PLANET: An ellipse fitting approach for simultaneous T1 and T2 mapping using phase-cycled balanced steady-state free precession

Development and validation of a deep learning-based method for automatic measurement of uterus, fibroid, and ablated volume in MRI after MR-HIFU treatment of uterine fibroids

INTRODUCTION

The non-perfused volume divided by total fibroid load (NPV/TFL) is a predictive outcome parameter for MRI-guided high-intensity focused ultrasound (MR-HIFU) treatments of uterine fibroids, which is related to long-term symptom relief. In current clinical practice, the MR-HIFU outcome parameters are typically determined by visual inspection, so an automated computer-aided method could facilitate objective outcome quantification. The objective of this study was to develop and evaluate a deep learning-based segmentation algorithm for volume measurements of the uterus, uterine fibroids, and NPVs in MRI in order to automatically quantify the NPV/TFL.

MATERIALS AND METHODS

A segmentation pipeline was developed and evaluated using expert manual segmentations of MRI scans of 115 uterine fibroid patients, screened for and/or undergoing MR-HIFU treatment. The pipeline contained three separate neural networks, one per target structure. The first step in the pipeline was uterus segmentation from contrast-enhanced (CE)-T1w scans. This segmentation was subsequently used to remove non-uterus background tissue for NPV and fibroid segmentation. In the following step, NPVs were segmented from uterus-only CE-T1w scans. Finally, fibroids were segmented from uterus-only T2w scans. The segmentations were used to calculate the volume for each structure. Reliability and agreement between manual and automatic segmentations, volumes, and NPV/TFLs were assessed.

RESULTS

For treatment scans, the Dice similarity coefficients (DSC) between the manually and automatically obtained segmentations were 0.90 (uterus), 0.84 (NPV) and 0.74 (fibroid). Intraclass correlation coefficients (ICC) were 1.00 [0.99, 1.00] (uterus), 0.99 [0.98, 1.00] (NPV) and 0.98 [0.95, 0.99] (fibroid) between manually and automatically derived volumes. For manually and automatically derived NPV/TFLs, the mean difference was 5% [-41%, 51%] (ICC: 0.66 [0.32, 0.85]).

CONCLUSION

The algorithm presented in this study automatically calculates uterus volume, fibroid load, and NPVs, which could lead to more objective outcome quantification after MR-HIFU treatments of uterine fibroids in comparison to visual inspection. When robustness has been ascertained in a future study, this tool may eventually be employed in clinical practice to automatically measure the NPV/TFL after MR-HIFU procedures of uterine fibroids.

Intra-scan RF power amplifier drift correction

PURPOSE

The drift in radiofrequency (RF) power amplifiers (RFPAs) is assessed and several contributing factors are investigated. Two approaches for prospective correction of drift are proposed and their effectiveness is evaluated.

METHODS

RFPA drift assessment encompasses both intra-pulse and inter-pulse drift analyses. Scan protocols with varying flip angle (FA), RF length, and pulse repetition time (TR) are used to gauge the influence of these parameters on drift. Directional couplers (DICOs) monitor the forward waveforms of the RFPA outputs. DICOs data is stored for evaluation, allowing calculation of correction factors to adjust RFPAs' transmit voltage. Two correction methods, predictive and run-time, are employed: predictive correction necessitates a calibration scan, while run-time correction calculates factors during the ongoing scan.

RESULTS

RFPA drift is indeed influenced by the RF duty-cycle, and in the cases examined with a maximum duty-cycle of 66%, the potential drift is approximately 41% or 15%, depending on the specific RFPA revision. Notably, in low transmit voltage scenarios, FA has minimal impact on RFPA drift. The application of predictive and run-time drift correction techniques effectively reduces the average drift from 10.0% to less than 1%, resulting in enhanced MR signal stability.

CONCLUSION

Utilizing DICO recordings and implementing a feedback mechanism enable the prospective correction of RFPA drift. Having a calibration scan, predictive correction can be utilized with fewer complexity; for enhanced performance, a run-time approach can be employed.

Getting the phase consistent: The importance of phase description in balanced steady-state free precession MRI of multi-compartment systems

PURPOSE

Determine the correct mathematical phase description for balanced steady-state free precession (bSSFP) signals in multi-compartment systems.

THEORY AND METHODS

Based on published bSSFP signal models, different phase descriptions can be formulated: one predicting the presence and the other predicting the absence of destructive interference effects in multi-compartment systems. Numerical simulations of bSSFP signals of water and acetone were performed to evaluate the predictions of these different phase descriptions. For experimental validation, bSSFP profiles were measured at 3T using phase-cycled bSSFP acquisitions performed in a phantom containing mixtures of water and acetone, which replicates a system with two signal components. Localized single voxel MRS was performed at 7T to determine the relative chemical shift of the acetone-water mixtures.

RESULTS

Based on the choice of phase description, the simulated bSSFP profiles of water-acetone mixtures varied significantly, either displaying or lacking destructive interference effects, as predicted theoretically. In phantom experiments, destructive interference was consistently observed in the measured bSSFP profiles of water-acetone mixtures, supporting the theoretical description that predicts such interference effects. The connection between the choice of phase description and predicted observation enables unambiguous experimental identification of the correct phase description for multi-compartment bSSFP profiles, which is consistent with the Bloch equations.

CONCLUSION

The study emphasizes that consistent phase descriptions are crucial for accurately describing multi-compartment bSSFP signals, as incorrect phase descriptions result in erroneous predictions.

Phantom evaluation of electrical conductivity mapping by MRI: Comparison to vector network analyzer measurements and spatial resolution assessment

PURPOSE

To evaluate the performance of various MR electrical properties tomography (MR-EPT) methods at 3 T in terms of absolute quantification and spatial resolution limit for electrical conductivity.

METHODS

Absolute quantification as well as spatial resolution performance were evaluated on homogeneous phantoms and a phantom with holes of different sizes, respectively. Ground-truth conductivities were measured with an open-ended coaxial probe connected to a vector network analyzer (VNA). Four widely used MR-EPT reconstruction methods were investigated: phase-based Helmholtz (PB), phase-based convection-reaction (PB-cr), image-based (IB), and generalized-image-based (GIB). These methods were compared using the same complex images from a 1 mm-isotropic UTE sequence. Alternative transceive phase acquisition sequences were also compared in PB and PB-cr.

