Collimating micro-lens fiber array for noncontact near-infrared diffuse correlation tomography.

Near-infrared diffuse correlation spectroscopy/tomography (DCS/DCT) has recently emerged as a noninvasive measurement/imaging technology for tissue blood flow. In DCT studies, the high-dense collection of light temporal autocorrelation curves (g 2(τ)) via fiber array are critical for image reconstruction of blood flow. Previously, the camera-based fiber array limits the field of view (FOV), precluding its applications on large-size human tissues. The line-shape fiber probe based on lens combination, which is predominantly used in current DCT studies, requires rotated-scanning over the surface of target tissue, substantially prolonging the measurement time and increasing the system instability. In this study, we design a noncontact optical probe for DCT based on collimating micro-lens fiber array, termed as FA-nc-DCT system. For each source/detector fiber, a single optical path was collimated by coupling with one micro-lens in the fiber array that is integrated in a square-shape base. Additionally, an 8×8 optical switch is used to share the hardware laser and detectors without spatial scanning. The FA-nc approach for the precise collection of g 2(τ) curves was validated through a speed-varied phantom experiment and the human experiments of cuff occlusion, from which the expected value of the blood flow index (BFI) was obtained. Furthermore, the flow anomaly in the phantom and the ischemic muscle in human were accurately reconstructed from the FA-nc-DCT system, which is combined with the imaging framework based on the Nth-order linear algorithm that we recently created. Those outcomes demonstrated the great potential of FA-nc-DCT technology for fast and robust imaging of various diseases such as human breast cancers.


Introduction
The blood flow measurement at microvasculature level is of importance for the diagnosis and treatment of many diseases [1,2], because malfunction of tissues are often associated with abnormal hemodynamics and metabolism. Near-infrared (NIR) diffuse correlation spectroscopy/tomography (DCS/DCT) is a relative new technology for deep tissue blood flow measurement/imaging [3][4][5][6][7][8][9][10][11][12][13][14]. Due to the relatively low tissue absorption at "NIR window" (650 to 900 nm), DCS/DCT provides a non-invasive, fast, portable, and low-cost alternative for assessing the time course of tissue blood flow changes or spatially localizing the flow anomaly. DCS used one or a few source-detector (S-D) pairs to collect the light temporal autocorrelation curve (g 2 (τ)), from which the time-course blood flow index (BFI) can be extracted by fitting the autocorrelation data with an analytical solution of correlation diffusion equation [5,15]. Generally, a near-infrared laser with long-coherence length (>5 m) is used as DCS light source. The avalanche photodiode (APD) single-photon-module is used as the DCS detector, in order to ensure the high sensitivity for probing the fluctuation of individual speckle. By extending DCS to tomography (DCT), which requires a large number of S-D pairs to form a fiber-array, the reconstructed 3D image of blood flow can be obtained.

