Real-time simultaneous single snapshot of optical properties and blood flow using coherent spatial frequency domain imaging (cSFDI)

: In this work we present and validate a wide-field method for the real-time mapping of tissue absorption, scattering and blood flow properties over wide regions of tissue (15 cm x 15 cm) with high temporal resolution (50 frames per second). We achieve this by applying Fourier Domain demodulation techniques to coherent spatial frequency domain imaging to extract optical properties and speckle flow index from a single snapshot. Applying this technique to forearm reactive hyperemia protocols demonstrates the ability to resolve intrinsic physiological signals such as the heart beat waveform and the buildup of deoxyhemoglobin associated with oxygen consumption.


Introduction
Cameras are used ubiquitously throughout medicine as a simple noncontact approach to illustrate and document diseases. In dermatology for example, color photography captures details of skin pathology to relay information to physicians working from a remote location and is capable of monitoring disease progression over time [1]. Although useful in numerous applications, digital photography is only able to relay qualitative information. Cameras are able to capture superficial structural details of the underlying disease, but are unable to retrieve quantitative information such as the absolute concentrations of tissue biochemical constituents. Improved quantitative accuracy would make the technique a more powerful means of diagnosis, disease staging and therapeutic monitoring.
One approach to improving quantitative accuracy of cameras is to manipulate the illumination characteristics of the light source. These manipulations can consist of modulating the source intensity in space or time, controlling the source coherence, and selective choice of the source wavelength [2][3][4]. Coherent spatial frequency domain imaging (cSFDI) utilizes spatially modulated coherent light to characterize tissue absorption and scattering characteristics over scalable fields-of-view [5][6][7]. cSFDI is essentially Laser Speckle Imaging (LSI) performed in the spatial frequency domain (SFD). LSI is a technique that uses coherent light to measure blood flow in superficial microcirculation by measuring the dynamic speckle interference pattern resulting from interactions occurring between the incident light and moving red blood cells, and extrapolating this to a metric referred to as the speckle flow index (SFI) [8][9][10][11]. Although LSI is capable of rapid measurements over large spatial regions, the data lack quantitative accuracy and are limited to detecting relative changes in blood flow [12]. One reason for this is the confounding effect of spatial and temporal variations in the tissue absorption and reduced scattering coefficients (µ a and µ s ', respectively) on SFI [13].
cSFDI can decouple µ a and µ s ' with the use of Spatial Frequency Domain (SFD) techniques, and then potentially use this information to correct for errors imparted on SFI. These SFD methods, which we have previously described in detail [3,14], employ structured coherent illumination. Images of back-scattered reflectance are then acquired at multiple spatial frequencies using a CCD or CMOS detector. Computational models of photon transport are then applied to the measurements to extract µ a and µ s ' from diffuse reflectance images acquired at multiple spatial frequencies. By acquiring µ a at multiple optical wavelengths, the Beer-Lambert law can be invoked to recover the concentration of tissue chromophores such as oxyhemoglobin, deoxyhemoglobin, water and lipid [15,16]. In addition µ s ' can reveal information pertaining to tissue structure and orientation [17]. The combination of these parameters allows for the assessment of the relative metabolic rate of oxygen consumption in accordance with Fick's Principle [18,19].
Conventional cSFDI techniques require large volumes of raw data, limiting the rate at which µ a , µ s ', and SFI can be recovered. This is due to the number of raw images needed to quantitatively characterize the light-tissue interactions [20]. Recently, signal processing techniques have been applied to SFD methods to demodulate data with fewer raw images [20,21]. One method introduced by Vervandier et al. is capable of extracting tissue optical properties from a single snapshot of raw data, reducing the number of raw images by a factor of 6 [21,22]. This technique applies spatial Discrete Fourier Transforms, followed by frequency domain processing to demodulate two spatial frequencies from a single frame of raw data. In comparison with conventional demodulation methods, this approachreferred to as Single Snapshot of Optical Properties (SSOP)reduces the number of frames by a factor of 6 allowing for real-time mapping of optical properties. In addition to reducing the amount of raw data, SSOP allows for the use of static objects as a spatial light modulator since only a single pattern is needed to recover optical properties. This is in contrast to conventional demodulation approaches which require multiple patterns demanding the use of computer controlled spatial light modulators such as a digital micromirror device (DMD) or liquid crystal on silicon (LCOS) chips. In short, the ability to extract all the necessary information from a single image allows for real-time property acquisition and simplified, cost-effective instrumentation.
