An extensive upgrading of contact diffuse CorrelationTomography system

Diffuse correlation tomography (DCT) is an emerging tissue blood flow index (BFI) imaging technique that typically requires a large number of source‐detector pairs, resulting in high instrumentation costs. We developed a low‐cost paradigm for upgrading the DCT system with time‐sharing hardware sensors via optical switches, wherein the S‐D configuration was spatially optimized and combined with a novelty Nth‐order linear algorithm for image reconstruction. We verified this system through the phantom experiment and the lower limb skeletal muscle cuff occlusion test. The reconstructed BFI images exhibit the excellent performance of the upgraded DCT system in retrieval of the target location, outline, and anomaly contrast. For the deepest quasi‐solid anomaly, location accuracy was 90% with the αDB‐contrast of 0.75. While, for the deepest liquid tube anomaly, a good linear relationship was achieved between contrast and pump speed, with the αDB‐contrast of 3.29 at 600 mL/h. For human experiments, it was found that the BFI in the relaxed state was ten times higher than in the cuff occlusion state. This study demonstrates the feasibility of the proposed upgraded low‐cost DCT system for diagnosing various diseases associated with local perfusion abnormalities.


| INTRODUCTION
Many diseases are accompanied by abnormal tissues' blood flow at microvascular level.][3][4][5] Currently, the clinical technologies available for BFI detection, such as, the ultrasound Doppler (limited to larger vessels), the laser Doppler and laser speckle imaging (limited to lower penetration depth), and the perfusion magnetic resonance imaging-MRI (limited to heavy and expensive equipment).8][19][20] In order to image the spatial contrast of the BFI, an extension of DCS technology, that is, diffuse correlation tomography (DCT), has been developed over the years. 21,22imilar to other tomographic techniques, DCT also requires a large number of source-detector (S-D) sensors to be placed on the tissue surface.The temporal autocorrelation function is yielded from each S-D, 23,24 and all the autocorrelation functions are used to reconstruct the blood flow imaging.In the past, a small number of S-D pairs were used for DCT, however, only applicable to the small animals with the limited region of interest (ROI), such as mouse and rat brains. 12,25Additionally, the image reconstruction is an ill-posed problem in mathematics, needs the advanced reconstruction algorithm to improve. 25,26Conventionally, an analytical solution for partial differential equation (PDE) was adopted for DCT, wherein a simple tissue geometry (e.g., semi-infinite) must be assumed. 12,27The finite element (FE) method overcomes the limits of simple geometry assumption, thus applicable to a variety of tissues, especially was used in non-contact DCT system, 12,[28][29][30][31][32][33] because sufficient data can be collected by moving the S-D.For example, a fan-shape grid containing 2 sources and 15 detectors was designed, leading to 30 S-D pairs. 24By rotating it around the central line 15 times to generate 450 S-D pairs, covering the 4.0 Â 5.6 cm2 target tissue.This type of measurement permits to obtain the optical signals from a relatively large ROI, but only in non-contact pattern. 242][33] The non-contact DCT system would prevent the tissue deformation due to contact pressure and is applicable to the wound or ulcer tissues.
For most in vivo measurements, however, the motion artifacts are unavoidable, particularly in the case of longitudinal monitoring for minutes or hours.Besides, the ambient light will also affect the optical signals.Hence, the contact measurement is more feasible for bedside testing.So far, there is no ideal contact DCT system for large ROI, due to the difficulties in both sensor spatial configuration (e.g., S-D number and distribution) and the reconstructed algorithm.
5][36] The NL algorithm incorporates the information of photon transportation, 20,37,38 into the light field autocorrelation function, therefore reflecting both tissue geometry and heterogeneity.Moreover, the NL algorithm can fully utilize the autocorrelation data based on the noise level.
9 In this study, we combined the NL algorithm and the S-D optimization to realize blood flow imaging over large ROI by using a small number of hardware sensors, and validated on the quasi-solid and speed-varied liquid anomaly embedded in the liquid phantom.Moreover, the DCT system was validated for detecting the BFI in a lower limb skeletal muscle cuff occlusion test.