Hardware system
The whole system of FA-nc-DCT is illustrated in Fig. 1(a). The system is composed of a long coherence laser at 785 nm (DL-785-120-SO, Crystallaser, Inc., USA) as light source, 6 APD single-photon modules (SPCM-780-13-FC, Excelitas Inc. Canada) as light detectors, an eight-channel digital correlator (correlator.com, USA) and an A/D board (USB-6009, National Instrument Inc., USA) for data acquisition. All these components are contained in an instrument box. To share the source/detector hardware among multiple locations over tissue surface, an 8×8 channel optical switch was designed [ Fig. 1(a)]. By using the optical switch, the light from the laser or to the 6 APDs were guided via fiber-array sequentially on specific locations (i.e., a source location and 6 detector locations at one time). In this way, a total of 6×8 array is achieved through 8 times of light switching, resulting in 48 S-D measurements. Figure 1(b) shows the fiber connections on the frontal panel of optical switch. The leftmost column represents the fibers connected to hardware laser/APDs, and the other 8 columns represents the fibers connect to 8 sets of S-D pairs over the FA-nc probe, labeled from Ch1 through Ch8. In the leftmost column, the blue fiber is connected to the laser, and the yellow fibers are connected to the six APDs respectively. When being switched, the light from/to the laser/APDs are distributed into a set of S-D pairs (including one source location and six detector locations), lasting for 1 second. During this period, the laser emits the light into the source location, and the escaping light from six detector locations were collected simultaneously, termed as one cycle of measurement. Once a cycle of measurement is completed, the light is switched to another set of S-D pairs, in sequential manner (i.e., Ch1, Ch2, . . . , Ch8). As such, the emitting/escaping light would cover the entire region of FA-nc probe after 8 times of switching. The specific arrangement for each set of S-D pairs is illustrated in Table 1 and Fig. 4(b). Figure 1(c) depicts a single collimating micro-lens fiber as well as the fiber array on FA-nc probe. The single collimating micro lens fiber (namely, c-lens fiber, Huaxin Inc., China) has the lens length of 1.0 cm and diameter of 2.8 mm. An inclined plane at 8-degree angle is selected to collimate the beam that is delivered via the fiber. With focal length of 50 mm and numerical aperture (NA) of 0.37, this c-lens would achieve good outcomes of light collimating at relatively lower cost. In addition, each collimating micro-lens is coated with a near-infrared anti-reflection film to reduce the influence from ambient light and the reflected light during the experiments.  Figure 2 shows the schematic diagram of the optical paths with the uses of collimating micro-lens fiber and the ordinary fiber (i.e., without collimating). Theoretically, the use of micro-lens can effectively collimate the divergent beam and minimize the spot size, while the light transmission from ordinary fiber would be severely diffused [ Fig. 2(a)]. These theories are confirmed through the spot sizes that were actually measured from ordinary fiber and a collimating micro-lens fiber at a working distance of 3 cm [ Fig. 2(b)]. As such, the light output from the

