Objective. Low-intensity focused ultrasound stimulation (LIFUS) emerges as an attracting technology for noninvasive modulation of neural circuits, yet the underlying action mechanisms remain unclear. The neuronal intramembrane cavitation excitation (NICE) model suggests that LIFUS excites neurons through a complex interplay between microsecond-scale mechanical oscillations of so-called sonophores in the plasma membrane and the development of a millisecond-scale electrical response. This model predicts cell-type-specific responses that correlate indirectly with experimental data, but it is computationally expensive and difficult to interpret, which hinders its potential validation. Here, we introduce a multi-scale optimized neuronal intramembrane cavitation (SONIC) model to achieve fast, accurate simulations and confer interpretability in terms of effective electrical response. Approach. The NICE system is recast in terms of smoothly evolving differential variables affected by cycle averaged internal variables that are a function of sonophore size and charge density, stimulus frequency and pressure amplitude. Problem separation allows to precompute lookup tables for these functions, which are interpolated at runtime to compute coarse-grained, electrophysiologically interpretable and spatially distributed predictions of neural responses. Main results. The SONIC model accelerates computation by more than three orders of magnitude, accurately captures millisecond-scale electrical responses of various cortical and thalamic neurons and offers an increased interpretability to the effects of ultrasonic stimuli in terms of effective membrane dynamics. Using this model, we explain how different spiking behaviors can be achieved in cortical neurons by varying LIFUS parameters, and interpret predictions of spike amplitude and firing rate in light of the effective electrical system. We demonstrate the substantial influence of sonophore size on excitation thresholds, and use a nanoscale spatially extended SONIC model to suggest that partial sonophore membrane coverage has a limited impact on neuronal excitability. Significance. By providing an electrophysiologically interpretable description, the SONIC model clarifies cell-type-specific LIFUS neuromodulation according to the intramembrane cavitation hypothesis.