| METHODS
In this section, the DCT principle, instrumentation, phantom, and lower limb skeletal muscle cuff occlusion test will be briefly introduced, with more details on the reconstruction algorithm and S-D array optimization.

| DCT instrumentation
The DCT principle can be found elsewhere. 15,18,24,40The diagram of the upgraded instrument is shown in Figure 1, and the corresponding experimental setup is shown in Figure 2. The system is equipped with a hardware source (785 nm, DL-785-120-SO, CrystaLaser, Inc, USA), and six hardware single-photon detectors (SPCM-780-13-FC APD module, Excelitas Inc., Canada) (Figures 1(A) and 2(A)).The source and detectors are sequentially switched to different channels (Ch 1 -Ch 8 ) by a custom-made 8Â8 optical switch (Figure 2B).At a specific switch time, the nearinfrared light at long coherence length (>5 m) is injected into the tissue (or phantom) via a multimode fiber (the red line connects with the source, k 1 and the tissue surface, as shown in Figure 1).After being scattered multiple times within the tissue, a few photons are concurrently collected by six detectors via single-mode fiber placed millimeters to centimeters away from the source fiber (Figure 1D). 41A digital correlator (eight channel OEM, correlator.com,USA) takes the detected photons and calculates the light intensity autocorrelation function g 2 (τ) for each detector.Furthermore, the normalized light electric field temporal autocorrelation function g 1 (τ) is derived from g 2 (τ) via Siegert relation, 15,42 and it is dependent on the motion of moving scatterers (primarily red blood cells) in the tissue.According to different approaches (e.g., analytical solution, FEM or NL algorithm) the three-dimensional image of blood flow can be reconstructed from the eight cycles of g 1 (τ) data by the computer, as illustrated in Figures 1(C) and 2(C).
The control panel of the custom-made optical switch (mechanical model, FSW8-1Â8-SM-C, the insertion loss is <2.0 dB, the response time is around 10 ms), including one column of inputs (1 Â 8) and eight columns of outputs (8 Â 8) is exhibited in Figure 1(B).Among the eight inputs, one input (k 1 ) was connected to the laser (785 nm) via multimode fiber and six outputs (k 2 through k 7 ) were connected, respectively, via single-mode fibers to six detectors, leaving one output (k 8 ) unconnected.At a moment, only one channel is activated by optical switch.As shown in Figure 1(B), Ch 1 is switched on, and the source and detectors (S-D) in the same group works simultaneously, such as, the source emits the photons to the tissue surface, and the six detectors, around this source, collect the escaped photons in parallel.As such, the eight S-D groups, each cover a quasi-hexagonal area (Figure 3(B)), are activated in timesequential to cover the entire surface of the target tissue.A complete cycle is the spanning of all eight channel at different time.Hence, there are eight source-fiber locations and 8 Â 6 detector-fiber locations over the target tissue (or phantom), forming a sensor map (Figure 1D).The switching time between two channels is less than 0.1 s.

