An empirical model was developed to interpret differences in the experimentally measured reflectance and fluorescence spectra of freshly excised human pancreatic tissues: normal, adenocarcinoma, and pancreatitis (inflammation). The model provided the first quantitative links between spectroscopic measurements and histological characteristics in the human pancreas. The reflectance model enabled the first (to our knowledge) extraction of wavelength resolved absorption and reduced scattering coefficients for normal and diseased human pancreatic tissues. The fluorescence model employed reflectance information to extract attenuation free “intrinsic” endogenous fluorescence spectra from normal pancreatic tissue, pancreatic adenocarcinoma, and pancreatitis. The method developed is simple, intuitive, and potentially useful for a range of applications in optical tissue diagnostics. This approach is potentially applicable to in vivo studies, because it can account for the absorptive effects of blood in tissues.
©2009 Optical Society of America
Pancreatic adenocarcinoma is the fourth-leading cause of cancer death in the United States, with a five-year survival rate of only 5% [1,2]. If a cancerous pancreatic tumor is accurately located and resected, and the patient then undergoes adjuvant therapy, the five-year survival rate only increases to about 20% . A main reason for these unfortunate statistics is the fact that no reliable diagnostic procedure for early stage disease has been developed. The current diagnostic standard is endoscopic ultrasound-guided fine needle aspiration (EUS-FNA), which has only 54% sensitivity for cancer in the setting of pancreatitis . For diagnosis of adenocarcinoma in solid pancreatic lesions (such as ductal lesions, in which malignancy is most likely), EUS-FNA has been reported to have a negative predictive value ranging from 16% to 92% ; this large spread illustrates a need to improve the diagnostic capabilities of EUS-FNA. Currently, if pancreatic cancer is diagnosed by EUS-FNA, the patient may undergo a Whipple resection , in which a significant portion of the pancreas is removed during an arduous surgical procedure that can last as long as seven hours. Histology has revealed that 9% of patients who underwent a Whipple resection did not have pancreatic cancer . Therefore, it is very important that a more effective procedure is developed for early detection of pancreatic cancer.
Optical methods, including quantitative reflectance and fluorescence spectroscopies, may prove to be effective, minimally invasive diagnostic tools for breast cancer , colon cancer , cervical cancer , and Barrett’s esophagus . Recently, an optical study of murine tumors consisting of human pancreatic cancer cells was conducted to quantitatively distinguish different tumor regions . However, to our knowledge, there has been no comparable work involving mathematical models of experimentally obtained reflectance and fluorescence data from normal and diseased human pancreatic tissues. Toward this end, prototype instrumentation [10,11] was developed at the University of Michigan to obtain reflectance and fluorescence spectra [10–12] from freshly excised human pancreatic tissues. In the study reported here, mathematical modeling of experimentally measured data was used to quantitatively describe differences in the reflectance and fluorescence spectra of normal pancreatic tissue, pancreatic adenocarcinoma, and pancreatitis. In particular, we sought to correlate the results of bimodal tissue optical spectroscopy with those of microscopic histological examination of tissue (Fig. 1 ), which is the current “gold standard” for cancer diagnostics.
As shown in Fig. 1, pancreatic adenocarcinoma has larger nuclei than benign pancreatic tissue, and both adenocarcinoma and chronic pancreatitis have more collagenous stroma than normal pancreatic tissue. The mathematical model of reflectance quantitatively linked increased nuclear size in adenocarcinoma to changes in the measured reflectance spectra from 455 to 525 nm. The fluorescence model quantitatively linked increased collagen content in pancreatitis and adenocarcinoma to changes in the composition of the measured fluorescence spectra. Fitting the reflectance model to the experimental data also enabled what is, to the best of our knowledge, the first-ever extraction of values for the optical absorption and reduced scattering coefficients of human pancreatic tissues.
The mathematical model provided a quantitative link between optical spectroscopy and tissue histology (Table 1 ), suggesting a potential clinical application of optical spectroscopy and modeling to minimally invasive early cancer diagnostics in the pancreas. Although this paper focuses exclusively on pancreatic tissues, the methods described are potentially useful for optical diagnostic applications in other biological tissues.
Section 2 of this paper describes the experimental methods employed for clinical measurements of human pancreatic tissues. Section 3 outlines the development and application of the algorithm used to model measured pancreatic tissue reflectance spectra, including the extraction of tissue absorption and reduced scattering coefficients. Section 4 describes the procedures used to obtain attenuation-free intrinsic fluorescence spectra and to model these spectra as linear combinations of native tissue fluorophores. Section 5 includes discussions on the correlation between the mathematical models and pancreatic tissue histology, as well as the potential to employ the methods described in this paper for in vivo optical diagnostics in the pancreas.
