1. Introduction

Each year there are approximately 6 million fractures that occur in the United States. Of these fractures, between 5 and 10% will result in nonunion [1]. Nonunions lead to an increased risk of infection, increased financial burden due to the need for extended treatment, and in some cases the injury may take years to heal or could even result in a permanent disability [2]. A fracture with a particularly elevated risk for nonunion is the Jones fracture. This fracture occurs at the junction of the proximal metaphysis and diaphysis of the fifth metatarsal and is estimated to result in nonunion in as many as 30% of cases [3]. The main reason attributed to the poor healing outcomes of Jones fractures is the avascular region in which they occur [4]. Sufficient blood supply to the tuberosity of the proximal fifth metatarsal is provided by the metaphyseal artery while the diaphysis is provided its share via the nutrient artery. However, between these regions no blood supply exists [5]. This low blood supply starves the fracture of nutrients, growth factors, oxygen, and other components needed for successful healing outcomes. Previous studies performed in mouse models have directly tied these ischemic conditions to impaired healing [6]. As the risk for nonunion with this fracture is caused by poor perfusion, diffuse optics is well suited to this application with its ability to non-invasively map hemodynamics in deep tissue.

Diffuse optical tomography (DOT) exploits the ability of near-infrared light (600-900 nm) to penetrate deep into tissue due to the low attenuation caused by biological tissue in this range. Frequency domain-DOT (FD-DOT) measures the attenuation as well as information related to the photon path length through tissue. Using this measured data and the diffusion approximation to radiative transfer we are able to decouple the effects of absorption and scattering. The varying absorption coefficients of different wavelengths then enables the extraction of bulk tissue parameters such as oxy-hemoglobin, deoxy-hemoglobin, water, and lipid content [7]. On the other hand, diffuse correlation tomography (DCT) and speckle contrast optical tomography (SCOT) use the time-varying speckle patterns caused by coherent light sources that occur due to dynamic motion deep in tissue to create three-dimensional maps of blood flow [8–10]. Specifically, the source of contrast that is measured by SCOT and enables quantitative recovery of flow, is the reduction of speckle contrast caused by moving scatterers within the sample of interest. Currently, most diffuse optical studies on bone have either focused on the recovery of optical properties [11,12] or on joint health for applications such as monitoring rheumatoid arthritis [13]. Early attempts to monitor hemodynamics during the bone healing process with diffuse optics have only been investigated in animal models and have been limited to the use of either spatial frequency domain imaging or DCT [14–16]. The use of these individual methods either requires assumptions of parameters based on literature to recover blood flow or provides no data on blood flow and limited depth penetration typically on the order of one to three millimeters [17]. Here, we detail the construction and validation of a fully co-registered, semi-noncontact, SCOT and FD-DOT instrument, which is applicable at the bedside, relatively low-cost, and capable of providing three-dimensional images of blood flow, scattering, tissue blood oxygen saturation ($St{O_2}$), and total hemoglobin concentration ($THC$) without the use of contrast agents. We describe instrument design, experimental methods, and present results from both in vitro tissue phantom experiments and in vivo measurements on human subjects. In the future, this system will be employed to longitudinally monitor subjects with injuries to the proximal fifth metatarsal to distinguish fractures at high risk for nonunion from those that will heal well.

2. Methods and Materials

2.1 Speckle Contrast Optical Tomography

SCOT is a relatively new technique for monitoring blood flow in deep tissue [9,10]. It provides several advantages over traditional diffuse correlation tomography, namely, the ability to use widefield detectors as well as decreased acquisition time. The SCOT system uses a long coherence length 785 nm laser (DL785-120-SO, CrystaLaser, Reno, NV) that is collimated, and steered onto the sample to be measured using a scanning galvanometer (GVS012, Thorlabs, Newton, NJ). The light re-emitted from the sample is then collected through a linear polarizer to limit the contribution from specular reflection and imaged through a 50 mm focal length lens (LM50XC, Kowa, Torrance, CA) onto a scientific CMOS camera (pco.edge 5.5, PCO-Tech, Wilmington, DE).

Stacks of 15 to 30 raw images, depending on signal-to-noise-ratio (SNR), are collected from each source position as the galvo is scanned across the sample surface using a single exposure time of 1 ms. This exposure time was chosen to balance the signal-to-noise ratio of both the measured intensity and the speckle contrast which decreases with increased exposure time. From these images the speckle contrast $(\mathrm{\kappa } )$ is computed spatially across adjacent pixels in each acquired frame using a window size of 7 × 7 pixels, as $\kappa ({{\boldsymbol r},T} )= \frac{\sigma }{I}$, where ${\boldsymbol r}$ is location on the tissue surface, T is the exposure time of the camera, $\sigma $ is standard deviation, and I is mean electron counts. Additional corrections for dark and shot noise are performed as outlined in [18] before averaging speckle contrast calculated across all acquired frames and spatially binning these values to improve SNR. In order to recover flow, we must also provide accurate measurements of the distance between our scanned point sources and the detectors (pixels). Using the intensity images collected during the SCOT scan, we extract the centroids of all point source locations and use the measured field of view (FOV) dimensions to discretize the camera FOV into two grids containing the x and y coordinates of each pixel in the image. Using this information, we can then calculate the source-detector separations as the distance from the centroid of each source location to each pixel in the image. The spatially resolved speckle contrast parameter along with the source-detector separations can then be related to a Brownian diffusion model of blood flow through a modified Siegert relation connecting $\kappa $ to the normalized electric field autocorrelation function ${g_1}({{\boldsymbol r},\tau } )$ [19].