Image reconstruction algorithm
We adopted the NL algorithm for both BFI calculations with DCS and BFI imaging with DCT. Unlike the conventional analytical solution and finite element method (FEM), the NL algorithm aims not to seek solutions for correlation diffusion equation. Instead, this approach combines the integral form of the light electric field temporal autocorrelation function g 1 (τ) with the Nth-order Taylor polynomials, and the tissue heterogeneity and irregular geometry are fully taken into consideration through the photon trajectory information. Suppose there are M light sources (1st,. . . , Mth) emitting the photons into the tissue, and there are J detectors (1st,. . . , Jth) receiving the photons that are escaping out from the tissue. The target tissue is spatially divided into n elements. The collected optical signals (i.e., g 2 (τ)) was firstly converted into the light electric field autocorrelation functions (g 1 (τ)) via Siegert relation [16]. The g 1 (τ) function collected at (mth,jth) S-D pair can be regarded as the integral of the autocorrelation attenuation of a single photon packet through different elements, as shown in Eq. (1) [24]: where P(m,j,s 1 ,. . . ,s n ) is the normalized distribution of the photon path length detected on the n elements, k 0 (i) is the light wave vector amplitude of the ith element, and the random walking step length of the ith photon is equal to 1/µ s ′ (µ s ′ is the reduced scattering coefficient of the ith element). <∆r 2 (τ)>is the mean square displacement of the moving scattering, and τ is the delay time of the autocorrelation function. According to different physical models, there will be different mathematical forms of red blood cell (RBC) movements (i.e., the blood flow model).
In the case of Brownian motions, <∆r 2 (τ)> = 6αD B τ. Here the variable αD B (i) represents the blood flow index (BFI) of the ith element.
On the other hand, the continuous function g 1 (m,j,τ) can be written as a Nth-order Taylor polynomial in the following form [12]: where The variable w (q,m,j) is termed as the photon weight, and it is also a discrete form of P (m,j,s 1 ,. . . ,s n ). P (m,j,s 1 ,. . . ,s n ) is the path length (s 1 ,. . . ,s n )of the qth photon (q = 1,. . . ,Q) over the n elements. s (i,q,m,j) represents the ith path length corresponding to the qth photon packet at the (mth, jth) S-D pair. Both w(q,m,j) and s(i,q,m,j) can be estimated from photon Monte Carlo simulation of heterogeneous tissues with arbitrary geometries.
In order to facilitate the calculation, according to the relation: MJ), and then we define some variables: A is an MJ×n matrix, and αD B is an n×1matrix. When the order N=1, the unknown variable αD B only appears on the right side of Eq. (3). Therefore, Eq. (3) can be written as the following equation: The combined term A*αD B (1) is the slope of the linear regression between τ and g 1 (h,τ)-1, which can be rewritten as: Once the slope (Sl) is determined by linear regression between τ and g 1 (h,τ)-1data, a specific image reconstruction algorithm can be used to calculate the unknown (αD B (1) ) according to Eq. (9).
When the order N>1, the unknown variable αD B appears on both sides of Eq. (4). Therefore, the calculation of blood flow index (BFI) is performed according to an iterative process: For the DCT imaging framework of the NL algorithm, the main calculation process includes obtaining the slope through linear regression and solving the linear equations to reconstruct the BFI value (i.e., αD B ). The linear regression between the delay time (τ) and the modified autocorrelation function [left side of Eq. (4)] can be easily achieved by the least-square method. Generally, more iteration would lead to more accurate outcomes. In phantom experiments, we used 48 S-D pairs, which is far less than the number of measured tissue voxels (i.e., 2250 unknown αD B ). This leads to severe ill-condition in Eqs. (9) and (11). Therefore, design of constraint and regularization methods to solve linear equations is the major challenge for implementation of BFI image reconstruction.
Previously, a hybrid algorithm that combines the total variation (TV) and split-Bregman were proposed by us. This hybrid algorithm, namely Bregman-TV, was used to perform BFI image reconstruction. Here, Bregman's algorithm provides a solution for non-differentiable equations. The TV algorithm can make non-edge areas more uniform, while well retaining the edges. In Eq. (9) and Eq. (11) (N) , and the minimization problem of Bregman-TV imaging framework is expressed in Eq. (12): TV regularization aims to sparsely represent an image by minimizing the L 1 norm of the gradient magnitude of the image. As for solving the TV minimization problem, the split-Bregman algorithm is proven to be an effective method [12].

Phantom configuration for DCS and DCT measurement
The liquid phantom experiments are commonly used in DCS and DCT studies for standard validation. Details of the phantom procedures were reported elsewhere [11,13,16]. Briefly, the liquid phantom, consisting of distilled water, India ink (Chenguang Inc., China) and Intralipid solution (30% solution, Huarui. Inc., China), are contained in a glass rectangular aquarium. The India ink is used to create the light absorption, and the Intralipid particles are used to create the light scattering and mimic the RBC movements in the phantom. With proper amount of ink solution and Intralipid solution being added, the optical properties of the liquid phantom reach µ a = 0.05 cm −1 and µ s ′ = 8.0cm −1 , which match the optical parameters of human tissues.

The liquid phantom with flowing anomaly
As the initial procedure of system validation, the FA-nc system was used to measure the g 2 (τ) curves from the liquid phantom, with aim to assess the quality of DCS signals. The detailed experimental configuration is shown in Fig. 3(a). To manipulate the flow speed in the phantom, an apparatus of transparent thin flat tube was designed and mounted on the aquarium. As shown on Fig. 3(b), the embedded flat glass tube was fixed at 5 mm below the surface of the liquid phantom. The tube was filled with the phantom solution, maintaining the same optical property inside and outside of tube. A syringe pump was used to manipulate the flow rate of liquid in the glass tube, creating the flow anomaly in the phantom. Thereafter, the flow rate in glass tube was manipulated by varying the syringe pump speed in the following steps: 0mL/H, 100mL/H, 200mL/H, 300mL/H, 400mL/H, 500mL/H. The DCS signals were longitudinally collected during the entire period of phantom experiment. The rectangular shape of flat tube provides a relatively homogeneous flow within the tube, with aim to match the DCS measurement which averages the flows over the region covered by the fiber array. For the purpose of DCT imaging, however, a cylinder tube [ Fig. 3(c)] is designed to create a spatial contrast of flow between the tube and the background (i.e., the liquid phantom in aquarium). The approaches to manipulate the flow inside cylinder tube by syringe pump is the same as those for rectangular tube, except that the optical signals collected by the fiber array are used for DCT imaging, instead for DCS measurements.

