Minimax current density gradient coils: Analysis of coil performance and heating

Standard gradient coils are designed by minimizing the inductance or resistance for an acceptable level of gradient field nonlinearity. Recently, a new method was proposed to minimize the maximum value of the current density in a coil additionally. The stated aim of that method was to increase the minimum wire spacing and to reduce the peak temperature in a coil for fixed efficiency. These claims are tested in this study with experimental measurements of magnetic field and temperature as well as simulations of the performance of many coils. Experimental results show a 90% increase in minimum wire spacing and 40% reduction in peak temperature for equal coil efficiency and field linearity. Simulations of many more coils indicate increase in minimum wire spacing of between 50 and 340% for the coils studied here. This method is shown to be able to increase coil efficiency when constrained by minimum wire spacing rather than switching times or total power dissipation. This increase in efficiency could be used to increase gradient strength, duty cycle, or buildability. Magn Reson Med, 2012. © 2011 Wiley Periodicals, Inc.     

Patient safety concept for multichannel transmit coils

PURPOSE: To propose and illustrate a safety concept for multichannel transmit coils in MRI based on finite-differences time-domain (FDTD) simulations and validated by measurements. MATERIALS AND METHODS: FDTD simulations of specific absorption rate (SAR) distributions in a cylindrical agarose phantom were carried out for various radio frequency (RF) driving conditions of a four-element coil array. Additionally, maps of transmit amplitude, signal phase, and temperature rise following RF heating were measured by MRI. RESULTS: Quantitative agreement was achieved between simulated and measured field distributions, thus validating the numerical modeling. When applying the same RF power to each element of the coil array but systematically varying the RF phase between its elements, the maximum of the SAR distribution was found to vary by a factor of about 15. CONCLUSION: Our results demonstrate that current RF safety approaches are inadequate to deal with the new challenge of multichannel transmit coils. We propose a new concept based on a systematic investigation of the parameter space for RF phases and amplitudes. In this way the driving conditions generating the highest local SAR values per unit power can be identified and appropriately considered in the RF safety concept of a given MRI system.     

Design and fabrication of a three-axis edge ROU head and neck gradient coil.

The design, fabrication, and testing of a complete three-axis gradient coil capable of imaging the human neck is described. The analytic method of constrained current minimum inductance (CCMI) was used to position the uniform region of the gradient coil adjacent to and extending beyond the physical edge of the coil. The average gradient efficiency of the three balanced axes is 0.37 mT/m/A and the average inductance is 827 microH. With maximum amplifier current of 200A and receive signal sweep width of +/-125 kHz, the average minimum FOV using this gradient set is 7.9 cm. The completed coil has an inner diameter of 32 cm, an outer diameter of 42 cm, and a length (including cabling connections) of 80 cm. The entire coil was built in-house. The structure is actively water cooled. Heating measurements were made to characterize the thermal response of the coil under various operating conditions and it was determined that a continuous current of 100A could be passed through all three axes simultaneously without increasing the internal coil temperature by more than 23 degrees C. Eddy current measurements were made for all axes. With digital compensation, the gradient eddy current components could be adequately compensated. A large B(o) eddy current field is produced by the Gz axis that could be corrected through the use of an auxiliary B(o) compensation coil. Preliminary imaging results are shown in both phantoms and human subjects.     

Specific absorption rates and induced current densities for an anatomy-based model of the human for exposure to time-varying magnetic fields of MRI.

A 6-mm resolution, 30-tissue anatomy-based model of the human body is used to calculate specific absorption rate (SAR) and the induced current density distributions for radiofrequency and switched gradient magnetic fields used for MRI, respectively. For SAR distributions, the finite-difference time-domain (FDTD) method is used including modeling of 16-conductor birdcage coils and outer shields of dimensions that are typical of body and head coils and a new high-frequency head coil proposed for the 300-400 MHz band. SARs at 64, 128, and 170 MHz have been found to increase with frequency (f) as f(k) where k is on the order of 1.1-1.2. The tables of the calculated maximum 1 kg and 100 g SAR may be used to calculate the maximum RF currents and/or magnetic fields that may be used in order not to exceed the safety guidelines. Because of the low frequencies associated with switched gradient magnetic fields, a quasi-static impedance method is used for calculation of induced current densities that are compared with the safety guidelines.     

