1. Introduction

Laser speckle contrast imaging (LSCI) is a technique capable of measuring blood flow dynamics that has gained broad interest since it was first introduced in the 1980s [1–3]. It has been utilized to measure blood flow in many organs including the brain [4–6], skin [7], and retina [8,9]. LSCI exploits the spatial statistics of speckle patterns, which arise from the interference of coherent light re-emitted from tissue. In LSCI, the spatial contrast $K$ of the measured intensity speckle pattern is calculated, and the reduction of $K$ due to the blurring of the speckles within a certain camera exposure time reflects the dynamics of the red blood cells. The spatial $K$ is directly related to the decorrelation time constant $\tau _c$ of the temporal intensity auto-correlation function $g_2(\tau )$ [10]. Methods such as multi-exposure LSCI and various models have been developed to quantify cerebral blood flow (CBF) from LSCI measurements [11–14].

Besides CBF, LSCI also has the potential to measure other sources of tissue dynamics such as intracellular motility [15–17] or optical signal variations of neurons due to brain activation [18,19]. The decorrelation time of these dynamics is typically a few orders of magnitude longer than that of CBF [20]. Existing models have taken into account the portion of scattered photons that have not experienced scattering events from red blood cells as a static component in the measured contrast in order to estimate CBF accurately [11,12,21]. But the static component as well as the slow decaying component, which is usually also incorporated into the static component, are much less studied. Also, in traditional wide-field LSCI (WF-LSCI), the two-dimensional maps of $K$ measured in the tissue are largely contaminated by blood flow in the neighboring blood vessels. A new method and data analysis pipeline that is capable to enhance the sensitivity to static and slow components will open up new avenues to the study of tissue dynamics other than CBF.

We have developed a short-separation speckle contrast optical spectroscopy (ss-SCOS) system to enhance the sensitivity to the static and slow components in the measured $K$ as compared to traditional WF-LSCI. SCOS is a technique derived from LSCI which also measures the speckle patterns, but uses point source and detector pairs to access CBF in the deeper brain region [22]. We have utilized a multi-mode fiber linear array with relatively short source-detector separations (SDS) of 125-750 $\mu$m focused on the surface of the mouse brain for point illumination and detection. The ss-SCOS system is integrated with a wide-field imaging system to identify the location of the multi-mode fiber array on the surface of the mouse brain. We have constructed the model to obtain the fractions and decorrelation time constants of both fast and slow components from ss-SCOS measurements. We calculated these components as functions of SDS from in vivo mouse brain measurements. The fraction of the static and slow components measured with ss-SCOS is greatly enhanced compared to the WF-LSCI by $\sim$ 6 times with an SDS of 125 $\mu$m in the parenchyma away from blood vessels. We then showed the measurements of the slow dynamics within an hour post-euthanasia in mice. We still observed the slow dynamics 50 mins after the cessation of blood flow, which confirms that the slow dynamics are related to cellular dynamics instead of motion-related artifacts. We also performed ss-SCOS measurements in mice post-stroke and demonstrated that the slow tissue dynamics is reduced, i.e. the decorrelation time constant is longer, within and near the stroke core region compared to that in the healthy tissue. Our system provides a way to measure both fast CBF and slow cellular dynamics simultaneously, which will impact studies of the brain dynamics in health and disease.

2. Methods

2.1 ss-SCOS system and speckle theory

The system schematic is shown in Fig. 1. To identify the fiber location on the surface of the brain cortex, the ss-SCOS system is integrated with a wide-field imaging system illuminated with 530 nm LED light. The field of view for this wide-field imaging system is 3 mm $\times$ 2.5 mm. The LED light is turned off when the region of interest (ROI) is identified. For the ss-SCOS system, we used a linear-to-linear multi-mode fiber array (105 $\mu m$ core for each multi-mode fiber, 0.9 mm $\times$ 0.13 mm, Thorlabs Inc.) with 1 source fiber and 6 detection fibers to investigate the slow and static components at different SDSs. The position of the fiber array with respect to the wide field CMOS camera (Basler acA1300-200uc) is fixed at the center of the field of view, and we translated the sample in x, y, z using translation stages to change the imaging ROI. The source fiber is connected to a laser light source (Topica WS, 853 nm) for point illumination. The speckle patterns from detection fibers are imaged onto a second CMOS camera (Basler acA1440-220umNIR). Examples of speckle patterns in the fiber array obtained with the ss-SCOS camera are shown in Fig. 1(c). Note that the distal end (on the camera) and the proximal end (on the sample) of the multi-mode fiber array are not in the same order, and the order of them on the proximal end from the closest (1) to the farthest (6) from the source fiber is indicated. The maximal achievable frame rate (FPS) is 327 Hz limited by the camera, and the minimum exposure time ($T_{exp0}$) was set to be 3 ms for each frame, such that the dead time between adjacent frames is approximately 0.05 ms, which is negligible ($1.7{\% }$ of $T_{exp0}$) in our study. We can then obtain the intensity $I(T_{exp})$ by binning camera frames [23], where $I$ is the intensity in the units of camera counts (arbitrary digital units, ADU) and $T_{exp}$ is the exposure time. The contrast $K(T_{exp})$ for each fiber was calculated as:

