This paper presents an analysis of magnetic field homogeneity of square and circular Helmholtz coils pairs. The analysis is based on the Bio-Savart law for which it performs a Taylor series approximation for the magnetic field at a point on the axis of symmetry, finding an approximate expression of the homogeneity with respect to the parameter radius / length. Finally, a computational model is performed in COMSOL and comparing the magnetic field distribution for both geometries.

This paper presents a comparative study of the magnetic field homogeneity for circular, square and equilateral triangular Helmholtz coils that includes a power consumption analysis. The magnetic field distribution is obtained using the Biot-Savart law, furthermore a Taylor series approximation is performed in order to obtain simple mathematical expressions that relate the area, with uniform magnetic field, to the length of the different coils. For the analysis of magnetic field homogeneity and power consumption, two scenarios were considered: by taking the radius of the circular coil equal to half of the side length of the square and equilateral triangular coils and then equating the perimeters of all of them. Therefore, computational models are constructed and simulated using finite element software in order to validate the calculated results of the magnetic field distribution and the experimental tests of each geometry considering equal perimeters. The results show that the circular geometry has the highest magnetic field homogeneity compared to other Helmholtz coil geometries with the same perimeter.

Se presenta una metodología de diseño e implementación de un sistema para generación de campos magnéticos uniformes de baja magnitud y frecuencia, sobre un volumen específico utilizando una bobina Helmholtz cuadrada tri-axial. El procedimiento de diseño se basa en conceptos teóricos y simulaciones a partir de expresiones matemáticas simples que relacionan el área, con campo magnético uniforme, con la longitud de las bobinas. Además, se conotruye el modelo computacional y se simula usando software de elementos finitos. Se observa que los resultados teóricos son consistentes con los resultados del modelo de simulación y las pruebas mediante medición de campo magnético. Se concluye que la metodología de diseño permite establecer un procedimiento simplificado y repetible, para obtener campo magnético uniforme en un volumen de trabajo adecuado para realizar estudios in-vitro o in-vivo.

A simple geomagnetic field compensation system for uniform magnetic field applications

This article presents the preliminary results obtained from an earlier publication of a design study performed to integrate a cellular culture bioreactor along with an external magnetic stimulation system, which was aimed at creating ideal environmental conditions that allowed for cellular culture and cellular tissue growth to take place in three dimensions, under a sterile environment favorable for the development of bioorganic grafts which were exposed to controlled electromagnetic fields. Cellular tissue was used from cellular lines of Normal Human Skin Fibroblast (NHSF) and was seeded on bio-synthetic scaffolds synthesized from polylactic acid (PLA) and Chitosan mixtures. The cellular tissue covered scaffold was then introduced into the cellular culture bioreactor, subsequently it was filled with cellular culture medium and put under dynamic flow conditions in while at the same time using the external magnetic stimulation system to irradiate the cellular tissue with controlled magnetic fields. The results present static tests of cell growth where the maximum change in growth was after 48 hours when the cells were exposed to a 1 mT, 60 Hz magnetic field; they proliferated at a rate of 52% without Chitosan, 75% with Chitosan and 53% under dynamic flow versus the non-exposed cellular tissue. These results have allowed us to continue our experimentation techniques to evaluate changes in 3-dimensional growth of magnetically stimulated tissues under dynamic flow.