1.1.

SFDI

SFDI combines “structured illumination” projections with a camera-based imaging system in order to quantify subsurface absorption (μ _a) and reduced-scattering (μ _s ^′) coefficients on a pixel-by-pixel basis.¹ Deduced optical properties may be diagnostically useful, or can be subsequently further reduced to chromophore concentrations via Beer's law. The SFDI platform consists of three basic components: a light source, a spatial light modulator, and a CCD camera for the detection of remitted light.¹ During skin imaging, a spatially-modulated illumination scheme with various spatial frequencies is projected over a large area of tissue. The remitted diffuse light is detected via a CCD camera and then demodulated in order to extract the structured ac component of the diffuse reflectance at multiple spatial frequencies.¹ Due to the differential sensitivity of the diffuse reflectance to absorption and scattering at specific spatial frequencies, these two coefficients can then be reconstructed using algorithms developed in the spatial frequency domain.¹ By repeating this process through different wavelengths, quantitative tissue chromophore concentrations can be generated.

1.2.

SFDI Optical Property Determination

Diffuse light-transport in turbid media is a complex phenomenon governed by multiple absorption and scattering events, both of which can be characterized by absorption coefficients, μ _a, and reduced-scattering coefficients, μ _s ^′.⁶ These fundamental optical properties of tissue can provide essential information for many therapeutic and diagnostic applications.^{2, 3, 4}

Optical properties can be deduced in the spatial frequency domain using the diffusion approximation to the Boltzmann transport equation where the diffuse reflectance is a function of the ratio between the effective attenuation coefficient, μ^′ _eff, and the transport coefficient, μ_tr, where μ^′ _eff = (3μ_aμ_tr + k ²)^1/2, μ_tr = (μ _a + μ_s ^′), and k is the spatial frequency.⁷ As shown by Cuccia, the spatial frequency, k, is directly related to the contribution of both the absorption and reduced-scattering coefficients to the diffuse reflectance. At lower spatial frequencies close to 0, the contribution of absorption is predominant and gradually decreases as the spatial frequency increases.¹ By utilizing this relationship across two or more spatial frequencies, the wavelength-dependent absorption and reduced-scattering coefficients can be solved analytically through a least-squares fitting method.

However, because diffusion approximation is only valid when μ _s ^′ ≫ μ _a, a transport-based forward-model such as a Monte Carlo simulation may be preferable in order to account for a larger range of absorption and reduced-scattering coefficients.¹ Due to the computationally intensive nature of this method, a rapid two-frequency lookup-table approach was generated from the “white” Monte Carlo simulation of a collimated point source illumination in a purely scattering medium.^{1, 8, 9} Lookup tables correlate modeled two-spatial frequency (ac and dc) diffuse reflectance to a population of absorption and reduced-scattering coefficient combinations. Compared to the computationally intensive full diffusion model or Monte Carlo simulation, using a lookup table can significantly decrease computation time while maintaining a deviation of less than 10% from expected reduced-scattering values and less than 15% from expected absorption values.¹ For example, while a Monte Carlo simulation may take 2 h in order to compute solutions, the lookup table-based process may take only 6 min running on a 1.86 Ghz dual-core desktop PC with 3 GB of RAM. In addition, the lookup table approach does not require an initial guess of optical properties, which is especially convenient when extracting optical properties over a wide range of values.¹

Once optical properties have been computed, chromophore concentrations can be obtained using Beer's Law. Specifically, after obtaining the pixel-by-pixel absorption and reduced-scattering coefficients at each wavelength, a basis set of molar extinction coefficients can be fit to the recovered absorption coefficients. Typically, in the 650 to 1000 nm near-infrared window, these include oxy- and deoxy-hemoglobin, water, and melanin.¹ Extraction of chromophore concentrations from motion corrected SFDI data acquired will be the focus of future work and will not be discussed further here.

1.3.

