High spatiotemporal mapping of cortical blood flow velocity with an enhanced accuracy

Tian Jin; Baochen Li; Linyang Li; Weizhi Qi; Lei Xi; Lei Xi

doi:10.1364/BOE.520886

1. Introduction

Cerebral vasculature, one of the most crucial systems for a properly functioning brain [1], provides glucose and oxygen, and maintains homeostasis of the cerebral microenvironment [2]. Compared to morphological characteristics of cerebral vasculatures, including vessel number, density, and length [3], physiological changes in hemodynamics are relatively inconspicuous. However, such dynamic fluctuation is considered as an essential indicator during immediate brain activation in both rest and task states [4] and a reliable biomarker for identifying brain diseases [5,6]. Cerebral blood flow is a primary hemodynamic feature with important research significance, and decreased blood flow has been proposed as the most common physiological deficit in neurodegenerative diseases [7] and even a factor initiating damage to the central nervous systems [8]. In addition, investigation of dynamic blood flow among cerebral vasculature is also beneficial to revealing brain functions responded to external stimulus and understanding the hemodynamic behaviors in microcirculations [9].

There are two primary categories of velocity-measuring methods for mapping cerebral blood flow: wide-field mapping method, and focused-spot-based mapping method. Generally, the wide-field mapping method employs an area excitation and a detector array to obtain backscattered signals within the field of view (FOV), and maps a wide-range velocity with a high temporal resolution. This method can be applied to imaging techniques with intrinsic contrast from particle flow, such as functional ultrasound imaging [10,11] and laser speckle contrast imaging [12]. However, the limitations of wide-field mapping include the difficulty in quantifying absolute velocity and incapability of detecting slow particle flow due to the underlying principles. Employing external microparticles is a partial solution that makes it possible to derive absolute flow velocity according to the frame rate and spatial displacement of each single particle [13–15]. However, the external contrast agent also introduces corresponding limitations, including a lower maximum measurable velocity restricted by the frame rate, and the trade-off between enhancement of velocity-measuring accuracy and improvement of signal-to-noise ratio [16].

The focused-spot-based mapping method can address these challenges. In detail, this method detects the fluctuation of signal intensity or phase transient induced by particles flowing through a focused excitation spot, calculates the flow velocity according to the transiting time and spot size, and employs a point-to-point scanning mechanism to cover the entire FOV. As a result, the focused-spot-based mapping method owns advantages of absolute velocity quantification, unlimited measuring range, and capillary-scale resolution, which are significantly important for studying inconspicuous dynamic velocity inside small vessels [7,8]. In addition, it could be widely applied in various optical microscopic modalities, including multi-photon fluorescence imaging [17], optical coherence tomographic angiography (OCTA) [18], and photoacoustic microscopy [19]. However, the excellent performance and adaptability sacrifice the temporal resolution due to the long residence time of the laser spot on each excitation point and the vast number of detection points over the FOV [20]. For cortex-wide detection, normally it will take hours to go through the entire FOV with the full spatial sampling strategy. In addition to the low temporal resolution, the non-ignorable size of red blood cells (RBCs) that is comparable to the excitation laser spot will significantly affect the quantitative accuracy in the focused-spot-based mapping method. Unfortunately, to the best of our knowledge, most existing studies consider the RBC as a particle whose size is largely smaller than that of the laser spot, leading to the inaccurate measurement of blood flow velocity.

Therefore, we propose a particle-size-related calibration method and a random-access strategy for accurate measurement and high-speed mapping of cerebral blood flow velocity, respectively. We first summarize the principle of correlation spectroscopy to measure flow velocity and show the necessity of particle-size-related calibration using simulations and in vitro experiments. Then, we introduce the detailed process of the random-access strategy, which includes image pre-acquisition, deep-learning-based vessel segmentation, feature extraction, and scanning modulation. Finally, we employ photoacoustic microscopy as a testing imaging technology [21,22] and apply this method to three in vivo studies with different requirements of temporal resolution in measuring cerebral blood flow velocity. The experimental results reveal that the random-access-based acquisition is a promising strategy to speed up the absolute flow velocity detection for the focused-spot-based mapping method.

2. Principle and calibration of the velocity measurement

The use of correlation spectroscopy to measure flow velocity was first reported in fluorescence microscopy [23,24] and has been widely applied in different laser scanning imaging techniques [18,19]. During the experiments, recording signals in a given position for a certain time could offer a time-resolved amplitude curve $A(t )$. The average period of $A(t )$ extracted using autocorrelation represents the average time of particles flowing through the laser spot. The normalized autocorrelation function $G(\tau )$ can be derived using $A(t )$ as:

(1)$${G(\tau )= \frac{{\langle\delta A(t )\delta A({t + \tau } )\rangle}}{{\langle A{{(t )}\rangle^2}}}}$$

where $\left\langle {} \right\rangle$ is an operation that calculates average value, and $\delta A(t )= A(t )- \langle A(t )\rangle$.

As the laser spot commonly owns a Gaussian distribution, the directional flow of particles generates a Gaussian-shaped fluctuation of the amplitude. Therefore, the normalized autocorrelation function $G(\tau )$ also meets the Gaussian distribution as:

(2)$${G(\tau )\sim \exp - {{\left( {\frac{\tau }{{{\tau_f}}}} \right)}^2}}$$

where $2{\tau _f}$ is the average transiting time of the particle flowing through the entire laser spot. Then, using Eq. (2) to fit the $G(\tau )$ can obtain ${\tau _f}$, and the flow velocity can be calculated using Eq. (3):

(3)$${v = \frac{\omega }{{{\tau _f}}}}$$

where $\omega $ is the flow distance of the particle during ${\tau _f}$, and is commonly considered as the waist radius ${\omega _0}$ of the laser spot [25,26].

