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.

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.