Modeling and measurement of lead tip heating and resonant length for implanted, insulated wires.

PURPOSE: To study implant lead tip heating because of the RF power deposition by developing mathematical models and comparing them with measurements acquired at 1.5 T and 3 T, especially to predict resonant length. THEORY AND METHODS: A simple exponential model and an adapted transmission line model for the electric field transfer function were developed. A set of wavenumbers, including that calculated from insulated antenna theory (King wavenumber) and that of the embedding medium were considered. Experiments on insulated, capped wires of varying lengths were performed to determine maximum temperature rise under RF exposure. The results are compared with model predictions from analytical expressions derived under the assumption of a constant electric field, and with those numerically calculated from spatially varying, simulated electric fields from body coil transmission. Simple expressions for the resonant length bounded between one-quarter and one-half wavelength are developed based on the roots of transcendental equations. RESULTS: The King wavenumber for both models more closely matched the experimental data with a maximum root mean square error of 9.81°C at 1.5 T and 5.71°C at 3 T compared to other wavenumbers with a maximum root mean square error of 27.52°C at 1.5 T and 22.01°C for 3 T. Resonant length was more accurately predicted compared to values solely based on the embedding medium. CONCLUSION: Analytical expressions were developed for implanted lead heating and resonant lengths under specific assumptions. The value of the wavenumber has a strong effect on the model predictions. Our work could be used to better manage implanted device lead tip heating.

Human prostate MRI at ultrahigh-performance gradient: A feasibility study.

PURPOSE: To demonstrate the technical feasibility and the value of ultrahigh-performance gradient in imaging the prostate in a 3T MRI system. METHODS: In this local institutional review board-approved study, prostate MRI was performed on 4 healthy men. Each subject was scanned in a prototype 3T MRI system with a 42-cm inner-diameter gradient coil that achieves a maximum gradient amplitude of 200 mT/m and slew rate of 500 T/m/s. PI-RADS V2.1-compliant axial T2 -weighted anatomical imaging and single-shot echo planar DWI at standard gradient of 70 mT/m and 150 T/m/s were obtained, followed by DWI at maximum performance (i.e., 200 mT/m and 500 T/m/s). In comparison to state-of-the-art clinical whole-body MRI systems, the high slew rate improved echo spacing from 1020 to 596 µs and, together with a high gradient amplitude for diffusion encoding, TE was reduced from 55 to 36 ms. RESULTS: In all 4 subjects (waist circumference = 81-91 cm, age = 45-65 years), no peripheral nerve stimulation sensation was reported during DWI. Reduced image distortion in the posterior peripheral zone prostate gland and higher signal intensity, such as in the surrounding muscle of high-gradient DWI, were noted. CONCLUSION: Human prostate MRI at simultaneously high gradient amplitude of 200 mT/m and slew rate of 500 T/m/s is feasible, demonstrating that improved gradient performance can address image distortion and T2 decay-induced SNR issues for in vivo prostate imaging.

Evaluation of a compact 3 T MRI scanner for patients with implanted devices.

Access to high-quality MR exams is severely limited for patients with some implanted devices due to labeled MR safety conditions, but small-bore systems can overcome this limitation. For example, a compact 3 T MR scanner (C3T) with high-performance gradients can acquire exams of the head, extremities, and infants. Because of its reduced bore size and the patient being advanced only partially into the bore, the associated electromagnetic (EM) fields drop off rapidly caudal to the head, compared to whole-body systems. Therefore, some patients with MR conditional implanted devices can safely receive 3 T brain exams on the C3T using its strong gradients and a multiple-channel receive coil, while a corresponding exam on whole-body MR is precluded. The purpose of this study is to evaluate the performance of a small-bore scanner for subjects with MR conditional spinal or sacral nerve stimulators, or abandoned cardiac implantable electronic device (CIED) leads. The spatial dependence of specific absorption rate (SAR) on the C3T was compared to whole-body scanners. A device assessment tool was developed and applied to evaluate MR safety individually on the C3T for 12 subjects with implanted devices or abandoned CIED leads. Once MR safety was established, the subjects received a C3T brain exam along with their clinical, 1.5 T exam. The resulting images were graded by three board-certified neuroradiologists. The C3T exams were well-tolerated with no adverse events, and significantly outperformed the whole-body 1.5 T exams in terms of overall image quality.

