Low-Field, Low-Cost, Point-of-Care Magnetic Resonance Imaging.

Low-field magnetic resonance imaging (MRI) has recently experienced a renaissance that is largely attributable to the numerous technological advancements made in MRI, including optimized pulse sequences, parallel receive and compressed sensing, improved calibrations and reconstruction algorithms, and the adoption of machine learning for image postprocessing. This new attention on low-field MRI originates from a lack of accessibility to traditional MRI and the need for affordable imaging. Low-field MRI provides a viable option due to its lack of reliance on radio-frequency shielding rooms, expensive liquid helium, and cryogen quench pipes. Moreover, its relatively small size and weight allow for easy and affordable installation in most settings. Rather than replacing conventional MRI, low-field MRI will provide new opportunities for imaging both in developing and developed countries. This article discusses the history of low-field MRI, low-field MRI hardware and software, current devices on the market, advantages and disadvantages, and low-field MRI's global potential.

Clinical physiology: the crucial role of MRI in evaluation of peripheral artery disease.

Peripheral artery disease (PAD) is a common vascular disease that primarily affects the lower limbs and is defined by the constriction or blockage of peripheral arteries and may involve microvascular dysfunction and tissue injury. Patients with diabetes have more prominent disease of microcirculation and develop peripheral neuropathy, autonomic dysfunction, and medial vascular calcification. Early and accurate diagnosis of PAD and disease characterization are essential for personalized management and therapy planning. Magnetic resonance imaging (MRI) provides excellent soft tissue contrast and multiplanar imaging capabilities and is useful as a noninvasive imaging tool in the comprehensive physiological assessment of PAD. This review provides an overview of the current state of the art of MRI in the evaluation and characterization of PAD, including an analysis of the many applicable MR imaging techniques, describing the advantages and disadvantages of each approach. We also present recent developments, future clinical applications, and future MRI directions in assessing PAD. The development of new MR imaging technologies and applications in preclinical models with translation to clinical research holds considerable potential for improving the understanding of the pathophysiology of PAD and clinical applications for improving diagnostic precision, risk stratification, and treatment outcomes in patients with PAD.

Practical utilization of nonlinear spatial encoding: Fast field mapping and FRONSAC-wave.

PURPOSE: To study the additional value of FRONSAC encoding in 2D and 3D wave sequences, implementing a simple strategy to trajectory mapping for FRONSAC encoding gradients. THEORY AND METHODS: The nonlinear gradient trajectory for each voxel was estimated by exploiting the sparsity of the point spread function in the frequency domain. Simulations and in-vivo experiments were used to analyze the performance of combinations of wave and FRONSAC encoding. RESULTS: Field mapping using the simplified approach produced similar image quality with much shorter calibration time than the comprehensive mapping schemes utilized in previous work. In-vivo human brain images showed that the addition of FRONSAC encoding could improve wave image quality, particularly at very high undersampling factors and in the context of limited wave amplitudes. These results were further supported by g-factor maps. CONCLUSION: Results show that FRONSAC can be used to improve image quality of wave at very high undersampling rates or in slew-limited acquisitions. Our study illustrates the potential of the proposed fast field mapping approach.

K-t PCA accelerated in-plane balanced steady-state free precession phase-contrast (PC-SSFP) for all-in-one diastolic function evaluation.

PURPOSE: Diastolic function evaluation requires estimates of early and late diastolic mitral filling velocities (E and A) and of mitral annulus tissue velocity (e'). We aimed to develop an MRI method for simultaneous all-in-one diastolic function evaluation in a single scan by generating a 2D phase-contrast (PC) sequence with balanced steady-state free precession (bSSFP) contrast (PC-SSFP). E and A could then be measured with PC, and e' estimated by valve tracking on the magnitude images, using an established deep learning framework. METHODS: Our PC-SSFP used in-plane flow-encoding, with zeroth and first moment nulling over each TR. For further acceleration, different k-t principal component analysis (PCA) methods were investigated with both retrospective and prospective undersampling. PC-SSFP was compared to separate balanced SSFP cine and PC-gradient echo acquisitions in phantoms and in 10 healthy subjects. RESULTS: Phantom experiments showed that PC-SSFP measured accurate velocities compared to PC-gradient echo (r = 0.98 for a range of pixel-wise velocities -80 cm/s to 80 cm/s). In subjects, PC-SSFP generated high SNR and myocardium-blood contrast, and excellent agreement for E (limits of agreement [LOA] 0.8 ± 2.4 cm/s, r = 0.98), A (LOA 2.5 ± 4.1 cm/s, r = 0.97), and e' (LOA 0.3 ± 2.6 cm/s, r = 1.00), versus the standard methods. The best k-t PCA approach processed the complex difference data and substituted in raw k-space data. With prospective k-t PCA acceleration, higher frame rates were achieved (50 vs. 25 frames per second without k-t PCA), yielding a 13% higher e'. CONCLUSION: The proposed PC-SSFP method achieved all-in-one diastolic function evaluation.

