System description

Diagrams of the experimental setup and fiberoptic probe face used to perform diffuse reflectance measurements are presented in Figure 1. The source is a 405 nm diode laser (LCDU 12/5431, Power Technology, Inc; Little Rock, AR) with a power level of 2.5 mW. The input power is adjusted using neutral density (ND) filters (CVI Laser Corporation, Albuquerque, NM). The custom designed fiberoptic probe (FiberTech Optica, Ontario, Canada) is used to deliver laser light from the source to the sample and guide diffuse reflectance from the sample to the detector. The diameter of the probe face is 0.5 cm which would make it practical for in vivo studies of internal organ sites. The probe contains 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. The detection legs are connected to five in-line filters (FHS-UV, Ocean Optics, Dunedin, FL) three of which contained ND filters. The filter holders are coupled to the legs of a second probe, the common end of which contains a linear fiber array that was aligned to the entrance slit of an imaging spectrometer (SpectraPro 300i, Acton Research Corp., Acton, MA). The output of the spectrometer is detected by a low noise, high dynamic range (16-bit) CCD camera (Princeton Instruments Spec10:400B, Trenton, New Jersey) and acquired using proprietary software (WinSpec Princeton Instruments, Trenton, NJ).

Experimental system modifications

In our previous system, the large range of light levels (Figure 2) incident on the detector necessitated measurements at multiple exposure durations to acquire a single reflectance distribution. By improving the homogeneity of light levels delivered by the fiberoptic probe, a single CCD acquisition could record all fiber intensities. This was achieved by using in-line ND filters [24] for each fiber. By analyzing the detected signal levels for four samples at the edges of the designated optical property parameter space (μ_a = 1, 25 cm^-1, ${{\mu }^{\prime }}_{\text{s}}$ = 5, 25 cm^-1) we identified a combination of ND filters for each fiber which would produce moderately high output levels on the CCD without inducing saturation. Combined attenuation levels of 2.2, 1.9, and 0.3 OD were used for the fibers at separation distances of 0.5, 1.0 and 2.0 mm. The ND levels chosen for these fibers appear irregular due to variations in fiber transmittance and in coupling efficiency of the in-line filters. Thus the system was optimized in such a way that a single set of ND filters could be used to collect reflectance for in vitro or in vivo samples having optical properties anywhere within the relevant range (μ_a = 1–25 cm^-1, ${{\mu }^{\prime }}_{\text{s}}$ = 5–25 cm^-1). Figure 2 shows computational modeling results for a sample with μ_a = 25 cm^-1, ${{\mu }^{\prime }}_{\text{s}}$ = 15 cm^-1 in order to illustrate the wide range of intensities that must be detected. This graph also includes a measurement of a tissue phantom with the same optical properties, indicating that the variation of intensity at the CCD has been reduced from five orders of magnitude to two through the use of ND filters. The exposure duration required for acquiring sufficient signal ranged from 0.12 to 25 seconds depending on the sample attenuation level.

The second optimization task involved enabling absolute measurements by calibrating the measured intensity to simulation results. In order to accomplish this goal, CCD measurements for all detection fibers were made at two different illumination intensities in three different phantoms : μ_a = 1 cm^-1 and ${{\mu }^{\prime }}_{\text{s}}$ = 5 cm^-1, μ_a = 1 cm^-1 and ${{\mu }^{\prime }}_{\text{s}}$ = 25 cm^-1 and μ_a = 2 cm^-1 and ${{\mu }^{\prime }}_{\text{s}}$ = 25 cm^-1. For each fiber position, the relationship between measured CCD counts and Monte Carlo-predicted intensity levels were graphed for the two phantoms. A linear fit to these points and the origin was calculated for each fiber. These linear fits were used as calibration equations to convert CCD counts to absolute intensity levels for all measurements during this study.

