic-based systems for tissue optical property measurement often combine reflectance spectroscopy hardware with software for forward and inverse modeling. The hardware includes laser[4, 10–12] or broadband [3, 5, 13, 14] light sources, a probe with multiple optical fibers, one or more detectors, and a computer. The design of the probe – a bundle of illumination and detection fibers arranged in a well-defined geometry – is a key issue during system construction. Forward models can be categorized as analytical or numerical. An analytical model is usually an approximation of the radiative transport equation. Light propagation in a tissue can be described by an integrodifferential equation of radiative transport whose general analytic solution does not exist [15]. A diffusion approximation of radiative transport is often applied to obtain a closed-form analytical solution [16, 17]. Analytical models are more elegant in principle since reflectance/transmittance can be expressed in a closed-form in terms of optical properties. However, the specific experimental conditions for which they apply are often simplified and the modeling equations are sometimes difficult to solve. Numerical models, however, enable incorporation of any source-tissue-detector geometry. Monte Carlo modeling, which uses random numbers and statistics to find solutions to mathematical problems that cannot be easily solved, is a common numerical model for estimating light propagation in a tissue. The Monte Carlo method has long been recognized as a powerful tool to solve problems that are too complicated for an analytical solution. Since the first paper that introduced Monte Carlo simulation of laser-tissue interaction [18], numerous improvements have been made[19–22]. Published works that provide a detailed description of the Monte Carlo approach as applied to light transport are available in the literature [23, 24]. Because the Monte Carlo method is computationally intensive, various techniques have been developed to improve its efficiency[25, 26]. The condensed Monte Carlo simulation introduced by Graaff, et al., [26] is theoretically transparent and relatively easy to implement. Palmer and Ramanujam[27] extended Graaff, et al., condensed Monte Carlo method from a point source to a beam source by convolution.

By training an inverse model on the relationship between optical properties of a sample and its reflectance distribution, it is possible to develop a model that can readily calculate the optical properties of any sample based on the spatially-resolved reflectance distribution measured from that sample. Neural network is an empirical method that is commonly used to develop inverse models for optical property determination[8, 9, 28]. While primarily used as an inverse model, it can also be used as a forward model to quickly determine reflectance distributions for arbitrary optical properties. Inverse neural network models for optical property determination require calibration with datasets that establish the relationship between sample optical properties and reflectance distribution. These datasets can come from phantom measurements [8], Monte Carlo simulations [9], or analytical models like diffusion theory [28].

Although the literature contains a wealth of data on tissue optical properties in the far visible (600–750nm) and near-infrared range (750–1400nm), there is a lack of information in the UVA to short VIS range where μ_a and μ_s′ may be high. Furthermore, there is a lack of established experimental and numerical approaches that are suitable for use in this spectral range. In this paper, we provide theoretical and experimental evidence of the capability of our novel system to yield accurate optical property measurements within the UVA-VIS wavelength range. We developed a neural network inverse model for the extraction of μ_a and μ_s′ from spatially resolved diffuse reflectance. The neural network algorithm was trained and evaluated on thousands of condensed Monte Carlo simulation datasets, and then tested by extracting optical properties from phantoms or tissues. The algorithm can be used in a wide range of optical properties with μ_a ranging from 0.1 to 85 cm^-1 and μ_s′ ranging from 0.1 to 118 cm^-1, which covers most of the optical properties of mammalian tissues within the UVA-VIS wavelength range. The experimental component of this study involves development of a multi-wavelength fiberoptic reflectance system for optical property measurement and validation of its performance using tissue-equivalent phantoms within the UVA-VIS wavelength range. With the fiberoptic reflectance system and the neural network inverse model, optical properties of porcine tissues within the UVA-VIS wavelength range were measured and analyzed.