| S-D array optimization and optical probe
According to the DCS/DCT theory, the optical signals collected from a S-D pair reflects the tissue hemodynamics  beneath this pair, and the penetration depth is approximately half of the S-D distance. 8,42Besides, the detected light intensity attenuates exponentially with S-D distance.Hence, there is a compromise between the penetration depth and light signal quality, particularly for DCT wherein each voxel's BFI is determined by multiple S-D data.It is important to optimize the S-D array, so that the optical signals span across different tissue depth, while maintaining sufficient signal-to-noise ratio (SNR).
The tissue model (with liquid tubular anomaly) and the S-D sensor map with elements (i.e., image voxels) are shown in Figure 3.The tissue model of 8 Â 8 Â 3 cm 3 is divided into 1536 voxels with voxel size of 0.5 Â 0.5 Â 0.5 cm 3 , as shown in Figure 3(B).The S-D sensors are placed over the surface of tissue model.In Figure 3(B), one source location (S i , i = 1,…, 8, denoted by the dot) is paired with six detector locations (D ij , i = 1,…, 8, source number; j = 1,…, 6, detector number, denoted by the asterisk) in a group with the same color.
Hence, there are 48 S-D pairs in this array.In each group, the S-D pairs were cross-distributed at 60 angle with different separations (a large 2.83 cm for S i -D i1 , S i -D i3 , S i -D i5 , a short 2 cm for S i -D i2 , S i -D i4 , S i -D i6 ), and covered a quasi-hexagonal area about 12 cm 2 .The large S-D distance and the short S-D distance are distributed alternating with 60 , aims to balance the detection area and maximize the depth (up to 15 mm). 8,42This distribution pattern forms five concentric circles (only four detectors on the outermost layer), which enables voxels of each layer acquiring the most balanced number of photons.
The eight groups of S-D, formed eight quasi-hexagonal areas with different color, are also cross-distributed.So, totally, it covers an area of 8.0 Â 8.0 cm 2 on tissue surface by time-sequential activation (Figure 3B).This pattern of S-D configuration allows for the best use of hardware sensors, subsequently reducing the instrument size and cost.In addition, the photon trajectories distributed among the voxels are more balanced, which improves the matrix illcondition for image reconstruction.
In accordance with the S-D configuration, a fiber-optic probe was designed for optical signal acquisition.As illustrated in Figure 2(D), all fibers are housed in a flat-shape base made from PVC material.A technology of 3D printing was utilized to produce the flat-shape base with small holes.The source and detector fibers are inserted into the holes, according to the sensor map depicted in Figure 3 (B).One end of each fiber (FC connector) is connected to one of the source/detector outputs in the optical switch.The other end of the fibers (ferrule) are contacted with the tissue (or phantom) surface.

| Phantom experiment
For validation, we designed a phantom system consisting of liquid solution in a rectangular aquarium (Figure 2D).By using a spectrometer (QE-Pro, Ocean Optics Inc., USA) and a frequency-modulated tissue oximeter (Imagent, ISS Inc., USA), proper amount of distilled water, India ink (Chenguang Inc., China) and intralipid solution (30% solution, Huarui Inc., China) were added in the aquarium, to reach the target value of absorption coefficient (μ a = 0.05 cm À1 ), and the reduced scattering coefficient (μ ' s = 8.0 cm À1 ) in homogenous solution.A quasi-solid or a speed-varied liquid anomaly was embedded in the homogenous solution, representing the low or high flow.The cross-shaped quasi-solid anomaly, at 0.5 cm bar width and 0.5 cm thick, is made of India ink, Intralipid and transparent silicone, natural drying, with the same optical property as the background solution.The speed-varied liquid anomaly, at 0.4 cm diameters, is made from transparent thin tube filled with the background solution and numerous small quasi-solid anomaly pieces (φ ≤ 0.8 mm), to mimic the complicated flow environment of the tissues.A peristaltic pump was used to manipulate the speed of this tubular liquid anomaly, so as to create different levels of spatial contrast within the phantom.
Both the anomalies were embedded at depths ranging from 0.1 to 0.5 cm, at step of 0.1 cm, to evaluate the depth sensitivity of the upgraded DCT systems.The maximum depth of the anomalies (0.5 cm depth) is determined by the anomaly thickness and the short S-D separation (about 1 cm).
For DCT measurements, every g 1 (τ) curve is obtained by repeated measurements to ensure the satisfied SNR.In these phantom experiments, the g 1 (τ) curve is stable for 20 times repeated measurements.The sample time for each g 1 (τ) curve is 1.2 s.Therefore, the entire data acquisition time for 8 S-D groups is 192 s.
Besides, to improve the SNR, the experiments were done in a dark environment and the tank was covered with black cloth.For human experiment, the room light was maintained as weak as possible and a flat PVC base was coated with black foam to minimize the influence of ambient light on DCT measurements.The continuous descent algorithm was used to eliminate abnormal g 1 (τ) caused by poor contact in human experiments.Voxels (at edge or bottom of the tested tissue) detected by <5% S-D pairs were removed to reduce the unknown quantities.

