Improved Color Doppler for Cerebral Blood Flow Axial Velocity Imaging

Abstract

Conventional color Doppler ultrasound imaging suffers from mutual frequency cancellation when applied to quantify axial blood flow velocities in the rodent brain where inverse flows exist within an ultrasound measurement voxel. Here, we report an improved color Doppler-based functional ultrasound imaging method (iCD-fUS) for axial blood flow velocity imaging of the rodent brain. By applying a directional filter and high frequency noise thresholding, iCD-fUS is able to accurately quantify blood flow velocities within the brain as validated with the ultrasound localization microscopy velocimetry method. We show that iCD-fUS is able to image and resolve the directional axial blood flow velocity throughout the entire coronal section of the brain at a temporal frame rate of up to 10 Hz with a spatial resolution of ~100 μm. We further applied iCD-fUS to image the axial blood flow velocity change in response to whisker stimulation in an awake mouse, showing its potential for studying brain activation. With these capabilities, iCD-fUS provides a powerful, quantitative tool for in vivo chronic research.

I. Introduction

VARIOUS ultrasound techniques have been applied for hemodynamic imaging of large vessels [1]–[3], but not until the emergence of the ultrafast ultrasound plane wave imaging technique has there been the potential for functional imaging of the micro-vasculature hemodynamics of the brain [4]. A major step toward realizing functional ultrasound imaging of the brain was the extension of the ultrafast coherent plane wave compounding approach [4], [5], which enables high frame rate compounded ultrasound imaging of a large field of view with enhanced contrast to noise ratio. By tracking the relative change of the measured signal during the same experiment session, Power Doppler-based functional ultrasound (PD-fUS) is of particular interest for studying cerebral hemodynamic change in response to functional stimulation [4]. Compared to PD-fUS, Color Doppler ultrasound imaging measures the absolute value of axial blood velocity based on the quantifiable Doppler frequency shifts, providing a tool for quantitative evaluation of blood flow speed over different experiment sessions [3], [9]. However, Color Doppler-based functional ultrasound (CD-fUS) [4] suffers from unstable frequency shifts estimation and significant underestimation of blood flow velocity when imaging the small vessels in rodent brain where descending and ascending flows commonly exist within an ultrasound measurement voxel. These opposite flows cause both positive and negative frequency shift in the signal frequency spectrum, which results in mutual frequency cancellation when estimating the Doppler frequency shift using the full spectrum, and consequently leads to underestimation of the axial blood flow velocity within the measurement voxel.

In this article, we introduce an improved color Doppler-based functional ultrasound imaging method (iCD-fUS) with the goal of providing quantitative maps of axial velocity flows in the brain microvasculature. A method [6] which provides a way of adding directionality to power Doppler to distinguish between axial flow directions, is accomplished by splitting the signal frequency power spectrum into positive and negative frequency signals, providing direction coded ascending and descending power Doppler images. However, a major difficulty in using directional filtering for color Doppler blood flow velocity calculations is that the residual high frequency noise for either positive or negative frequencies will result in overestimation of the ascending and descending Doppler frequency, respectively; consequently, color Doppler measurements of the directional filtered signal is significantly overestimated when applied to imaging the brain.

We introduce a method which solves the noise problem to more accurately image the axial blood flow velocity of the microvasculature in the rodent brain. We compare the iCD-fUS with conventional color Doppler when applied for brain imaging, and validate the axial velocity measurements obtained with iCD-fUS with the microbubble tracking-based ultrasound localization microscopy velocimetry method (vULM) [12]. We also test the acceptable maximum temporal frame rate that can be achieved with iCD-fUS for axial flow speed measurements in the rodent brain. Further, we demonstrate quantitative functional ultrasound by using iCD-fUS to monitor the blood flow axial velocity changes in response to whisker stimulation in an awake head restrained mouse.

II. Materials and Methods

A. Experimental Setup

Our experimental setup and data acquisition flow is shown from left to right in Fig. 1(a). The inset on the left of Fig. 1(a) is a top view of a cranial window used for in vivo study in this work. A linear translational stage was used to move the transducer probe (L22-14v, 18.5 MHz center frequency, Verasonics Inc. Kirkland, WA, USA) for imaging at different coronal planes (in the Y direction) and the transducer probe was immersed in a water container with water temperature maintained at 37 ± 0.5°C. Warmed ultrasound gel was used to fill the space between the transparent film at the bottom of the water container and the cranial window to provide acoustic transmission. The animal’s body temperature was maintained at 37°C with a homeothermic blanket control unit (Harvard Apparatus) and the head was fixed in a stereotaxic frame.