 

Fig. 1. (a) Schematic of the fiber-based LSCI system. DM: dichroic mirror. The red circle in the inset indicates the source fiber tip and the gray circles represent the 6 detection fiber tips. FPS is the frames per second. (b) An example of the wide-field image of a mouse brain surface obtained from the wide field camera. The light path of the wide-field imaging is indicated in green. (c) An example of the speckle pattern of the detection fibers obtained at the ss-SCOS camera. The order of the fibers shown on the speckle image is based on the source-detector distance from 125 $\mu m$ to 750 $\mu m$. The light path of ss-SCOS is indicated in red.

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We compared our ss-SCOS system with traditional WF-LSCI system. For the WF-LSCI system, we used a CMOS camera (Basler acA2040-180kmNIR, $2048 \times 2048$ pixels, 4.4 $\mu m$ pixel size) with a 5x objective (Mitutoyo, Japan). The camera was operated at 165 Hz of frame rate and with a 6 ms of exposure time such that the dead time between adjacent frames is 0.06 ms. A laser diode (785 nm, LP785-SAV50) was used to deliver the coherent light to the object. The optical power density on the object was controlled by expanding the size of laser beam for uniform illumination.

In conventional multi-exposure laser speckle imaging (MESI) theory [11,23] considering the presence of fast blood dynamics and static scattering, the ensemble-averaged intensity correlation function $g_2(\tau ) = \frac {\langle I(t)I(t + \tau )\rangle }{\langle I(t)\rangle ^2}$ is [24]

The speckle contrast is a function of the exposure time $T_{exp}$ and is related to the intensity auto-correlation function $g_2(\tau )$ by [10]:

For the cases where $g_{1,f}(\tau )= e^{-\frac {\tau }{\tau _{c1}}}$, where $\tau _{c1}$ is the decorrelation time constant, taking Eq. (2) into Eq. (3), $K(T_{exp})$ is obtained as [1,11,13]:

Here $1-\rho _1-\rho _2$ indicates the fraction of the true static component or any dynamics that are slower than tissue cellular dynamics (on the order of seconds); $g_{1,s}$ is the slow tissue decay function with the functional form $g_{1,s}(\tau )= e^{-\frac {\tau }{\tau _{c2}}}$, which is validated with the experiments post-euthanasia and shown in Supplement 1. Then Eq. (4) can be re-derived as:

2.2 Animal preparations

All animal procedures were approved by the Boston University Institutional Animal Care and Use Committee and were conducted following the Guide for the Care and Use of Laboratory Animals. Two 15-month-old male mice (Jackson Labs Strain:008241) were used in this study, one receiving pentobarbital injection and the other undergoing the photothrombotic stroke procedure. A craniotomy was performed over one hemisphere of the brain in both mice to implant a half-crystal skull over the brain [25] (modified from Crystal Skull, LabMaker, Germany), and a 12 mm aluminum head bar was installed around the window and attached to the exposed skull using dental acrylic. After the procedure, mice were given a recovery period of 10 days before the imaging sessions. Throughout the imaging sessions, mice were lightly sedated using 1.5% isoflurane anesthesia with a controlled airflow of 0.8-1 L/min to minimize movement. To obtain the post-euthanasia data, we performed pentobarbital overdose injection intraperitoneally with a lethal dose of >200 mg/kg while keeping the mice under the ss-SCOS system to maintain a consistent ROI throughout the entire imaging period. The respiratory arrest was determined to happen around 9 minutes after injection by visual inspection for the lack of respiratory muscle movements. The photothrombotic stroke model was conducted following the protocol described by Sunil et al. [26]. In brief, Rose Bengal was retroorbitally injected and a distal branch of the middle cerebral artery was specifically targeted for occlusion using a 520 nm laser diode. The location of the stroke core was determined 2 days after stroke with spatial frequency domain imaging (SFDI) as described in [27] and the post-stroke measurement with ss-SCOS was performed after confirming the relative location of the ROI to the stroke core.

