Numerical analysis of coil designs to expedite fracture healing using dielectrophoresis with S method

Classical methods for speeding up fracture healing usually rely on direct electrical stimulation and electromagnetic fields to boost the levels of growth factors at the fracture site. However, these techniques often concentrate on bone cells themselves rather than addressing the critical blood flow dynamics necessary for effective healing. This study introduces a mathematical model designed to explore the potential of dielectrophoretic forces (DEPFs) in improving blood flow at the fracture site. By adjusting blood flow, the model seeks to enhance the delivery of vital nutrients, hormones, and growth factors, including endothelial cells (ECs), vascular endothelial growth factor (VEGF) and oxygen, which are essential for accelerating the fracture healing process.

The proposed approach includes a new technique, termed the S method, which assesses the non-uniformity of DEPFs by algebraically analyzing the electric field lines associated with positive and negative dielectrophoresis. We developed analytical equations to simulate various coil configurations, focusing on long bone fractures where blood flow is vertically oriented. The DEPF Factor (χDEPF) was used to measure the ratio of blood flow velocity in the presence of DEPFs compared to the absence of DEPFs, thus indicating the effectiveness of DEPF in enhancing blood flow.

The simulation results revealed that DEPF reaches its peak efficacy at the gamma dispersion band, with the most significant enhancement occurring at a frequency of 15 MHz. Specifically, the average values of χDEPF were 1.8, 3.2, and 7.9 for the catenary, lintearia, and valeria coils, respectively. Our computational model, which incorporated VEGF, ECs, and oxygen tension, demonstrated that the catenary coil slightly improved healing rates in impaired fractures, the lintearia coil normalized healing times between impaired and normal fractures, and the valeria coil not only accelerated healing in impaired fractures but also enhanced healing in normal fractures.

This paper's findings suggest that the valeria coil exhibits the best DEPF functionality, making it the optimal configuration for future experimental studies aimed at evaluating the efficacy of DEPF in promoting fracture healing. The ability of DEPFs to significantly enhance blood flow could represent a substantial advancement in the treatment of both normal and impaired fractures.