Improved large tip angle parallel transmission pulse design through a perturbation analysis of the Bloch equation

Accuracy and performance analysis for Bloch and Bloch-McConnell simulation methods

PURPOSE

To introduce new solution methods for the Bloch and Bloch-McConnell equations and compare them quantitatively to different known approaches.

THEORY AND METHODS

A new exact solution per time step is derived by means of eigenvalues and generalized eigenvectors. Fast numerical solution methods based on asymmetric and symmetric operator splitting, which are already known for the Bloch equations, are extended to the Bloch-McConnell equations. Those methods are compared to other numerical methods including spin domain, one-step and multi-step methods, and matrix exponential. Error metrics are introduced based on the exact solution method, which allows to assess the accuracy of each solution method quantitatively for arbitrary example data.

RESULTS

Accuracy and performance properties for nine different solution methods are analyzed and compared in extensive numerical experiments including various examples for non-selective and slice-selective MR imaging applications. The accuracy of the methods heavily varies, in particular for short relaxation times and long pulse durations.

CONCLUSION

In absence of relaxation effects, the numerical results confirm the rotation matrices approach as accurate and computationally efficient Bloch solution method. Otherwise, as well as for the Bloch-McConnell equations, symmetric operator splitting methods are recommended due to their excellent numerical accuracy paired with efficient run time.

Parallel transmission for ultrahigh-field imaging

The development of MRI systems operating at or above 7 T has provided researchers with a new window into the human body, yielding improved imaging speed, resolution and signal-to-noise ratio. In order to fully realise the potential of ultrahigh-field MRI, a range of technical hurdles must be overcome. The non-uniformity of the transmit field is one of such issues, as it leads to non-uniform images with spatially varying contrast. Parallel transmission (i.e. the use of multiple independent transmission channels) provides previously unavailable degrees of freedom that allow full spatial and temporal control of the radiofrequency (RF) fields. This review discusses the many ways in which these degrees of freedom can be used, ranging from making more uniform transmit fields to the design of subject-tailored RF pulses for both uniform excitation and spatial selection, and also the control of the specific absorption rate. © 2015 The Authors. NMR in Biomedicine published by John Wiley & Sons Ltd.

Phase relaxed localized excitation pulses for inner volume fast spin echo imaging

PURPOSE

To design multidimensional spatially selective radiofrequency (RF) pulses for inner volume imaging (IVI) with three-dimensional (3D) fast spin echo (FSE) sequences. Enhanced background suppression is achieved by exploiting particular signal properties of FSE sequences.

THEORY AND METHODS

The CPMG condition dictates that echo amplitudes will rapidly decrease if a 90° phase difference between excitation and refocusing pulses is not present, and refocusing flip angles are not precisely 180°. This mechanism is proposed as a means for generating additional background suppression for spatially selective excitation, by biasing residual excitation errors toward violating the CPMG condition. 3D RF pulses were designed using this method with a 3D spherical spiral trajectory, under-sampled by factor 5.6 for an eight-channel PTx system, at 3 Tesla.

RESULTS

3D-FSE IVI with pulse durations of approximately 12 ms was demonstrated in phantoms and for T2 -weighted brain imaging in vivo. Good image quality was obtained, with mean background suppression factors of 103 and 82 ± 6 in phantoms and in vivo, respectively.

CONCLUSION

Inner Volume Imaging with 3D-FSE has been demonstrated in vivo with tailored 3D-RF pulses. The proposed design methods are also applicable to 2D pulses. Magn Reson Med 76:848-861, 2016. © 2015 The Authors. Magnetic Resonance in Medicine published by Wiley Periodicals, Inc. on behalf of International Society for Magnetic Resonance in Medicine.

Joint design of large-tip-angle parallel RF pulses and blipped gradient trajectories

PURPOSE

To design multichannel large-tip-angle kT-points and spokes radiofrequency (RF) pulses and gradient waveforms for transmit field inhomogeneity compensation in high field magnetic resonance imaging.

THEORY AND METHODS

An algorithm to design RF subpulse weights and gradient blip areas is proposed to minimize a magnitude least-squares cost function that measures the difference between realized and desired state parameters in the spin domain, and penalizes integrated RF power. The minimization problem is solved iteratively with interleaved target phase updates, RF subpulse weights updates using the conjugate gradient method with optimal control-based derivatives, and gradient blip area updates using the conjugate gradient method. Two-channel parallel transmit simulations and experiments were conducted in phantoms and human subjects at 7 T to demonstrate the method and compare it to small-tip-angle-designed pulses and circularly polarized excitations.

RESULTS

The proposed algorithm designed more homogeneous and accurate 180° inversion and refocusing pulses than other methods. It also designed large-tip-angle pulses on multiple frequency bands with independent and joint phase relaxation. Pulses designed by the method improved specificity and contrast-to-noise ratio in a finger-tapping spin echo blood oxygen level dependent functional magnetic resonance imaging study, compared with circularly polarized mode refocusing.