Based on this principle, it is obvious that the particle size was not taken into account during the process, leading to an inaccurate measurement of flow velocity. In detail, the amplitude fluctuation results from the convolution of the absorption distribution of the particle and the power distribution of the laser spot, meanwhile the convolution stride relates to the flow velocity. As a result, particles with different sizes flowing through a Gaussian spot at the same velocity will produce amplitude fluctuations with varying widths, leading to different measured flow velocities. In the fluorescence correlation spectroscopy, such a phenomenon does not affect the result since the sizes of fluorescent particles are commonly one or two orders of magnitude smaller than that of the laser spot. However, for imaging techniques using inherent absorbers such as RBCs, the average diameter in rodents is nearly 6 µm, which is comparable to, or even larger than that of the laser spot. Hence, direct employment of the formulas in the fluorescence correlation spectroscopy will lead to a lower estimated value than the real value, as the exact distance of a larger particle flowing within the transiting time ${\tau _f}$ is longer than the waist radius ${\omega _0}$ of the laser spot.

We carried out a numerical simulation to explain how the particle size influences the velocity measurement. The laser beam was focused using a 4× objective with a numerical aperture (NA) of 0.1, and a waist diameter of 3.4 µm. The spherical particles were distributed randomly in space with a concentration of 16000/mL and flowed through the laser spot with a preset flow velocity of 1 mm/s. We varied the particle diameters from 0.1 µm to 10 µm with a step of 0.1 µm (Fig. 1(a)) and plotted the measured flow velocity versus the fraction ratio between particle size and waist diameter, as shown in Fig. 1(b). The light blue curves are the measured results from 10 randomly distributed cases without calibrating the distance $\omega $, whereas the deep blue curve is the corresponding average data. The decreasing tendency indicates that the measured flow velocity gradually deviates from the preset value as the particle size increases. Such a phenomenon is caused by the misjudgment of the flow distance $\omega $. The actual flow distance during ${\tau _f}$ is longer than the waist radius ${\omega _0}$ of the laser spot and increases as the particle size gradually dominates the width of the normalized autocorrelation function $G(\tau )$. In this study, we calculated the effective flow distance $\omega $ as the width at ${e^{ - 2}}$ maximum of the convolution between laser energy distribution and uniform absorption distribution of particles with certain sizes. In particular, supposing that the particle radius is 3 µm and the laser waist radius is 1.7 µm, the effective flow distance $\omega $ will be 3.45 µm. As a result, the red curve represents the calibrated flow velocity, which fluctuates around the preset velocity of 1 mm/s, as shown in Fig. 1(b).

Fig. 1. Primary test of measuring velocity using correlation spectroscopy. (a) The scheme of simulation for measuring flow velocity; (b) Simulation results of the measured flow velocity versus the fractional ratio between the particle size and waist diameter before and after performing the particle-size-related calibration; (c) The schematic diagram of a microchannel used for in vitro experiment of measuring blood flow velocity; (d) Experimental results of the measured flow velocity versus the preset flow velocity before and after the particle-size-related calibration; (e) In vivo results of measuring blood flow velocity in a mouse brain with single-pixel dwelling times of 0.2 s, 0.1 s, and 0.05 s, respectively. The scale bar in (e) is 0.4 mm.

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We then further performed in vitro experiments of measuring blood flow velocity in a microchannel to verify the phenomenon. A commercial desktop optical resolution photoacoustic microscopy (ORPAM) was used as a testing technique in this study (VIS-200, PAOMTEK Inc.). The system employs a laser with a wavelength of 532 nm, a maximum repetition of 600 kHz and a pulse duration of 5 ns to generate the photoacoustic signal. A 4× objective (RMS-4X, Olympus Inc.) was selected to meet the requirement of velocity measurement. The photoacoustic signal was detected by a 15-MHz cylindrical focused ultrasound transducer (V324-SU, Olympus IMS), amplified using a 69-dB amplifier and digitized through a high-speed data acquisition card (ATS-9350, Alazartech Inc.) with a maximum sampling rate of 500 MS/s. A functional generator (PCI-6731, National Instrument) controlled the experimental sequences.

The whole blood extracted from mice was first treated with anticoagulation and injected into a microchannel with both width and height of 100 µm, as shown in Fig. 1(c). A syringe pump was used to shift the flow velocity inside the microchannel from 1 mm/s to 7 mm/s. The laser spot was fixed at the center of the channel to generate photoacoustic signals. As shown in Fig. 1(d), where we plotted the measured flow velocity versus the preset flow velocity, the experimental results show that the calibrated measured velocity has a slope of 1.02 and a determination coefficient of 0.98, whereas the uncalibrated result has a slope of 0.59 and a determination coefficient of 0.98. Both the simulations and in vitro experiments show how the neglected particle size significantly affects the results of blood flow measurement, which could be a common issue in existing measuring techniques and cause misinterpretation of biological phenomena.

3. Random-access strategy for efficient velocity imaging

3.1 Details of flow velocity measurement

According to the principle, the maximum measurable flow velocity is related to the diameter of the laser spot and the sampling rate. For example, supposing that the diameter of the laser spot is 5 µm and there needs at least 5 points to accurately reproduce the amplitude fluctuation induced by a flowing particle, a 20-kHz sampling rate will have a maximum measurable flow velocity of 20 mm/s. Employing a high sampling rate and an objective with a lower NA will effectively increase the maximum measurable flow velocity. In addition, the minimum measurable flow velocity is related to the diameter of the laser spot and the dwelling time on each pixel. For example, supposing that the diameter of the laser spot is 5 µm and the velocity can be accurately measured by recording the entire course of a particle flowing through the laser spot, a 50-ms dwelling time will have a minimum measurable flow velocity of 0.1 mm/s. Therefore, increasing the dwelling time will effectively extend the minimum measurable flow velocity. Furthermore, increasing the NA value of objectives will also extend the minimum measurable flow velocity due to the reason that the size of RBC will dominate the decorrelation curve $G(\tau )$. Taking the FOV into consideration, a 4× objective with an NA value of 0.1 is appropriate for the study of cortex-wide blood flow.

