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Logo of nihpaAbout Author manuscriptsSubmit a manuscriptNIH Public Access; Author Manuscript; Accepted for publication in peer reviewed journal;
Magn Reson Med. Author manuscript; available in PMC Sep 1, 2012.
Published in final edited form as:
PMCID: PMC3136546
Multi-Coil Shimming of the Mouse Brain
Christoph Juchem, Peter B. Brown, Terence W. Nixon, Scott McIntyre, Douglas L. Rothman, and Robin A. de Graaf
Yale University School of Medicine, Department of Diagnostic Radiology, MR Research Center (MRRC), 300 Cedar Street, New Haven, CT 06520, USA
Address correspondence to: Christoph Juchem, MR Research Center (MRRC), 300 Cedar Street, TAC N142, New Haven, CT 06520, USA, Phone: +1 (203) 785-7021, Fax: +1 (203) 785-6643, christoph.juchem/at/
MR imaging and spectroscopy allow the non-invasive measurement of brain function and physiology, but excellent magnetic field homogeneity is required for meaningful results. The homogenization of the magnetic field distribution in the mouse brain (i.e. shimming) is a difficult task due to complex susceptibility-induced field distortions combined with the small size of the object. To date, the achievement of satisfactory whole brain shimming in the mouse remains a major challenge.
The magnetic fields generated by a set of 48 circular coils (diameter 13 mm) that were arranged in a cylinder-shaped pattern of 32 mm diameter and driven with individual dynamic current ranges of ±1 A are shown to be capable of substantially reducing the field distortions encountered in the mouse brain at 9.4 Tesla. Static multi-coil shim fields allowed the reduction of the standard deviation of Larmor frequencies by 31% compared to second order spherical harmonics shimming and a 66% narrowing was achieved with the slice-specific application of the multi-coil shimming with a dynamic approach. For gradient echo imaging, multi-coil shimming minimized shim-related signal voids in the brain periphery and allowed overall signal gains of up to 51% compared to spherical harmonics shimming.
Keywords: rodent brain, magnetic field modeling, shimming, spherical harmonic functions, dynamic shim updating
The mouse brain is the prime target for studying neurodegenerative disorders such as Parkinson's, Huntington's and Alzheimer's disease and plays an essential role in neuroscientific research of brain function and physiology. Magnetic resonance imaging and spectroscopy allow the retrieval of a variety of relevant anatomical, physiological and biochemical properties from the brain in a non-invasive fashion and the mouse model has been proven useful for studying the underlying mechanisms of the brain's metabolism in vivo.
High-quality magnetic field homogeneity is an essential prerequisite for most MR imaging and spectroscopy applications to guarantee, among others, the correct spatial registration, the best signal strength and optimal spectral resolution (1). Unfortunately, the homogenization of magnetic field distributions (i.e. shimming) of the mouse brain is a difficult task. Air-tissue interfaces e.g. between the auditory cavities and the brain create complex, strong and localized magnetic field distortions.
‘Passive shimming’, i.e. the strategic placement of magnetized pieces, has been shown to be capable of correcting a large part of the magnetic field distortions observed in the mouse brain (2). The labor-intensiveness of the method and the lack of flexibility to account for specific conditions in single experiments such as inter-subject variation in brain anatomy or head positioning might be reasons why passive shimming to date has not prevailed in experimental setups.
The most widely used shim method called ‘active shimming’ generates shim fields by driving coils with electric current. Fast and accurate field alterations are accomplished by changing the currents through the field producing coils and enable the method to account for experiment-specific conditions. To date, dedicated coils are used for active shimming, each of which provides a magnetic field shape to resemble one of the low order (n≤4) spherical harmonic (SH) functions. In practice, however, the available sets for active SH shimming are often times limited to first and second order SH terms only. The exclusive use of SH-shaped magnetic fields for shimming has been accepted by the MR community as a historical given for the last 60 years. If the SH functions are motivated in the literature at all, this is done by the notion that they form an orthonormal basis set satisfying Laplace's equation (3,4). An infinite series of SH terms with unconstrained amplitudes is indeed capable of modeling arbitrary field shapes. However, the realization of such field modeling system is not possible experimentally due to the infinite number of necessary coils and because efficiency (i.e. the generated magnetic field amplitude per unit current) faces increasingly strong limitations for higher order SH terms (4). The acceptance of the limitation of SH basis sets to low order terms corresponds to the assumption that the apparent field distortions can be satisfactorily modeled with the available low order SH field terms. However, given the large number of studies dedicated to whole brain shimming (2,5-11) this is clearly not the case in the human nor the rodent brain. Active shimming with low order SH basis sets is capable of compensating for shallow, large-scale magnetic field distortions, but it is not able to fully address the complex field distortions with localized hot spots as they are observed in the human (11) or the rodent brain (1).
