Multi-speckle diffuse correlation spectroscopy to measure cerebral blood flow

: We present a multi-speckle diﬀuse correlation spectroscopy (DCS) system for measuring cerebral blood ﬂow in the healthy adult human brain. In contrast to the need for a high frame rate camera to measure the multi-speckle intensity auto-correlation, we employ a low frame rate camera to measure the auto-correlation using the recently introduced multi-step volterra integral method (MVIM). The results are validated by comparison against the blood ﬂow measured using standard DCS system. values of tissue optical properties such as µ a and µ (cid:48) s ; (b) An arbitrary exponential model based prior x b 0 = 1 + uexp (− v τ ) was used to recover g 2 , where u and v are the co-eﬃcients of the ﬁt. In this model, explicit values on tissue optical properties are not needed. Here, for the ﬁrst iteration, the prior x c 0 = 1 + β (based on the fact that g 2 → ( 1 + β ) at lower values of τ ) was used and for the subsequent iterations, prior x b 0 was used to ﬁt the result of the recovered g 2 from the previous iteration; (c) The prior x c 0 was taken as the third type of prior to perform a comparative study to check the need of exponential model based priors in recovering g 2 and rCBF; and (d) For recovering ∆ g 2 from changes in speckle contrast, we have used prior of the form x d 0 = u ( exp (− v τ ) − exp (− w τ )) , where u, v and w are the co-eﬃcients of the ﬁt. In this case, for the ﬁrst iteration, no prior (or x 0 = 0) was used and x d 0 was used as prior for subsequent iterations. The comparative study between recovered ∆ g 2 with prior x d 0 and without prior (i.e. x 0 = 0) has also been performed, to check if M-DCS can work without using any prior values of x 0 .For the voluntary apnea test, the ﬁeld auto-correlation g 1 was obtained using M-DCS and was ﬁtted for semi-inﬁnite medium solution of CDE to obtain the particle diﬀusion co-eﬃcient D B and subsequently relative cerebral blood ﬂow (rCBF = D P B / D 0 B ). Here, the prior x a 0 was used.


