Acousto-Optical Functional Brain Imaging

Acousto-Optical Functional Brain Imaging uses focused ultrasound to encode ultrasonic signatures onto multiply scattered light in tissue. Ultrasound waves induce three principal effects: (i) density fluctuations that modulate absorption/scattering coefficients, (ii) scatterer displacements that alter optical path lengths, and (iii) refractive index changes that shift optical phase. The resulting modulation of speckle intensity at the acoustic frequency can be detected externally.

Mechanism 1 - Scatterer Displacement: Ultrasound-driven displacement

$$u(t) = \frac{P}{\rho\,v_a\,\omega_a}$$

induces phase shifts

$$\phi_{\mathrm{disp}}(t) = k_0\,u(t), \quad k_0 = \frac{2\pi}{\lambda}.$$

With $\lambda \approx 800\,\mathrm{nm}$, $v_a \approx 1500\,\mathrm{m/s}$, and $\omega_a = 2\pi\times1\,\mathrm{MHz}$, one finds $u \approx 0.1\,\mu\mathrm{m}$, $\phi_{\mathrm{disp}}\approx10^{-3}\,\mathrm{rad}$, and $M_2\propto\phi_{\mathrm{disp}}^2\approx10^{-6}$.

Mechanism 2 (the main one) - Refractive Index Modulation: Pressure-dependent index change

$$\phi_n(t) = k_0\,L\,\Delta n(t), \quad \Delta n = \frac{\partial n}{\partial p}\,P.$$

With $\frac{\partial n}{\partial p}\approx10^{-10}\,\mathrm{Pa}^{-1}$, $P\approx0.5\,\mathrm{MPa}$, and $L\approx10\,\mathrm{mm}$, one obtains $\Delta n\approx10^{-4}$, $\phi_n\approx1\,\mathrm{rad}$, and $M_3\propto\phi_n^2\approx1$.