Four-dimensional ultrasound imaging of complex biological systems such as the brain is technically challenging because of the spatiotemporal sampling requirements. We present computational ultrasound imaging (cUSi), an imaging method that uses complex ultrasound fields that can be generated with simple hardware and a physical wave prediction model to alleviate the sampling constraints. cUSi allows for high-resolution four-dimensional imaging of brain hemodynamics in awake and anesthetized mice.

Analysis of functional neuroimaging data aims to unveil spatial and temporal patterns of interest. Existing analysis methods fall into two categories: fully data-driven approaches and those reliant on prior information, e.g. the stimulus time course. While using the stimulus signal directly can help identify the activated brain areas, it is known that the relationship between stimuli and the brain's response exhibits nonlinear and time-varying characteristics. As such, relying completely on the stimulus signal to describe the brain's temporal response leads to a restricted interpretation of the brain function. In this paper, we present a new technique called Evoked Component Analysis (ECA), which leverages prior information up to a defined extent. This is achieved by including the general linear model (GLM) design matrix as a regulatory term and estimating the factor matrices in both space and time through an alternating minimization approach. We apply ECA to 2D and swept-3D functional ultrasound (fUS) experiments conducted with mice. When decomposing 2D fUS data, we employ GLM regularization at various intensities to emphasize the role of prior information. Furthermore, we show that incorporating multiple hemodynamic response functions within the design matrix can provide valuable insights into region-specific characteristics of evoked activity. Finally, we use ECA to analyze swept-3D fUS data recorded from five mice engaged in two distinct visual tasks. Swept-3D fUS images the 3D brain sequentially using a moving probe, resulting in different slice acquisition time instants. We show that ECA can estimate factor matrices with a fine resolution at each slice acquisition time instant and yield higher t-statistics compared to GLM and correlation analysis for all subjects.

Volumetric 3-D Doppler ultrasound imaging can be used to investigate large scale blood dynamics outside of the limited view that conventional 2-D power Doppler images (PDIs) provide. To create 3-D PDIs, 2-D-matrix array transducers can be used to insonify a large volume for every transmission; however, these matrices suffer from low sensitivity, high complexity, and high cost. More typically, a 1-D-Array transducer is used to scan a series of stationary 2-D PDIs, after which a 3-D volume is created by concatenating the 2-D PDIs in postprocessing, which results in long scan times due to repeated measurements. Our objective was to achieve volumetric 3-D Doppler ultrasound imaging with a high Doppler sensitivity, similar to that of a typical stationary recording using a 1-D-Array transducer, while being more affordable than using 2-D-matrix arrays. We achieved this by mounting a 1-D-Array transducer to a high-precision motorized linear stage and continuously translating over the mouse brain in a sweeping manner. For Part I of this article, we focused on creating the best vascular images by investigating how to best combine filtered beamformed ultrasound frames, which were not acquired at the same spatial locations, into PDIs. Part II focuses on the implications of sampling transient brain hemodynamics through functional ultrasound (fUS) while continuously translating over the mouse brain. In Part I, we show how the speed at which we sweep our 1-D-Array transducer affects the Doppler spectrum in a flow phantom. In vivo recordings were performed on the mouse brain while varying the sweeping speed, showing how higher sweeping speeds negatively affect the PDI quality. A weighting vector is found to combine frames while continuously moving over the mouse brain, allowing us to create swept PDIs of similar sensitivity when compared with those obtained using a stationary 1-D-Array while allowing a significantly higher 3-D Doppler volume rate and maintaining the benefits of having a low computational and monetary cost. We show that a vascular subvolume of 6 mm can be scanned in 2.5 s, with a PDI reconstructed every $200 \mu \text{m}$ , outperforming classical staged recording methods.

Functional ultrasound (fUS) using a 1-D-array transducer normally is insufficient to capture volumetric functional activity due to being restricted to imaging a single brain slice at a time. Typically, for volumetric fUS, functional recordings are repeated many times as the transducer is moved to a new location after each recording, resulting in a nonunique average mapping of the brain response and long scan times. Our objective was to perform volumetric 3-D fUS in an efficient and cost-effective manner. This was achieved by mounting a 1-D-array transducer to a high-precision motorized linear stage and continuously translating over the mouse brain in a sweeping manner. We show how the speed at which the 1-D-array is translated over the brain affects the sampling of the hemodynamic response (HR) during visual stimulation as well as the quality of the resulting power Doppler image (PDI). Functional activation maps were compared between stationary recordings, where only one functional slice is obtained for every recording, and our swept-3-D method, where volumetric fUS was achieved in a single functional recording. The results show that the activation maps obtained with our method closely resemble those obtained during a stationary recording for that same location, while our method is not restricted to functional imaging of a single slice. Lastly, a mouse brain subvolume of 6 mm is scanned at a volume rate of 1.5 s per volume, with a functional PDI reconstructed every 200\mu \text{m} , highlighting swept-3-D's potential for volumetric fUS. Our method provides an affordable alternative to volumetric fUS using 2-D-matrix transducers, with a high SNR due to using a fully sampled 1-D-array transducer, and without the need to repeat functional measurements for every 2-D slice, as is most often the case when using a 1-D-array. This places our swept-3-D method as a potentially valuable addition to conventional 2-D fUS, especially when investigating whole-brain functional connectivity, or when shorter recording durations are desired.

Functional ultrasound (fUS) is an emerging neuroimaging modality that indirectly measures neural activity by detecting fluctuations in local blood dynamics. fUS acquisitions typically rely on the use of a 1D array transducer, which records hemodynamic activity in a single plane. A new technique named swept-3D fUS imaging obtains a full 3D volume of the brain by continuously moving a 1D array back-and-forth over the volume of interest. The standard procedure in fUS imaging involves filtering and averaging a number of ultrasound frames obtained at a single location to compute power-Doppler images, yet, in case of swept-3D fUS, the location of the recorded slice shifts at each time instant due to probe motion. In this work, we aim at discovering task-relevant components from 3D fUS data while taking into account the spatiotemporal differences in adjacent slices. We propose an alternating optimization scheme with general liner model-based regularization, and validate our method on swept-3D fUS data by identifying active regions and time traces within the mouse brain during a visual experiment.

Functional ultrasound (fUS) indirectly measures brain activity by detecting changes in cerebral blood volume following neural activation. Conventional approaches model such functional neuroimaging data as the convolution between an impulse response, known as the hemodynamic response function (HRF), and a binarized representation of the input signal based on the stimulus onsets, the so-called experimental paradigm (EP). However, the EP may not characterize the whole complexity of the activity-inducing signals that evoke the hemodynamic changes. Furthermore, the HRF is known to vary across brain areas and stimuli. To achieve an adaptable framework that can capture such dynamics of the brain function, we model the multivariate fUS time-series as convolutive mixtures and apply block-term decomposition on a set of lagged fUS autocorrelation matrices, revealing both the region-specific HRFs and the source signals that induce the hemodynamic responses. We test our approach on two mouse-based fUS experiments. In the first experiment, we present a single type of visual stimulus to the mouse, and deconvolve the fUS signal measured within the mouse brain’s lateral geniculate nucleus, superior colliculus and visual cortex. We show that the proposed method is able to recover back the time instants at which the stimulus was displayed, and we validate the estimated region-specific HRFs based on prior studies. In the second experiment, we alter the location of the visual stimulus displayed to the mouse, and aim at differentiating the various stimulus locations over time by identifying them as separate sources.

The original version of this article was revised to update the Figure 8 (panel B) image. The correct image should have a yellow shape as presented below. (Figure presented.). The original article has been corrected.