2. Clinical measurements of tissue optical spectra
The Reflectance and Fluorescence Lifetime Spectrometer (RFLS), developed at the University of Michigan and described previously in the literature [10,11,13], was used to obtain reflectance and fluorescence measurements of human pancreatic tissue within 15 minutes of removal via Whipple resection at the University of Michigan Medical Center. Reflectance measurements were acquired by using a CW tungsten halogen lamp (HL 2000FHSA, Ocean Optics, Dunedin, FL) to deliver white light (400-750 nm) to the tissue; fluorescence measurements utilized a 355 nm pulsed excitation source (PNV001525-140, JDS Uniphase, San Jose, CA). A spectrograph (MS 125, Oriel Instruments, Stratford, CT) and an intensified charge-coupled device (ICCD) camera (ICCD 2063, Andor Technology, Belfast, Northern Ireland) were used to detect tissue reflectance (400-750 nm) and fluorescence (360-700 nm) spectra. The light from the lamp and the laser was delivered to the tissue via two separate optical fibers with core diameters of 600 μm. The reflected or emitted fluorescence photons from the tissue were collected and transported to the detectors by a third identical fiber.
Measurements were taken at five sites on each tissue specimen. One pancreatectomy specimen was evaluated from each of two different patients. Each measured site was biopsied under the supervision of a clinical pathologist, and the biopsied samples were evaluated histologically. For the first patient, two of the sites were histologically normal and three were pancreatitis, while for the second patient, all five sites sampled were adenocarcinoma [10–12]. There were noticeable differences in both the reflectance and fluorescence spectra of the three tissue types, most notably around 500 nm for the reflectance spectra and near 400 nm for the fluorescence spectra [10–12]. The study was approved by the Institutional Review Board of the University of Michigan Medical Center and written consent was obtained from the patients.
3. Mathematical model of reflectance spectra: theory and results
3.1 Modeling scattering and absorption coefficients of pancreatic tissues
The lineshapes of reflectance spectra from biological tissues are known to be primarily dependent on the absorption and scattering coefficients of the media. Absorbers such as blood will attenuate the light, while scatterers such as cell nuclei and collagen fibers will change the paths of the photons, eventually leading some of them back to the tissue surface. Mie theory [14–17] was used to describe the scattering coefficient μs, as a function of wavelength, in terms of the size and density of the scatterers in the tissue. Two Mie theory terms were used: one for spherical scatterers (cell nuclei) [14–16] and another for cylindrical scatterers (collagen fibers) [15,17]. For the spherical Mie scattering term, the Van de Hulst approximation was used [14,16]:
In Eq. (1), Lo is the scatterer diameter, Ns is the number of scatterers per unit volume, and ns (nm) is the index of refraction of the scatterer (surrounding medium). The wavelength λ is defined as λvac/nm, where λvac is the wavelength of the incident light in vacuum. For all pancreatic tissue types in this study, nm was assumed to be 1.33 (for water), while ns was set as a free parameter and varied over a range previously measured for cell nuclei in freshly excised colon tissues , as detailed in Section 3.3. For normal pancreatic tissue, the values of Lo and Ns were estimated from histology to be 9 μm and 7 x 107 cm−3, respectively. The parameter Ns was kept constant for all tissue types. For both pancreatitis and adenocarcinoma, a dilation factor Ld/Lo was applied to the nuclear diameter. It was expected that Ld/Lo would be equal to 1.0 for pancreatitis but greater than 1.0 for adenocarcinoma because cancer cells are known to exhibit enlarged nuclei [19–21].
The cylindrical scattering term was modeled by a combination of Bessel functions, in which the diameter, refractive index, and anisotropy of the collagen fibers were set to 3 μm, 1.35, and 0.975, respectively . Both pancreatitis and adenocarcinoma were modeled to have three times the concentration of collagen fibers as normal pancreatic tissue, as previously determined quantitatively for human pancreatic tissues using the Blumenkrantz and Asboe-Hansen method to assess hydroxyproline content . Since the spherical and cylindrical Mie scattering terms are explicit functions of scatterer size and concentration, they were chosen over the commonly used approximation μs′ = Aλ-b  (where μs′ is the reduced scattering coefficient, equal to μs(1-g) in a tissue with anisotropy g).