MR thermometry imaging for low intensity focused ultrasound modulation of spinal nervous tissue.

OBJECTIVES: Previously in rodent and swine models, we have shown that external low intensity focused ultrasound (liFUS) can be used to modulate pain responses. To ensure no adverse heating events occur with liFUS modulation in a non-invasive manner, we perform initial work in swine to show that magnetic resonance thermometry imaging (MRTI) is capable of measuring <2.0 °C changes at the L5 DRG. Further, we show that our device can be constructed in an MR-compatible fashion to minimize artifact. METHODS: Three MRTI techniques (referenceless, corrected proton resonance frequency shift (PRFS), and PRFS) were applied to assess accuracy of detecting thermal changes at the L5 DRG in unheated euthanized swine. A region of interest (ROI) that includes the L5 DRG was delineated, within which MRTI temperature changes were spatially averaged (ground truth 0 °C). In separate experiments with phantoms, B0 field-inhomogeneity, RF transmit (B1+) and fast gradient echo (fSPGR) magnitude images were acquired to downselect liFUS device materials that produce the least MRI artifacts. RESULTS: Referenceless, corrected PRFS, and PRFS MRTI resulted in temperature measurements of 0.8 ± 1.1 °C, 1.1 ± 1.3 °C and 5.2 ± 5 °C, respectively. Both materials caused B0 perturbation but minimal B1+ and MRTI artifacts. The presence of imaging artifacts did not preclude thermal imaging of the region. SIGNIFICANCE: We provide preliminary data suggesting that referenceless MRTI can adequately detect small thermal changes at the DRG that may occur with neuromodulation, which is one of the first steps in creating a table of safe parameters for liFUS therapy in humans.

A hybrid deformable registration method to generate motion-compensated 3D virtual MRI for fusion with interventional real-time 3D ultrasound.

PURPOSE: Ultrasound is often the preferred modality for image-guided therapy or treatment in organs such as liver due to real-time imaging capabilities. However, the reduced conspicuity of tumors in ultrasound images adversely impacts the precision and accuracy of treatment delivery. This problem is compounded by deformable motion due to breathing and other physiological activity. This creates the need for a fusion method to align interventional US with pre-interventional modalities that provide superior soft-tissue contrast (e.g., MRI) to accurately target a structure-of-interest and compensate for liver motion. METHOD: In this work, we developed a hybrid deformable fusion method to align 3D pre-interventional MRI and 3D interventional US volumes to target the structures-of-interest in liver accurately in real-time. The deformable multimodal fusion method involved an offline alignment of a pre-intervention MRI with a pre-intervention US volume using a traditional registration method, followed by real-time prediction of deformation using a trained deep-learning model between interventional US volumes across different respiratory states. This framework enables motion-compensated MRI-US image fusion in real-time for image-guided treatment. RESULTS: The proposed hybrid deformable registration method was evaluated on three healthy volunteers across the pre-intervention MRI and 20 US volume pairs in the free-breathing respiratory cycle. The mean Euclidean landmark distance of three homologous targets in all three volunteers was less than 3 mm for percutaneous liver procedures. CONCLUSIONS: Preliminary results show that clinically acceptable registration accuracies for near real-time, deformable MRI-US fusion can be achieved by our proposed hybrid approach. The proposed combination of traditional and deep-learning deformable registration techniques is thus a promising approach for motion-compensated MRI-US fusion to improve targeting in image-guided liver interventions.

What happens to brain outside the thermal ablation zones? An assessment of needle-based therapeutic ultrasound in survival swine.