2. Methods

In this investigation, a forward Monte Carlo simulation was run, followed by condensed Monte Carlo simulations to extend the datasets. With the datasets from condensed Monte Carlo simulations, inverse neural network models were developed. Then a fiberoptic reflectance system was constructed and calibrated with phantoms. A Matlab^® (The MathWorks, Inc.) routine, which would call the inverse neural networks and was coupled into the LabView virtual instrument software, was applied to extract μ_a and μ_s′ from the measured reflectance with the system. The whole system including the developed models was in vitro validated with phantoms and was finally used to measure porcine tissues ex vivo. Figure 1 shows the flow chart of this investigation.

 

Fig. 1. Flow chart of the investigation

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2.1 Condensed Monte Carlo modeling

Spatially resolved diffuse reflectance was calculated with a condensed Monte Carlo approach [26, 27]. Light propagation in a medium with absorption coefficient of 0 cm^-1(μ_a,sim), scattering coefficient of 150 cm^-1 (μ_s,sim), and g=0.9 was simulated with a elementary Monte Carlo model at first. It should be noted that non-zero μ_a,sim values can also be used in this simulation. The Henyey-Greenstein phase function was used to mimic the scattering angle. The index of refraction (n) of the fibers was 1.45 and n=1.37 for tissues. The numerical aperture (NA) for both the illumination and collection fibers was 0.22. The incident light was a ray or “pencil beam” source from which 40,000,000 photons were launched in a uniform distribution over all angles within the cone specified by NA=n·sinθ, where θ is the incident/acceptance angle measured from the normal to the tissue surface. For each detected photon which was governed by the acceptance angle, the number of interactions with scatterers (N), the distance from entrance to exit (r_sim), and the weight of the remitted photon (W_sim) were recorded. The value of W_sim was determined according to standard Monte Carlo approaches including weight reduction due to specular reflectance and absorption (in our case, the latter was minimal)[23, 24]. In order to simulate a medium with new absorption coefficient (μ_a,new) and scattering coefficient (μ_s,new), scaling was performed for each photon to obtain the new distance from entrance to exit (r_new) and the new weight of the remitted photon (W_new) according to following equations (note that the following represent the general forms, whereas in our specific case, μ_a,sim is zero)[26, 27]:

Since the probe’s illumination fiber was not a ray source, the following convolution equation [27] was used to calculate the probability (p) of a photon being collected by a collection fiber with radius r_c after traveling a distance of r_new from an illumination fiber with radius r_i.

where s was the center to center distance between illumination fiber and detection fiber. This convolution equation was only used if s≥r_i+r_c and s-r_i-r_c<r_new<s+r_i+r_c, otherwise, p=0. Therefore, the collected weight (W_collect) of a photon by the detection fiber was calculated by the following equation.

The reflectance from a collection fiber was obtained by dividing the sum of total collected weight by the total number of launched photon.

By applying above condensed Monte Carlo technique, reflectance datasets within a wide range of optical properties in μ_a (0.1-85 cm^-1) and μ_s′ (0.1-118 cm^-1) were generated. In total, 2805 datasets with even spacing of 2.5 cm^-1 for both μ_a and μ_s′ while μ_a>30 cm^-1 and μ_s′>5 cm^-1 and smaller spacing while μ_a<30 cm^-1 or μ_s′<5 cm^-1 were obtained, as well as 220 random datasets.

The geometry used in the condensed Monte Carlo simulations replicated the design of our fiberoptic probe. A diagram of the probe face is shown in Fig. 2. The probe contains linearly arranged fibers, a single illumination fiber and five detection fibers, spaced at consecutive center-to-center distances of 0.5 mm. The core diameter of each fiber is 0.2 mm with a NA of 0.22.

 

Fig. 2. The 4mm diameter face of the fiberoptic probe

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2.2 Development and evaluation of neural network models

Reflectance datasets generated with the condensed Monte Carlo simulations were used to train and evaluate feed-forward back-propagation neural network models with the Neural Network Toolbox in Matlab^®. The input vector for each network (sometimes referred to as an “input layer”) consisted of 2–5 reflectance values corresponding to the number of detection fibers used. The network also contained two hidden layers of seven neurons each with logarithmic sigmoid transfer functions, and an output layer of two neurons with linear transfer functions. The output vector consisted of the absorption and reduced scattering values. A Levenberg-Marquardt backpropagation training function was used. The number of neurons came from our optimization results. The reflectance datasets used for training included 2805 optical property combinations determined from the condensed Monte Carlo model. Two-thirds of these datasets were used for training and one-third of them were used for evaluation during training.

