Magnetic Resonance Imaging Magnet Research Articles

Study on Magnetic Field Mapping Method in the Center Volume of the Air-Core Solenoid

Mapping is a useful tool in the magnetic field analysis and design. In some specific research area, such as the nuclear magnetic resonance or the magnetic resonance imaging (MRI), it is important to map the magnetic field in the interesting space with high accuracy and low time consumption. In this paper, a numerical way for mapping the magnetic field in the center volume of an air-core solenoid is presented, based on the solution of the Laplace's equation for the field. Through the mathematical analysis on the mapping calculation, the error of the mapping can be estimated using the condition number of the matrix, which is related by the measurement points and the highest order of the solution of the Laplace's equation. Considering the simplicity and the accuracy, the helical cylindrical line (HCL) method is described to measure the magnetic flux density using one probe. As an example, a practical MRI magnet was mapped by the HCL method. The measurement values of the magnetic flux density are simulated according to the parameters of the MRI magnet. Based on these values, the magnetic flux density in the estimated volume can be obtained through the HCL method. Comparing the measurement value with the mapping result, the method is feasible and convenient to produce satisfactory results in the field mapping. This method will give some convenience and accuracy for mapping the magnetic field in the center volume of the air-core solenoid.

R&D Project on HTS Magnets for Ultrahigh-Field MRI Systems

An RD $\text{RE}=\text{rare earth}$ ) wires for ultrahigh-field (UHF) magnetic resonance imaging (MRI) systems is described. Our targets are 9.4-T MRI systems for whole-body imaging and brain imaging. REBCO wires are promising components for UHF-MRI because REBCO wires have high critical current density in high magnetic fields and high strength against hoop stresses, which allows MRI magnets to be smaller and lighter than conventional ones. The aim of the project is to establish basic magnet technologies for adapting REBCO coils for UHF-MRI. The project term is three years, and this year is the final year. We have already demonstrated the generation of an 8.27-T magnetic field with a small test coil composed of 22 REBCO pancake coils. A magnetic field spatial distribution with inhomogeneity of several hundreds of parts per million within 100-mm diameter spherical volume (DSV) was demonstrated with a 1-T model magnet. A stable magnetic field of a few parts per million per hour was also demonstrated with the 1-T model magnet. The targets of the project, to be achieved by March 2016, are to demonstrate the generation of a 9.4-T field with the small REBCO coil, and to demonstrate a homogeneous magnetic field in 200-mm DSV with a 1.5-T magnet having three pairs of split coils. Imaging will be performed with the 1.5-T magnet.

A multiscale and multiphysics model of strain development in a 1.5 T MRI magnet designed with 36 filament composite MgB2 superconducting wire

High temperature superconductors such as MgB2 focus on conduction cooling of electromagnets that eliminates the use of liquid helium. With the recent advances in the strain sustainability of MgB2, a full body 1.5 T conduction cooled magnetic resonance imaging (MRI) magnet shows promise. In this article, a 36 filament MgB2 superconducting wire is considered for a 1.5 T full-body MRI system and is analyzed in terms of strain development. In order to facilitate analysis, this composite wire is homogenized and the orthotropic wire material properties are employed to solve for strain development using a 2D-axisymmetric finite element analysis (FEA) model of the entire set of MRI magnet. The entire multiscale multiphysics analysis is considered from the wire to the magnet bundles addressing winding, cooling and electromagnetic excitation. The FEA solution is verified with proven analytical equations and acceptable agreement is reported. The results show a maximum mechanical strain development of 0.06% that is within the failure criteria of −0.6% to 0.4% (−0.3% to 0.2% for design) for the 36 filament MgB2 wire. Therefore, the study indicates the safe operation of the conduction cooled MgB2 based MRI magnet as far as strain development is concerned.

A multifunctional contrast dye for morphological research.