Need for SFDI Motion Correction

While SFDI has been a useful tool in various research endeavors,^{2, 3, 4} there is still the important challenge of developing a clinically deployable SFDI system. Part of this challenge, and the main topic of this paper, is related to the development of a strategy for effective compensation of subject motion, which in turn is critical for recording high fidelity optical properties. Depending on the hardware and autoexposure settings, a typical clinical data collection using the SFDI system described above can require the integration of signal for several seconds for each desired combination of wavelengths, spatial frequencies, and phases. During this time, the region-of-interest (ROI) will be displaced slightly by patient movement. The longer an SFDI measurement session takes to acquire data, the more likely the ROI will deviate from its initial position and shift the phase relations of the spatially-modulated projections in the lateral direction of the sinusoid. This, in turn, suggests that SFDI motion-correction will consist of a two-part procedure:

In order to reposition and align the imaging ROI, a Canny edge detection algorithm is used for the purpose of detecting and tracking the position of a skin-surface fiduciary-marker. Motion-induced phase-shifts are subsequently sampled before the entire image-set is processed by a modified demodulation equation.

2.1.

Instrumentation and Data Acquisition Settings

In terms of specific instrumentation used in this investigation, the SFDI apparatus consists of a 250 W tungsten lamp connected to a Newport Corporation (Irvine, California) power source.⁷ This light is used to illuminate the spatially modulated projections created by the 1,024 × 768 pixels DLP Developer's Kit digital micromirror device (DMD) (Texas Instruments, Dallas, Texas). Sinusoidal intensity patterns for specified spatial frequencies are generated by a computer and sequentially projected via the DMD at 3 phases: 0, 120, and 240 deg. Diffusely reflected light images are acquired using a Nuance Multispectral Imaging System (CRi, Inc., Woburn, Massachusetts) consisting of a liquid-crystal tunable filter capable of passing discrete 10 nm bandwidth wavelengths between 650 and 1050 nm into a 1040 ×1392 pixel front-illuminated CCD camera. Specular diffuse skin reflectance is rejected through the incorporation of cross-linear polarizers into the optics of the camera and projection system. The measurement images were saved as binary files for post-acquisition processing. The diffuse reflectance images are calibrated for system response by using a 96 mm ×96 mm ×10 mm tissue simulating phantom with known optical properties (μ _a = 0.0188 mm⁻¹ and μ _s ^′ = 1.098 mm⁻¹ at 650 nm). The phantoms were created using silicon-based polydimethylsiloxane with homogeneously distributed India ink as an absorber and TiO₂ as a scattering agent.¹⁰ Spectral absorption and reduced-scattering coefficients of the calibration phantoms were verified using two-distance frequency domain photon migration (FDPM) measurement, which is an inherently self-calibrating measurement.¹¹

While the FOV for the SFDI system is highly scalable, for the purpose of this study, we maintained a FOV with a 70 mm × 95 mm dimension. Data acquisition times are largely dependent on the CCD exposure settings for each recorded image. While acquisition times could have been reduced (though not fully eliminated) by imaging fewer wavelengths and frequencies, in order to ensure a comprehensive data-set capable of being reprocessed under wide range of settings for future studies, the following parameters were used for this study: SFDI measurements were acquired at five spatial frequencies equally spaced between 0 and 0.25 mm⁻¹: the first being the zero-frequency followed by four progressively higher frequencies. Seventeen spectral wavelengths between 650 and 970 nm were acquired in 20 nm intervals. Data acquisition times averaged about 2.5 min per measurement comprised of 5 frequencies, 3 phases, 17 wavelengths, and 255 images total.

Figure 1 depicts the acquisition process. Imaging times are dependent on the optical properties of the target at the specified wavelengths, and can vary from 100 ms up to 3 s. Frequency switching and phase-shifting times are about 20 μs and are not a significant contribution to the acquisition time. Due to the acquisition times for each imaged wavelength within a phase acquisition as seen in Fig. 1, motion artifacts from seemingly trivial actions such as breathing have the potential of altering the position of the projected phase-shifts in relation to the target. For example, if the total acquisition time for all wavelengths for a given spatial frequency at a given phase shift is about 10 s and 3 phase shifts are required to generate the demodulated reflectance image, M _ac, for a specified spatial frequency and wavelength combination, then the 3 images required for demodulation are inherently separated by about 10 s in time.

Fig. 1

Diagram illustrating the SFDI acquisition process with respect to time, t. Each block represents an image acquired at a specific wavelength, λ _. After the first set of specified wavelengths has been imaged, the same wavelengths are then acquired with the following phase shift, Φ. After all phase shifts are complete, another set of wavelengths and phase shifts are then completed at the next specified spatial frequency until all required measurements are complete. Three phase-shifted images, *, are required to generate the demodulated reflectance images for each specified wavelength and frequency combination.