In summary, increasing the sampling rate and dwelling time are practical solutions to extend the measuring limits of velocity with a given objective. In order to determine the appropriate parameters, we carried out imaging experiments of a mouse cortex. The sampling rate, which refers explicitly to the laser repetition rate in photoacoustic microscopy, was set to be 20 kHz to avoid potential laser damage to the brain tissues and cover the range of blood flow velocity in most cortical vessels. Additionally, we imaged blood flow velocity in a small FOV of 2.4 × 2.4 mm² using different dwelling times of 0.2 s, 0.1 s, and 0.05 s, respectively. A thresholding method was performed to screen pixels with a determination coefficient higher than 0.3. The results shown in Fig. 1(e) indicate that a 0.2-s dwelling time can acquire most blood vessels in the cortex, whereas the vessels are discontinuous by using a dwelling time of 0.05 s. Considering the total acquisition time, the dwelling time of 0.1 s on each point is chosen for the specific ORPAM system used in this study. As a result, it will take hours to traverse the vast number of points within the cortex-wide FOV.

3.2 Concept of the random-access strategy

To improve the temporal resolution, we propose an optimized strategy based on random-access scanning. The strategy mainly contains four steps: pre-acquisition of the cortical vasculature, vessel segmentation, feature extraction, and scanning modulation. All these processes were realized using MATLAB.

1) Pre-acquisition of the cortical vasculature: The first step is to capture an image of the entire cortical vasculature, which serves as a mask for the following selection of points for velocity mapping. The pre-acquisition process was based on the rotatory imaging mechanism [27], and the galvanometer was steered using a triangular wave depending on the mapping relationship between the pixel coordinate and driving voltages. The acquired image went through Gaussian filtering to smooth the vascular boundary and eliminate noise. A typical photoacoustic maximum amplitude projection (MAP) image of the cortical vasculature is shown in Fig. 2(a).
2) Vessel segmentation: The second step is to segment the vessel area and calculate the corresponding coordinates of the segmented pixels. From the MAP image, the signal-to-noise ratio (SNR) of the artery and vein is much higher than that of arteriole, venule, and capillary, which causes the non-uniform distribution of SNR over the FOV. Such a phenomenon leads to the fact that conventional thresholding methods such as global thresholding and local thresholding [28] are not sensitive enough to segment different sized vessels. Hence, we employed a U-net-based deep-learning framework optimized from a reported U-net model [29] to effectively extract vessel regions from original photoacoustic images as shown in Fig. 2(b). The encoder network repeatedly applies two 3 × 3 convolutions, followed by a rectified linear unit (LeakyReLU) and a 2 × 2 max pooling operation with a stride of 2 for downsampling. The number of feature channels is doubled synchronously at each downsampling step. Each step in the decoder network consists of an upsampling step followed by a 2 × 2 convolution that halves the number of feature channels, a concatenation with the correspondingly cropped feature map from the contracting path, and two 3 × 3 convolutions, each followed by a LeakyReLU. We also applied the Adam algorithm [30] to optimize the network and the learning rate was 0.0002. As the training data requires tedious manual labeling, we performed data augmentation through rotation, displacement, and splicing, and effectively enhanced the invariance and robustness properties of the trained network. The training datasets comprised 100 sets of original and labeled images that correspond to each other. The loss function was defined by the binary cross entropy between the labeled image and the output of the model. The model was trained for 200 epochs. The U-net model in this study is implemented using Python v3.7. The workstation included an Intel Core i7-7700 K CPU 3.60 GHz, 32 GB system RAM, and an NVIDIA GPU (GeForce GTX 1080Ti).

Fig. 2. Flow chart of the random-access strategy for fast blood flow measurement. (a) A typical image of cerebral vasculature acquired using photoacoustic microscopy; (b) Architectures of the U-net-based deep-learning framework; (c) Quantitative evaluation of three vessel segmentation methods. GT, global thresholding, LT, local thresholding, DL, deep learning; (d) The result of vessel segmentation using deep learning method; (e) Enlarged windows that show detailed information including vessel regions, skeletons, and midpoints. Two windows show the areas marked by dashed boxes in (d); (f) A schematic diagram of the final random-access modality. Figures (a, b) share the same scale bar of 1 mm, and the size of the enlarged windows in (e) is 2.1 × 2.1 mm². Figures (a, d-f) with the black background show the complete process of random-access modality for blood flow detection.

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In addition, we derived three accepted parameters, which were mean square error (MSE), SNR [28], and F-score [31], to compare the performance of the proposed deep-learning method (DL) with conventional global thresholding (GT) and local thresholding (LT) methods. The manually segmented vascular image was considered the ground truth, and was further added white noise and multiplicative noise to serve as the original image processed by these three methods. The parameters were defined as follows:

(4)$${MSE = \mathop \sum \limits_{i,j} \frac{{{{({truth({i,j} )- output({i,j} )} )}^2}}}{{pixel\; number}}}$$

(5)$${SNR = \; \frac{{\mathop \sum \nolimits_{i,j} truth({i,j} )}}{{\mathop \sum \nolimits_{i,j} {{({truth({i,j} )- output({i,j} )} )}^2}}}}$$

(6)$${F - score = \frac{{2 \times precision \times recall}}{{precision + recall}}}$$

where FP, TP, FN indicate pixel numbers of false positive, true positive and false negative, respectively, recall = TP/(TP + FN), and precision = TP/(TP + FP). For accurate segmentation, the MSE value should be lower, in contrary the values of SNR and F-score should be higher.