Fig. 1.

(a) Experimental setup. The ultrasound transducer array probe was carried by a linear translation stage for data acquisition at different coronal planes (the Y axis); water temperature was maintained at 37 ± 0.5° in the reservoir; acoustic data was acquired and transferred to host computer and saved for post data processing. (b) Five-angle (−6°, −3°, 0°, 3°, 6°) based coherent plane wave compounding data acquisition. (c) Singular value decomposition-based clutter rejection.

The transducer probe was connected to a commercial ultrafast ultrasound research and imaging system (Vantage 256, Verasonics Inc. Kirkland, WA, USA, middle pannel of Fig. 1a) which acquired raw radio frequency (RF) data at ultrafast rates and was transferred to the host computer (right pannel of Fig. 1a). At the right of Fig. 1(a) is a representative iCD-fUS axial blood flow velocity image with descending flows overlaped on ascending flows.

Fig. 1(b) shows the data acqusition and pre-data processing procedure. Ultrasound pulses were emitted at a center frequency of 18.5 MHz and consisted of 3 half-excitation cycle. Plane waves were acquired with a frame rate of 30 KHz and digitally tilted at 5 angles (−6°, −3°, 0°, 3°, 6°) which were then coherently compounded to form a single compounded image [7]. We fixed the time interval between the first emisson angle of compounded images to be 200 μs, thus the compounded image frame rate is 5 KHz. We used a linear stage to move the transducer probe in the Y direction for data acquisition at different coronal planes. In this work, we acquired a duration of 200 ms of data, i.e. 1000 compounded images, for each velocity map calculation.

B. Animal Preparation

The animal experiments were conducted following the Guide for the Care and Use of Laboratory Animals, and the experiment protocol was approved by the Institutional Animal Care and Use Committees of Boston University.

12-to-16-week old C57BL/6 mice (22-28g, either sex, Charles River Laboratories) were used in this study. Animals were housed under diurnal lighting conditions with free access to food and water. For the craniotomy preparation, mice were anesthetized with isoflurane (3% induction, 1–1.5% maintenance, in 1L/min oxygen) while the body temperature was maintained with a homeothermic blanket control unit (Kent Scientific). A custom-made PEEK head bar (inset of Fig. 1(a)) was attached to the skull using dental acrylic and bone screws. A cranial window was prepared by removing the skull between lambda and bregma extending to the temporal ridges as a strip (~ 2 × 10 mm²), as shown in the inset figure of Fig. 1(a). A PMP film was then secured to the skull edges using glue and dental acrylic. The animals were allowed to recover for 3 weeks before the imaging sessions. For awake imaging, animals were trained to be head fixed for at least two weeks before the imaging session using sweetened condensed milk as a treat [8].

C. Clutter Rejection

A spatiotemporal clutter rejection filter using singular value decomposition [9] was applied to remove bulk motion, as shown in Fig. 1(c). The first 20 highest singular value signal components were removed (N_C =21) and this threshold was chosen empirically.

$$\mathrm{sIQ}=\underset{i=N_c}{\overset{N}{\Sigma }}S(z,x){\lambda }_{i}V(t)$$ (1)

where, sIQ is the clutter-rejected ultrasound quadrature signal; Nc is the cutoff rank for SVD processing; S(z, x) is the spatial singular matrix; λ_i is the singular value corresponding to the i^th rank; and V(t) is the temporal singular vector.

D. Conventional Color Doppler (CD)

In conventional color Doppler data processing, the Doppler frequency shift is estimated by integrating the product of frequency and corresponding power over the full frequency range [3]. The axial velocity along the z axis based on the conventional Color Doppler calculation is obtained with,

$${\upsilon }_{cz}=-\frac{c}{2f_0}\frac{{\int }_{-f_s/2}^{f_s/2}f\cdot |\mathcal{F}(sIQ){|}^2)df}{{\int }_{-f_s/2}^{f_s/2}|\mathcal{F}(sIQ){|}^2)df}$$ (2)

where, c is the sound speed in the medium and c = 1540 m/s was used in this stud; f₀ is the transducer center frequency; f_s is the frame rat; and $\mathcal{F}$ denotes the Fourier transform.

