Magnetic field visualization in applications to pulsed electromagnetic field stimulation of tissues

Electromagnetic field visualization is important in multidisciplinary research on the molecular basis of therapeutic effects of pulsed electromagnetic fields (PEMF). We have compared classic PEMF representations by two-dimensional field lines and field magnitude contour plots with a field representation using three-dimensional field isosurfaces. Field simulations were performed for a clinically approved Spinal-Stim Lite system (Orthofix Inc., McKinney, TX). The relatively simple coil system geometry and the predominantly dielectric properties of the surrounding medium (air and human connective tissue) allowed us to develop analytical expressions for the field. The field model was validated by comparison with experimentally measured field values, and with values calculated using a commercial finite-element analysis software package. Two-dimensional field representations by field lines and field contour plots were less intuitive than three-dimensional field isosurface representations to members of the group without an engineering background. Field isosurfaces, represented as three-dimensional solids, allowed for direct visualization of PEMF targeting of individual organs (lumbar spine), the extent of the therapeutic field value, and the directional field characteristics. The dynamic characteristic of the field was well illustrated by a sequence of field isosurfaces corresponding to the evolution with time of the electric current waveform (sawtooth) powering the coils. The isosurface representation of the field can be extended to any three-dimensional coil system geometry using plotting capabilities of current computer algebra software packages.