Due to the lack of satisfactory whole brain SH shimming, in reality, the shim procedures as well as the subsequent MR experiments are often times limited to single brain slices (12,13) or cubic volumes (14-17) to better explore the capabilities of the SH functions. Efficient methods have been presented to provide fast and reliable magnetic field optimization in these selected geometries (12,13,16).
Dynamic shim updating (DSU) employs this principle for the homogenization of larger volumes by breaking them down into subvolumes such as single slices or voxels that are compatible with the MR experiment (5,7,18). The fast adjustment of volume-specific shim settings then allows the optimization of the magnetic field homogeneity in larger volumes based on the improvement in the constituent subvolumes within the same experiment. Switched SH shim coils typically generate a multitude of eddy current-related artifactual magnetic fields due to their proximity to the scanners' cold, conducting structures. Even if eddy current-related fields are compensated diligently (10) and although dynamic SH shimming is more powerful than static global SH shimming, it is still limited to relatively simple magnetic field distortions that do not adequately approximate the complex magnetic field distortions encountered in the mouse brain (19).
Due to limitations in whole brain shimming of the mouse, regions-of-interest for MR experiments are typically chosen small compared to the size of the brain and placed well inside the brain. The corresponding (static) shim areas, therefore, can avoid the vicinity close to the brain surface and more importantly the major distortion areas (14,20-24). Practical whole brain shimming of the mouse brain has not been achieved yet with any method, nor has whole brain slice shimming that is not limited to arbitrary, e.g. cubical or elliptical subsections.
The SH functions are only one of many possible basis sets for the description and synthesis of magnetic fields. The orthogonality of the SH terms has been accepted by the MR community as an essential prerequisite based on early papers (3). However, when magnetic field homogenization is achieved through the use of least-squares methods, orthogonality of the basis set is not a requirement. In this study, a paradigm shift away from the SH functions towards an alternate set of non orthogonal basis functions is proposed. SH shapes for shimming were replaced by a set of generic basis fields generated by circular, electrical coils placed on a cylindrical grid that provides highly localized gradient patterns. It is demonstrated that magnetic field modeling is possible with such an approach and that greatly improved shimming of the mouse brain can be obtained. After the introduction of the multi-coil (MC) concept for the synthesis of low order SH fields (25) here we show that shim fields generated by a set of independent non-SH coils allow improved slice and whole brain shimming of the mouse brain at 9.4 Tesla.
Preliminary results of this work have been published in abstract form (19).
General Experimental Setup
Experiments were performed on a 9.4 Tesla magnet (Magnex Scientific, Oxford, UK) that was equipped with a BFG-150/90-750-S gradient and shim system (Resonance Research Inc., Billerica/MA, USA) interfaced to a Varian Direct Drive spectrometer and operated with VnmrJ 2.3A software (Varian Inc., Palo Alto/CA, USA). Gradient echo images with multiple echo times were measured with a custom-made imaging and field mapping sequence (echo time 2.1 / 2.2 / 2.3 / 2.6 / 3.1 / 4.1 / 5.1 ms, repetition time 1.2 s, field-of-view 15 × 15 × 22 mm3, matrix 75 × 75 × 44). Phase maps were calculated using voxel-by-voxel temporal phase unwrapping and field maps were computed using linear regression of signal phase and echo time (1) in combination with an echo-time exclusion algorithm for the minimization of frequency noise (25).