E. Improved Color Doppler (iCD)

Fig. 2(a) shows an ultrasound measurement voxel where particles are moving in the same direction. In this case, the Doppler frequency shift (f_D) of the vertical component of flow can be accurately estimated with Eq. (2). However, f_D is largely underestimated using Eq. (2) when opposite flows exist within the measurement voxel, such as the micro-vasculature networks of the brain as shown in the high resolution ULM image in Fig. 2(b). Please refer to Supplementary for more information regarding the Doppler frequency underestimation caused by mutual frequency cancellation.

Fig. 2.

The problem of conventional CD-fUS for brain imaging and principle of iCD-fUS. (a) Doppler frequency shift (f_D) (right) calculated with the conventional color Doppler method for measurements on a phantom with blood flowing through a 580 diameter μm plastic tube (left). (b) Left panel: Ultrasound localization microscopy (ULM) image of the brain microvasculature indicates that opposite flows commonly exist within an ultrasound resolution voxel (white diffuse spot); right panel: the opposite flows cause mutual frequency cancellation resulting in underestimation of the Doppler frequency. (c) With proper noise thresholding for the directional filtered data, f_D can be accurately estimated for both negative frequency (flow away from transducer) and positive frequency (flow towards the transducer) signal; vertical black dashed lines indicate the Doppler frequency obtained without noise thresholding. (d) Representative descending (left) and ascending (right) axial velocity maps obtained with iCD-fUS from a single data set of a coronal plane.

From ULM images of the rodent brain (left panel of Fig 2(b)), we note that most vessels have an axial flow component along the z axis, which causes the signal frequency shift to be negative if it’s flowing away from the transducer and shift to positive if it’s flowing towards the transducer. Inverse flows within an ultrasound measurement voxel cause mutual frequency cancellation, resulting in underestimated Doppler frequency shift if using full spectrum for calculation, as shown in the right panel of Fig. 2(b). Thus, we used a directional filter to separate the negative frequency signal (descending flow vessels) from the positive frequency signal (ascending flow vessels), similar to the directional power Doppler data processing [6]. Unlike the power Doppler studies, we aim to quantify blood flow velocities.

However, the directional filtering causes overestimation of the Doppler frequency shift, as indicated by the vertical black dashed lines in Fig. 2(c). This is due to the non-negligible power of the high frequency noise compared to the signal power when the opposite frequency components were separately analyzed using the directional filtering. Without directional filtering, the positive and negative high frequency noise is balanced and canceled. But this cancellation does not happen after directional filtering.

To address the overestimation of the Doppler frequency (f_D) caused by high frequency noise, we used a power threshold to remove the high frequency noise from Doppler frequency (f_D) estimation, as shown in Fig. 2(c). According to the literature [10], [11] and the microbubble tracking-based ULM velocimetry, the blood flow velocity within the mouse brain is in the range of ~1 mm/s for capillaries to ~40 mm/s for large arteries and ~ 10-20 mm/s for the majority of middle sized vessels, i.e. the maximum frequency shift is ~986 Hz given the acoustic transducer’s center frequency of 18.5 MHz. To account for spectrum widening due to the transverse flow component, we used 1.5 times the maximum power in the frequency range of 2000-2500 Hz (Eq. 3) as the threshold level to remove the noise which corresponds to a speed cutoff of ~>80 mm/s, far beyond the blood flow speed in a rodent brain.

$$Threshold=1.5\cdot \max (|\mathcal{F}{(\mathrm{sIQ})}_{|f|>2\mathrm{kHz}}|)$$ (3)

where, $\mathcal{F}$ denotes the Fourier transform; sIQ is the temporal ultrasound quadrature signal after clutter rejection; and f is the frequency coordinate. In addition, with the SVD filtering our lowest detectable velocity is about 1.5 mm/s.