Efficient standardization of clinical T2-weighted images: Phase-conjugacy e-CAMP with projected gradient descent.

PURPOSE: To standardize T 2 $$ {}_2 $$ -weighted images from clinical Turbo Spin Echo (TSE) scans by generating corresponding T 2 $$ {}_2 $$ maps with the goal of removing scanner- and/or protocol-specific heterogeneity. METHODS: The T 2 $$ {}_2 $$ map is estimated by minimizing an objective function containing a data fidelity term in a Virtual Conjugate Coils (VCC) framework, where the signal evolution model is expressed as a linear constraint. The objective function is minimized by Projected Gradient Descent (PGD). RESULTS: The algorithm achieves accuracy comparable to methods with customized sampling schemes for accelerated T 2 $$ {}_2 $$ mapping. The results are insensitive to the tunable parameters, and the relaxed background phase prior produces better T 2 $$ {}_2 $$ maps compared to the strict real-value enforcement. It is worth noting that the algorithm works well with challenging T 2 $$ {}_2 $$ w-TSE data using typical clinical parameters. The observed normalized root mean square error ranges from 6.8% to 12.3% over grey and white matter, a clinically common level of quantitative map error. CONCLUSION: The novel methodological development creates an efficient algorithm that allows for T 2 $$ {}_2 $$ map generated from TSE data with typical clinical parameters, such as high resolution, long echo train length, and low echo spacing. Reconstruction of T 2 $$ {}_2 $$ maps from TSE data with typical clinical parameters has not been previously reported.

HALO: A software tool for real-time head alignment in the MR scanner.

PURPOSE: MRI studies in human subjects often require multiple scanning sessions/visits. Changes in a subject's head position across sessions result in different alignment between brain tissues and the magnetic field which leads to changes in magnetic susceptibility. These changes can have considerable impacts on acquired signals. Head ALignment Optimization (HALO), a software tool was developed by the authors for active head alignment between sessions. METHODS: HALO provides real-time visual feedback of a subject's current head position relative to the position in a previous session. The tool was evaluated in a pilot sample of seven healthy human subjects. RESULTS: HALO was shown to enable subjects to actively align their head positions to the desired position of their initial sessions. The subjects were able to improve their head alignment significantly using HALO and achieved good alignment with their first session meeting stringent criteria similar to that used for within-run head motion (less than 2 mm translation or 2 degrees rotation in any direction from the desired position). Moreover, we found a negative correlation between the post-alignment rotation and similarity in inter-session BOLD patterns around the air-tissue interface near sinus which further highlighted the impact of tissue-field alignment on BOLD data quality. CONCLUSION: Utilization of HALO in longitudinal studies may help to improve data quality by ensuring the consistency of susceptibility gradients in brain tissues across sessions. HALO has been made publicly available.

Targeting prostate cancer with Clostridium perfringens enterotoxin functionalized nanoparticles co-encapsulating imaging cargo enhances magnetic resonance imaging specificity.

Magnetic resonance is a key imaging tool for the detection of prostate cancer; however, better tools focusing on cancer specificity are required to distinguish benign from cancerous regions. We found higher expression of claudin-3 (CLDN-3) and -4 (CLDN-4) in higher grade than lower-grade human prostate cancer biopsies (n = 174), leading to the design of functionalized nanoparticles (NPs) with a non-toxic truncated version of the natural ligand Clostridium perfringens enterotoxin (C-CPE) that has a strong binding affinity to Cldn-3 and Cldn-4 receptors. We developed a first-of-its-type, C-CPE-NP-based MRI detection tool in a prostate tumor-bearing mouse model. NPs with an average diameter of 152.9 ±â€¯15.7 nm (RS1) had a 2-fold enhancement of tumor specificity compared to larger (421.2 ±â€¯33.8 nm) NPs (RS4). There was a 1.8-fold (P < 0.01) and 1.6-fold (P < 0.01) upregulation of the tumor-to-liver signal intensities of C-RS1 and C-RS4 (functionalized NPs) compared to controls, respectively. Also, tumor specificity was 3.1-fold higher (P < 0.001) when comparing C-RS1 to C-RS4. This detection tool improved tumor localization of contrast-enhanced MRI, supporting potential clinical applicability.