3D tomographic reconstructions of SCOT data were performed using a modified version of the open-source finite element solver NIRFAST [20], which was developed by Han et al. [14]. All reconstructions were performed on a computer with 128 Gb of random-access memory and a processor operating at 3.6 GHz. Time to complete each reconstruction ranged from 3 to 8 hours depending on number of source-detector separations used and mesh nodes. This toolbox is capable of solving for ${G_1}({{\boldsymbol r},\tau } )$ using the correlation diffusion equation (CDE) which has the form [21]:

The term $\Delta \left\langle {{r^2}({{\boldsymbol r},\tau } )} \right\rangle$ is the mean square displacement of dynamic scatterers for which we only consider Brownian motion and not ballistic flow. To perform tomographic reconstructions using this tool, we first generate a finite element mesh using the open-source toolbox Iso2Mesh [22]. This mesh is then modified to a NIRFAST compatible version and has all necessary optical properties assigned to each node in the mesh. The assignment of these optical properties is either assumed based off published literature or is recovered from measurements with FD-DOT as discussed later. An initial guess of the flow parameter $\alpha {D_B}$ is determined as the median of the topographic $\alpha {D_B}$ values recovered using the semi-infinite solution [23] to the CDE and assigned to each node in the mesh. The topographically recovered $\alpha {D_B}$ is also used to recover the value of ${g_1}({{\boldsymbol r},\tau } )$ to be used for minimizing the cost function for the tomographic reconstruction. A single value of $\tau $ is used to reduce computational time. Using this provided information the CDE solver performs the forward problem to calculate ${g_{{1_{calc}}}}({{\boldsymbol r},\tau } )$ at the mesh boundary and its difference from ${g_{{1_{meas}}}}({{\boldsymbol r},\tau } )$ selected from the measured ${\kappa }({{\boldsymbol r},\tau } )$ according to the Rytov method [21]. Summing over all measurements the cost function to ultimately be satisfied by the reconstruction is given as [14]:

Our first step for validation of the SCOT system involved in vitro measurements on a tissue-mimicking phantom constructed from nigrosine ink and intralipid 20% (Fresenius Kabi, Bad Homburg, Germany). A phantom was constructed that had a tube through the middle with the topmost portion being ∼2 mm below the surface as shown in Fig. 1. The liquid phantom both inside and outside the tube were concocted such that the absorption and scattering coefficients were the same (${{\mu} _a} = 0.005\; m{m^{ - 1}}$ and ${\mu} _s^{\prime} = 1\; m{m^{ - 1}}$), but the liquid phantom outside of the tube was made with 30% glycerol to decrease the flow rate. As at this point no FD-DOS system was available, we matched absorption and scattering properties of the phantoms by following a procedure to compensate for the altering effects of glycerol on tissue phantom optical properties [24]. Sources were scanned in a 4 × 4 grid across the ROI. After thresholding to ensure an SNR >3.5 this resulted in a total of 6,386 source detector pairs with separations ranging from 5 mm to 12 mm. Reconstructions were performed on a finite element mesh consisting of 98,198 nodes with dimensions of 50 × 50 × 25 mm. A total of 20 images were obtained at each source location to improve SNR resulting in a sampling time of 0.66 seconds and a total scan time of less than 15 seconds.

 

Fig. 1. SCOT heterogeneous flow experiment

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Once we had confirmed the accuracy of our stand-alone SCOT system using tissue-mimicking phantoms, we then performed an in vivo cuff occlusion experiment on a 27-year-old, healthy, male subject. A blood pressure cuff was placed just distal to the gastrocnemius muscle of the healthy human subject to perturb blood flow to the region of the proximal fifth metatarsal. First a baseline scan was acquired using a scan pattern consisting of 15 × 6 sources. At each source location, 30 frames were collected at 1 ms exposure time. This results in a 1 second per spatial location sampling time after accounting for the additional time needed to read out each frame. A total of 90 spatial locations were sampled in a 15 × 6 grid layout. All data was thresholded to ensure SNR > 3.5, which resulted in 14,139 source-detector separations from 5 mm to 15 mm. Then, the blood pressure cuff was inflated, and a period of 30 seconds was allowed to pass before a second scan was performed using the same scan parameters. Once the second scan was completed a solid phantom was imaged with one final scan to provide a flat source-displacement reference. This allowed us to produce an accurate surface profile of the subject’s foot to create the mesh for the 3D reconstruction of rBF as discussed in section 2.4. As no FD information was available for this experiment, optical properties of ${{\mu} _a} = 0.01\; m{m^{ - 1}}$ and ${\mu} _s^{\prime} = 1\; m{m^{ - 1}}$ were assumed based on available literature [11]. This cuff occlusion data was reconstructed on an irregularly shaped mesh (representing the foot of the healthy human subject) consisting of 71,236 nodes with bounding dimensions of 71 × 24 × 17 mm.

2.2 Frequency domain-diffuse optical tomography

FD-DOT is a well-established method for extracting the absorption (${{\mu} _a}$) and reduced scattering (${\mu} _s^{\prime}$) coefficients of tissue while significantly reducing the crosstalk between these variables compared to continuous wave methods. In this paper, we present strategies to improve control and adaptability for source and detector geometries which enable collection of spatially dense datasets by scanning the FD sources independently of the detectors through a scanning galvanometer. This is achieved by sending the light sources through a scanning galvanometer while the detector fibers are placed immediately outside of the region of interest. With this method we are able to collect an arbitrary number of source-detector separations with large ROIs in either reflection or transmission geometry while avoiding the issues common to mechanically scanning probes such as increased data collection time due to slow mechanical scanning or the complexity of smoothly scanning a flat probe over an uneven surface.