Introduction
Blood flow acts as an important biomarker as it is essential for the supply of oxygen to tissues and clearance of metabolic waste products from various parts of the body [1]. Specifically, cerebral blood flow (CBF) is known to be directly linked to the metabolic demand of oxygen supply [2,3], to neuro-vascular coupling [4,5] and metabolic response to functional stimuli [6,7]. Thus it is essential to study blood flow in general and CBF in specific as it is an indicator for well-being of the brain and can have important implications in the areas of neuroscience and rehabilitation engineering. Optical modalities usually employed to measure blood flow are laser doppler flowmetry (LDF), laser speckle contrast imaging (LSCI) and diffuse correlation spectroscopy (DCS). While LDF [8,9] and LSCI [10][11][12] are used to quantify surface blood flow (<1mm deep), DCS is employed to measure deep tissue blood flow [13,14].
DCS utilizes the speckle statistics of the scattered light measured at several spatially separated distances from the source using avalanche photodiodes (APD) or photo-multiplier tubes (PMT) [3,13,14]. One of the limitations of DCS is that it essentially collects the speckle data by independent single mode fibres, thus confining to a small detection site. To increase the signal to noise ratio (SNR) of the system, it is essential to collect multi-speckles with multiple detectors allowing parallel simultaneous detection, which would increase the cost of the system by several folds [15]. As an alternative to APD/PMT, speckle contrast based methods as in Ref. [16][17][18][19], combines the array detection as in LSCI and deep tissue imaging capability of DCS. Among these, speckle contrast optical spectroscopy (SCOS) uses multi-distance or multi-exposure speckle contrast to directly fit for deep tissue blood flow using correlation diffusion equation (CDE) [13,14].
With the advent of high-speed cameras, direct measurement of the intensity auto-correlation for quantifying surface and deep tissue blood flow were reported. In Ref. [20], the intensity auto-correlation is measured using a high frame rate camera (around 20000 frames per second (fps)) to quantify surface blood flow in mice brain and was used for selecting appropriate models for electric field auto-correlation in various types of tissues/ blood vessels. A microfluidic channel based platelet function testing system has been proposed in Ref. [21], where a camera of 1250 fps has been employed to distinguish different concentration of platelets from measured the intensity auto-correlation. In Ref. [22], the researches have employed a high frame rate camera (9250 fps) to measure deep tissue blood flow in mouse brain by measuring the speckle de-correlation time at a maximum source-detector (SD) separation of 3.2 mm. Here, the SD separation was limited to smaller range due to the fact that, for a larger SD separation, the auto-correlation curve decorrelates faster, which inturn necessitates still higher frame rate (in order of few MHz). Nevertheless, in Ref. [23], authors have employed high frame rate camera for DCS in adult human brain (at a SD separation of 2.5 cm) by using interferometric method. In Ref. [24,25], a single photon avalanche diode array with a high frame rate (in order of MHz) has been employed to measure the intensity auto-correlation curve to a maximum SD separation of 1.5 cm.
In contrast to all the above-mentioned works, we use a low frame rate camera (< 100 fps) to compute the field auto-correlation at a larger SD separation (2 cm) for quantifying in-vivo blood flow. In Ref. [26], we have recently introduced a low frame rate camera based DCS system to measure blood flow from multi-exposure speckle contrast data using a multi-step volterra integral method (MVIM). We validated the system by human hand blood occlusion experiment for a smaller SD separation of 0.75 cm. In this paper, we present the MVIM based DCS system, hereafter called as M-DCS (to distinguish from standard DCS), to measure cerebral blood flow in the adult human brain. We compare the results of M-DCS against the standard DCS measurements to validate the system. We have recently shown the quantification of blood flow using the multi-exposure speckle contrast and the intensity auto-correlation are equivalent [27]. However, the extraction of field/intensity auto-correlation from multi exposure speckle contrast data carried out in M-DCS is highly ill-posed, which inturn necessitates the need of regularization. M-DCS is employed to measure changes in the blood flow in pre-frontal cortex of healthy human adult volunteers, associated with volunteers undergoing voluntary apnea test and quantitative number processing test.

M-DCS: theory and algorithm
When the tissue is illuminated with a coherent light source, the scattered light will form a speckle pattern due to the mutual interference at the detector [10,11]. The speckle contrast (κ(r, T)) and the normalized electric field auto-correlation (g 1 (r, τ)), associated with the time varying speckle pattern is related to each other as given by the following relation [28], Here, r is the SD separation, T is the exposure time of the detector, τ is the correlation delay time and β is the experimental constant accounting for the collection optics. The objective of MVIM is to recover g 1 (r, τ), for every τ, from the measurement κ(r, T), for every r and exposure times T. A detailed analysis of MVIM algorithm is given in Refs. [26,29] and hence will be avoided for brevity. Nevertheless, we briefly present the essential features of MVIM as follows.
The recovery of g 1 (r, τ) from κ(r, T), can be posed as a regularized least square minimization problem, where the function Here A is the kernel matrix obtained by discretizing Eq. (1), x is defined to be g 1 (r, τ) and b is the multi exposure speckle contrast data κ(r, T). λ and x 0 are the pre-defined regularization parameter and apriori function respectively. The solution to the above minimization problem is given by Here, iterative scheme is employed to recover g 1 , by using prior information based on the recovered g 1 from the previous iteration. The above mentioned MVIM algorithm can also be employed to recover the normalized intensity auto-correlation g 2 (r, τ), by discretizing the equation, (κ 2 (r, T) Eq. (1) using Siegert's relation [14,28]. The Eq. (1) can be modified to relate changes in intensity auto-correlation (∆g 2 ) and changes in speckle contrast (∆κ), as ∆κ 2 ≡ κ 2 Here, κ b and κ p denote the speckle contrast at baseline and perturbed blood flow respectively. Using MVIM, ∆g 2 (r, τ) can be recovered from ∆κ 2 (r, T) measurements, which can subsequently be related to the blood flow using the Taylor series expansion: denote the baseline and the perturbed particle diffusion co-efficient, which are related to the blood flow. The Jacobian, J, can be analytically expressed using the semi-infinite solution of CDE as, Here, a = 3µ a µ s and b = 6αk 2 0 (µ s ) 2 . The quantities µ a , µ s and k 0 represent absorption coefficient, scattering coefficient and wave number respectively and α represents the fraction of moving particles in the medium. The r 1 and r b can be obtained by using the method of images as given in Ref. [14].