ROI's were manually defined by the user in order to select a large enough region encompassing the lesion and normal skin sample. Optical property determination was achieved by using the two-frequency (0 and 0.15 mm⁻¹) lookup table for rapid calculation of optical properties generated from Monte Carlo forward predictions as described earlier. In order to reduce the processing time, the lookup table was limited to an absorption range of 0.003 to 0.5 mm⁻¹ and a reduced-scattering range of 0.3 to 6 mm⁻¹. All computations were done in MATLAB using a 1.86 Ghz dual-core desktop PC with 3 GB of RAM.

2.2.

Motion Tracking and Correction

The first part of SFDI motion-correction involves motion tracking of the collected images and collating the set so that the ROI in each frame stays consistent throughout post-acquisition data processing. This is accomplished through the use of a fiduciary marker and the Canny edge detection function included in MATLAB. The fiducial is used as a fixed reference point that is easily identifiable by an edge detection operator since it maintains high contrast from tissue at all near-infrared wavelengths imaged with this system. By tracking the frame-to-frame movement of the fiducial, motion information is recorded and used to crop and reposition the image set for consistent data processing as seen in Fig. 2.

Fig. 2

Illustration outlining SFDI motion tracking and correction. (a) A fiduciary marker (upper left) is placed near the pigmented lesion (center) before imaging. (b) During data processing, Canny edge detection is used to mark and track the position of the fiducial. For each individual frame, a ROI is specified with relation to the fiducial's position. (c) The specified ROI's are cropped and collated in order to maintain frame-by-frame consistencies during demodulation. (d) The same ROI is applied to a reference phantom measurement in order to sample ROI specific phase-shifts, (e), for later use in demodulation correction.

The same frame-to-frame motion and ROI cropping information is then applied to a large field-of-view calibration phantom measurement in order to sample (through sine-wave fitting of the summed intensities) the motion-altered phase-shifts, Φ_{s ,} for later use in demodulation. This is done once per sample. The use of a well characterized calibration phantom with homogeneous and well-characterized optical properties ensures accurate phase-shift reproductions whereas direct sampling of the subject's skin would be inaccurate due to the heterogeneities in optical properties present.

Fiducial markers can take the form of just about anything as long as they remain in one place on the subject, are easy to remove after imaging, and are visible at all wavelengths of interest. For this investigation, we used circular shaped reflective stickers (Michael's craft store, Costa Mesa, California). These markers, as opposed to the actual skin-lesion, are used as the motion-tracking reference because skin-lesion surface visibility decreases significantly at longer wavelengths (>800 nm).

2.3.

Demodulation Correction

The diffusely-reflected image intensities, I, collected by the CCD camera are described as a sum of the illuminated spatially modulated ac and background planar dc components. These can be written as:

This leads us to the second part of motion-correction in SFDI: modification of the demodulation equation in order to account for motion-related phase-shifts. For arbitrary phase-shifts in Eq. 1, Eq. 2 will reduce into a value consisting of a function, κ(x), multiplied by the ac magnitude squared:

2.4.

Clinical Subjects

In vivo data was collected under the IRB approved protocol HS No. 2008-6307. Under this protocol, patients with suspicious skin-lesions were consented and imaged before subsequently being diagnosed by a dermatologist.

SFDI data was gathered from 7 subjects, including 1 case study subject. All lesions were clinically benign. Subjects were all middle-aged and light-skinned Caucasian. Data was subsequently analyzed with and without the motion correction scheme described herein.

3.1.

Testing and Validation on Tissue Simulating Phantoms

In order to assess the validity of the motion-correction technique, moving phantom measurements were conducted followed by measurements in which the phantom was stationary. Artificial tissue-simulating phantoms with superficial lesions located at the surface (5 mm in diameter and 3 mm deep) were created from silicon-based polydimethylsiloxane with homogeneously distributed India ink as an absorber and TiO₂ as a scattering agent.¹⁰ The absorption and reduced scattering coefficients of the test-lesion was μ _a = 0.299 mm⁻¹ at 650 nm and μ_s ^′ = 1.013 mm⁻¹ at 650 nm, respectively. The absorption and reduced scattering coefficients of the phantom-skin surrounding the lesion was μ_a = 0.0233 mm⁻¹ at 650 nm and μ_s ^′ = 0.728 mm⁻¹ at 650 nm, respectively. Both were verified using two-distance, multifrequency FDPM measurement, as mentioned in Sec. 2.1.

