Ultrafast 3D Bloch-Siegert B <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msubsup><mml:mrow/> <mml:mn>1</mml:mn> <mml:mo>+</mml:mo></mml:msubsup> </mml:math> -mapping using variational modeling

Generating accurate tip angles for NMR outside the rotating-wave approximation

The generation of accurate tip angles is critical for many applications of nuclear magnetic resonance. In low static field, with a linear rather than circular polarized rf field, the rotating-wave approximation may no longer hold and significant deviations from expected trajectories on the Bloch sphere can occur. For rectangular rf pulses, the effects depend strongly on the phase of the rf field and can be further compounded by transients at the start and end of the pulse. The desired terminus can be still be achieved, however, through the application of a phase-dependent Bloch-Siegert shift and appropriate consideration of pulse timings. For suitably shaped rf pulses, the Bloch-Siegert shift is largely phase independent, but its magnitude can vary significantly depending on details of the pulse shape as well as the characteristics of the rf coil circuit. We present numerical simulations and low-field NMR experiments with ¹H and ³He that demonstrate several main consequences and accompanying strategies that one should consider when wanting to generate accurate tip angles outside the validity of the rotating-wave approximation and in low static field.

Advanced design of MRI inversion pulses for inhomogeneous field conditions by optimal control

Non-selective inversion pulses find widespread use in MRI applications, where requirements on them are increasingly demanding. With the use of high and ultra-high field strength systems, robustness to Δ B 0 and B 1 + inhomogeneities, while tackling SAR and hardware limitations, has rapidly become important. In this work, we propose a time-optimal control framework for the optimization of Δ B 0 - and B 1 + -robust inversion pulses. Robustness is addressed by means of ensemble formulations, while allowing inclusion of hardware and energy limitations. The framework is flexible and performs excellently for various optimization goals. The optimization results are analyzed extensively in numerical experiments. Furthermore, they are validated, and compared with adiabatic RF pulses, in various phantom and in vivo measurements on a 3 T MRI system.

Free-breathing self-gated continuous-IR spiral T1 mapping: Comparison of dual flip-angle and Bloch-Siegert B1-corrected techniques

Purpose

To develop a B1‐corrrected single flip‐angle continuous acquisition strategy with free‐breathing and cardiac self‐gating for spiral T1 mapping, and compare it to a previous dual flip‐angle technique.

Methods

Data were continuously acquired using a spiral‐out trajectory, rotated by the golden angle in time. During the first 2 s, off‐resonance Fermi RF pulses were applied to generate a Bloch‐Siegert shift B1 map, and the subsequent data were acquired with an inversion RF pulse applied every 4 s to create a T1* map. The final T1 map was generated from the B1 and the T1* maps by using a look‐up table that accounted for slice profile effects, yielding more accurate T1 values. T1 values were compared to those from inversion recovery (IR) spin echo (phantom only), MOLLI, SAturation‐recovery single‐SHot Acquisition (SASHA), and previously proposed dual flip‐angle results. This strategy was evaluated in a phantom and 25 human subjects.

Results

The proposed technique showed good agreement with IR spin‐echo results in the phantom experiment. For in‐vivo studies, the proposed technique and the previously proposed dual flip‐angle method were more similar to SASHA results than to MOLLI results.

Conclusions

B1‐corrected single flip‐angle T1 mapping successfully acquired B1 and T1 maps in a free‐breathing, continuous‐IR spiral acquisition, providing a method with improved accuracy to measure T1 using a continuous Look‐Locker acquisition, as compared to the previously proposed dual excitation flip‐angle technique.

Characterization of B1 + field variation in brain at 3 T using 385 healthy individuals across the lifespan

PURPOSE

The transmit field B 1 + at 3 T in brain affects the spatial uniformity and contrast of most image acquisitions. Here, B 1 + spatial variation in brain at 3 T is characterized in a large healthy population.

METHODS

Bloch-Siegert B 1 + maps were acquired at 3 T from 385 healthy subjects aged 5-90 years on a single MRI system. After transforming all B 1 + maps to a standard brain atlas space, region-of-interest analysis was performed, and intersubject voxel-wise coefficient of variation was calculated across the whole brain. The B 1 + variability due to age and brain size was studied separately in males and females, along with B 1 + variability due to nonideal transmit calibration.

RESULTS

The voxel-based mean coefficient of variation was 4.0% across all subjects, and the difference in B 1 + between central (left thalamus) and outer regions (left frontal gray matter) was 24.2% ± 2.3%. The least intersubject variability occurred in central regions, whereas regions toward brain edges increased markedly in variation. The B 1 + variability with age was mostly attributed to lifespan changes in CSF volume (which alters brain conductivity) and head orientation. Larger brain size correlated with more B 1 + inhomogeneity (p < .001). Varying head position and anatomy resulted in an inaccurate transmit calibration.

