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).

Magnetic susceptibility of structurally intact bone may play a role in low frequency (below 10 kHz), low field (below 10 mT amplitude) pulsed electromagnetic field (LF PEMF) treatment of fracture non-unions and an adjunct to cervical fusion surgery, approved by the U.S Food and Drug Administration (FDA). The aim of this study was to determine if a difference in PEMF treatment results in measurable differences in the bone magnetic susceptibility using a model of structurally intact rat vertebrae. We measured bone volume magnetic susceptibility by a custom built mechanical resonator comprising a diametrically-polarized NdFeB permanent dipole magnet cylinder (25.4 x 25.4 mm, height by diameter) rotated about its axis by a stepper motor at even intervals from 53 to 63 RPM, acting as a source of a local, oscillating magnetic field (mean field of 95 mT, gradient of 12 T/m) on an intact laboratory rat lumbar vertebrae (n = 21, from tissue repository from past studies on LF PEMF treatment in vivo) suspended 26.0 mm from magnet axis on a thin line of 80 mm nominal length forming a pendulum of nominal eigenfrequency of 100 Hz. The vertebra motion was captured by a video camera and the geometrical center of its 2D image motion was analyzed by ImagePro (R) and MATLAB (R) routines. The amplitude of bone oscillations (at twice the angular frequency of the rotating magnet) showed a characteristic pattern of resonance with the magnet rotational frequency. The amplitude maximum agreed with that calculated from a model of forced, damped harmonic oscillator and the diamagnetic tension force acting on bone. The calculated mean volume magnetic susceptibility (SI) of -was on the order of magnitude of literature value (vertical bar chi vertical bar approximate to 10(-5)). The results point to the bone site-specific aspect of LF PEMF therapy and provide experimental and theoretical basis for a novel, rational method of designing next generation of effective LF PEMF therapies.