3. Results

We have conducted measurements using traditional WF-LSCI and compared the results with ss-SCOS in in vivo mouse brain measurements. The WF-LSCI image was obtained from the same ROI in the same mouse cortex as illustrated in Fig. 2(a). We see from the results in Fig. 2(b) that $K$ obtained using WF-LSCI in the tissue away from the vessels decays to a smaller value compared to ss-SCOS at $T_{exp}$ of 150 $ms$, which is longer than the decorrelation time of the fast dynamics but shorter than that of the slow dynamics, indicating that the fraction of the static and slow component of $K$ obtained from ss-SCOS is enhanced compared to WF-LSCI. Using Eq. (4), we have obtained the fraction of the static component $1-\rho _1$ for both ss-SCOS and WF-LSCI. We see that the fraction is enhanced by $\sim$ 6 times using the ss-SCOS with the shortest SDS of 125 $\mu m$ as compared to WF-LSCI. We also found the decorrelation time $\tau _{c1}$ obtained from ss-SCOS ($\sim$5 ms) is much longer than that from wide-field LSCI ($\sim$0.4 ms), also indicating less contamination from multiply scattered light from neighboring vessels. Here $\beta$ was calibrated using a static agarose phantom with $\beta =K^2$ [28], and is estimated to be 0.49 for our ss-SCOS system and 0.62 for the WF-LSCI system, respectively.

 

Fig. 2. (a1) An example of wide field image of mouse brain surface using our ss-SCOS system shown in Fig. 1, with the circles indicating the locations of the source fiber (red) and the 6 detection fibers (labeled with numbers) on the mouse brain surface. (a2) An example of WF-LSCI showing the spatial contrast of the same ROI in the mouse brain as in (a1). Gray rectangle indicates the ROI that is used to get the spatially averaged K in (b) $\&$ (c). (b) K versus $T_{exp}$ varying from 3 ms up to 150 ms and the fitting curves (dot dash) for the first 4 detection fibers compared with WF-LSCI. (c1) and (c2) $\rho _1$, $1-\rho _1$ and $\tau _{c1}$ for different SDS measured with ss-SCOS compared with wide field LSCI. Results were obtained from fitting the speckle contrast model Eq. (4). (d) K versus $T_{exp}$ varying from 3 ms up to 4 s and the fitting curves (dot dash) for the first 4 detection fibers compared with WF-LSCI. (e1) and (e2) $\rho _1$, $\rho _2$, $1-\rho _1-\rho _2$, $\tau _{c1}$ and $\tau _{c2}$ for different SDS measured with ss-SCOS. Results were obtained from fitting using the new speckle contrast model Eq. (6). Error bar represents the standard error of 10 repetitive measurements.

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To quantify slow tissue dynamics, we obtain $K(T_{exp})$ for $T_{exp}$ up to 4 s, which is on the order of the decorrelation time of the slow cellular dynamics. We then used the model in Eq. (6) to conduct fitting for $K(T_{exp})$ as shown in Fig. 2(d). Since the fast decay of speckle contrast in the first hundreds of ms is dominated by blood flow, we obtain the dynamic component $\rho _1$ and $\tau _{c1}$ from the K($T_{exp}$) in Fig. 2(b), i.e., fitting from the first 150 ms of the $K(T_{exp})$ data points using Eq. (4). We apply $\rho _1$ and $\tau _{c1}$ to Eq. (6) in the fitting of $K(T_{exp})$ with a longer $T_{exp}$ to obtain $\rho _2$ and $\tau _{c2}$ as shown in Fig. 2(d), which we found to be more robust than to simultaneously fit all the parameters using Eq. (6), with fitting accuracy $R>0.99$ for the ss-SCOS measurements. Here we only investigated the first 4 fibers with SDS varying from 125 $\mu m$ to 500 $\mu m$ since the last 2 detection fibers have lower photon counts with a noise contribution that cannot be neglected [28], and we found that they are more contaminated from neighboring fibers due to fiber cross-talks. From Fig. 2(e), we see that the fast blood flow component $\rho _1$ increases while the slow tissue dynamics $\rho _2$ decreases with increasing the SDS. This is due to the fact that the number of photon scattering events increases with SDS, and thus the contribution of blood flow also increases. The decorrelation times for fast dynamics ($\tau _{c1}$) and slow dynamics ($\tau _{c2}$) both decrease with SDS due to more scattering events inducing faster speckle fluctuations. The difference of the time scale of $\tau _{c1}$ and $\tau _{c2}$ is consistent with the speed difference of red blood cells and intracellular organelles [15]. To study the slow tissue dynamics, we use the closest source-detector fiber pair with an SDS of 125 $\mu m$ for all the results in the rest of this manuscript. In addition, we applied the same fitting procedure to fit the WF-LSCI data with long exposure times. The fitting accuracy was found to be lower and the slow dynamic component $\rho _2$ was only 0.026, with a much slower decay time $\tau _{c2}$ of $\sim$ 26 seconds. This result suggests that the slow dynamics obtained with WF-LSCI is negligible. It is also contaminated by noise since at long $T_{exp}\sim$s relevant for the slow dynamics, the value of $K$ is low and close to the noise level. In contrast, our ss-SCOS method provides more reliable and accurate measurements of the slow dynamics, offering a distinct advantage over traditional WF-LSCI.