The FD-DOT system uses two source wavelengths (785 and 830 nm). Each of these laser diode sources is amplitude modulated at 140 MHz using the signal provided by an oscillator (Wenzel Associates, 500-24970, Austin, TX) which is also used as a local reference signal for four, in-phase and quadrature (I/Q) demodulators, (ID-07-412, Pulsar Microwave, Clifton, NJ). The re-emitted light is acquired through 4 custom 1500 ${\mu} m$ diameter multimode fibers (Thorlabs, Newton, NJ) in contact with the tissue. Each optical fiber is coupled to an avalanche photodiode (APD) module (C5331, Hamamatsu, Bridgewater, NJ). The outputs of each APD are amplified, passed through a bandpass filter centered around 140 MHz, and amplified again before being sent to the in-phase and quadrature (I/Q) demodulators. The homodyne [25] system’s I/Q demodulators produce two direct current (DC) outputs per detector (I and Q) which are then low pass filtered at 1 MHz to remove out of band noise and recorded using an analog to digital converter (ADC) board (USB-6218, National Instruments, Austin, TX). The recorded I and Q values for each detector are used to calculate the $phase = ta{n^{ - 1}}\left( {\frac{Q}{I}} \right)$, and the $amplitude = \; \sqrt {{I^2} + {Q^2}} $.

To compensate for measurement offsets due to the instrumentation, a reference measurement is first performed on an optical tissue phantom with known ${{\mu} _a}$ and ${\mu} _s^{\prime}$ properties. Measurements on unknown samples are then calibrated using the reference amplitude and phase data, which is then used in a nonlinear fitting program to recover the optical properties of interest. The program to recover topographic optical properties uses the solution to the frequency domain diffusion equation of the homogeneous semi-infinite geometry. Details of the semi-infinite approximation may be found here [23].

In addition to 2D topography, FD-DOT enables us to perform 3D tomographic reconstructions using the NIRFAST (Dartmouth, NH), software package to recover the spatial distributions of parameters such as total hemoglobin concentration ($THC$) and tissue oxygenation ($St{O_2}$) [20]. These reconstructions were performed with the same hardware as the SCOT reconstructions. The amount of time required to perform each reconstruction varied depending on factors such as whether it is a 2D or 3D reconstruction, number of source-detector pairs, and number of mesh nodes. 2D reconstructions were performed in approximately 1 minute, while 3D reconstructions took in the range of 3 to 5 hours. First, the measured data is calibrated by extracting the difference in the amplitude and phase offset measured in the reference measurement and a forward simulation on a mesh with equivalent homogeneous optical properties. This calibration is then applied to the heterogeneous measured data. Reconstructions of acquired data are carried out using the formulation $\delta {\mu} = \; {({{W^T}W + \lambda (z )I} )^{ - 1}}{W^T}\delta \mathrm{\Phi }$, where $\delta \mathrm{\Phi }$ quantifies the difference between the measured and calculated boundary data, and $\delta {\mu} $ is the update for the optical properties. One exception is the 2D reconstruction presented in Fig. 11(a), which due to the limited number of source-detector separations available uses the under-determined formulation $\delta {\mu} = \; {W^T}{({W{W^T} + \lambda (z )I} )^{ - 1}}\delta \mathrm{\Phi }$ [20]. The parameter $\lambda (z )$, is a depth dependent regularization parameter based on [26] with the addition of an extra parameter $\eta $ that was only used in the in vitro co-registered SCOT and FD-DOT experiments due to the lower sensitivity in the reflectance imaging geometry. The remainder of experiments used a constant $\lambda = 10$. This parameter is used to correct for errors in the reconstructed depth of heterogeneities and has the form $\lambda (z )= {\lambda _1}\exp \left( { - \frac{{\eta z}}{{{z_{max}}}}} \right) + {\lambda _2}$, where ${\lambda _1}$ and ${\lambda _2}$ are factors chosen based on the desired level of regularization, z is the layer depth, ${z_{max}}$ is the maximum layer depth, and $\eta $ is an extra dampening coefficient to provide a more rapid fall-off of regularization with depth. Regularization parameters for the reconstructed 785 nm in vitro data are, ${\lambda _1} = 10$, ${\lambda _2} = 2$, and $\eta = 25$. As with SCOT, the reconstructions terminate iterations when the error falls below 2%. In the case of in vivo reconstructions, the parameter $\lambda $ is held constant with no dependence on depth.

The FD-DOT system was first characterized using contact measurements on homogeneous optical phantoms with varying absorption and reduced scattering coefficients. Two sets of phantoms were constructed using Intralipid 20% intravenous fat emulsion and nigrosine ink. The first set of phantoms had constant $\mathrm{\mu} _s^{\prime} = 0.8\, m{m^{ - 1}}$ while ${\mathrm{\mu} _a}$ was varied from $0.005 \, m{m^{ - 1}}$ to $0.015 \, m{m^{ - 1}}$ in steps of $0.0025 \,m{m^{ - 1}}$. The second set of phantoms had constant ${\mathrm{\mu} _a} = 0.005 \, m{m^{ - 1}}$ while $\mathrm{\mu} _s^{\prime}$ varied from $0.4 \, m{m^{ - 1}}$ to $1.4 \, m{m^{ - 1}}$ in steps of $0.2 \, m{m^{ - 1}}$. To ensure the measurements are properly calibrated, one phantom in each set of measurements was used as a reference. While varying ${\mathrm{\mu} _a}$, the phantom with ${\mathrm{\mu} _a} = 0.0125 \, m{m^{ - 1}}$ was used as a reference, and when varying $\mathrm{\mu} _s^{\prime}$ the phantom with $\mathrm{\mu} _s^{\prime} = 0.8\, m{m^{ - 1}}$ was used as a reference. All contact measurements were performed with custom-made contact optical probe at a source-detector separation of 15 mm. Data was collected at a 1kHz sampling rate for 500 ms.