Using Eq. (2), μa was represented as a function of the total tissue hemoglobin concentration [Hb]tot = [Hb] + [HbO2] and the blood oxygen saturation SO2 = [HbO2]/[Hb]tot.
3.2 Modeling key features in reflectance spectra of pancreatitis and adenocarcinoma
The key diagnostic feature of the measured reflectance was increased amplitude between 455 nm and 525 nm in the adenocarcinoma spectra, relative to normal pancreatic tissue spectra. An empirical model, previously shown to be accurate in the case of small source-detector separations [24,25], was used to model this feature by describing the reflectance spectra REMPi(λ) as functions of tissue absorption and scattering:
Since Eq. (1) gives the scattering coefficient μs(λ) and Eq. (3) is a function of the reduced scattering coefficient μs′(λ), it was necessary to estimate a value for the tissue anisotropy, so g was set to 0.9 at all λ for each tissue type . The factor Ccorr(λ) describes the confinement of oxy- and deoxy-hemoglobin to cylindrical blood vessels . The value of Ccorr was modeled to be dependent on the mean radius of the blood vessels (set to 7 μm for all tissue types ) and the absorption coefficient of blood (given by Eq. (2) for each tissue type) .
The parameters a, b, and c are related to probe design; their respective values were estimated [24,25] to be 0.11, 0.22, and 0.2. These values do not vary significantly when the tissue-probe refractive index mismatch is changed . The value of b is somewhat dependent on probe source-detector separation , but changing b by as much as 50% was found to have very little effect on modeled pancreatic tissue spectra. Therefore, it was considered reasonable to approximate a, b, and c as noted. For the remainder of the text, the subscript i in Eq. (3) will be denoted as N for normal pancreatic tissue, P for pancreatitis, or A for pancreatic adenocarcinoma.
To model the reflectance spectra of diseased pancreatic tissue, Eq. (3) was used to generate a wavelength-resolved scaling factor to transform the experimentally measured reflectance spectrum RMEASN(λ) of normal pancreatic tissue into an accurate model for the adenocarcinoma reflectance spectrum RMODELA(λ) and the pancreatitis reflectance spectrum RMODELP(λ), according to the equations:
3.3 Procedure for fitting reflectance model to measured spectra
Optimal fits of Eqs. (4) and (5) to the respective measured adenocarcinoma and pancreatitis reflectance spectra were determined via minimization of a cost function CR, which was equal to the average magnitude of the difference between the reflectance model and measured reflectance spectrum over the 400-700 nm wavelength range. For each tissue type, every individual measured spectrum was first normalized to peak intensity, then these spectra were averaged and the result was normalized to peak intensity again. All of the modeled reflectance spectra were also normalized to peak intensity.
In the fitting procedure described above, the nuclear dilation factor Ld/Lo for diseased pancreatic tissue (adenocarcinoma and pancreatitis) was varied from 1.0 to 1.9 in steps of 0.1, and the nuclear refractive index nsd of diseased pancreatic tissue was varied from 1.370 to 1.400, in steps of 0.005. The total hemoglobin concentration [Hb]tot was varied from 15 μM to 25 μM for normal pancreatic tissue and 2.5 μM to 25 μM for diseased tissue (in steps of 2.5 μM for all tissue types). The blood oxygen saturation SO2 was varied from 0.1 to 0.9 (in steps of 0.2) for all tissue types.
The fitting procedure described above was performed for each of three different values of the nuclear refractive index nsn of normal pancreatic tissue: 1.370, 1.375, and 1.380. This range and these values were identified in part because of the results of studies conducted on freshly excised diseased and normal human tissues , and in part because we observed that the algorithm extracted physically reasonable values of both Ld/Lo and nsd that did not vary much as nsn was changed. The set of free parameter values that minimized CR was extracted from each fit, as reported below. The fitting method described here was compared with a nonlinear least-squares method, and t-tests demonstrated that there were no statistically significant differences (p > 0.25) between the tissue parameters extracted from the two fitting methods.
3.4 Results of reflectance fitting algorithm
Optimal fits of the mathematical model to experimentally measured reflectance data for adenocarcinoma and pancreatitis are shown in Fig. 2 . The error bars on the modeled reflectance spectra represent the standard deviation associated with varying nsn over the range described in Section 3.3. In the diagnostically important wavelength range between 455 and 525 nm, where the adenocarcinoma reflectance spectra differed significantly from both the normal and pancreatitis spectra, the mean error in fit of the adenocarcinoma model to the average measured spectrum was less than 6%.