The liquid phantom with solid anomaly
To comprehensively valuate the capacity of FA-nc system for DCT flow imaging, we also set up a solid anomaly (i.e., zero flow) as a representative of lower flow than the background. The basic phantom configuration is similar to that for flowing anomaly, except embedding a solid rectangular-shape anomaly instead of a tube filled with liquid phantom. The anomaly was made of solid phantom, with same optical properties (µ a and µ s ′ ) as the liquid phantom. The solid anomaly, at size of 15mm×5mm×5mm, are embedded in the phantom at the 5 mm below the liquid surface, as shown in Fig. 4(a). A very thin needle, with one end being inserted into a base placed on the bottom of the aquarium, was used to fix the solid anomaly with its other end.  Table 1.

S-D array for FA-nc system
The detailed S-D array for FA-nc system is depicted in Fig. 4(b). There are a total of 8 sets of S-D pairs in the array, covering the entire region of optical measurements. Each set include one source and six detectors whose specific labels are listed in Table 1. The reason for this design is to balance the measurement direction, S-D separation and the covering sub-regions. As such, the condition number of matrix in NL algorithm [Eqs. (9) and (11)] remain normal which ensures the robust reconstruction of flow imaging. Specifically, each source location is surrounded by six detector locations at the S-D separation of 2.0 cm or 2.8 cm. The sources and detectors are mostly cross-arranged, which is more flexible when compared with the rotated-scanning of the line-shape fiber array that is dominantly adopted. With the sequentially light switching for 8 times by the optical switch, a 48 (6×8) times of data acquisitions are attained, at a sampling time of 1 second for each switch. The integration time for each set of source-detector (i.e., one source and six detectors) is 1 second, similar to that for diffuse correlation spectroscopy (DCS). Hence, the SNR with 1-second integration time is sufficient for both phantom and human arm experiments. As such, the measurement time for a complete DCT data acquisition is around 10 seconds (including 8 set of S-D measurement time and 8 times of switching time). Although the CCD-based DCT system would great accelerate the measurement speed, the SNR is much lower, limiting the penetration depth.
To comply with the NL algorithm for DCT imaging, photon Monte Carlo simulation was performed on the volume with size of 8cm×8cm×3cm. During this process, both the rectangular and cylinder shapes of glass tube were taken into account when establishing the geometrical model for photon Monte Carlo simulation. Specifically, a refractive index of 1.5 and zero values of flow, absorption and scattering coefficients were assumed for glass tubes in the geometrical model. The Nth-order linear algorithm (NL) incorporates these information for image reconstruction and minimizes the boundary effect. The simulation outcomes, especially the photon path lengths and weight factors, are incorporated with the optical signals (g 1 (τ)) to form the imaging framework [i.e., Eqs. (10)- (12)]. By using the strategy of image reconstruction (i.e., Bregman-TV) illustrated in Section 2.2, the BFI imaging was obtained and evaluated.

