Deconvolution of the Functional Ultrasound Response in the Mouse Visual Pathway Using Block-Term Decomposition

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.