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

ORACLE: An analytical approach for T1, T2, proton density, and off-resonance mapping with phase-cycled balanced steady-state free precession

PURPOSE

To develop and validate a novel analytical approach simplifyingT 1 $$ {T}_1 $$ ,T 2 $$ {T}_2 $$ , proton density (PD), and off-resonanceΔ f $$ \Delta f $$ quantifications from phase-cycled balanced steady-state free precession (bSSFP) data. Additionally, to introduce a method to correct aliasing effects in undersampled bSSFP profiles.

THEORY AND METHODS

Off-resonant-encoded analytical parameter quantification using complex linearized equations (ORACLE) provides analytical solutions for bSSFP profiles. which instantaneously quantifyT 1 $$ {T}_1 $$ ,T 2 $$ {T}_2 $$ , proton density (PD), andΔ f $$ \Delta f $$ . An aliasing correction formalism was derived to allow undersampling of bSSFP profiles. ORACLE was used to quantifyT 1 $$ {T}_1 $$ ,T 2 $$ {T}_2 $$ , PD,T 1 $$ {T}_1 $$ /T 2 $$ {T}_2 $$ , andΔ f $$ \Delta f $$ based on fully sampled (N = 20 $$ N=20 $$ ) bSSFP profiles from numerical simulations and 3T MRI experiments in phantom and 10 healthy subjects' brains. Obtained values were compared with reference scans in the same scan session. Aliasing correction was validated in subsampled (N = 4 $$ N=4 $$ ) bSSFP profiles in numerical simulations and human brains.

RESULTS

ORACLE quantifications agreed well with input values from simulations and phantom reference values (R2 = 0.99). In human brains,T 1 $$ {T}_1 $$ andT 2 $$ {T}_2 $$ quantifications when compared with reference methods showed coefficients of variation below 2.9% and 3.9%, biases of 182 and 16.6 ms, and mean white-matter values of 642 and 51 ms using ORACLE. TheΔ f $$ \Delta f $$ quantification differed less than 3 Hz between both methods. PD andT 1 $$ {T}_1 $$ maps had comparable histograms. TheΛ $$ \varLambda $$ maps effectively identified cerebrospinal fluid. Aliasing correction removed aliasing-related quantification errors in undersampled bSSFP profiles, significantly reducing scan time.

CONCLUSION

ORACLE enables simplified and rapid quantification ofT 1 $$ {T}_1 $$ ,T 2 $$ {T}_2 $$ , PD, andΔ f $$ \Delta f $$ from phase-cycled bSSFP profiles, reducing acquisition time and eliminating biomarker maps' coregistration issues.

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.

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.

Phase-based fast 3D high-resolution quantitative T2 MRI in 7 T human brain imaging

Magnetic resonance imaging (MRI) is a powerful and versatile technique that offers a range of physiological, diagnostic, structural, and functional measurements. One of the most widely used basic contrasts in MRI diagnostics is transverse relaxation time (T₂)-weighted imaging, but it provides only qualitative information. Realizing quantitative high-resolution T₂ mapping is imperative for the development of personalized medicine, as it can enable the characterization of diseases progression. While ultra-high-field (≥ 7 T) MRI offers the means to gain new insights by increasing the spatial resolution, implementing fast quantitative T₂ mapping cannot be achieved without overcoming the increased power deposition and radio frequency (RF) field inhomogeneity at ultra-high-fields. A recent study has demonstrated a new phase-based T₂ mapping approach based on fast steady-state acquisitions. We extend this new approach to ultra-high field MRI, achieving quantitative high-resolution 3D T₂ mapping at 7 T while addressing RF field inhomogeneity and utilizing low flip angle pulses; overcoming two main ultra-high field challenges. The method is based on controlling the coherent transverse magnetization in a steady-state gradient echo acquisition; achieved by utilizing low flip angles, a specific phase increment for the RF pulses, and short repetition times. This approach simultaneously extracts both T₂ and RF field maps from the phase of the signal. Prior to in vivo experiments, the method was assessed using a 3D head-shaped phantom that was designed to model the RF field distribution in the brain. Our approach delivers fast 3D whole brain images with submillimeter resolution without requiring special hardware, such as multi-channel transmit coil, thus promoting high usability of the ultra-high field MRI in clinical practice.

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.

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.

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.

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.

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.