Transcranial Functional Ultrasound Imaging

Transcranial functional ultrasound (fUS) imaging leverages ultrafast plane‐wave emissions and Power Doppler processing to map cerebral blood volume (CBV) changes that correlate with neuronal activity. By emitting plane waves at pulse repetition frequencies of several kilohertz and coherently compounding backscattered echoes, fUS achieves high spatial resolution (~100–300 μm) and temporal resolution (10–100 ms) not attainable with conventional ultrasound.

Implementing fUS through the intact human skull requires optimized center frequencies (5–7 MHz) to balance penetration depth and resolution, along with skull‐aberration correction algorithms. After beamforming, the sequence of raw echoes is Doppler‐filtered to isolate moving scatterers (red blood cells) and extract microvascular flow dynamics.

Key equations:

$$f_D = \frac{2\,v\,f_0\,\cos\theta}{c}$$

where (f_0\approx6,\text{MHz}), (c\approx1540,\text{m/s}), and flow velocities (v\sim1,\text{mm/s}) yield Doppler shifts (f_D\approx7.8,\text{kHz}).
The Power Doppler signal at pixel ((x,y)) is computed as

$$P_{\mathrm{PD}}(x,y) = \sum_{k=1}^{N} \lvert s_k(x,y)\rvert^2$$

with (s_k) the beamformed echoes over (N) frames, yielding hemodynamic fluctuations of (\Delta P/P_0\approx2\text{–}5%).