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Old 2010-08-30, 01:05 AM
MMarkov MMarkov is offline
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Default Ann Biomed Eng. 2003 Feb;31(2):195-206.

Ann Biomed Eng. 2003 Feb;31(2):195-206.
Magnetic field visualization in applications to pulsed electromagnetic field stimulation of tissues.
Zborowski M, Midura RJ, Wolfman A, Patterson T, Ibiwoye M, Sakai Y, Grabiner M.

Department of Biomedical Engineering, Lerner Research Institute, The Cleveland Clinic Foundation, 9500 Euclid Avenue, Cleveland, OH 44195, USA. zborow@bme.ri.ccf.org
Abstract
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.
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Old 2010-09-01, 12:04 AM
MMarkov MMarkov is offline
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Default Magnetic Field Visualization in Applications to Pulsed Electromagnetic Field Stimulation of Tissues

The influence of pulsed electromagnetic fields on bone in general has been demonstrated by double-blind studies directed at interbody lumbar fusions in humans, bone formation and loss during limb lengthening, and healing of tibial osteotomies. Iin vivo use of electromagnetic devices may be associated with changes in the relationship between the coils from which the signal emanates and the target tissue. This geometrical change may be associated with substantial changes in the extent to which the desired signal characteristics envelop the target tissue. As part of the effort to define the molecular mechanisms by which pulsed electromagnetic fields influence tissue biology, we have to emphasize the ability to visualize and control variations in the pulsed electromagnetic fields to which cells, tissues, animals, and patients are exposed.
A typical representation of the magnetic field in classical electrodynamics is that of field lines Field lines representation is widely used in electrical engineering, such as electrical machinery and electrical power transmission applications. Magnetic field lines representation is particularly useful in the analysis of two-dimensional problems. The particular problem is how to represent threedimensional pulsed magnetic field distributions in tissues that could be made intuitively obvious to all members of the team. Authors set out to explore magnetic field representations that would be more intuitive to the nontechnical professionals of the team, without losing the biologically relevant information. They we were guided by the principle ‘‘to construct a mathematical model and then visualize,’’ which is particularly important in an
interdisciplinary investigation. In an effort to develop tools for field visualization, authors have focused on the existing, clinically approved PEMF coil transducer Spinal-Stim® Lite, Orthofix Inc., McKinney, TX
The PEMF signal consists of bursts of triangular (sawtooth) pulses, pulse frequency of 3.8 kHz, with a
burst frequency of 1.5 Hz, a burst duration of 25.6 ms, and a burst period of 670 ms.
The results of this study could be easily extended to any coil system operating in a predominantly dielectric medium, such as human tissues.
The field line representation required projection of the anatomical features on the plane of the field lines. In a multidisciplinary team field magnitude representation by contour plots also required projections on selected plane sections of the transducer coils. The analytical model correctly predicted the relatively flat field region at the center of the coil system, which is a part of the field saddle point neighborhood, where the field assumes a local minimum as one moves along the coil system axis, and a local maximum in the direction perpendicular to the coil axis.
A three-dimensional representation of the field as isosurfaces of constant field magnitude provided the most intuitive field visualization tool. For low frequency, oscillating magnetic fields, the field isosurfaces represented both the surfaces of constant dB/dt, and the surfaces of the constant, transient values of the B field. Both types of surfaces provide important, therapeutically relevant information. By selecting a minimum therapeutic value of dB/dt, one obtains a direct, visual information about the spatial boundary at which the dB/dt attains that value, as well as the spatial extension of the field for which the dB/dt is not less than the minimum therapeutic value.
Isosurfaces of the transient B field values visualize well the dynamics of the expanding and contracting magnetic field during the waveform cycle. By selecting a therapeutic value for the B field, one obtains a visual representation of the field front as it sweeps across the volume of interest, and the maximum extension of the given field from the coils. This provides information about directional characteristics of the magnetic field. Again, isometric image superposition of the advancing and receding B field front and the anatomical features of interest provide visual information about the therapeutic parameters. The field model developed in this work is currently applied in the project on the determination of early biochemical events caused by oscillating magnetic fields.
The authors have a heavy mathematics, but the most impressive is the set of figures that demonstrate the field distribution in general and specifically in location of the Spinal Stim device.
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