48-Channel Multi-Coil Setup
A total of 48 circular, constant-current coils (30 turns, center diameter 13 mm, resistance 0.15 Ohm) were distributed in 6 rings of 8 coils on a cylinder-shaped pattern with a ring-to-ring distance of 11 mm (Fig. 1, left). The coils with an effective thickness of approximately 3 mm were made of heavy armored polythermaleze copper wire (Belden Electronic Division, St. Louis/MO, USA) of 0.4 mm diameter and mounted on the inside of an acrylic, cylindrical former with an inner diameter of 35 mm (Fig. 1, right). A fundamental property of the MC approach is that the field shaping capacity does not critically rely on the exact number, size and positioning of the applied coil setup or the geometry of the individual coils as long as a reasonably large number of coils is used that creates a sufficiently large parameter space (25). The number of applied coils was increased from 24 (in (25)) to 48 in this study for improved field modeling capacity over an extended space range and was limited by the number of available current power-supplies. The size and the positioning of the individual coils was chosen to closely surround the center part of the cylindrical volume and to provide localized and large scale gradient field patterns in volumes covering a mouse head. In-house developed and built amplifier electronics allowed well-defined current alterations in the individual, low-inductance (10 μH) coils over the full dynamic range of ±1 A in as little as 10 μs (26). The amplifier system consisted of a controller and 3 identical amplifier boards. Each amplifier board contained 16 digital-to-analog converters along with 16 constant current power amplifiers. A standard constant current topology where the demand current generated by the digital-to-analog converters was compared to that of the sampled current through the coil via a precision shunt resistor provided a current stability better than ±50 ppm over an hour continuous usage. Notably, no significant coil-to-coil interactions or eddy currents were observed as a result of the fast MC field switching most likely due to the low inductances of the individual coils relative to the driving capabilities of the amplifiers as well as the separation of the MC unit from the magnet bore (26), respectively. Furthermore, interactions between the scanners' gradient system and the MC setup were found to be negligible (26). C-based software was developed to run on the consoles' Linux computer to control the MC shim interface via the serial port using the RS232 protocol. A custom-built Bolinger RF coil (27) was placed inside the MC setup to surround the head of the mouse and was used for RF transmission and signal reception.
Fig. 1
Fig. 1
Technical drawing (left) and experimental realization (right) of the MC setup for magnetic field homogenization of the mouse brain at 9.4 Tesla. The head of the mouse is surrounded by a Bolinger RF coil and the MC setup on the outside of the RF coil. (more ...)
Each MC channel was calibrated based on 11 independent 3-dimensional field mapping experiments that covered the dynamic range of the corresponding current power supply as described in (25). Similarly, the first and second SH order terms of the scanners' gradient and shim system were calibrated to allow the comparison of the MC approach with SH shimming that was provided by the conventional gradient and shim system. The dynamic range of the SH shim coils was determined to be X = ±6407 Hz/cm, Z = ±6657 Hz/cm, Y = ±6603 Hz/cm, X2-Y2 = ±484 Hz/cm2, Z X = ±683 Hz/cm2, Z 2 = ±5294 Hz/cm2, Z Y = ±689 Hz/cm2, XY = ±474 Hz/cm2. The average error of the linear regression between the applied shim settings and the generated SH terms was < 0.5% in all cases.
Global and Slice-Specific Shimming of the Mouse Brain
The performance of three different shimming techniques for the homogenization of the in vivo mouse brain (7 mice, 24 ± 1 g, mean ± S.D.) at 9.4 Tesla was compared. Static whole brain shimming with static zero to second SH order functions was done as well as static MC shimming. Furthermore, magnetic field distortions were analyzed over brain sections in axial slices and slice-specific dynamic MC (DMC) shimming was applied in a DSU-style approach.
All mice were maintained and experiments were performed in accordance with the Institutional Animal Care and Use Committee of Yale University School of Medicine. The computational extraction of the mouse brain for the shim analysis was achieved by a combination of image and reliability based criteria including a minimum signal-to-noise ratio, a maximum frequency (i.e. magnetic field) error and a minimum cluster criterion (25). Constrained least-squares fitting based on the Levenberg-Marquardt method was applied for magnetic field decomposition of the whole brain or single slices thereof into sets of basis fields and the determination of the corresponding coil currents for shimming. Through-slice magnetic field components were minimized in the slice-specific field analysis for DMC shimming by inclusion of the brain voxels from immediately neighboring slices into the fitting procedure. For global static MC shimming, a single set of 48 individual current values was loaded to the MC shim interface. The corresponding currents were generated by 48 individual amplifiers and stayed on during the entire experiment. For slice-specific DMC shimming, slice-specific sets of MC currents were loaded to local memory of the MC shim interface and applied under the control of the pulse program in a slice-specific fashion via real-time TTL pulses from the scanner (26).