We sought to devise and test a multifunctional contrast dye agent for X-ray based digital radiography (DR) or computer tomography (CT), magnetic resonance imaging (MRI), and colored staining in ex vivo validation part of animal experiments. The custom-formulated contrast dye namely red iodized oil (RIO) was prepared by solubilizing a lipophilic dye Oil Red O in iodized poppy seed oil (Lipiodol or LPD) followed by physicochemical characterizations. To explore and test the utility of RIO, normal rats (n = 10) and rabbits (n = 10) with myocardial infarction (MI) were euthanized by overdose of pentobarbital for infusion of RIO through catheterization. The bodies and/or excised organs including heart, liver, spleen, kidneys, pancreas, and intestines of the rats and rabbits were imaged at clinical mammography, CT and MRI units. These images were qualitatively studied and quantitatively analyzed using Wilcoxon Rank test with a P value < 0.05 being considered of a statistically significant difference. Imaging findings were verified by histomorphology. All experimental procedures were carried out successfully with the use of RIO. T1 and T2 relaxation time was 234.2 ± 2.6 ms and 141.9 ± 3.0 ms for RIO, close to that of native LPD. Proton ((1) H) NMR spectroscopy revealed almost identical profiles between RIO and native LPD. The clinical mammography unit, 128-slice CT scanner and 3.0T MRI magnet were well adapted for the animal experiments. Combined use of RIO with DR, MRI, CT and histology enabled microangiography of the organs, 3D visualization of rat pancreas, validation of in vivo cardiac quantification of MI and cause determination of the rabbit death after coronary occlusion. RIO appeared as red droplets and vacuoles in vessels by frozen and paraffin sections. Image analysis showed the superiority of DR images, which provided better overall image quality (4.35 ± 0.49) for all analyzed liver vessel segments. MRI images revealed moderate to good overall image quality ratings (3.45 ± 0.52). Comparing the signal intensities of vessel and liver with different MRI sequences, all P values were <0.01. RIO proved to be a multifunctional contrast dye, which could be applied as an imaging biomarker for tissue vascularity or blood perfusion, for visualization of organ anatomy and for ex vivo validation of in vivo animal experiments.

R&D Progress of HTS Magnet Project for Ultrahigh-field MRI

An R&D project on high-temperature superconducting (HTS) magnets using rare-earth Ba2Cu3O7 (REBCO) wires was started in 2013. The project objective is to investigate the feasibility of adapting REBCO magnets to ultrahigh field (UHF) magnetic resonance imaging (MRI) systems. REBCO wires are promising components for UHF-MRI magnets because of their superior superconducting and mechanical properties, which make them smaller and lighter than conventional ones. Moreover, REBCO magnets can be cooled by the conduction-cooling method, making liquid helium unnecessary. In the past two years, some test coils and model magnets have been fabricated and tested. This year is the final year of the project. The goals of the project are: (1) to generate a 9.4 T magnetic field with a small test coil, (2) to generate a homogeneous magnetic field in a 200mm diameter spherical volume with a 1.5 T model magnet, and (3) to perform imaging with the 1.5 T model magnet. In this paper, the progress of this R&D is described. The knowledge gained through these R&D results will be reflected in the design of 9.4 T MRI magnets for brain and whole body imaging.

Design of Shimming Rings for Small Permanent MRI Magnet Using Sensitivity-Analysis-Based Particle Swarm Optimization Algorithm

The main magnet in a magnetic resonance imaging (MRI) system creates a static magnetic field that determines the final imaging quality. In a permanent MRI system, shimming rings are commonly used to improve field homogeneity. However, the optimization of the ring structure is challenging owing to the nonlinear properties of the ferromagnetic material. To design a small permanent magnet system, this study explores the application of sensitivity analysis (SA) and particle swarm optimization (PSO) algorithm for the optimization of shimming rings. SA is used to identify the most important parameter of the shimming rings that affects the quality of the magnetic field to simplify the optimization process and improve optimization accuracy and efficiency. PSO is used to solve the complex and nonlinear optimizations of the magnetic field. To illustrate the effectiveness of the proposed method, a specific permanent MRI magnet was modeled. The results show that the inner radius of the shimming ring crucially affects magnetic field quality, with ring height having relatively smaller impact. Compared with the PSO-only optimization procedure, the combined SA-PSO optimization more rapidly converges to a better solution. The optimized shimming rings significantly improve the magnetic field uniformity (~10 fold) compared with that of the initial magnet without shimming rings.

