Induced electric field and current density patterns in bone fractures.

We have used the low frequency solver of the computer program SEMCAD-X to model the induced electric field and current density patterns in simple models of a fractured femur embedded off-center in cylindrical muscle tissue; a 1 cm fracture gap is filled with callus. The model is exposed to a 1 kHz, 1 mT sinusoidal magnetic field. The frequency chosen is typical of the major Fourier components of many waveforms used to stimulate fracture healing using pulsed magnetic fields; the intensity is also a typical level. Models include fractures perpendicular to the bone and at an angle from the perpendicular, each exposed to a field applied parallel to the bone or parallel to either of the two axes perpendicular to it. We find that all directions of applied magnetic fields produce essentially parallel induced electric fields and current densities through the plane of the callus, but that a magnetic field applied parallel to the bone induces considerably higher fields and currents than the same strength field applied in either perpendicular direction. Because investigations of pulsed-field devices, including modeling of induced fields and currents, peaked more than a decade ago, this is the first application to our knowledge of the current capabilities of computer modeling systems to biological systems at low frequencies.