We evaluated the performance of the proposed method in vascular segmentation using normal (n = 4) and glioma-bearing (n = 4) mice and compared the results with that of GT and LT. As shown in Fig. 2(c), the light red and blue curves represent the estimated values of individual normal and diseased mice, respectively. The deep red and blue curves are the corresponding averaged values. The quantitative result shows that the GT, LT, and DL methods have averaged MSEs of 0.057, 0.053, 0.034 in normal group and 0.060, 0.056, 0.047 in diseased group; mean SNRs of 7.86, 8.14, 10.06 in normal group and 7.75, 8.03, 8.95 in diseased group; averaged F-scores of 0.919, 0.923, 0.948 in normal group and 0.917, 0.919, 0.930 in diseased group. Apparently, the DL method revealed the best performance in both normal and diseased groups. Figure 2(d) shows the binarized image extracted from the original image using the DL method, where the small vessels with weak amplitudes were successfully segmented with intact sizes and shapes.

3) Feature extraction and scanning modulation: The third step is to extract vascular features, including vessel region, skeleton, and midpoints from the binarized image. The skeleton algorithm adopted from a previous study [32] involves the boundary evolution and thresholding to produce a skeleton based on a given vessel size. Then, we convoluted the binarized skeleton with a 3 × 3 array and a convolution stride of 1. In the resulting array, pixels with values of 2 represent the endpoints, and pixels with values larger than 3 stand for the branch points. In addition, we divided the vessel skeleton into detached line segments by subtracting the branch points, and further obtained the midpoints by gradually removing the endpoints of each segment. Figure 2(e) shows two enlarged windows marked in Fig. 2(d) and illustrates the detailed features of the vessel region, skeleton, and midpoint.

As all the characteristic pixels are parameterized with coordinates, we can steer the galvanometer to scan the laser spot only on the chosen pixels and skip the pixels without flow information or unnecessary for the study. In order to avoid the damage of the galvanometer due to high-frequent jumping scan, the sampling sequence of pixels must follow specific rules with a descending priority: a) Manually choose the first sampling pixel; b) Choose the unsampled pixel within the current scanning vessel as the next sampling pixel; c) Select the unsampled pixel closest in distance to the current pixel as the next sampling pixel; d) Prioritize selecting the unsampled pixel in the vertical direction as the next sampling pixel; e) Select the unsampled vessel with the minimum averaged distance from the current pixel as the next sampling vessel. Additionally, select the pixel closest to the endpoint of the vessel skeleton at the border, and return to step b).

The proposed rules allow the converged laser spot to scan along curved vessels and switch to another vessel after completing the current one, as shown in Fig. 2(f), and more than 95% of galvanometer scans are small-angle tilting. Based on this sampling sequence, we demonstrated three scanning modalities with different total sampling pixels: vessel region scanning, vessel skeleton scanning, and vessel midpoint scanning, which can satisfy different requirements of temporal resolution in different studies. Specifically, the vessel region scanning is suitable for reducing the single acquisition time in long-term studies, while the vessel skeleton scanning and vessel midpoint scanning focus on monitoring the dynamic and instantaneous changes of flow velocity.

4. In vivo cortical vascular studies

To reveal the advantages of the random-access strategy, we studied the progressive interruption of cerebral blood flow due to glioma growth, the general increase and decrease of cerebral blood flow induced by regulation of anesthetic depth, and the correlation of rapid fluctuation in blood flow velocity during seizure onset.

We used female C57BL/6J mice for all animal experiments. The average age of the mice was 7∼8 weeks at the time of experiments. A cranial window was made to reduce the optical and acoustical attenuation. All the mice were sacrificed using the standard protocol after experiments. All the procedures were conducted with approval from the Southern University of Science and Technology.

4.1 Long-term study

The development of glioma will disable brain activation, blood-brain barrier, and neurovascular coupling [33–35]. To investigate the vascular hemodynamics during the progress of glioma, we employed the vessel region scanning to visualize microvasculature and map corresponding flow velocities. The imaging experiments started on the 4^th day post injection of 3 × 10⁵ C6 cells in 10 µL of phosphate-buffered saline (PBS). According to the protocol, we first acquired an image of the cortical vasculature, which not only served as the raw data for vessel segmentation but also depicted the concentration of total hemoglobin (HbT) as the intensity of the photoacoustic signal is proportional to the chromophore concentration. We then measured the blood flow velocities within the vessel regions, and set the pixels with coefficients of determination lower than 0.3 to 0 in the final velocity map.

Figure 3(a) shows a typical image of the cerebral vasculature on the 4^th day post the injection of tumor cells, where there is a blurry area at the upper right corner marked with an orange arrow. The corresponding velocity map in Fig. 3(d) indicates that the blood flow in this area has slowed down. Such a phenomenon could be attributed to the bleeding and mild inflammation caused by the syringe needle since we also observed the same phenomenon in the control group as shown in Figs. 3(g) and (j). As indicated by the red circles in Figs. 3(b) and (e), although the blood vessels are clearly visible in the HbT image, the velocity map reveals that the blood flow within the glioma area is too slow to be detected on the 8^th day. This result suggests that the occurrence of blood flow abnormality might precede the morphological changes in blood vessels during the early stage of glioma, which is consistent with the fact that gliomas are one of the most angiogenic and most intensely vascularized tumors, and will cause damage to cell function and further promote hypoxia and dysfunction of blood perfusion [36,37]. As the glioma grows, the region with glioma-induced decreased velocity further expands along with the disappearance of blood vessels, as shown in Figs. 3(c) and (f). In contrast, in the control group, the decreased blood flow recovered on the 8^th day (Figs. 3(h, k)) and remained stable until the 12^th day (Figs. 3(i, l)).

Fig. 3. The study of long-term hemodynamic changes during the progress of glioma using the vessel region scanning modality. (a-c) Structural changes of cortical vasculature in a glioma-bearing mouse; (d-f) Changes of blood flow velocity in a glioma-bearing mouse; (g-i) Structural changes of cortical vasculature in a control mouse; (j-l) Changes of blood flow velocity in a control mouse. Orange arrows indicate positions that were injected C6 cells or PBS. Red dashed circles indicate a growing glioma area. All images share the same scale bar of 1 mm.

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It should be noted that the improvement of temporal resolution based on the vessel region scanning depends on the vascular density as well as the lateral resolution of the system. For the 4-µm lateral resolution, the vessel region scanning can halve the total sampling time for cortex-wide vascular imaging, resulting in a duration of 45 minutes.

