2H transmit–receive NMR probes for magnetic field monitoring in MRI



Measuring image encoding fields in real time and applying the information in postprocessing offer improved image quality for MRI, particularly for applications that are intrinsically sensitive to gradient imperfections. For this task, a stand-alone magnetometer system based on multiple 2H transmit–receive NMR probes has been developed. The conceptual advantages of changing to 2H NMR probes for 1H magnetic field monitoring are elucidated here, and the practical design of the probes is described. In comparison to previous 1H NMR probe-based designs, 2H probes are perfectly decoupled from standard 1H imaging. Utilization of RF shielding or other nonoptimal decoupling schemes is therefore not needed. Probes based on 2H nuclei are also more easily miniaturized for high-resolution imaging. This is particularly important for diffusion tensor and phase-contrast imaging, which rely on strong motion-sensitizing gradients. The presented 2H NMR probes have been shown to fulfill the requirements for accurate 1H imaging down to image resolutions of 0.2 mm. Using susceptibility matching techniques, the probe's B0 inhomogeneity-induced signal dephasing is reduced and monitoring periods beyond 200 msec are achieved. The benefit of real time magnetic field monitoring is highlighted for phase-contrast and non-Cartesian multishot imaging. Magn Reson Med, 2011. © 2010 Wiley-Liss, Inc.

Gradient imperfections, such as eddy currents, (anisotropic) gradient delays, gradient heating, and gradient amplifier nonlinearities, can result in encoding errors and subsequently, image artifacts. Depending on the applied gradient encoding, image quality can be severely degraded. Although the utilization of shielded gradient coils (1) and gradient waveform preemphasis (2, 3) has reduced the level of experienced eddy currents, the limitations of present-day clinical gradient systems continue to plague sequences that use high gradient strengths or rapid gradient switching. Quantitative flow, diffusion, and fast non-Cartesian, single-shot imaging sequences are good examples of such modalities (4–6). In addition, high-resolution imaging relying on stronger gradient strengths and dedicated gradient inserts is hindered in a similar fashion by gradient encoding imperfections (7, 8).

Calibration scans of k-space trajectories can be applied to improve image quality at the expense of increased acquisition time (9–11). Typically, calibration scans are applied for each gradient axis separately and neglect coupling between different gradient axes. Furthermore, the accuracy of calibration scans is impacted by parameter drifts, e.g., heating of the gradient system due to extensive gradient switching (12).

Recently, efforts have been made to develop NMR-based magnetometers for real time magnetic field monitoring, rMFM (13–16). The work conducted with NMR probes has shown the most promising results, and with susceptibility matching techniques, the probes also fulfill the requirement for > 100msec long read-out times (17). To date, work in this area has concentrated on developing probes that are based on 1H samples, because 1H probes are easily integrated into a standard multichannel MRI receiver system.

Transmit–receive NMR probes are preferred to gain independence from imaging sequences and especially the slice-selective radio frequency (RF) excitation (18). Because 1H NMR probes and normal imaging coils operate at the same Larmor frequency, electromagnetic coupling effects come into play. This interference gives rise to undesired image artifacts and inaccuracy in the field monitoring performance. Adding counter-windings to the solenoid coil geometry results in a faster sensitivity drop-off further away from the NMR probe and therefore also reduces coupling to the imaging object to some extent. More effective isolation can be achieved by using thin metal shielding around the probe (19). The drawback of this method is that high-frequency gradient components and eddy current fields are also partially screened. Furthermore, bulky conductive structures in the vicinity of the imaging coil and the patient are undesirable because of potentially reduced image signal-to-noise ratio (SNR) and jeopardized patient safety.

In this work, the advantages of using a low-gamma nonproton NMR probe design are elucidated, and the design considerations of transmit–receive 2H NMR probes for rMFM are presented. Because of a factor of 6.5 smaller Larmor frequency, it is shown that coupling to 1H imaging is effectively eliminated without using RF shielding. Because of larger allowable sample sizes, probe manufacturing becomes simpler, and higher filling factors are achievable. 2H probes are therefore better suited for high-resolution and nonproton imaging.

Multinuclear transmit–receive hardware has been developed for operating the NMR probes; the system is implemented as an independent add-on toolkit, which can be simply connected to normal clinical MRI scanners. The manufactured NMR probes are characterized, and the achieved performance is projected with simulated requirements for field monitoring. The application to rMFM-assisted MRI for improved image quality is demonstrated using circular echo-plans imaging (EPI) and spiral imaging as well as with phase-contrast velocity encoding.