In this work we introduce and validate the application of SSOP demodulation to cSFDI in order to extract optical properties and speckle contrast from a single snapshot. We present the algorithmic implementation of SSOP demonstrating the steps required to extract µ a , µ s ', and SFI from a single image of spatially modulated coherent light. In addition, we introduce a simple cSFDI instrument build that requires only one sinusoidal-patterned slide to achieve spatial light modulation. Next, in two in vitro experiments we present data validating single snapshot cSFDI in comparison with conventional techniques. In the first set of experiments we use homogeneous phantoms to demonstrate our ability to accurately recover bulk optical properties. In the second validation experiment we use a flow-phantom to compare single snapshot cSFDI with conventional LSI in terms of sensitivity to changes in flow speed. Finally, we report on in vivo experiments on a human forearm undergoing post-occlusive reactive hyperemia via a cuff-occlusion-release protocol. The in vivo data demonstrate sensitivity to intrinsic physiological signals such as the accumulation of deoxyhemoglobin in occluded tissue and heartbeat fluctuations observed from SFI values. Although optical property correction can be performed on flow measurements, this computational step is left to future studies.

Materials and methods
Single snapshot cSFDI instrument setup (Fig. 1) A 120 mW 660 nm laser diode (HL6545MG Opnext Inc.) was powered and stabilized using a combined laser diode and temperature controller (Newport Corporation). Coherent light from the laser diode was spatially homogenized using a ground glass diffuser and then condensed onto a sinusoidal-patterned slide (Applied Image Inc.). The pattern was imaged onto the sample using an objective lens in off-axis configuration. The sinusoidal projection pattern had a fixed spatial frequency of 0.185 mm 1 . Data was recorded using a high-speed sCMOS camera (Hamamatsu Photonics, Orca Flash 4.0) with a cross polarizer placed in front of a 16 mm fixed focal length lens (Edmund Optics). For all experiments mentioned below, the lens aperture was f/5.6 and the integration time was 20 ms, allowing for a data acquisition rate of 50 frames per second. The aperture and integration time were set to manage the trade-off in accuracy between speckle contrast and optical properties (Fig. 1). Fig. 1. Experimental setup. Light from a coherent source is spatially modulated and projected onto a diffuse medium. Remitted light from the sample is collected using a high-speed sCMOS camera.

Three-phase demodulation from conventional SFDI
Conventional SFDI and cSFDI utilize an algebraic demodulation technique referred to as the three-phase method. This method recovers AC intensity from three frames with relative modulation phases of 0, 120, and 240 degrees. A simple algebraic formula (Eq. (1)) is applied to these phase-offset images to extract pixel-by-pixel AC information content. It should be noted that only a single spatial frequency is demodulated at a time from these three phases. 2 2 2 0 120 120 Single snapshot cSFDI data processing (Fig. 2) A single raw image is used to simultaneously extract µ a , µ s ', and SFI. In order to calculate µ a and µ s ', a Fourier transform is applied line by line to raw data to calculate the spatial frequency spectrum of each column vector. This frequency domain data is subdivided into the DC and AC component spectra using top-hat window functions. The cutoff frequency of the window functions was set to 0.11 mm 1 , and was selected to optimize demodulated image quality specific to our selected spatial frequency. The DC and AC demodulated images are then computed by performing line-by-line inverse Fourier transforms (Fig. 2). The process of converting raw data to demodulated DC and AC data is more fully described in Vervandier et al. [21] The data is calibrated using a phantom with known optical properties to calculate the calibrated diffuse reflectance (step not pictured). The calibration process is outlined extensively in Cuccia et al. [3,14]. Finally, optical properties are recovered pixel-by-pixel from the DC and AC diffuse reflectance using a Levenberg-Marquardt fit of experimental data to a light-transport model data based on Monte Carlo simulations or the photon diffusion equation [14]. The speckle flow index (SFI) is calculated from the same raw image. Similar to conventional LSI approaches, a 7 pixel x 7 pixel sliding window filter is used to calculate the local spatial standard deviation σ (I) and mean intensity <I>. The ratio of these two components is the speckle contrast (K). Finally, the SFI is calculated pixel-by-pixel according to the equation SFI = 1/(2TK 2 ) where T is the integration time and K is the speckle contrast [23]. SFI is a non-quantitative measurement used as a proxy for relative flow [23].