Stationary phantom measurements were used both as a gold standard reference for the evaluation of the correction method on data collected from a moving phantom and to verify that this correction method does not introduce any additional errors or artifacts when applied to stationary samples. Under ideal, stationary conditions, SFDI measurements would consistently maintain symmetrical 120 deg phase-shifts and the motion-corrected demodulation equation, Eq. 6, would simplify into the noncorrected demodulation formula, Eq. 3. In this case, both processing methods should become identical and produce similar results. With motion involved, the phase-shifts and ROI's would no longer be consistent and any noncorrected data would be skewed. Figures 3a, 3b show the results from a stationary phantom-measurement, and Figs. 4a, 4b show the results from a moving-phantom measurement. Data points on the plots indicate the ROI pixel averages while error bars indicate the distribution of variances within the same ROI.

Fig. 3

Comparison between noncorrected and motion-corrected SFDI processing on a stationary phantom-lesion measurement. The absorption versus wavelength plots (a) and reduced-scattering versus wavelength plots (b) in both results show no significant difference (<1.3%) between noncorrected and motion corrected data, thus implying that the proposed motion-correction technique does not induce artifacts into the data processing.

Fig. 4

Comparison between noncorrected and motion-corrected SFDI processing on a moving phantom-lesion measurement. Both the absorption versus wavelength (a) and reduced-scattering versus wavelength plots (b) exhibit a wide difference between wavelength specific mean values for noncorrected and motion corrected data. Large variances can also be seen in the noncorrected data.

In Fig. 3, there are no significant differences (<1.3% for any wavelength measured) between the absorption and scattering results when using both the standard and motion correction processing methods. Variance is minuscule in the absorption and scattering plots for both noncorrected and motion-corrected results. The lack of difference in the results implies that the proposed motion-correction technique does not introduce artifacts into the data processing despite the requirement of additional data sampling and processing steps, and suggests that the proposed motion-correction technique is valid for additional clinical studies.

Further validating the technique and illustrating its necessity are the “absorption versus wavelength” [Fig. 4a] and “reduced-scattering versus wavelength” [Fig. 4b] plots from the moving phantom measurement. In order to simulate arbitrary phase-shifts, the phantom was displaced about 2.5 mm manually in the lateral direction of the sinusoid at approximately 0.5 Hz during the entire measurement. This amount and rate of displacement is much higher than would be expected in a clinical setting and serves as an extreme case for motion-correction. Motion-corrected results are nearly identical to those found in Fig. 3, while the noncorrected data exhibits large variances and wide differences between wavelength specific mean values compared to the motion-corrected data. This is most likely attributed to crosstalk between the test-lesion's and phantom-skin's contrasting optical properties and can be visually seen in optical property maps as a “blurring” artifact in Fig. 5a. Reduced-scattering values [Fig. 4b] in particular were most affected due to increased sensitivity at higher spatial-frequencies,¹ and because of the greater relative phase-shifts produced by motion artifacts at higher spatial frequencies.

Fig. 5

Comparison of absorption maps at 650 nm for a moving test lesion where: (a) no motion correction is applied, (b) images are reregistered to compensate for motion, but the demodulation calculation still assumes 120 deg phase separation [i.e., Eq. 3] (c) is motion corrected using a consistent ROI and demodulation correction. (d) The absorption map at 650 nm for an ideal stationary test phantom. Dashed squares indicate areas sampled for extracting data.

Figure 5 also illustrates the consequences of only applying intermediate steps of this correction process. Fig. 5a shows the resulting absorption map of the lesion at 650 nm without applying any motion correction. Here the lesion is blurred laterally. As the lowest spatial frequency holds the greatest contrast with absorption, the overlaid three circular lesions in this image actually represent the motion artifact induced between the three phase images acquired at the spatial frequency, f _x = 0 mm⁻¹. Reregistering the images in order to maintain consistent ROI's of the lesion removes this artifact; however, without demodulation correction, introduces significant background noise into the extracted data [“striations” in Fig. 5b] due to phase-shift errors.¹ In order to compensate for all motion-related effects in SFDI, both ROI correction and demodulation correction must be implemented in order to reduce all motion artifacts as seen in Fig. 5c.