Human experiment of arterial occlusion for DCS and DCT on human forearm
The human experimental protocol was approved by the Ethics Committee of North University of China. All of the seven volunteers participating in the study have signed the consent form before the measurements. For the in vivo measurement, subject laid supine on the table with the right arm relax on the table. An elastic strap was used to stabilize the arm in the middle. Besides, we monitored the entire process of optical measurements and excluded all of the data that might be affected by motion artifacts. The details of source-detector separation are also illustrated in Fig. 4(b). A cuff tourniquet was placed on the upper arm. For the purpose of comparison, the FA-nc system and a conventional contact probe were focused/placed on the surface of right forearm. The integration time of DCS is set as 1 second for both contact and noncontact studies. The laser was controlled by the optical switch to emit light into noncontact (FA-nc) and contact tissue area alternately, at the sampling time of 2 seconds, so as to avoid the light interference between the two measurements. After 60-second baseline measurement, the cuff tourniquet was inflated to 230 mmHg, with aim to temporally block the arterial flow into forearm muscles for 150 seconds. The cuff pressure was then released and the optical signals were collected for another 90 seconds. Throughout the 5-minute measurement, the subject remained still to minimize the motion artifacts on the DCS/DCT measurements

Results
At the largest source-detector separation (i.e., 3.0 cm), the light intensity derived from the noncontact probe is around 60 kcps in liquid phantom and 50 kcps in human arm tissue. These integration time and light intensity are sufficient for the Nth-order linear algorithm to generate stable slopes of the linear regression as well as flow imaging. The light intensity derived from the contact probe are at the same order as that derived from the noncontact probe.

Phantom experiment for DCS and DCT measurement
The results of phantom experiments for DCS measurements are shown in Fig. 5. According to the Siegert relation [16],the ideal value for the first data point of g 2 (τ) curves is 1.50, which matches well with the measured values from the phantom experiments [between 1.46 and 1.50, see Fig. 5(a)]. These observations indicate that the g 2 (τ) curves collected by the FA-nc probe are typical, with little effects from the ambient light. When subjected to speed manipulation by syringe pump, the flow inside the glass tube varies accordingly. As illustrated in Fig. 5(b), the BFI (i.e., αD B ) values extracted from the autocorrelation data increase linearly with the pump speed, with excellent correlations (R 2 =0.998, p<10 −5 ). These outcomes verify the capacity of FA-nc system for minimizing the light interference between sources and detectors as well as yielding high quality of autocorrelation curves.  Figures 6(a) and 6(c) shows respectively the 3D flow imaging of solid anomaly and flowing anomaly within the transparent tube (at pump speed of 400ml/H) that were derived from the FA-nc-DCT system, wherein the image reconstruction was implemented by the NL imaging framework. Figures 6(b) and 6(d) shows the 2D cross-section views (i.e., X-Y plane) of anomaly imaging at the depths of 3 mm, 5 mm and 7 mm below the phantom surface, respectively, which can illustrate both solid anomaly and the flowing anomaly within the transparent tube. The location and size of anomaly match exactly with the experimental configuration.

Human experiment of arterial occlusion for DCS and DCT on human forearm
Figure 7(a) shows the representative time course of blood flow changes throughout the manipulation protocol of arterial occlusion, measured by the contact and FA-nc systems respectively. As clearly seen, the temporally arterial occlusion by cuff tourniquet causes a sharp and large decrease in BFI value. Upon the release of cuff tourniquet, there is a hyperemia response (i.e., the BFI promptly surges into the peak value), followed by the gradual recovery to its baseline. The BFI responses to the arterial occlusion measured by the FA-nc probe (red curve) is very similar to that measured by contact probe (blue curve), with the average difference small than 5%. Note that the focusing areas by the two probes are 2 cm apart on the forearm surface. The small difference between the two measurements may due to the tissue heterogeneous response to the ischemic muscles. On average (n=7), the BFI declines caused by arterial occlusion is 65.7 ± 2.43% and 69.0 ± 9.51% (mean ± SD) measured by noncontact and contact probe respectively [ Fig. 7(b)]. These observations demonstrate that the FA-nc measurements are stable and little affected by the ambient light as well as the possible trembling of the human body. Figure 8 shows the BFI imaging of skeletal muscle at normal (before occlusion) and ischemic status (during occlusion) respectively, both of which are reconstructed by FA-nc-DCT system and NL imaging framework. At either status, the BFI value are evenly distributed over the target tissue, with small spatial variation. However, a large imaging contrast is clearly seen between the   7. (a) The time-course changes of blood flow throughout the arm cuff occlusion, measured by contact and noncontact probe (i.e., FA-nc system) respectively. (b) The relative blood flow during cuff occlusion measured by contact and noncontact probes in all of the seven healthy subjects, in which the baseline flow is set as 100% before occlusion. two states (normal and ischemic), which coincides with the DCS measurements subjected to the same physiological protocol.