Homogeneous phantom experiments
Homogeneous phantoms were used to validate the ability of single snapshot cSFDI to estimate bulk optical properties by demonstrating agreement with conventional SFDI. Seven silicone phantoms with unique optical properties were constructed according to Ayers et al. [24]. The µ a of these phantoms ranged from 0.01 to 0.05 mm 1 while µ s ' ranged from 0.5 to 1.5 mm 1 . Recovered bulk optical properties were calculated using single snapshot cSFDI and the standard three-phase SFDI technique. µ a and µ s ' were determined by averaging over a 10 cm x 10 cm region over the center of each phantom. The phantom properties were chosen to demonstrate agreement between single snapshot cSFDI and conventional SFDI. The accuracy, linearity and agreement between SFDI and single snapshot SFDI has already been established over a wide range of optical properties [14,21]. Due to the non-trivial nature of the phantom making process, the optical properties are not equally spaced. The image is Fourier transformed line-by-line then window-filtered in frequency space. Component spectra are inverse-transformed and calibrated to phantom data to produce DC and AC images. Calibrated data are used to calculate µa and µs'. Right: Speckle flow index is calculated from the same raw image. A sliding window filter is used to compute the spatial standard deviation and mean intensity. The ratio of these quantities produces the speckle contrast (K) image. Speckle Flow Index (SFI) is then calculated from speckle contrast according to the equation above where T is the integration time.

Flow-phantom experiments
A wide-field flow phantom (Fig. 4) was constructed and used to validate single snapshot cSFDI. More specifically, this experiment was used to evaluate the sensitivity of this technique to changes in flow compared to conventional LSI. The phantom was constructed out of silicone using India ink as the absorbing agent and titanium dioxide as the scattering agent. A 13 mm x 13 mm square acrylic tube was embedded during the curing process to act as a flow channel. The wall thickness of the acrylic was 1.7 mm and the proximal surface of the tube was less than 500 μm beneath the surface of the silicone. The plastic tube was coupled to a syringe pump (New Era Pump Systems) to precisely control the flow speed. During the experiment, the phantom was imaged using both single snapshot cSFDI and conventional LSI while varying the speed of 1% Intralipid from 1 to 5 mm/s in 1 mm/s increments. This range was chosen to reflect red blood cell velocities encountered in microcirculation [25]. Conventional LSI was performed by projecting planar coherent illumination, while single snapshot cSFDI was performed by projecting spatially modulated coherent illumination. In every other way (aperture, exposure time, optics) the two measurements were completely identical. Fifty sequential frames were acquired at each flow speed. SFI maps were calculated for each frame and averaged over a region of interest that was positioned over the entire length of the tube. Additionally, µ a and µ s ' maps were recovered from one of the single snapshot cSFDI data sets to demonstrate its ability to recover spatial maps of all three sources of optical contrast.