CONCLUSION

A joint RF and gradient waveform design algorithm was proposed and validated to improve large-tip-angle inversion and refocusing at ultrahigh field.

First and second order derivatives for optimizing parallel RF excitation waveforms

For piecewise constant magnetic fields, the Bloch equations (without relaxation terms) can be solved explicitly. This way the magnetization created by an excitation pulse can be written as a concatenation of rotations applied to the initial magnetization. For fixed gradient trajectories, the problem of finding parallel RF waveforms, which minimize the difference between achieved and desired magnetization on a number of voxels, can thus be represented as a finite-dimensional minimization problem. We use quaternion calculus to formulate this optimization problem in the magnitude least squares variant and specify first and second order derivatives of the objective function. We obtain a small tip angle approximation as first order Taylor development from the first order derivatives and also develop algorithms for first and second order derivatives for this small tip angle approximation. All algorithms are accompanied by precise floating point operation counts to assess and compare the computational efforts. We have implemented these algorithms as callback functions of an interior-point solver. We have applied this numerical optimization method to example problems from the literature and report key observations.

Strategies for improved 3D small-tip fast recovery imaging

PURPOSE

Small-tip fast recovery (STFR) imaging is a recently proposed steady-state sequence that has similar image contrast as balanced steady-state free precession but has the potential to simultaneously remove banding artifacts and transient fluctuation. STFR relies on a "tip-up" radiofrequency (RF) pulse tailored to the accumulated phase during the free precession (data acquisition) interval, designed to bring spins back to the longitudinal axis, thereby preserving transverse magnetization as longitudinal magnetization for the next pulse repetition time. We recently proposed an RF-spoiled STFR sequence suitable for thin slab imaging, however, in many applications, e.g., functional magnetic resonance imaging or isotropic-resolution structural imaging, three-dimensional (3D) steady-state imaging is desirable. Unfortunately, 3D STFR imaging is challenging due to the need for 3D tailored RF pulses. Here, we propose new strategies for improved 3D STFR imaging, based on (i) unspoiled imaging, and (ii) joint design of nonslice-selective tip-down/tip-up RF pulses.

THEORY AND METHODS

We derive an analytic signal model for the proposed unspoiled STFR sequence, and propose two strategies for designing the 3D tailored tip-down/tip-up RF pulses. We validate the analytic results using phantom and in vivo imaging experiments.

RESULTS

Our analytic model and imaging experiments demonstrate that the proposed unspoiled STFR sequence is less sensitive to tip-up excitation error compared to the corresponding spoiled sequence, and may, therefore, be an attractive candidate for 3D imaging. The proposed "joint" RF pulse design method, in which we formulate the tip-down/tip-up RF pulse design task as a magnitude least squares problem, produces modest improvement over a simpler "Separate" design approach. Using the proposed unspoiled sequence and joint RF pulse design, we demonstrate proof-of-principle 3D STFR brain images with balanced steady-state free precession-like signal properties but with reduced banding.

CONCLUSION

Using the proposed unspoiled sequence and joint RF pulse design, STFR brain images in a 3D region of interest with balanced steady-state free precession-like signal properties but with reduced banding can be obtained.

Multi-slice parallel transmission three-dimensional tailored RF (PTX 3DTRF) pulse design for signal recovery in ultra high field functional MRI

T(2)(∗) weighted fMRI at high and ultra high field (UHF) is often hampered by susceptibility-induced, through-plane, signal loss. Three-dimensional tailored RF (3DTRF) pulses have been shown to be an effective approach for mitigating through-plane signal loss at UHF. However, the required RF pulse lengths are too long for practical applications. Recently, parallel transmission (PTX) has emerged as a very effective means for shortening the RF pulse duration for 3DTRF without sacrificing the excitation performance. In this article, we demonstrate a RF pulse design strategy for 3DTRF based on the use of multi-slice PTX 3DTRF to simultaneously and precisely recover signal with whole-brain coverage. Phantom and human experiments are used to demonstrate the effectiveness and robustness of the proposed method on three subjects using an eight-channel whole body parallel transmission system.

Parallel transmission RF pulse design for eddy current correction at ultra high field

Multidimensional spatially selective RF pulses have been used in MRI applications such as B₁ and B₀ inhomogeneities mitigation. However, the long pulse duration has limited their practical applications. Recently, theoretical and experimental studies have shown that parallel transmission can effectively shorten pulse duration without sacrificing the quality of the excitation pattern. Nonetheless, parallel transmission with accelerated pulses can be severely impeded by hardware and/or system imperfections. One of such imperfections is the effect of the eddy current field. In this paper, we first show the effects of the eddy current field on the excitation pattern and then report an RF pulse the design method to correct eddy current fields caused by the RF coil and the gradient system. Experimental results on a 7 T human eight-channel parallel transmit system show substantial improvements on excitation patterns with the use of eddy current correction. Moreover, the proposed model-based correction method not only demonstrates comparable excitation patterns as the trajectory measurement method, but also significantly improves time efficiency.