| Skeletal muscle cuff occlusion test
To assess the capability of the DCT system for in vivo applications, we designed the physiological protocol of temporary cuff occlusion on lower limb skeletal muscle.A total of 20 healthy volunteers (healthy, regardless of gender, aged 18⁓45; normal blood pressure, 90⁓140 mmHg for systolic blood pressure, and 60⁓90 mmHg for diastolic blood pressure; no history of vascular disease; able to participate in testing multiple times within a month; Fully understand and voluntarily sign the informed consent form) participated in the study.The procedures of this study were conducted in accordance with the Declaration of Helsinki and approved by the Ethics Committee of North University of China.The signed consent forms were obtained from all participants.Each of the subjects lay supine on the table and his/her right leg was slightly bent and relaxed, as shown in Figure 4A.A cuff tourniquet was placed on the right upper leg, and the optical probe was placed on the surface of the same right lower leg (calf muscle) for DCT data acquisition.After a 192-s baseline measurement, the cuff tourniquet was inflated to 230 mmHg (Figure 4B), so as to temporally block the arterial flow into calf muscles for 192 s.The cuff occlusion was then released and the DCT data were collected for another 192 s.
For in vivo experiments, black foam was applied to the flat-shaped PVC base to make it more comfortable for volunteers and minimize the ambient light influence during the experiment.

| Nth-order linear algorithm
NL algorithm for DCT, namely NL-DCT, is a frame-work developed in our laboratory for 3D flow imaging.The detailed procedures can be found elsewhere. 34,35When τ is sufficient small, the final form of the first-order (N = 1) and Nth-order (N > 1) discrete Taylor approximate solution are expressed by Equation (1) and Equation (2), respectively.
here, g 1 (m, j, τ) is the light electric field autocorrelation function at the mth source and jth detector, during τ delay time.w(q, m, j) is the weight factor, for the qth photon (q = 1,…, Q) packet with path length (s 1 ,…,s n ) over all n elements (voxels).s(i, q, m, j) is the path length within the ith element. 36Both the w(q, m, j) and s(i, q, m, j) could be estimated by using an open-source software MCVM, [37][38][39]43 with the assumed optical property (mainly, μ a and μ ' s ). Whn N = 1, the unknown variables αD B only appear on the right side of Equation (1).The term P n i¼1 B m, j, i ð ÞαD ð Þ is the slope of linear regression between τ and g 1 (m, j, τ)À1.Once the slope (Sl) is determined, the unknowns (αD B ) can be calculated from Equation (4) with proper image reconstruction algorithm.
When N > 1, the unknown variables αD B appear on both sides of Equation ( 2).Thus, BFI reconstruction can be implemented in iterative procedures by Equations ( 2) and (4). 34,35he advantage of NL algorithm is that it can select multiple τ points (multiple data points on g 1 (τ)) to fit more stable slopes according to noise level.For example, τ = 10 À7 ⁓3.5 Â 10 À6 , 25 data points are used in the NL DCT system (Zhang X, Biomed.Opt.Express, 2018; Zuo J, IEEE access, 2020; Zhang X, IEEE access, 2020; Feng S, Biomed.Opt.Express,2021).Although, FEM also determines the optimal τ = 3.2 Â 10 À6 based on optical parameters (mainly, μ a and μ ' s ), S-D position (r S , r D ), blood flow values (αD B ) of the forward model, and condition number of weight matrix W, 12,24 it still cannot select the data points that are least affected by random noise.In addition, the least squares method based on shape search is prone to falling into local minima traps.Only the NL method, which is based on multiple random data points, can derive the slope closest to noiseless g 1 (τ) curve and greatly increase the accuracy and stability of reconstructed images.

| Image reconstruction approach
For the NL-DCT imaging framework, the key steps include obtaining the slope of g 1 (m, j, τ)À1 and solving the linear equation of Equation ( 4).The slope of g 1 (m, j, τ)À1 can be readily obtained by least-squared estimation, and generally, the higher iteration order (N > 1), the more accurate outcomes.As mentioned earlier, the DCT signal is collected from a total of 48 S-D measurements, which is far less than the tissue elements (i.e., 1536 unknown αD B ), and results in a severely ill-posed problem of Equation ( 4).According to our previous efforts, the split-Bregman algorithm combined with total variation (TV) regularization, namely, Bregman-TV algorithm, would greatly improve the quality of image reconstruction. 44,45Specifically, let v = αD B , b = Sl, the target function of the Bregman-TV proposed for NL-DCT is as follow.
here, non-negativity of solutions is enforced.