CONCLUSION

In standard atlas space, intersubject B 1 + variability at 3 T was relatively small in a large population aged 5-90 years. The B 1 + varied with age-related changes of CSF volume and head orientation, as well as differences in brain size and transmit calibration.

A multi-inversion multi-echo spin and gradient echo echo planar imaging sequence with low image distortion for rapid quantitative parameter mapping and synthetic image contrasts

PURPOSE

Brain imaging exams typically take 10-20 min and involve multiple sequential acquisitions. A low-distortion whole-brain echo planar imaging (EPI)-based approach was developed to efficiently encode multiple contrasts in one acquisition, allowing for calculation of quantitative parameter maps and synthetic contrast-weighted images.

METHODS

Inversion prepared spin- and gradient-echo EPI was developed with slice-order shuffling across measurements for efficient acquisition with T1 , T2 , and T 2 ∗ weighting. A dictionary-matching approach was used to fit the images to quantitative parameter maps, which in turn were used to create synthetic weighted images with typical clinical contrasts. Dynamic slice-optimized multi-coil shimming with a B0 shim array was used to reduce B0 inhomogeneity and, therefore, image distortion by >50%. Multi-shot EPI was also implemented to minimize distortion and blurring while enabling high in-plane resolution. A low-rank reconstruction approach was used to mitigate errors from shot-to-shot phase variation.

RESULTS

The slice-optimized shimming approach was combined with in-plane parallel-imaging acceleration of 4× to enable single-shot EPI with more than eight-fold distortion reduction. The proposed sequence efficiently obtained 40 contrasts across the whole-brain in just over 1 min at 1.2 × 1.2 × 3 mm resolution. The multi-shot variant of the sequence achieved higher in-plane resolution of 1 × 1 × 4 mm with good image quality in 4 min. Derived quantitative maps showed comparable values to conventional mapping methods.

CONCLUSION

The approach allows fast whole-brain imaging with quantitative parameter maps and synthetic weighted contrasts. The slice-optimized multi-coil shimming and multi-shot reconstruction approaches result in minimal EPI distortion, giving the sequence the potential to be used in rapid screening applications.

Bloch modelling enables robust T2 mapping using retrospective proton density and T2-weighted images from different vendors and sites

T2 quantification is commonly attempted by applying an exponential fit to proton density (PD) and transverse relaxation (T2)-weighted fast spin echo (FSE) images. However, inter-site studies have noted systematic differences between vendors in T2 maps computed via standard exponential fitting due to imperfect slice refocusing, different refocusing angles and transmit field (B1⁺) inhomogeneity. We examine T2 mapping at 3T across 13 sites and two vendors in healthy volunteers from the Alzheimer's Disease Neuroimaging Initiative (ADNI) database using both a standard exponential and a Bloch modelling approach. The standard exponential approach resulted in highly variable T2 values across different sites and vendors. The two-echo fitting method based on Bloch equation modelling of the pulse sequence with prior knowledge of the nominal refocusing angles, slice profiles, and estimated B1⁺ maps yielded similar T2 values across sites and vendors by accounting for the effects of indirect and stimulated echoes. By modelling the actual refocusing angles used, T2 quantification from PD and T2-weighted images can be applied in studies across multiple sites and vendors.

Adaptive slice-specific z-shimming for 2D spoiled gradient-echo sequences

Purpose

To reduce the misbalance between compensation gradients and macroscopic field gradients, we introduce an adaptive slice‐specific z‐shimming approach for 2D spoiled multi‐echo gradient‐echoe sequences in combination with modeling of the signal decay.

Methods

Macroscopic field gradients were estimated for each slice from a fast prescan (15 seconds) and then used to calculate slice‐specific compensation moments along the echo train. The coverage of the compensated field gradients was increased by applying three positive and three negative moments. With a forward model, which considered the effect of the slice profile, the z‐shim moment, and the field gradient, R2∗ maps were estimated. The method was evaluated in phantom and in vivo measurements at 3 T and compared with a spoiled multi‐echo gradient‐echo and a global z‐shimming approach without slice‐specific compensation.

Results

The proposed method yielded higher SNR in R2∗ maps due to a broader range of compensated macroscopic field gradients compared with global z‐shimming. In global white matter, the mean interquartile range, proxy for SNR, could be decreased to 3.06 s⁻¹ with the proposed approach, compared with 3.37 s⁻¹ for global z‐shimming and 3.52 s⁻¹ for uncompensated multi‐echo gradient‐echo.