Once the FD-DOT system had been validated on homogeneous tissue phantoms we performed a heterogeneous tissue phantom experiment. The same probe used in the homogeneous experiments was attached to a set of x-y linear stages (Zaber, Vancouver, British Columbia, Canada). At the time 3 APDs were available for use and the source detector separations in the probe were 5, 7.5, and 10 mm. A phantom was constructed with a tube running through the center such that the topmost portion of the tube was ∼2 mm below the surface of the phantom. The optical properties of the surrounding medium were ${{\mu} _a} = 0.005 \, m{m^{ - 1}}$ and $\mathrm{\mu} _s^{\prime} = 0.8 \, m{m^{ - 1}}$, while the optical properties within the tube were set to ${{\mu} _a} = 0.015 \, m{m^{ - 1}}$ and $\mathrm{\mu} _s^{\prime} = 0.8 \, m{m^{ - 1}}$. The stage was scanned across this phantom at 81 locations in a 9 × 9 grid resulting in a total of 243 source-detector pairs all with SNR > 3.5. Sampling at each location was performed at 1kHz for 500 ms. The tube containing the heterogeneity was then filled with liquid phantom matching the background and the measurement repeated to serve as a reference measurement. Once all data had been collected the measured amplitude and phase information was used to perform a tomographic reconstruction with NIRFAST. This reconstruction was performed using a finite element mesh consisting of 108,531 nodes with dimensions of 50 × 50 × 25 mm.

2.3 Co-registered speckle contrast and frequency domain-diffuse optical tomography

Once we had validated the individual systems, we then converted them to their co-registered semi-contact form in which both FD-DOT and SCOT sources are scanned onto the tissue via a scanning galvanometer as shown in Fig. 2. Selection of all sources, including the SCOT 785 nm long coherence source and the FD 785 nm and 830 nm sources, is performed using a linear stage (ELL9K, Thorlabs, Newton, NJ). The use of this linear stage removes any losses in optical power that would occur when using an optical switch. The 1.5 mm diameter collection fibers for the FD-DOT system are placed just outside of the SCOT ROI as shown in Fig. 3. The use of contact fibers helps to increase signal-to-noise ratio when imaging the highly attenuating, bone dominated, volume of interest. This setup enables us to recover the absorption and reduced scattering coefficients for the region of interest using the FD-DOT measurements. A tomographic reconstruction is then performed and the mesh containing the recovered optical properties can then be used in the SCOT reconstruction for blood flow to prevent errors due to inaccurate assumptions of optical properties. Validation of this co-registered system was then performed using both in vitro tissue-mimicking phantoms, and in vivo cuff occlusion measurements.

 

Fig. 2. Combined setup for FD-DOT and SCOT. FD-DOT detection fibers are placed in contact with foot.

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Fig. 3. Example of typical source and detector layout.

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The tissue phantoms were constructed from nigrosine ink and Intralipid 20% and measurements were performed in the reflectance geometry using a similar source and detector scheme as shown in Fig. 3. A homogeneous liquid phantom was constructed with 30% glycerol to provide decreased flow. The optical properties of this phantom were measured using FD-DOS with a contact probe using a source-detector separation of 10 mm. The phantom had a tube, with inner diameter 3 mm, run through the center such that the topmost portion was ∼2 mm below the surface. The mesh used for 3D reconstructions was refined in this region to reflect this. A second batch of phantom was then made with an increased absorption coefficient and 0% glycerol. Optical properties for both phantoms are provided in Table 1. Using this phantom setup, the tube could first be filled with liquid phantom matching the background for a reference measurement and then the phantom with increased absorption and flow. All data can then be normalized to ensure the recovered optical properties have minimal contribution from the tube itself. Acquisition of all data was performed using custom LabView software (National Instruments). The scanned source locations consisted of a 7 × 9 grid. For FD-DOT, in combination with 4 detectors this provides a total of 252 source-detector pairs. The data was thresholded to ensure a signal-to-noise ratio of at least 3.5, resulting in a total of 213 source-detector pairs. For SCOT acquisition 30 images were collected at each source location with an exposure time of 1 ms. The same 7 × 9 grid of sources provided a total of 39,963 source-detector pairs after thresholding to remove low SNR data. In total the data acquisition for all wavelengths and modalities took approximately 3 minutes. For FD-DOT each source location was sampled for 500 ms at 1kHz, whereas for SCOT each spatial location took approximately 1 second to collect 30 images at 1 ms exposure.

Table 1. Optical properties and flow of phantoms measured using a contact FD-DOS and DCS system. *NA: Not available

View Table

Additional processing of the SCOT data was also used to display our ability to improve accuracy of the FD-DOT reconstructed ${{\mu} _a}$ values. By averaging all collected raw intensity images from SCOT we are able to recover high SNR continuous wave (CW) data. This CW data is then used to perform a reconstruction, using the FD reconstruction as an initial guess. The total number of source-detector pairs used was equivalent to SCOT at 39,963. In doing so, we are able to get closer to the expected ${{\mu} _a}$ value of the tube heterogeneity. It is this reconstructed ${{\mu} _a}$ distribution, along with the FD-DOT reconstructed ${\mu} _s^{\prime}$ distribution that is used in the SCOT reconstructions. All reconstructions utilized the same finite element mesh with 129,564 nodes and dimensions of 60 × 80 × 30 mm.