RESULTS

In large homogeneous phantoms, all methods showed a strong correlation with ground truth conductivities (r > 0.99); however, GIB was the best in terms of accuracy, spatial uniformity, and robustness to boundary artifacts. In the resolution phantom, the normalized root-mean-squared error of all methods grew rapidly (>0.40) when the hole size was below 10 mm, with simplified methods (PB and IB), or below 5 mm, with generalized methods (PB-cr and GIB).

CONCLUSION

VNA measurements are essential to assess the accuracy of MR-EPT. In this study, all tested MR-EPT methods correlated strongly with the VNA measurements. The UTE sequence is recommended for MR-EPT, with the GIB method providing good accuracy for structures down to 5 mm. Structures below 5 mm may still be detected in the conductivity maps, but with significantly lower accuracy.

Robust T2 estimation with balanced steady state free precession

PURPOSE

To develop a novel signal representation for balanced steady state free precession (bSSFP) displaying its T2 independence on B1 and on magnetization transfer (MT) effects.

METHODS

A signal model for bSSFP is developed that shows only an explicit dependence (up to a scaling factor) on E2 (and, therefore, T2) and a novel parameter c (with implicit dependence on the flip angle and E1). Moreover, it is shown that MT effects, entering the bSSFP signal via a binary spin bath model, can be captured by a redefinition of T1 and, therefore, leading to modification of E1, resulting in the same signal model. Various sets of phase-cycled bSSFP brain scans (different flip angles, different TR, different RF pulse durations, and different number of phase cycles) were recorded at 3 T. The parameters T2 (E2) and c were estimated using a variable projection (VARPRO) method and Monte-Carlo simulations were performed to assess T2 estimation precision.

RESULTS

Initial experiments confirmed the expected independence of T2 on various protocol settings, such as TR, the flip angle, B1 field inhomogeneity, and the RF pulse duration. Any variation (within the explored range) appears to directly affect the estimation of the parameter c only-in agreement with theory.

CONCLUSION

BSSFP theory predicts an extraordinary feature that all MT and B1-related variational aspects do not enter T2 estimation, making it a potentially robust methodology for T2 quantification, pending validation against existing standards.

Rapid quantitative magnetization transfer imaging: Utilizing the hybrid state and the generalized Bloch model

PURPOSE

To explore efficient encoding schemes for quantitative magnetization transfer (qMT) imaging with few constraints on model parameters.

THEORY AND METHODS

We combine two recently proposed models in a Bloch-McConnell equation: the dynamics of the free spin pool are confined to the hybrid state, and the dynamics of the semi-solid spin pool are described by the generalized Bloch model. We numerically optimize the flip angles and durations of a train of radio frequency pulses to enhance the encoding of three qMT parameters while accounting for all eight parameters of the two-pool model. We sparsely sample each time frame along this spin dynamics with a three-dimensional radial koosh-ball trajectory, reconstruct the data with subspace modeling, and fit the qMT model with a neural network for computational efficiency.

RESULTS

We extracted qMT parameter maps of the whole brain with an effective resolution of 1.24 mm from a 12.6-min scan. In lesions of multiple sclerosis subjects, we observe a decreased size of the semi-solid spin pool and longer relaxation times, consistent with previous reports.

CONCLUSION

The encoding power of the hybrid state, combined with regularized image reconstruction, and the accuracy of the generalized Bloch model provide an excellent basis for efficient quantitative magnetization transfer imaging with few constraints on model parameters.

Fast T2 mapping of short-T2 tissues in knee using 3D radial dual-echo balanced steady-state free precession

BACKGROUND

T2 mapping of short-T2 tissues in the knee (meniscus, tendon, and ligament) is needed to aid the clinical MRI knee diagnosis, which is hard to realize using traditional clinical methods.

PURPOSE

To accelerate the acquisition of T2 values for short-T2 tissues in the knee by analyzing the signal equation of balanced steady-state free precession (bSSFP) sequence in MRI.

METHODS

Effect of half-radial acquisition on pixel bandwidth was analyzed mathematically. A modified 3D radial dual-echo bSSFP sequence was proposed for 0.53 mm isotropic resolution knee imaging with 2 different TEs at 3 T, which alleviated the problem of off-resonance artifacts caused by traditional half-radial acquisition scheme. A novel pixel-based optimization method was proposed for efficient T2 mapping of short-T2 tissues in the knee given off-resonance values. Simulation was conducted to evaluate the sensitivity of the proposed method to other parameters. Phantom results were compared with 2D spin-echo (SE), and in vivo results were compared with SE and previously studies.

RESULTS

Simulation showed that the proposed method is insensitive to T1 and B1 variations (estimation error < 1% for T1/B1 error of ±90%), avoiding the need for separated T1 and B1 scans. High isotropic resolution knee imaging was achieved using the modified dual-echo bSSFP. The total scan time was within 3.5 min, including a separate off-resonance scan for T2 measurement. Measured mean T2 values for phantoms correlated well with SE (R2 = 0.99), and no significant difference was observed (P = 0.45). In vivo meniscus T2 measurements and ligament T2 measurements agreed with the literature, while tendon T2 measurements were much lower (31.7% lower for patellar tendon, and 13.5% lower for quadriceps tendon), which might result in its bi-component property.

CONCLUSIONS

The proposed method provides an efficient way for fast, robust, high-resolution imaging and T2 mapping of short-T2 tissues in the knee.