In order to identify appropriate model designs for performing optical property estimations, we evaluated the influence of detection fiber quantity (i.e., the size of the input vector). This analysis was performed using simulation datasets both with and without the addition of artificially generated noise. A set of four neural network models, based on 2, 3, 4 and 5 detection fibers was generated and trained within the optical property range of 0.1-85 cm^-1 for μ_a and 0.1-118 cm^-1 for μ_s′.

2.3 Reflectance system construction and calibration

A multi-wavelength, fiberoptic diffuse reflectance system was developed as illustrated in Fig. 3. The system included five laser sources with wavelengths of 325 nm, 375 nm, 405 nm, 445 nm and 543 nm. The power output of the lasers was approximately one milliwatt except the 543 nm laser whose power output was about 50 μW. The laser sources were coupled via a fiber switch to a linear array fiberoptic probe (Fig. 2). The diffuse reflected light was collected via five detection fibers at different distances from the illumination center and recorded as a spectrogram with a high-sensitivity charge-coupled device (CCD) camera (Princeton Instruments, Inc.). In-line neutral density (ND) filters were applied to attenuate signals in some fibers and thus maximize the dynamic range. A LabView (National Instruments Corporation) routine was developed to control the instrumentation, acquire data and calculate the reflectance based on calibration results described below.

Data from the CCD camera is a 2-D matrix that represents light intensity in each pixel. For each detection fiber, the reflectance is the fraction of incident light from the illumination fiber that is collected by this fiber. It is proportional to the ratio of intensity per unit time from this fiber to the incident power (measured with a power meter) or the ratio of intensity within the exposure time from this fiber to the incident energy within the exposure time. These relations can be expressed by the following equations:

where P is the power of light collected through a detection fiber in watts, P₀ the incident power from the illumination fiber in watts, I the dimensionless intensity from CCD camera, t the exposure time in seconds, and E₀ the incident energy within the exposure time in joules. Therefore, there is a linear relation between the reflectance and the intensity per unit energy of illumination light for each detection fiber as shown below:

where k is a constant for a given detection fiber at a given wavelength in joules.

 

Fig. 3. Multi-wavelength, fiberoptic diffuse reflectance system for optical property measurement

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The value of k for each detection fiber and at each wavelength was obtained during calibration. For a phantom with known μ_a and μ_s′, R from each detection fiber and at each wavelength was calculated from the condensed Monte Carlo simulation and I was measured by the CCD camera. E₀ was the product of the incident power P₀ and the exposure time t. Then, k was calculated according to Eq. (6), and should remain constant for samples with different μ_a and μ_s′. During calibration, a series of phantoms were constructed as described in section 2.4 and measured to determine I for each phantom and fiber. For each fiber, a graph of R versus I/E₀ was constructed and used to determine a linear best fit. The slope of this line was k. In all cases, the r² values were above 0.99. Once k for each detection fiber at each wavelength was obtained, the reflectance of a phantom with unknown optical properties could be calculated according to Eq. (6). This process was performed with a Matlab^® routine coupled into the LabView virtual instrument software. The k values were calculated once and occasionally verified using phantoms. Drift of k from its original value was not significant.

2.4 In vitro validation of reflectance system

To evaluate the performance of the fiber optic reflectance system and the mathematical models, tissue phantoms were constructed from deionized water, polystyrene microspheres (Polybead^® Microspheres 1.00 µm, Polysciences, Inc.) and hemoglobin (Hb) (hemoglobin A0, ferrous stabilized human, Sigma H0267). Microspheres and Hb were chosen for their optical similarity to tissue scatterers and chromophores within the UVA-VIS spectral range. Microspheres of 1 µm diameter have commonly been used to simulate the cellular and structural protein scatters in tissue [29]. Theoretical estimates of phantom μ_a and μ_s′ were determined according to Beer’s law and Mie theory. From the spatially-resolved reflectance, μ_a and μ_s′ were calculated by the developed neural network based on 4 collection fibers. System accuracy was evaluated by comparing the theoretical μ_a and μ_s′ with the values predicted from diffuse reflectance measurements.

