The sensors

The sensors used in this work are based on purified liquids with high density of magnetically equivalent 1H or 19F nuclei, such as H 2 O and C 6 F 6 , encapsulated in a borosilicate capillary. The capillary is surrounded by a copper solenoid for signal excitation and detection and encased in epoxy polymer (Fig. 1). To tailor the magnetostatics of this setup we first performed high-precision magnetic susceptibility measurement of the materials involved. This was achieved by spatial mapping of phase changes that a reference volume of target material induces in NMR signals of a surrounding liquid. The resulting phase maps were subject to regression based on corresponding maps of two calibration materials, water and air, yielding volume susceptibility values with precision and accuracy of a few parts per billion (p.p.b.). Based on such characterization the susceptibility of the epoxy material was then matched, again with p.p.b. precision, to that of the solenoid by doping the epoxy resin with Cu2+ ions in solution. Uniform susceptibility outside the capillary, combined with ellipsoidal shape of the casing, prevents the magnetized probehead from distorting the field inside the capillary. Similarly, the sensor’s epoxy neck was rendered magnetically invisible by doping with Dy3+ such as to exactly match its susceptibility to the surrounding air. To prevent the formation of microscopic gaseous inclusions and variation in eventual volume susceptibility the epoxy resin was polymerized under temperature and volume control. MR field mapping confirmed the expected level of field uniformity in the sensitive volume at a s.d. of 5.7 p.p.b. Sensor signals were excited and acquired with custom-built instrumentation including a high-rate direct-undersampling spectrometer optimized for high-SNR operation (see Methods). Thermal relaxation of the detector liquids is controlled by doping with paramagnetic compounds, which permits minimizing dead times for high temporal resolution. Notably, homogeneous broadening does not violate equation (1) and thus permits controlling temporal resolution without introducing systematic error. For different measurement purposes the temporal resolution was varied between 6 and 100 ms.

Figure 1: Sensor design. The nuclear magnetic resonance (NMR) active sensor liquid is contained in a 2.2 mm diameter borosilicate capillary. A transmit/receive solenoid coil is tightly wound onto the capillary and encapsulated in an ellipsoidal epoxy casing. To prevent detrimental field non-uniformity the polymer is doped to exactly match the magnetic susceptibility of the coil wire. Likewise, the probe neck is susceptibility-matched to the surrounding air. Full size image

Figure 2 illustrates the measurement principle and shows typical performance of a CuSO 4 -doped 1H 2 O sensor laid out for operation in a background field of 7 T at a temporal resolution of 100 ms. The sensor’s bandwidth-compensated initial SNR amounts to ξ=3.1 × 106 Hz1/2 (Supplementary Fig. 1), corresponding to a phase noise level of σ ϕ =0.23 μrad Hz−1/2. On this basis, noise propagation, accounting for signal decay, yields a thermal sensitivity limit for the sensor itself of less than 1 pT (≈0.14 × 10−12 in relative terms). Overall sensitivity was governed by the receiver electronics whose phase noise limited the field precision to 6 pT and thus to below one part per trillion (<0.9 × 10−12) for the given signal characteristics (see Methods and Supplementary Fig. 2 for details).

Figure 2: Measurement principle and raw signal of a 1H 2 O sensor operated at 7 tesla. Primary signal-to-noise ratio (SNR, 3.1 × 106 Hz1/2 in the data shown) and exploitable signal lifetime determine the sensor’s intrinsic field sensitivity, which was assessed at better than 1 pT. The lower part of the figure shows the phase difference between a measurement and a calibration free induction decay (FID) signal (at 50 kHz bandwidth). The slope of the linear fit yields the change of magnetic field strength ΔB between the two measurements, a magnet drift in this case. Non-thermal noise in these data mostly reflects actual minute fluctuation of observed field. Full size image

This level of sensitivity is realized in measurements of field dynamics as targeted in this work. For absolute measurements of static fields, raw field values would require correction for the field offset caused by the magnetized sensor material. This offset is readily calculated from the known susceptibilities and geometry17,18. However, the accuracy of resulting absolute field values will still be fundamentally limited by the remaining uncertainty of the gyromagnetic ratio of the proton, which currently amounts to 6.9 p.p.b.19.

Sensing of nuclear magnetism

One immediate area of application of enhanced high-field magnetometry is nuclear magnetism itself. The transverse components of nuclear magnetization are subject to Larmor precession and hence readily observed by induction, typically in the high MHz range. By contrast, the axial magnetization component varies much more slowly, typically on the scale of milliseconds to seconds, and thus eludes inductive detection. Nuclear polarization is also exceedingly weak with the largest nuclear susceptibilities reaching the order of 10−9. In low background field, detection of such faint axial magnetization has been accomplished using SQUIDs20, atomic magnetometers21, anisotropic magnetoresistance22 and nitrogen-vacancy centres in diamond23. However, in the high-field realm, where nuclear magnetism is most commonly studied and used, the ability to observe axial nuclear magnetization is limited to-date. In magnetic resonance force microscopy24, it is sensed via force coupling to a detection cantilever. Yet, relying on active nutation of the magnetization in question this mechanism perturbs and largely masks the native spin dynamics. Another option, the Hall effect, has been successfully used to detect axial electronic polarization25 yet remains to be rendered sufficiently sensitive for the nuclear pendant.