Neuroimaging of Parkinson's disease by quantitative susceptibility mapping

Parkinson's disease (PD) is a common neurodegenerative disease, and apart from a few rare genetic causes, its pathogenesis remains largely unclear. Recent scientific interest has been captured by the involvement of iron biochemistry and the disruption of iron homeostasis, particularly within the brain regions specifically affected in PD. The advent of Quantitative Susceptibility Mapping (QSM) has enabled non-invasive quantification of brain iron in vivo by MRI, which has contributed to the understanding of iron-associated pathogenesis and has the potential for the development of iron-based biomarkers in PD. This review elucidates the biochemical underpinnings of brain iron accumulation, details advancements in iron-sensitive MRI technologies, and discusses the role of QSM as a biomarker of iron deposition in PD. Despite considerable progress, several challenges impede its clinical application after a decade of QSM studies. The initiation of multi-site research is warranted for developing robust, interpretable, and disease-specific biomarkers for monitoring PD disease progression.

Water diffusion and T2 quantification in transient-state MRI: the effect of RF pulse sequence

In quantitative measurement of the T 2 value of tissues, the diffusion of water molecules has been recognized as a confounder. This is most notably so for transient-state quantitative mapping techniques, which allow simultaneous estimation of T 1 and T 2 . In prior work, apparently conflicting conclusions are presented on the level of diffusion-induced bias on the T2 estimate. So far there is a lack of studies on the effect of the RF pulse angle sequence on the level of diffusion-induced bias. In this work, we show that the specific transient-state RF pulse sequence has a large effect on this level of bias. In particular, the bias level is strongly influenced by the mean value of the RF pulse angles. Also, for realistic values of the spoiling gradient area, we infer that the diffusion-induced bias is negligible for non-liquid human tissues; yet, for phantoms, the effect can be substantial (15% of the true T 2 value) for some RF pulse sequences. This should be taken into account in validation procedures.

SIMPLEX: Multiple phase-cycled bSSFP quantitative magnetization transfer imaging with physic-guided simulation learning of neural network

Most quantitative magnetization transfer (qMT) imaging methods require acquiring additional quantitative maps (such as T1) for data fitting. A method based on multiple phase-cycled bSSFP was recently proposed to enable high-resolution 3D qMT imaging based on least square fitting without any extra acquisition, and thus has high potential for simplifying the qMT procedure. However, the quantification of qMT parameters with this method was suboptimal, limiting its potential for clinical application despite its simpler protocol and higher spatial resolution. To improve the fitting of qMT data obtained with multiple phase-cycled bSSFP, we propose SIMulation-based Physics-guided Learning of neural network for qMT parameters EXtraction, or SIMPLEX. In contrast to previous deep learning supervised approaches for quantitative MR that require the acquisition of input data and corresponding ground truth for training, we leveraged the MR signal model to generate training samples without expensive data curation. The network was trained exclusively with simulation data by predicting the simulation parameters. The same network was applied directly to in-vivo data without additional training. The approach was verified with both simulation and in-vivo data. SIMPLEX showed a decrease in fitting mean squared error for all simulation data compared to the existing least-square fitting method. The in-vivo experiment revealed that the network performed well with the real in vivo data unseen during training. For all experiments, we observed that SIMPLEX consistently improved the quantification quality of the qMT parameters whilst being more robust to noise compared to the prior technique. The proposed SIMPLEX will expedite the routine clinical application of qMT by providing qMT parameters (exchange rate, pool fraction) as well as T1, T2, and ΔB0 maps simultaneously with high spatial resolution, better reliability, and reduced processing time.

Multi-parametric MRI for radiotherapy simulation

Magnetic resonance imaging (MRI) has become an important imaging modality in the field of radiotherapy (RT) in the past decade, especially with the development of various novel MRI and image-guidance techniques. In this review article, we will describe recent developments and discuss the applications of multi-parametric MRI (mpMRI) in RT simulation. In this review, mpMRI refers to a general and loose definition which includes various multi-contrast MRI techniques. Specifically, we will focus on the implementation, challenges, and future directions of mpMRI techniques for RT simulation.

Efficient performance analysis and optimization of transient-state sequences for multiparametric magnetic resonance imaging

In transient-state multiparametric MRI sequences such as Magnetic Resonance Spin TomogrAphy in Time-domain (MR-STAT), MR fingerprinting, or hybrid-state imaging, the flip angle pattern of the RF excitation varies over the sequence. This gives considerable freedom to choose an optimal pattern of flip angles. For pragmatic reasons, most optimization methodologies choose for a single-voxel approach (i.e., without taking the spatial encoding scheme into account). Particularly in MR-STAT, the context of spatial encoding is important. In the current study, we present a methodology, called BLock Analysis of a K-space-domain Jacobian (BLAKJac), which is sufficiently fast to optimize a sequence in the context of a predetermined phase-encoding pattern. Based on MR-STAT acquisitions and reconstructions, we show that sequences optimized using BLAKJac are more reliable in terms of actually achieved precision than conventional single-voxel-optimized sequences. In addition, BLAKJac provides analytical tools that give insights into the performance of the sequence in a very limited computation time. Our experiments are based on MR-STAT, but the theory is equally valid for other transient-state multiparametric methods.

Approximate B 1 + scaling of the SSFP steady state

PURPOSE

It is shown that the steady state of rapid, TR-periodic steady-state free precession (SSFP) sequences at small to moderate flip angles exhibits a universal, approximate scaling law with respect to variations of B 1 + $$ {B}_1^{+} $$ . Implications for the accuracy and precision of relaxometry experiments are discussed.

METHODS

The approximate scaling law is derived from and numerically tested against known analytical solutions. To assess the attainable estimator precision in a typical relaxometry experiment, we calculate the Cramér-Rao bound (CRB) and perform Monte Carlo (MC) simulations.

RESULTS

The approximate universal scaling holds well up to moderate flip angles. For pure steady state relaxometry, we observe a significant precision penalty for simultaneous estimation of R 1 $$ {R}_1 $$ and B 1 + $$ {B}_1^{+} $$ , whereas good R 2 $$ {R}_2 $$ estimates can be obtained without even knowing the correct actual flip angle.

CONCLUSION

Simultaneous estimation of R 1 $$ {R}_1 $$ and B 1 + $$ {B}_1^{+} $$ from a set of SSFP steady states alone is not advisable. Apart from separate B 1 + $$ {B}_1^{+} $$ measurements, the problem can be addressed by adding transient state information, but, depending on the situation, residual effects due to the scaling may still require some attention.