2.5 Ex vivo tissue measurements

Fresh porcine esophagus, bladder, colon, oral mucosa, and liver tissues were brought back to our lab in a cooler filled with ice immediately after animals were sacrificed. The colon, esophagus, and bladder were dissected longitudinally. All tissues were placed in a Petri dish and covered with gauze moistened with saline to prevent desiccation after they were flushed with saline to remove excess materials on the surface. The time between sacrifice and commencement of measurements was approximately three hours. According to a recent study [30], these tissue handling procedures should have been sufficient to avoid significant changes in reflectance, which can be altered by processes such as freezing and thawing. To perform a measurement, the fiber-optic probe was placed gently on a tissue such that the tip was flush with the tissue surface. Reflectance data were collected at three different sites on each tissue. At each site, three measurements were taken followed by a background measurement with the light source blocked. Each site was moistened with saline before measurements. All tissue samples were measured within four hours of sacrifice. Typical measurement-to-measurement variation at a single site was approximately 1%. The tissue optical properties were determined from reflectance datasets with inverse neural network models (based on 2 collection fibers for liver and 4 collection fibers for other tissues). To evaluate the optical property results, forward condensed Monte Carlo simulations were run with the optical properties obtained from neural networks. The generated reflectance values for tissues at different wavelengths were then compared with the measured values.

3. Results and discussion

3.1 Condensed Monte Carlo simulation

Figure 4 shows the contour curves of dimensionless reflectance from five detection fibers from condensed Monte Carlo simulations. Reflectance per unit area can be obtained by dividing the dimensionless values by the cross section area of each detection fiber. There contour curves indicate that the sensitivity of reflectance to optical properties varies with μ_a and μ_s′. For each curve, its slope changes continuously. A steeper slope at a point means that the reflectance is less sensitive to μ_s′ there. On the other hand, a shallower slope at a point means that the reflectance is less sensitive to μ_a. For example, reflectance is more sensitive to μ_s′ than to μ_a when μ_s′ is less than 5 cm^-1. This may affect the accuracy of neural networks in different μ_a and μ_s′ ranges. For a fixed μ_a, reflectance increases to a maximum value and then decreases with increasing μ_s′. This trend seems to be related to prior findings that for a source-detector separation of 1.7 mm both the average photon path length and reflectance intensity are relatively insensitive to scattering properties (over a μ_s′ range of 7.5 to 22 cm^-1)[31]. A similar insensitivity to scattering was also seen in reflectance data presented in our prior study [8]. Although we do not show the results for source-detector separation of 1.7 mm here, a similar conclusion can still be obtained from Fig. 4(c) which shows the reflectance for source-detector separation of 1.5 mm. From this graph, the contours are roughly vertical when μ_s′ ranges from 7.5 to 22 cm^-1, which means the reflectance is insensitive to changes in μ_s′. Furthermore, it is possible to identify similar μ_s′ range for other source-detector separation distance from similar contours in Fig. 4(a), 4(b), 4(d) and 4(e).

 

Fig. 4. Contours of dimensionless reflectance from each detection fiber with radius of 0.1mm, where graphs a, b, c, d and e correspond to center-to-center distances of 0.5, 1.0, 1.5, 2.0 and 2.5 mm, respectively, between the illumination and collection fibers.

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Overall, the plots for each fiber are similar. The contours of a nearer fiber resemble a close-up of those of a further fiber, except that the absolute values are higher. This shows the scaling theory of the condensed Monte Carlo method in another way. The irregular contour patterns at high μ_a and μ_s′ for farther fibers originate from the fact that the quantity of launched photons is insufficient for convergence to an accurate solution for reflectance in these regions. Therefore, neural networks trained with these datasets may be prone to larger errors. For Fig. 4(c), 4(d) and 4(e), it should be noted that the blank areas at the top of each graph indicate regions for which almost no photon were collected.