BACKGROUND: In stereotactic radiosurgery, isodose lines must be considered to determine how surrounding tissue is affected. In thermal ablative therapy, such as laser interstitial thermal therapy (LITT), transcranial MR-guided focused ultrasound (tcMRgFUS), and needle-based therapeutic ultrasound (NBTU), how the surrounding area is affected has not been well studied. OBJECTIVE: We aimed to quantify the transition zone surrounding the ablation core created by magnetic resonance-guided robotically-assisted (MRgRA) delivery of NBTU using multi-slice volumetric 2-D magnetic resonance thermal imaging (MRTI) and subsequent characterization of the resultant tissue damage using histopathologic analysis. METHODS: Four swine underwent MRgRA NBTU using varying duration and wattage for treatment delivery. Serial MRI images were obtained, and the most representative were overlaid with isodose lines and compared to brain tissue acquired postmortem which underwent histopathologic analysis. These results were also compared to predicted volumes using a finite element analysis model. Contralateral brain tissue was used for control data. RESULTS: Intraoperative MRTI thermal isodose contours were characterized and comprehensively mapped to post-operative MRI images and qualitatively compared with histological tissue sections postmortem. NBTU 360° ablations induced smaller lesion volumes (33.19 mm3; 120 s, 3 W; 30.05 mm3, 180 s, 4 W) versus 180° ablations (77.20 mm3, 120 s, 3 W; 109.29 mm3; 180 s; 4 W). MRTI/MRI overlay demonstrated the lesion within the proximal isodose lines. The ablation-zone was characterized by dense macrophage infiltration and glial/neuronal loss as demonstrated by glial fibrillary acidic protein (GFAP) and neurofilament (NF) absence and avid CD163 staining. The transition-zone between lesion and normal brain demonstrated decreased macrophage infiltration and measured ∼345 microns (n - 3). We did not detect overt hemorrhages or signs of edema in the adjacent spared tissue. CONCLUSION: We successfully performed MRgRA NBTU ablation in swine and demonstrated minimal histologic changes extended past the ablation-zone. The lesion was characterized by macrophage infiltration and glial/neuronal loss which decreased through the transition-zone.

Heat Modulation of Intrinsic MR Contrasts for Tumor Characterization.

(1) Background: The longitudinal relaxation time (T1), transverse relaxation time (T2), water proton chemical shift (CS), and apparent diffusion coefficient (ADC) are MR quantities that change with temperature. In this work, we investigate heat-induced intrinsic MR contrast types to add salient information to conventional MR imaging to improve tumor characterization. (2) Methods: Imaging tests were performed in vivo using different rat tumor models. The rats were cooled/heated to steady-state temperatures from 26-36 °C and quantitative measurements of T1, T2, and ADC were obtained. Temperature maps were measured using the proton resonance frequency shift (PRFS) method during the heating and cooling cycles. (3) Results: All tissue samples show repeatable relaxation parameter measurement over a range of 26-36 °C. Most notably, we observed a more than 3.3% change in T1/°C in breast adenocarcinoma tumors compared to a 1% change in benign breast fibroadenoma lesions. In addition, we note distinct values of T2/°C change for rat prostate carcinoma cells compared to benign tissue. (4) Conclusion: These findings suggest the possibility of improving MR imaging visualization and characterization of tissue with heat-induced contrast types. Specifically, these results suggest that the temporal thermal responses of heat-sensitive MR imaging contrast mechanisms in different tissue types contain information for improved (i) characterization of tumor/tissue boundaries for diagnostic and therapy purposes, and (ii) characterization of salient behavior of tissues, e.g., malignant versus benign tumors.

Predicting ablation zones with multislice volumetric 2-D magnetic resonance thermal imaging.

BACKGROUND: High-intensity focused ultrasound (HIFU) serves as a noninvasive stereotactic system for the ablation of brain metastases; however, treatments are limited to simple geometries and energy delivery is limited by the high acoustic attenuation of the calvarium. Minimally-invasive magnetic resonance-guided robotically-assisted (MRgRA) needle-based therapeutic ultrasound (NBTU) using multislice volumetric 2-D magnetic resonance thermal imaging (MRTI) overcomes these limitations and has potential to produce less collateral tissue damage than current methods. OBJECTIVE: To correlate multislice volumetric 2-D MRTI volumes with histologically confirmed regions of tissue damage in MRgRA NBTU. METHODS: Seven swine underwent a total of 8 frontal MRgRA NBTU lesions. MRTI ablation volumes were compared to histologic tissue damage on brain sections stained with 2,3,5-triphenyltetrazolium chloride (TTC). Bland-Altman analyses and correlation trends were used to compare MRTI and TTC ablation volumes. RESULTS: Data from the initial and third swine's ablations were excluded due to sub-optimal tissue staining. For the remaining ablations (n = 6), the limits of agreement between the MRTI and histologic volumes ranged from -0.149 cm3 to 0.252 cm3 with a mean difference of 0.052 ± 0.042 cm3 (11.1%). There was a high correlation between the MRTI and histology volumes (r2 = 0.831) with a strong linear relationship (r = 0.868). CONCLUSION: We used a volumetric MRTI technique to accurately track thermal changes during MRgRA NBTU in preparation for human trials. Improved volumetric coverage with MRTI enhanced our delivery of therapy and has far-reaching implications for focused ultrasound in the broader clinical setting.