Primary Multiparametric Quantitative Brain MRI: State-of-the-Art Relaxometric and Proton Density Mapping Techniques

This review on brain multiparametric quantitative MRI (MP-qMRI) focuses on the primary subset of quantitative MRI (qMRI) parameters that represent the mobile ("free") and bound ("motion-restricted") proton pools. Such primary parameters are the proton densities, relaxation times, and magnetization transfer parameters. Diffusion qMRI is also included because of its wide implementation in complete clinical MP-qMRI application. MP-qMRI advances were reviewed over the past 2 decades, with substantial progress observed toward accelerating image acquisition and increasing mapping accuracy. Areas that need further investigation and refinement are identified as follows: (a) the biologic underpinnings of qMRI parameter values and their changes with age and/or disease and (b) the theoretical limitations implicitly built into most qMRI mapping algorithms that do not distinguish between the different spatial scales of voxels versus spin packets, the central physical object of the Bloch theory. With rapidly improving image processing techniques and continuous advances in computer hardware, MP-qMRI has the potential for implementation in a wide range of clinical applications. Currently, three emerging MP-qMRI applications are synthetic MRI, macrostructural qMRI, and microstructural tissue modeling.

High-resolution neural network-driven mapping of multiple diffusion metrics leveraging asymmetries in the balanced steady-state free precession frequency profile

We propose to utilize the rich information content about microstructural tissue properties entangled in asymmetric balanced steady-state free precession (bSSFP) profiles to estimate multiple diffusion metrics simultaneously by neural network (NN) parameter quantification. A 12-point bSSFP phase-cycling scheme with high-resolution whole-brain coverage is employed at 3 and 9.4 T for NN input. Low-resolution target diffusion data are derived based on diffusion-weighted spin-echo echo-planar-imaging (SE-EPI) scans, that is, mean, axial, and radial diffusivity (MD, AD, and RD), fractional anisotropy (FA), as well as the spherical coordinates (azimuth Φ and inclination ϴ) of the principal diffusion eigenvector. A feedforward NN is trained with incorporated probabilistic uncertainty estimation. The NN predictions yielded highly reliable results in white matter (WM) and gray matter structures for MD. The quantification of FA, AD, and RD was overall in good agreement with the reference but the dependence of these parameters on WM anisotropy was somewhat biased (e.g. in corpus callosum). The inclination ϴ was well predicted for anisotropic WM structures, while the azimuth Φ was overall poorly predicted. The findings were highly consistent across both field strengths. Application of the optimized NN to high-resolution input data provided whole-brain maps with rich structural details. In conclusion, the proposed NN-driven approach showed potential to provide distortion-free high-resolution whole-brain maps of multiple diffusion metrics at high to ultrahigh field strengths in clinically relevant scan times.

Challenges in ensuring the generalizability of image quantitation methods for MRI

Image quantitation methods including quantitative MRI, multiparametric MRI, and radiomics offer great promise for clinical use. However, many of these methods have limited clinical adoption, in part due to issues of generalizability, that is, the ability to translate methods and models across institutions. Researchers can assess generalizability through measurement of repeatability and reproducibility, thus quantifying different aspects of measurement variance. In this article, we review the challenges to ensuring repeatability and reproducibility of image quantitation methods as well as present strategies to minimize their variance to enable wider clinical implementation. We present possible solutions for achieving clinically acceptable performance of image quantitation methods and briefly discuss the impact of minimizing variance and achieving generalizability towards clinical implementation and adoption.

Constrained Ellipse Fitting for Efficient Parameter Mapping With Phase-Cycled bSSFP MRI

Balanced steady-state free precession (bSSFP) imaging enables high scan efficiency in MRI, but differs from conventional sequences in terms of elevated sensitivity to main field inhomogeneity and nonstandard [Formula: see text]-weighted tissue contrast. To address these limitations, multiple bSSFP images of the same anatomy are commonly acquired with a set of different RF phase-cycling increments. Joint processing of phase-cycled acquisitions serves to mitigate sensitivity to field inhomogeneity. Recently phase-cycled bSSFP acquisitions were also leveraged to estimate relaxation parameters based on explicit signal models. While effective, these model-based methods often involve a large number of acquisitions (N ≈ 10-16), degrading scan efficiency. Here, we propose a new constrained ellipse fitting method (CELF) for parameter estimation with improved efficiency and accuracy in phase-cycled bSSFP MRI. CELF is based on the elliptical signal model framework for complex bSSFP signals; and it introduces geometrical constraints on ellipse properties to improve estimation efficiency, and dictionary-based identification to improve estimation accuracy. CELF generates maps of [Formula: see text], [Formula: see text], off-resonance and on-resonant bSSFP signal by employing a separate [Formula: see text] map to mitigate sensitivity to flip angle variations. Our results indicate that CELF can produce accurate off-resonance and banding-free bSSFP maps with as few as N = 4 acquisitions, while estimation accuracy for relaxation parameters is notably limited by biases from microstructural sensitivity of bSSFP imaging.

Pure balanced steady-state free precession imaging (pure bSSFP)

Purpose

To show that for tissues the conspicuous asymmetries in the frequency response function of bSSFP can be mitigated by using a short enough TR.

Theory and Methods

Configuration theory indicates that bSSFP becomes apparently “pure” (i.e., exhibiting a symmetric profile) in the limit of TR →0. To this end, the frequency profile of bSSFP was measured as a function of the TR using a manganese‐doped aqueous probe, as well as brain tissue that was shown to exhibit a pronounced asymmetry due to its microstructure. The frequency response function was sampled using N=72 (phantom) and N=36 (in vivo) equally distributed linear RF phase increments in the interval [0,2π). Imaging was performed with 2.0 mm isotropic resolution over a TR range of 1.5–8 ms at 3 and 1.5 T.