Study of temperature rise in RF irradiation during MR imaging: measurement of local temperature using a loop phantom

Cases have been reported of a local rise in temperature at the patient's skin and of burns occurring during MR imaging. To verify this phenomenon, we created a phantom from agarose, saline, and preservative, and measured the increase in local temperature. In addition, phantoms of limbs of the human body shaped such that a closed loop was formed were also used. The temperature of the phantom was measured for 50 minutes in each state, i.e., where a closed loop was formed and where the loop was incomplete. Moreover, the radio frequency (RF) and gradient fields were set as respectively independent states, and the temperature of the phantom was measured. Results of the experiment showed that temperature changed from approximately 6 degrees to 11.5 degrees in the closed loop part of the phantom, whereas there was no significant change when the loop was incomplete. In addition, with exposure to RF, a significant rise in temperature occurred where the loop was closed, whereas there was no significant increase in temperature in gradient fields. This experiment demonstrated that the increase in temperature as a result of RF irradiation occurred in the closed part of the loop phantom. Consequently, a loop formed in the human body may be subject to burns in the area of contact.     

Radiofrequency power deposition utilizing thermal imaging.

Wavelength effects influence radiofrequency (RF) power deposition distributions and limit magnetic resonance (MR) medical applications at very high magnetic fields. The power depositions in spherical saline gel phantoms were deduced from proton resonance shift thermal maps at both 1.5 T and 3.0 T over a range of conductivities. Phase differences before and after RF heating were measured for both a quadrature head coil and a circular surface coil. A long echo time (TE) pulse sequence with a 3D phase unwrap algorithm provided increased thermal sensitivity. The measured thermal maps agreed with a model of eddy-current heating by circularly polarized oscillating RF fields in a conducting dielectric sphere. At 3.0 T, thermal maps were acquired with a <0.32 degrees C temperature rise at 4 W. Proton resonance shift thermal maps provided a measure of hot spots in very-high-field MR imaging (MRI), in which both the phase sensitivity and signal-to-noise ratio (SNR) were increased. The method provides a means of studying the heat distribution generated by RF coils excited by clinical pulse sequences.     

Three-dimensional time-of-flight MR angiography with a specialized gradient head coil

A gradient head coil has been developed, incorporating two independent gradients within the conventional body coil of the magnetic resonance (MR) system, with reduced rise times (200 μsec) and maximum amplitudes of 37 and 18 mT/m in the z and y directions, respectively. This gradient coil was systematically evaluated by testing two-dimensional (2D) and three-dimensional (3D) time-of-flight (TOF) MR angiography sequences applied to a pulsatile flow phantom simulating a carotid stenosis and the intracranial vasculature. When standard 2D and 3D TOF MR angiography techniques were used to image the carotid stenosis model, dramatic signal loss in the stenotic segment and a large flow void distal to the stenosis were seen. The shorter (3.8 msec) absolute echo times (TEs) achievable with the gradient coil in 3D sequences substantially reduced the phase dispersion and associated signal loss in the region of stenosis. Shorter TEs alone (3.2 msec) did not minimize signal loss, and firstorder flow compensation in the read and section-select directions provided further improvements (despite slightly longer TEs). Reduction of TEs in 2D sequences yielded relatively poor results regardless of the refocusing scheme or TE. This study confirms the predicted benefits of a dedicated coil with improved gradient capabilities for 3D MR angiography. The study suggests the limitations of 2D TOF MR angiography in the evaluation of severe stenoses.     

Planar gradient coil design by scaling the spatial frequencies of minimum-inductance current density

Gradient coil inductance has been remarkably reduced by the minimum-inductance design technique, which minimizes the magnetic energy stored by the gradient coil. The planar gradient coil designed by this technique, however, often has poor magnetic field linearity. Scaling the spatial frequencies of the current density function derived by this method, the magnetic field linearity of the planar gradient coil can be greatly improved with a small sacrifice of gradient coil inductance. A figure of merit of the planar gradient coil has been found to be improved by scaling the spatial frequencies.     

Thermal analysis of titanium drive-in target for D–D neutron generation

Thermal analysis was performed for a titanium drive-in target of a D–D neutron generator. Computational fluid dynamics code CFX-5 was used in this study. To define the heat flux term for the thermal analysis, beam current profile was measured. Temperature of the target was calculated at some of the operating conditions. The cooling performance of the target was evaluated by means of the comparison of the calculated maximum target temperature and the critical temperature of titanium.     

