  Functional ultrasound (fUS) indirectly measures brain activity by recording
changes in cerebral blood volume and flow in response to 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 (i.e., source)
signal based on the stimulus onsets, the so-called experimental paradigm (EP).
However, the EP may not be enough to characterize the whole complexity of the
underlying source signals that evoke the hemodynamic changes, such as in the
case of spontaneous resting state activity. Furthermore, the HRF varies across
brain areas and stimuli. To achieve an adaptable framework that can capture
such dynamics and unknowns of the brain function, we propose a deconvolution
method for multivariate fUS time-series that reveals both the region-specific
HRFs, and the source signals that induce the hemodynamic responses in the
studied regions. We start by modeling the fUS time-series as convolutive
mixtures and use a tensor-based approach for deconvolution based on two
assumptions: (1) HRFs are parametrizable, and (2) source signals are
uncorrelated. We test our approach on fUS data acquired during a visual
experiment on a mouse subject, focusing on three regions within the mouse
brain's colliculo-cortical, image-forming pathway: the lateral geniculate
nucleus, superior colliculus and visual cortex. The estimated HRFs in each
region are in agreement with prior works, whereas the estimated source signal
is observed to closely follow the EP. Yet, we note a few deviations from the EP
in the estimated source signal that most likely arise due to the trial-by-trial
variability of the neural response across different repetitions of the stimulus
observed in the selected regions.