Conclusion

Adaptive slice‐specific compensation gradients between echoes substantially improved the SNR of R2∗ maps, and the signal could also be rephased in anatomical areas, where it has already been completely dephased.

Demonstration and suppression of respiration-related artifacts in Bloch-Siegert shift-based B1+ maps of the human brain

Respiration-induced movement of the chest wall and internal organs causes temporal B₀ variations extending throughout the brain. This study demonstrates that these variations can cause significant artifacts in B1+ maps obtained at 7 T with the Bloch-Siegert shift (BSS) B1+ mapping technique. To suppress these artifacts, a navigator correction scheme was proposed. Two sets of experiments were performed. In the first set of experiments, phase shifts induced by respiration-related B₀ variations were assessed for five subjects at 7 T by using a gradient echo (GRE) sequence without phase-encoding. In the second set of experiments, B1+ maps were acquired using a GRE-based BSS pulse sequence with navigator echoes. For this set, the measurements were consecutively repeated 16 times for the same imaging slice. These measurements were averaged to obtain the reference B1+ map. Due to the periodicity of respiration-related phase shifts, their effect on the reference B1+ map was assumed to be negligible through averaging. The individual B1+ maps of the 16 repetitions were calculated with and without using the proposed navigator scheme. These maps were compared with the B1+ reference map. The peak-to-peak value of respiration-related phase shifts varied between subjects. Without navigator correction, the interquartile range of percentage error in B1+ varied between 4.0% and 8.3% among subjects. When the proposed navigator scheme was used, these numbers were reduced to 2.5% and 2.9%, indicating an improvement in the precision of GRE-based BSS B1+ mapping at high magnetic fields.

Assessment and correction of macroscopic field variations in 2D spoiled gradient-echo sequences

Purpose

To model and correct the dephasing effects in the gradient‐echo signal for arbitrary RF excitation pulses with large flip angles in the presence of macroscopic field variations.

Methods

The dephasing of the spoiled 2D gradient‐echo signal was modeled using a numerical solution of the Bloch equations to calculate the magnitude and phase of the transverse magnetization across the slice profile. Additionally, regional variations of the transmit RF field and slice profile scaling due to macroscopic field gradients were included. Simulations, phantom, and in vivo measurements at 3 T were conducted for R2∗ and myelin water fraction (MWF) mapping.

Results

The influence of macroscopic field gradients on R2∗ and myelin water fraction estimation can be substantially reduced by applying the proposed model. Moreover, it was shown that the dephasing over time for flip angles of 60° or greater also depends on the polarity of the slice‐selection gradient because of phase variation along the slice profile.

Conclusion

Substantial improvements in R2∗ accuracy and myelin water fraction mapping coverage can be achieved using the proposed model if higher flip angles are required. In this context, we demonstrated that the phase along the slice profile and the polarity of the slice‐selection gradient are essential for proper modeling of the gradient‐echo signal in the presence of macroscopic field variations.

A time domain signal equation for multi-echo spin-echo sequences with arbitrary excitation and refocusing angle and phase

Accurate T₂ mapping using multi-echo spin-echo is usually impaired by non-ideal refocusing due to B₁+ inhomogeneities and slice profile effects. Incomplete refocusing gives rise to stimulated echo and so called "T₁-mixing" and consequently a non-exponential signal decay. Here we present a time domain formula that incorporates all relaxation and pulse parameters and enables accurate and realistic modelling of the magnetization decay curve. By pulse parameters here we specifically mean the actual refocusing angle and axis, and phase angle of both the excitation and refocusing pulse. The method used for derivation comprises the so called Generating functions approach with subsequent back-transformation to the time domain. The proposed approach was validated by simulations using realistic RF pulse shapes as well as by comparison to phantom measurements. Excellent agreement between simulations and measurements underpin the validity of the presented approach. Conclusively, we here present a complete time domain formula ready to use for accurate T₂ mapping with multi-echo spin-echo sequences.

Robust 3D Bloch-Siegert based B 1 + mapping using multi-echo general linear modeling

PURPOSE

Quantitative MRI applications, such as mapping the T₁ time of tissue, puts high demands on the accuracy and precision of transmit field ( B 1 + ) estimation. A candidate approach to satisfy these requirements exploits the difference in phase induced by the Bloch-Siegert frequency shift (BSS) of 2 acquisitions with opposite off-resonance frequency radiofrequency pulses. Interleaving these radiofrequency pulses ensures robustness to motion and scanner drifts; however, here we demonstrate that doing so also introduces a bias in the B 1 + estimates.