Constrained length minimum inductance gradient coil design

A gradient coil design algorithm capable of controlling the position of the homogeneous region of interest (ROI) with respect to the current-carrying wires is required for many advanced imaging and spectroscopy applications. A modified minimum inductance target field method that allows the placement of a set of constraints on the final current density is presented. This constrained current minimum inductance method is derived in the context of previous target field methods. Complete details are shown and all equations required for implementation of the algorithm are given. The method has been implemented on computer and applied to the design of both a 1:1 aspect ratio (length:diameter) central ROI and a 2:1 aspect ratio edge ROI gradient coil. The 1:1 design demonstrates that a general analytic method can be used to easily obtain very short gradient coil designs for use with specialized magnet systems. The edge gradient design demonstrates that designs that allow imaging of the neck region with a head-sized gradient coil can be obtained, as well as other applications requiring edge-of-cylinder regions of uniformity.     

Practical design of a high-strength breast gradient coil

A high-strength three-axis local gradient coil set was constructed for MRI of the breast. Gradient fields with good uniformity (<10% deviation from the desired gradient) over most of the volume required for breast imaging were generated with efficiencies of up to 3.3 mT/m/A. The coils will allow diffusion breast imaging in clinically acceptable examination times. The electrical design, water cooling system, and fabrication techniques are described. Preliminary tests of the coil included images of a grid phantom and diffusion measurements in a short-T₂ agarose gel phantom.     

Dependence of RF heating on SAR and implant position in a 1.5T MR system

PURPOSE: We evaluated radiofrequency (RF) heating of a humerus implant embedded in a gel phantom during magnetic resonance (MR) imaging for the specific absorption rate (SAR), angle between the implant and static magnetic field (B(0)), and position of the implant in the irradiation coil. METHODS: We embedded a stainless steel humerus implant 2 cm deep in tissue-equivalent loop and mass phantoms, placed it parallel to the static magnetic field of a 1.5T MR scanner, and recorded the temperatures of the implant surface with RF-transparent fiberoptic sensors. We measured rises in temperature at the tips of the implant by varying the SAR from 0.2 to 4.0 W/kg and evaluated RF heating of the implant for its angle to B(0) and its displacement along B(0) from the center of the RF irradiation coil. RESULTS: RF heating was similar for the loop and mass phantoms because the eddy current flows through the periphery of both. As the SAR increased, the temperature at the implant tip increased, and there was a linear relationship between the SAR and temperature rise. The values were 6.4 degrees C at 2.0 W/kg and 12.7 degrees C at 4.0 W/kg. Rise in temperature decreased steeply as the angle between the implant and B(0) surpassed 45 degrees . In addition, as the implant was displaced from the center of the RF coil to both ends, the rise in temperature decreased. CONCLUSION: The rise in temperature in deep tissue was estimated to be higher than 1.0 degrees C for SAR above 0.4 W/kg. RF heating was greatest when the implant was set parallel to B(0). In MR imaging of patients with implants, there is a risk of RF heating when the loop of the eddy current is formed inside the body.     

A comparison between human magnetostimulation thresholds in whole-body and head/neck gradient coils.

Gradient coil magnetostimulation thresholds were measured in a group of 20 volunteers in both a whole-body gradient coil and a head/neck gradient coil. Both coils were operated using both x and y axes simultaneously (xy oblique mode). The waveform applied was a 64-lobe trapezoidal train with 1-ms flat-tops and varying rise times. Thresholds were based on the subjects' perception of stimulation, and painful sensations were not elicited. Thresholds were expressed in terms of the total gradient excursion required to cause stimulation as a function of the duration of the excursion. Thresholds for each subject were fit to a linear model, and values for the threshold curve slope (SR(min)) and vertical axis intercept (DeltaG(min)) were extracted. For the body coil, the mean values were: SR(min) = 62.2 mT/m/ms, DeltaG(min) = 44.4 mT/m. For the head/neck coil, the mean values were: SR(min) = 87.3 mT/m/ms, DeltaG(min) = 78.9 mT/m. These curve parameters were combined with calculated values for the induced electric field as a function of position within the coil to yield the tissue specific parameters E(r) (electric field rheobase) and tau(c) (chronaxie). For tissue stimulated within the body coil, the mean values were: E(r) = 1.8 V/m, tau(c) = 770 micros. For tissue stimulated within the head/neck coil, the mean values were: E(r) = 1.3 V/m, tau(c) = 1100 micros. Scalar potential contributions were not included in the calculation of induced electric fields. The mean threshold curves were combined with the gradient system performance curves to produce operational limit curves. The operational limit curves for the head/neck coil system were verified to be higher than those of the whole-body coil; however, the head/neck system was also found to be physiologically limited over a greater range of its operation than was the body coil. Subject thresholds between the two coils were not well correlated.     