| Evaluation criteria
The outcomes of the reconstructed BFI images by the upgraded DCT system will be evaluated visually and quantitatively with the image contrast, αD B-contrast , which is defined as follows.
here, αD B-anomaly is the average reconstructed BFI of the quasisolid cross-shaped anomaly or the tubular liquid anomaly.αD B-background is the average BFI of the background solution.
The location accuracy is defined as a percentage of the reconstructed anomaly matches with the real locations set up in a phantom experiment.
For human experiments, the average blood flow over all voxels was calculated to quantify the flow contrast at relaxed and cuff-occlusion state.

| RESULTS
In this section, the reconstructed images of the phantom and human cuff occlusion experiments were demonstrated, while deeply investigating the linear relationship between the pump-speed and the reconstructed BFI.

| Reconstruction of quasi-solid anomaly
The reconstructed images of quasi-solid anomaly, 20 voxels, with 0.5 cm depth of the anomaly surface, were shown in Figure 5, exhibited in cross-slice (the second slice) view (Figure 5A) and in 3D view (Figure 5B).The cross shape and outline of the anomaly can be seen clearly, and its location matches exactly with the true one, but the bottom-end voxel on the vertical bar and the right-end voxel on the horizontal bar were little blurred, that is, 2 out of 20 voxels are not correctly reconstructed.Therefore, the location accuracy is 90%.According to Equation ( 6), the αD B-contrast is about 0.75, which permits precise identification of the target.
The relationship between the anomaly depth and evaluation criteria is shown in Table 1.Overall, the shallower the anomaly, the clearer the reconstructed anomaly will be.However, due to the cross-shaped anomaly only occupying 20 voxels, any reconstructed voxel with defect will result in a location accuracy of 95%.

| Reconstruction of tubular anomaly
Figure 6 shows the 3D reconstructed images (transverse section at 0.5 cm depth) of the tubular anomaly (28 voxels) at the pump speed of 0 mL/h (a), 100 mL/h (b), 200 mL/h (c), 300 mL/h (d), 400 mL/h (e), 500 mL/h (f), and 600 mL/h (g), respectively.For better visual illustration of the background and anomaly, the color bar ranges are different in subfigures.As such, the tubular anomaly could be visually separated from the background solution.Moreover, the parameters αD B-background , αD B-anomaly , and αD B-contrast of the tubular anomaly with different flow rates are shown in Table 2. the αD B-contrast (1.00, 1.47, 2.18, 2.43, 2.87, 3.05 and 3.35) is gradually enhanced as the pump speed is increased.contrast.An excellent linear relation (R 2 > 0.99, p < 0.0001) between the two variables was found.These observations coincide with the outcomes of previous studies that require much more g 1 (τ) measurements for image reconstruction. 24ecause of the average effect of the algorithm, the reconstructed BFI of the background is increasing as the anomaly flow is increased, such as, αD B-background BFI of 500 mL/h increase 62.33% than 0 mL/h.While, the reconstructed anomaly BFI increases much faster, it still contributes to a linear growth of the αD B-contrast , as shown in Table 2 and Figure 6(F).
Due to the inhomogenous nature of the optical scatterers (the small quasi-solid anomaly pieces) caused by the peristaltic pump, the two ends of the tubular anomaly are blurred, that is, 6 out of 28 voxels are not correctly reconstructed.According to the definition, location accuracy is about 79%.
At the depth of 0.3 cm, the contrast is increased to 3.12 at 400 mL/h, and 3.64 at 600 mL/h pump speed, respectively.That means the shallower anomalies can be visible more clearly.

