Active Shimming Research Articles

Active shimming method for a 21.3 MHz small-animal MRI magnet

In a 21.3 MHz animal nuclear magnetic resonance (NMR) analyzer and imaging system, high uniformity of the static field B0 is a crucial prerequisite for obtaining high-quality images and detecting weak signals with short relaxation time. Using only passive shimming and gradient shimming, it is impossible to achieve perfect B0 uniformity. This paper presents an approach involving high-order active shimming for an NMR analyzer and an imaging magnet. The diameter spherical volume (DSV) of the magnet is only 60 mm. The spherical harmonic function is introduced to analyze the magnetic field and provide a foundation for active shimming. Eleven pairs of bi-planar active shim coils (X, Y, Z, XZ, YZ, Z2, X2 + Y2, X2 − Y2, Z3, Z4, Z5) were designed using the target field-and stream-function methods, and coils were manufactured with printed circuit board technology in this research. The magnetic field created by these electrified shim coils compensates effectively and accurately for the static magnetic field B0. The full width at half maximum of the resonance spectrum was used to measure the shimming effect. The results of practical shimming experiments in a 21.3 MHz animal NMR analyzer and imaging device showed that this new approach helps to reduce inhomogeneity from 24 ppm (24 × 10−6) to 0.39 ppm (0.39 × 10−6) over a 60 mm DSV, which meets the requirements of imaging and analytical practice.

The Design of Decoupled Even-Order Zonal Superconducting Shim Coils for a 9.4 T Whole-Body MRI

A novel active shimming method is proposed for the correction of magnetic field nonuniformity of superconducting (SC) magnet for magnetic resonance imaging. Active shimming utilizes several coils to correct specific field harmonic components appear in the inhomogeneous field, and each coil is usually designed independently to the others, and also takes no account of the presence of the main magnet coil blocks. However, the magnetic coupling among these SC shim coils exists, and also the interaction between those zonal even-order shim coils and the main magnet are particularly significant. This coupling/interaction can lead to the drift of main field and even a possible destruction of shim coils by quench due to tremendous energy transferred from the main magnet. In this paper, we attempt to develop magnetic decoupling technologies for the reduction of magnetic interactions between the shim coil and main magnet. Specifically, a hybrid optimization algorithm, including linear and nonlinear programming, is proposed to design a set of decoupled even-order zonal shim coils. The linear programming determines the globally optimal topology and preliminary position of the shim coils. Then, the nonlinear programming is applied to further optimize the position and the turn number of the shim coils, ensuring the designed coils are capable of correcting the unwanted field deviation. Taking the example of Z2 shim coil, compared with the conventional Z2 shim coil, the proposed method significantly reduces the mutual inductance between the Z2 shim coil and the main magnet. For the same field deviation in the tested case, the mutual inductance has been decreased from 83 to 2.3 H. We also further analyze the influence of system parameters and main magnet structure on the optimal topology of decoupled Z2 shim coil. Z4 and Z6 shim coils are also designed with excellent decoupling effect. In our future work, a whole set of active shim coils decoupled from each other and also the main magnet and will be designed and tested in the 9.4 T whole-body MRI system.

Shimming for the 1020 MHz LTS/Bi-2223 NMR Magnet

Using a Bi-2223 innermost coil, the world's first NMR magnet with a frequency beyond 1 GHz has been developed and operated at the National Institute for Materials Science during 2014-2015. The existing 920 MHz (21.6 T) NMR magnet was successfully upgraded to a 1030 MHz (24.2 T) magnet by replacing the Nb3Sn innermost coil with a Bi-2223 coil. After charging the magnet to 1020 MHz (24.0 T), a shimming operation was started to obtain the homogeneous magnetic field required for NMR measurements. However, a large magnetic field inhomogeneity appeared, which could not be compensated using conventional shimming methods, i.e., superconducting and room temperature shim coils. Therefore, a new ferromagnetic shimming technology was applied, which achieved powerful and fast-acting field compensation and performed comparably to active shimming. This enabled effective compensation of the magnetic field inhomogeneity, leading to a subsequently excellent NMR resolution test result of 0.7 ppb. This NMR resolution enables NMR measurements for a membrane protein sample.

