Optimization of coil geometries for bone fracture healing via dielectrophoretic force stimulation - a simulation study

In this paper we propose a novel technique for shortening fracture healing times based on the use of dielectrophoretic forces (DEPFs). If a non-uniform electromagnetic field is applied around a fracture site, red blood cells within the blood will be polarized; creating electrical dipoles. The dielectrophoretic forces resulting from the interaction of these dipoles and the electromagnetic field, can be used to manipulate blood flow at a fracture site, promote vascularization, increase transmembrane signaling, increase supply of nutrients, necessary hormones and growth factors at the fracture site and thus may help bone healing. For the generation of non-uniform fields we considered three different coil designs (linear, parabolic and square root) and using Mathcad numerically studied the dielectrophoretic forces for a long bone fracture where the main arteries are vertically-oriented and the blood flow is downward. The gravitational force and the drag force on the red blood cells determine the steady state blood flow. The dielectrophoretic force added to the force balance is functional in increasing the blood flow. The ratio of the velocity in the presence of dielectrophoresis to the velocity without dielectrophoresis (called here as the Dielectrophoretic Force Factor, KDEpF) is a good measure of the performance of the dielectrophoresis, since it indicates the increase in blood flow. It was found that the dielectorophoretic force reaches peak levels at a frequency range between 5-15 Hz. At 5 Hz, the average value of dielectrophoretic force factor is 1.90, 2.51 and 1.61 for the linear, parabolic and the square root coils, respectively. The parabolic coil results in the best DEPF and therefore would be the configuration to use in an experimental study to determine if DEPF is useful for bone healing.