Network and Field Analysis of Koch Snowflake Fractal Geometry Radiofrequency Coils for Sodium MRI

Sodium is one of the most abundant physiological cations and is a key element in many cellular processes. It has been shown that several pathologies, including degenerative brain disorders, cancers, and brain traumas, express sodium deviations from normal. Therefore, sodium magnetic resonance imaging (MRI) can prove to be valuable for physicians. However, sodium MRI has its limitations, the most significant being a signal-to-noise ratio (SNR) thousands of times lower than a typical proton MRI. Radiofrequency coils are the components of the MRI system directly responsible for signal generation and acquisition. This paper explores the intrinsic properties of a Koch snowflake fractal radiofrequency surface coil compared to that of a standard circular surface coil to investigate a fractal geometry’s role in increasing SNR of sodium MRI scans. By first analyzing the network parameters of the two coils, it was found that the fractal coil had a better impedance match than the circular coil when loaded by various anatomical regions. Although this maximizes signal transfer between the coil and the system, this is at the expense of a lower Q, indicating greater signal loss between the tissue and coil. A second version of each coil was constructed to test the mutual inductance between the coils of the same geometry to see how they would behave as a phased array. It was found that the fractal coils were less sensitive to each other than the two circular coils, which would be beneficial when constructing and using phased array systems. The performance of each coil was then assessed for B1+ field homogeneity and signal. A sodium phantom was imaged using a B1+ mapping sequence, and a 3D radial acquisition was performed to determine SNR and image quality. The results indicated that the circular coil had a more homogeneous field and higher SNR. Overall while the circular coil proved to generate a higher signal-to-noise ratio than the fractal, the Koch coil showed higher versatility when in a multichannel network which could prove to be a benefit when designing, constructing, and using a phased array coil.

Design of a dedicated circular coil for Magnetic Resonance Spectroscopy studies in small phantoms and animal acquisition with a 3 Tesla Magnetic Resonance clinical scanner

Introduction: Magnetic Resonance Spectroscopy (MRS) is a very powerful tool to explore the tissue components, by allowing a selective identification of molecules and molecular distribution mapping. Due to intrinsic Signal-to-Noise Ratio limitations (SNR), MRS in small phantoms and animals with a clinical scanner requires the design and development of dedicated radiofrequency (RF) coils, a task of fundamental importance. In this article, the authors describe the simulation, design, and application of a 1H transmit/receive circular coil suitable for MRS studies in small phantoms and small animal models with a clinical 3T scanner. In particular, the circular coil could be an improvement in animal experiments for tumor studies in which the lesions are localized in specific areas.Material and methods: The magnetic field pattern was calculated using the Biot–Savart law and the inductance was evaluated with analytical calculations. Finally, the coil sensitivity was measured with the perturbing sphere method. Successively, a prototype of the coil was built and tested on the workbench and by the acquisition of MRS data.Results: In this work, we demonstrate the design trade-offs for successfully developing a dedicated coil for MRS experiments in small phantoms and animals with a clinical scanner. The coil designed in the study offers the potential for obtaining MRS data with a high SNR and good spectral resolution.Conclusions: The paper provides details of the design, modelling, and construction of a dedicated circular coil, which represents a low cost and easy to build answer for MRS experiments in small samples with a clinical scanner.

MFV: Application software for the visualization and characterization of the DC magnetic field distribution in circular coil systems

The characterization of the magnetic field distribution is essential in experiments and devices that use magnetic field coil systems. We present an open-source application software, MFV (Magnetic Field Visualizer), for the visualization of the distribution of the magnetic field produced by circular coil systems. MFV models, simulates, and plots the magnetic field of coil systems composed by any number of circular coils of any size placed symmetrically along the same axis. Therefore, any new design or well-known coil system, such as the Helmholtz or the Maxwell coil, can be easily modeled and simulated using MFV. A graph of the homogeneity of the magnetic field can be also produced, showing the work region where the magnetic field is homogeneous according to a percentage of homogeneity given by the user. A standardized input and output file format are employed to facilitate the exchange and archiving of data. We include some results obtained using MFV, showing its applicability to characterize the magnetic field in different coil systems. Furthermore, the magnetic field results provided by MFV were validated by comparing them with results obtained experimentally in a commercial Helmholtz coil. Obtaining the maximum variability between the experimental and simulation magnetic flux density values along the axis of symmetry is 0.87%.

Design, Simulation, Modeling, and Implementation of a Square Helmholtz Coil in Contrast with a Circular Coil for MRI Applications

This paper focuses on Helmholtz-type coils that can produce a second-order homogeneity field to be used for Magnetic Resonance Imaging (MRI) applications. A Helmholtz coil is a device used for producing a region of a nearly uniform magnetic field. It consists of two identical magnetic coils that are placed symmetrically along a common axis, one on either side of the experimental area, separated by a distance equal to the radius of the circular coil and half-length of the side of the square coils. Each coil carries an equal electrical current flowing in the same direction. The main objective of this article is to calculate the magnetic field provided by the coils at any point in space and to show and compare the uniform magnetic field induced by the square and circular Helmholtz coils. With the aid of MATLAB simulation tool, mathematical equations are simulated to demonstrate the axial magnetic field produced by one and two loops. Also, the design and simulation of electrical modeling for square and circular Helmholtz coils are performed using PSPICE. Finally, these coils are realized and tested experimentally, and the results for square and circular Helmholtz coils are compared.