Forearm reactive hyperemia experiment
An imaging study was performed on the forearm of a healthy subject undergoing a standard reactive hyperemia protocol. During this protocol an automatic inflatable cuff was wrapped around the subject's left upper arm. A full arterial occlusion was applied by inflating the cuff to 210 mmHg. During the imaging study, the volar forearm was imaged at 50 frames per second for 1 minute of baseline, followed by 3 minutes of arterial occlusion, followed by 3 minutes immediately after the release of the occlusion. Each of the 21,000 frames of data was used to reconstruct 2D maps of µ a , µ s ', and SFI. Regions of interest were analyzed to obtain time course data of µ a , µ s ' and SFI. Studies here were carried out under the UC Irvine IRB approved protocol, and informed consent was obtained from all subjects (HS# 2011-8370). Figure 3 shows the results of the homogeneous phantom experiments comparing the optical properties recovered with single snapshot cSFDI and conventional SFDI. The graph at the bottom-left of Fig. 3 shows absorption recovered with single snapshot cSFDI plotted against absorption recovered using conventional SFDI. Each point corresponds to a different homogeneous phantom with unique optical properties. The blue horizontal lines are the standard deviation over the region of interest using SFDI, while the red vertical lines are the standard deviation using single snapshot cSFDI. Each error bar in Fig. 3 is calculated from a single reconstructed image and represents the spatial standard deviation over a 10 cm x 10 cm region of interest as described in Cuccia et al. and Vervandier et al. [14,21]. The diagonal dashed line is a reference line representing perfect agreement between the two techniques. The average percent difference in µ a between the two methods was less than 1.2%. On average, the standard deviation of µ a over the region of interest using SFDI was 0.00083 mm 1 while the standard deviation using single snapshot cSFDI was 0.0013 mm 1 . The bottom right of Fig. 3 shows the comparison between bulk µ s ' reconstructed using both methods. Again, each of the points corresponds to a different phantom with unique µ s '. Due to overlap in µ s ' of some of the phantoms, only five points are shown. The average percent difference between the two methods was 0.59%. The average standard deviation in µ s ' was 0.033 and 0.045 mm 1 for conventional SFDI and single snapshot cSFDI, respectively. Overall, these plots of µ a and µ s ' demonstrate very good agreement in bulk optical property recovery. The images along the top are the reconstructed optical property maps recovered from one of the phantoms using conventional SFDI and single snapshot cSFDI. Flow phantom experiment Figure 4 shows a comparison between SFI recovered using modulated AC illumination (single snapshot cSFDI) and planar DC illumination (conventional LSI). Figure 4(A) contains snapshot SFI images of the phantom demonstrating comparable image quality using both methods. Figure 4(B) presents the comparison between SFI recovered with AC (single snapshot cSFDI) and DC (conventional LSI) projections over the area of flow as speed is increased from 1 to 5 mm/s. Each point corresponds to the SFI at a unique flow speed. These measurements were calculated by averaging over 50 frames of SFI maps. The red error bars represent the standard deviation over the 50 frames calculated from the AC projections while the blue error bars are the standard deviation using DC projections. The dashed line is a trend line fit to these points demonstrating a linear relationship among them. Unlike Fig. 3, this line is not a "y = x" reference line.  Figure 5 shows the results from the reactive hyperemia experiment. The images across the top of the figure from left to right are the reconstructed µ a , µ s ', and SFI maps. The plots along the bottom from left to right are the time-series data for µ a , µ s ', and SFI. The red and blue curves in the time-series data are derived from the correspondingly-colored red and blue regions of interest (ROI) overlaid on the property maps. Both ROIs were chosen by visually assessing the absorption image in Fig. 5. The blue ROI was placed over an area with a subcutaneous vein, while the red ROI was placed over an area without one. The time-series data also indicate when the occlusion and release of the pressure cuff occurred. During the occlusion, there was a 32% increase in absorption in the blue channel and a 71% increase in the red ROI. These increases in µ a were gradual and corresponded primarily to the accumulation of deoxyhemoglobin during the occlusion. Following the release there was a 43% decrease in µ a in the blue ROI and a 72% decrease in the red ROI. This decrease occurred in less than 25 seconds and was caused by the reperfusion of oxyhemoglobin and the washout of deoxyhemoglobin. SFI showed a decrease of 51% in the red ROI and 28% in the blue ROI during the occlusion. After the release, there was a 190% increase in the red ROI and a 146% increase in the blue ROI. These large increases occurred over the course of 10 seconds indicating the immediate return of flow to the forearm. Changes in µ s ' are also seen during the occlusion and release portion of the experiment. However, these variations were significantly smaller than those witnessed in µ a and SFI. Elucidating the nature and significance of these slight variations is left to future studies.  