3.2 Neural network study – accuracy, robustness and sensitivity

During initial measurements of highly attenuating tissues, it was found that under highly attenuating conditions (tissues, wavelengths) larger separation distance fibers did not collect sufficient signal. In order to assess the accuracy and robustness of our inverse modeling approach when fewer than five detection fibers were implemented, we performed the following theoretical analysis. Four neural networks based on 2, 3, 4, and 5 detection fibers were evaluated with the 220 random datasets generated with condensed Monte Carlo simulations. This evaluation was performed both without added noise and with 5% random noise added to the reflectance values at all fibers. The noise level of 5% was based on measured variations in ex vivo tissues, which was likely dominated by spatial inhomogeneity. Table 1 summarizes the average values of absolute errors from the evaluations. The results for 5% noise are the average of three evaluations.

Table 1. Absolute errors of four neural networks (cm^-1)

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Fig. 5. The calculated μ_a and μ_s′ from the neural network based on four detection fibers versus their theoretical values (straight lines indicate where the calculated values are equal to the theoretical values).

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From Table 1, the absolute errors of optical properties from the neural networks decrease with an increasing number of detection fibers except for the five-fiber network which shows similar accuracy with the four-fiber network. This is likely because the greater noise in reflectance at high μ_a and μ_s′ for fiber No. 5 (Fig. 4(e)) render the reflectance from detection fiber No. 5 of little use. In general, the errors of μ_s′ are larger than the errors of μ_a, particularly for the 5% noise cases. Although noise increases error, the accuracy is still quite good in all cases and compares favorably with peer research to date [7]. Figure 5 shows the calculated μ_a and μ_s′ from the neural network based on 4 detection fibers versus their theoretical values when no noise was added as well as 5% noise was added to reflectance. From Fig. 5, the calculated values match the theoretical values well even with noise added to the reflectance.

To study the sensitivity of neural networks at different optical property ranges, 3D plots of absolute errors (from the neural network with 4 detection fibers) of μ_a and μ_s′ of each evaluation dataset are shown in Fig. 6. When no noise is added to the reflectance for evaluation, the error of μ_a is larger when μ_s′ is less than 10 cm^-1 (Fig. 6(a)). This agrees with Fig. 4 which shows that reflectance is not sensitive to μ_a at low μ_s′. In general, μ_s′ is rather accurate when no noise is added to the reflectance (Fig. 6(b)). When 5% noise is added to the reflectance for evaluation, the error of μ_a is larger at regions of lower-μ_a-higher-μ_s′ and higher-μ_a-lower-μ_s′ (Fig. 6(c)). From Fig. 6 (d), the errors of μ_s′ are larger at lower-μ_a-higher-μ_s′ region with 5% noise added. All these conclusions can also be obtained according to reflectance contours for each μ_a and μ_s′ set (Fig. 4)

 

Fig. 6. Absolute errors of μ_a and μ_s′ of each evaluation dataset from neural network based on 4 detection fibers.

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3.3 Evaluation of fiberoptic reflectance system with phantoms

Results for four tissue phantoms measured at all five wavelengths are shown in Fig. 7. The phantoms included two levels of absorption and scattering, as indicated in the graphs by Hb and polystyrene sphere concentrations. Figures 7(a) and 7(b) came from the neural network based on two detection fibers. Figures 7(c) and 7(d) came from the neural network based on four detection fibers. In general, these graphs show good agreement between theoretical and measured data, especially for μ_a. Absorption coefficient data display the well-known absorption signature of oxyhemoglobin, including a strong peak at 415 nm. While the 405 nm wavelength used in our measurements does not coincide with he peak of the oxyhemoglobin absorption curve, the phantom μ_a values at this wavelength are more than 3 times greater than at any of the other four wavelengths studied. The average error in predicting μ_a is 1.0 cm^-1 for both Fig. 7(a) and Fig. 7(c). Figures 7(b) and 7(d) display the expected monotonic decrease in μ_s′ with wavelength. It is worth noting that the greatest errors in μ_s′ occur at 325 nm – where μ_a is low and μ_s′ is high, which agrees with Fig. 6. The average error for μ_s′ estimates are 3.0 cm^-1 for Fig. 7(b) and 2.7 cm^-1 for Fig. 7(d). Data points in Fig. 7(a) and Fig. 7(c) appear in pairs due to the fact that for each μ_a, two different μ_s′ were investigated, and vice versa in Fig. 7(b) and Fig. 7(d).

