Magnetoacoustic effect

The magnetoacoustic effect refers to the generation of acoustic waves when a time‐varying magnetic field induces eddy currents in a conductive medium. These currents, in the presence of a static magnetic field, produce Lorentz forces that cause rapid mechanical vibrations within the tissue.

These vibrations propagate as acoustic waves, which can be detected by ultrasound transducers placed around the sample. Analysis of the amplitude and time‐of‐flight of these waves allows reconstruction of spatial maps of local electrical conductivity and permittivity. Being non‐ionizing, the magnetoacoustic effect provides a unique contrast mechanism based on tissue electrical properties, complementing other modalities such as photoacoustic imaging and magnetic resonance imaging.

The key equations governing this mechanism are:

• Faraday's law: $\nabla \times \mathbf{E} = -\frac{\partial \mathbf{B_1}}{\partial t}$

• Ohm's law: $\mathbf{J} = \sigma \mathbf{E}$

• Lorentz force density: $\mathbf{f} = \mathbf{J} \times \mathbf{B_0}$

• Acoustic wave equation: $\nabla^2 p - \frac{1}{c^2}\frac{\partial^2 p}{\partial t^2} = \nabla \cdot \mathbf{f}$

For typical experimental parameters:

• Static field $B_0 \approx 0.5$ T, pulsed field $\Delta B \approx 0.1$ T over $\Delta t \approx 100$ μs $\Rightarrow \partial B/\partial t \approx 10^3$ T/s
• Characteristic length $L \approx 10$ mm $\Rightarrow$ induced $E \approx L \cdot \partial B/\partial t \approx 10$ V/m
• Tissue conductivity $\sigma \approx 0.5$ S/m $\Rightarrow J \approx \sigma E \approx 5$ A/m²
• Force density $f \approx J \cdot B_0 \approx 2.5$ N/m³ $\Rightarrow$ peak acoustic pressure $p \approx f \cdot L \approx 0.025$ Pa
• Acoustic speed $c \approx 1500$ m/s, frequency $\sim 1$ MHz