THEORY AND METHODS

It is shown here by means of simulation and experiments that the amplitude of the error depends on MR pulse sequence parameters, such as repetition time and radiofrequency spoiling increment, but more problematically, on the intrinsic properties, T₁ and T₂ , of the investigated tissue. To solve these problems, a new approach to BSS-based B 1 + estimation that uses a multi-echo acquisition and a general linear model to estimate the correct BSS-induced phase is presented.

RESULTS

In line with simulations, phantom and in vivo experiments confirmed that the general linear model-based method removed the dependency on tissue properties and pulse sequence settings.

CONCLUSION

The general linear model-based method is recommended as a more accurate approach to BSS-based B 1 + mapping.

Rapid T1 quantification from high resolution 3D data with model-based reconstruction

Purpose

Magnetic resonance imaging protocols for the assessment of quantitative information suffer from long acquisition times since multiple measurements in a parametric dimension are required. To facilitate the clinical applicability, accelerating the acquisition is of high importance. To this end, we propose a model‐based optimization framework in conjunction with undersampling 3D radial stack‐of‐stars data.

Theory and Methods

High resolution 3D T₁ maps are generated from subsampled data by employing model‐based reconstruction combined with a regularization functional, coupling information from the spatial and parametric dimension, to exploit redundancies in the acquired parameter encodings and across parameter maps. To cope with the resulting non‐linear, non‐differentiable optimization problem, we propose a solution strategy based on the iteratively regularized Gauss‐Newton method. The importance of 3D‐spectral regularization is demonstrated by a comparison to 2D‐spectral regularized results. The algorithm is validated for the variable flip angle (VFA) and inversion recovery Look‐Locker (IRLL) method on numerical simulated data, MRI phantoms, and in vivo data.

Results

Evaluation of the proposed method using numerical simulations and phantom scans shows excellent quantitative agreement and image quality. T₁ maps from accelerated 3D in vivo measurements, e.g. 1.8 s/slice with the VFA method, are in high accordance with fully sampled reference reconstructions.

Conclusions

The proposed algorithm is able to recover T₁ maps with an isotropic resolution of 1 mm³ from highly undersampled radial data by exploiting structural similarities in the imaging volume and across parameter maps.

Ultrafast 3D Bloch-Siegert B <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msubsup><mml:mrow/> <mml:mn>1</mml:mn> <mml:mo>+</mml:mo></mml:msubsup> </mml:math> -mapping using variational modeling

PURPOSE

Highly accelerated B <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msubsup><mml:mrow/> <mml:mn>1</mml:mn> <mml:mo>+</mml:mo></mml:msubsup> </mml:math> -mapping based on the Bloch-Siegert shift to allow 3D acquisitions even within a brief period of a single breath-hold.

THEORY AND METHODS

The B <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msubsup><mml:mrow/> <mml:mn>1</mml:mn> <mml:mo>+</mml:mo></mml:msubsup> </mml:math> dependent Bloch-Siegert phase shift is measured within a highly subsampled 3D-volume and reconstructed using a two-step variational approach, exploiting the different spatial distribution of morphology and B <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msubsup><mml:mrow/> <mml:mn>1</mml:mn> <mml:mo>+</mml:mo></mml:msubsup> </mml:math> -field. By appropriate variable substitution the basic non-convex optimization problem is transformed in a sequential solution of two convex optimization problems with a total generalized variation (TGV) regularization for the morphology part and a smoothness constraint for the B <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msubsup><mml:mrow/> <mml:mn>1</mml:mn> <mml:mo>+</mml:mo></mml:msubsup> </mml:math> -field. The method is evaluated on 3D in vivo data with retro- and prospective subsampling. The reconstructed B <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msubsup><mml:mrow/> <mml:mn>1</mml:mn> <mml:mo>+</mml:mo></mml:msubsup> </mml:math> -maps are compared to a zero-padded low resolution reconstruction and a fully sampled reference.

RESULTS

The reconstructed B <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msubsup><mml:mrow/> <mml:mn>1</mml:mn> <mml:mo>+</mml:mo></mml:msubsup> </mml:math> -field maps are in high accordance to the reference for all measurements with a mean error below 1% and a maximum of about 4% for acceleration factors up to 100. The minimal error for different sampling patterns was achieved by sampling a dense region in k-space center with acquisition times of around 10-12 s for 3D-acquistions.

CONCLUSIONS

The proposed variational approach enables highly accelerated 3D acquisitions of Bloch-Siegert data and thus full liver coverage in a single breath hold.