| Cuff occlusion test result
Figure 7 shows the BFI reconstruction images at the relaxed state (Figure 7(A,C)), and the cuff occlusion state (Figure 7(B,D)), respectively.The mean BFI of the reconstructed second slice is 8.93 Â 10 À9 cm 2 /s at the relaxed state and 9.68 Â 10 À10 cm 2 /s at the cuff occlusion state, as shown in Figure 7(A,B), with the color bar next to them.The Figure 7(C,D), registered with 3D leg images, are the coronal images of the leg in two states.Both of them are in the color bar of Figure 7(A), which is too high for Figure 7(D) to distinguish each voxel.These results coincide with the outcomes of previous studies. 5,23,24,28However, due to the long measurement time (192 s), the reconstructed images of baseline and relaxed states are almost identical.Therefore, the direct reconstructed BFI is used to display reconstructed images before and after the cuff occlusion.
During the human cuff occlusion experiments, we carefully monitored the subject to avoid any influences of motion artifacts on BFI imaging.However, the paradigm of cuff occlusion induced the complicated physiological turbulence, such as, vascular vasoconstriction, tissue compression and relaxation, blood hyperemia responses.Moreover, the leg tissues (containing skin, fat, skeletal) are heterogenous rather than homogenous.Hence, it is reasonable that the BFI distributions are not uniform and different in two states, as shown in Figure 7.
Some BFI parameters of each subject are shown in Table 3.Among all 20 volunteers, the mean reconstructed BFI of the relaxed state and the cuff occlusion state are 12.3 ± 3.1 Â 10 À9 cm 2 /s and 0.9 ± 0.1 Â 10 À9 cm 2 /s, respectively.The reasons for variance may include blood pressure baseline, vascular elasticity, peripheral nerve response, subcutaneous fat thickness, 46 or other physiologic reasons. 47,48While the BFI value at the relaxed state is almost 10 times higher than that at the cuff occlusion state.It indicates the DCT system constructed in this study is able to probe the BFI changes in human subjects.