Optimization of magnetic resonance imaging high-order axial shim coils using boundary element method

In this paper, we present a novel nonlinear optimization algorithm for designing a shim coil system, especially a high-order axial shim coil, for a magnetic resonance imaging（MRI) system. In an MRI equipment, in order to eliminate higher-order harmonic components of the magnetic field within the volume of interest（VOI), passive shimming（PS) is adopted in traditional methods. However, such a method is suitable for the global shimming with low accuracy and poor target. Active shimming（AS) makes up for the shortcomings from PS with a set of shim coils which are designed to generate a specific magnetic fields to improve magnetic field homogeneity within the VOI. Because the complexity of wire pattern increases with the order of AS coil increasing, conventional optimization model cannot meet the design requirements for producing the complicated magnetic field. In this paper, we propose a nonlinear optimization method of designing the axial shim coils for an open-style bi-planar MRI system, based on boundary element method. The optimization model is built in light of influence extents of the various parameters on the coil characteristics for different shim coils. In such a new method, the field error between the magnetic field produced by designed shim coil and the desired target value is selected to be an optimal value subjected to some constraints including line spacing and coil radius, which makes it possible to realize the manufacture process. Meanwhile, the more design parameters, which involve not only the stream function values at each node, but also the compensation parameters and/or the number of grid nodes, are regarded as optimized variables to control the magnetic deviation and characteristics of designed coil. By using some designed shim coils for a 0.5 T open style bi-planar superconducting MRI, including Z1, Z2, Z3 and Z4, the efficiency of such a numerical design method is displayed. Especially for high-order shim coils, more optimized parameters are involved to control the magnetic deviation of the coils, thereby providing a more flexible and straightforward method of designing the axial shim coils.

Active Shimming for the Entire Components of Magnetic Field Using Tilted Ellipsoidal Correction Coils

Magnets creating highly homogeneous and high magnetic field have been used in MRI, NMR, accelerator, and so on. Coils have various shapes, such as solenoid, dipole, D-shape, toroid. When employing a high-field superconducting magnet, it is hard to use ferromagnetic material for shimming because of its magnetic saturation. Commonly, a superconducting magnet is shimmed with currents, called “active shimming.” Usually, for shimming, a magnetic field is expressed with spherical harmonics function. To achieve a highly homogeneous field, the higher order spherical harmonic coefficients than the 0th are vanished by suitably arranging shim coils. So far, a formulation of spherical harmonic expression of a circular coil is presented in many papers. However, the circular coil is restricted to eliminate inhomogeneity coefficients. Moreover, only the axial component of the spherical harmonics is represented in these papers. Recently, a few magnets are under development to create a magnetic field tilted from the axis. It is, therefore, necessary to vanish the inhomogeneous field of the entire components. This paper presents the spherical harmonic expression of the entire field components for an ellipsoidal coil, and the translation and rotation of spherical harmonics. Finally, an example of active shimming is shown.

Hybrid PET/MRI Insert: <formula formulatype="inline"><tex Notation="TeX">${B_0}$</tex></formula> Field Optimization by Applying Active and Passive Shimming on PET Detector Level

The design of an MRI (Magnetic Resonance Imaging) compatible PET (Positron Emission Tomography) detector is regarded to be a challenging task since both imaging devices are likely interacting with each other potentially leading to performance degradation. A typically expected consequence of this interaction is the distortion of the MRI system’s ${B_0}$ field homogeneity. The ${B_0}$ field gets distorted by any material with non-zero susceptibility brought into the MRI system. Typically, MRI machines have a so-called active shimming system available which allows the field optimization by using additional dedicated shim coils. However, this active shimming mechanism is limited and might not be capable to compensate localized higher order field patterns caused by e.g. a PET system. Since the high ${B_0}$ field quality is needed for an undisturbed MRI acquisition in general and especially for more advanced MR sequences (spectroscopic studies, sequences which utilizes spectral selective pre-pulses), the PET system’s hardware needs to be designed carefully. Consequently, the typical design paradigm regarding this ${B_0}$ field distortion is the careful selection of all components according to their susceptibility (as low as possible). This design paradigm certainly limits the flexibility of the system design since worse performing components might be chosen over better alternatives because of their higher susceptibility. To overcome this limitation and to retain the MRI capabilities, we propose the application of localized shimming on PET detector level, meaning that the distortion profile caused by PET modules is compensated using either additional components such as magnetic materials (passive shimming) or DC coils (active shimming) on the PET modules or by intelligently arranging the hardware components of the PET detector. We have implemented a software framework which covers three parts: firstly, it calculates the ${B_0}$ distortion of various objects (susceptibility objects, conductor configuration). Secondly, it allows the characterization of magnetic objects by fitting the implemented models to data and thirdly, it performs a ${B_0}$ field homogenization of measured distortion maps by superimposing field disturbances of additional simulated objects. We tested this software framework in a first attempt with a single PET module of the Hyperion-II $^ {\rm D}$ scanner. The measured distortion map of the single PET module shows a strong localized ${B_0}$ distortion with a volume RMS value of about $0.6~\hbox{ppm}$ . After optimization, the homogeneity of the simulated field distribution is strongly improved by a factor of 8 (volume RMS $ \approx 0.075~\hbox{ppm}$ ).