Global static SH shimming of the mouse brain was achieved with the scanners' gradient and shim system. The shim settings were derived from the SH field components detected in the mouse brain using the full calibration matrix of the SH coil system, thereby also taking the cross-term imperfections of the SH coils into account (10). All SH and MC shim fields were determined from the a single reference field map from the beginning of each study with no shim fields applied.
The magnetic field homogeneity of the seven mouse brains after shimming was assessed by the standard deviation (S.D.) of the Larmor frequency distribution and the spans including 80%, 85%, 90%, 95% and 98% of the frequency values (10). The analysis of the different shim scenarios was always applied to the same voxels of the extracted brain volume from the reference scan of the considered mouse to ensure comparability of the results. Only obvious outliers with frequencies larger than 4 times the span including 99% of the frequency distribution were excluded (corresponding to less than 0.02% of the voxels) to prevent adulterant effects on the S.D. of the frequency distribution.
Impact of Shimming on Gradient Echo Imaging
The impact of the different shimming techniques on the quality of gradient echo images was evaluated at echo times typically used for functional MRI at 9.4 Tesla (echo times 15 / 20 ms, repetition time 1.1 s, field-of-view 15 × 15 × 22 mm3, matrix 75 × 75 × 44, resolution 0.2 × 0.2 × 0.5 mm3). To this end, axial images were acquired after shimming with one of the three techniques, i.e. in the presence of global static SH, global static MC or slice-specific DMC shim fields. The image quality was then assessed qualitatively by means of the existence of signal dropout in brain areas as well as quantitatively through the whole brain signal strength.
Magnetic Field Distortions in the Mouse Brain at 9.4 Tesla Before Shimming
The extraction of the seven mouse brains revealed target volumes for shimming of 23179 ± 1307 voxels corresponding to 0.464 ± 0.026 mL (mean ± S.D., Fig. 2A). The frequency spans covering 80%, 85%, 90%, 95% and 98% of the brain voxels before shimming were determined to 260 ± 21 Hz, 296 ± 24 Hz, 338 ± 21 Hz, 410 ± 21 Hz and 505 ± 31 Hz (mean ± S.D.), respectively, and the standard deviation of the brains' frequency distribution was measured to 100 ± 6 Hz (mean ± S.D.). Even before shimming, the magnetic field distributions were dominated by the localized susceptibility-induced field perturbations close to the auditory cavities and multiple other peripheral brain areas (Fig. 2B). The distortion patterns were similar for all mice and the variations of the frequency measures were correspondingly small (S.D. / mean < 10%).
Fig. 2
Fig. 2
Magnetic field homogenization of the mouse brain at 9.4 Tesla with different shimming techniques. (A) A three-dimensional anatomical image of the head of the mouse allowed the extraction of the mouse brain (overlayed in purple). (B) Reference field map (more ...)
Shimming of the Mouse Brain with Static Spherical Harmonic Fields
The zero to second SH order terms X, Z, Y, X2-Y2, ZX, Z2, ZY and XY were determined as 178 ± 12 Hz/cm, -25 ± 55 Hz/cm, -220 ± 64 Hz/cm, -31 ± 20 Hz/cm2, -8 ± 24 Hz/cm2, 13 ± 77 Hz/cm2, -88 ± 63 Hz/cm2 and -2 ± 9 Hz/cm2, respectively (mean ± S.D.). Static zero to second SH order shimming of the mouse brain reduced the frequency span measures to 152 to 409 Hz, and the S.D. to 69 Hz (Table 1). The experimental results accurately resembled the theoretical predictions of the field analysis procedure with an average deviation of the frequency measures of 7 Hz or 3% (Table 1, column 3). The shallow components of the magnetic field distributions could be removed with static SH shimming, but multiple high amplitude spots remained as well as multiple broad band transitions throughout the brain to connect them (Fig. 2C).
Table 1
Table 1
Comparison of global zero to second SH order, global MC and slice-specific, dynamic MC shimming of the mouse brain at 9.4 Tesla. Theoretical predictions and experimental results (in Hertz, mean ± S.D.) of the 80%..98% frequency width measures (more ...)
Shimming of the Mouse Brain with Static Multi-Coil Fields
Shimming of the mouse brain with static shim fields that were generated with the MC approach further reduced the frequency span measures to 84 to 316 Hz, and the S.D. to 48 Hz. Theoretical predictions and experimental results largely matched with an average deviation of the frequency measures of 4 Hz or 3% (Table 1, column 6). The magnetic field distributions were largely flat after static MC shimming, however, the confined and high amplitude field spots, e.g. close to the auditory cavities, could only be partially compensated since the shape of these localized field gradients exceeded the modeling capability of the static MC approach (Fig. 2D).