Bifurcated fiberoptic probe measurements

The objective of this component of the study was to evaluate the utility of adding a bifurcated illumination fiber to the linear-array geometry. This work was performed for two primary reasons: (1) computational results that indicate that at positions near the illumination fiber there is a relatively high level of variation in reflectance intensity as ${{\mu }^{\prime }}_{\text{s}}$ changes [23]; and (2) a prior investigation has indicated that a sized-fiber approach involving collecting reflectance at the site of illumination is highly effective for determining tissue optical properties [19]. A bifurcated fiberoptic probe (Innova Quartz, Phoenix, AZ) – illumination and collection fibers fused to a third common fiber which contacted the sample – with a core diameter of 0.2 mm and NA of 0.22 was used to perform the measurements (Figure 3) [25]. Light collected from the detection leg of the probe was measured by a power meter (Newport Model 1930C, 818-ST-UV detector, Irvine, CA) for each of the 60 samples previously used for the linear array measurements.

The reflectance collected at the illumination site of the sample is the total reflectance (R_total) which consists of two components: diffuse reflectance (R_diffuse) and specular reflectance (R_specular). Fresnel reflections for both fiber core/air and fiber core/water were measured. The probe geometry resulted in multiple reflections at the bifurcation point. Thus, baseline reflectance measurement was made using fiber core refractive index matching liquid (n = 1.47, Cargille Laboratories, Inc; Cedar Grove, NJ). R_diffuse was obtained by normalizing all the data points to the Fresnel reflections for the fiber core/water as shown below:

R _diffuse = R _total - R _specular     (1)

$R_{total}=\frac{\left(P_{sample}-P_{\eta }\right)}{E.F.\ast P_{input}}\left(2\right)$

$R_{specular}=\frac{\left(P_{water}-P_{\eta }\right)}{E.F.\ast P_{input}}\left(3\right)$

Where,

P _sample = Power measured from the sample

P _η = Power measured from the index matching liquid

P _water = Power output from fiber core/water

P _input = Power output from the probe

E.F. = Fiber efficiency factor obtained for the collection fiber

Experimentally measured Fresnel reflectance was within 10% of the theoretical value for the fiber core/water interface. The fiber efficiency factor was obtained by coupling light from a 100 μm core diameter fiber into the common end of the bifurcated fiber and measuring the output from the detection leg of the probe. Measurements were made on the same sets of phantoms used for linear-array fiber system.

Tissue phantoms

Since the validity of the system evaluation is dependent on the accuracy of tissue phantom optical properties, evaluation of phantom materials and benchmarking of phantoms was performed at the outset of this study. The optical properties of individual tissue phantoms were determined using an inverse adding-doubling approach [26] and a spectrophotometer (Shimadzu UV-3101PC, Columbia, MD). This data was compared to theoretical estimates based on Mie theory and direct collimated absorption measurements of the scatterer and absorber, respectively.

Polystyrene microspheres have been used to provide scattering for tissue phantoms in prior studies due to their minimal levels of fluorescence and absorbance as well as their ability to remain in suspension for a long durations. Furthermore, microspheres have a g value which is close to that of biological tissue [27, 28]. In order to achieve a g of approximately 0.9, microspheres with a particle size of 1.053 μm (and thus a g of 0.912) were chosen for this study. In order to insure that the absorber used was a pure absorber, absorption and thus transmission should be linear with the concentration in the desired range of absorption coefficient. These measurements were validated against an independent laser setup. As observed in a prior study [29], India ink is particulate in nature with a significant scattering component. Thus, Nigrosin which is the most common absorber cited in literature and which has a linear transmittance with concentration, was chosen as the absorber. The stock absorption coefficient was measured in a spectrophotometer and subsequently diluted to get the required μ_a for the phantom within the range 1 to 25 cm^-1.