In vivo validation was obtained by performing a cuff-occlusion experiment on a healthy human subject. The camera was aimed at the top of the proximal end of the fifth metatarsal while the detector optical fibers for the FD-DOT system were distributed linearly underneath the proximal end of the fifth metatarsal. The sources were scanned in a linear array with a total of 9 locations. At each location data was collected with the same 1kHz sampling rate for 500 ms for FD-DOT and 30 frames at 1 ms exposure time for SCOT. All data was thresholded to ensure an SNR > 3.5. A blood pressure cuff placed just distal to the gastrocnemius muscle was used to occlude the blood supply to the foot for 60 seconds, which results in both decreased blood flow and $St{O_2}$. Immediately after performing the cuff occlusion measurement, a reference measurement was performed on a solid phantom of known optical properties using the same source scanning pattern. The measured phase and amplitude data recovered from scanning the solid phantom was then used to calibrate the human subject data. In order to ensure measurements of phase are not influenced by a change in distance to the tissue from the scanning galvanometer itself, we measured the distance to the subject’s foot and placed the phantom the same distance away while the arrangement of the detector fibers was not altered. As limited sources were used in this measurement to decrease the amount of time needed for the scan, the reconstructions for the FD-DOT data were performed on a rectangular 2D mesh setup in the transmission geometry. The rectangular mesh used in the FD-DOT reconstruction covers the area shown by the red box in Fig. 10(a), has dimensions of 100 × 13 mm, and consists of 12,628 nodes. Data from a total of 28 source-detector pairs were used for the reconstruction with source-detector separations from 13 mm to 40 mm. Detectors were located on the bottom of this box while sources were distributed along the top as shown in Fig. 10(b). The angle between the sources and detectors was not a perfect $180^\circ $, but approximately $120^\circ $. Due to the necessary 2D reconstruction this is much closer to a transmission setup than a reflection one. These results were then interpolated onto a 3D mesh to enable use of all SCOT detectors. The mesh contained 59,799 nodes, had dimensions of 100 × 40 × 13 mm, and used data from 12,548 source-detector pairs with separations from 5 mm to 15 mm. Following completion of the SCOT reconstruction a single slice aligned with the FD-DOT sources and detectors was extracted for comparison.

2.4 Surface profile determination

In order to perform tomographic reconstructions that are accurate, we must create meshes with boundaries that reflect the measurement geometry. To do this we have incorporated surface profilometry into our system. The flat solid phantom that is used to acquire the FD-DOT reference data is placed such that the distance from its surface to the camera is equal to the distance to the middle of the camera’s FOV on the subjects foot from the camera. Since the scan pattern used by the galvo does not change between images of the flat calibration phantom and a subject, and the light projected onto the sample from the scanning galvanometer must travel in a straight line, any difference in the location of the point source on the surface of the foot as imaged by the camera, can only arise due to a variation in the surface depth, as shown in Fig. 4(a). By determining the vector describing the distance from the scanning galvanometer to the flat tissue phantom surface and scaling it by a constant factor to make the difference between the x and y locations of the source centroid on the foot and the reference phantom zero, we are able to extract the surface profile.

 

Fig. 4. a) Visualization of effect on lateral displacement of source (Src) position caused by change in depth. (Ref: reference) b) The 3D printed object used to verify accuracy of profilometry method. c) The reconstructed surface profile of the object based on source positions shown by red dots. d) The finite element mesh generated using the reconstructed surface profile.

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To ensure the accuracy of this method of profilometry, we performed a test scan on the 3D printed object with known dimensions depicted in Fig. 4(b). The height of the object to the highest point (center) was 12 mm while the lower portion (sides) was 4 mm. The average error of the profilometry results were 0.37 mm and the maximum error was 1.2 mm. This maximum error corresponds to a phase shift of $0.2^\circ $ at 140 MHz which is less than the measured error in phase found during system testing. Results of the surface profiling of a healthy subject’s foot are given in Fig. 5.

 

Fig. 5. Reconstructed surface profile of subject's foot. Foot mesh is oriented such that the -z direction moves from the lateral to medial aspect of the foot.

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The use of this profile is two-fold. First, as the FD sources are scanned onto the surface, any variation in the distance from the scanning galvanometer to the surface of the tissue as compared to the reference phantom will have an additional phase offset. If not corrected, this phase offset will cause erroneous results when recovering optical properties. Secondly, the surface measurement is used to generate a mesh that maintains this surface profile to ensure accurate boundary conditions. Briefly, the recovered surface data is extended in the $- z$ direction and is subsampled onto a 3D grid. Additional information collected during the imaging session such as the height of the foot can then be added in if necessary. For all meshes, the bottom of the foot is assumed to be flat. The 3D image is then converted into a solid mesh using the MATLAB (MathWorks Inc., Natick, MA) package Iso2Mesh. An example of the generated mesh is shown in Fig. 5.