Modeling of Interstitial Ultrasound Ablation for Continuous Applicator Rotation With MR Validation.

The primary objective of cancer intervention is the selective removal of malignant cells while conserving surrounding healthy tissues. However, the accessibility, size and shape of the cancer can make achieving appropriate margins a challenge. One minimally invasive treatment option for these clinical cases is interstitial needle based therapeutic ultrasound (NBTU). In this work, we develop a finite element model (FEM) capable of simulating continuous rotation of a directional NBTU applicator. The developed model was used to simulate the thermal deposition for different rotation trajectories. The actual thermal deposition patterns for the simulated trajectories were then evaluated using magnetic resonance thermal imaging (MRTI) in a porcine skin gelatin phantom. An MRI-compatible robot was used to control the rotation motion profile of the physical NBTU applicator to match the simulated trajectory. The model showed agreement when compared to experimental measurements with Pearson correlation coefficients greater than 0.839 when comparing temperature fields within an area of 12.6 mm radius from the ultrasound applicator. The average temperature error along a 6.3 mm radius profile from the applicator was 1.27 °C. The model was able to compute 1 s of thermal deposition by the applicator in 0.2 s on average with a 0.1 mm spatial resolution and 0.5 s time steps. The developed simulation demonstrates performance suitable for real-time control which may enable robotically-actuated closed-loop conformal tumor ablation.

Highly efficient head-only magnetic field insert gradient coil for achieving simultaneous high gradient amplitude and slew rate at 3.0T (MAGNUS) for brain microstructure imaging.

PURPOSE: To develop a highly efficient magnetic field gradient coil for head imaging that achieves 200 mT/m and 500 T/m/s on each axis using a standard 1 MVA gradient driver in clinical whole-body 3.0T MR magnet. METHODS: A 42-cm inner diameter head-gradient used the available 89- to 91-cm warm bore space in a whole-body 3.0T magnet by increasing the radial separation between the primary and the shield coil windings to 18.6 cm. This required the removal of the standard whole-body gradient and radiofrequency coils. To achieve a coil efficiency ~4× that of whole-body gradients, a double-layer primary coil design with asymmetric x-y axes, and symmetric z-axis was used. The use of all-hollow conductor with direct fluid cooling of the gradient coil enabled ≥50 kW of total heat dissipation. RESULTS: This design achieved a coil efficiency of 0.32 mT/m/A, allowing 200 mT/m and 500 T/m/s for a 620 A/1500 V driver. The gradient coil yielded substantially reduced echo spacing, and minimum repetition time and echo time. In high b = 10,000 s/mm2 diffusion, echo time (TE) < 50 ms was achieved (>50% reduction compared with whole-body gradients). The gradient coil passed the American College of Radiology tests for gradient linearity and distortion, and met acoustic requirements for nonsignificant risk operation. CONCLUSIONS: Ultra-high gradient coil performance was achieved for head imaging without substantial increases in gradient driver power in a whole-body 3.0T magnet after removing the standard gradient coil. As such, any clinical whole-body 3.0T MR system could be upgraded with 3-4× improvement in gradient performance for brain imaging.

Minimizing eddy currents induced in the ground plane of a large phased-array ultrasound applicator for echo-planar imaging-based MR thermometry.

BACKGROUND: The study aims to investigate different ground plane segmentation designs of an ultrasound transducer to reduce gradient field induced eddy currents and the associated geometric distortion and temperature map errors in echo-planar imaging (EPI)-based MR thermometry in transcranial magnetic resonance (MR)-guided focused ultrasound (tcMRgFUS). METHODS: Six different ground plane segmentations were considered and the efficacy of each in suppressing eddy currents was investigated in silico and in operando. For the latter case, the segmented ground planes were implemented in a transducer mockup model for validation. Robust spoiled gradient (SPGR) echo sequences and multi-shot EPI sequences were acquired. For each sequence and pattern, geometric distortions were quantified in the magnitude images and expressed in millimeters. Phase images were used for extracting the temperature maps on the basis of the temperature-dependent proton resonance frequency shift phenomenon. The means, standard deviations, and signal-to-noise ratios (SNRs) were extracted and contrasted with the geometric distortions of all patterns. RESULTS: The geometric distortion analysis and temperature map evaluations showed that more than one pattern could be considered the best-performing transducer. In the sagittal plane, the star (d) (3.46 ± 2.33 mm) and star-ring patterns (f) (2.72 ± 2.8 mm) showed smaller geometric distortions than the currently available seven-segment sheet (c) (5.54 ± 4.21 mm) and were both comparable to the reference scenario (a) (2.77 ± 2.24 mm). Contrasting these results with the temperature maps revealed that (d) performs as well as (a) in SPGR and EPI. CONCLUSIONS: We demonstrated that segmenting the transducer ground plane into a star pattern reduces eddy currents to a level wherein multi-plane EPI for accurate MR thermometry in tcMRgFUS is feasible.