4.2 Short-term studies

In contrast to the vessel region scanning that is more suitable for the long-term study, vessel skeleton scanning and vessel midpoints scanning are preferable to brain activities with short-term fluctuation of blood flow velocity.

We acquired an original image of cortical vasculature (Fig. 4(a)), extracted and parameterized the vessel skeleton (Fig. 4(b)), and continuously measured the fluctuation of blood flow velocity across the cortex. Similarly, the acquiring time of one velocity map was also related to the vascular density. For the mouse cortical vasculature imaged by current ORPAM system, it needs 6 min to cover all the pixels of the skeleton. We modulated the anesthetic depth of the mouse by changing the isoflurane concentrations with a sequence of 0 vol%, 1.5 vol%, 3 vol%, and 0 vol%. As shown in Fig. 4(c), when we increased the isoflurane concentration from 0 vol% to 1.5 vol%, there was a significant increase of flow velocity in vessels marked by red arrows, as well as an overall increase of blood flow velocity within the FOV. This increase in cerebral blood flow was caused by the impact of isoflurane that reduced the vascular resistance in the brain and redistributed the systemic blood. Hence, the cerebral flow velocity under the mild anesthetic state was higher than that under the awake state, although the cardiac outflow decreased due to the reduced heart rate under the anesthetic state [38,39]. Then, we adjusted the isoflurane concentration to 3 vol%, which induced a deep anesthetic state in the mouse and further reduced its heart rate. As a result, the flow velocity returned to the baseline. Subsequently, we turned the isoflurane concentration back to 0 vol%. The flow velocity kept below the baseline even when the mouse recovered to awake. We repeated this experiment using 6 mice and carried out the statistical analysis of total hemoglobin and flow velocity, as shown in Fig. 4(d). The plot represents an approximate tendency that has a significant increase under the mild anesthetic state, followed by a decreased velocity under the deep anesthetic and awake states. Quantitatively, the median fractional changes of HbT and velocity are +11.9% and +25.1% under the mild anesthetic state, + 1.4% and -1.1% under the deep anesthetic state, and -4.0% and -21.7% when recovering to the awake state, respectively.

Fig. 4. The studies of rapid fluctuations of blood flow velocity over the entire cortex using vessel skeleton scanning and vessel midpoint scanning modalities. (a) An original image of a typical cortical vasculature; (b) The skeleton image corresponds to (a); (c) Dynamic changes in cortical blood flow velocity under varying anesthetic states. The red arrows indicate the vessels with significant changes of flow velocity; (d) Statistical results of fluctuations of HbT and blood velocity induced by anesthesia; (e) Seed-based correlation map of a typical seizure case; (f) Velocity fluctuations of typical nodes in the seizure case; (g) Seed-based correlation map of a control case; (h) Velocity fluctuations of specific nodes in a control case. The red arrow indicates the seed pixel, and the white arrows indicate the typical nodes. (a-c) share the same scale bar of 1 mm, and (e, g) share the same scale bar of 1 mm.

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In addition, for the vessel midpoint scanning, we steered the laser spot to pause only at midpoints of the skeleton to capture blood flow velocity. As the number of vascular midpoints in a 5 × 5-mm² area is 400, the total sampling time is 20 s, making it accessible to study faster dynamics of flow velocity during the seizure onset. In detail, for each experiment, we used vessel midpoint scanning modality to record cerebral blood flow velocity for 50 minutes. We intraperitoneally injected 4-aminopyridine (4AP) and PBS at the 10^th minute to mice in the seizure group and control group, respectively. We applied the seed-based correlation method to analyze the relationship between blood flow velocity fluctuations in different vessels. This method calculates the Pearson correlation between the selected seed pixel and all other pixels. As shown in Fig. 4(e), in the seizure case, the velocity fluctuation of the seed pixel (marked by the red arrow) correlates strongly with that of the pixels at the sagittal sinus and the branched vessels (marked by white arrows). This phenomenon indicates that these vessels have the synchronized response of blood flow to the epileptic activities. In contrast, as shown in Fig. 4(g), the correlation of velocity fluctuation is much weaker in the control group. Only adjacent pixels show strong correlations to the seed pixel, and the correlation decays rapidly as the spatial distance gradually increases. We also compared the velocity fluctuation curves of the seed pixels and typical nodes in seizure and control cases, respectively. As shown in Fig. 4(f), the fractional fluctuation of the blood flow velocity is below 10% before the injection of 4AP, and gradually increases up to over 40% in various vessels after the induction of seizure onset. In contrast, the control case exhibits smoother fluctuations characterized by low-frequency increases and decreases, likely attributable to shifts in physiological states and brain activation induced by the injection (Fig. 4(h)).

5. Discussion and conclusion

In this study, we demonstrated a particle-size-related calibration method for measuring velocity with a higher accuracy. In essence, this calibration is an extension of the formula commonly used in fluorescence correlation spectroscopy, in which the tracers such as fluorescent dyes or fluorescent polymer spheres have much smaller sizes compared to the focused laser spot [23,24]. As the particle size gets larger, the measured velocity will gradually deviate from the true value, as shown in Fig. 1(b). Actually, such inaccuracy was mentioned in the previous studies [19,25,26], and the conventional solution was to use a calibration coefficient to correct the measured velocity based on preliminary experiments. In this study, we figured out how this inaccuracy exists in multiple optical microscopies, identified the dominant factor as the particle size, and carried out a particle-size-related calibration to improve the measuring accuracy. This calibration method is beneficial for optical velocimetry to quantify cerebral blood flow velocity more precisely, and study the physiological mechanisms. For example, decreased blood flow velocity has been reported as an early pathological mechanism in Alzheimer's disease (AD) [8,40]. Thus, the absolute quantification and accurate mapping of blood flow velocity are of great importance to explore the progressive mechanism of AD. However, there are still other factors that affect the accuracy of the measured velocity. Specifically, particles flowing through the divergence region instead of the focused area of the laser could result in a measured velocity with a decreased value. On the contrary, particles flowing through the peripheral position of the laser instead of the central position could result in an increase in the measured velocity. These influencing factors are completely random and only related to the relative position of the particle and the laser focus. To avoid the potential side impact, it is required to sample each pixel for a long period as shown in Fig. 1(e). As a result, due to the vast number of pixels and the required dwelling time on each pixel, the total acquisition time will be significantly extended, which makes it hard to study the fast events in blood flow.