 

Fig. 7. Comparison of theoretical optical properties (curves in the graphs) with estimates based on reflectance measured with the fiberoptic system.

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3.4 Ex vivo tissue measurement

Average μ_a and μ_s′ values measured in porcine liver and mucosal tissues of the bladder, colon, esophagus and oral cavity from three swine are displayed in Fig. 8. Data in these graphs were calculated by the neural network based on reflectance from four detection fibers, except for the liver data which was based on two detection fibers because of its high absorption. When the two fiber approach and four fiber approach were compared during mucosal tissue measurements, the former was shown to have 7% greater variability. However, very highly attenuating tissue measurements are limited by the detector noise floor and the potential for thermal damage due to higher irradiation levels.

The ex vivo tissues show relatively consistent spectral trends in μ_a and μ_s′, specifically, a decrease in μ_a from 325 nm to 375 nm, followed by an increase to 405 nm and consecutive decreases to 445 and 543 nm. Estimates of μ_s′ showed a monotonic decrease with wavelength, although the magnitude of this decrease varied from tissue to tissue.

Exceptions to these trends are also evident, most notably, the minimal decrease in μ_s′ with wavelength for colon tissue (Fig. 8(d)) and a higher than expected μ_a value at 543 nm for esophageal tissue (Fig. 8(e)). These results may be due to significant tissue inhomogeneities, irregularities in placement of the probe (e.g., an air bubble between the probe and tissue), variations in laser power or some combination of these issues.

The similarities in results are even greater for the epithelial tissue samples: bladder, colon, esophagus, and oral mucosa. These tissues show similar optical property magnitudes as well, with μ_a ranging from 1 cm^-1 to 15 cm^-1 and μ_s′ ranging from 15 cm^-1 to 65 cm^-1. In general, μ_a of bladder and colon is higher than μ_a of esophagus and oral mucosa, μ_s′ of bladder is higher than μ_s′ of other tissues at 325 nm. While the μ_s′ level of the one non-epithelial tissue – liver – is similar to other tissues, its μ_a is significantly higher, likely due to high blood content.

The error bars in Fig. 8 demonstrate the significant variation in optical properties found in this study. It is worth noting that these error levels are approximately equal to or less than the levels documented in the literature [32–34]. For example, Zonios, et al., showed that the typical SD of optical properties of colons from different animals were in the ±30–50% range[34]. This level of standard deviation helps to explain the wide variations in the optical properties reported in different papers, such as μ_a values of human colons at 475 nm measured as 12 cm^-1 and 2 cm^-1 in two different papers [11, 32]. Our preliminary findings in comparing repeat measurements at a single location to measurements at different sites and in different animals indicate that a significant portion of this variation may be due to local, regional or animal–to-animal variations (e.g. collagen fibers, animal growth stage). One possible source of error is discrete blood vessels which it may be possible to account for using correction factors [35]. Another variable may be the presence, thickness and optical properties of mucosal epithelia. [36, 37] While several techniques for measuring the optical properties of multi-layer tissues have been proposed, there is no consensus in the literature as to the best way to accomplish this task, nor is there significant tissue data using these proposed methods. [38, 39]

 

Fig. 8. Optical properties of porcine tissues (average values of three animals)

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To evaluate the optical property results in Fig. 8 in a direct way, forward condensed Monte Carlo simulations were run with the optical properties obtained from tissues using neural networks. The generated reflectance values were then compared with the measured ones. Data on oral mucosa and liver are presented in Fig. 9. In general, the reflectance values from Monte Carlo simulation matched very well with the measured values, providing further validation of our approach in nonhomoneneous tissue.