Results

As expected, pure substances showed a symmetric TR‐independent frequency profile, whereas brain tissue revealed a pronounced asymmetry. The observed asymmetry for the tissue, however, decreases with decreasing TR and gives strong evidence that the frequency response function of bSSFP becomes symmetric in the limit of TR →0, in agreement with theory. The limit of apparently pure bSSFP imaging can thus be achieved for a TR ∼ 1.5 ms at 1.5 T, whereas at 3 T, tissues still show some residual asymmetry.

Conclusion

In the limit of short enough TR, tissues become apparently pure for bSSFP. This limit can be reached for brain tissue at 1.5 T with TR ∼ 1–2 ms at clinically relevant resolutions.

Temperature dependence, accuracy, and repeatability of T1 and T2 relaxation times for the ISMRM/NIST system phantom measured using MR fingerprinting

PURPOSE

Before MR fingerprinting (MRF) can be adopted clinically, the derived quantitative values must be proven accurate and repeatable over a range of T₁ and T₂ values and temperatures. Correct assessment of accuracy and precision as well as comparison between measurements can only be performed when temperature is either controlled or corrected for. The purpose of this study was to investigate the temperature dependence of T₁ and T₂ MRF values and evaluate the accuracy and repeatability of temperature-corrected relaxation values derived from a B₁ -corrected MRF-fast imaging with steady-state precession implementation using 2 different dictionary sizes.

METHODS

The International Society of MR in Medicine/National Institute of Standards and Technology phantom was scanned using an MRF sequence of 2 different lengths, a variable flip angle T₁ , and a multi-echo spin echo T₂ at 14 temperatures ranging from 15°C to 28°C and investigated with a linear regression model. Temperature-corrected accuracy was evaluated by correlating T₁ and T₂ times from each MRF dictionary with reference values. Repeatability was assessed using the coefficient of variation, with measurements taken over 30 separate sessions.

RESULTS

There was a statistically significant fit of the model for MRF-derived T₁ and T₂ and temperature (p < 0.05) for all the spheres with a T₁ > 500 ms. Both MRF methods showed a strong linear correlation with reference values for T₁ (R² = 0.996) and T₂ (R² = 0.982). MRF repeatability for T₁ values was ≤1.4% and for T₂ values was ≤3.4%.

CONCLUSION

MRF demonstrated relaxation times with a temperature dependence similar to that of conventional mapping methods. Temperature-corrected T₁ and T₂ values from both dictionaries showed adequate accuracy and excellent repeatability in this phantom study.

Accuracy and repeatability of QRAPMASTER and MRF-vFA

Our purpose is to evaluate bias and repeatability of the quantitative MRI sequences QRAPMASTER, based on steady-state imaging, and variable Flip Angle MRF (MRF-VFA), based on the transient response. Both techniques are assessed with a standardized phantom and five volunteers on 1.5 T and 3 T clinical scanners. All scans were repeated eight times in consecutive weeks. In the phantom, the mean bias±95% confidence interval for T1 values with QRAPMASTER was 10 ± 10% on 1.5 T and 4 ± 13% on 3.0 T. The mean bias for T1 values with MRF-vFA was 21 ± 17% on 1.5 T and 9 ± 9% on 3.0 T. For T2 values the mean bias with QRAPMASTER was 12 ± 3% on 1.5 T and 23 ± 1% on 3.0 T. For T2 values the mean bias with MRF-vFA was 17 ± 1% on 1.5 T and 19 ± 2% on 3.0 T. QRAPMASTER estimated lower T1 and T2 values than MRF-vFA. Repeatability was good with low coefficients of variation (CoV). Mean CoV ± 95% confidence interval for T1 were 3.2 ± 0.4% on 1.5 T and 4.5 ± 0.8% on 3.0 T with QRAPMASTER and 2.7% ± 0.2% on 1.5 T and 2.5 ± 0.2% on 3.0 T with MRF-vFA. For T2 were 3.3 ± 1.9% on 1.5 T and 3.2 ± 0.6% on 3.0 T with QRAPMASTER and 2.0 ± 0.4% on 1.5 T and 5.7 ± 1.0% on 3.0 T with MRF-vFA. The in-vivo T1 and T2 are in the range of values previously reported by other authors. The in-vivo mean CoV ± 95% confidence interval in gray matter were for T1 1.7 ± 0.2% using QRAPMASTER and 0.7 ± 0.5% using MRF-vFA and for T2 were 0.9 ± 0.4% using QRAPMASTER and 2.4 ± 0.5% using MRF-vFA. In white matter were for T1 0.9 ± 0.3% using QRAPMASTER and 1.3 ± 1.1% using MRF-vFA and for T2 were 0.7 ± 0.4% using QRAPMASTER and 2.4 ± 0.4% using MRF-vFA. A GLM analysis showed that the variations in T1 and T2 mainly depend on the field strength and the subject, but not on the follow-up repetition in different days. This confirms the high repeatability of QRAPMASTER and MRF-vFA. In summary, QRAPMASTER and MRF-vFA on both systems were highly repeatable with moderate accuracy, providing results comparable to standard references. While repeatability was similar for both methods, QRAPMASTER was more accurate. QRAPMASTER is a tested commercial product but MRF-vFA is 4.77 times faster, which would ease the inclusion of quantitative relaxometry.

From signal-based to comprehensive magnetic resonance imaging

We present and evaluate a new insight into magnetic resonance imaging (MRI). It is based on the algebraic description of the magnetization during the transient response—including intrinsic magnetic resonance parameters such as longitudinal and transverse relaxation times (T₁, T₂) and proton density (PD) and experimental conditions such as radiofrequency field (B₁) and constant/homogeneous magnetic field (B₀) from associated scanners. We exploit the correspondence among three different elements: the signal evolution as a result of a repetitive sequence of blocks of radiofrequency excitation pulses and encoding gradients, the continuous Bloch equations and the mathematical description of a sequence as a linear system. This approach simultaneously provides, in a single measurement, all quantitative parameters of interest as well as associated system imperfections. Finally, we demonstrate the in-vivo applicability of the new concept on a clinical MRI scanner.