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.

Evaluation of PET performance and MR compatibility of a preclinical PET/MR insert with digital silicon photomultiplier technology

In this work we present detailed characterizations of our preclinical high resolution PET/MR insert based on the Hyperion-IID platform. The PET/MR insert consists of a ring of 10 singles detection modules, each comprising 2x3 scintillation detector stacks. Each detector stack features a 30x30 pixelated LYSO crystal array with a height of 12 mm and a pitch of 1 mm, coupled via a slit 2 mm light guide to a digital SiPM tile. The PET performance is stable under a wide range of operating points. The spatial resolution is below 1A,mm and the CRT reaches 260 or 450 ps depending on trigger settings. The energy resolution is 12.6% FWHM. The characterization of the MR compatibility showed no relevant degradation in PET performance during MRI operation. On the MRI side, we observe a degradation in B0 homogeneity from a VRMS of 0.03 ppm to 0.08 ppm with active shimming, while observing only minor degradations in the B0 field. The noise floor is slightly increased by 2-15% without any observable dependence on the activity. The Z gradients induces an observable eddy current inside the PET inserts which can lead to ghosting artifacts for EPI sequences. However, we don't observe any visible image degradation for widely used anatomical imaging sequences such as gradient echo and turbo spin echo sequences. To prove the viability of our PET/MR insert for in vivo small animal studies, we successfully performed a longitudinal mouse study with subcutaneously injected tumor model cells. The simultaneously acquired PET/MR images provide a high level of anatomical information and soft tissue contrast in the MR layer together with a high resolution image of the FDG tracer distribution in the PET layer.

The effect of high-permittivity pads on specific absorption rate in radiofrequency-shimmed dual-transmit cardiovascular magnetic resonance at 3T.

BackgroundDual-channel transmit technology improves the image quality in cardiovascular magnetic resonance (CMR) at 3 T by reducing the degree of radiofrequency (RF) shading over the heart by using RF shimming. Further improvements in image quality have been shown on a dual-transmit system using high permittivity pads. The aim of this study is to investigate the transmit field (B1+) homogeneity and the specific absorption rate (SAR) using high permittivity pads as a function of the complete range of possible RF-shim settings in order to gauge the efficacy and safety of this approach.MethodsElectromagnetic (EM) simulations were performed in five different body models using a dual-transmit RF coil, with and without high permittivity pads. The RF shimming behaviour in terms of B1+ homogeneity and local SAR were determined as a function of different RF-shim settings. Comparative experimental data were obtained in healthy volunteers (n = 33) on either a standard-bore (60 cm diameter) or wide-bore (70 cm diameter) 3 T CMR system.ResultsEM simulations and experimental data showed higher (B1+) homogeneity and lower SAR for optimized RF-shim settings when using the high permittivity pads. The power distribution between the two channels was also much closer to being equal using the pads. EM simulations showed that for all five body models studied, optimized RF-shim settings corresponded to reduced local SAR using high permittivity pads. However, there are also specific, non-optimal RF-shim settings for which the actual SAR using the pads would be higher (up to ~20 %) than that calculated by the CMR system.ConclusionsThe combination of active (dual transmit) and passive (high permittivity pads) RF shimming shows great promise for increasing image quality for cardiac imaging at 3 T. Optimized RF-shim settings result in increased B1+ homogeneity and reduced SAR with the high permittivity pads: however, there are non-optimal cases in which SAR might be underestimated, and these merit further investigation.