With this thresholding, the noise is removed as shown in Fig. 2(c) and the Doppler frequency shift is then calculated and transformed to descending and ascending axial velocities with Eq. 4 & 5.

$${\upsilon }_{z,descend}=-\frac{c}{2f_0}\frac{{\int }_{F_n}f\cdot |\mathcal{F}(sIQ){|}^2)df}{{\int }_{F_n}|\mathcal{F}(sIQ){|}^2)df}$$ (4)

$${\upsilon }_{z,ascend}=-\frac{c}{2f_0}\frac{{\int }_{F_p}f\cdot |\mathcal{F}(sIQ){|}^2)df}{{\int }_{F_p}|\mathcal{F}(sIQ){|}^2)df}$$ (5)

where, c is the sound speed in the medium and c = 1540 m/s was used in this study; f₀ is the transducer center frequency; F_n is the signal frequency range after thresholding for the negative frequency component (left panel of Fig. 2(c)); F_p is the signal frequency range after thresholding for the positive frequency component (right panel of Fig. 2(c)); and $\mathcal{F}$ denotes the Fourier transform.

Fig. 2(d) shows the axial velocity maps obtained with iCD-fUS where the left panel was obtained from the negative frequency components (descending flow) and the right panel was obtained from the positive frequency component (ascending flow).

F. Directional Power Doppler (PD)

The positive and negative frequency parts of the signal power spectrum were integrated separately to produce ascending and descending flow PD images.

The directional PD images (PD-fUS) were calculated as [6],

$$\begin{gathered} P{D}_{neg}={\int }_{-f_s/2}^0|\mathcal{F}(sIQ){|}^2)df \\ P{D}_{pos}={\int }_0^{f_s/2}|\mathcal{F}(sIQ){|}^2)df \end{gathered}$$ (6)

where, f_s is the frame rate; $\mathcal{F}$ denotes the Fourier transform; and sIQ is the complex ultrasound quadrature signal of the moving particles.

G. Ultrasound Localization Microscopy (ULM)

To validate the axial velocity measured with iCD-fUS, we acquired ULM datasets at the same coronal plane and reconstructed the axial flow velocity by tracking the axial movement of microbubbles in the blood vessel (vULM [12], [13]). The ultrasound localization microscopy (ULM) image and the ULM-based velocity maps (vULM) were obtained using a microbubble tracking and accumulation method described in [12], [13]. Briefly, the moving microbubbles were identified with frame-to-frame subtraction of the high frame rate (500 Hz) image data after beamforming. The obtained images were rescaled to have a pixel size of 10 μm × 10 μm. The centroid position for each microbubble was then identified and accumulated over time to form a high resolution image of the cerebral vasculature image (ULM). The in-plane flow velocity of the microbubble was obtained by tracking the flow of microbubbles. Comparison of measurement results with vULM are discussed in section III-A.

H. Whisker Stimulation

One mouse was trained and used for the whisker stimulation experiments. An air puff machine (Picospritzer III, Parker Inc.) was used to stimulate the whiskers. We performed two stimulation protocols to test the functional imaging ability of iCD-fUS with one following the reported fUS whisker stimulation protocol [4] that was consisted of 30 s of baseline followed by 10 trials of 15 s stimulation and a 45 s inter-stimulus interval; and the other one having a shorter stimulation duration consisted of 20 s of baseline followed by 10 trials of 5 s stimulation and a 25 s inter-stimulus interval. The stimulation frequency was 3 Hz.

The functional stimulation activation regions were identified by calculating the correlation coefficient between the velocity time trace of each voxel and the hemodynamic response function. The hemodynamic response function (HRF) was obtained by fitting the time trace in the activation region with the Gamma function,

$$HRF(t)=a{(t-t_0)}^2\cdot e^{-b{(t-t_0)}^c}\cdot s(t-t_0)$$ (7)

where, a, b, and c are fitting coefficients, t₀ is the stimulation start time, and s(t) is the step function. Then the correlation coefficient map was calculated for all voxels.

$$r(z,x)=\frac{\underset{t=1}{\overset{N}{\Sigma }}({\upsilon }_z(z,x,t)-{\upsilon }_z(\overline{z},x))(HRF(t)-H\overline{R}F)}{\sqrt{{\Sigma }_{t=1}^N{({\upsilon }_z(z,x,t)-{\upsilon }_z(\overline{z},x))}^2}\sqrt{{\Sigma }_{t=1}^N(HRF(t)-H\overline{R}F{)}^2}}$$ (8)

where,

$${\upsilon }_z(\overline{z},x)=\frac{1}{N}\sum _{t=1}^N{\upsilon }_z(z,x,t)\text{and}H\overline{R}F=\frac{1}{N}\sum _{t=1}^{N}HRF(t)$$

where, N is the total acquisition.