At the level of sensitivity reported above, enhanced NMR sensors can readily fill this gap. When used to measure the magnetic field generated by other atomic nuclei they effectively leverage dipolar coupling, which occurs both between single spins26,27,28 and remotely between spin ensembles29,30,31. Here we report the use of four 19F NMR sensors to measure field excursions produced by magnetization dynamics of 1H nuclei. Arranged in the fashion shown in Fig. 3a, their recordings were averaged with alternating sign such as to capture the dipolar field pattern of the 1H sample while suppressing external field fluctuations and clock jitter. As an example, Fig. 3b shows use of this setup for the direct observation of spin-lattice relaxation in 1H 2 O. After pulsed spin inversion the ensuing recovery is recorded by continuous field measurement at a temporal resolution of 84 ms. An immediate application of this capability is relaxometry as illustrated by doping the water sample with varying concentrations of gadoteric acid, a magnetic resonance imaging (MRI) contrast agent. The obtained data were found to conform excellently to expected exponential behaviour, which validates the actual observation of axial nuclear magnetization dynamics. Based on single experiments of several seconds each, exponential fitting yielded the resulting relaxation rates with precisions better than 1%, comparing favourably with conventional fast methods of spin-lattice relaxometry such as the Look-Locker technique32,33. An even more salient benefit of direct nuclear relaxometry is the avoidance of systematic errors that afflict NMR relaxometry with transverse detection. Residual error of radiofrequency transmission and confounding spin and higher-order echoes typically limit the accuracy of Look-Locker techniques, for instance, to several percent33. High accuracy of direct sensing is confirmed by the inset graph, which reflects the linear relationship between the dopant concentration and the measured relaxation rate. It immediately yields the dopant’s relaxivity, r 1 , which is a key quantity in contrast agent design and application.

Figure 3: Direct observation of axial nuclear magnetization. (a) The sample substance is contained in a cylindrical glass vial at the centre of the setup placed in a 7-tesla magnet. The dipole field of its nuclear magnetization is sampled by four 19F nuclear magnetic resonance sensors (figure not exactly to scale, capillaries and distances magnified by a factor 2 for visibility). (b) Axial 1H relaxation in water at varying concentration of gadoteric acid. Regression of fitted relaxation rates yields a high-precision estimate of the dopant’s relaxivity. Full size image

For the broader field of NMR the capability of observing axial magnetization in a direct, time-resolved fashion is a novel, generic means of investigation. For instance, it enables studies also of more complex magnetization dynamics involving phenomena such as cross-relaxation, magnetization transfer and chemical exchange. An intriguing variant of such studies will target hyperpolarized samples whose enhanced level of polarization is expected to reveal yet finer detail of axial magnetization dynamics. Given the added effort of preparing suitable hyperpolarized states it is particularly beneficial that direct magnetometry does not diminish or otherwise alter axial magnetization under study. Further promising applications include nuclear magnetization studies of solid-state samples that hamper inductive detection by fast transverse relaxation.

Background fluctuation

In the reported measurement of axial nuclear magnetization the recorded relaxation curves deviated from exact exponentials by 26–72 pT (root-mean-square error) and thus by significantly more than the previously assessed level of sensitivity. The discrepancy arises from incomplete gradiometric cancellation of fluctuations of the ambient magnetic field rather than from error introduced by the sensors. This was confirmed by a stability measurement of the magnet used, a 7-tesla superconducting electromagnet designed for MRI in humans. We used two 1H 2 O sensors of the same type as above, placed close to each other at a distance of 1.2 cm, and measured the two field strengths simultaneously at a temporal resolution of 100 ms. The recordings exhibited s.d. of 306 pT (over 1 s) to 428 pT (over 10 s) and statistics of non-thermal nature (Supplementary Fig. 3). The difference of the two time series was found to fluctuate much less, with s.d. of 30 and 43 pT over periods of 1 and 10 s, respectively. This indicates that the fluctuating readouts mostly reflect spatially coherent fluctuation of the background field rather than detection noise. In the difference the noise spectrum was still not flat (Supplementary Fig. 3) as it would be for intrinsic sensor noise. It thus indicates that the fluctuation of the background field involves spatially varying components that differ up to several tens of pT between the two sensors. This is conceivable given a range of potential fluctuation sources such as mechanical behaviour of the superconducting magnet.

Observation of the beating heart

Besides nuclear magnetism, enhanced high-field magnetometry also expands the capability of observing magnetization of electronic nature. The magnetic field that emanates from magnetized material offers non-invasive access to a large variety of observables ranging from material properties to chemical, biological, and even physiological processes. As an example of the latter, we demonstrate the recording of dynamic susceptibility effects caused by the beating human heart when exposed to an external magnetic field. Termed magnetic susceptibility plethysmography (MSPG)34, such measurement has so far been limited to SQUID detection and thus to low background field34,35. At field strengths below 1 mT, the method has yielded cardiac field SNR of about 20. To improve net sensitivity, MSPG signals have typically been averaged over large numbers of heartbeats, capturing only dominant features and no beat-to-beat variation35.

Here we report MSPG in real-time and with vastly higher sensitivity, enabled by high ambient field and NMR detection. Three NMR sensors were placed on a healthy volunteer for operation in the 7 T magnet used previously. One was positioned on the sternum, one close to the apex of the heart above the fifth intercostal space and one on the neck near the right carotid artery. The sensors were operated simultaneously at a temporal resolution of 6 ms, yielding cardiac field SNRs in excess of 4,000. Figure 4 shows resulting real-time readouts along with a concurrently acquired electrocardiogram (ECG). The field dynamics primarily reflect mechanics of magnetized material such as myocardial contraction, distension of the aorta and valve closure. Likely they also involve magnetohydrodynamics arising from electric charges in flowing blood36, which are equally visible in the ECG in Fig. 4. As proposed in the earlier MSPG literature, such data hold promise to permit extraction of physiological parameters and potentially of diagnostic information34,35. Real-time recordings of greatly enhanced dynamic range, as reported here, render a major boost to these prospects. Other, immediate applications include cardiac synchronization of MRI scans, which today depends on ECG and tends to be unreliable at high field, as well as the use of MSPG regressors for removing physiological confound from fMRI time series37.