| DISCUSSION
In this study, we extensively upgraded the contact DCT system via time-sharing hardware, S-D spatial configuration, as well as algorithm optimization.
For the purpose of reducing the instrumentation cost, an 8 Â 8 optical switch is used to time-sharing the hardware source and detectors, so as to cover a large ROI with 8 Â 6 measurement locations.This contact pattern avoids any influence on the optical signal acquisition from ambient light and motion artifacts, which will be generated by previous spatial scanning. 24Certainly, due to the insertion loss of the optical switch, the light intensity will attenuate about 40%-50%, it still has hundreds of millions of escaped photons to be detected.It will not burn the skin, and also meets the experimental requirements.
As for the sensor configuration, the ultimate goal is to minimize the ill-condition of the reconstruction matrix and improve the accuracy of BFI imaging.So the S-D pairs are arranged in symmetrical and cross-distributed pattern with different separation to minimize the ill-conditions of the matrix (Equation ( 4)) for image reconstruction.The eight groups of S-D pairs cover a relative large ROI, with a deeper penetration depth of 1.5 cm for phantom experiments.
Based on our previous efforts, 36 the NL algorithm and Bregman-TV solution were combined in this study for solving the target function (Equation ( 5)), which is termed as NL-DCT framework.In order to highlight the effectiveness of this contact-DCT with N-order linear algorithm, a comparison was made with FEM algorithm by transplanting the method of reference "Zuo J, IEEE access, 2020."For fair comparison, both imaging frameworks of the two methods are implemented in the same geometrical models, and the number of voxels as well as Reconstructed images (unit: cm 2 /s) of tubular anomaly at different pump speed: (A) 0 mL/h, i.e. homogenous, (B) 100 mL/h, (C) 200 mL/h, (D) 300 mL/h, (E) 400 mL/h, (F) 500 mL/h and (G) 600 mL/h, and (H) the linear regression between the pump speed and BFI contrast.
spatial resolutions are kept as balance.Specifically, the same tissue model with almost the equivalent voxel number (8315 for FEM and 8624 for NL approach, but tetrahedron voxel vs. hexahedron voxel), and the S-D configuration in Figure 3(B) are used in two methods.Take the computer simulation (tubular anomaly (2 Â 10 À8 ) twice of the background (1 Â 10 À8 )) and phantom experiments (tubular anomaly with 600 mL/h) as examples, the αD B-contrast of the simulation reconstructed images are about 1.21 and 1.87 for FEM and NL approach respectively.And the tubular anomaly appears more broken by FEM.The αD B-contrast of the phantom experiment reconstructed images are 2.12 and 2.95 for two methods.Additionally, the NL approach greatly shortens the imaging time when compared with FEM algorithm (186 s vs. 385 s).All the evaluation criteria indicate that the NL algorithm is superior to the traditional FEM algorithm.Note, the more voxels lead to worse reconstruction results, such as, αD B-contrast of 600 mL/h decreases to 2.95 from 3.35.A series of phantom experiments were designed to reflect the realistic situations in clinic.Specifically, the peristaltic pump at different speed was used to manipulate the tubular-shape microvascular system, mimicking the high perfusion in local regions, such as malignant tumor 18 or transient flow elevation due to neurological activation or exercises. 12,40On the other hand, the quasisolid anomaly was adopted to mimic local ischemia or calcified tissues wherein the blood flow is lower than the surrounding tissues.
The outcomes derived from phantom experiments show that both quasi-solid anomaly and tubular flow anomaly could be well reconstructed by the upgraded DCT system and Bregman-TV algorithm (Figures 5 and 6), with perfect match in target location.The shape and outline of anomalies are also clearly preserved.While it appears that higher flow of the anomalies leads to the higher flow of the reconstructed background, because the TV (total variation) criterion tend to seek the minimal gradient among the flow voxels.Nevertheless, the excellent linear relation between the reconstructed αD B and pump speed (Figure 6) can still be observed, which is also consistent with previous reports with non-contact DCT system. 24though the Bregman-TV algorithm has the limitations as mentioned above, by comparing various algorithms, such as analytical and ART methods, the Bregman-TV algorithm is the most popular, efficient, and convergence algorithm in image reconstruction (J.F. Abascal et al., Med.Phys.2011 and J. Chamorro-Servent et al., J. Biomed.Opt.2013).The TV-regularization (i.e., L 1-norm minimization) was adopted as the target function of the optimization problem, because it permits the image sparse representation by minimizing the L 1-norm of image voxels.Practically, the split-Bregman algorithm has been proved to be an efficient approach to reach the optimal solution, and it has been used for diffuse optical tomography.The combination of TVregularization and split Bregman algorithm would effectively solve the ill-posed linear equations for image reconstruction (Equation ( 4)).Nevertheless, due to the illposed linear equations, this algorithm, like other iterative algorithms, inevitably homogenizes the reconstructed images (termed as "homogenization effect").Especially the back-projection values were used as the iterate initial values of the Bregman-TV algorithm, which blur the image due to star-like artifacts (C Anam et al.Institute of Physics, 2019).We are planning to solve this problem through machine learning approaches due to its powerful Note: The unit of BFI is 10 À9 cm 2 /s, "0" represents the relaxed state, and "1" represents the cuff occlusion state."mean" is the mean value of the BFI, and "max" is the maximum value, "min" is the minimum value.
learning ability based on big data, especially the deep learning network, which is our ongoing project.
According to the DCS/DCT theory, such as, D A Boas, Ann Arbor, 1996 and J. M. Murkin and M. Arango, British Journal of Anesthesia.2009, the optical signals collected from a S-D pair reflects the tissue hemodynamics beneath this pair, and the penetration depth is approximately half of the S-D distance.Nevertheless, the penetration depth is also dependent on the SNR, and ultimately should be verified by the experimental observations.In our phantom experiment, the cross-shaped anomaly could be observed in the third-layer slice (0.5 cm thickness for each layer).Hence, the penetration depth is no <1.5 cm.
Furthermore, we performed the cuff occlusion experiment on human lower limb skeletal muscles, so as to further access the capability of DCT system for in vivo applications.Although there is large variability across the subjects and the discrepancy between the local maximum and minimum is also different, it was found that the mean reconstructed BFI in relaxed state is much higher than that in cull occlusion state.This makes sense and is consistent with previous DCS arm cuff occlusion experiments. 5This system can also be implied to monitor thrombotic therapeutic processing on the basis of blood flow detection, and to evaluate microvascular stress response based on hyperemia reaction time.
The microvascular blood flow measured by DCT involves the complicated physiological process, and many factors affect the BFI values, such as oxygen demand, neurological control capacity, vascular vasoconstriction, spirit, as well as healthy and active status (M.Bentourkia