Unbiased signal equation for quantitative magnetization transfer mapping in balanced steady-state free precession MRI

Purpose

Quantitative magnetization transfer (qMT) imaging can be used to quantify the proportion of protons in a voxel attached to macromolecules. Here, we show that the original qMT balanced steady‐state free precession (bSSFP) model is biased due to over‐simplistic assumptions made in its derivation.

Theory and Methods

We present an improved model for qMT bSSFP, which incorporates finite radiofrequency (RF) pulse effects as well as simultaneous exchange and relaxation. Furthermore, a correction relating to finite RF pulse effects for sinc‐shaped excitations is derived. The new model is compared to the original one in numerical simulations of the Bloch‐McConnell equations and in previously acquired in vivo data.

Results

Our numerical simulations show that the original signal equation is significantly biased in typical brain tissue structures (by 7%‐20%), whereas the new signal equation outperforms the original one with minimal bias (<1%). It is further shown that the bias of the original model strongly affects the acquired qMT parameters in human brain structures, with differences in the clinically relevant parameter of pool‐size‐ratio of up to 31%. Particularly high biases of the original signal equation are expected in an MS lesion within diseased brain tissue (due to a low T2/T1‐ratio), demanding a more accurate model for clinical applications.

Conclusion

The improved model for qMT bSSFP is recommended for accurate qMT parameter mapping in healthy and diseased brain tissue structures.

Efficiency analysis for quantitative MRI of T1 and T2 relaxometry methods

This study presents a comparison of quantitative MRI methods based on an efficiency metric that quantifies their intrinsic ability to extract information about tissue parameters. Under a regime of unbiased parameter estimates, an intrinsic efficiency metricηwas derived for fully-sampled experiments which can be used to both optimize and compare sequences. Here we optimize and compare several steady-state and transient gradient-echo based qMRI methods, such as magnetic resonance fingerprinting (MRF), for jointT1andT2mapping. The impact of undersampling was also evaluated, assuming incoherent aliasing that is treated as noise by parameter estimation.In vivovalidation of the efficiency metric was also performed. Transient methods such as MRF can be up to 3.5 times more efficient than steady-state methods, when spatial undersampling is ignored. If incoherent aliasing is treated as noise during least-squares parameter estimation, the efficiency is reduced in proportion to the SNR of the data, with reduction factors of 5 often seen for practical SNR levels.In vivovalidation showed a very good agreement between the theoretical and experimentally predicted efficiency. This work presents and validates an efficiency metric to optimize and compare the performance of qMRI methods. Transient methods were found to be intrinsically more efficient than steady-state methods, however the effect of spatial undersampling can significantly erode this advantage.

Unbalanced SSFP for super-resolution in MRI

Purpose:

To achieve rapid, low specific absorption rate (SAR) super-resolution imaging by exploiting the characteristic magnetization off-resonance profile in SSFP.

Theory and Methods:

In the presented technique, low flip angle unbalanced SSFP imaging is used to acquire a series of images at a low nominal resolution that are then combined in a super-resolution strategy analogous to non-linear structured illumination microscopy. This is demonstrated in principle via Bloch simulations and synthetic phantoms, and the performance is quantified in terms of point-spread function (PSF) and SNR for gray and white matter from field strengths of 0.35T to 9.4T. A k-space reconstruction approach is proposed to account for B₀ effects. This was applied to reconstruct super-resolution images from a test object at 9.4T.

Results:

Artifact-free super-resolution images were produced after incorporating sufficient preparation time for the magnetization to approach the steady state. High-resolution images of a test object were obtained at 9.4T, in the presence of considerable B₀ inhomogeneity. For gray matter, the highest achievable resolution ranges from 3% of the acquired voxel dimension at 0.35T, to 9% at 9.4T. For white matter, this corresponds to 3% and 10%, respectively. Compared to an equivalent segmented gradient echo acquisition at the optimal flip angle, with a fixed TR of 8 ms, gray matter has up to 34% of the SNR at 9.4T while using a ×10 smaller flip angle. For white matter, this corresponds to 29% with a ×11 smaller flip angle.

Conclusion:

This approach achieves high degrees of super-resolution enhancement with minimal RF power requirements.

Configuration-based electrical properties tomography

PURPOSE

To introduce phase-based conductivity mapping from a configuration space analysis.

METHODS

The frequency response function of balanced SSFP (bSSFP) is used to perform a configuration space analysis. It is shown that the transceive phase for conductivity mapping can be directly obtained by a simple fast Fourier transform of a series of phase-cycled bSSFP scans. For validation, transceive phase and off-resonance mapping with fast Fourier transform is compared with phase estimation using a recently proposed method, termed PLANET. Experiments were performed in phantoms and for in vivo brain imaging at 3 T using a quadrature head coil.

RESULTS

For fast Fourier transform, aliasing can lead to systematic phase errors. This bias, however, decreases rapidly with increasing sampling points. Interestingly, Monte Carlo simulations revealed a lower uncertainty for the transceive phase and the off-resonance using fast Fourier transform as compared with PLANET. Both methods, however, essentially retrieve the same phase information from a set of phase-cycled bSSFP scans. As a result, configuration-based conductivity mapping was successfully performed using eight phase-cycled bSSFP scans in the phantoms and for brain tissues. Overall, the retrieved values were in good agreement with expectations. Conductivity estimation and mapping of the field inhomogeneities can therefore be performed in conjunction with the estimation of other quantitative parameters, such as relaxation, using configuration theory.

CONCLUSIONS

Phase-based conductivity mapping can be estimated directly from a simple Fourier analysis, such as in conjunction with relaxometry, using a series of phase-cycled bSSFP scans.

Multi-parametric artificial neural network fitting of phase-cycled balanced steady-state free precession data

PURPOSE

Standard relaxation time quantification using phase-cycled balanced steady-state free precession (bSSFP), eg, motion-insensitive rapid configuration relaxometry (MIRACLE), is subject to a considerable underestimation of tissue T₁ and T₂ due to asymmetric intra-voxel frequency distributions. In this work, an artificial neural network (ANN) fitting approach is proposed to simultaneously extract accurate reference relaxation times (T₁ , T₂ ) and robust field map estimates ( B 1 + , ΔB₀ ) from the bSSFP profile.