3.2.

Clinical Case Study

After verifying that the motion-correction technique was comparable to the original noncorrected method, measurements on human subjects were conducted. The goal of these experiments was to verify the algorithm's deduction of optical properties from moving tissue and to determine the adequacy of the overall approach. In presenting and discussing the results of this study, we will first show the results from two case studies followed by a set of clinical measurements.

Both the stationary and moving results presented below were collected from the same subject, a middle-aged Caucasian male with a 5-mm diameter pigmented-lesion located on the upper-right portion of their back. In both measurements, the subject was prone on a hospital gurney.

Stationary case study.

During this measurement, the subject was instructed to lie as still as possible. Regardless, autonomic actions such as breathing and involuntary twitches were still present. Motion tracking data indicated lesion displacements of up to 0.5 mm (the lesion itself was about 5-mm wide).

Looking at the absorption versus wavelength and reduced-scattering versus wavelength plots for the noncorrected data set [Figs. 6a, 6c], it is apparent that even the slightest movement can cause a significant increase in optical property variance for the ROI’s, especially in the shorter wavelengths (650 to 730 nm) where melanin is a primary absorber. It is also clear that motion-correction minimizes the variance in optical properties. For this particular stationary clinical subject, an 83.88% variance decrease was observed in the absorption versus wavelength plot after applying motion-correction. An 84.29% variance decrease was observed in the scattering versus wavelength plot after applying motion-correction.

Fig. 6

Comparison between noncorrected and motion-corrected SFDI processing on the case subject's 5-mm wide skin-lesion. Stationary measurements [(a) and (c)] included lesion displacements of up to 0.5 mm while moving measurements [(b) and (d)] included lesion displacements of up 7.1 mm. At the shorter wavelengths (650 to 710 nm), there is a noticeable decrease in variance between the noncorrected and motion-corrected absorption versus wavelength plots [(a) and (b)]. A similar trend can be seen between the noncorrected and motion-corrected reduced-scattering versus wavelength plots [(c) and (d)].

Average results from other clinical measurements.

The results presented in this section represent the average optical property values from six other clinical measurements. Unlike the case-study described earlier, these subjects were only imaged once and were only instructed to move as little as possible during the measurements. Lesions varied in locations around the body, but were all imaged on a relatively flat two-dimensional (2D) plane as the depth of focus of the instrument is ±1 cm. Data acquisition and processing methods have been developed to address surface curvatures of a larger ±3 cm range;¹³ however, these methods were not deployed in this study because the goal was to evaluate the performance of the 2D motion correction technique. The average skin-lesion size was 4.16 mm in diameter with the smallest lesion having a 3-mm width and the biggest lesion having a 6-mm width. Motion tracking indicated an average fiducial displacement of about 2.08 mm per measurement, with 0.5 mm being the smallest displacement and 5 mm being the largest displacement.

As shown in Fig. 7, the average optical property plots for these six other clinical measurements display very similar trends to those found in the case study depicted in Fig. 6. At the shorter 650 to 730 nm wavelengths where melanin is a primary absorber, data distribution is much more pronounced and varied in the noncorrected absorption versus wavelength [Fig. 7a] and reduced-scattering versus wavelength plots [Fig. 7c]. While the large error bars could be solely due to interpatient variation in absorption and scattering, had this been the case, the variations would have also been apparent in the motion-corrected plots [Fig. 7b, 7d]. When comparing the results, it can be seen that the error bars in the motion-corrected plots are significantly smaller than those found in the noncorrected plots.

Fig. 7

Comparison between the average optical property results from six clinical patient measurements using noncorrected [(a) and (c)] and motion-corrected [(b) and (d)] SFDI processing. Similar to the results found in the previous case study (Fig. 6), there is a very noticeable decrease in data variation between the noncorrected (a) and motion-corrected (b) absorption versus wavelength plots at the shorter 650 to 730 nm wavelengths. The same trend is noticeable between the noncorrected (c) and motion-corrected (d) reduced-scattering versus wavelength plots, however, with a much more significant impact where the noncorrected reduced-scattering versus wavelength plot (c) implies that reduced-scattering values are generally larger in pigmented lesions than compared to normal skin. The motion-corrected reduced-scattering versus wavelength plot (d) suggests otherwise.