Dynamic-flip-angle ECG-gating with nuisance signal regression improves resting-state BOLD functional connectivity mapping by reducing cardiogenic noise.

PURPOSE: To investigate an ECG-gated dynamic-flip-angle BOLD sequence with improved robustness against cardiogenic noise in resting-state fMRI. METHODS: ECG-gating minimizes the cardiogenic noise but introduces T1 -dependent signal variation, which is minimized by combination of a dynamic-flip-angle technique and retrospective nuisance signal regression (NSR) using signals of white matter, CSF, and global average. The technique was studied with simulations in a wide range of T1 and B1 fields and phantom imaging with pre-programmed TR variations. Resting-state fMRI of 20 healthy subjects was acquired with non-gated BOLD (NG), ECG-gated constant-flip-angle BOLD (GCFA), ECG-gated BOLD with retrospective T1 -correction (GRC), and ECG-gated dynamic-flip-angle BOLD (GDFA), all processed by the same NSR method. GDFA was compared to alternative methods over temporal SNR (tSNR), seed-based connectivity, and whole-brain voxelwise connectivity based on intrinsic connectivity distribution (ICD). A previous large-cohort data set (N = 100) was used as a connectivity gold standard. RESULTS: Simulations and phantom imaging show substantial reduction of the T1 -dependent signal variation with GDFA alone, and further reduction with NSR. The resting-state study shows improved tSNR in the basal brain, comparing GDFA to NG, after both processed with NSR. Furthermore, GDFA significantly improved subcortical-subcortical and cortical-subcortical connectivity for several representative seeds and significantly improved ICD in the brainstem, thalamus, striatum, and prefrontal cortex, compared to the other 3 approaches. CONCLUSION: GDFA with NSR improves mapping of the resting-state functional connectivity of the basal-brain regions by reducing cardiogenic noise.

Fast rotary nonlinear spatial acquisition (FRONSAC) imaging.

PURPOSE: Nonlinear spatial encoding magnetic fields (SEMs) have been studied to reconstruct images from a minimum number of echoes. Previous work has also explored single shot trajectories in nonlinear SEMs. However, the search continues for optimal schemes that apply nonlinear SEMs to improve spatial encoding efficiency and image quality. THEORY AND METHODS: We enhance the encoding efficiency of standard linear gradient trajectories by adding a rapidly rotating nonlinear SEM of moderate amplitude, the so called FRONSAC (Fast ROtary Nonlinear Spatial ACquisition) imaging. This additional gradient greatly improves the image quality of highly undersampled single-shot trajectories, including EPI, Spiral, and Rosette trajectories. RESULTS: Our simulations, including noise and dephasing effects, test the effect of adding FRONSAC gradients, demonstrating the applicability of this approach. Performance is explained by demonstrating the additional k-space sampling the nonlinear gradient provides. Studies of the optimal amplitude and frequency of the additional FRONSAC field are presented, and the role of enhanced sampling during the readout demonstrated. Dynamic field mapping in a second-order gradient system shows the proposed gradient waveforms are feasible. CONCLUSION: Images resulting from highly undersampled existing k-space trajectories, such as EPI, Spiral, and Rosette, are greatly enhanced simply by adding a rotating nonlinear SEM field.

Experimental O-space turbo spin echo imaging.

PURPOSE: Turbo spin echo (TSE) imaging reduces imaging time by acquiring multiple echoes per repetition (TR), requiring fewer TRs. O-space can also require fewer TRs by using a combination of nonlinear magnetic gradient fields and surface coil arrays. Although to date, O-space has only been demonstrated for gradient echo imaging, it is valuable to combine these two techniques. However, collecting multiple O-space echoes per TR is difficult because of the different local k-space trajectories and variable T2-weighting. THEORY AND METHODS: A practical scheme is demonstrated to combine the benefits of TSE and O-space for highly accelerated T2-weighted images. The scheme uses a modified acquisition order and filtered projection reconstruction to reduce artifacts caused by T2 decay, while retaining T2 contrast that corresponds to a specific echo time. RESULTS: The experiments revealed that the proposed method can produce highly accelerated T2-weighted images. Moreover, the method can generate multiple images with different T2 contrasts from a single dataset. CONCLUSIONS: The proposed O-space TSE imaging method requires fewer echoes than conventional TSE and fewer repetitions than conventional O-space imaging. It retains resilience to undersampling, clearly outperforming Cartesian SENSE at high levels of undersampling, and can generate undistorted images with a range of T2 contrast from a single acquired dataset.