System Requirements for Magnetic Field Monitoring

Simulations were conducted to derive the required specifications for magnetic field sensors for rMFM. Using Fourier gradient encoding, the k -space location (k) at a certain time point after RF excitation (t) is determined by the the gyromagnetic ratio (γ) and the gradient waveform (G) according to:

equation image(1)

A generic MR raw data set was derived from a Shepp-Logan phantom for single-shot EPI k-space trajectory sampling (20). The ideal single-shot EPI k-space trajectory was assumed to precisely follow a Cartesian grid of matrix size 256. Error sources corresponding to linear drift (Δkdrift), random uncertainty in measured k -space location (Δknoise), and timing offsets (t0) were subsequently introduced to the ideal imaging trajectory. Thus, the effective image encoding k-space trajectory (keff) became:

equation image(2)

with FOV describing the field-of-view and Tacq describing the acquisition period. According to Eq. 2, Δkdrift and Δknoise were provided in normalized k-space units of 2π /FOV. Single-shot EPI k -space data were obtained by inverse gridding the Shepp-Logan phantom along the corrupted k -space trajectory. Subsequently, the k-space data were reconstructed via gridding by assuming the undistorted k-space trajectory. To quantitatively study the level of image artifacts, an error norm was introduced according to:

equation image(3)

where i and j are the pixel indices, and Sdist and Strue are the pixel values of the distorted and true image, respectively.

The relationship between |Δknoise| and the field measurement precision (ΔBnoise) can be written as

equation image(4)

where the imaging sampling time is noted as Δt. Typically, the magnetic field sensors are placed close to the edges of the FOV, i.e., |r| ≈ FOV. The factor equation image in the uncertainty of monitoring k-space trajectory arises from the fact that the noise of two magnetic field sensors is assumed to be uncorrelated. The assumption is expected to be justified for NMR probes: of which, noise is coil dominated and the coupling is insignificant because of large probe-to-probe distance.

Similarly, the relationship between field measurement drift, ΔBdrift, and k-space drift can be written as

equation image(5)

Thus, drift-related measurement errors become increasingly detrimental for imaging with longer acquisition periods. Therefore, sensors suffering from high levels of 1/f noise are less suitable for rMFM.

From the simulations, it was found that equation image does not violate the error norm criteria. From Eq. 4, it can be noted that longer imaging sampling intervals set higher precision requirements for field sensing. If imaging and monitoring sampling rates are considered to be separate, the Nyquist limit for the relevant gradient activity limits the minimum monitoring bandwidth, which is considered to be 50 kHz: with this sampling rate, it is obtained from Eq. 4 that ΔB ≤ 2.7μT, i.e., 12 nT/ equation image.

For the maximum applicable measurement drift, a criterion of equation image is obtained with |r| = FOV. In typical MRI experiments, acquisitions can be up to 100 msec long, and the criteria transform to a measurement drift of ΔBdrift ≤ 1.7 nT. Regarding time synchronization, an error of t0 ≤ 40 nsec fulfills the error-norm criterion. The potential magnetometers should also be MRI compatible so as to produce no susceptibility artifacts in images if placed close to or within the FOV. In addition, the complete sensing system should be robust and economically feasible for convenient implementation in standard clinical MRI scanners.

NMR-Based Magnetic Field Monitoring in MRI

Different magnetometer schemes used to measure the background field and gradient profiles in MRI have been developed (14, 21–23). Among the available methodologies (24, 25), NMR probes are considered to best fulfill the requirements estimated in Section “System Requirements for Magnetic Field Monitoring.” The local magnetic field evolution is extracted from the NMR signal's phase, as defined by the Larmor relation. Spatial Taylor expansion can be applied to describe the magnetic field B(r, t): in such a case, the phase of the nth probe's signal becomes:

equation image(6)

Here, ΔB0(t) denotes the time-dependent spatially constant field offset, and ϕn,0 and rn are the intrinsic phase offset and the spatial location of the n th probe, respectively.