The optimal fits between the predicted and measured adenocarcinoma reflectance spectra extracted a (mean ± standard deviation) value of Ld/Lo = 1.33 ± 0.06 for the nuclear dilation factor and a value of nsd = 1.375 for the nuclear refractive index. The optimal fits between the predicted and measured pancreatitis reflectance spectra extracted a (mean ± standard deviation) value of Ld/Lo = 1.03 ± 0.06 for the nuclear dilation factor and nsd = 1.372 ± 0.003 for the nuclear refractive index. The model revealed that differences in the reflectance spectra of normal pancreatic tissue, pancreatitis, and adenocarcinoma could be quantitatively linked to an increase in nuclear size for adenocarcinoma relative to pancreatitis and normal tissue, a result that is supported by histology [19–21].
The reflectance fits extracted (mean ± standard deviation) [Hb]tot values of 18.8 ± 4.1 μM for normal pancreatic tissue, 7.5 ± 2.5 μM for pancreatitis, and 20.0 ± 5.0 μM for adenocarcinoma. The fits extracted (mean ± standard deviation) SO2 values of 0.13 ± 0.08 for normal pancreatic tissue, 0.57 ± 0.23 for pancreatitis, and 0.9 for adenocarcinoma. T-tests demonstrated that there were no statistically significant differences (p > 0.25) between either the [Hb]tot or SO2 values of normal pancreatic tissue that were extracted from the fits to the measured adenocarcinoma spectra and those extracted from the pancreatitis spectra.
Since spectra were obtained ex vivo, it is possible that these values reflect the amount of blood that drained from the tissue and the time the tissue was exposed to air prior to measurements. However, these results signify a promising step toward the eventual extraction of hemoglobin concentration and blood oxygen saturation values from in vivo measurements of the human pancreas.
The spectra from Fig. 2 were also compared with a previously published reflectance spectrum taken in vivo from a pancreatic adenocarcinoma xenograft created by injecting human pancreatic cancer cells into the pancreas of a Non-Obese Diabetic/Severe Combined Immunodeficiency (NOD/SCID) mouse . Due to the suppressed immune response in SCID mice, the xenograft had a very low amount of collagen relative to cells. In spite of this difference, the reflectance spectrum of the xenograft was similar to that of freshly excised human adenocarcinoma from 400 to 525 nm, a result attributed to the increased size of the cell nuclei in both the xenograft and the ex vivo human adenocarcinoma tissue samples.
3.5 Extracting absorption and reduced scattering coefficients from reflectance data
Model fits to experimental data were employed to estimate wavelength-resolved absorption and reduced scattering coefficients for each tissue type via Eqs. (1) and (2) and the formula for Mie scattering from cylinders . The results shown in Fig. 3 represent the first extraction (to our knowledge) of absorption and reduced scattering coefficients of human pancreatic tissues. The error bars represent the standard error over a set of fits for different values of the nuclear refractive index nsn of normal pancreatic tissue (see Section 3.3). The values of the coefficients in Fig. 3 are in the range expected for gastrointestinal tissue . However, it is important to note that these values are specific to the pancreatic tissue samples measured in this particular study.
This study was primarily concerned with the lineshapes of the absorption and reduced scattering spectra, because differences in these lineshapes were indicative of differences in the measured reflectance spectra. For instance, the reduced scattering coefficient of adenocarcinoma was highest from 400 to 525 nm, whereas the reduced scattering coefficients of normal pancreatic tissue and pancreatitis were lowest. In this range there is also a prominent increase in the amplitude of the adenocarcinoma reflectance spectrum relative to that of normal pancreatic tissue and pancreatitis.
The differences in the mean extracted absorption coefficients for normal pancreatic tissue, pancreatitis, and adenocarcinoma could be attributed to the ex vivo nature of the measurements, in which tissue hemoglobin concentration and blood oxygen saturation were likely affected by the amount of blood that drained from the tissue and the time the tissue was exposed to air prior to measurements.