METHODS

Whole-brain bSSFP data acquired at 3T were used for the training of a feedforward ANN with N = 12, 6, and 4 phase-cycles. The magnitude and phase of the Fourier transformed complex bSSFP frequency response served as input and the multi-parametric reference set [T₁ , T₂ , B 1 + , ∆B₀ ] as target. The ANN predicted relaxation times were validated against the target and MIRACLE.

RESULTS

The ANN prediction of T₁ and T₂ for trained and untrained data agreed well with the reference, even for only four acquired phase-cycles. In contrast, relaxometry based on 4-point MIRACLE was prone to severe off-resonance-related artifacts. ANN predicted B 1 + and ∆B₀ maps showed the expected spatial inhomogeneity patterns in high agreement with the reference measurements for 12-point, 6-point, and 4-point bSSFP phase-cycling schemes.

CONCLUSION

ANNs show promise to provide accurate brain tissue T₁ and T₂ values as well as reliable field map estimates. Moreover, the bSSFP acquisition can be accelerated by reducing the number of phase-cycles while still delivering robust T₁ , T₂ , B 1 + , and ∆B₀ estimates.

High-resolution in vivo MR-STAT using a matrix-free and parallelized reconstruction algorithm

MR-STAT is a recently proposed framework that allows the reconstruction of multiple quantitative parameter maps from a single short scan by performing spatial localisation and parameter estimation on the time-domain data simultaneously, without relying on the fast Fourier transform (FFT). To do this at high resolution, specialized algorithms are required to solve the underlying large-scale nonlinear optimisation problem. We propose a matrix-free and parallelized inexact Gauss-Newton based reconstruction algorithm for this purpose. The proposed algorithm is implemented on a high-performance computing cluster and is demonstrated to be able to generate high-resolution (1 mm  ×  1 mm in-plane resolution) quantitative parameter maps in simulation, phantom, and in vivo brain experiments. Reconstructed T1 and T2 values for the gel phantoms are in agreement with results from gold standard measurements and, for the in vivo experiments, the quantitative values show good agreement with literature values. In all experiments, short pulse sequences with robust Cartesian sampling are used, for which MR fingerprinting reconstructions are shown to fail.

Magnetization transfer and frequency distribution effects in the SSFP ellipse

Purpose

To demonstrate that quantitative magnetization transfer (qMT) parameters can be extracted from steady‐state free‐precession (SSFP) data with no external T₁ map or banding artifacts.

Methods

SSFP images with multiple MT weightings were acquired and qMT parameters fitted with a two‐stage elliptical signal model.

Results

Monte Carlo simulations and data from a 3T scanner indicated that most qMT parameters could be recovered with reasonable accuracy. Systematic deviations from theory were observed in white matter, consistent with previous literature on frequency distribution effects.

Conclusions

qMT parameters can be extracted from SSFP data alone, in a manner robust to banding artifacts, despite several confounds.

Transceive phase mapping using the PLANET method and its application for conductivity mapping in the brain

Purpose

To demonstrate feasibility of transceive phase mapping with the PLANET method and its application for conductivity reconstruction in the brain.

Methods

Accuracy and precision of transceive phase (ϕ^±) estimation with PLANET, an ellipse fitting approach to phase‐cycled balanced steady state free precession (bSSFP) data, were assessed with simulations and measurements and compared to standard bSSFP. Measurements were conducted on a homogeneous phantom and in the brain of healthy volunteers at 3 tesla. Conductivity maps were reconstructed with Helmholtz‐based electrical properties tomography. In measurements, PLANET was also compared to a reference technique for transceive phase mapping, i.e., spin echo.

Results

Accuracy and precision of ϕ^± estimated with PLANET depended on the chosen flip angle and TR. PLANET‐based ϕ^± was less sensitive to perturbations induced by off‐resonance effects and partial volume (e.g., white matter + myelin) than bSSFP‐based ϕ^±. For flip angle = 25° and TR = 4.6 ms, PLANET showed an accuracy comparable to that of reference spin echo but a higher precision than bSSFP and spin echo (factor of 2 and 3, respectively). The acquisition time for PLANET was ~5 min; 2 min faster than spin echo and 8 times slower than bSSFP. However, PLANET simultaneously reconstructed T₁, T₂, B₀ maps besides mapping ϕ^±. In the phantom, PLANET‐based conductivity matched the true value and had the smallest spread of the three methods. In vivo, PLANET‐based conductivity was similar to spin echo‐based conductivity.

Conclusion

Provided that appropriate sequence parameters are used, PLANET delivers accurate and precise ϕ^± maps, which can be used to reconstruct brain tissue conductivity while simultaneously recovering T₁, T₂, and B₀ maps.

Investigation of the influence of B0 drift on the performance of the PLANET method and an algorithm for drift correction

Purpose

The PLANET method was designed to simultaneously reconstruct maps of T₁ and T₂, the off‐resonance, the RF phase, and the banding free signal magnitude. The method requires a stationary B₀ field over the course of a phase‐cycled balanced SSFP acquisition. In this work we investigated the influence of B₀ drift on the performance of the PLANET method for single‐component and two‐component signal models, and we propose a strategy for drift correction.

Methods

The complex phase‐cycled balanced SSFP signal was modeled with and without frequency drift. The behavior of the signal influenced by drift was mathematically interpreted as a sum of drift‐dependent displacement of the data points along an ellipse and drift‐dependent rotation around the origin. The influence of drift on parameter estimates was investigated experimentally on a phantom and on the brain of healthy volunteers and was verified by numerical simulations. A drift correction algorithm was proposed and tested on a phantom and in vivo.

Results

Drift can be assumed to be linear over the typical duration of a PLANET acquisition. In a phantom (a single‐component signal model), drift induced errors of 4% and 8% in the estimated T₁ and T₂ values. In the brain, where multiple components are present, drift only had a minor effect. For both single‐component and two‐component signal models, drift‐induced errors were successfully corrected by applying the proposed drift correction algorithm.

Conclusion

We have demonstrated theoretically and experimentally the sensitivity of the PLANET method to B₀ drift and have proposed a drift correction method.