For the reflectance study, a set of 10 phantoms with uniform optical properties and a set of 60 phantoms with random optical properties were constructed. All phantoms were in liquid form, which enabled us to slightly submerge the tip of the fiberoptic probe for optimal fiber-sample coupling. The uniform optical properties had the following values: 1) with μ_a held constant at 15 cm^-1 and ${{\mu }^{\prime }}_{\text{s}}$ = 5, 10, 15, 20 and 25 cm^-1; and, 2) with ${{\mu }^{\prime }}_{\text{s}}$ held constant at 15 cm^-1 and μ_a = 1, 5, 10, 15, 20 and 25 cm^-1. The random optical properties were distributed over a μ_a range of 1 to 25 cm^-1 and ${{\mu }^{\prime }}_{\text{s}}$ range of 5 to 25 cm^-1.

Neural network modeling

Evaluation of the optical property measurement technique was performed by developing a NN based inverse model [23] which when provided reflectance data collected from a sample will generate an estimation of μ_a and ${{\mu }^{\prime }}_{\text{s}}$. The NN algorithm implemented a feed-forward backpropagation network with a Levenburg-Marquardt training function. The input layer contained five and six nodes for the linear array and bifurcated designs, respectively. The output layer contained two nodes, for the predicted optical properties. Optical property calculations were performed offline and required minimal processing time (< 1 sec) for data files that incorporated as many as 60 samples.

Raw reflectance data from computational or experimental results for linear-array probe were preprocessed prior to use in the neural network model:

S = -log R     (4)

where R is the power of the detected reflectance normalized to the illumination power. NN model calibration was performed using 30 sets of simulated-uniform reflectance (S) distributions, generated by the Monte Carlo modeling approach described previously [23, 30]. Validation was performed against the 30 simulated-uniform (self-validation) and 60 measured phantoms with randomly distributed optical properties.

The linear-array probe data used to calibrate and test the NN models contained reflectance sets comprised of five S values, corresponding to the five detection fibers. When evaluating the models for the bifurcated probe system, the sixth unprocessed (no log taken) reflectance value – R_diffuse from the illumination site – was added to the linear-array data.

The NN prediction results were analyzed according to the percent deviation from the expected values as follows:

$\%Error=\frac{\left({\mu }_{True}-{\mu }_{Estimated}\right)}{{\mu }_{True}}\left(5\right)$

$\overline{\%Error}=\frac{{\displaystyle \sum _{i=1}^{i=n}\left|Erro{r}_i\right|}}{n}\left(6\right)$

Equation (5) denotes the formula used to generate each of the error data points in the results graphs, whereas equation (6) was used to calculate the overall error for a set of data.

Validation of calibrated system

Initial validation of the fiberoptic based diffuse reflectance was carried out for the linear-array probe system. The calibration curves for converting CCD pixel counts to absolute intensity measurements were well-behaved, producing linear fits with R² values of 0.99 for all five detection fibers. Comparisons between experimental phantom measurements and Monte Carlo simulations for uniformly distributed optical property pairs (n = 10) indicated excellent agreement over a wide range of μ_a and ${{\mu }^{\prime }}_{\text{s}}$ values (Figure 4).

Linear-array probe

A self-validation analysis was performed on simulated data to evaluate the performance and the theoretical limit of inverse model accuracy. The results of this analysis are shown in terms of mean prediction error in Table 1. Experimental evaluation was performed by measuring reflectance in 60 tissue phantoms with random optical properties over the following ranges: μ_a from 1 to 25 cm^-1 and ${{\mu }^{\prime }}_{\text{s}}$ from 5 to 25 cm^-1. The optical property prediction accuracy for each measurement is displayed in Figure 5, with mean values displayed in Table 1. Low levels of error – less than 6% – are seen across most of the μ_a range (3 cm^-1 up to 25 cm^-1). However, in the μ_a < 3 cm^-1 region, accuracy degraded rapidly, with four data points showing errors of 14–19%. This increased error is likely due to two factors: (a) the accuracy of the neural network routine degrades at the boundaries of the range over which it was calibrated and (b) since the μ_a values in the aforementioned region are small, the same absolute levels of error that occur for larger μ_a values result in much greater percentage errors. Figure 5b indicates that although the vast majority of ${{\mu }^{\prime }}_{\text{s}}$ predictions were within ± 10% of the true value, a minor trend towards under-prediction at higher ${{\mu }^{\prime }}_{\text{s}}$ values is seen. Two of the 20% under-predictions in this graph occurred for samples in which the true μ_a value was low and prediction error for μ_a was large. The data point showing the greatest error in ${{\mu }^{\prime }}_{\text{s}}$ (43%), however, did not occur for a sample in which μ_a error was high. One potential reason for this error may be air bubbles at the fiber tip which disrupt the fiber-sample coupling.