Therefore, in addition to accuracy, we need to improve the temporal resolution of mapping cortical blood flow velocity. Several approaches have been proposed to overcome this limitation by suppressing the necessary sampling time based on sparse sampling [41] and the utilization of high-performance devices [42]. Apart from previous studies, we proposed the random-access strategy to programmatically reduce the number of sampling pixels. To map the cortex-wide blood flow velocity, we used a 4-fold objective and determined a dwelling time of 0.1 s, which reduced the total sampling times to 40 min, 6 min, and 30 s for the vessel region scanning, the vessel skeleton scanning, and the vessel midpoint scanning, respectively. We can further reduce the sampling time in other studies by employing an objective with a higher NA value and selecting sampling pixels more flexibly. For example, besides the proposed scanning methods in this study, we can track a loop of artery, arteriole, capillary, venule, and vein to study the specific process in the microcirculation, and view a vessel and its associate branches to study the blood redistribution induced by neural activities or stimuluses. Moreover, the random-access strategy is essentially an optimization of the scanning mechanism and rarely relies on the hardware. Besides ORPAM, other microscopic imaging techniques such as multi-photon microscopy and OCT can directly use this strategy to improve the temporal resolution. Meanwhile, based on the imaging contrasts, different techniques also produce unique functional parameters such as distinctive layer, oxygen saturation, and metabolic activities [22,43,44].

In this study, we employed photoacoustic microscopy as a representative technology to reveal the advantages of the proposed methods. The photoacoustic microscopy is a powerful technique that can provide multiple hemodynamic information simultaneously [22,45–47], which is advantageous for studying brain functions. Therefore, we will present our future plan to improve this technique. The first goal is to take advantage of a high laser frequency. According to the principle of focused-spot-based mapping method, the increase of laser repetition rate only extends the upper limit of the velocity measurement without improving the temporal resolution, leading to the insufficient use of the laser pulses. Currently limitation lies on the maximum scanning rate of the optical scanner, which cannot scan several pixels and return to the first pixel before one single RBC flows through the laser spot. We plan to solve this issue by using some powerful scanners like electrostatic micro-electro-mechanical system (MEMS) scanners [48] that provide an ultra-high scanning frequency in the resonant mode. Modulating the laser source in the frequency domain and detecting fluctuations in intensity and phase induced by red blood cell flow could serve as an alternative method to accelerate the mapping of cerebral blood flow velocity [49]. These methods will additionally enhance temporal resolution, enabling us to monitor rapid brain activity, including the periodic fluctuations in blood flow [50]. Another goal is to avoid potential laser-induced damage. The selection of 20-kHz laser repetition in this study is to balance the laser-induced tissue damage and the maximum measurable flow velocity. Therefore, in order to use a high repetition laser to reduce the sampling time, a more sensitive acoustic transducer [51,52] or a powerful image recovery method [53] is required.

In summary, we presented the particle-size-related calibration method and the random-access strategy that improve the accuracy and achieve a higher temporal resolution of flow velocity mapping, respectively. In the future, we plan to use the enhanced photoacoustic velocimeter to study more aspects of cerebral hemodynamics, such as monitoring blood redistribution within different levels of vessels during stimulation, identifying non-neural factors that influence blood flow, and so on. Moreover, applying the particle-size-related calibration method and the random-access strategy to various optical techniques is also a significant route, which correlates the cerebral blood flow and neural activity and provides more insights into the pathophysiology of different neurological disorders.

Funding

National Natural Science Foundation of China (61528401, 61775028, 62022037, 62105140, 81571722); Guangdong Science and Technology Department (2019ZT08Y191, 2022B1212010003); Shenzhen Science and Technology Program (JCYJ20200109141222892, JCYJ20220818101403008, KQTD20190929172743294, RCBS202110706092213005); Startup grant from Southern University of Science and Technology (PDJH2021C008).

Acknowledgment

We thank the members who took part in this study. L. Xi conceived this concept and supervised the overall project design and execution; T. Jin and B. Li designed and performed the experiments; L. Li developed the neural network framework; T. Jin processed the data; T. Jin, W. Qi, L. Xi drafted the paper; All authors provided critical feedback to the paper.

Disclosures

The authors declare no conflicts of interest.

Data availability

The main data supporting the results in this study are available within the paper. The raw datasets are too large to be publicly shared, yet they are available for research purposes upon reasonable request.

References

1. T. Wälchli, J. Bisschop, P. Carmeliet, et al., “Shaping the brain vasculature in development and disease in the single-cell era,” Nat. Rev. Neurosci. 24(5), 271–298 (2023). [CrossRef]

2. J. M. Tarasoff-Conway, R. O. Carare, R. S. Osorio, et al., “Clearance systems in the brain—implications for Alzheimer disease,” Nat. Rev. Neurol. 11(8), 457–470 (2015). [CrossRef]

3. S. Quick, J. Moss, R. M. Rajani, et al., “A vessel for change: endothelial dysfunction in cerebral small vessel disease,” Trends Neurosci. 44(4), 289–305 (2021). [CrossRef]

4. R. B. Buxton, K. Uludağ, D. J. Dubowitz, et al., “Modeling the hemodynamic response to brain activation,” Neuroimage 23, S220–S233 (2004). [CrossRef]

5. M. K. Montgomery, S. H. Kim, A. Dovas, et al., “Glioma-induced alterations in neuronal activity and neurovascular coupling during disease progression,” Cell Rep. 31(2), 107500 (2020). [CrossRef]