Discussion and conclusions
Blood flow is a critical physiological parameter for the diagnosis of many diseases. However, the technologies currently available for assessment of the blood flow at microvasculature level is limited. The ultrasound Doppler routinely used in clinic can only measure the blood flow of the major vessels [25]. The imaging modality of arterial spin labeling-magnetic resonance imaging (ASL-MRI) relies on heavy and expensive instruments, and it thus not feasible for early diagnosis and bed-side monitoring [26].Other modalities such as laser Doppler or laser speckle flowmetry, can only assess the blood flow at superficial tissues, up to 2 mm [27,28]. There is an urgent clinical need for portable and inexpensive measurement and imaging of the microvasculature blood flow in deep tissues. In recently years, the DCS/DCT have been rapidly developed to assess the tissue blood flow at relatively large depths (up to several centimeters). The contact probe was primarily use for DCS measurement due to multiple advantages such as easy-to-setup and less sensitivity to the ambient light and motion artifacts. In some situations that tissue surface cannot be touched or deformed (e.g., would and ulcer tissues), the noncontact probe should be used, primarily for DCT studies. For example, a camera-based noncontract probe was used to focus all of source and detector fibers on the tissue surface via an identical lens system. However, the aberration effects limit the FOV, precluding the use of this sort of probe for large human tissues. To overcome this limit, a line-shape probe with independent lens systems was designed to separate the optical path of sources and detectors. The line-shape probe enables large FOV through rotated-scanning over the target tissue. Nevertheless, the scanning pattern prolongs the measurement time and increase the instability. On the other hand, the use of regular combined lens for both source and detector makes it difficult to achieve the small S-D separation (e.g., <1 cm), which, however, is important for algorithm optimization of image reconstruction.
In this study, we designed a new noncontact probe for DCT based on micro lens collimating fiber array (i.e., FA-nc-DCT). Unlike the previous camera-based and line-shape probes, we do not use the regular combined lens to collimate and focus the optical paths, but manage to couple micro lens system in front end of each optical fiber. This unique design significantly reduces the S-D separation and allows for flexible positioning of the S-D fiber array. Moreover, an 8×8 optical switch is designed to rapidly distribute the light to different S-D locations without the effects from scanning vibrations. The collimating micro-lens fiber array would allow for the arbitrary arrangement of the source-detector (S-D) pair within the entire FOV region. Hence, this pattern can be more efficiently integrated with the Nth-order linear (NL) algorithm that was previously created by us. By contrast, the scanning-based system is similar to the duplication of one set of S-D arrangement (e.g., a source and six detectors) among different locations or directions, i.e., moving this arrangement from one location/direction to another location/direction. Hence, the flexible S-D arrangement is limited. The use of optical switch avoids the influence of motion artifacts caused by the mechanical scanning. Additionally, the individual fiber collimating minimizes the light interference between the source and detector that is caused by any form of shared lens. Although the form of serial data collection by optical switch lowers down the imaging speed, it greatly reduces the cost of hardware (i.e., the number of lasers and APDs). Compared with spatial scanning (e.g., around 20 seconds for each step of scanning [11]), the optical switching is much faster (e.g., 10 milliseconds for each switching in this study). We are trying to denoise the optical signals meanwhile reducing the measurement time within each switch cycle. This is a way to speed up the data collection and will be one part of our future works.
For DCT studies, the optical measurements (i.e., number of S-D pairs) are far less than the imaging voxels [i.e., the elements in Eqs. (4)- (11)], causing severe ill-conditions in mathematics. Hence, optimization of reconstruction algorithm is critical in order to improve the flow imaging quality. Recently, we developed an DCT imaging framework based on Nth-order linear (NL) algorithm [12], which permits fully utilization of the autocorrelation data, hence more robust to the data noise. The advantages of the NL algorithm over the conventional FEM approach were confirmed through extensive computer simulations and phantom experiments [29]. Further optimization of NL algorithm requires flexible arrangement of S-D fiber array, which could be achieved by the FA-nc system, rather than the current line-shape strategy that strictly separates the optical paths of sources and detectors for large FOV.
