Electromagnetic dose in long bone fractures: Theoretical determination of in vivo electromagnetic fields resulting from 60 KHz stimulation using epidermal electrodes

Edward Joseph Vresilovic, University of Pennsylvania


The purpose of this work was to determine the electromagnetic fields for the osteogenic tissues in long bone fractures when applying 60 KHz electrical stimulation via external surface electrodes. Additionally the dependencies of these electromagnetic fields on anatomic and clinical parameters were analyzed, and the electromagnetic fields in experimental animal studies and in human clinical trials were compared. An experimental fracture model using a New Zealand White Rabbit fibular osteotomy and a human clinical trial using a tibial non-union were studied. The three dimensional, macroscopic continuum fields were determined by constructing and solving boundary value problems. The boundary value problems were constructed from Maxwell's equations under the assumption of the quasi-electrostatic condition. Multiple tissue models of fractured limb geometries were obtained from computer tomography scans. Solutions were obtained using finite element numerical methods. Results were obtained for both a cylindrical and an anatomic model of the rabbit fibular osteotomy, as well as, for an anatomic model of the human tibial non-union. These results were primarily presented in the form of histograms of the percent of a tissue volume as a function of field strength. Application of a constant amplitude driving signal at the stimulating electrodes produced a spectrum of electric field and current density amplitudes in and about the tissues of the fracture site. Field values showed strong dependence on callus conductivity, electrode-dermal admittance, subcutaneous fat and limb diameter, and showed negligible dependence on the fracture gap width, limb length, small changes in electrode position, and the presents of fracture fixation plates. The voltage amplitude found effective on an empirical basis in human clinical trials for non-unions was 20 times greater than the effective voltage in acute rabbit fracture experiments; however, comparisons of the local fracture site fields in both rabbit and human anatomic models indicated that the effective applied voltages produced similar field spectra, especially within the callus of both models. The nominal effective electric field range was 10$\sp{-1}$-10$\sp{-2}$ mA/cm$\sp2$.

Subject Area

Biomedical research|Surgery|Electrical engineering

Recommended Citation

Vresilovic, Edward Joseph, "Electromagnetic dose in long bone fractures: Theoretical determination of in vivo electromagnetic fields resulting from 60 KHz stimulation using epidermal electrodes" (1992). Dissertations available from ProQuest. AAI9235214.