According to Eq. 6, a minimum of four probes is required for 3D imaging. With more probes, spatially higher order magnetic field components can also be resolved (26). Before extracting the magnetic field data from the probe signals, the spatial locations and the phase offset must be calibrated. The spatial calibration is done in analogy to tracking localization (27). After exciting the NMR probes, trapezoidal gradient waveforms are subsequently applied along all three spatial dimensions for single-shot, 3D NMR probe localization. Moderate gradient amplitudes and slew rates are applied to minimize undesired gradient waveform distortions.

Signal dephasing during imaging restricts NMR sample sizes. For a cylinder with a length 2Δr that is oriented along the single active gradient axis, the induced signal voltage can be written as:

equation image(7)

where U0 is the signal in the absence of gradient activity. From Eq. 7, 1H NMR sample sizes are constrained to dimensions that are less than twice that of the imaging resolution. In high-resolution imaging (≤ 0.5mm), the sample size restriction can introduce manufacturing challenges and a subsequent loss in signal strength, as achievable filling factors are compromised. Nuclei with smaller values of γ are less shifted in k-space by the image encoding gradients (cf. Eq. 1), and for their benefit, larger sample sizes or higher image resolution become applicable.

In addition to signal drop out, signal unwrapping is another factor that limits continuous tracking of a k-space trajectory. Thus:

equation image(8)

where fm stands for the monitoring bandwidth. The likelihood of a failure increases at stronger gradients. If fm remains fixed, a low-γ nuclei can be exploited for higher applicable gradient strengths or further displaced probes. According to Eq. 5, wider probe separation translates to relaxed precision requirements (cf. Eq. 5). Other benefits of lower γ probes include reduced probe-to-probe coupling and elimination of coupling to the patient and the 1H imaging coils.

NMR Probe Signal-to-Noise Ratio

Optimized solenoid coils provide higher SNR when compared with other geometries of comparable dimensions (28–30). The detected SNR can be derived from Faraday's law of induction: (28, 31)

equation image(9)

Here, U is the signal amplitude, |Ψ| is the receive sensitivity of the RF coil, V is the sample volume, n is the nuclear spin density, equation image = h/2π is the Planck's constant, I is the spin quantum number, kb is the Boltzmann's constant, and T is the temperature. The equivalent noise resistance, Rprobe, consists of the electromagnetic losses in the sample, coil losses, losses of the matching and tuning network, and additional noise that originates from the rest of the sensing hardware. In microcoils with dimensions < 10mm, the coil losses typically dominate Rprobe.

Low-gamma probes can be geometrically scaled up by a factor of γmath formula/γ before they reach the same signal dephasing as a 1H probe for a given |k| (cf. Eqs. 6 and 7). Scaling up the probe dimensions reduces the solenoid coil sensitivity by the same factor. This is understood by studying the sensitivity in the middle of a solenoid coil based on Biot-Savart's law given by (30):

equation image(10)

Here, the integer N stands for the number of turns of the solenoid, μ stands for the permeability of the medium, lcoil stands for the coil length, and dcoil stands for the coil diameter. For the coil resistance, one can derive (30):

equation image(11)

where ρ is the resistivity, and it is assumed that the coil wire diameter, dwire, is much larger than the skin depth, δ. From Eq. 11, it is seen that the scaling up the coil dimensions has no influence on coil resistance, and only the effect of reduced skin depth due to lower γ is observable.

Noise levels are smaller because of the lower γ because sampling bandwidths can be reduced by the ratio of the gyromagnetic ratios. This holds true for 1H imaging bandwidths larger than 50 kHz, which is estimated to be the Nyquist sampling rate for the highest relevant error component. Below this limit, the monitoring bandwidth should match the imaging bandwidth.

The influence of all components affecting the measurement SNR can be combined, and using Eq. 9, the expression for the ratio of low-gamma probe SNR and 1H probe SNR can be derived:

equation image(12)

Thus, only limited reduction in SNR is expected when changing to low-gamma nuclei in NMR probe design. Furthermore, nuclei with a larger spin quantum number can be used for additional SNR increase.

Measurement Uncertainty

The relationship between the probe SNR and uncertainty in the measured NMR phase Δϕ can be written as (14):

equation image(13)

Here, uniformly distributed spectral noise is assumed. By assuming that the monitoring rate fm = γ/γmath formulafs, where fs is the imaging sampling rate, and that |r| = FOV, Eq. 4 can be used to derive 6 and 13 that

equation image(14)

Thus, the SNR requirement becomes independent of the applied MRI acquisition bandwidth. If the bound of equation image from Section “System Requirements for Magnetic Field Monitoring” is inserted into Eq. 14, the SNR of field monitoring should be larger than 50 at the chosen monitoring bandwidth.