Figure 6 demonstrates the ability of single snapshot cSFDI to detect the heartbeat waveform within the SFI at multiple regions of interest within the field of view. Figure 6(a) shows one frame from the recovered SFI map overlaid on the subject's forearm during the reactive hyperemia protocol. The black and blue regions of interest correspond to the black and blue time-series data within the rest of Fig. 6. Figure 6(b) shows the entire cuff-occlusionrelease time-series data. The brown shaded region lies over the occlusion segment while the green shaded region lies over the release of the occlusion. These data both demonstrate sensitivity to reactive hyperemia signified by the increase in SFI following the occlusion. Figure 6(c) shows the frequency spectrum of the blue curve in Fig. 6(b) for the segment during the occlusion (brown box) and the release (green box). The peak in the release at 1.2 Hz corresponds to the heartbeat signal (72 beats per minute). These spectra demonstrate the presence of the heartbeat component during the release that is absent during the occlusion due to the upstream arterial blockade of blood flow. This is confirmed intuitively by Fig. 6(d) which shows zoomed-in plots of both curves during 30 seconds of the occlusion and 30 seconds of the release. Note the periodic signal that is present during the release. Upon close inspection it is apparent that these two curves (black and blue) are both of the same frequency and phase over the entire duration. In contrast the segment from the occlusion data is more chaotic and lacks a clear periodic signal. Finally, Fig. 6(e) shows an even more zoomed-in view of the release segment, revealing a more detailed look at the heartbeat. Here it is possible to see structure within the signal during each heartbeat. These features could possibly contain information about the vasculature such as the dicrotic notch and reflections within the arterial tree. The spacing of the peaks was analyzed and shown to be at 1.2 Hz, in agreement with the Fourier analysis.  Fig. 6(b). The brown shaded box is a zoomed in interval from the brown rectangle with the asterisk in Fig. 6(b). e) An even closer look at the signal during the release. These data correspond to the green rectangle with two asterisks (**) in Fig. 6(d).

Discussion
In this work we introduce a noncontact noninvasive imaging technique capable of extracting µ a , µ s ', and SFI in real-time (50 fps) over large (15 x 15 cm) tissue regions. By applying advanced processing techniques to single raw images of spatially modulated coherent light, we are able to calculate optical properties from a single frame of data. Additionally, speckle contrast can be extracted from the same image because of its coherent properties. Needing only a single frame of data allows for simplified hardware; a fixed object such as a sinusoidalpatterned slide can be used in place of a DMD or LCOS projector in the case of conventional SFDI.
Homogeneous phantom experiments demonstrate that single snapshot cSFDI can be used to recover accurate optical properties over large ranges of absorption and reduced-scattering when compared with conventional 3-phase SFDI using an incoherent light source. Flow phantom experiments show that single snapshot cSFDI has comparable sensitivity to LSI in terms of measuring dynamic scatterer flow speeds. These same experiments also demonstrate the ability of single snapshot cSFDI to extract all three contrast mechanisms from a single frame of raw data. Access to this information enables the correction of speckle contrast for optical properties. In addition, an advantage to calculating speckle contrast from an AC projection is that it is possible to achieve higher speckle contrast values by rejecting long path-length photons [5,6]. This is why in Fig. 4 the SFI is lower for the AC modulation pattern; SFI is inversely proportional to speckle contrast, and speckle contrast from an AC projection is higher than the corresponding DC illumination. This potentially enables more accurate characterization of superficial microcirculation.
