Electromagnetic Field Simulation of Helmholtz Coils for Biological Applications

Shilpi Pandey1, Oliver Hayden1
1Technical University of Munich, Germany
Published in 2026

Osteoporosis, a common degenerative disease, weakens bones, increasing fracture risk, involving structural deterioration and decreased mineral density. As people age, their risk of bone and joint issues rises. Metabolic illnesses like gout can cause inflammation, limiting movement. Older adults are more vulnerable to serious side effects from invasive procedures due to frail bones and slow healing. Safe, non- invasive treatments promoting bone healing are essential [1]. Bone tissue is about 60% inorganic minerals, mainly hydroxyapatite, 30% organic matrix, mainly type I collagen, and 10% water. The organic matrix maintains bone strength and flexibility, serving as a framework for mineral deposition. Osteoblasts produce collagen and enzymes like osteocalcin (OCN) and alkaline phosphatase (ALP); these are vital for bone remodeling and mineralization. Studies suggest electromagnetic stimulation may boost osteoblast activity, enhancing bone development and markers [1]. This study models low-frequency electromagnetic fields generated by circular air-core coils at 10 Hz. COMSOL simulations assess magnetic flux density and uniformity for various coil geometries in Pulsed Electromagnetic Field (PEMF) therapy. A portable, easy-to-use, low-power device is ideal for home use. Simulations used the Magnetic Fields module in COMSOL Multiphysics. Since 10 Hz is below the electromagnetic wave regime, the system is treated as a magneto-quasi-static. A Helmholtz configuration with identical circular coils (radius 0. 05 m, separation 0. 1 m) was modeled. Each coil has a 0.0125 m square cross-section, with 50 to 200 turns, energized by a 20 A sinusoidal current at 10 Hz. Copper (σ = 6 × 10^7 S/m, μr = 1) was used. The air surrounding the setup (radius 0. 0.325 m) prevents interference. The mesh was refined near the coil and tissue regions, and the study was solved in the frequency domain. This electromagnetic simulation aims to generate low-frequency magnetic fields (~2 mT) for pulsed electromagnetic therapy, similar to those produced by therapeutic magnetic stimulators. The simulation environment is modeled with air alone, allowing examination of the magnetic field’s distribution, uniformity, and decay with distance in free space. The results offer a conceptual insight into how coil shape, the number of turns, and the distance from the coil’s center influence magnetic flux density and uniformity, supporting the design and optimization of low-frequency magnetic stimulation coils. The computed magnetic flux density (B-field, as shown in Fig 2 for 200 turns 200 turns at different distances from the center) exhibits strong localization around the coil, located at 0.05 m (represented by the orange dotted line in the plot), with a maximum amplitude of approximately 13.62 mT (50 turns), as illustrated in Fig. 3(A). The field at 0.125 m (from the center of the Helmholz coil (HC) configuration) is ~2.2 mT, which is comparable to a pulsed electromagnetic field (PEMF), i.e., required for therapy.

ダウンロード