Functional Ultrasound (fUS) is an emerging neuroimaging technique capable of capturing brain activity similarly to functional magnetic resonance imaging (fMRI) but with higher spatiotemporal resolution and lower operational cost. This thesis investigates the extension of the joint detection-estimation (JDE) framework to jointly estimate both the hemodynamic response function (HRF) and neural response function (NRF) from fUS imaging data. In the proposed model, the two response functions are represented as a cascade linear time-invariant (LTI) convolution systems, enabling indirect estimation of neural activity signals from fUS measurements. Since direct recordings of neural activity are often unavailable, this Bayesian approach offers a data-driven means of probing the brain’s functional organization.
Inference is performed within a coordinate ascent variational inference (CAVI) framework. The proposed algorithm was applied to fUS datasets and validated against simultaneous recordings of neural firing rates. Results demonstrate that the model successfully captures neural activity, achieving a Pearson correlation coefficient (PCC) of approximately 0.24-0.30, and provides a modest improvement over the conventional boxcar input stimulus model. Additionally, the jointly estimated HRFs were consistent with existing literature, and regional HRF estimates revealed differences in response dynamics between the visual cortex and hippocampus, highlighting region-specific hemodynamic properties.