4. Extracting and modeling intrinsic fluorescence: theory and results
4.1 Correcting fluorescence data for scattering- and absorption-related artifacts
Once the fits of the reflectance model to the adenocarcinoma and pancreatitis data were obtained, the extracted scattering parameters were used in an algorithm to remove artifacts of scattering and absorption from the measured fluorescence spectra of normal pancreatic tissue, pancreatitis and adenocarcinoma. To perform this task, a separate Beer-Lambert attenuation factor was constructed for each tissue type by using μa(λ) and μs′(λ) values specific to that tissue type. The intrinsic fluorescence spectrum FINTRINSIC(λ) was then extracted according to the equation:
The variable z represented the length of the average path of travel to the surface for photons that had been absorbed and re-emitted by a fluorophore within the tissue. The average value of z over the wavelength range of 400-638 nm was estimated to be 0.064 cm for all tissue types. This value was calculated from time-resolved Monte Carlo simulations of photon propagation in pancreatic tissue models . Separate simulations were run for normal pancreatic tissue, pancreatitis, and adenocarcinoma. For each of these simulations, the absorption and reduced scattering coefficients were obtained by averaging the absorption and reduced scattering spectra (Fig. 3) of the tissue type being modeled. The anisotropy g was approximated to be 0.9 for all tissue types. The average path length of emission photon travel was determined by finding the time at which the greatest number of simulated photons exited the tissue, multiplying that by the speed of light in the medium, and dividing by two to account for only the fluorescence photons’ travel back to the surface (under the approximation that on average, a photon would be absorbed by a fluorophore at its point of greatest depth in the tissue). Calculation of the same z value for all tissue types likely resulted from the coarseness of the time resolution (1 ps) used in the simulations, as well as the use of average absorption and reduced scattering coefficients as inputs.
We note that Eq. (6) does not include the absorption coefficient at the excitation wavelength. This omission affects only the amplitudes and not the lineshapes of the intrinsic fluorescence spectra; thus it will not cause errors in the relative contributions of fluorophores extracted from these spectra.
4.2 Fitting intrinsic fluorescence to endogenous fluorophore component spectra
Once the intrinsic fluorescence spectra were obtained for each tissue type (solid green lines in Fig. 4 ), their lineshapes could be decomposed into the component spectra of collagen, NADH, and FAD, three principal contributors to tissue autofluorescence in the 400-700 nm wavelength range. For each tissue type, the intrinsic fluorescence spectrum was fit to a linear combination (BasisFit(λ)) of experimentally measured basis spectra of collagen, NADH, and FAD:
The basis spectra FCOLLAGEN(λ) and FFAD(λ) were measured at 355 nm excitation on a spectrofluorometer (SPEX® FL3-22 Fluorolog-3, Jobin-Yvon Horiba, Japan) while the FNADH(λ) was measured on the RFLS. Solutions of 0.005 mg/ml of NADH (N-8129, Sigma Aldrich, St. Louis, Missouri) in water, 0.7 mg/ml of FAD (F6625, Sigma Aldrich) in water, and 1 mg/ml of collagen (C5483, Sigma Aldrich) in acetic acid were used for the measurements.
To fit the intrinsic fluorescence spectra to Eq. (7), the values of CCOLLAGEN, CNADH, and CFAD were treated as free parameters whose values were varied between 0 and 0.9 (in steps of 0.1) until a minimal value of a cost function CF was obtained. The cost function CF was defined to be the average magnitude of the difference between BasisFit(λ) and FINTRINSIC(λ) over the wavelength range of 400 nm to 638 nm. For each tissue type, every individual fluorescence spectrum was normalized to the area under the curve from 400 to 638 nm; these spectra were then averaged and this average spectrum was corrected for attenuation to produce FINTRINSIC(λ). For all tissue types, BasisFit(λ) and FINTRINSIC(λ) were both normalized to the peak intensity. Each of the basis spectra (FCOLLAGEN(λ), FNADH(λ), and FFAD(λ)) was blue shifted by about 12 nm, which accounted for the fact that the component spectra were measured in various chemical solvents and not within a biological tissue environment .
In the algorithm to minimize CF, the values of Ld/Lo and nsd were taken to be those extracted from the reflectance fits (Section 3.4) and the value of nsn was fixed at 1.375 (the midpoint of the range over which this parameter was varied in the reflectance fits). To minimize the presence of artifacts from under-correction or over-correction of the measured fluorescence spectra, the values of [Hb]tot and SO2 were once again treated as free parameters. This procedure was considered reasonable because Ld/Lo and ns were not expected to change much from site to site over the time period that ex vivo measurements were taken, but [Hb]tot and SO2 were expected to be much more variable. For all tissue types, [Hb]tot was varied from 15 to 25 μM (in steps of 2.5 μM) and SO2 was varied from 0.1 to 0.9 (in steps of 0.2). These ranges were considered reasonable given the means and standard deviations of the [Hb]tot and SO2 values reported in Section 3.4, in addition to the fact that measurements were performed ex vivo.
