In the last decade, the new functional neuroimaging technique functional ultrasound (fUS) has emerged as a potential new tool for clinical and neuroscientific applications. Unlike several conventional methods for functional brain imaging, fUS offers an unparalleled combination of submillimeter-subsecond spatiotemporal resolution and the ability to penetrate deep into brain tissue and capture large areas of interest. This makes fUS an exceptionally valuable tool for investigating brain function. The principal physiological mechanism utilized by fUS imaging is neurovascular coupling, which connects neuronal activity with local hemodynamic changes. Within the brain, increased neuronal activity results in the dilation of nearby blood vessels, subsequently leading to an increased local blood flow and volume.
In fUS, the increase in blood volume is measured by the intensity of the Doppler signal caused by the Doppler effect. To obtain relevant information from functional neuroimaging data, blind source separation (BSS) is often used. BSS is the separation of a set of source signals from a set of mixed signals, without the aid of information about the source signals or the mixing process. A commonly used BSS method for identifying brain networks and artifacts in functional neuroimaging techniques like fMRI is independent component analysis, which is a low-rank matrix decomposition. This work explores the use of canonical polyadic decomposition (CPD), a low-rank tensor decomposition, for BSS of fUS data. The CPD approximates a 3rd-order tensor, consisting of a space, frequency, and time dimension, by a sum of rank-1 tensors. The proposed method offers three key advantages that make it highly relevant to the field of fUS signal processing: 1) Tensor-based BSS by CPD allows for frequency as a third dimension to complement the spatial and temporal dimensions; 2) Tensor-based BSS by CPD allows for the use of all raw fUS data (compound images) rather than only power doppler images, exploiting more available information; and 3) Tensor-based BSS by CPD allows for a BSS method without strong constraints such as the case with matrix-based methods like independent component analysis. The full processing pipeline developed in this work consists of four distinct stages. In stage one, pre-processing is carried out through SVD filtering, temporal demeaning, and pixel-based normalization. During the SVD filtering, normalization of the singular values is performed, which is novel. In stage two, compression is performed using truncated multilinear singular value decomposition. In stage three, BSS is carried out using CPD on the compressed data. In stage four, stable components are extracted by running the CPD 100 times and clustering the resulting components. These clusters were then averaged to create mean components. The CPD rank was estimated based on two quantifiable aspects: 1) Correlation between mean components and 2) Frequency of occurrence of mean components. The method is entirely data-driven, can be applied to entire raw fUS datasets, and can run on a laptop with standard RAM. Application to task experiment data of a mouse verified that activity that is temporally correlated with the stimulus can be extracted in expected regions. The components also indicate expected functional connectivity, which is often not the case for matrix-based methods. Moreover, frequency spectra showed different characteristics for different types of components, which displays the relevance of this dimension for BSS, especially for nuisance components. In conclusion, the proposed tensor-based blind source separation pipeline for raw fUS data was able to identify artifacts and meaningful neurological components based on distinctive characteristics in the temporal, spatial, and spectral domains. This work serves as a starting point for more advanced denoising, the identification of novel brain networks, and the comparison of brain networks across healthy and pathological conditions. Nevertheless, further research is necessary to ensure the utility of the method.