Furthermore, different size of ROI was selected for the phantom experiment and human cuff occlusion experiments. Larger ROI is selected for phantom experiment because the phantom container has larger area and rectangular shape. By contrast, the human arm has smaller area and larger curvature. Hence the smaller ROI on arm is selected to match the square-shape probe. The optical properties used for phantom and human arm are the same (i.e., µ a = 0.05cm −1 and µ s ′ = 8.0cm −1 ), except with distinct geometrical models. Specifically, a rectangular geometry was established for phantom experiment, while a cylinder geometry was established for human arm. As mentioned in our previous studies [12,24], the Nth-order linear algorithm would account for the individual geometry and well solve the issues of tissue curvature. The FA-nc system for minimizing the light interference between the sources and detectors were firstly verified by DCS measurements on liquid phantom and human experiments. The typical curves of light autocorrelation (g 2 (τ)) were generated [ Fig. 5(a)], indicating that the DCS signals are little affected by the FA-nc probe. Additionally, the excellent correlations (R 2 =0.998, and p<10 −5 ) between the BFI values in the glass tube and pump speed also meet our expectation. As for the practical applications in human tissues, typical blood flow responses to transient muscle ischemia and reperfusion were observed, which also coincides with the concurrent blood flow measurements with contact DCS probe. For application of FA-nc system on DCT, the NL imaging framework was adopted to process the autocorrelation data, and the rectangular-shape flow anomaly was successfully reconstructed. In addition, the location and edges are well reserved. These observations demonstrate that the FA-nc system has the capacity to accurately detect and localize flow anomaly. Moreover, the FA-nc-DCT for blood flow imaging of the normal and ischemic human skeletal muscles were also clearly observed.
Despite of the merits, the current FA-nc probe, along with the optical switch, permits only forming a 6×8 S-D array. Accordingly, the flow imaging with voxel size of 2 mm is attained. High density of S-D array is required for further improving the image quality and elevating the spatial resolution. The high density of S-D array would be achieved by micro-scanning of the fiber-array in two perpendicular directions, without increase the instrumentation costs. Besides, the FA-nc system could be comprehensively applied on various clinical studies, which is also the subject of future works.
According to the physical principle, the microvascular flow (measured by DCS/DCT) is much slower than the flow rate by syringe pump. Nevertheless, it is reported that the DCS/DCT flow is proportional to the pump speed [11]. The pump speed of 400ml/h was adopted in this study for better illustration. Our previous study has shown that the pump speed of 200ml/h is still detectable by the contact system and Nth-order linear (NL) algorithm [29]. Nevertheless, determination of the minimal detectable flow is an interesting task for improving the DCT technique. A potential solution is combining the galvanometer-based scanning with optical switch, which would greatly increase the DCT measurement density, yielding high-resolution imaging of tissue blood flow. This combination will be a main direction of our future study.
In summary, a novel noncontact system based on collimating micro lens fiber array (FA-nc) was designed by us for DCT blood flow imaging. With a micro-lens installed on each fiber, the optical path from individual fiber was collimated and focused on the tissue surface without sharing an identical lens system among the sources and detectors. The FA-nc system for minimizing the light interference were validated on the speed-varied liquid phantom and human experiments. Moreover, the integration of flexible S-D array and the NL algorithm has been extensively proven to be effective for 3D imaging of both phantom and in vivo tissue flow. The accurate reconstruction outcomes demonstrate the great potential of FA-nc-DCT system for future blood flow imaging that are associated with disease diagnosis and therapeutic assessment.