3. Results

3.1 Stand-alone SCOT results

The results of the heterogeneous SCOT flow phantom measurements are given in Fig. 6. These results display the ability of SCOT to extract heterogeneous flow from the background. Prior to the SCOT measurements, a contact diffuse correlation spectroscopy (DCS) system was used to measure the true flow of both the phantom containing 30% glycerol and the phantom with 0% glycerol in separate large containers with no heterogeneities. The measurements were fitted using semi-infinite approximation to the CDE assuming only Brownian motion (Eq. (2)). This revealed the flow index of the phantom containing 0% glycerol to be $16\ast {10^{ - 7}}\; {\raise0.7ex\hbox{${m{m^2}}$} \!\mathord{/ {\vphantom {{m{m^2}} {sec}}} }\!\lower0.7ex\hbox{${sec}$}}$ and the flow for the phantom containing 30% glycerol to be $4.7\ast {10^{ - 7}}\; {\raise0.7ex\hbox{${m{m^2}}$} \!\mathord{/ {\vphantom {{m{m^2}} {sec}}} }\!\lower0.7ex\hbox{${sec}$}}$. The instrument used for these measurements has been described in prior publications [7]. The results displayed in Fig. 6 clearly show the importance of performing the tomographic reconstruction. In the topographic data displayed in Fig. 6(a) it can be seen that the recovered flow in the region of the tube is much lower than the difference measured by DCS. In Fig. 6(b), we display slices from the reconstruction at the boundary, 2 mm, and 4 mm in depth. While it does not reach the full 3.4x difference that was measured using DCS, the tomographic data is much closer than the topographic data (Fig. 6(a)) at around 2.2x the background on average.

 

Fig. 6. a) Displays the recovered flow values at the boundary. The resemblance of the boundary data to an annulus is due to the inclusion of source-detector separations greater than 5 mm and less than 12 mm. Data outside this annulus has been thresholded out and was not used for analysis. b) Shows the 3D tomographic reconstruction results. Black lines show approximate size of tube at each depth.

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Results of the in vivo cuff occlusion data are presented in Fig. 7. The slices are aligned with the long axis of the fifth metatarsal, with a decreasing z-axis representing movement from the lateral aspect of the foot, towards the medial aspect. To obtain rBF distributions the recovered $\mathrm{\alpha }{\textrm{D}_\textrm{B}}$ values from the SCOT reconstructions were all normalized to the median value of $\mathrm{\alpha }{\textrm{D}_\textrm{B}}$ from the baseline reconstruction. A clear and global decrease in rBF is present once the cuff is occluded.

 

Fig. 7. 3D reconstruction of SCOT cuff occlusion experiment. Results on the left show the baseline blood flow of the foot and results shown on the right show the drop in blood flow caused by the cuff occlusion. All results were converted to rBF by normalization to the median value of the baseline reconstruction. Decreasing z-axis represents moving from lateral side of foot towards the medial side. Note, the white areas seen in the figures is not a region of high flow but area outside of the mesh that appears white due to the methods used to display the data.

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3.2 Stand-alone FD-DOS results

The recovered optical properties from all contact homogeneous phantom FD-DOS measurements are given in Fig. 8(a). All recovered ${\mathrm{\mu} _a}$ and $\mathrm{\mu} _s^{\prime}$ values are in good agreement with the expected values. These results show the ability of this system to act as a stand-alone contact FD-DOS system and to recover optical properties with good precision across a range of optical properties.

 

Fig. 8. a) Characterization of FD-DOT system using contact measurements on optical phantoms with varying absorption and scattering properties. b) Tomographic reconstruction of absorption (left) and reduced scattering coefficient (right) heterogeneity collected using a probe mounted on two linear stages. Black lines depict approximate size of tube at given depth.

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The tomographic reconstruction of a tube heterogeneity containing an increased absorption coefficient is presented in Fig. 8(b). The reconstructed results do show an increase in absorption as well as a relatively constant scattering coefficient. However, the entirety of the tube was not well reconstructed. Instead, the lower portion of the tube is more accurate while the topmost portion is underestimated. We believe this is due to difficulties in maintaining a flat scanning plane at the surface of the liquid phantom when using the linear stages to maneuver the imaging probe.

3.3 Co-registered SCOT and FD-DOT tissue phantom experiment

Figure 9 displays the reconstructed ${{\mu} _a}$ values at multiple depths. The top row displays the FD reconstruction of ${{\mu} _a}$ at 785 nm. Here, the tube is well localized but underestimated the true optical properties within the tube as reported in Table 1. On the second line we present the FD reconstructed ${\mu} _s^{\prime}$ at 785 nm which reflect the true values well and show a small increase in the region of the tube heterogeneity. In the third row we present an improved CW derived ${{\mu} _a}$ reconstruction. This achieves an improved estimate of ${{\mu} _a}$ within the region of the tube while also removing gaps of low sensitivity in the reconstruction which were caused by the relatively small amount of FD detectors available. The last row displays the SCOT derived flow index. Again, due to the larger number of available detectors due to the camera-based detection, we are able to produce smoother images. While this again results in an underestimation of the true ∼1.9x flow difference, it provides an accurate mapping of spatial flow heterogeneity location. In the future, denser scans will be performed, and more complex methods of regularization will be investigated to improve reconstruction results. Overall, the reconstructions accurately locate the heterogeneity within the medium and are capable of reconstructing a rather large ROI (60 mm x 40 mm) in a reflection geometry.

 

Fig. 9. a) FD reconstruction of ${{\mu} _a}$ at 785 nm. b) FD reconstruction of ${\mu} _s^{\prime}$ at 785 nm. c) Improved CW reconstruction at 785 nm. d) SCOT reconstruction of rBF at 785 nm. Black line depicts approximate size of tube at given depth.