Tuned RF coils, MRI low-noise preamplifiers, and RF filters can introduce dispersion-related phase shifts in measured signals. Performed simulations with respect to typical coil designs, combined with S-parameter measurements of the receiver chain, show that the dispersion is essentialy linear over the relative narrow bandwidths of MRI signals with dispersion constants that correspond to time delays of 0.8 −1.6 μsec. Such errors are significant for image reconstruction (i.e., > 40 nsec, cf. Section “System Requirements for Magnetic Field Monitoring”) and should be accounted for during calibration.

NMR Probe Design

Heavy water, 2H2O, was chosen to substitute 1H2O-based NMR samples; the use of 2H2O conveys several advantages. Most importantly, changing to a different nuclei with a different Larmor frequency from 1H completely eliminates coupling and other interferences between the NMR probes and 1H imaging. This consequently eliminates undesired artifacts in the 1H images and also improves the accuracy of field monitoring. The higher nuclear spin quantum number of 1 directly translates to increased SNR as expressed in Eq 12. 2H2O retains the favorable chemical properties of 1H2O, such as high spin density and long T2 relaxation times (T2 = 770msec) that are required for long readout times. Almost identical chemical and magnetic properties allow for the use of the same susceptibility matching methods used in 1H2O NMR probe design.

Susceptibility-matching methods are applied to homogenize the B0 field across the signal droplet and thereby maximize T2* limited readout times (14). The solenoid coil, wound around the sample capillary, was cast into an epoxy whose susceptibility was matched to copper (Fig. 1a). An inert paramagnetic Er3+-based, epoxy-soluble compound was applied to tune the susceptibility of the epoxy. Signal contribution along the capillary was limited by the intrinsic, sharp drop-off, of the coil sensitivity profile along that direction. This technique was found to be more robust to impurities than methods using liquid or solid plugs.

Figure 1.

a: Schematic of the NMR design using the sensitivity profile to constrain the effective sample size along the symmetry axis of the capillary. b: The 2H transmit–receive NMR probe with a low-noise amplifier and a passive duplexer switch.

The coil geometry for optimal SNR was determined using Eqs. 911. The results of the corresponding SNR simulations with various sample sizes and number of turns are shown in Fig. 2. Gradient-induced signal dephasing for different sample sizes was simulated, and the results are shown in Fig. 3. In the simulations, a gradient field was applied perpendicular to the coil's symmetry axes, and the gradient-induced dephasing was altered to match various 1H imaging resolution values. The total signal level was determining by calculating the sensitivity maps using Biot-Savart's law (30) and subsequently summing the signals originating from all spin isochromats in the NMR sample. Figure 3 verifies the assumption that NMR probes with a larger sample diameter are not suited for high-resolution imaging because of undesired signal dephasing at high k-space encoding values.

Figure 2.

Simulated SNR versus the number of solenoid turns for multiple sample diameters. Here, the sample length is equal to the sample diameter; the number of turns is limited by the coil length, which is set to be 1.25 times the sample diameter. The reduction in the SNR curves with a high number of turns is due to the proximity effect, which is enhanced as the increasing number of turns are packed more closely. For comparison, the SNR of an 1H NMR probe with a typical 0.9-mm sample size and optimal geometry is also plotted.

Figure 3.

Signal loss due to field gradient-induced dephasing for various sample sizes. Although a higher baseline SNR is achieved with larger sample sizes, severe signal loss is expected if strong gradients are applied. Optimal SNR coil geometries are used for each sample size, as shown in Fig. 2. For comparison, the performance of an 1H NMR probe with a typical sample size and optimal coil geometry is also plotted.

Based on the performed simulations, NMR probe prototypes with a sample diameter of 1.7 mm and with a filling factor (i.e., sample radius vs. coil radius) of 76% were manufactured. The RF coils had five closely wound turns made of 0.5-mm copper wire. Different wire diameters change the optimal coil geometry but do not significantly affect the achievable SNR. A counter winding-based probe-to-probe decoupling strategy was omitted because it was deemed unnecessary. The minimum applicable resolution with the NMR probes was determined by the drop-off of the coil sensitivity profile along its longitudinal axis of symmetry. In the presented implementation, the sensitivity drop-off corresponded to a minimum voxel dimension of ∼ 0.2mm .