To further validate that the slow decorrelation comes from tissue dynamics related to cellular motility instead of potential motion artifacts, we measured the speckle contrast of the mouse brain cortex before and after euthanizing the mouse with an overdose injection of pentobarbital. We still use Eq. (6) for fitting for the data obtained after euthanizing the mouse. Cessation of heartbeat and breathing was observed 9 minutes after injection [29]. After confirming the heart is stopped, we waited 10 minutes for the blood to stop flowing completely before measuring the post-euthanasia tissue dynamics at several time points shown in Fig. 3(a). We found that fast decay vanishes and the fast dynamic component $\rho _1$ drops significantly from $\sim$ 52 ${\% }$ to $\sim$ 1 ${\% }$, indicating the cessation of blood flow. No slow decay was observed for the static phantom, while the speckle contrast for the post-euthanasia mouse data still has a slow decay, which indicates that the slow decay measured with ss-SCOS arises from the cellular motility and tissue dynamics instead of motion artifacts and any vibration of the imaging system. This measurement also confirms that the decorrelation of the cellular dynamics follows the expression of $e^{-\tau /\tau _{c2}}$, which is what we have utilized in the model of Eq. (6) (See Supplement 1). Fig. 3(b) shows that the slow tissue dynamics component $\rho _2$ reduced from $\sim$ 18 ${\% }$ to $\sim$ 4 ${\% }$. The reduction of $\rho _2$ is caused likely by the variety in the lifetimes of different cells after the animal is sacrificed. For instance, the death of neurons is known to be relatively rapid (within a few minutes) once the blood circulation stops to oxygenate the brain tissue [30–32], while other brain cells such as glial cells have been observed to still be alive for up to a few hours depending on the temperature and conditions of the environment [33–35]. The decorrelation time $\tau _{c2}$ was $\sim 0.8$ s at baseline and maintained at $\sim 0.7$ s post-death, indicating the cellular motility is maintained for the fractions of the cells that are still alive within 50 minutes after the animal is euthanized. The slow dynamics measured post-euthanasia can be potentially contaminated by the Brownian motion of red blood cells in large vessels. We have avoided large vessels when choosing ROIs to minimize this effect.

 

Fig. 3. (a) K versus $T_{exp}$ for measurements at baseline, 20, 35, 50 minutes after pentobarbital overdose injection, compared with a static agarose phantom measurement. (b) Bar plots of slow tissue dynamics component (b1) $\rho _2$ and (b2) $\tau _{c2}$ for measurements at baseline, 20, 35, and 50 minutes after injection. The error bar represents the standard error of 5 repetitive measurements.

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We then conducted ss-SCOS measurements of the mouse brain before and one week post photothrombotic stroke in the motor cortex, with the results shown in Fig. 4. We calculated the relative change in the reduced scattering coefficient ($\mu _s'$) using SFDI, comparing measurements taken on post-stroke week 1 to the pre-stroke baseline. Scattering increases following stroke and the stroke core can be visualized in the map of the relative reduced scattering coefficient [27]. We performed ss-SCOS measurements radially across the brain surface from the stroke core to the healthy tissue, with 4 ROIs identified in the stroke core and 4 ROIs identified in healthy brain tissue as shown in Fig. 4(a). The fitting results for both fast blood flow dynamics ($\rho _1$, $\tau _{c1}$) and slow tissue dynamics ($\rho _2$, $\tau _{c2}$) are illustrated in Fig. 4(b) for each ROI. We observed comparable values of the fractions of the fast blood flow component ($\rho _1$) as well as the slow tissue component ($\rho _2$) between the stroke core and healthy brain tissue. This suggests similar levels of perfusion in both regions at week 1 post-stroke. Additionally, we did not observe a significant change in the decorrelation time of the fast blood flow dynamics ($\tau _{c1}$) near the stroke core one-week post-stroke. However, we found that the slow tissue dynamics ($\tau _{c2}$) in the stroke core were approximately three times longer than those in the healthy brain tissue, indicating a reduction in cellular motility or metabolism following stroke, as expected.