III. Results and Discussion

A. Comparison of Axial Velocity Measured With Conventional Color Doppler, Directional Filtering-Based Color Doppler, and the Proposed iCD-fUS

Fig. 3 compares the axial velocity measured with conventional color Doppler (CD-fUS), CD-fUS processing with the directional filtered data (npCD-fUS), and the proposed iCD-fUS and vULM. Opposite flows within a measurement voxel cause mutual frequency cancellation when using the standard CD-fUS calculation, resulting in underestimation of the Doppler frequency shift and thus incorrect estimation of axial velocities, as shown in Fig. 3(a). To show the high frequency noise issue after directional filtering, we calculated the axial velocity obtained without thresholding (npCD-fUS) as shown in Fig. 3(b). Note that the obtained axial velocity is overestimated which is due to the residual high frequency noise which is not canceled out when processing the directional filtered data separately.

Fig. 3.

(a) Axial velocity map of a mouse brain obtained by applying conventional color Doppler calculations. (b) Axial velocity map of a mouse brain obtained by applying conventional color Doppler calculations on directionally filtered data. (c) Axial velocity map obtained with the improved color Doppler method (iCD-fUS). (d) Axial velocity map obtained with vULM. (e) Histograms compare the axial velocity distribution measured with the aforementioned techniques. For (b), (c) and (d): descending flow velocity were overlapped on the ascending flow velocity.

Benefitting from high frame rate (5kHz), iCD-fUS is able to determine a power threshold in the high frequency range (|f| > 2kHz) which is far outside the frequency range of the speed of interest in the brain. With this threshold, the noise power is removed from the calculation for the Doppler frequency shift as shown in Fig. 2(c), resulting in an accurate estimation of the Doppler frequency shift arising from the flowing signal as shown in Fig. 3(c). Taking the axial velocity map measured with vULM at the same coronal plane as the comparison standard (Fig. 3(d)), the axial velocity measured with iCD-fUS is close to the vULM measurement, while the conventional CD-fUS measurement, Fig. 3(a), is significantly underestimated and the npCD-fUS measurement, Fig. 3(b), is overestimated due to high frequency noise. Fig. 3(e) further compares the histograms of the axial velocity distribution obtained with aforementioned techniques. Clearly, we see that the iCD-fUS measurement overlaps well with the vULM measurement, while CD-fUS is underestimating the distribution and npCD-fUS is overestimating the distribution. We also note that there are more low speed-voxels obtained with iCD-fUS compared to vULM. This is due to the fact that vULM measures speed within the blood vessel while iCD-fUS has a resolution (point spread function) larger than the blood vessel in the brain which results in ‘enlarged’ blood vessels obtained with iCD-fUS, i.e. there are more voxels identified as a ‘blood vessel voxel’ with iCD-fUS, as shown in Fig. 3(c) and (d).

B. Validation With vULM

To facilitate the comparison between iCD-fUS and high resolution vULM images, a spatial mask based on the ULM image was applied to the iCD-fUS axial velocity map, as shown in Fig. 4(a). The comparison qualitatively shows that the iCD-fUS and vULM measurements agree well with each other. We further compared the mean value of 50 vessels identified in the coronal plane (20 ascending vessels and 30 descending vessels) and observed that the iCD-fUS measurements agree well with the vULM measurements, as shown in Fig. 4(b1). The scatter plot also shows high correlation between iCD-fUS and vULM measurements, as shown in Fig. 4(b2).

Fig. 4.

(a) To facilitate the validation, the same ULM spatial mask obtained at the same coronal plane was applied to iCD-fUS (top) and vULM (bottom). (b1) Mean axial velocity value of 50 vessels (20 ascending vessels and 30 descending vessels) obtained with iCD-fUS (V_zCD) and vULM (V_zULM); (b2) scatter plot indicates that the iCD-fUS measurement is highly correlated with the vULM measurment. (c) A representative scatter plot of all pixel values of the vessel # 23 (inset).