A summary of mean errors is presented in Table 1 for both the self-validation and experimental evaluation data. While the self-validation data set shows less error for ${{\mu }^{\prime }}_{\text{s}}$ than for μ_a, measured results indicate the opposite trend. The reason for this is addressed in the discussion section. In general, the self-validation results indicate significantly better estimations than the experimental results, due in part to unavoidable experimental errors (e.g., noise in the detected signal, nonuniformity of the sample, imperfect coupling, etc.). These small errors tend to be amplified for small μ_a values, due to the two factors mentioned in the prior paragraph. Nevertheless, over the vast majority of the optical property range of interest, our approach provides a mean error level of less than 5%.

Bifurcated probe and combined approach

Initial measurements were performed to assess the accuracy of bifurcated probe technique. A comparison of measured reflectance and simulated data for a range of μ_a and ${{\mu }^{\prime }}_{\text{s}}$ values is presented in Figure 6. Excellent agreement is observed between experimental and simulated data for most cases. However, a small deviation is seen at μ_a = 5 cm^-1 and a large (25%) deviation is seen for μ_a = 1 cm^-1.

A predictive model was calibrated using simulated reflectance data corresponding to both linear array and bifurcated probe geometries. Self-validation analysis was performed using simulated data to evaluate the operation and theoretical limits of the model. The mean prediction errors for this case are presented in Table 2. The 60 tissue phantoms described in the prior section were then measured with the bifurcated probe and this data combined with the corresponding linear-array probe data. Prediction errors for this case are presented in Figure 7. The error graph for μ_a shows all five samples with true values of 2.2 cm^-1 or less as being predicted with absolute errors of 14 to 42%. The model's diffuculty with low μ_a samples also extended to ${{\mu }^{\prime }}_{\text{s}}$ predictions, likely for the same reasons that large errors were produced at low optical property values for the linear array probe. Of the four data points showing the greatest ${{\mu }^{\prime }}_{\text{s}}$ error levels, three corresponded to samples with μ_a values under 2.2 cm^-1 that were poorly predicted by the model. The remaining value may be due to air bubbles as mentioned previously. Average percent errors (Table 2) for μ_a and ${{\mu }^{\prime }}_{\text{s}}$ were calculated for simulated as well as experimental data using both the complete set of samples and a set containing only samples with μ_a values greater than 5 cm^-1. When the entire data set was considered, the addition of the bifurcated probe data caused an increase in error for μ_a while the ${{\mu }^{\prime }}_{\text{s}}$ error level did not change appreciably. However, when the limited data set was analyzed, the change in geometry resulted in a 1% reduction in prediction error for ${{\mu }^{\prime }}_{\text{s}}$ (a relative improvement of 24%) while the error for μ_a remained unchanged.

Evaluation of reflectance measurements

Initial comparisons between measured and simulated data helped to validate the basic system performance for the linear array (Figure 4) and bifurcated fiber (Figure 6) probes. These graphs indicate that good agreement was achieved between the experimentally measured diffuse reflectance and simulation results over the entire range of optical properties studied. For the linear array probe, experimental and modeled data showed small discrepancies at the most distant fiber and highest μ_a values, as well as at lower ${{\mu }^{\prime }}_{\text{s}}$ values. Bifurcated probe data show good agreement as well, with the exception of very low μ_a values, where the experimental values are significantly larger than the simulation data. Further discussion of the source of this discrepancy is provided in the "Analysis of Combined Probe Approach" section.