Validation of MR thermometry: method for temperature probe sensor registration accuracy in head and neck phantoms.

PURPOSE: Magnetic resonance thermometry (MRT) is an attractive means to non-invasively monitor in vivo temperature during head and neck hyperthermia treatments because it can provide multi-dimensional temperature information with high spatial resolution over large regions of interest. However, validation of MRT measurements in a head and neck clinical set-up is crucial to ensure the temperature maps are accurate. Here we demonstrate a unique approach for temperature probe sensor localisation in head and neck hyperthermia test phantoms. METHODS: We characterise the proton resonance frequency shift temperature coefficient and validate MRT measurements in an oil-gel phantom by applying a combination of MR imaging and 3D spline fitting for accurate probe localisation. We also investigate how uncertainties in both the probe localisation and the proton resonance frequency shift (PRFS) thermal coefficient affect the registration of fibre-optic reference temperature probe and MRT readings. RESULTS: The method provides a two-fold advantage of sensor localisation and PRFS thermal coefficient calibration. We provide experimental data for two distinct head and neck phantoms showing the significance of this method as it mitigates temperature probe localisation errors and thereby increases accuracy of MRT validation results. CONCLUSIONS: The techniques presented here may be used to simplify calibration experiments that use an interstitial heating device, or any heating method that provides rapid and spatially localised heat distributions. Overall, the experimental verification of the data registration and PRFS thermal coefficient calibration technique provides a useful benchmarking method to maximise MRT accuracy in any similar context.

Coherent NMR Stark spectroscopy.

We demonstrate phase-coherent Stark effects from a radiofrequency E field at twice the NMR frequency (2ω(0)) of (69)Ga in GaAs. The 2ω(0) phase (ϕ(E)) selects component responses from the nuclear quadrupole Hamiltonian (H(Q)). This is possible by synchronizing few-µs 2ω(0) pulses with an NMR line-narrowing sequence, which averages the Stark interaction to dominate spectra on a background with 10(3)× enhanced resolution. Spectra vs ϕ(E) reveal relative sizes of tensorial factors in H(Q). Comparative modeling and numerical simulations evaluate spectral features unexplained by average Hamiltonian theory, and suggest improvements for quantitative calibration of individual response components. Application of this approach to bulk samples is of value to define Stark responses that may later be used to interrogate the internal electrostatics of structured samples.

Quantitative calibration of radiofrequency NMR Stark effects.

Nuclear magnetic resonance (NMR) Stark responses can occur in quadrupolar nuclei for an electric field oscillating at twice the usual NMR frequency (2ω(0)). Calibration of responses to an applied E field is needed to establish nuclear spins as probes of native E fields within material and molecular systems. We present an improved approach and apparatus for accurate measurement of quadrupolar Stark effects. Updated values of C(14) (the response parameter in cubic crystals) were obtained for both (69)Ga and (75)As in GaAs. Keys to improvement include a modified implementation of voltage dividers to assess the 2ω(0) amplitude, |E|, and the stabilization of divider response by reduction of stray couplings in 2ω(0) circuitry. Finally, accuracy was enhanced by filtering sets of |E| through a linear response function that we established for the radiofrequency amplifier. Our approach is verified by two types of spectral results. Steady-state 2ω(0) excitation to presaturate NMR spectra yielded C(14) = (2.59 ± 0.06) × 10(12) m(-1) for (69)Ga at room-temperature and 14.1 T. For (75)As, we obtained (3.1 ± 0.1) × 10(12) m(-1). Both values reconcile with earlier results from 77 K and below 1 T, whereas current experiments are at room temperature and 14.1 T. Finally, we present results where few-microsecond pulses of the 2ω(0) field induced small (tens of Hz) changes in high-resolution NMR line shapes. There too, spectra collected vs |E| agree with the model for response, further establishing the validity of our protocols to specify |E|.

