The purpose of our study was to test the hypothesis that the electromagnetic pulse (EMP) is capable of inducing mechanical vibrations in bone ex vivo . A thin segment of human femur diaphysis (from a tissue repository) suspended on a tensioned line (range $T =$ 2.2–123 N) was exposed to EMP (mean $B =0.64$ T, dB / dt = 5877 T/s, and the mean $B$ -field gradient of 127 T/m) from a solenoid with axis orthogonal to tensioning line, forming a harmonic oscillator whose mechanical vibrations were measured using laser Doppler vibrometry (LDV, noise floor 1 $\mu \text{m}$ /s). Calculated mean Maxwell stress and Lorentz forces acting on a weakly conducting, diamagnetic bone slice point away from the solenoid for maximum sensitivity of LDV measurement. The electromechanical origin of the LDV signal was confirmed by the order-of-magnitude agreement between calculated (range from 12 to 50 $\mu \text{m}$ /s) and measured initial bone velocity amplitudes (e.g., $35.5~\mu \text{m}$ /s ± $7.5~\mu \text{m}$ /s at $T =22.2$ N and $17.7~\mu \text{m}$ /s ± $2.5~\mu \text{m}$ /s at $T =58.2$ N) and the increasing frequency (25–180 Hz) of decaying oscillations with the square root of $T$ over the range of line tensions ( $r^{2} =0.978$ , $p < 10^{-4}$ , and $n =17$ ). Theory and experiment show that magnetic field impulses are capable of exerting measurable mechanical forces on bone ex vivo . The results raise an interesting question if the electromechanical effect could be sufficiently large to contribute to bone remodeling, reportedly sensitive to vibration amplitudes as small as 1 nm, and considering long duration of orthopedic therapy using repetitive EMP (months).

We studied the PEMF power attenuation in tissues representative of clinical applications (blood and cortical bone) to determine the amount of power available for PEMF purported biological effects. The experimental system consisted of a pair of nearly circular, parallel and coaxial coils separated by a distance of one coil diameter. The power attenuation was measured using a small search coil connected to a digital oscilloscope. The coils were powered by a voltage switch operating at two different frequencies (3.8 and 63 kHz) producing bursts of pulses (numbering 21 and 1619) and triggered at two different frequencies (1.5 and 15 Hz, respectively). The tissue samples were placed inside the coils so as to expose them to either transverse electric field (at the center of coils) or the transverse magnetic field (at the coil wire). The cylindrical coil geometry yielded closed-form expressions for power attenuation based on magnetic diffusion equation and ohmic losses due to bulk tissue magnetic permeability and electrical conductivity. The measured power attenuation at these PEMF frequencies of not more than one decibel (1 dB) was well explained by the theory for the 3.8 kHz but less so for the 63 kHz frequency PEMF. The results provide important insights regarding physical mechanism of weak PEMF power dissipation in tissues.