Notable trends in reflectance

Data in Figures 4 and 6 provide insight into general trends in reflectance as well as the performance of optical property estimation models. As seen in these figures and noted in our prior study [23], an increase in μ_a causes relatively large decreases in reflectance, whereas increasing ${{\mu }^{\prime }}_{\text{s}}$ produces less substantial variations. This is due to the fact that μ_a directly affects absorption of photons all along the path from source to detector, whereas ${{\mu }^{\prime }}_{\text{s}}$, influences the diffuse nature of photon propagation which has a less direct influence on attenuation. Given the larger changes in reflectance with μ_a than ${{\mu }^{\prime }}_{\text{s}}$, one would expect that for measurements with any significant level of error, the optical property estimation error would be greater for ${{\mu }^{\prime }}_{\text{s}}$ than for μ_a. This was shown to be true for evaluations with experimental data (Tables 1 and 2). While the self-validation results produced equivalent or greater errors for μ_a than ${{\mu }^{\prime }}_{\text{s}}$, these error levels were minimal. Figure 4a also indicates that the measured reflectance is slightly greater than the simulated reflectance for high ${{\mu }^{\prime }}_{\text{s}}$ at the 2.5 mm position. These discrepancies appear to have been small enough to not significantly impact the predictions in Figure 5.

Reflectance data in Figure 4(b) indicate other interesting trends. Changes in reflectance intensity with ${{\mu }^{\prime }}_{\text{s}}$ at the 0.5 mm fiber are significant when ${{\mu }^{\prime }}_{\text{s}}$ values are small, but minimal when ${{\mu }^{\prime }}_{\text{s}}$ is large. Conversely, at the 2.5 mm fiber, the change in reflectance as a function of ${{\mu }^{\prime }}_{\text{s}}$ is small when ${{\mu }^{\prime }}_{\text{s}}$ is low, and becomes larger at higher ${{\mu }^{\prime }}_{\text{s}}$ values. Therefore, it is likely that reflectance from the 0.5 mm fiber is not very useful when ${{\mu }^{\prime }}_{\text{s}}$ is high and reflectance from the 2.5 mm fiber is not very useful when ${{\mu }^{\prime }}_{\text{s}}$ is low. Additionally, since reflectance at the 1.5 mm and 2 mm fibers does not appear to change significantly with ${{\mu }^{\prime }}_{\text{s}}$, these values have minimal predictive value.

For the bifurcated probe geometry (Figure 6), increases in ${{\mu }^{\prime }}_{\text{s}}$ produced an approximately linear increase in reflectance. As ${{\mu }^{\prime }}_{\text{s}}$ was increased across the entire range from 5 to 25 cm^-1, reflectance increased by 370% This early result formed the basis of our hypothesis that reflectance data at the point of illumination might provide useful information on ${{\mu }^{\prime }}_{\text{s}}$ which could be measured via a combined bifurcated-linear probe geometry.

Analysis of linear-array approach

The goal of this study was to develop a well-characterized second generation system that was highly accurate in the optical property range of interest. As mentioned previously, our prior system [23] was capable of estimating μ_a and ${{\mu }^{\prime }}_{\text{s}}$ with average errors of 12.5% and 16.2%, respectively. In the current study, the best results for the full optical property range was provided by the linear-array approach, which enabled prediction of μ_a and ${{\mu }^{\prime }}_{\text{s}}$ with errors of 3.2% and 5.6%, respectively. This represents reductions in error of 74% and 65% over our prior system. However, if the optical property range is restricted to include only μ_a values above 5 cm^-1, the combined approach provides even lower error levels: 2.2% and 3.7% for μ_a and ${{\mu }^{\prime }}_{\text{s}}$, respectively. These results represent a significant improvement over our prior system and provide evidence that the current approach has strong potential to provide accurate estimates of in vivo optical properties.