NMR Probe Electronics

The electronic layout of the transmit–receive NMR probes is shown in Figs. 1b and 4. The NMR probes were designed for operation at a 3.0 T background field. Commercial 2H low-input impedance LNAs (Microwave Technology, Fremont, CA) were placed at a distance more than half a wavelength away from the probes themselves (Fig. 4). This slightly longer length permitted the use of low-input impedance preamplifier decoupling in combination with the parallel capacitor at the coil (32).

Figure 4.

The electric schematic of an NMR probe connected via a matching and tuning network and a passive transmit–receive duplexer to the input of a low-noise amplifier. Capacitors Cs and Cp are for matching and tuning of the probe.

The half a wavelength cable construction also functions as part of a duplexer transmit–receive switch (33); a passive duplexer based on crossed diodes was chosen rather than a PIN diode-driven active duplexer for faster switching (∼10 nsec) and reduced implementation complexity. As a trade-off, the transition losses during RF transmission were higher (−4.0 dB at 27 dBm). The passive duplexer implementation makes no compromises with respect to the insertion losses during receive operation.

The NMR probes experience high B1 fields at the 1H frequency during standard imaging sequences. The induced voltage was determined to be nondamaging for the given coil geometries, and the power coupling was negligible because of the narrow resonance bandwidth of the 2H probes. Thus, no additional hardware, such as active detuning or parallel LC resonator-based 1H frequency traps, was required to block 1H excitations.

Independent Transmit–Receive Hardware

For independent operation of the 2H NMR probes, a broadband transmit–receive spectrometer was developed (34). The home-made receiver was based on a digital direct-conversion architecture (cf. Fig. 5) that was implemented with high-speed digitizers (PXIe-5122, National Instruments, Austin, Tx) and PC-based software (LabVIEW, National Instruments, Austin, TX).

Figure 5.

Schematic of a transmit–receive chain required for operating the NMR probes. The ATmega16 microcontroller ensures proper timing of the transmit pulses according to the system's “‘start sequence’” trigger. The microcontroller shares a clock signal with the MRI scanner for increased synchronization. A home-made, medium power, passive duplexer switch is placed between the power amplifier and splitter to avoid any noise coupling from the transmit chain during signal reception.

The transmitter system (cf. Fig. 5) provides hard-pulse excitation of the 2H NMR probes by chopping the output of a frequency synthesizer (PXI-5404, National Instruments, Austin, TX). The full-width-half-maximum bandwidth of the transmit pulses becomes ∼1/(1.21 · Tpulse), where Tpulse is the pulse width. A 5-W power amplifier (ZHL-03-5WF, Mini-Circuits, Brooklyn, NY) provided the desired ∼90° excitations for the considered four-probe configuration in ∼25 μsec. This is insufficient to cover the full Larmor frequency swing that the NMR probes can experience in the presence of strong gradient activity and large object dimensions. Thus, timing circuitry was implemented to accurately control the widths of the RF pulses and to ensure that the NMR probes were excited at time points with no gradient activity.

In the used NMR probes, the dominant RF loss mechanism was the coil resistivity; hence, only a fraction of the applied power was expected to be deposited into a patient. Furthermore, the limited operational power levels with short RF pulse widths ensured that NMR probes did not exceed the federal limits for specific absorption ratio.

A 16-bit microcontroller (ATmega16, Atmel, San Jose, CA), sharing the 10-MHz clock of the MRI scanner, was used for the timing and the RF pulse width control. The 10-MHz clock and the “start” trigger signal were readily available from the MRI system, and no modifications to the scanner were required. For the data acquisitions, timing and synchronization were controlled via the microcontroller circuitry. The measured jitter-induced inaccuracy of 1 nsec in timing is well below the acceptable limit of 40 nsec as dictated by the performance requirements.

Magnetic Field Monitoring Set-Up

MFM experiments in a 3.0-T MRI scanner (GE Healthcare, Milwaukee, WI) were performed using the described 2H NMR probes. Standard imaging phantoms were used, and spin excitation and signal reception were performed using a clinical head birdcage coil (GE Healthcare, Milwaukee, WI). Four 2H NMR probes were equally distributed around the phantom. Imaging experiments were performed using an 16-fold interleaved circular EPI (bandwidth = 250kHz; matrix resolution = 256 × 256; echo-train length = 16; Pulse repetition time (TR) = 2 sec; FOV = 20 cm; and slice thickness = 10 mm) and spiral trajectories (bandwidth = 125 kHz; number of points = 8192; number of arms = 16; TR = 2 sec; FOV = 20 cm; and slice thickness = 10 mm).