Field Mapping and Automated Shimming of an HTS Magnet by “Internal” Active Shim Coils Located in the Bore of the Magnet

In order to obtain the target field homogeneity of a nuclear magnetic resonance (NMR) or magnetic resonance imaging (MRI) magnet, commonly used are active shim coils, i.e., axial and radial, that typically locate radially outside of the magnet. In a high-temperature superconducting (HTS) magnet, however, we reported a “strong” hysteresis in the field-to-current ratio of an external (placed radially outside the HTS magnet) active shim coil by the screening-current-induced fields (SCFs). This nonlinear behavior of an external active shim due to the SCF is one of the major technical challenges to achieve the target field homogeneity of an HTS NMR or MRI magnet. In this paper, we constructed and operated active shim coils, i.e., two axial ( Z1 and Z2) and two radial (X and Y) , that were installed inside of an HTS magnet to investigate effectiveness of internal shim coils. The HTS magnet, wound with GdBCO coated conductors, consists of ten double pancakes. With the active shim coils, a customized field mapping and shimming system was constructed, which consists of a 3-D field mapper, a field analysis software package, and a set of power supplies to control the shim coils. A pre-shim field error of 953 ppm at a 10-mm-diameter cylinder was improved to 464 ppm after iterative automated shimming using the internal shim coils. The results demonstrate that the internal shim coils are effective to eliminate the SCF-oriented field errors, both radial and axial, which was practically impossible for the external shim coils.

Status of the Shielding Coils Fabrication for the Iseult/INUMAC Whole Body 11.75 T MRI Magnet

A neuroscience research center with a very high field magnetic resonance imaging (MRI) equipment was opened in November 2006 in the Neurospin site at CEA Saclay. One of the imaging systems requires a whole body 11.75 T MRI magnet with a 900 mm warm bore. Operating at a homogeneous field level of 11.75 T, the cryostat has external dimensions of 4.8 m in diameter and 5.0 m in length. With the large aperture and high field strength, this magnet represents a real challenge when compared to the largest MRI systems ever built. The coil is made from a copper-stabilized niobium-titanium conductor cooled by a superfluid helium bath at 1.8 K and permanently connected to a cryo-plant. The main coil is constructed from a stack of 170 double pancakes and the magnet is actively shielded by two large coils connected in series to fulfill the stray field specifications. The two shielding coils, each of about 4 m in diameter, are presently being manufactured by Alstom Power Systems STTG Magnets, Belfort. This paper describes the design of these coils and presents the latest progress of their fabrication. Details are given of the winding technique, impregnation method, and the first results of electrical and geometrical tests.

Project Overview of HTS Magnet for Ultra-high-field MRI System

A project to develop an ultra-high-field magnetic resonance imaging (MRI) system based on HTS magnets using (RE)Ba2Cu3O7 (REBCO; RE=rear earth) coils is underway. The project is supported by the Japanese Ministry of Economy, Trade and Industry and aims to establish magnet technologies for a whole-body 9.4 T MRI system. REBCO wires have high critical current density in high magnetic fields and high strength against hoop stresses, and therefore, MRI magnets using REBCO coils are expected to have cryogenic systems that are smaller, lighter, and simpler than the conventional ones. A major problem in using REBCO coils for MRI magnets is the huge irregular magnetic field generated by the screening current in REBCO tapes. Thus, the main purpose of this project is to make the influence of this screening current predictable and controllable. Fundamental technologies, including treatment of the screening currents, were studied via experiments and numerical simulations using small coils. Two types of model magnets are planned to be manufactured, and the knowledge gained in the development of the model magnets will be reflected in the magnet design of a whole-body 9.4 T MRI system.

The Use of MRI as a Technique for Hydrophilic Polymer Swelling Characterization

ABSTRACTThe advantage of magnetic resonance imaging (MRI) is mainly the direct visualization of the physico-chemical processes occurring during the polymer dissolution in real time. Nowadays, polymeric matrices as a means to control the release of the active pharmaceutical ingredient (API) are widely used. Hence it seems necessary to describe the polymer swelling and find the relationship between the type of used polymer and the dissolution profile of API.The aim of our research was to monitor the dissolution kinetics of polymeric matrices with the different ratio of hydrophilic and lipophilic components utilizing MRI technology. For this purpose, six different matrices were prepared. For the dissolution experiments in MRI magnet, plastic flow through cell and tablet holder were designed and manufactured using a 3-D printer. The experiments were performed under specific conditions i.e. phosphate buffer saline pH 6 as a medium, medium temperature - 37°C, the flow rate of medium - 4 ml/min, the time of experiment - 8 hours. To improve the visibility of the erosion front, composite magnetic nanoparticles SiO2/FeOx as a MRI contrast agent were used. Each matrix was measured three times and the thickness of gel layer was evaluated in three different regions. Results from MRI experiments were compared to the results obtained by utilizing the texture analyzer, and then the relationship between polymer swelling and drug release was evaluated.To sum up, MRI turned out to be a suitable imaging method for polymer swelling quantification. For the future measurements, the effect of different additives on the polymer swelling kinetics will be evaluated. The results from the whole research should lead to the database of matrix components and conditions of technological processes and their effects on the dissolution profile of API, thus simplifying the formulation of dosage forms with the desired drug release.