Evaluation of active and passive shimming in magnetic resonance imaging

Evaluation of active and passive shimming in magnetic resonance imaging Keith Wachowicz Division of Medical Physics, Department of Oncology, University of Alberta, Edmonton, AB, Canada Abstract: With higher magnet strengths for magnetic resonance imaging (MRI) units becoming more commonplace, both for animal imaging systems as well as whole-body in vivo systems, magnetic field distortions due to inhomogeneous distributions of magnetic susceptibility and air–tissue interfaces will become more intense. Further, the popularization of MRI-hybrid devices, such as positron emission tomography/MR or MR/radiotherapy hybrids, which rely on the assumption of geometric accuracy for their diagnostic or therapeutic effectiveness, will lead to greater restrictions on permissible geometric error. As a result, shimming procedures (methods by which the distortions induced on the main magnetic field, B0, are remedied) are requiring greater flexibility and corrective range. Shimming methods can be broadly classified into passive (using materials with magnetic properties to remedy field distortions through their passive response to B0) and active techniques (utilizing strategically placed and energized electric coils to produce corrective magnetic fields). Both these techniques have promise to address the additional challenges brought about by the changing MRI landscape. This work reviews traditional shimming methods and principles, and gives an overview of new and novel approaches to this ever-important issue in MRI. Keywords: MRI, shim, passive, active, high-order

Hybrid PET/MRI insert: B0 field optimization by applying active and passive shimming on PET detector level.

Combining PET and MRI into a hybrid device is challenging since both systems might influence each other. A typical interference problem of such a combined device is the distortion of the MRI’s B0 field distribution due to the material brought inside the MRI’s FOV which is in particular challenging for small-bore PET-systems. High field homogeneity is needed for a good MRI acquisition in general as well as in certain applications. Typically, active shimming using dedicated coils is applied to improve the field homogeneity. However, these techniques are limited especially for localized distortion profiles with higher-order characteristics caused by PET/MRI inserts. As a consequence, we are exploring the potential application of shimming on PET detector level (for the Hyperion-IID PET/MRI insert), meaning that the distortion profile caused by PET modules is compensated using additional magnetic materials (passive shimming) and DC coils (active shimming). To explore the technique, B0 field measurements have been performed using a whole-body phantom in combination with the MRI body coil. An FFE sequence was used to measure distortion maps of DC loops and small magnetic objects (capacitors, ferrites). These distortion maps served as input for a software framework which has been written to perform the field optimization. The implementation was verified by measurements and fits were performed to extract characteristic parameters of the tested objects. Finally, the implemented software framework was used to homogenize a measured distortion map produced by a single PET module by superimposing distortion corrections from additional simulated materials. The resulting superimposed distortion map showed a significantly improved B0 field map quality (reduced spectral width and improved homogeneity). The simulated susceptibility distribution will be applied on PET module level and tested in experiments. Results and details about this study will be presented at the conference.

Formulation of the spherical harmonic coefficients of the entire magnetic field components generated by magnetic moment and current for shimming

For MRI and NMR magnet design, a highly homogeneous and high magnetic field has to be achieved by active and/or passive shimming. The active and passive shimming commonly homogenize the magnetic field around the magnet center by cancellation of the higher terms of a spherical harmonic series than the 0th term. So far, the spherical harmonic expression in the cylindrical coordinate system is well known for a circular coil, a solenoid coil, and magnetization of ferromagnetic material with/without its volume. In a shimming design, only the z-component of an inhomogeneous magnetic field is compensated because it is dominant to the performance of MRI/NMR. However, various kinds of MRI and NMR systems have recently been developed, and these magnets sometimes have an axially asymmetric configuration or generate a tilted magnetic field. Therefore, the entire x-, y-, and z-components have to be homogenized for such magnets. I derive the spherical harmonic expression of the entire components of magnetic field generated by a circular coil, a dipole coil, and a straight line current. In addition, since the entire magnetization components of the ferromagnetic material having the volume contribute the entire components of the magnetic field around the magnet center, I also derive the equations of the spherical harmonic coefficients of the magnetic field generated by ferromagnetic material. Since these equations need a numerical integration, such as the Gauss quadrature integration, the computation accuracy of the spherical harmonic coefficients is investigated against the number of the evaluation points. We can calculate the highly accurate spherical harmonic coefficients with the small number of the evaluation points.

Passive Shimming for Magic-Angle-Spinning NMR

The superconducting dipole magnets wound with HTS wires have been developed for a magic-angle-spinning NMR. The magnetic field of the dipole magnets is tilted from z-axis. Since the highly homogeneous magnetic field is required, the magnetic field of the dipole magnets is necessarily compensated by passive and/or active shimming. However, the compensation of all the components has not been reported. Usually, due to the axial symmetry of a solenoid magnet, only z component of the magnetic field is homogenized. In this paper, all the x, y, and z components of the magnetic field generated by the superconducitng dipole magnet are compensated because of the tilt from the z-axis.