 

Fig. 9. Reflectance as a function of distance from center of illumination fiber (r) (Hollow symbols indicate the values from forward condensed Monte Carlo simulations. Solid symbols indicate the measured values.)

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Table 2 provides a summary of relevant published data on tissue optical properties. Some data in this table were estimated from printed graphs. The μ_s′ of human esophagus in Holmer, et al.’s paper [33] roughly matches our value at 325 nm. However, the μ_a is about six times higher than our value. The results of human esophagus by Georgakoudi, et al., [40] agree with our porcine results. The μ_a and μ_s′ of human colon in Wei, et al.’s paper [11] match our results of porcine colon, while the μ_a values of human colon in Zonios, et al.’s paper[34] are higher than our porcine colon results and their μ_s′ values are lower. From Ritz, et al.’s paper [41], their μ_a values of porcine liver are lower than ours and μ_s′ values are higher. The μ_a values in Parsa, et al.’s paper [42] is consistent with our porcine results. Their μ_s′ values are higher than ours. When comparing these results, it is important to note that the optical properties may change during tissue preparation[30].

As noted previously, the curves in Fig. 8 have several features in common. The peak in μ_a at 405 nm is consistent with the established concept that Hb is the dominant chromophore for most tissues in the visible range. However, the intensity of this peak relative to values at nearby wavelengths is much less than shown in tissue phantoms, and the decrease in μ_a from 325 nm to 375 nm is not consistent with the Hb-dominated phantom results. These findings support the idea that at short visible wavelengths other chromophores become increasingly significant. According to the literature, tissue constituents such as collagen, elastin, DNA and some other proteins (especially those with high aromatic amino acid content such as tryptophan and tyrosine) also contribute to the absorption of UVA light[43–45].

Table 2. Optical properties from literature

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In order to clarify the role of structural proteins such as collagen, we have performed preliminary spectrophotometric measurements of collagen (type I, bovine, BD Biosciences 354231) absorption. These data are graphed in Fig. 10 along with the μ_a of Hb (hemoglobin A0, ferrous stabilized human, Sigma H0267). The μ_a of collagen increases exponentially with decreasing wavelength within the UVA range. Although the absolute value of collagen μ_a is two magnitudes less than that of Hb, the contribution of other chromophores such as collagen and elastin to μ_a of tissues can still be remarkable considering the higher concentration of these chromophores relative to Hb. Therefore, it is likely that the μ_a distributions in Fig. 8 are due to the superposition of Hb and other chromophores such as collagen and elastin. In the future, it may be possible to determine the concentrations of these chromophores through fitting algorithms.

 

Fig. 10. Absorption coefficient of Hb and type I collagen

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4. Conclusions

Towards the goal of accurate in vivo measurements of tissue optical properties, we have constructed and evaluated a system for optical property measurement within the UVA-VIS wavelength range. Our approach involves a neural network-based inverse model calibrated with reflectance datasets simulated using a condensed Monte Carlo approach with μ_a up to 85 cm^-1 and μ_s′ up to 118 cm^-1. Theoretical evaluation of the inverse model showed good agreement between calculated and theoretical values. Experimental evaluation on tissue phantoms showed average errors in predicting μ_a and μ_s′ of 1.0 cm^-1 and 2.7 cm^-1.

Optical property data collected in unprocessed mucosal and liver tissues ex vivo provide evidence that the current approach can produce useful data on tissue optical properties over a wide range of optical characteristics. Significant tissue-specific variations in scattering and absorption were found. Scattering coefficients decreased monotonically with wavelength. Variations in absorption with wavelength indicate a shift in primary chromophore from hemoglobin at visible wavelengths to other components, likely other proteins, in the ultraviolet. While significant variability in optical properties was found for individual tissue types, this variability tended to be less than in prior studies. However, additional research is needed to investigate their origin.