Microbubble Backscattering Intensity Improves the Sensitivity of Three-Dimensional (3-D) Functional Ultrasound Localization Microscopy (fULM)

Functional ultrasound localization micro- scopy (fULM) enables brain-wide mapping of neural activity at micron-scale resolution but suffers from limited sensitivity due to sparse and noisy microbubble (MB) detections. Extending fULM into three dimensions (3D) further exacerbates these challenges because of low-frequency matrix arrays, reduced localization efficiency, and severe data sparsity. To address these limitations, we developed a statistical framework that models MB arrivals in 3D as a Poisson process accounting for localization efficiency, detection probability, and backscattered amplitude. This analysis predicts that integrating amplitude with count-based fULM improves functional sensitivity, particularly under high MB concentrations where localization saturates. Three-dimensional MB advection simulations confirmed these predictions, showing that backscattering fULM (B-fULM) maintains sensitivity at higher MB concentrations where conventional fULM fails. In rat brain experiments, B-fULM yielded stronger and more robust stimulus-evoked responses, with SNR gains of 18% in the somatosensory cortex and 61% in the thalamus, while preserving super-resolved spatial detail ( $33.4~\mu $ m for B-fULM vs $35.7~\mu $ m for fULM). These results establish B-fULM as a practical and sensitive approach for super-resolved 3D functional neuroimaging.