6. B. Sabayan, S. Jansen, A. M. Oleksik, et al., “Cerebrovascular hemodynamics in Alzheimer's disease and vascular dementia: a meta-analysis of transcranial Doppler studies,” Ageing Res. Rev. 11(2), 271–277 (2012). [CrossRef]

7. G. A. Bateman, G. A. Bateman, C. R. Levi, et al., “Quantitative measurement of cerebral haemodynamics in early vascular dementia and Alzheimer’s disease,” J. Clin. Neurosci. 13(5), 563–568 (2006). [CrossRef]

8. C. Iadecola, “Neurovascular regulation in the normal brain and in Alzheimer's disease,” Nat. Rev. Neurosci. 5(5), 347–360 (2004). [CrossRef]

9. C. Bourquin, C. Bourquin, J. Porée, et al., “In vivo pulsatility measurement of cerebral microcirculation in rodents using dynamic ultrasound localization microscopy,” IEEE Trans. Med. Imaging 41(4), 782–792 (2022). [CrossRef]

10. E. Macé, E. Macé, G. Montaldo, et al., “Functional ultrasound imaging of the brain,” Nat. Methods 8(8), 662–664 (2011). [CrossRef]

11. C. Rabut, M. Correia, V. Finel, et al., “4D functional ultrasound imaging of whole-brain activity in rodents,” Nat. Methods 16(10), 994–997 (2019). [CrossRef]

12. A. Mangraviti, F. Volpin, J. Cha, et al., “Intraoperative laser speckle contrast imaging for real-time visualization of cerebral blood flow in cerebrovascular surgery: results from pre-clinical studies,” Sci. Rep. 10(1), 7614 (2020). [CrossRef]

13. K. Ohmi and H. Y Li, “Particle-tracking velocimetry with new algorithms,” Meas. Sci. Technol. 11(6), 603–616 (2000). [CrossRef]

14. Q. Zhou, Z. Chen, Y.-H. Liu, et al., “Three-dimensional wide-field fluorescence microscopy for transcranial mapping of cortical microcirculation,” Nat. Commun. 13(1), 7969 (2022). [CrossRef]

15. Z. Zhang, Z. Zhang, M. Hwang, et al., “Cerebral microcirculation mapped by echo particle tracking velocimetry quantifies the intracranial pressure and detects ischemia,” Nat. Commun. 13(1), 666 (2022). [CrossRef]

16. C. Cierpka, B. Lütke, and C. J. Kähler, “Higher order multi-frame particle tracking velocimetry,” Exp. Fluids 54(5), 1533 (2013). [CrossRef]

17. X. Fu, P. Sompol, J. A. Brandon, et al., “In vivo single-molecule detection of nanoparticles for multiphoton fluorescence correlation spectroscopy to quantify cerebral blood flow,” Nano Lett. 20(8), 6135–6141 (2020). [CrossRef]

18. J. Tang, J. Tang, S. E. Erdener, et al., “Capillary red blood cell velocimetry by phase-resolved optical coherence tomography,” Opt. Lett. 42(19), 3976–3979 (2017). [CrossRef]

19. B. Ning, M. J. Kennedy, A. J. Dixon, et al., “Simultaneous photoacoustic microscopy of microvascular anatomy, oxygen saturation, and blood flow,” Opt. Lett. 40(6), 910–913 (2015). [CrossRef]

20. T. J. Arbour and J. Enderlein, “Application of dual-focus fluorescence correlation spectroscopy to microfluidic flow-velocity measurement,” Lab Chip 10(10), 1286–1292 (2010). [CrossRef]

21. T. Jin, T. Jin, H. Guo, et al., “Portable optical resolution photoacoustic microscopy (pORPAM) for human oral imaging,” Opt. Lett. 42(21), 4434–4437 (2017). [CrossRef]

22. T. Jin, T. Jin, W. Qi, et al., “Photoacoustic imaging of brain functions: wide field-of-view functional imaging with high spatiotemporal resolution,” Laser Photonics Rev. 16(2), 2100304 (2022). [CrossRef]

23. R. H. Kohler, R. H. Kohler, P. Schwille, et al., “Active protein transport through plastid tubules: velocity quantified by fluorescence correlation spectroscopy,” J. Cell Sci. 113(22), 3921–3930 (2000). [CrossRef]

24. S. T. Hess, S. T. Hess, S. Huang, et al., “Biological and chemical applications of fluorescence correlation spectroscopy: a review,” Biochemistry 41(3), 697–705 (2002). [CrossRef]

25. S. L. Chen, S. L. Chen, Z. Xie, et al., “In vivo flow speed measurement of capillaries by photoacoustic correlation spectroscopy,” Opt. Lett. 36(20), 4017–4019 (2011). [CrossRef]

26. S. L. Chen, S. L. Chen, T. Ling, et al., “Photoacoustic correlation spectroscopy and its application to low-speed flow measurement,” Opt. Lett. 35(8), 1200–1202 (2010). [CrossRef]

27. W. Qi, W. Qi, T. Jin, et al., “Inverted multiscale optical resolution photoacoustic microscopy,” J. Biophotonics 10(12), 1580–1585 (2017). [CrossRef]

28. P. Stathis, E. Kavallieratou, and N. Papamarkos, “An evaluation technique for binarization algorithms,” J. Univers. Comput. Sci. 14(18), 3011–3030 (2008).

29. O. Ronneberger, P. Fischer, and T. Brox, “U-net: Convolutional networks for biomedical image segmentation,” InMedical Image Computing and Computer-Assisted Intervention-MICCAI 2015: 18th International Conference, Munich, Germany, October 5-9, 2015, Proceedings, Part III 18, 234–241 (2015).