Optimal fits of BasisFit(λ) to FINTRINSIC(λ) for normal pancreatic tissue, pancreatitis, and pancreatic adenocarcinoma are shown in Fig. 4. The values of CCOLL, CNADH, and CFAD extracted from these fits are displayed in Table 2 . The deviation of the basis fits to the intrinsic fluorescence spectra of normal pancreatic tissue and pancreatitis around 600 nm may be attributed to the fact that the model does not include porphyrin fluorescence, which is known to peak around 635 nm when excited with 380-440 nm light .
The data in Fig. 4 were also compared to the intrinsic fluorescence extracted from a fluorescence spectrum obtained in vivo from a pancreatic adenocarcinoma xenograft in a NOD/SCID mouse . Mathematical modeling showed that the xenograft fluorescence could be mostly attributed to intracellular components, a conclusion that made sense given that the xenograft tumor was predominantly comprised of cells.
In Fig. 4, the intrinsic fluorescence between 500 and 600 nm (where intracellular NADH and FAD emit prominently) was observed to decrease in pancreatitis and adenocarcinoma, relative to normal pancreatic tissue. Since the spectra in Fig. 4 were normalized to their peak values, these differences are consistent with the known higher concentrations of collagen in both pancreatitis and adenocarcinoma, relative to normal pancreatic tissue . This trend was also revealed by the increase in the percentage contribution of collagen (determined via the collagen fit coefficient CCOLL) to the intrinsic fluorescence of pancreatitis and adenocarcinoma, relative to normal pancreatic tissue, as illustrated in Table 2.
The trend shown in Table 2 was further confirmed by qualitative examination of Fig. 1, which shows representative histology slides of tissue samples from the patients involved in the study. In these slides, the amount of collagen incursion observed amidst the cells in the tissue samples clearly increases in pancreatitis and adenocarcinoma, relative to normal pancreatic tissue. In the diagnostically relevant region between 500 and 550 nm, the mean error in fit between Eq. (7) and the intrinsic fluorescence was less than 4% for normal pancreatic tissue and pancreatitis, and less than 8% for adenocarcinoma.
5. Discussion and conclusions
5.1 Overview of mathematical models developed
In this study, mathematical models of reflectance and intrinsic fluorescence were developed and employed to quantitatively describe the effects of key histologically observed tissue parameters on the measured optical spectra of pancreatitis and pancreatic adenocarcinoma (relative to normal pancreatic tissue). An empirical mathematical model of reflectance was able to fit the prominent feature in the average adenocarcinoma spectrum (increased amplitude from 455 to 525 nm, relative to normal pancreatic tissue) with less than 6% error. Fitting the reflectance model to the measured optical spectra enabled the first-ever (to our knowledge) extraction of wavelength-resolved absorption and reduced scattering coefficients of human pancreatic tissues. Obtaining values for the optical coefficients is an important result, because knowledge of these coefficients is essential for accurate computational studies of photon migration in pancreatic tissue models. One such computational method is Monte Carlo simulation [29,31], which is accurate throughout optical parameter space for modeling photon transport in biological tissue.
We note that in this study, Eq. (3) is not employed to model the reflectance spectrum of normal pancreatic tissue. The “normal” data shown in Fig. 2 is averaged, experimentally measured data from normal pancreatic tissue. This “canonical normal” data is RMEASN(λ) in Eqs. (4) and (5). In principle, it could be useful to employ a normal spectrum from each individual patient, but this scenario would not always be possible in a clinical diagnostic application, so here we employ a “canonical normal” spectrum as our general approach.
In theory, it is also possible to obtain the absorption and scattering parameters by fitting the measured reflectance spectra directly with Eq. (3), but we did not use this approach here. Our approach focuses on modeling key differences between the reflectance spectra of normal and diseased pancreatic tissues. One potential advantage of this approach is that many of the characteristics of pancreatic tissue (such as size distributions for scatterers, fluctuations in refractive index, and packaging of hemoglobin into red blood cells ) are implicitly contained (at least approximately) in the measured “canonical normal” reflectance spectrum.