Slice-by-Slice Shimming of the Mouse Brain with Dynamic Multi-Coil Fields
The dynamic updating of slice-specific shim settings with the DMC approach allowed the best removal of the apparent field inhomogeneities in the mouse brain and a further reduction of the frequency span measures to 36 to 148 Hz. The S.D. of the frequency distribution after shimming was 23 Hz. The frequency measures of the theoretical prediction and the experimental results of DMC shimming deviated on average by 5 Hz or 8% (Table 1, column 9). With DMC shimming, not only the shallow components of the original field distribution of the mouse brain could be removed, but also most of the localized field distortions from multiple parts of the brain (Fig. 2E).
The full ±1 A dynamic range of the current amplifier system was frequently applied for optimal results in both, static and dynamic MC shimming. Note that in contrast to SH shimming, the lack of orthogonality of the applied MC fields in combination with the non-linear constrained optimization of the shim fields allowed optimized shim results even if individual current requirements exceeded the available dynamic range. The combined power dissipation of all 48 coils for static and dynamic MC shimming stayed below 5 Watts in all experiments and no active cooling was necessary.
Impact of Shimming on Gradient Echo Imaging
Figure 3 shows a selection of axial images with a slice thickness of 500 μm at an echo time of 15 ms that cover the mouse brain at a 2 mm spacing after global SH shimming (column 2), after global MC shimming (column 3) and after slice-specific DMC shimming (column 4). The anatomical reference images (column 1) were calculated from the multi-echo reference field map data by summation of the magnitude images over all echo times. The inclusion of the minimum echo time delays allowed minimum signal dropout in areas of strong field distortions and the consideration of all 7 images provided high, global signal-to-noise (at a mixed contrast). The acquired images after global SH shimming (column 2) show multiple localized signal dropouts at the brain border at locations that coincide with remaining field variations (white arrows). Not only were these localized signal dropouts strongly reduced with global MC shimming (column 3), but the overall signal intensity over the brain was also improved by an average of 25% over all slices and all mice. Dynamic MC shimming (column 4) further reduced localized signal dropout at the brain boundaries and allowed a 42% average signal increase compared to global SH shimming. Note that consistent scaling for the signal intensities of the slice images allows the direct comparison of the impact of the different shimming techniques on the image quality.
Fig. 3
Fig. 3
Impact of the magnetic field homogeneity on the quality of gradient echo images in the mouse brain at 9.4 Tesla. Multi-slice axial images with a slice thickness of 500 μm were acquired at an echo time of 15 ms after static whole brain SH shimming (more ...)
At 20 ms echo time an average signal increase of 11% over all slices and all mice was achieved with static MC shimming compared to static SH shimming (data not shown). The average signal gain with DMC shimming was 51% compared to static SH shimming. Besides the lower overall signal strength with static SH shimming, the image signal of additional areas that were still visible at 15 ms echo time decayed to the noise level at 20 ms. This effect was minimized with the static MC shimming and with DMC shimming, reasonable signal strength was achieved in all parts of the brain even at 20 ms echo time i.e. signal dropouts that alter the brain outline were avoided.
The paper introduces the generation of complex magnetic field shapes for volume- and slice-shimming with a set of generic, circular coils. The array of localized coils has been shown to allow the reliable synthesis of static and dynamic shim fields that resemble the magnetic field distortions encountered in the in vivo mouse brain at 9.4 Tesla. The combination of generic basis fields that are generated with simple circular coils is shown to be better suited to resemble and compensate the non trivial and high amplitude field distortions in the mouse brain than conventional low order SH shimming. The slice-specific optimization and the application of the MC shimming in a dynamic fashion provided further, major gains in the field modeling capability and resulted in largely improved shimming of the mouse brain.