Status of the Shielding Coil Fabrication for the Iseult/INUMAC Whole Body 11.75 T MRI Magnet

A neuroscience research center with a very high field magnetic resonance imaging (MRI) equipment was opened in November 2006 in the Neurospin site at CEA Saclay. One of the imaging systems requires a whole body 11.75 T MRI magnet with a 900 mm warm bore. Operating at a homogeneous field level of 11.75 T, the cryostat has external dimensions of 4.8 m in diameter and 5.0 m in length. With the large aperture and high field strength, this magnet represents a real challenge when compared to the largest MRI systems ever built. The coil is made from a copper-stabilized niobium-titanium conductor cooled by a superfluid helium bath at 1.8 K and permanently connected to a cryo-plant. The main coil is constructed from a stack of 170 double pancakes and the magnet is actively shielded by two large coils connected in series to fulfill the stray field specifications. The two shielding coils, each of about 4 m in diameter, are presently being manufactured by Alstom Power Systems STTG Magnets, Belfort. This paper describes the design of these coils and presents the latest progress of their fabrication. Details are given of the winding technique, impregnation method, and the first results of electrical and geometrical tests.

Analysis of an Abnormal Event in a 3-T MRI Magnet Wound With Bi-2223 Tape Conductors

We have designed and fabricated a 3-T Magnetic Resonance Imaging (MRI) magnet system for the human brain, which was wound with Bi-2223 tape conductors. The magnet was successfully energized to 1.5 T and then up to 3.0 T. The magnet experienced more than 60 ramp-up and down processes to 1.5 T with no trouble. A magnetic field of 3.0 T (184.8 A) could be maintained for longer than 3 h without any problems. However, abnormal voltage behavior was observed during the ramp down for the third trial to 3.0 T, and the temperature rapidly increased with a ramping rate of 1.7 K/min. To investigate the cause, we opened the cryostat and inspected the inside of the magnet. In addition, we have analyzed the details of this event using the recorded current, voltage, and temperature data. The purpose of this paper is to report the investigation of this abnormal event in the magnet.

Open MRI Magnet With Iron Rings Correcting the Lorentz Force and Field Quality

A magnetic resonance imaging (MRI) superconducting magnet with openness can reduce claustrophobia of a patient. To fabricate an open MRI magnet, a new magnet configuration with iron rings and pole plates balancing the force between the coil and the yoke, and correcting the field homogeneity has been proposed. An MRI magnet with the center field of 0.7 T generated by split-pair coils and yokes is fabricated. The coils are contained in the cryostat with separated vessels connected with two pipes. The coils are separated with a room temperature gap of 480 mm and the diameter spherical volume (DSV) of 300 mm in which the homogeneity is 3 ppm in peak-to-peak. The cryogenic system is cooled by one GM cryo-cooler to realize the zero boiling off liquid helium. In the paper, the detailed design, fabrication, and test will be reported.

Globally Optimal Superconducting Homogeneous Magnet Design for an Asymmetric 3.0 T Head MRI Scanner

This paper describes a hybrid numerical method with a combination of linear programming (LP) and nonlinear programming to design an asymmetric magnetic resonance imaging (MRI) system for head imaging. The method was successfully employed to a 0.7 T open-style MRI. Recently, we have updated the LP mathematical model in the hybrid optimization strategy by adding maximum axial and radial magnetic field strength limitation to make the magnet safe. The whole magnet consists of eight coaxial coils asymmetry about the z-axis. The six innermost coils are the main coils with positive current direction and the two outermost coils are shielding coils with negative current direction. All coils contribute their efforts to produce a central magnetic field strength of 3.0 T over a 20 cm diameter of spherical volume, and the peak to peak homogeneity is 12 ppm. The temperature bore for the magnet is formed with two different diameters cylindrical bores which makes head and shoulder access to the imaging volume easier. A 5 Gauss footprint area is restricted larger than an elliptical region with the sizes of 3.5 m in radial and 4.0 m in axial direction. The results show that the methodology is very flexible and efficient for asymmetric MRI magnet design.