The scattering parameters extracted from the reflectance fits were used in an algorithm that corrected the measured fluorescence spectra for attenuation artifacts and fit the resulting “intrinsic” endogenous fluorescence spectra to a linear combination of basis spectra from native tissue fluorophores (collagen, NADH, FAD). This procedure determined the relative contributions from both extracellular (collagen, 400-450 nm emission peak) and intracellular (NADH and FAD, 500-600 nm emission peak) autofluorescence for each tissue type. The relative contribution of collagen was found to be greater in the intrinsic fluorescence spectra of pancreatitis and adenocarcinoma. Since the spectra were normalized to the peak, the intrinsic fluorescence of pancreatitis and adenocarcinoma spectra exhibited a decrease in amplitude in the 500-600 nm range, where NADH and FAD emission are prominent. These results were consistent with the increased collagen fibrosis [22,33] seen in histology of pancreatitis and adenocarcinoma.
5.2 Correlation of optical tissue models with histology
As seen in Fig. 2, Fig. 4, and Table 3 , empirical models of reflectance and intrinsic fluorescence were able to quantitatively describe the major differences between normal pancreatic tissue, adenocarcinoma, and pancreatitis in terms of histologically observed changes in biologically meaningful parameters.
The reflectance spectra of cancerous tissue differed most noticeably from normal pancreatic tissue at around 500 nm (Fig. 2), a change that could be quantitatively linked, via spherical Mie scattering, to larger cell nuclei in pancreatic adenocarcinoma. Subtle differences throughout the reflectance spectra of both pancreatitis and adenocarcinoma were found, via modeling of cylindrical Mie scattering, to correlate with the increased number of collagen fibers in both pancreatitis and cancer. These results agree with histology in that both pancreatitis and pancreatic adenocarcinoma are marked by greater collagen content than normal pancreatic tissue, but only adenocarcinoma is characterized by larger cell nuclei [22,33–35].
The intrinsic fluorescence model (Fig. 4, Table 2) showed that for both pancreatitis and adenocarcinoma, there was an increased contribution from the collagen in the stroma, relative to normal pancreatic tissues. This result is consistent with the histological observation that the change from normal pancreatic tissue to both pancreatitis and adenocarcinoma is characterized by increased collagen amidst the cells [22,33]. However, the intrinsic fluorescence spectra of pancreatitis and cancer were also shown to be different from each other. Whereas the reflectance model was most useful for discriminating pancreatic adenocarcinoma from pancreatitis, the intrinsic fluorescence model was more effective at distinguishing between all three tissue types. The results of this study lend credence to the idea that combining reflectance and fluorescence spectroscopies has a diagnostic advantage over using just one of these modalities to detect pancreatic cancer.
5.3 Comparison of empirical reflectance model with diffusion approximation
The empirical reflectance model was compared with the diffusion approximation, which is often employed to extract tissue absorption and scattering properties from experimentally measured tissue reflectance spectra [5,6,36]. When the reflectance fitting procedure of Section 3.3 was employed with a subset of the [Hb]tot and SO2 ranges described in Section 3.1, the diffusion approximation model was noticeably less effective than the empirical model for fitting the adenocarcinoma reflectance spectrum. In the diagnostically-relevant wavelength range of 455-525 nm, the error in fit to the measured adenocarcinoma spectrum was less than 6% for the empirical model, but it rose to as high as 13% with the diffusion approximation model. These results were not surprising because the fiber-optic probe in this study had a source-detector separation of only about 660 μm. Using the reduced scattering coefficients μs′ from Fig. 2, it can be shown that the source-detector separation of the probe was often smaller than 1/μs′. This condition causes the diffusion approximation to break down , but the empirical model is accurate in this regime .
5.4 Limitations of reflectance and fluorescence models
Although the reflectance and fluorescence models employed in this paper are useful for extracting physical information from experimental measurements of pancreatic tissue, the models do have several key limitations. The empirical reflectance model approximated tissue scattering as originating from only two sources: sub-cellular nuclei and extracellular collagen fibers. As a first approximation, this model is reasonable, because cell nuclei are known to be important contributors to forward scattering [37,38] and collagen fibers have been shown to be a significant source of extracellular scattering . In addition, the experimentally measured “canonical normal” tissue spectrum used in the reflectance model contains some level of information about the optical scattering and absorption from other intracellular and extracellular sources. Cell components such as mitochondria, cytoplasm, and plasma membrane also contribute to tissue scattering [37,38] and are reflected here in the “canonical normal” tissue spectrum for normal, but not diseased, pancreatic tissues.