Since the concept of low SH order shimming does not allow satisfactory results for brain shimming in rodents (and humans), specific passive (2,6,8) and active (9,11) shim methods have been presented in which non-orthogonal, non-SH terms are added to the SH basis that are tailored to field distortions in the most problematic shim areas. The MC shim approach differed from these previous shimming techniques by the use of a generic coil matrix and by a complete refusal of SH shaped terms. The MC field shapes were not specifically tailored to the targeted field distortions like in (11) nor were the basis shapes required to be orthogonal. However, together they provided a repertoire of field shapes that included strong local gradient patterns close to the individual coils and shallow field shapes further away from the coils. The combination of individual coils with the MC approach, therefore, allowed the generation of magnetic fields with a degree of complexity that exceeded the capabilities of traditional SH shim coils. In fact, the low order SH terms just form a subsection of the repertoire of fields that can be generated with the MC approach. To this end, the SH fields could be discarded completely with the presented MC shimming, as they did not add to the available degrees of freedom.
The seven mice in this study had similar weight and predictable head positioning with inter-subject variation of ≤1 mm was achieved through the use of a bite bar. The essential patterns of the anatomy-based and susceptibility-induced field distortions before shimming were similar in all mice which was represented by the standard deviations of the different frequency measures being less than 10% of their average values. The requirements for SH shimming, however, showed major mouse-specific variations (although the limits of the dynamic range of the used SH shim system were never exceeded). In other words, SH shimming was not limited by the available shim field amplitudes, but by the inadequacy of the SH shapes. A down-scaling of the SH coil system from the size of the scanner bore to the size of the applied MC setup would lead to efficiency gains of the SH field generation, but the shapes of the generated fields as well as the shim performance would remain the same as SH fields are self-similar, i.e. they are scalable.
It has been demonstrated previously that the experimental generation of SH (10) and MC (25) fields can be predicted very accurately. The thorough calibration of the MC system is considered key for the determination of all 48 coil currents from a single reference field map. Similarly, the thorough calibration of the scanners' SH shim system allowed the reliable adjustment of the SH shim fields in a single step process. Multiple iterations as reported for SH shimming of the mouse brain in (20) were not necessary. The close congruence of theoretical predictions and experimental results in all mice and for all methods is represented in the low average deviations between them (Tab. 1, columns 3, 6 and 9). The variations of the reported frequency measures themselves, i.e. the S.D. of theoretical predictions and the experimental results in Table 1, therefore, can be attributed to inter-subject differences of the 7 mice with respect to the performance of the considered shim methods.
Spurious signals from outside the brain can pose problems for MR imaging and spectroscopy. Examples include the artificial excitation of the non-brain magnetization due to imperfect RF localization schemes or the spatial reconstruction of lipid signals from outside the brain to brain locations based on the different chemical shift. A commonly applied remedy is the active destruction of the non-brain magnetization before or during the experiment. The DMC shim fields in this study were tailored to the magnetic field distortions in the brain. Shim fields to address strong magnetic field gradients in the periphery of the brain also typically generated strong gradient terms in other parts of the considered slices outside the brain. Depending on the required shim fields, the outer brain components led to very effective phase spoiling that removed the largest part of the non-brain imaging signals (Fig. 3, column 4, slices 4-6) and spectroscopic acquisitions of these slices were essentially free of lipid contaminations (data not shown). Although phase spoiling of non-brain areas has not been the primary focus in this study, the DMC approach has the potential to include the generation of dedicated phase spoiling gradients outside the brain into the brain shimming routine.
Simulations have shown that the inclusion of the third order SH terms for static, global SH shimming of the mouse brain improves the frequency measures by only 7%. The reduction e.g. of the S.D. of the frequency distribution from 69 Hz to 62 Hz can hardly justify the additional effort and expenses that are necessary for the installation of the third order SH terms. The limited improvements of mouse shimming with the inclusion of further low order SH terms other than perhaps for very specialized applications is due to the complexity of the magnetic field artifacts in the mouse brain (Fig. 2C) which is beyond the modeling capability of low order SHs and much higher order SH terms would be required to describe them. The magnetic field shapes of the MC basis set scale from large to shallow local gradients based on the distance and relative positioning of the considered volume-of-interest to the individual MC coil. The availability of strong localized field gradients is the basis for the largely improved field modeling capabilities and the reduction of the homogeneity measures even in the static case (Fig. 2D). Simulations have furthermore shown that second SH order DSU can compete with the static MC shimming as presented in this study. However, the achievable frequency measures are on average still 52% broader than with DMC shimming for the considered axial slicing.