Pseudo-random center placement O-space imaging for improved incoherence compressed sensing parallel MRI.

PURPOSE: Nonlinear spatial encoding magnetic (SEM) field strategies such as O-space imaging have previously reported dispersed artifacts during accelerated scans. Compressed sensing (CS) has shown a sparsity-promoting convex program allows image reconstruction from a reduced data set when using the appropriate sampling. The development of a pseudo-random center placement (CP) O-space CS approach optimizes incoherence through SEM field modulation to reconstruct an image with reduced error. THEORY AND METHODS: The incoherence parameter determines the sparsity levels for which CS is valid and the related transform point spread function measures the maximum interference for a single point. The O-space acquisition is optimized for CS by perturbing the Z(2) strength within 30% of the nominal value and demonstrated on a human 3T scanner. RESULTS: Pseudo-random CP O-space imaging is shown to improve incoherence between the sensing and sparse domains. Images indicate pseudo-random CP O-space has reduced mean squared error compared with a typical linear SEM field acquisition method. CONCLUSION: Pseudo-random CP O-space imaging, with a nonlinear SEM field designed for CS, is shown to reduce mean squared error of images at high acceleration over linear encoding methods for a 2D slice when using an eight channel circumferential receiver array for parallel imaging.

Algebraic reconstruction technique for parallel imaging reconstruction of undersampled radial data: application to cardiac cine.

PURPOSE: To investigate algebraic reconstruction technique (ART) for parallel imaging reconstruction of radial data, applied to accelerated cardiac cine. METHODS: A graphics processing unit (GPU)-accelerated ART reconstruction was implemented and applied to simulations, point spread functions and in 12 subjects imaged with radial cardiac cine acquisitions. Cine images were reconstructed with radial ART at multiple undersampling levels (192 Nr × Np = 96 to 16). Images were qualitatively and quantitatively analyzed for sharpness and artifacts, and compared to filtered back-projection, and conjugate gradient SENSE. RESULTS: Radial ART provided reduced artifacts and mainly preserved spatial resolution, for both simulations and in vivo data. Artifacts were qualitatively and quantitatively less with ART than filtered back-projection using 48, 32, and 24 Np , although filtered back-projection provided quantitatively sharper images at undersampling levels of 48-24 Np (all P < 0.05). Use of undersampled radial data for generating auto-calibrated coil-sensitivity profiles resulted in slightly reduced quality. ART was comparable to conjugate gradient SENSE. GPU-acceleration increased ART reconstruction speed 15-fold, with little impact on the images. CONCLUSION: GPU-accelerated ART is an alternative approach to image reconstruction for parallel radial MR imaging, providing reduced artifacts while mainly maintaining sharpness compared to filtered back-projection, as shown by its first application in cardiac studies.

Multiecho acquisition of O-space data.

PURPOSE: Nonlinear gradient encoding methods, such as O-Space imaging, have been shown to provide good images from very few echoes. Acquiring data in a train of spin or gradient echoes is a very flexible way to further speed acquisition time. However, combining these strategies presents significant challenges, both in terms of the contrast and artifacts. We present strategies in both pulse sequence design and image processing to mitigate these effects. THEORY AND METHODS: The three strategies include a new echo ordering that takes into account the unique way that O-Space samples the k-space of the image; a new postprocessing filter that allows tuning of T2-weighting by emphasizing the contribution of low frequency spatial information at selectable points in space and time; and an offset between linear and nonlinear gradients that makes the central point of each echo unique. RESULTS: Simulations indicate that these strategies mitigate artifacts introduced by T2 (or T2*) decay and produce contrast that reflects relaxation at a given echo time. CONCLUSION: Turbo spin echo O-Space is theoretically feasible, and the greater undersampling should make it possible to use shorter echo trains for a given scan time.