Fig. 4(c) shows a representative scatter plot of all pixel values of a single vessel (#23), which indicates that the vULM measurement is more broadly distributed compared to the iCD-fUS measurement, represented by the red line. This difference is due to the fact that the vULM measurement has higher spatial resolution and a larger dynamic range by tracking the centroid of sparsely distributed individual microbubbles while the iCD-fUS image has lower spatial resolution determined by the ultrasound point spread function and it measures the averaged dynamics of blood cells flowing within the measurement voxel. Nevertheless, the mean values obtained with these two methods agree well with each other.

C. Tradeoff of Temporal Resolution and Measurement Accuracy

We further tested the acceptable maximum temporal resolution of iCD-fUS, as shown in Fig. 5. We calculated the mean difference of absolute speed measured with vULM and iCD-fUS that was calculated with different acquisition data lengths (T). The iCD-fUS image was overlaid with an ULM spatial mask for the comparison. We see that T=100 ms provides an acceptable tradeoff between the measurement accuracy and the temporal frame rate, providing a maximum image frame rate of 10 Hz in principle. It is worth noting that the actual frame rate may be limited by the data transfer and processing rate of the acquisition system.

Fig. 5.

Acquisition duration (T) affects the axial velocity measurement accuracy obtained with iCD-fUS. (a) Axial velocity maps calculated with different data lengths (T). (b) Reconstruction error mDiff.: mean difference compared to the axial velocity measured with vULM.

D. Axial Velocity Changes in Response to Whisker Stimulation

We further applied iCD-fUS to study blood flow velocity change in response to whisker stimulation. The experimental setup is shown in Fig. 6(a). The experimental animal was trained for two weeks before the experiment and treated with condensed milk about 5 mins before the stimulation and after the experiment. We performed the functional study experiments with two stimulation protocols as described in section II. G Whisker Stimulation. Limited by the data transfer rate and computing ability, we transferred and saved the raw RF data to the host computer and performed post data processing afterwards. The data acquisition rate was set to be 1 frame/s which is sufficient to detect the relatively slow blood flow change in response to whisker stimulation. Each experimental session lasted for ~15 mins.

Fig. 6.

Blood flow velocity changes in response to whisker stimulation in awake mice. (a) Experimental setup. (b) Hemodynamic response function (HRF) was obtained by fitting the averaged signal response in the activated region with Eq. 4. (c) and (d) Activation maps obtained with PD-fUS and iCD-fUS, respectively. Hot color map shows correlation coefficient obtained from descending flow and cool color map shows correlation coefficient obtained from ascending flow. S1BF: Primary somatosensory barrel field; PO: Posterior complex of the thalamus; VPM: Ventral posteromedial nucleus of the thalamus. The ROIs were identified according to Allen Mouse Brain Atlas [17]. (d1) Axial velocity time course of vessels V1, V2, and V3 as marked in (d). Red shades indicate stimulation. (d2) All trial averaged axial velocity relative change. Error bar: standard error of the mean. (d3) Frequency spectrum of a voxel signal in the responding vessel V1 during baseline and stimulation shows higher frequency shift during stimulation.

The stimulation protocol used to produce the results shown in Fig. 6 consisted of ten trials of 15 seconds stimulation followed by 30 seconds recovery. Fig. 6(b) illustrates how the hemodynamic response function (HRF) was obtained by fitting the Gamma function (Eq. 7) with the experimental data. With the obtained HRF we calculated the activation maps (correlation coefficients) based on the directional PD-fUS (Fig. 6(c)) and iCD-fUS (Fig. 6(d)) using the same data sets but with directional filtered power Doppler data processing and iCD-fUS data processing, respectively. In Fig. 6 (c)&(d), the bluish pseudo color coded ascending activation map is overlapped on the reddish pseudo color coded descending activation map. Please refer to Supplementary Fig. 4 for non-overlapped activation maps.

We note that both PD-fUS and iCD-fUS activation maps exhibited significant activation in the brain regions of the primary somatosensory barrel field (BF), the posterior complex (PO) and ventral posteromedial nucleus (VPM) of the thalamus. These observations are in agreement with previous PD-fUS studies [4], [14], and the underlying mechanism is explained as the mechanoreceptive whisker information reaching the barrel cortex via the thalamic VPM nuclei [15], and by the PO acting as a paralemniscal pathway for whisker signal processing [16]. We also noticed differences between the PD-fUS and iCD-fUS activation maps that PD-fUS result shows strong activation in parenchyma while iCD-fUS shows significant blood flow velocity increase in blood vessels in the activated regions. This is due to the fact that PD-fUS measures blood volume change which is more significant in the parenchyma region while iCD-fUS measures the blood flow velocity change which is mostly detectable in inflowing and draining vessels near the activated region. Therefore, iCD-fUS and PD-fUS are complementary for functional studies.