 

Fig. 4. (a) Vascular reflectance image (top) and relative change in $\mu _s'$ spatial frequency domain imaging (SFDI) (bottom) with circles indicating the locations of measured ROIs using ss-SCOS. ROIs are ordered from 1 to 8 sequentially from stroke core (pink) to healthy tissue (black) and indicate the locations of the shortest source-detector fiber pair (SDS = 125 $\mu m$). (b) $\rho _1$, $\rho _2$, $\tau _{c1}$ and $\tau _{c2}$ obtained at different ROIs across stroke core and healthy tissue. The error bar represents the standard error of 5 repetitive measurements. (c) Mean values of $\rho _1$, $\rho _2$, $\tau _{c1}$ and $\tau _{c2}$ over 4 stroke ROIs (pink) and 4 healthy ROIs (grey), respectively. The error bar represents the standard error from the averaged data of the 4 ROIs.

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4. Discussion and conclusion

We have illustrated enhanced sensitivity of the spatial contrast to the slow tissue dynamics using ss-SCOS as compared to traditional WF-LSCI. We have constructed a multi-exposure model for spatial contrast in LSCI and SCOS measurements. Most multi-exposure LSCI techniques modulate the intensity of light incident on the camera to ensure the average camera counts stay constant throughout the measurements to minimize the variation of the noise-induced bias at different $T_{exp}$, but at the expense of increased complexity of the system. Recently, we have constructed the model to remove the bias induced by noise using LSCI at the low photon flux regime relevant for human brain measurements [28]. We have conducted an analysis that shows that the bias term in the speckle contrast measurement of the mouse brain is negligible thus we can use the camera frame binning method on the raw data to obtain $K^2 (T_{exp})$, thanks to the rapid development of camera technology. We have utilized $e^{-\tau /\tau _c}$ as the model for the field auto-correlation function of both CBF and tissue dynamics. It has been shown that more accurate models can be used for different types of motion in blood flow measurements [13]. It is out of the scope of the current manuscript to explore the impact of all the motion types, but these can be done by revising Eq. (6) taking into account different functional forms of $g_2 (\tau )$.

As we have shown, the slow dynamics are related to cellular dynamics which is collectively defined as intracellular motility. To the best of our knowledge, most studies investigating intracellular motility have been conducted ex vivo. For instance, Li et al. [15] developed a Doppler fluctuation spectroscopy technique to measure intracellular dynamics originating from persistent walks in tumor samples, where the speeds of intracellular motion range from several micrometers per second to several nanometers per second. Leung et al. [16] reported on a dynamic $\mu$-OCT technique that enabled cellular-resolution imaging of intracellular motion in human esophageal and cervical biopsy samples based on spectral analysis of OCT fluctuating signals, with frequencies below 20 Hz for most cellular constituents. In our study, we propose an in vivo approach using the ss-SCOS system, which is suitable for the measurements of the collection of a broad range of intracellular dynamics beyond CBF. The decorrelation time for slow dynamics measured with ss-SCOS is about 3 orders of magnitude slower than that of fast blood dynamics, comparable to the speed differences of these organelles ($\sim \mu$m) and red blood cells ($\sim$ms) reported in previous in vitro studies. In the future, we will further explore the exact origin of the intracellular motility including its relation with cellular metabolism.

The slower dynamics can also be potentially utilized to measure the optical signal associated with cell swelling during neuronal activation [18]. However, our preliminary analysis using whisker stimulus shows that the stimulus-related motion artifacts will largely affect the measured contrast on the time scale of the slow components, thus making it difficult to distinguish neuronal cell activation from these event-related artifacts. The study of neuronal cell activation in vivo using speckle statistics will require the implementation of a system that is even more robust against the motion, such as using mounted miniscopes on the mouse head instead of the free space system we are utilizing in this work.

In summary, We have constructed a label-free ss-SCOS system to obtain both fast CBF dynamics and slow cellular dynamics simultaneously from speckle contrast measurements in in vivo mouse brain. It opens up opportunities to monitor brain dynamics that will impact many studies in neuroscience such as the relation between cellular dynamics and stroke recovery.