Experimental method
The experimental setup for the M-DCS system to measure cerebral blood flow is depicted in Fig. 1. A 785 nm laser source (L785P090, Thorlabs, USA) was focused to form a pointed source (using appropriate beam shaping optics that includes anamorphic prism, aspheric lens, focusing lens and a mirror to form a focused source of diameter approximately 1 mm) on the adult human forehead at FP1 (in the standard 10-20 EEG system), with a power of 15 mW at the skin surface as depicted in Fig. 1(b). A sCMOS camera (Prime BSI Photometerics) was used to capture the scattered intensity at 2 cm away from the source at FP1 position. The detection was done by 50 × 50 pixels in an area around 0.3 mm 2 (0.5mm × 0.5mm), with an appropriate f-number to match the pixel to speckle ratio. The f-number of the objective lens (Navitar Zoom 7000) was calculated by matching the pixel size to speckle size, ρ s , using the relation ρ s = 2.44λ(1 + M)f /# [11] which gives a value of f /# = 2.5. The data was captured at five exposure times (10, 28, 50, 112, 215 microseconds) with 50 frames for each exposure. The speckle contrast was computed as a ratio of the standard deviation to the mean of the intensity data detected by 125000 pixels (50 × 50 × 50) at a given exposure time. The temporal resolution of the system at this spatial resolution is 3.4 s, as it was the total time taken to capture the above-mentioned multi-exposure data. Concurrently, a DCS probe, consisting of single-mode fibre connected to an APD (SPCM-AQRH-14, Excelitas technologies) and a hardware correlator (correlator.com), was used to measure the intensity auto-correlation [13,14].

In vivo experimental protocol
Participants Three healthy adults with mean age of 30.4±4.9 volunteered for the experimental validation. All participants provided informed consent before the study and the study was approved by the Institute ethical committee.

Baseline measurements
The participants were asked to lie in the supine position and the laser was focused to FP1 area above the frontal cortex, as in standard EEG system, and the scattered intensity data at multiple exposures was collected at 2 cm away from the source. The multi-exposure speckle contrast was computed from the measured intensity speckles and is fed to MVIM algorithm to recover g 1 . Concurrently, a DCS probe was placed at the nearby region of interest (ROI), but with a same SD separation of 2 cm to measure the intensity auto-correlation. Both M-DCS and standard DCS data was collected for five trials on each participant. Here a continuous wave (CW) laser source is focused into adult human brain and scattered intensity is measured using a camera. (b) The schematic indicating the position of laser source, DCS probe and the area in which scattered intensity is collected by the camera. Here, N denotes the nasion, while FP1 and FPZ are the standard 10-20 EEG positions.

Voluntary apnea task
The data acquisition follows the same procedure as done in baseline measurement with participants in supine position. Initially, the baseline readings were acquired for 1 minute. Subsequently, measurements were acquired for the cases where the participants were asked to hold their breath for 30 seconds after which they were asked to breathe normally for 2 minutes and it was considered as one trial. The study was carried out on three subjects with three trials per subject. Before the start of the study, one practise session was performed by all the participants.

Quantitative number processing task
The same data acquisition procedure as done in baseline measurement and voluntary apnea test was adopted here. After the baseline reading was acquired for 1 minute, a randomly generated three digit number (between 500 and 600) was given as an auditory cue and the participant was asked to subtract the number "seven" serially from the given three digit number for 1 minute. After one minute, a bell sound was given as an indication for the subject to stop the mental calculations. A post task reading was acquired for 1 minute, while continuing the measurements. The above procedure is denoted as one trial and we conduct three trials per participant and the whole process was repeated for three different participants. There was one practice trial before starting the experiment.