A Physics-Based Algorithm to Universally Standardize Routinely Obtained Clinical T2-Weighted Images.

RATIONALE AND OBJECTIVES: MR images can be challenging for machine learning and other large-scale analyses because most clinical images, for example, T2-weighted (T2w) images, reflect not only the biologically relevant T2 of tissue but also hardware and acquisition parameters that vary from site to site. Quantitative T2 mapping avoids these confounds because it quantitatively isolates the biological parameter of interest, thus representing a universal standardization across sites. However, efforts to incorporate quantitative mapping sequences into routine clinical practice have seen slow adoption. Here we show, for the first time, that the routine T2w complex raw dataset can be successfully regarded as a quantitative mapping sequence that can be reconstructed with classical optimization methods and physics-based constraints. MATERIALS AND METHODS: While previous constrained reconstruction methods are unable to reconstruct a T2 map based on this data, the expanding-constrained alternating minimization for parameter mapping (e-CAMP), which employs stepwise initialization, a linearized version of the exponential model and a phase conjugacy constraint, is demonstrated to provide useful quantitative maps directly from a vendor T2w single image data. RESULTS: This paper introduces the method and demonstrates its performance using simulations, retrospectively undersampled brain images, and prospectively acquired T2w images taken on both phantom and brain. CONCLUSION: Because T2w scans are included in nearly every protocol, this approach could open the door to creating large, standardized datasets without requiring widespread changes in clinical protocols.

Encoding scheme design for gradient-free, nonlinear projection imaging using Bloch-Siegert RF spatial encoding in a low-field, open MRI system.

Eliminating conventional pulsed B0-gradient coils for magnetic resonance imaging (MRI) can significantly reduce the cost of and increase access to these devices. Phase shifts induced by the Bloch-Siegert shift effect have been proposed as a means for gradient-free, RF spatial encoding for low-field MR imaging. However, nonlinear phasor patterns like those generated from loop coils have not been systematically studied in the context of 2D spatial encoding. This work presents an optimization algorithm to select an efficient encoding trajectory among the nonlinear patterns achievable with a given hardware setup. Performance of encoding trajectories or projections was evaluated through simulated and experimental image reconstructions. Results show that the encodings schemes designed by this algorithm provide more efficient spatial encoding than comparison encoding sets, and the method produces images with the predicted spatial resolution and minimal artifacts. Overall, the work demonstrates the feasibility of performing 2D gradient-free, low-field imaging using the Bloch-Siegert shift which is an important step towards creating low-cost, point-of-care MR systems.

Constrained alternating minimization for parameter mapping (CAMP).

OBJECTIVE: To improve image quality in highly accelerated parameter mapping by incorporating a linear constraint that relates consecutive images. APPROACH: In multi-echo T1 or T2 mapping, scan time is often shortened by acquiring undersampled but complementary measures of k-space at each TE or TI. However, residual undersampling artifacts from the individual images can then degrade the quality of the final parameter maps. In this work, a new reconstruction method, dubbed Constrained Alternating Minimization for Parameter mapping (CAMP), is introduced. This method simultaneously extracts T2 or T1* maps in addition to an image for each TE or TI from accelerated datasets, leveraging the constraints of the decay to improve the reconstructed image quality. The model enforces exponential decay through a linear constraint, resulting in a biconvex objective function that lends itself to alternating minimization. The method was tested in four in vivo volunteer experiments and validated in phantom studies and healthy subjects, using T2 and T1 mapping, with accelerations of up to 12. MAIN RESULTS: CAMP is demonstrated for accelerated radial and Cartesian acquisitions in T2 and T1 mapping. The method is even applied to generate an entire T2 weighted image series from a single TSE dataset, despite the blockwise k-space sampling at each echo time. Experimental undersampled phantom and in vivo results processed with CAMP exhibit reduced artifacts without introducing bias. SIGNIFICANCE: For a wide array of applications, CAMP linearizes the model cost function without sacrificing model accuracy so that the well-conditioned and highly efficient reconstruction algorithm improves the image quality of accelerated parameter maps.

In vivo O-Space imaging with a dedicated 12 cm Z2 insert coil on a human 3T scanner using phase map calibration.