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3.5 Co-registered SCOT and FD-DOT in vivo experiments

Results of the in vivo co-registered cuff occlusion experiment are presented in Figs. 11 and 12. A depiction of the ROI is presented in Fig. 10 for reference. To calculate $St{O_2}$, the measured absorption coefficients at 785 nm and 830 nm were used with Beer-Lambert Law assuming contributions from only oxy-hemoglobin ($\textrm{Hb}{\textrm{O}_2}$), deoxy-hemoglobin ($\textrm{Hb}$), and a fixed water concentration of 25%. Once $\textrm{Hb}$ and $\textrm{Hb}{\textrm{O}_2}$ concentrations (${\textrm{C}_{\textrm{Hb}}}$ and ${\textrm{C}_{\textrm{Hb}{\textrm{O}_2}}}$, respectively) were known, $St{O_2}$ is acquired as, $St{O_2} = {\raise0.7ex\hbox{${{C_{Hb{O_2}}}}$} \!\mathord{/ {\vphantom {{{C_{Hb{O_2}}}} {({{C_{Hb}} + {C_{Hb{O_2}}}} )}}}}\!\lower0.7ex\hbox{${({{C_{Hb}} + {C_{Hb{O_2}}}} )}$}}$. To obtain rBF distributions, the recovered $\mathrm{\alpha }{\textrm{D}_\textrm{B}}$ values from the SCOT reconstructions were all normalized to the median value of $\alpha {D_B}$ from the baseline reconstruction. In Fig. 11(a) and 11(b) we see the baseline and occluded, $St{O_2}$ and rBF levels which decrease as expected. These decreases are larger in rBF than in $St{O_2}$ which is expected due to the one-minute-long occlusion period and the faster rate of change for blood flow during a venous-arterial occlusion, as opposed to $St{O_2}$. To further quantify these differences, three ROIs were selected which are displayed in the dotted boxes. Regions 1, 2, and 3 in the bar plot correspond to these regions in order from left to right.

 

Fig. 10. a) Region of interest for in vivo cuff occlusion experiment showing location of fifth metatarsal and Jones fracture occurrence. Red box shows region represented by 2D mesh. Created from open-source data provided in [35]. b) Depiction of sources (red dots) and detector layout (fibers along bottom of foot) for cuff occlusion experiment.

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Fig. 11. Reconstructed values for a) $St{O_2}$ and b) rBF. Bar charts at bottom display the average decreases in the selected regions for c) $St{O_2}$ and d) rBF referred to as regions 1, 2, and 3 (boxes named from left to right in reconstructed images).

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Fig. 12. Reconstructed values for both a) 785 nm and b) 830 nm. Results show a small change in ${\mu} _s^{\prime}$ from the baseline measurement to the occlusion measurement which may be a result of cross-talk and/or subject movement.

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Figure 12 shows the FD reconstructed values of ${\mu} _s^{\prime}$ for both 785 and 830 nm. The overall values are in good agreement with those reported in the literature [11] and the spatial distribution appears to agree with the anatomy expected in this region.

4. Discussion

In this paper we have presented a fully co-registered, semi-contact system for the simultaneous recovery of blood flow and optical properties. We have validated the system using both in vitro heterogeneous tissue phantoms and in vivo cuff-occlusion experiments. The system was able to localize heterogeneities in both absorption and flow during in vitro testing while also recovering both spatial and temporal changes in $St{O_2}$ and flow during an ­­in vivo cuff occlusion experiment. The ­­in vivo results also gave values and spatial distributions of ${\mu} _s^{\prime}$ that are well representative of both the expected anatomy of the fifth metatarsal and the values reported in literature regarding the optical properties of bone [11]. The system is able to be applied to large ROIs as shown by our results with dimensions exceeding 60 × 40 mm. To the best of our knowledge, this system is the first of its kind with respect to recovering blood flow, absorption, and reduced scattering parameters in a relatively large region of interest through non-contact scanning of the sources with dense source-detector pairs to enable full tomographic reconstructions.

Initial tests of our SCOT system displayed its ability to accurately recover heterogeneities in flow. The reconstructions show greatly improved estimates of flow within the tube over topography data alone. One thing of note with regards to the SCOT related experiments is that although our earlier glycerol experiment described in section 3.1 provided a larger difference in flow, the co-registered experiment provided a smaller difference even though the same glycerol concentration was used. This was due to the fact that our stand-alone SCOT experiment used a glycerol phantom that was stored in the refrigerator overnight while the high flow, 0% glycerol phantom was made immediately prior to the experiment. This difference in temperature resulted in a larger difference in flow due to the increased viscosity of the 30% glycerol phantom. In order to test that this temperature difference would provide a difference in flow large enough to explain this increased contrast, we performed a simple experiment using an established diffuse correlation spectrocopy (DCS) instrument. We first constructed a phantom with 30% glycerol and optical properties matching the stand-alone SCOT phantom experiment. We then performed a point measurement with a custom-made, contact probe at a source-detector separation of 15 mm while the phantom was at room temperature (22°C). After this initial measurement, the phantom was stored at 5°C overnight. The next morning the DCS measurement was repeated. To recover flow the measured data was fit to the semi-infinite solution of the correlation diffusion equation. The results show the 22°C had 1.94x greater flow than the 5°C phantom, providing an explanaition as to why the stand-alone SCOT experiment provided greater flow contrast than the co-registered experiment.

Initial testing of our FD-DOT system displays its ability to accurately recover homogenous optical properties and also its ability to be used for tomographic reconstructions albeit with an understimation in the recovered absorption. One issue with this method was the difficulty in ensuring the probe attached to the linear stages stayed aligned to the surface of the liquid phantom. This issue is removed in the final version of the system by scanning the sources in a non-contact method.