WE-G-17A-09: Novel Magnetic Shielding Design for Inline and Perpendicular Integrated 6 MV Linac and 1.0 T MRI Systems

Purpose: The influence of fringe magnetic fields delivered by magnetic resonance imaging (MRI) on the beam generation and transportation in Linac is still a major challenge for the integration of linear accelerator and MRI (Linac-MRI). In this study, we investigated an optimal magnetic shielding design for Linac-MRI and further characterized the beam trajectory in electron gun. Methods: Both inline and perpendicular configurations were analyzed in this study. The configurations, comprising a Linac-MRI with a 100cm SAD and an open 1.0 T superconductive magnet, were simulated by the 3D finite element method (FEM). The steel shielding around the Linac was included in the 3D model, the thickness of which was varied from 1mm to 20mm, and magnetic field maps were acquired with and without additional shielding. The treatment beam trajectory in electron gun was evaluated using OPERA 3d SCALA with and without shielding cases. Results: When Linac was not shielded, the uniformity of diameter sphere volume (DSV) (30cm) was about 5 parts per million (ppm) and the fringe magnetic fields in electron gun were more than 0.3 T. With shielding, the magnetic fields in electron gun were reduced to less than 0.01 T. For the inline configuration, the radial magnetic fieldsmore » in the Linac were about 0.02T. A cylinder steel shield used (5mm thick) altered the uniformity of DSV to 1000 ppm. For the perpendicular configuration, the Linac transverse magnetic fields were more than 0.3T, which altered the beam trajectory significantly. A 8mm-thick cylinder steel shield surrounding the Linac was used to compensate the output losses of Linac, which shifted the magnetic fields' uniformity of DSV to 400 ppm. Conclusion: For both configurations, the Linac shielding was used to ensure normal operation of the Linac. The effect of magnetic fields on the uniformity of DSV could be modulated by the shimming technique of the MRI magnet. NIH/NIGMS grant U54 GM104944, Lincy Endowed Assistant Professorship.« less

Uniformity Aspects of Superconducting MRI Magnet Developed by IHEP

A 1.5-T whole-body magnetic resonance imaging (MRI) magnet was designed and manufactured at the Institute of High Energy Physics, Chinese Academy of Sciences, Beijing, China. The designed field inhomogeneity is less than 50 parts per million peak-to-peak in a sphere with a diameter of 50 cm. Unfortunately, during the process, there are many different manufacturing errors that can generate field inhomogeneity. In this paper, the different manufacturing errors have been discussed, through the accurate calculation of the magnet, and we shall focus on the position offset while manufacturing. In addition, there are several methods that can be used in this situation, and the principle of each of these methods will be given. Finally, comparing with the measured data, the main reasons that lead to inhomogeneity were given in the MRI magnet.

A novel electron gun for inline MRI‐linac configurations

This work introduces a new electron gun geometry capable of robust functioning in the presence of a high strength external magnetic field for axisymmetric magnetic resonance imaging (MRI)-linac configurations. This allows an inline MRI-linac to operate without the need to isolate the linear accelerator (linac) using a magnetic shield. This MRI-linac integration approach not only leaves the magnet homogeneity unchanged but also provides the linac flexibility to move along the magnet axis of symmetry if the source to target distance needs to be adjusted. Simple electron gun geometry modifications of a Varian 600 C electron gun are considered and solved in the presence of an external magnetic field in order to determine a set of design principles for the new geometry. Based on these results, a new gun geometry is proposed and optimized in the fringe field of a 0.5 T open bore MRI magnet (GE Signa SP). A computer model for the 6 MeV Varian 600 C linac is used to determine the capture efficiency of the new electron gun-linac system in the presence of the fringe field of the same MRI scanner. The behavior of the new electron gun plus the linac system is also studied in the fringe fields of two other magnets, a 1.0 T prototype open bore magnet and a 1.5 T GE Conquest scanner. Simple geometrical modifications of the original electron gun geometry do not provide feasible solutions. However, these tests show that a smaller transverse cathode diameter with a flat surface and a slightly larger anode diameter could alleviate the current loss due to beam interactions with the anode in the presence of magnetic fields. Based on these findings, an initial geometry resembling a parallel plate capacitor with a hole in the anode is proposed. The optimization procedure finds a cathode-anode distance of 5 mm, a focusing electrode angle of 5°, and an anode drift tube length of 17.1 mm. Also, the linac can be displaced with ± 15 cm along the axis of the 0.5 T magnet without capture efficiency reduction below the experimental value in zero field. In this range of linac displacements, the electron beam generated by the new gun geometry is more effectively injected into the linac in the presence of an external magnetic field, resulting in approximately 20% increase of the target current compared to the original gun geometry behavior at zero field. The new gun geometry can generate and accelerate electron beams in external magnetic fields without current loss for fields higher than 0.11 T. The new electron-gun geometry is robust enough to function in the fringe fields of the other two magnets with a target current loss of no more than 16% with respect to the current obtained with no external magnetic fields. In this work, a specially designed electron gun was presented which can operate in the presence of axisymmetric strong magnetic fringe fields of MRI magnets. Computer simulations show that the electron gun can produce high quality beams which can be injected into a straight through linac such as Varian 600 C and accelerated with more efficiency in the presence of the external magnetic fields. Also, the new configuration allows linac displacements along the magnet axis in a range equal to the diameter of the imaging spherical volume of the magnet under consideration. The new electron gun-linac system can function in the fringe field of a MRI magnet if the field strength at the cathode position is higher than 0.11 T. The capture efficiency of the linac depends on the magnetic field strength and the field gradient. The higher the gradient the better the capture efficiency. The capture efficiency does not degrade more than 16%.