Enhancing time-suspension sequences for the measurement of weak perturbations.

We detail key features for implementation of time-suspension multiple-pulse line-narrowing sequences. This sequence class is designed to null the average Hamiltonian (H¯(°)) over the period of the multiple-pulse cycle, typically to provide for high-resolution isolation of evolution from a switched interaction, such as field gradients for imaging or small sample perturbations. Sequence designs to further ensure null contributions from correction terms (H¯((¹)) and H¯(²)) of the Magnus expansion are also well known, as are a variety of approaches to second averaging, the process by which diagonal content is incorporated in H¯(°) to truncate unwanted terms. In spite of such designs, we observed spin evolution not explicable by H¯(°) using 16-, 24- and 48-pulse time-suspension sequences. We found three approaches to effectively remove artifacts that included splitting of the lineshape into unexpected multiplets as well as chirped evolution. The noted approaches are simultaneously compatible for combination of their benefits. The first ensures constant power deposition from RF excitation as the evolution period is incremented. This removes chirping and allows more effective 2nd averaging. Two schemes for the latter are evaluated: the noted introduction of a diagonal term in H¯(°), and phase-stepping the line-narrowing sequence on successive instances during the evolution period. Either of these was sufficient to remove artifactual splittings and to further enhance resolution, while in combination enhancements were maintained. Finally, numerical simulations provide evidence that our experimental line-narrowing results with 75As in crystalline GaAs approach performance limits of idealized sequences (e.g., with ideal square pulses, etc.). The three noted experimental techniques should likewise benefit ultimate implementation with switched interactions and corresponding new error contributions, which place further demand on sequence performance.

Radiofrequency quadrupolar NMR stark spectroscopy: steady state response calibration and tensorial mapping.

Radiofrequency electric (E) fields oscillating at twice the usual NMR frequency (2ω(0)) can induce double-quantum transitions in quadrupolar nuclei, an NMR Stark effect. Characterization of such is of interest to aid understanding of electrostatic effects in NMR spectra. Calibration of Stark responses to an applied electric field may also be used to assess native fields within molecules and materials. We present high-field (14.1 T), room-temperature NMR experiments to calibrate the 2ω(0) Stark response in crystalline GaAs. This system presents an important test of current techniques and conditions, as historical studies at low field (500-900 mT) and low temperature (77 K) provide a basis for comparison. Our measurements of steady state response reveal the quadrupolar Stark tuning rate for (69)Ga in this material. The value, ß(Q) = (11.5 ± 0.1) × 10(12) m(-1), is 3.6 times larger than the most-reliable prior result. In the process, we also uncovered a previously unobserved double-quantum steady state coherence. It appears as a completely separable dispersive signal component in quadrature-detected presaturation spectra versus offset from 2ω(0). The new component may eventually afford an independent route to calibrating ß(Q). Finally, we demonstrated exceptional agreement with theory of the orientation-dependent Stark response for rotation of the sample relative to B(0) over a range of 90° and for E-field amplitudes from 30-180 V/cm.

A system for NMR stark spectroscopy of quadrupolar nuclei.

Electrostatic influences on NMR parameters are well accepted. Experimental and computational routes have been long pursued to understand and utilize such Stark effects. However, existing approaches are largely indirect informants on electric fields, and/or are complicated by multiple causal factors in spectroscopic change. We present a system to directly measure quadrupolar Stark effects from an applied electric (E) field. Our apparatus and applications are relevant in two contexts. Each uses a radiofrequency (rf) E field at twice the nuclear Larmor frequency (2omega(0)). The mechanism is a distortion of the E-field gradient tensor that is linear in the amplitude (E(0)) of the rf E field. The first uses 2omega(0) excitation of double-quantum transitions for times similar to T(1) (the longitudinal spin relaxation time). This perturbs the steady state distribution of spin population. Nonlinear analysis versus E(0) can be used to determine the Stark response rate. The second context uses POWER (perturbations observed with enhanced resolution) NMR. Here, coherent, short-time (<