Recently, spatial encoding with nonlinear magnetic fields has drawn attention for its potential to achieve faster gradient switching within safety limits, tailored resolution in regions of interest, and improved parallel imaging using encoding fields that complement the sensitivity profiles of radio frequency receive arrays. Proposed methods can broadly be divided into those that use phase encoding (Cartesian-trajectory PatLoc and COGNAC) and those that acquire nonlinear projections (O-Space, Null space imaging, radial PatLoc, and 4D-RIO). Nonlinear projection data are most often reconstructed with iterative algorithms that backproject data using the full encoding matrix. Just like conventional radial sequences that use linear spatial encoding magnetic fields, nonlinear projection methods are more sensitive than phase encoding methods to imperfect calibration of the encoding fields. In this work, voxel-wise phase evolution is mapped at each acquired point in an O-Space trajectory using a variant of chemical shift imaging, capturing all spin dynamics caused by encoding fields, eddy currents, and pulse timing. Phase map calibration is then applied to data acquired from a high-power, 12 cm, Z2 insert coil with an eight-channel radio frequency transmit-receive array on a 3T human scanner. We show the first experimental proof-of-concept O-Space images on in vivo and phantom samples, paving the way for more in-depth exploration of O-Space and similar imaging methods.

3D FRONSAC with PSF reconstruction.

PURPOSE: This study extends the Fast ROtary Nonlinear Spatial ACquisition (FRONSAC) method to include 3D acquisitions and reconstructions. It uses a transform domain reconstruction which is needed to make 3D reconstructions practical and provides new insights into how parallel imaging performance is enhanced by FRONSAC encoding. METHODS: This work developed the first examples of FRONSAC incorporated into a 3D acquisition. 3D FRONSAC was tested on human subjects with both simple gradient echo and MPRAGE Cartesian acquisitions. The quality of the 3D FRONSAC images was evaluated using structural similarity index measure (SSIM), and normalized root mean square error (NRMSE). RESULTS: FRONSAC encoding did not significantly modify the contrast obtained in either sequence, but it substantially improves the image quality of undersampled reconstruction. FRONSAC images have reduced undersampling ghosts and consistently improved SSIM and NRMSE. CONCLUSIONS: Acquisition and reconstruction of 3D FRONSAC images are feasible, and the additional FRONSAC encoding improves image quality in highly undersampled images.

Magnetic resonance imaging using a nonuniform Bo (NuBo) field-cycling magnet.

Magnetic resonance imaging (MRI) is a powerful noninvasive diagnostic tool with superior soft tissue contrast. However, access to MRI is limited since current systems depend on homogeneous, high field strength main magnets (B0-fields), with strong switchable gradients which are expensive to install and maintain. In this work we propose a new approach to MRI where imaging is performed in an inhomogeneous field using radiofrequency spatial encoding, thereby eliminating the need for uniform B0-fields and conventional cylindrical gradient coils. The proposed technology uses an innovative data acquisition and reconstruction approach by integrating developments in field cycling, parallel imaging and non-Fourier based algebraic reconstruction. The scanner uses field cycling to image in an inhomogeneous B0-field; in this way magnetization is maximized during the high field polarization phase, and B0 inhomogeneity effects are minimized by using a low field during image acquisition. In addition to presenting the concept, this work provides experimental verification of a long-lived spin echo signal, spatially varying resolution, as well as both simulated and experimental 2D images. Our initial design creates an open MR system that can be installed in a patient examination table for body imaging (e.g., breast or liver) or built into a wall for weighted-spine imaging. The proposed system introduces a new class of inexpensive, open, silent MRIs that could be housed in doctor's offices much like ultrasound is today, making MRI more widely accessible.

Spin dephasing under nonlinear gradients: implications for imaging and field mapping.

This work examines the prototypical MR echo that would be expected for a voxel of spins evolving in a strong nonlinear field, specifically focusing on the quadratic z(2) - ½(x(2) + y(2) ) field. Dephasing under nonlinear gradients is increasingly relevant given the growing interest in nonlinear imaging, and here, we report several notable differences from the linear case. Most notably, in addition to signal loss, intravoxel dephasing under gradients creating a wide and asymmetric frequency distribution across the voxel can cause skewed and nonlinear phase evolution. After presenting the qualitative and analytical origins of this difference, we experimentally demonstrate that neglecting these dynamics can lead to significant errors in sequences that assume phase evolution is proportional to voxel frequency, such as those used for field mapping. Finally, simplifying approximations to the signal equations are presented, which not only provide more intuitive forms of the exact expression but also result in simple rules to predict key features of the nonlinear evolution.