Data analysis and algorithm: implementation details
The multi-exposure speckle contrast was computed, as a ratio of standard deviation to the mean intensity, using 50 frames (with each frame of size 50 × 50 pixels) for given exposure and for 5 such exposures with appropriate noise corrections. MVIM algorithm was employed to calculate g 1 (or g 2 ) for the given SD separation of 2 cm and for τ ranging from 10 −10 s to 0.22s equally divided in logarithmic scale with 250 values. For comparing the g 1 obtained using M-DCS and standard DCS for the baseline blood flow, the experiment was repeated for 5 trials to compute the mean and the standard deviation at each τ. Here, the prior values based on the solution of CDE was used for recovering g 1 . The g 1 measured using both M-DCS and standard DCS was fitted against the semi-inifinte solution of CDE model to quantify the blood flow αD B .
To show that M-DCS works independent of the prior values, we have used four different types of priors and compared the results with each other. The different priors used were: (a) x a 0 which is the semi-infinite medium solution of CDE [14]. Note that, for using CDE we need values of tissue optical properties such as µ a and µ s ; (b) An arbitrary exponential model based prior x b 0 = 1 + uexp(−vτ) was used to recover g 2 , where u and v are the co-efficients of the fit. In this model, explicit values on tissue optical properties are not needed. Here, for the first iteration, the prior x c 0 = 1 + β (based on the fact that g 2 → (1 + β) at lower values of τ) was used and for the subsequent iterations, prior x b 0 was used to fit the result of the recovered g 2 from the previous iteration; (c) The prior x c 0 was taken as the third type of prior to perform a comparative study to check the need of exponential model based priors in recovering g 2 and rCBF; and (d) For recovering ∆g 2 from changes in speckle contrast, we have used prior of the form where u, v and w are the co-efficients of the fit. In this case, for the first iteration, no prior (or x 0 = 0) was used and x d 0 was used as prior for subsequent iterations. The comparative study between recovered ∆g 2 with prior x d 0 and without prior (i.e. x 0 = 0) has also been performed, to check if M-DCS can work without using any prior values of x 0 .
For the voluntary apnea test, the field auto-correlation g 1 was obtained using M-DCS and was fitted for semi-infinite medium solution of CDE to obtain the particle diffusion co-efficient D B and subsequently relative cerebral blood flow (rCBF=D P B /D 0 B ). Here, the prior x a 0 was used. The capability of M-DCS to recover the intensity auto-correlation g 2 is demonstrated in the quantitative number processing task. Here, the prior x b 0 was used and the recovered g 2 was fitted to the semi-infinite solution of CDE to obtain the rCBF. By using the prior x b 0 , we show that M-DCS does not require any explicit values about tissue optical properties (µ a and µ s ) for recovering g 2 . In addition, we also recover the change in intensity auto-correlation ∆g 2 associated with change in speckle contrast by the proposed M-DCS system. Here, for the first iteration, prior used is x 0 = 0 (or no prior) and for subsequent iterations, x d 0 is used as prior. The rCBF was quantified by using jacobian, J, calculated by using equation (2), wherein the absorption and scattering coefficients were assumed to be constants as 0.12cm −1 and 12cm −1 respectively [14,19]. The baseline blood flow D 0 B was assumed to be 2 × 10 −8 cm 2 /s and τ was chosen at 4 µs for the calculation of Jacobian J and ∆g 2 . The mean speckle contrast of first 17 s of the baseline was taken as κ b . We also compare the cases of recovering g 2 from κ(T), by using two different priors (i.e. x b 0 and x c 0 ), to show that no explicit values of tissue optical and dynamic properties (µ a , µ s and D 0 B ) are required for M-DCS. The regularization parameter was chosen using L-curve approach [26,30] for all methods without iteration (when x c 0 was used as prior) and was linearly varied from 0.5 to 30 times the initial regularization parameter (determined by L-curve approach) for the methods with iteration. The maximum number of iterations were fixed to be 5 for all calculations in this paper.