Phase-contrast flow quantification relies on bipolar gradient pulses to cause signal dephasing for moving spins. 2H rMFM was applied to monitor all gradient activity following spin excitation. In this way, both the bipolar gradients for flow encoding and the imaging gradients for spatial localization are captured. Phantom-based 2D phase-contrast measurements were performed by applying the following parameters: V ENC = 20cm/sec; FOV = 24cm; slice thickness = 10mm; matrix resolution = 128 × 128; TR = 500ms; flip angle = 60°; and receiver bandwidth = 15.63 kHz.


NMR Probe Performance

Based on S-parameter measurements, the probe-to-probe coupling between the manufactured probes was observed to be less than −50 dB at a displacement of 40 mm or greater. These results verify the prediction that the probe-to-probe coupling in normal operation is well below the SNR limit. Thus, no significant signal or noise interferences were expected, and no further decoupling strategies, e.g., shielding, were required.

Optimal 90° flip angles were achieved with ∼25-μ sec pulse widths, yielding SNR values of equation image and T2 * values up to 250 msec. The favorable difference between acquired and simulated SNR values was due to the larger effective sample volume in the chosen design, where the sample length is restricted by the coil sensitivity profile rather than by physical plugs (as was assumed in the simulations).

The achieved spectral SNR of equation image, with the 1.7-mm sample diameter probes, fulfilled the derived SNR requirement of 50 up to monitoring bandwidths of 100 kHz, i.e., beyond the estimated limit for relevant gradient activity. Thus, it is concluded that the manufactured 2H NMR probes are suitable for effective MFM at any applied MRI acquisition bandwidths with the existing clinical gradient hardware. However, it is expected that the probes would behave suboptimally in monitoring ultra-short TR sequences, as they were optimized for long readouts and therefore possess long T2*, which, when combined with noncoherent RF excitation, yields pseudo-random transverse magnetization. Even in the case of perfect spoiling, a significant reduction in SNR is expected at low TR values. For example, at TR = 0.02 · T1 and perfectly spoiled conditions, steady-state signal level is 20 dB less than it would be at fully-relaxed conditions (35).

Magnetic Field Monitoring

Figure 6 compares axial circular EPI images that are obtained without MFM and image reconstruction based on the nominal, prescribed gradient waveform (a) and MFM with gridding reconstruction based on rMFM-measured k-space encoding information (b and c). Figure 6b was obtained using 1H NMR probes and shows EPI ghosting correction at the expense of additional artifacts caused by the off-resonant 1H droplets inside the NMR probes and detected by the 1H imaging coils. In comparison, Fig. 6c was obtained using 2H NMR probes and illustrates similar image artifact reduction but without causing additional interference effects. These results demonstrate that 2H NMR probes are able to fulfill the stringent requirements for accurate rMFM without introducing undesired interference effects. Figure 7 shows examples of a 2H magnetic field-monitored, 16-fold interleaved circular EPI and spiral k -space trajectories.

Figure 6.

Images of a resolution phantom taken with a circular echo-planar sequence. a: Image with standard gradient performance provided by a 3.0-T MRI scanner. b: The improvement with respect to the reduced level of artifacts when gradient imperfections are corrected based on the data acquired with rMFM probes is shown. c: This is the same setup as with case b, but now the field monitoring data are acquired using 2H -based NMR probes. As observed, coupling between the probes and imaging elements is completely eliminated.

Figure 7.

Monitored real time 2H k-space trajectories. A 16-fold interleaved circular EPI trajectory is shown on the left and and a spiral trajectory is shown on the right.

A phase-contrast imaging experiment was also performed with rMFM hardware. Corresponding velocity maps are shown in Fig. 8 with image reconstruction based on the nominal gradient waveforms (left) and 2H rMFM-measured waveforms (right). 2H rMFM results in significantly more accurate flow maps with a mean value that is very close to zero, as is expected for a static imaging phantom.

Figure 8.

Flow velocity maps of a static phantom without (left) and with (right) rMFM. This was acquired using a 2D phase-contrast sequence with a VENC value of 20 cm/sec. The use of rMFM results in a significantly more accurate flow estimate that is very close to zero, as was expected for a static phantom.