The model fixed the diameter and concentration of normal cell nuclei in pancreatic tissue at constant values even though there was uncertainty in the estimation of these parameters. The model also approximated the anisotropy to be constant for all tissue types, when that parameter would likely be different for normal pancreatic tissue, pancreatitis, and adenocarcinoma because each of these tissue types is associated with a different distribution of scatterer sizes and shapes. Furthermore, the fluorescence model approximated the average emission photon path to have the same length for normal pancreatic tissue, pancreatitis, and adenocarcinoma. Future work to improve the model will include an investigation into the effect of including additional scattering terms for other cellular and extracellular components, as well as variations between the anisotropy values for the different tissue types. An expanded study will include an investigation into the effect of incorporating a term into the reflectance model to explicitly correct for the packaging of hemoglobin into erythrocytes , as well as further consideration of changes in the distribution of blood vessel sizes for the different tissue types. Preliminary studies showed that when the mean blood vessel radius for adenocarcinoma was doubled (to 14 μm) or halved (to 3.5 μm), relative to that of normal tissue (7 μm), there was no change in the tissue parameters extracted from the reflectance model. However, more sophisticated models of pancreatic tissue vasculature could be incorporated in the future. In addition, a more rigorous calculation of the average emission photon path length as a function of wavelength for each different tissue type will be explored.
5.5 Potential of optical spectroscopy to fulfill unmet clinical need
Current methods to detect pancreatic adenocarcinoma are highly invasive and fail to find the disease early or to distinguish it from inflammation (pancreatitis). Hence, there is great biomedical need for an endoscopic screening procedure for early detection of pancreatic adenocarcinoma. Bimodal reflectance and fluorescence spectroscopy is a potential inroad into addressing this unmet clinical need. In this study, mathematical models of measured reflectance and fluorescence spectra were employed to quantitatively describe differences between normal pancreatic tissue, pancreatic adenocarcinoma, and pancreatitis. By using biomedically relevant parameters, the model provided a link between the results of optical spectroscopy and histology. Features in the reflectance spectra were quantitatively linked to larger cell nuclei in cancer and increased collagen content in both cancer and pancreatitis. The intrinsic fluorescence spectra were fit to a linear combination of collagen, NADH, and FAD basis spectra to show quantitative differences in the contribution of collagen to the measured fluorescence from normal pancreatic tissue, pancreatic adenocarcinoma, and pancreatitis.
Translation to an in vivo setting is feasible because the model can extract the optical absorption coefficient from increased blood content in the tissues. We believe that the reflectance model should be effective even if the blood content is higher, especially because we were able to model the reflectance obtained in vivo from a xenograft in a mouse with an average error in fit of less than 12% in the diagnostically relevant wavelength range of 455 nm to 525 nm. Challenges associated with obtaining an accurate reflectance fit near 425 and 550 nm (where hemoglobin absorption is noticeable) can potentially be resolved by fitting each individual reflectance spectrum to an empirical equation [24,25], a photon migration model [39,40], or the P3 approximation . Another test of the model could involve comparing the intrinsic fluorescence extracted via a Beer-Lambert factor (Eq. (6)) with that obtained with a more detailed photon migration model [39,40]. Plans for an in vivo human study have been developed and are pending institutional approval.
Overall, the mathematical models of reflectance and fluorescence developed in this paper are potentially useful tools for pancreatic cancer diagnostics because of their ability to quantitatively link the experimental results of optical spectroscopy with those of histopathology. Figures 1 and 2 show that the mathematical model of reflectance presented in this paper was able to quantitatively describe the reflectance spectra of normal pancreatic tissue, pancreatitis, and pancreatic adenocarcinoma in terms of biomedically relevant parameters. The algorithm to model the reflectance was rapid, taking less than 7 minutes to execute. Furthermore, the concept of scaling an average measured normal pancreatic tissue reflectance spectrum to obtain the pancreatitis and adenocarcinoma spectra was found to be helpful with data interpretation due to its intuitive nature. Figure 3 shows the capability of the reflectance model to extract, for the first time (to our knowledge), absorption and reduced scattering coefficients of the aforementioned human pancreatic tissue types. When the measured fluorescence spectra were corrected for attenuation artifacts (Fig. 4), the resulting intrinsic fluorescence spectra revealed differences in collagen content that correlated with histology (Table 2). The, rapid, intuitive, and biomedically relevant nature of these methods suggests that the approach outlined in this work may be of potential use not only for pancreatic cancer detection, but also for other optical diagnostic applications involving a wider range of biological tissues.
This project is supported in part by the National Institutes of Health (NIH CA-114542), The National Pancreas Foundation, the Wallace H. Coulter Foundation, the University of Michigan Comprehensive Cancer Center, and a grant from the University of Michigan Medical School Translational Research Program.
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