In vivo studies of reactive hyperemia demonstrate the ability of single snapshot cSFDI to measure intrinsic signals relevant to dynamic physiology. During the occlusion we observed increases in µ a at 660 nm indicative of a buildup of deoxyhemoglobin. Following the release of the occlusion we observe a sharp decrease in µ a signifying the washout of deoxyhemoglobin as oxyhemoglobin re-entered the tissue compartment. The increase in SFI above baseline observed after the occlusion demonstrates sensitivity to post occlusive reactive hyperemia, a well-established physiological phenomenon.
Beyond demonstrating sensitivity to dynamic physiological processes, these in vivo measurements point to the potential of single snapshot cSFDI to measure the tissue metabolic rate of oxygen consumption. The current system presented in this paper has only a single optical wavelength, and is therefore only capable of extracting tissue absorption and scattering coefficients. However, by extending this system to multiple wavelengths it would have the ability to decouple the chromophore concentrations of oxy-and deoxyhemoglobin ([HbO 2 ] and [HHb], respectively). Combining blood hemoglobin concentrations with flow measurements can be used to generate an index for oxygen consumption in accordance with Fick's principle. Measuring the metabolic rate of oxygen consumption has multiple potential applications and can provide important insight into pathologic conditions where flow and metabolism are uncoupled. For example, oxygen utilization is known to be decreased in conditions of chronic hypoxia caused by prolonged arterial occlusion, such as peripheral arterial disease (PAD). Real-time measurements could provide clinicians with important information relevant to early diagnosis, disease staging, and treatment response monitoring.
The ability to extract spatial maps of multiple contrast sources in real-time has numerous potential benefits outside of oxygen metabolism. In this work we were able to observe the heartbeat in the SFI channel. Characterization of the heartbeat waveform has potential to unlock information related to arterial stiffness and blood pressure [26,27]. By observing the heartbeat over large tissue areas it may be possible to directly observe pulse transit time by measuring how the waveform changes in phase over areas of tissue. In this work we performed imaging using a 660 nm laser diode, a wavelength with greater sensitivity to deoxyhemoglobin than oxyhemoglobin. By performing single snapshot cSFDI with a wavelength with greater HbO 2 sensitivity (e.g. 850 nm) there is potential to measure the plethysmographic waveform in the absorption or DC reflectance data. In this case, single snapshot cSFDI would be able to measure the heartbeat simultaneously in absorption and SFI, and potentially be used to look at shifts in phase associated with intrinsic physiology.
Beyond physiology, mapping multiple contrast sources has the potential to improve quantitative accuracy of SFI. Previous work has demonstrated that speckle contrast is dependent on tissue optical properties and the sampling volume. Changes in the absorption and reduced scattering coefficients were shown to change speckle contrast for a given flow speed. Likewise, the depth at which flow occurs also affects the speckle contrast recovered at a given flow speed. Single snapshot cSFDI has the ability to correct for both of these effects. An optical property alteration algorithm, based on Monte-Carlo simulations of light transport, can take into account the optical properties recovered using single snapshot cSFDI to adjust the speckle contrast, and thus SFI values. Additionally, speckle contrast calculated in the spatial frequency domain can be used to control for the measurement depth. Together, these effects can be used to improve quantitative accuracy of the speckle contrast measurements in single snapshot cSFDI [5,6].
In summary the information rich spatiotemporal data set recovered by single snapshot cSFDI has significant potential. By combining blood concentrations with blood flow speed there is the possibility to measure chromophore concentrations. Measuring the heartbeat in the absorption parameter and speckle contrast channels may reveal physiologically relevant information about microcirculatory physiology. Finally, single snapshot cSFDI offers the potential to improve quantitative accuracy of speckle information by controlling for optical properties and measurement volume. In future work, this system will be extended to multiple wavelengths to measure chromophores then transformed into a portable clinic-ready device suitable for in vivo physiological measurements.