The in vitro tissue phantom experiment results shown in Fig. 9 show the system’s ability to simultaneously detect heterogeneities in both optical properties and flow. The depth regularization does an excellent job of preventing surface artifacts that often plague tomographic reconstructions and increasing sensitivity to deeper regions, however, there is still an issue of underestimation in the optical properties which is a commonly reported issue [27–30]. This issue is improved through the use of the averaged SCOT data to perform a CW reconstruction, using the FD-DOT reconstructions as an initial guess. However, the CW improved ${{\mu} _a}$ reconstructions are much more prone to surface artifacts due to their lack of depth regularization. In the case of the SCOT reconstructions, there was an underestimation of flow which is partially due to the methods used for 3D reconstructions and the scanning of fewer sources to reduce total acquisition time. In the future we will work to address these issues through further system optimization such as the inclusion of more wavelengths which will allow more accurate calculations of $St{O_2}$. We will also investigate performing higher density scans for SCOT, as well as even more dense scans for the FD-DOT system as compared with SCOT to help the imbalance in the number of detectors.

The results of the in vivo cuff occlusion experiment show an overall decrease in both $St{O_2}$ and rBF during occlusion with respect to the baseline measurement as expected. The decrease in rBF was larger from baseline to occlusion as compared to $St{O_2}$. This is expected due to the one-minute length of the occlusion and the faster rate of change for rBF. Further analysis of the cuff occlusion is presented in the bar graphs at the bottom of Fig. 11. Here, we selected three distinct regions for a more quantitative look at the change in rBF and $St{O_2}$ during the experiment. These regions were all selected using the same area within the ROI and the mean value within this region is plotted in the bar graph. The baseline $St{O_2}$ values recovered by FD-DOT prior to the cuff occlusion are in line with those reported in the literature [31–33]. In the future additional measurements will be performed on healthy subjects to determine whether this response is maintained in a larger subject pool. Note that these experiments involving assumptions of a slab transmission geometry do not perfectly describe the true geometry of the foot in which the angle between the sources and detectors was closer to 120 degrees. However, any error arising from this assumption is highly unlikely to change the trend seen in the results. In addition to this, the cuff occlusion experiments are employed as a tool that provides well-known physiological changes to ensure our system is working in the in vivo foot and is not the intended use of the system in terms of speed of hemodynamic changes. Future fracture studies will not require recovery of fast hemodynamic trends that vary within several seconds as with arterial occlusion, but instead will focus on the recovery of baseline hemodynamics at rest, allowing for acquisition of dense datasets enabling full 3D reconstruction. Performing these full 3D reconstructions enables us to use the true geometry of the foot and avoid any assumptions regarding the orientation of sources and detectors.

In Fig. 12, we display the reconstructed ${\mu} _s^{\prime}$ values for both 785 nm and 830 nm before and after the occlusion. These values agree well with those reported in the literature [11]. A small amount of variation in the reduced scattering parameter is seen in the 785 nm results which may be due to motion artifacts. The 830 nm results remain quite constant from the baseline to the occlusion. Overall, the reconstructed reduced scattering coefficients appear quite accurate and are representative of the expected anatomy.

Another advantage of our system is its ability to utilize the reference phantom measurement, which is required to calibrate out offsets caused by the instrumentation, to perform accurate profilometry of samples. Proper representation of sample boundary conditions in the finite element mesh is vital to accurately locating heterogeneities within a medium as was shown by Mazdeyasna et al. [34]. By exploiting the fact that the sources will be displaced in the x and y directions if there is a change in the surface profile of the imaged object, we were able to back solve for the distance from the scanning galvanometer to the object. Testing of this method showed an average error of under a millimeter. These accurate surface profiles, along with the open-source toolbox Iso2Mesh allowed us to create accurate finite element meshes with no additional equipment.

Some limitations of this study include the underestimation of reconstructed flow and optical properties, and the error in reconstructed depths of heterogeneities, all of which are commonly reported issues in the literature. To address the underestimation of the in vitro results for the FD phantom study we applied a spatially variant regularization parameter. This parameter was only necessary due to the reflection style measurements. We applied this regularization only to the FD derived results to enable closer comparison of the in vitro and in vivo data. As the in vivo­ data was collected in a manner closely resembling a slab transmission geometry the sensitivity of the tomographic data was much better distributed, making the spatial regularization unnecessary. However, as the use of spatial regularization did improve the accuracy of the results it is likely it will improve in vivo recovered data as well. In the future we will investigate more rigorous applications of the spatial regularization that can be applied to the complex geometry of the human foot. Although our in vivo validation methods were limited to a single human subject, we have made sure to thoroughly validate our system by not only testing the completed, co-registered system but also each individual component prior to co-registration. Note that, the cuff occlusion experiments served only as a tool to qualitatively assess our system’s ability to recover a well-known physiological response. Recovery of fast hemodynamics was not the goal and is not the intended use of the system. In the future, we will also investigate the use of a denser scanning grid for FD-DOT and its effect on quantification accuracy. Currently, the amount of information from FD-DOT and SCOT does not achieve an optimal balance as camera-based SCOT easily acquires hundreds to thousands of source-detector pairs per measurement. However, it should be noted that even with this less-than-optimal balance, we were able to recover accurate reconstructions of optical properties and flow.

In the future this system will be utilized in the clinic to perform longitudinal monitoring on human subjects as they heal from fractures of the proximal fifth metatarsal. We will apply our system to recover high density scans to provide full 3D reconstructions at many time points during the healing process. In doing so, we will establish the normal hemodynamic response to fracture healing and determine whether regions with poor perfusion have an altered response that may be used to predict the ultimate outcome as either a union or a nonunion. In doing so, we will enable timely intervention for those with poor healing outcomes and help reduce the time to a full recovery.

5. Conclusion

We have presented a novel co-registered FD-DOT and SCOT system for the recovery of spatially dense datasets that enable 3D tomographic reconstructions of relatively large regions of interest. We detailed the instrument designed and characterized it using both in vitro tissue phantom experiments and in vivo cuff occlusion experiments. Application of this instrument will provide insight into the hemodynamics of healing bone fractures.