Optimized quantification of spin relaxation times in the hybrid state

PURPOSE

The optimization and analysis of spin ensemble trajectories in the hybrid state-a state in which the direction of the magnetization adiabatically follows the steady state while the magnitude remains in a transient state.

METHODS

Numerical optimizations were performed to find spin ensemble trajectories that minimize the Cramér-Rao bound for T 1 -encoding, T 2 -encoding, and their weighted sum, respectively, followed by a comparison between the Cramér-Rao bounds obtained with our optimized spin-trajectories, Look-Locker sequences, and multi-spin-echo methods. Finally, we experimentally tested our optimized spin trajectories with in vivo scans of the human brain.

RESULTS

After a nonrecurring inversion segment on the southern half of the Bloch sphere, all optimized spin trajectories pursue repetitive loops on the northern hemisphere in which the beginning of the first and the end of the last loop deviate from the others. The numerical results obtained in this work align well with intuitive insights gleaned directly from the governing equation. Our results suggest that hybrid-state sequences outperform traditional methods. Moreover, hybrid-state sequences that balance T 1 - and T 2 -encoding still result in near optimal signal-to-noise efficiency for each relaxation time. Thus, the second parameter can be encoded at virtually no extra cost.

CONCLUSIONS

We provided new insights into the optimal encoding processes of spin relaxation times in order to guide the design of robust and efficient pulse sequences. We found that joint acquisitions of T 1 and T 2 in the hybrid state are substantially more efficient than sequential encoding techniques.

Frequency-modulated SSFP with radial sampling and subspace reconstruction: A time-efficient alternative to phase-cycled bSSFP

PURPOSE

A novel subspace-based reconstruction method for frequency-modulated balanced steady-state free precession (fmSSFP) MRI is presented. In this work, suitable data acquisition schemes, subspace sizes, and efficiencies for banding removal are investigated.

THEORY AND METHODS

By combining a fmSSFP MRI sequence with a 3D stack-of-stars trajectory, scan efficiency is maximized as spectral information is obtained without intermediate preparation phases. A memory-efficient reconstruction routine is implemented by introducing the low-frequency Fourier transform as a subspace which allows for the formulation of a convex reconstruction problem. The removal of banding artifacts is investigated by comparing the proposed acquisition and reconstruction technique to phase-cycled bSSFP MRI. Aliasing properties of different undersampling schemes are analyzed and water/fat separation is demonstrated by reweighting the reconstructed subspace coefficients to generate virtual spectral responses in a post-processing step.

RESULTS

A simple root-of-sum-of-squares combination of the reconstructed subspace coefficients yields high-SNR images with the characteristic bSSFP contrast but without banding artifacts. Compared to Golden-Angle trajectories, turn-based sampling schemes were superior in minimizing aliasing across reconstructed subspace coefficients. Water/fat separated images of the human knee were obtained by reweighting subspace coefficients.

CONCLUSIONS

The novel subspace-based fmSSFP MRI technique emerges as a time-efficient alternative to phase-cycled bSFFP. The method does not need intermediate preparation phases, offers high SNR and avoids banding artifacts. Reweighting of the reconstructed subspace coefficients allows for generating virtual spectral responses with applications to water/fat separation.

bSSFP phase correction and its use in magnetic resonance electrical properties tomography

PURPOSE

Balanced steady-state free precession (bSSFP) sequence is widely used because of its high SNR and high speed. However, bSSFP images suffer from "banding artifact" caused by B₀ inhomogeneity. In this article, we propose a method to remove this artifact in bSSFP phase images and investigate the usage of the corrected phase images in phase-based magnetic resonance electrical properties tomography (MREPT).

THEORY AND METHODS

Two bSSFP phase images, obtained with different excitation frequencies, are collaged to get rid of the regions containing banding artifacts. Phase of the collaged bSSFP image is the sum of the transceive phase of the RF system and an error term that depends on B₀ and T₂ . By using B₀ and T₂ maps, this error is eliminated from bSSFP phase images by using pixel-wise corrections. Conductivity maps are obtained from the uncorrected and the corrected phase images using the phase-based cr-MREPT method.

RESULTS

Phantom and human experiment results of the proposed method are illustrated for both phase images and conductivity maps. It is shown that uncorrected phase images yield unacceptable conductivity images. When only B₀ information is used for phase correction conductivity, reconstructions are substantially improved, and yet T₂ information is still needed to fully recover accurate and undistorted conductivity images.

CONCLUSIONS

With the proposed technique, B₀ sensitivity of the bSSFP phase images can be removed by using B₀ and T₂ maps. It is also shown that corrected bSSFP phase images are of sufficient quality to be used in conductivity imaging.

On the accuracy and precision of PLANET for multiparametric MRI using phase-cycled bSSFP imaging

Purpose

In this work we demonstrate how sequence parameter settings influence the accuracy and precision in T₁, T₂, and off‐resonance maps obtained with the PLANET method for a single‐component signal model. In addition, the performance of the method for the particular case of a two‐component relaxation model for white matter tissue was assessed.

Methods

Numerical simulations were performed to investigate the influence of sequence parameter settings on the accuracy and precision in the estimated parameters for a single‐component model, as well as for a two‐component white matter model. Phantom and in vivo experiments were performed for validation. In addition, the effects of Gibbs ringing were investigated.

Results

By making a proper choice for sequence parameter settings, accurate and precise parameter estimation can be achieved for a single‐component signal model over a wide range of relaxation times at realistic SNR levels. Due to the presence of a second myelin‐related signal component in white matter, an underestimation of approximately 30% in T₁ and T₂ was observed, predicted by simulations and confirmed by measurements. Gibbs ringing artifacts correction improved the precision and accuracy of the parameter estimates.

Conclusion

For a single‐component signal model there is a broad “sweet spot” of sequence parameter combinations for which a high accuracy and precision in the parameter estimates is achieved over a wide range of relaxation times. For a multicomponent signal model, the single‐component PLANET reconstruction results in systematic errors in the parameter estimates as expected.