Estimating radiofrequency power deposition in body NMR imaging

Simple theoretical estimates of the average, maximum, and spatial variation of the radiofrequency power deposition (specific absorption rate) during hydrogen nuclear magnetic resonance imaging are deduced for homogeneous spheres and for cylinders of biological tissue with a uniformly penetrating linear rf field directed axially and transverse to the cylindrical axis. These are all simple scalar multiples of the expression for the cylinder in an axial field published earlier (Med. Phys. 8 , 510 (1981). Exact solutions for the power deposition in the cylinder with axial (Phys. Med. Biol. 23 , 630 (1978) and transversely directed rf field are also presented, and the spatial variation of power deposition in head and body models is examined. In the exact models, the specific absorption rates decrease rapidly and monotonically with decreasing radius despite local increases in rf field amplitude. Conversion factors are provided for calculating the power deposited by Gaussian and sinc-modulated rf pulses used for slice selection in NMR imaging, relative to rectangular profiled pulses. Theoretical estimates are compared with direct measurements of the total power deposited in the bodies of nine adult males by a 63-MHz body-imaging system with transversely directed field, taking account of cable and NMR coil losses. The results for the average power deposition agree within about 20% for the exact model of the cylinder with axial field, when applied to the exposed torso volume enclosed by the rf coil. The average values predicted by the simple spherical and cylindrical models with axial fields, the exact cylindrical model with transverse field, and the simple truncated cylinder model with transverse field were about two to three times that measured, while the simple model consisting of an infinitely long cylinder with transverse field gave results about six times that measured. The surface power deposition measured by observing the incremental power as a function of external torso radius was comparable to the average value. This is consistent with the presence of a variable thickness peripheral adipose layer which does not substantially increase surface power deposition with increasing torso radius. The absence of highly localized intensity artifacts in 63-MHz body images does not suggest anomalously intense power deposition at localized internal sites, although peak power is difficult to measure.     

Skin temperature increase during local exposure to high-power RF levels in humans.

The local temperature response of the skin on heating due to prolonged exposure to RF radiation by a surface coil was investigated in five healthy volunteers. Temperature changes induced by RF radiation were measured at the skin of the calf muscle by a fluoroptic probe. Exposure to superficial specific absorption rate (SAR) levels of 6.5, 12 and 22 W/kg resulted in skin temperature increases, the highest temperature recorded was 38.3 degrees C. Although the maximum values of each temperature curve correlated with the applied superficial SAR levels, these values did not exceed the recommended temperature limit for the extremities such as given by the Food and Drug Administration (FDA).     

Reduction of MRI acoustic noise achieved by manipulation of scan parameters – A study using veterinary MR sequences

Sound pressure levels were measured within an MR scan room for a range of sequences employed in veterinary brain scanning, using a test phantom in an extremity coil. Variation of TR and TE, and use of a quieter gradient mode (‘whisper’ mode) were evaluated to determine their effect on sound pressure levels (SPLs). Use of a human head coil and a human brain sequence was also evaluated. Significant differences in SPL were achieved for T2, T1, T2* gradient echo and VIBE sequences by varying TR or TE, or by selecting the ‘whisper’ gradient mode. An appreciable reduction was achieved for the FLAIR sequence. Noise levels were not affected when a head coil was used in place of an extremity coil. Due to sequence parameters employed, veterinary patients and anaesthetists may be exposed to higher sound levels than those experienced in human MR examinations. The techniques described are particularly valuable in small animal MR scanning where ear protection is not routinely provided for the patient.     