Numerical Safety Study of Currents Induced in the Patient During Rotations in the Static Field Produced by a Hybrid MRI-LINAC System

MRI-LINAC is a new image-guided radiotherapy treatment system that combines magnetic resonance imaging (MRI) and a linear particle accelerator (LINAC) into a single unit. Moving (i.e., rotating or translating) the patient inside the strong magnetic field of the split MRI-LINAC magnet can potentially induce high levels of electric fields and corresponding current densities in the conducting tissues. The prediction and assessment of patient safety in terms of electromagnetic field exposure have received very little attention for a split cylindrical MRI magnet configuration, especially in the vicinity of the gap region. In this novel numerical study, based on the quasi-static finite-difference method, rotation-induced electric fields and current densities are calculated considering a split 1-T magnet and a tissue-accurate 2-mm-resolution human body model. The patient was modeled in both axial and radial orientations relative to the magnet gap in a number of treatment/imaging scenarios. It was found that rotating the patient in the radial orientation produced an order of magnitude larger field exposure in the central nervous system than when the patient was rotated in the axial orientation. Also, rotating the patient with periods lower than about Trot = 43.3 s may result in field exposures above the limits set out in the international safety guidelines. The novel results of this investigation can provide useful insights into the safe use of the MRI-LINAC technology and optimal orientations of the patient during the treatment.

Simulation and Optimization of a Permanent Magnet for Small-Sized MRI by Genetic Algorithm

The main magnet produces the main magnetic field in the imaging area as one of the important parts of the magnetic resonance imaging (MRI) system. In a permanent MRI magnet, the widespread end effect causes a non-uniform magnetic field distribution and affects the imaging quality. In this paper, an H-type permanent magnet for small-sized MRI applications was designed; in particular, we added an optimized shimming ring outside the pole piece to improve the magnetic field uniformity. Genetic algorithms are used to solve the complex and nonlinear calculation of the magnetic field. The simulation results show that the magnet optimized by the proposed method generates a homogeneous magnetic field that can be easily implemented in practice.

Consideration on Current and Coil Block Placements With Good Homogeneity for MRI Magnets Using Truncated SVD

This paper describes a new method to determine the current and coil block placements with good homogeneity for magnetic resonance imaging (MRI) magnets, and discusses the relationships between the placements and homogeneity, using regularization of the truncated singular value decomposition (SVD). In the first step, the main coil (MC) is modeled as filament loop currents (FLCs) on a solenoid and the shield coil (SC) is modeled by coil blocks. The FLCs are determined so as to get a homogeneous magnetic field using a superposition of eigenmodes obtained by the SVD. In the second step, the FLCs are replaced by MC blocks. The findings are as follows. 1) The obtained FLC distribution in the axial direction has several peaks, which can be suitably replaced by MC blocks and the number of the peaks is equal to the number of MC blocks. 2) There is an optimum length to minimize the absolutely summed current and the 1542-mm length is the optimum for a 525-mm radius with six MC blocks. 3) A one-eigenmode (one MC block) increase or decrease changes the length by $+$ 87 or $-$ 105 mm, respectively. 4) Six MC blocks can provide 1-ppm peak-to-peak homogeneity in the 400-mm diameter spherical imaging volume and this is adequate for MRI magnets.