Baseline measurements
The field auto-correlation (g 1 ) measured by M-DCS and standard DCS during baseline blood flow in the adult human head at a SD separation of 2 cm for 5 trials is shown in Fig. 2. The standard deviation (σ) of M-DCS measurements is also shown, where it is relatively smaller at lower values of τ, when compared to the standard deviation obtained using standard DCS measurements. We infer that this is due to the presence of CDE model as prior information in case of M-DCS. To verify it, the results were fitted for semi-infinite solution of CDE model (g and are shown in the inset. The corresponding standard deviation of the fitted g 1 called σ f is also plotted in the inset and it can be seen that σ f of M-DCS and standard DCS are in reasonable agreement with each other. The mean D B values (for a given subject) obtained for M-DCS was 7.42 × 10 −9 cm 2 /s and for standard DCS was 7.20 × 10 −9 cm 2 /s, which are comparable to one another.

Optimizing the number of pixels
The number of pixels needed to compute speckle contrast is determined by the overall signal to noise (SNR) of the camera pixels. The percentage error E is the relative error between blood flow calculated by M-DCS against standard DCS. E is plotted as a function of number of pixels used to compute speckle contrast, as shown in Fig. 3. It can be seen that around 8000 to 10000 pixels are needed to get E less than 0.1%. The requirement of larger number of pixels (for smaller E) will demand more frames to be acquired, which inturn reduces the temporal resolution. Nevertheless, for this study, we have used a high density of 125000 pixels for computing the blood flow. Fig. 3. Optimal number of pixels needed for M-DCS system was found to between 8000 to 10000 pixels, wherein the error E, the relative change in blood flow calculated by M-DCS and standard DCS, is less than 0.1 %