Exact comparisons of current results with prior studies are not possible due to a lack of data for diffuse-reflectance based systems in the optical property range of interest. However, our findings compare favorably with the limited data available in the literature. In one recent study [31], tissue phantoms with μ_a values in the range of 1.3 cm^-1 to 31.8 cm^-1 were measured. The prediction error in this study ranged from 0.3% for a μ_a of 14.4 cm^-1 to 14% for a μ_a of 21.2 cm^-1. A second study [32] found accuracy levels within 10% for μ_a and 5% for ${{\mu }^{\prime }}_{\text{s}}$ using tissue phantoms over an optical property range that included μ_a values from 0.6 to 3.3 cm^-1 and ${{\mu }^{\prime }}_{\text{s}}$ values from 10 to 22 cm^-1. Not only are our current results comparable to those from prior studies in terms of prediction error, but the measurement of 60 random tissue phantoms enabled a more rigorous evaluation process than provided by prior studies.

Analysis of combined probe approach

The linear-array geometry (Table 1) produced a higher level of prediction accuracy for μ_a than for ${{\mu }^{\prime }}_{\text{s}}$. Given the initial results from bifurcated probe measurements (Figure 6), it was expected that the combined linear-bifurcated approach would improve the accuracy of ${{\mu }^{\prime }}_{\text{s}}$ predictions. Our findings confirm this hypothesis, although the improvements in accuracy are not obvious in all results. When all samples are considered, the implementation of the combined approach was seen to reduce the ${{\mu }^{\prime }}_{\text{s}}$ estimation error from 5.6% to 5.5 %, while the error for μ_a increased from 3.2 to 4.0%. When only samples with μ_a > 5 cm^-1 were analyzed, ${{\mu }^{\prime }}_{\text{s}}$ error improved from 4.6% to 3.7% (an improvement of 20%) while the μ_a error remained constant at 2.2%. Therefore, in general, the implementation of the bifurcated approach produced an improvement in ${{\mu }^{\prime }}_{\text{s}}$, possibly at the expense of a slight increase in μ_a error.

The limited success of the bifurcated probe geometry and discrepancy between measured and simulated data at low μ_a values (Figure 6) are likely related to two factors: (1) reflection off the probe face, which was simulated in our model as a perfect absorber and (2) discrepancies between the Henyey-Greenstein phase function used in the current study and the true phase function of the sample. While the probe face is not a perfect absorber, additional simulations performed with our model indicate that even if it were 100% reflective, the increase in detected signal for μ_a = 1 cm^-1, ${{\mu }^{\prime }}_{\text{s}}$ = 15 cm^-1 would only be about 15%. Therefore, it is not likely that this is the primary for the discrepancy noted in Figure 6. Prior studies have indicated that for small source-detector separation distances, models based on the Henyey-Greenstein phase function may not produce accurate reflectance predictions due to underestimation of backscattered photons [33, 34]. While neither of these prior studies included high μ_a values, Mourant et al. provided simulation data for ${{\mu }^{\prime }}_{\text{s}}$ = 12.2 cm^-1 and μ_a = 0–2 cm^-1 in an adjacent fiber geometry which provides qualitative corroboration of the errors found with our bifurcated probe for μ_a<5 cm^-1. While the Mie phase function employed by Mourant et al. produces greater accuracy when simulating the behaviour of microspheres of a single diameter, the benefit of this approach may be reduced in complex biological tissue with a variety of scatterers. One of the only recent studies involving measurements of reflectance with a bifurcated probe showed minimal discrepancy between experimental results and Monte Carlo simulations employing a Henyey-Greenstein phase function [19]. Given these prior results, we believe that a bifurcated approach is valid at least for samples with μ_a values of 5 cm^-1 or more. However, given the apparent lack of agreement in the literature there exists a need to further elucidate the true effect of phase function on reflectance measurements and in highly attenuating turbid media. Therefore, we intend perform a future study to thoroughly characterize the influence of phase function in highly attenuating samples and thus generate more definitive answers regarding the conditions (e.g., optical properties, probe geometries, scatterer sizes) for which Henyey-Greenstein and Mie phase functions are valid. Such research will further facilitate the simulation and development of reflectance systems that employ both single- and multi-fiber probes.