It is worth noting that in addition to identifying the functional activation region as power Doppler-fUS does, iCD-fUS is further able to quantify the axial blood flow velocities as shown in Fig. 6(d1). The velocity time traces indicate robust and highly correlated velocity increases in vessels V1 and V2 while a negligible change is observed in vessel V3 in the ipsilateral cortex. Fig. 6(d2) shows the relative changes of all averaged trials compared to baseline for vessels V1, V2, and V3. We note a speed increase of ~15% in V1 and V2 and negligible change in V3. Fig. 6(d3) shows the frequency power spectrums of the same voxel in V1 during baseline (black) and activation (red). We can see that the frequency power spectrum shifts towards higher frequency during activation, suggesting faster flow speed.

We also tested if iCD-fUS is able to detect blood flow velocity change in response to shorter functional stimulation. We employed the stimulation protocol used in optical functional studies that consisted of 5 s of stimulation followed by 20 s of rest time. The results are shown in Supplementary Fig. 5. We see that iCD-fUS successfully detected blood flow velocity change in both cortical and subcortical brain regions, indicating its potential for functional studies.

IV. Conclusion

To summarize, the conventional color Doppler method which estimates the Doppler frequency shift using the whole spectrum is able to accurately estimate the Doppler frequency shift for a single-directional flow, as shown in Fig. 2(a). However, this simple scenario of flow in a single-direction is not generally applicable for microvascular imaging in the rodent brain. In this work, we introduce an improved color Doppler ultrasound imaging method (iCD-fUS) for accurate quantitative axial blood flow velocity imaging of the rodent brain. We applied directional filtering in combination with noise thresholding to estimate the Doppler frequency shifts. We validated the axial velocity measured with iCD-fUS with the microbubble tracking-based ultrasound localization microscopy velocimetry (vULM). The iCD-fUS method is able to obtain accurate axial velocity images of the whole coronal section of the brain at a theoretical frame rate of 10 Hz and a velocity range from 1.5 to 80 mm/s. The spatial resolution of iCD-fUS is determined by the transducer’s center frequency and the beamforming processing, which is ~100 μm for our system. We further applied iCD-fUS to measure the cerebral blood flow velocity change in response to whisker stimulation and the results showed that iCD-fUS is able to map the activation region and detect blood flow velocity change in response to each stimulation. iCD-fUS is not only an alternative to the Power Doppler-based functional ultrasound (PD-fUS) for functional hemodynamic imaging, but goes further to provide quantitative measurement of the absolute axial blood flow velocity. This ability enables iCD-fUS to chronically monitor the blood flow velocity change over disease progression, which, however, is challenging for PD-fUS.

The iCD-fUS is robust and easy to be implemented. The ultrafast coherent plane wave compounding ensures a sufficient temporal sampling rate and enhanced contrast, and the singular value decomposition (SVD) spatio-temporal filtering removes the bulk motion signal providing iCD-fUS the ability to measure the axial velocity of the intrinsic contrast of the red blood cells. We note that iCD-fUS also exhibits resistance to moderate animal motion artifacts, which may be due to the fact that both slow bulk motion signal (high spatial-temporal correlation signal) and high frequency noise were filtered by SVD filtering and high frequency noise thresholding, respectively. By providing an accurate measurement of the absolute value of axial blood flow velocity, iCD-fUS will be of great interest to those in need of quantifying cerebral blood flow parameters. Further, it is straightforward and easy to integrate iCD-fUS with another emerging imaging technique, multispectral photoacoustic tomography (mPAT) [18], [19], to obtain both blood flow velocity and oxygen saturation distribution simultaneously since both iCD-fUS and mPAT can share the same ultrasound engine. This integration will enable the direct measurement of metabolic rate of oxygen with high spatial temporal resolution and deep penetration, which has been challenging due to the lack of appropriate techniques.