Voluntary apnea test and quantitative number processing task
The results of voluntary apnea task and quantitative number processing task obtained by M-DCS by recovering auto-correlation is given in Fig. 4. For the voluntary apnea task, the mean rCBF for three subjects with three trials each (nine trials in total) is plotted in Fig. 4(a). Figure 4(b) shows two representative g 1 curves for a given trial, plotted at two data points: one at 'a' in the baseline and other at 'b', after holding the breathe. The g 1 curve shifts to the left, with an increase in blood flow index of around 8% (on the given trial shown here), after holding the breathe for 30 s. The inset plot in Fig. 4(b), shows the standard deviation over five g 1 curves in a given trial during the baseline (near point 'a') and after the task (near point 'b'). The changes in rCBF obtained for voluntary apnea test are comparable to that of results obtained in Ref. [19], where the change in rCBF was around 12 to 15 % and to that of Ref. [31] obtained using MRI, wherein similar trends of increase in total blood flow can be observed, after holding the breathe.
By using the proposed M-DCS system, the intensity auto-correlation was recovered for the quantitative number processing task and the corresponding rCBF is shown in Fig. 4(c) and (d). The mean and standard deviation of the rCBF for the nine trials (on three subjects) is shown in Fig. 4(c). The results shows an elevated blood flow during the task and recedes to the baseline after the task. The g 2 curves in a given trial for two data points, one in baseline and one during the task is shown in Fig. 4(d). It can be seen that the curve shifts to the left, with an increase in blood flow index of around 14% (on the given trial shown here). The inset plot in Fig. 4(d), shows the standard deviation over five g 2 curves in the given trial. The changes in rCBF obtained for quantitative number processing, also called serial subtraction task, are comparable to that of the results obtained in Ref. [32], where funtional near infrared spectroscopy was used to measure changes in oxy and deoxy Haemoglobin (HbO and HbR) concentrations. The changes in HbD (difference in oxy and deoxy Haemoglobin concentrations) is highly correlated with rCBF [33] and similar trends on increase in HbD during the task and decrease in HbD after the task is observed in Ref. [32], which are comparable to rCBF obtained by M-DCS. To show that the problem of recovering both g 1 and g 2 can be implemented using MVIM, in Fig. 4(e) we have shown that both the g 1 and g 2 recovered using M-DCS (for a given trail during the baseline). By using the Siegert's relation, g 2 recovered by M-DCS is converted to g 1 and is plotted in Fig. 4(e) for comparison.
The above results use priors (either CDE or arbitrary exponential model x b 0 ) to iteratively recover the auto-correlation from speckle contrast data. We have compared the results of g 2 recovered in quantitative number processing task (at the representative points 'a' and 'b' indicated in Fig. 4(c)), obtained in two cases: with and without using arbitrary exponential prior (i.e. by using x b 0 and x c 0 as prior respectively) in Fig. 4(f). Although in both the cases, g 2 is comparable, in case of not using exponential model based priors iteratively, we can see ripples at larger values of τ due to the presence of noise in speckle contrast data. This is due to the inherent ill-posed nature of the problem [26,27] and can be minimized by using aprior information (on g 1 or g 2 , as seen Fig. 4(d)) and also by employing dense speckle contrast data (dense interms of exposure times). Nevertheless, the recovered g 2 without using exponential model based prior are reliable to measure the changes in blood flow rather than absolute blood flow. Figure 4(g) shows the correlation plot between mean rCBF (of the nine trials), with and without exponential model based priors. With a correlation co-efficient of R = 0.86, the results are in reasonable agreement with each other. This indicates that, even without any exponential model based priors, M-DCS can pickup changes in blood flow. We would like to reassert here, that regularization is essential for M-DCS due to the fact that recovering field/intensity auto-correlation from multi exposure speckle contrast data is an ill-posed problem [27].
The changes in g 2 was measured by the M-DCS system from the changes in speckle contrast, as explained in section 2.1. We compute ∆g 2 = g 2 (D p B ) − g 2 (D 0 B ) using the M-DCS system with multi exposure speckle contrast data. The recovered ∆g 2 curves corresponding to the two representative points (in quantitative number processing task, as the one indicated in Fig. 4(c)) is shown in Fig. 5(a). During the task ∆g 2 will decrease as shown in Fig. 5(a), which can be clearly deduced from Fig. 4(d). The Jacobian J was computed at τ = 4µs and the corresponding rCBF is shown in Fig. 5(b). It can be seen that rCBF obtained using ∆g 2 is comparable to that of rCBF obtained by g 2 as shown in Fig. 5(b). In Fig. 5(a), we have shown the results of M-DCS based ∆g 2 recovered with and without using prior values of x 0 (i.e by using x d 0 and x 0 = 0 as priors respectively). We can see that ∆g 2 curves are comparable to one another, at earlier values of τ. This shows that we do not need any prior values of x 0 to measure changes in blood flow (not absolute blood flow) using M-DCS. ) is compared to that of the g 2 recovered without using exponential model as prior (i.e.x c 0 ). It can be seen that curve shifts to the left in both the cases indicating that both the cases can pick up relative changes in the blood flow. The correlation plot between mean rCBF (of the nine trials) between the two cases (i.e. rCBF NP , where no exponential prior was used and rCBF P , where exponential prior was used) is shown in (g), indicating that the rCBF between both the cases are reasonably well correlated (Correlation coefficient R was 0.86,with slope of 1.05 and intercept of 5.28).  Fig. 4(c)). It can be seen that as ∆g 2 decreases, there is an increase in the blood flow. The ∆g 2 curves obtained with and without using priors are comparable to one another, showing that M-DCS does not need any prior values of x 0 for measuring changes in blood flow. (b) Comparison of rCBF obtained by using ∆g 2 to that of rCBF obtained by using g 2 , indicating that rCBF is comparable to one another.