| CONCLUSIONS
To conclude, a low-cost paradigm for upgrading the contact DCT flow imaging system was developed in this study, through time-sharing hardware sensors and optimization of S-D spatial configuration.Moreover, the Bregman-TV optimization approach is incorporated with the NL algorithm to efficiently reconstruct the flow images.The liquid phantom containing a cross-shaped quasi-solid anomaly or tubular anomaly liquid at stepvaried speed was designed to extensively validate the upgraded DCT system, yielding the excellently matched reconstruction location, outline and flow contrast.In addition, we have performed in vivo experiments to assess the actual effect of the DCT system in human applications, and the result is consistent with the human hemodynamics.So this methodology can be used to continuously and quantitatively detect the blood flow changes of macrovascular and microvascular in deep tissues.Therefore, it can be applied in the diagnosis of various diseases associated with local abnormal perfusion, such as neurological deficits (acute stroke, intracerebral hemorrhage, traumatic brain injury, subarachnoid hemorrhage, Alzheimer's disease, etc.) and skeletal muscle lesions (myasthenia gravis, progressive muscular dystrophy, periodic paralysis, etc.) slow down the blood flow response to stimulation, as well as breast diseases (hyperplasia or tumors) speed up the blood flow.Future research will continue focus on clinical implications and evaluation of the upgraded DCT system through in vivo tests, such as optimizing the S-D distribution, analyzing the impact of optical parameter misestimation on reconstructed BFI, filter and calibrate the clinical noisy g 1 (τ) curves, and combine the DCT with NIRS technology to enhance diagnostic capabilities, particularly in terms of sensitivity and specificity.Another focus is to directly map the intensity autocorrelation function (g 2 (τ) curves) to BFI image by deep learning methods, in order to reduce the data conversion (g 2 (τ) convert to g 1 (τ)) and image reconstruction time, and improve the reconstruction accuracy.

F
I G U R E 1 The schematic of Diffuse Correlation Tomography instrumentation for flow imaging.

F I G U R E 2
The Diffuse Correlation Tomography instrumentation and the setup of phantom experiment for flow imaging.

F
I G U R E 3 (A) The spatial distribution of S-D sensors over the phantom surface, with an embedded tubular anomaly (B) the top view of S-D distribution.

F I G U R E 4
Subjects posture during skeletal muscle cuff occlusion experiments.(A)the relaxed state, (B) the cuff occlusion state.

Figure 6 (
Figure6shows the 3D reconstructed images (transverse section at 0.5 cm depth) of the tubular anomaly (28 voxels) at the pump speed of 0 mL/h (a), 100 mL/h (b), 200 mL/h (c), 300 mL/h (d), 400 mL/h (e), 500 mL/h (f), and 600 mL/h (g), respectively.For better visual illustration of the background and anomaly, the color bar ranges are different in subfigures.As such, the tubular anomaly could be visually separated from the background solution.Moreover, the parameters αD B-background , αD B-anomaly , and αD B-contrast of the tubular anomaly with different flow rates are shown in Table2.the αD B-contrast (1.00, 1.47, 2.18, 2.43, 2.87, 3.05 and 3.35) is gradually enhanced as the pump speed is increased.Figure6(F) exhibits the regression analysis between the pump speed and flow et al.J. Neurol.Sci.2000 and O. M. Henriksen et al.Journal of Cerebral Blood Flow & Metabolism.2013).Hence, there are large variabilities in BFI value among different people.
T A B L E 1 The evaluation criteria with different anomaly depths.
The αD B-contrast of the tubular anomaly with different flow rates.Reconstructed images of lower limb skeletal muscle test, 2D reconstructed blood flow index (BFI) image (A) in relaxed state and (B) in cuff occlusion state, coronal image of 3D reconstructed BFI (C) in relaxed state and (D) in cuff occlusion state.
T A B L E 2