In earlier studies, NMR probes have been successfully demonstrated as accurate magnetometers for rMFM. In this work, novel 2H transmit–receive NMR probes are presented. The technique showed superior performance to 1H probes with respect to coupling to 1H imaging. Coupling artifact-free MR images were obtained without using RF shielding or any other decoupling techniques with suboptimal performance. In particular, RF shields can distort the time-varying fields being measured and can introduce detuning and increased noise in nearby receiver coils. In the worst-case scenario, shielded NMR probes in close proximity to a patient can increase SAR due to RF currents in the RF shield and their associated electric field.

With the appropriate probe design, one can effectively offset the reduction in the SNR that is otherwise expected when using low-gamma nuclei. Although a large NMR sample size is generally desirable for high SNR, in practice, the sample dimensions are limited by gradient-induced signal dephasing. 2H nuclei permit larger sample sizes than do 1H samples because of their lower γ. This simplifies probe construction due to larger permissible filling factors and facilitates the monitoring of pulse sequences with higher effective gradient encoding. The lower gyromagnetic ratio of 2H samples also reduces their susceptibility matching requirements as well as their sensitivity to sample impurities (e.g., air bubbles). These characteristics are beneficial if the probes are miniaturized, or if the probes are placed in highly inhomogeneous magnetic fields or inside imaging coils.

To resolve performance specifications for rMFM systems, forward image encoding and backward image reconstruction simulations were performed based on an ideal, equidistant EPI sampling scheme, which is known to be a particularly sensitive test case for the propagation of gradient imperfections into image artifacts. It was obtained from the simulations that, to keep the artifact-to-image ratio below 40 dB, the measurement precision and linear drift should not exceed the values of ΔBnoiseΔt ≤ 53 pTs and ΔBdriftTacq ≤ 170 pTs, respectively.

The presented 2H probes with a 1.7-mm sample diameter were shown to fulfill the SNR requirements down to 1H image resolutions of 0.2 mm. Higher measurement precision can be achieved with probes with larger samples, though at the expense of lower achievable image resolutions. The T2* values of the NMR samples were optimized for acquisitions with readout windows of up to 100 msec. The probe performance becomes suboptimal for short-TR excitation schemes because of incomplete T1 relaxation and undesired signal coherence effects. To address this issue, a novel operation scheme has been described based on coherent short-TR NMR probe excitation (36).

To operate the 2H NMR probes, a dedicated, transmit–receive system was constructed; the rMFM hardware was easily operated in a synchronized manner with an MRI system. In particular, the home-made system was designed as an add-on toolkit that did not require any modifications to be made to the MRI scanner, but rather operates in parallel based on readily available signal outputs from the scanner.

For clinical acceptance, the unobtrusive placement of the NMR probes is of critical importance. Integrating probes into the magnet bore is difficult because of the presence of spatially significant higher order field components in the primary gradient fields as well as their associated eddy current fields. NMR probes could, however, be integrated into imaging coils with some effort. For nonrigid coils, patient movement during the examination can lead to undesired motion effects that need to be taken into account. For example, redundancy regarding the number of probes and the placement of some of the probes in fixed locations could be used to distinguish motion from eddy current effects.

The presented rMFM system was designed to correct dynamic magnetic field errors only; the applicability of using NMR probes for simultaneous static magnetic field correction would be interesting but is complicated because of the difficulty of inferring static magnetic field distributions inside the body based on measurements taken at the outside. Nevertheless, in the absence of a patient, the rMFM hardware can be used for scanner-intrinsic magnetic field calibration purposes.

Real-time magnetic field monitoring based on 2H transmit–receive probes has been shown to effectively address gradient imperfections in fast acquisition schemes and motion encoding applications. In addition, rMFM probes can be attached to the patient and used for motion correction (37); furthermore, rMFM could also be used as instantaneous feedback for gradient drivers for correcting magnetic gradient errors real time and would therefore make the use of current monitoring, which is currently used in clinical MRI scanners, obsolete.

Modern clinical scanners are provided with increasing number of RF channels, and a part of these can be exploited to introduce rMFM hardware with only limited cost burden. Alternatively, novel techniques of frequency domain multiplexing and multiband receivers can be used to keep the count of required RF channels low (38, 34), and hence the need to simplify the implementation of rMFM hardware for clinical applications.