30. D. P. Kingma and J. Ba, “Adam: A method for stochastic optimization,” arXiv, arXiv:1412.6980 (2014). [CrossRef]

31. K. Ntirogiannis, B. Gatos, and I. Pratikakis, “Performance evaluation methodology for historical document image binarization,” IEEE Trans. on Image Process. 22(2), 595–609 (2013). [CrossRef]

32. A. Telea and J. J. Van Wijk, “An augmented fast marching method for computing skeletons and centerlines,” In EPRINTS-BOOK-TITLE (University of Groningen, Johann Bernoulli Institute for Mathematics and Computer Science, 2022).

33. C. M. McCann, C. M. McCann, P. Waterman, et al., “Combined magnetic resonance and fluorescence imaging of the living mouse brain reveals glioma response to chemotherapy,” Neuroimage 45(2), 360–369 (2009). [CrossRef]

34. C. Brighi, L. Reid, L. A. Genovesi, et al., “Comparative study of preclinical mouse models of high-grade glioma for nanomedicine research: the importance of reproducing blood-brain barrier heterogeneity,” Theranostics 10(14), 6361–6371 (2020). [CrossRef]

35. P. Vajkoczy and M. D. Menger, “Vascular microenvironment in gliomas,” J. Neuro-Oncol. 50(1/2), 99–108 (2000). [CrossRef]

36. B. K. Ahir, H. H. Engelhard, and S. S. Lakka, “Tumor development and angiogenesis in adult brain tumor: glioblastoma,” Mol. Neurobiol. 57(5), 2461–2478 (2020). [CrossRef]

37. N. H. Boyd, A. N. Tran, J. D. Bernstock, et al., “Glioma stem cells and their roles within the hypoxic tumor microenvironment,” Theranostics 11(2), 665–683 (2021). [CrossRef]

38. P. F. Conzen, P. F. Conzen, B. Vollmar, et al., “Systemic and regional hemodynamics of isoflurane and sevoflurane in rats,” Anesth. Analg. 74(1), 79–88 (1992). [CrossRef]

39. A. M. Slupe and J. R. Kirsch, “Effects of anesthesia on cerebral blood flow, metabolism, and neuroprotection,” J. Cereb. Blood Flow Metab. 38(12), 2192–2208 (2018). [CrossRef]

40. N. Korte, R. Nortley, and D. Attwell, “Cerebral blood flow decrease as an early pathological mechanism in Alzheimer's disease,” Acta Neuropathol. 140(6), 793–810 (2020). [CrossRef]

41. S. G. Sathyanarayana, S. G. Sathyanarayana, Z. Wang, et al., “Recovery of blood flow from undersampled photoacoustic microscopy data using sparse modeling,” IEEE Trans. Med. Imaging 41(1), 103–120 (2022). [CrossRef]

42. F. Zhong and S. Hu, “Thin-film optical-acoustic combiner enables high-speed wide-field multi-parametric photoacoustic microscopy in reflection mode,” Opt. Lett. 48(2), 195–198 (2023). [CrossRef]

43. J. Tang, J. Tang, X. Cheng, et al., “Imaging localized fast optical signals of neural activation with optical coherence tomography in awake mice,” Opt. Lett. 46(7), 1744–1747 (2021). [CrossRef]

44. C. Liu, Y. Liang, and L. Wang, “Single-shot photoacoustic microscopy of hemoglobin concentration, oxygen saturation, and blood flow in sub-microseconds,” Photoacoustics 17, 100156 (2020). [CrossRef]

45. J. Yao, L. Wang, J.-M. Yang, et al., “High-speed label-free functional photoacoustic microscopy of mouse brain in action,” Nat. Methods 12(5), 407–410 (2015). [CrossRef]

46. R. Cao, R. Cao, J. Li, et al., “Functional and oxygen-metabolic photoacoustic microscopy of the awake mouse brain,” Neuroimage 150, 77–87 (2017). [CrossRef]

47. C. Liu, C. Liu, J. Chen, et al., “Five-wavelength optical-resolution photoacoustic microscopy of blood and lymphatic vessels,” Adv. Photonics 3(1), 016002 (2021). [CrossRef]

48. L. Li, X. Liang, W. Qin, et al., “Double spiral resonant MEMS scanning for ultra-high-speed miniaturized optical microscopy,” Optica 10(9), 1195–1202 (2023). [CrossRef]

49. N. Chen, J. Yu, L. Liu, et al., “Video-rate high-resolution single-pixel nonscanning photoacoustic microscopy,” Biomed. Opt. Express 13(7), 3823–3835 (2022). [CrossRef]

50. G. Meng, J. Zhong, Q. Zhang, et al., “Ultrafast two-photon fluorescence imaging of cerebral blood circulation in the mouse brain in vivo,” Proc. Natl. Acad. Sci. U.S.A. 119(23), e2117346119 (2022). [CrossRef]

51. Y. H. Liu, Y. H. Liu, A. Kurnikov, et al., “Sensitive ultrawideband transparent PVDF-ITO ultrasound detector for optoacoustic microscopy,” Opt. Lett. 47(16), 4163–4166 (2022). [CrossRef]

52. R. Chen, “Transparent high-frequency ultrasonic transducer for photoacoustic microscopy application,” IEEE Trans. Ultrason., Ferroelect., Freq. Contr. 67(9), 1848–1853 (2020). [CrossRef]

53. R. Manwar, R. Manwar, X. Li, et al., “Deep learning protocol for improved photoacoustic brain imaging,” J. Biophotonics 13(10), e202000212 (2020). [CrossRef]

High spatiotemporal mapping of cortical blood flow velocity with an enhanced accuracy

Abstract

1. Introduction

2. Principle and calibration of the velocity measurement

3. Random-access strategy for efficient velocity imaging

3.1 Details of flow velocity measurement

3.2 Concept of the random-access strategy

4. In vivo cortical vascular studies

4.1 Long-term study

4.2 Short-term studies

5. Discussion and conclusion

Funding

Acknowledgment

Disclosures

Data availability

References

Data availability

Cited By

Figures (4)

Equations (6)

Biomedical Optics Express