Discussion
A camera based DCS system, termed as M-DCS, to measure deep tissue blood flow is presented. M-DCS utilizes multi-exposure multi-distance speckle contrast data to measure field / intensity autocorrelation using the recently introduced MVIM algorithm. We have successfully demonstrated M-DCS in measuring cerebral blood flow in the prefrontal cortex of adult human brain. In order to demonstrate M-DCS, we have measured the intensity / field auto-correlation associated with the blood flow in pre-frontal cortex of the healthy human volunteers as shown in Fig. 2. We validated this measurement by comparing it against a concurrently obtained auto-correlation data from the same region of interest using a standard DCS probe. A good agreement of the blood flow index (αD B ) obtained by the two methods was observed as shown in inset of Fig. 2.
DCS system is quite often employed to measure blood flow changes rather than absolute blood flow. In order to initiate blood flow changes in pre-frontal cortex, we adopted two functional activation tasks namely, voluntary apnea task and quantitative number processing task. To show that both g 1 and g 2 can be measured using M-DCS, we have used one task as an example to illustrate the same. The g 1 and g 2 curves measured by M-DCS during the above experiments are plotted in Fig. 4(b) and Fig. 4(d) respectively, whereas Fig. 4(a) and Fig. 4(c) shows the mean and standard deviation of rCBF and are comparable to that of the results shown in previously published literatures [19,31,32]. We have reformulated MVIM algorithm to accommodate the changes in multi-exposure speckle contrast as given in section 2.1, to recover the changes in intensity auto-correlation (∆g 2 ). The rCBF obtained using ∆g 2 , as shown in Fig. 5(b) was also in good agreement with the previously reported data.
The major drawback of employing a multi-speckle DCS using cameras is the requirement of very high frame rate. The requirement of high frame rate increases as one attempts to probe deeper due to the fact that intensity speckles de-correlates faster. This problem is circumvented in M-DCS using the MVIM algorithm, where fastly de-correlating speckles can be quantified by using multi-exposure speckle contrast data, captured with a low frame rate camera. Additionally, this makes M-DCS a low cost, multi-speckle alternative to conventional DCS system.
The major limitation of M-DCS system is associated with MVIM algorithm. We have recently shown in Ref. [27] that the measurement of blood flow index by using standard DCS system and speckle contrast based systems (eg: SCOS, diffuse speckle contrast analysis (DSCA) [17] and M-DCS) are equivalent. However, it was also proved that recovery of field / intensity auto-correlation from multi-exposure speckle contrast is ill-posed and hence necessitates the use of regularized inversion. In other words, the noise in the multi-exposure speckle contrast data will be amplified by the MVIM algorithm, while attempting to recover g 1 (or g 2 ), if proper regularization scheme is not adopted. Any prior information used in the regularization scheme will make MVIM less ill-posed resulting in better recovery of g 1 or g 2 . Hence we have studied the effect of apriori information in the M-DCS measurements as shown in Fig. 4(f) & (g) and Fig. 5(a).
Another limitation of the system is its current temporal resolution of 3.4 s. One of the reasons for low temporal resolution is the inability of the camera to adapt for the faster changes in exposure time through inbuilt camera software. This, in future, can be controlled by either hardware triggering or by controlling the duration of input light (through spatial light modulators or acousto-optic modulator modulators), as used in Ref. [12], resulting in better temporal resolution. Also, currently we use 125000 pixels for calculation of speckle contrast in a spatio-temporal manner. We have optimized the number of pixels needed for optimal estimate of blood flow to be around 10000 pixels. This high density data can be achieved by using a better objective wherein a single image of 100 × 100 pixels can be employed in the same ROI. With the above mentioned modifications, the temporal resolution of the M-DCS system can be enhanced. Currently, we have shown the working of the system in the human forehead to quantify the blood flow in prefrontal cortex. It can be extended to other parts of the brain, however, hair present may act as a hindering factor. To overcome this problem, we can use cameras coupled to optical fibers, as used Refs. [34,35].

Funding
Indian Institute of Technology Bombay (Seed grant); Department of Science and Technology, Ministry of Science and Technology, India (SERB-Early career research award); Department of Biotechnology, Ministry of Science and Technology, India (Ramalingaswamy Fellowship-2016).