The MC method is by no means limited to the details of the selected coil geometry. Simulations have shown that other matrix coil setups, e.g. with 8 rings of 6 coils, or even completely different coil configurations such as a series of coils spiraling around the used cylindrical former are also possible. Each geometry will have fundamental limitations on the magnetic field complexity that can be realized, but a wide range of configurations are possible to achieve satisfactory magnetic field homogeneity in the mouse brain. However, increased modeling capabilities are expected from further improvements of the MC matrix. A further miniaturization of the coils will be beneficial for the generation of even more localized field patterns that will be even better suited to correct highly confined field artifacts in the mouse brain. Similarly, a cone-shaped former for coil mounting will minimize the distances between the coils and the mouse brain and will facilitate the use of smaller coils. The choice of 48 coils in this study was determined by the available space surrounding the mouse head, the number of available power supplies and theoretical simulations predicting the benefits of (D)MC shimming. Simulations have shown, however, that (D)MC shimming of the mouse brain is also possible with the center 32 coils of the presented setup, i.e. if the outer two rows of coils are removed or not used. Global static MC shimming after removal of a third of the coil matrix is expected to still achieve a 22% average narrowing of the frequency measures compared to SH shimming, but a 23% broadening compared to static MC shimming with 48 coils has to be accepted (data not shown). The reduction of the peripheral 16 coils is expected to make essentially no difference for the outcome of DMC shimming, i.e. a significant reduction of the hardware requirements is possible at no cost if the amplifiers are switchable. Even if good shimming can be achieved over small volumes in uncritical brain areas, limited magnetic field homogeneity still poses the main bottleneck for MR spectroscopy of specific brain areas such as the olfactory bulb (21) or the brain stem of the mouse (28). The MC field modeling approach is capable of synthesizing advanced magnetic shim fields over the whole brain and in selected regions. It has been shown in this study that optimized shim fields generated with the MC approach in axial slices from the olfactory bulb, throughout the entire brain and up to the brain stem largely improved the quality of gradient echo imaging (Fig. 3). However, DMC shimming is by no means limited to axial slices and advanced shim fields can be synthesized in any other slice orientation for MR imaging and spectroscopic imaging or in other volumes such as cubic voxels for MR spectroscopy (data not shown). The dynamic application of MC fields as being presented in this study is possible at the same short time scale of the current switches. In fact, 10 μs is considerably shorter than minimum rise times of state-of-the-art gradient systems in the order of 100 μs and allows the incorporation of dynamic MC shimming into any MR sequence without duration penalty. The MC approach is expected to improve the outcome of MR experiments, especially if the entire brain is considered, and enable studies in brain areas that do not allow meaningful MR investigations so far because of limited magnetic field homogeneity.
Functional MR imaging based on gradient echo methods is particularly sensitive to magnetic field inaccuracies including those that are based on suboptimal shim (29). Global MC shimming has been shown to outperform global SH shimming and led to reduced signal dropout due to intra-voxel phase cancellation (Fig. 3). The dynamic updating of slice-specific MC shim fields allowed a further limitation of in-slice and through-slice field gradients and resulted in largely improved image quality. The major homogeneity improvements that can be realized with MC shimming are expected to directly translate in to improvements of the data quality for functional MR imaging in the mouse brain.
Dynamic MC shimming has been applied to the mouse brain at 9.4 Tesla in this study. The presented setup can be adopted to even higher scanner B0 field strengths through an increase of the number of turns per coil or an increase of the available current range. Notably, the quality of the realizable shim fields was mostly limited by the available basis shapes and less so by the imposed current limitation. Simulations have furthermore shown that similar results can also be achieved in the rat brain. In the same vein, MC shimming has been shown theoretically to allow largely improved shimming of the human brain (30). The experimental realization of (D)MC shimming in the human brain is part of the ongoing research at the Yale MRRC.
A novel shimming technique has been introduced that is based on the combination of generic, non-SH field shapes generated by simple circular coils. The MC field modeling approach enabled the flexible and accurate generation of complex magnetic field shapes and MC shimming was shown to allow largely improved magnetic field homogenization of the mouse brain at 9.4 Tesla compared to conventional low order SH shimming. For gradient echo imaging, static and dynamic MC shimming minimized shim-related signal voids in the brain periphery and allowed overall signal gains of up to 51%. The presented MC shimming technique paves the way for MR applications of the mouse brain as a whole or parts thereof for which excellent magnetic field homogeneity is a prerequisite.
This research was supported by NIH grants R21/R33-CA118503, R01-EB000473 and P30-NS052519. The authors would like to thank Mrs. Bei Wang for expert animal handling.
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