Modelling postmortem surface cooling in continuously changing environmental temperature

Heat loss depends on the temperature gradient between body surface and environment. Skin cooling data in the forensic literature are scarce and models for skin cooling have not been developed. The dependence on the environmental temperature is a general problem in modelling postmortem cooling processes; most models of rectal cooling are therefore restricted to constant ambient temperatures. Since surface in contrast to core temperatures are highly sensitive to changes of ambient temperature, a model for skin cooling has to take into account such changes. The present study provides an estimator for the time-dependent function of the temperature decrease of the skin and presents a model of the cooling process. The formulae are developed on the basis of skin cooling data of the exposed skin of the forehead in a 40-year-old female (163 cm, 62.1 kg). The single exponential Newtonian model for the surface temperature T(S) valid for constant environmental temperature T(E):T(S)(t)=(T(S)(0)-T(E))e(-lambda(t))+T(E) is localized to small time intervals. By Taylor series expansions a differential equation directly providing an estimator for the temperature decrease rate lambda is derived. The solution of this differential equation represents the extended Newtonian model valid for non-constant environmental temperatures and non-constant temperature decrease rates. The extended model is tested successfully by reinserting the estimated values for the temperature decrease rate: the reconstructed and the measured skin temperature decrease curves completely overlap each other. The temperature decrease rate is a function of the difference between skin and environmental temperature and of the actual change of the skin temperature. A scatter plot of this function shows a structured cloud of points lying in one plane. The temperature decrease rate can thus be parametrized by a simple affine equation with three coefficients determined by linear regression. Inserting the affine equation in the extended Newtonian model leads to an inhomogeneous, non-linear differential equation which is solved by recursion. With knowledge of the initial temperature and the course of the environmental temperature the decrease of the skin temperature can be predicted with very good results. The model is validated with good results in 12 further experimental skin cooling curves of ten different individuals.     

Temperature and SAR calculations for a human head within volume and surface coils at 64 and 300 MHz

PURPOSE: To examine relationships between specific energy absorption rate (SAR) and temperature distributions in the human head during radio frequency energy deposition in MRI. MATERIALS AND METHODS: A multi-tissue numerical model of the head was developed that considered thermal conductivity, heat capacity, perfusion, heat of metabolism, electrical properties, and density. Calculations of SAR and the resulting temperature increase were performed for different coils at different frequencies. RESULTS: Because of tissue-dependent perfusion rates and thermal conduction, there is not a good overall spatial correlation between SAR and temperature increase. When a volume coil is driven to induce a head average SAR level of either 3.0 or 3.2 W/kg, it is unlikely that a significant temperature increase in the brain will occur due to its high rate of perfusion, although limits on SAR in any 1 g of tissue in the head may be exceeded. CONCLUSION: Attempts to ensure RF safety in MRI often rely on assumptions about local temperature from local SAR levels. The relationship between local SAR and local temperature is not, however, straightforward. In cases where high SAR levels are required due to pulse sequence demands, calculations of temperature may be preferable to calculations of SAR because of the more direct relationship between temperature and safety.     

Minimum maximum temperature gradient coil design

Ohmic heating is a serious problem in gradient coil operation. A method is presented for redesigning cylindrical gradient coils to operate at minimum peak temperature, while maintaining field homogeneity and coil performance. To generate these minimaxT coil windings, an existing analytic method for simulating the spatial temperature distribution of single layer gradient coils is combined with a minimax optimization routine based on sequential quadratic programming. Simulations are provided for symmetric and asymmetric gradient coils that show considerable improvements in reducing maximum temperature over existing methods. The winding patterns of the minimaxT coils were found to be heavily dependent on the assumed thermal material properties and generally display an interesting “fish‐eye” spreading of windings in the dense regions of the coil. Small prototype coils were constructed and tested for experimental validation and these demonstrate that with a reasonable estimate of material properties, thermal performance can be improved considerably with negligible change to the field error or standard figures of merit. Magn Reson Med 70:584–594, 2013. © 2012 Wiley Periodicals, Inc.     

Localization by nonlinear phase preparation and k-space trajectory design

A technique is described to localize MR signals from a target volume using nonlinear pulsed magnetic fields and spatial encoding trajectories designed using local k-space theory. The concept of local k-space is outlined theoretically, and this principle is applied to simulated phantom and cardiac MRI data in the presence of surface and quadrupolar gradient coil phase modulation. Phantom and in vivo human brain images are obtained using a custom, high-performance quadrupolar gradient coil integrated with a whole-body 3-T MRI system to demonstrate target localization using three-dimensional T 2*-weighted spoiled gradient echo, two-dimensional segmented, multiple gradient encoded spin echo, and three-dimensional balanced steady-state free precession acquisitions. This method may provide a practical alternative to selective radiofrequency excitation at ultra-high-field, particularly for steady-state applications where repetition time (TR) must be minimized and when the amount of energy deposited in human tissues is prohibitive. There are several limitations to the approach including the spatial variation in resolution, high frequency aliasing artifacts, and spatial variation in echo times and contrast.