Optimization of Active Shimming for Magnetic Resonance Imaging Magnet

An iterative method of active shimming has been presented, which is based on the Laplaces Spherical Harmonics and the least square theory. This approach makes the inhomogeneity of magnetic field to acceptable restriction. With analysis of the method, this paper gives the computer-aided program. The simulation results approve that the method is feasible and valid. Because of its simple and easy to implements, this approach can also be used for the shimming of the other magnets such as the nuclear magnetic resonance magnets.

WE‐G‐WAB‐07: Commissioning of a Novel Integrated Platform for Online MRIgRT

Purpose: An integrated system for online MRIgRT comprising an MR scanner‐on‐rails proximal to a Varian TrueBeam linac is currently under installation at our institution. This study presents the development of a procedure to commission this platform along with the synthesis, testing, and validation of several unique tools/methods central to this challenging frontier. Methods: The commissioning procedure is organized into three phases: 1) the linac and a modified patient couch are commissioned in the absence of magnetic fields; 2) the MR magnet is energized, followed by experimental field mapping and verification of linac/couch performance proximal to the magnet; 3) MR imaging is evaluated and integrated guidance functionalities are tested. Novel methods/technologies embedded in these steps include: magnetic field finite element simulations to confirm magnetic decoupling of the MR scanner, linac, and couch; development of a novel harmonic distortion analysis/shim evaluation technique and associated phantom design incorporating comprehensive imaging QA; simulation of patient‐induced susceptibility distortions and pulse sequence optimization; development of a phantom/method to evaluate the accuracy/stability of MR scanner/couch travel. Results: The finite element simulations of the MRIgRT platform indicated acceptable magnetic forces on critical couch/linac components, undisturbed x‐ray beam production, and acceptable field uniformity within the MRI active volume (via active shimming). Validation of the harmonic distortion analysis demonstrated that complete volumetric mapping of the geometric distortion could be performed with an error bound by the imaging voxel size. Susceptibility‐induced distortions were simulated for various anatomical sites and can be reduced to within 1–2 mm by increasing the frequency encoding gradient strength with acceptable SNR losses. Lastly, the accuracy of translation and rotation measurements was established for evaluating MR scanner/couch travel. Conclusion: A comprehensive procedure has been established for the commissioning of an integrated MRIgRT platform, and various key tools/methods for assessing system performance have been developed and tested. J. Winter and L. Petropoulos are employees of IMRIS. J. Marle and M. Sweitzer are employees of Varian Medical Systems. IMRIS and Varian are companies co‐developing the MRgRT system. Funding for the MRgRT project at Princess Margaret Hospital was provided by the Canadian Foundation for Innovation.

3-D Field Mapping and Active Shimming of a Screening-Current-Induced Field in an HTS Coil Using Harmonic Analysis for High-Resolution NMR Magnets

A screening-current-induced field (SCF) in a superconducting magnet is now considered as one of the major technical challenges for HTS (high-temperature superconducting) magnets, particularly wound with tape-shape conductors such as Bi2223 and YBCO, to be used for NMR (nuclear magnetic resonance) applications where a ppb (part-per-billion) level of field homogeneity is required. To date, many attempts to characterize the SCF and minimize its impact on field homogeneity have been undertaken, but it is still one of bottlenecks for HTS NMR magnets. In general, magnetic fields generated by an NMR magnet are expressed by the spatial harmonics in order to systematically characterize the field errors and obtain a target field homogeneity by shimming. Thus, it is important to analyze the spatial harmonics of the SCF in an HTS magnet for its application to a high-resolution NMR device. In this paper, magnetic fields of an HTS coil were measured within a target space using an in-house 3-D field mapper, and their spatial harmonics were obtained using associated Legendre equations. Also, the temporal behavior of the SCF was investigated by continuous field mappings and their analyses. Finally, a radial shim coil, ZY, was designed, constructed, and operated with the HTS test coil, and the hysteresis and the temporal behavior of the SCF during shimming were also studied. With a shim coil current, the ZY gradient of the SCF was reduced by 70%.

Bulk and Plate Annulus Stacks for Compact NMR Magnets: Trapped Field Characteristics and Active Shimming Performance.

We have constructed two "annulus" magnets, YP2800 and YB10; each consists of 2800 YBCO thin square "plate annuli" (YP2800) and 10 YBCO thick "bulk annuli" (YB10). Their trapped field characteristics, spatial and temporal, were investigated and compared, experimentally and analytically. Two sets of field-cooling tests were performed at 77 K: (1) maximum trapped field tests, where a 2-T background field was applied to investigate the maximum trapped field capability of the two magnets; and (2) reduced trapped field tests, where spatial homogeneity improvement of the two magnets was investigated after field cooling with a reduced background field. Also, a Z1 copper shim coil was designed, constructed, and operated, alone and with YP2800 and YB10. When it was operated with the annulus magnets at 77 K, a significant attenuation of the shim coil strength was observed due to the screening currents induced within the annulus magnets.

A novel design methodology for active shim coil

A novel design approach for active shimming coils for superconducting magnets is proposed to compensate for the previous ten components of the field deviation. The analytic method is first used to obtain the topologies of coils of various order fields and establish a coil model. Then the particle swarm optimization method is adopted to optimize parameters, and the deviation of the magnetic field is taken as the fitness function for minimization of the bias of a magnetic field. The results from the analytic method are taken as a reference to set the initial value ranges of parameters. The results have shown that, compared with the traditional analytic method, the coils with this method can generate a field of better quality. Also the method involves less internal memory and CPU usage than the pure numerical algorithm. In addition, it has fast searching ability and demonstrates high efficiency; and the global solution can be effectively found, which facilitates directly winding.

Active Shim Design of a 7 T Highly Homogeneous Superconducting Magnet for Lanzhou Penning Trap

Lanzhou Penning Trap (LPT) is now being developed for precise mass measurements in Institute of Modern Physics (IMP). Homogeneity of magnetic field in LPT was about 3 ppm when without active shimming, while the required value is less than 0.5 ppm. Linear programming algorithm was employed to design a 9-coil cylindrical shim set for main magnet in LPT. First, mesh on the cylinder and current paths are expressed by connectings between the grid nodes. Then current paths are calculated to compensate the high order components of magnet field through linear programming algorithm optimization. The resulting designs are relatively sparse and can be readily constructed. The method has good flexibility, which can uses current paths on any given surface to generate any order shim field and set allowable errors separately over different arbitrary regions of interest (ROI). Software simulation is used to evaluate the influence on field due to bend corners and limited current density for actual windings.

Geometric distortion and shimming considerations in a rotating MR‐linac design due to the influence of low‐level external magnetic fields

This work investigates with simulation the effect of external stray magnetic fields on a recently reported MRI-linac hybrid, which by design will rotate about the patient axis during therapy. During rotation, interactions with magnetic fields from the earth or nearby ferromagnetic structures may cause unacceptable field distortions in the imaging field of view. Optimal approaches for passive shimming implementation, the degree and significance of residual distortion, and an analysis of the active shimming requirements for further correction are examined. Finite element simulations were implemented on two representative types of biplanar magnet designs. Each of these magnet designs, consisting of a 0.2 T four-post and a 0.5 T C-type unit, was simulated with and without an external field on the order of the earth's field (0.5 G) over a range of rotated positions. Through subtraction, the field distribution resulting from the external field alone could be determined. These measured distributions were decomposed into spherical harmonic components, which were then used to investigate the effect of their selective removal to simulate the effects of passive and active shimming. Residual fields after different levels of shim treatment were measured and assessed in terms of their imaging consequence. For both magnet types, the overall success of a passive shim implementation was highly dependent on the orientation for which it was based. If this orientation was chosen incorrectly, the passive shim would correct for the induced fields at that location, but the overall maximal distortion at other locations was exacerbated by up to a factor of two. The choice of passive shim orientation with the least negative consequence was found to be that where the magnet B(0) axis and transaxial component of the external field were aligned. Residual fields after passive shimming and frequency offset were found to be low in the simulated scenarios, contributing to <1 mm of distortion for most standard imaging sequences (based on a 0.5 G external field). However, extremely rapid single-shot sequences could be distorted by these residual fields to well over 5 mm. These residuals when analyzed were found to correspond primarily to second-order spherical harmonic terms. One term in particular was found to account for the vast majority of these residual fields, defined by the product of the two axes perpendicular to the axis of rotation. The implementation of this term would allow the resulting geometric distortion to fall to the order of 1 mm, even for single-shot sequences. After appropriate passive shimming, the imaging distortion due to an external field of 0.5 G was found to be important only in rapid single-shot sequences, which are especially susceptible to field inhomogeneity. Should it be desirable to use these sequences for real-time tracking, made conceivable due to the lower susceptibility concerns at low field, these residual fields should be addressed. The ability to use only one second-order term for this correction will reduce the cost impact of this decision.