A z‐gradient array for simultaneous multi‐slice excitation with a single‐band RF pulse

Funding information UC BerkeleyPurpose: To develop a classical geometric interpretation of multiphoton excitation and apply it to MRI. To investigate ways in which multiphoton excitation can enable novel imaging techniques. Theory and Methods: We present a fully geometric view of multiphoton excitation by taking a particular rotating frame transformation. In this rotating frame, we find that multiphoton excitations appear just like single-photon excitations again, and therefore, we can readily generalize concepts already explored in standard singlephoton excitation. With a homebuilt low frequency coil, we execute a standard slice selective pulse sequence with all of its excitations replaced by their equivalent twophoton versions. In the case of no extra hardware, we use oscillating gradients as a source of extra photons for excitation. Finally, with the multiphoton interpretation of oscillating gradients, we present a novel way to transform a standard slice selective adiabatic inversion pulse into a multiband version without modifying the RF pulse itself. The addition of oscillating gradients creates multiphoton resonances at multiple spatial locations and allows for adiabatic inversions at each location. Results: With Bloch-Siegert shift corrections, analytical multiphoton excitation expressions match with Bloch equation simulations. Two-photon gradient-echo images of a lemon and a pork rib match with their single-photon counterparts.Frequency-offset RF combined with oscillating gradients generate excitation where the RF alone does not. Conclusion: The multiphoton interpretation presents new flexibilities for imaging.Excitation needs not be bound to the Larmor frequency, which opens doors to RF pulse design beyond the usual filter design and the potential for further imaging innovations. K E Y W O R D Sadiabatic, Bloch-Siegert shift, multiband, multiphoton, selective excitation, two-photon ORCID Victor Han https://orcid.org/0000-0003-3093-2549 Chunlei Liu https://orcid.org/0000-0001-8816-4832

Section: Discussionmentioning

confidence: 99%

Multiphoton magnetic resonance in imaging: A classical description and implementation

Han

2020

“…Schematic illustration and photograph of the Z‐gradient array are provided in Figure C and D, respectively. More detailed information about the gradient array coil can be found in Ertan et al…”

Section: Methodsmentioning

confidence: 99%

“…All computations are performed in MATLAB 2017a (The MathWorks, Natick, MA). Magnetic field map measurements from the previous study are used to obtain the target magnetic field distribution.…”

Section: Methodsmentioning

confidence: 99%

“…In conventional MRI, linear gradients are used to encode the spatial coordinates of spins onto the resonance frequency. In the past decade, gradient coil arrays with arbitrary magnetic field profiles have proven to be useful for encoding purposes at the expense of increased hardware complexity. Conventional linear gradient coils are generally designed to have minimal coupling, which is not the case for generalized array of coils.…”

Section: Introductionmentioning

confidence: 99%

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Driving mutually coupled gradient array coils in magnetic resonance imaging

Ertan

Taraghinia

Atalar

2019

Self Cite

Purpose:In contrast to conventional linear gradients, gradient coil arrays with arbitrary spatial dependency might experience strong mutual coupling. Although conventional gradient power amplifiers with feedback loop might compensate the effect of coupling, required voltages for the compensation are generally unknown and has to be considered beforehand to ensure that amplifier voltage limits are not exceeded. A first-order circuit model is proposed to be used as a feedforward model which enables analytical formulas of required voltages to drive the mutually coupled gradient coil arrays. Theory and Methods: A first-order circuit model including the mutual couplings is provided to analytically calculate the input voltages and minimum achievable rise times for a given set of gradient array currents and amplifier limitations. Previously designed 9-channel Z-gradient coil array and home-built gradient amplifiers (50 V and 20 A) are used in the experiments. Three sets of currents optimized for linear Z-gradient, second-order Z2, and third-order Z3 fields are used in the bench-top experiments. The current weightings for the linear Z-gradient are also used as the readout gradient in the 3T MRI experiments. Results: Current measurements for the example magnetic field profiles with minimum rise times are demonstrated for the simultaneous use of 9-channel gradient coils and amplifiers. MRI experiments verify that a linear Z-gradient field with a desired time waveform can be generated using a mutually coupled array coils. Conclusion: Bench-top and MRI experiments demonstrate the feasibility of the proposed circuit model and analytical formulas to drive the mutually coupled gradient coils. K E Y W O R D Sfeedforward model, gradient arrays, gradient power amplifiers, MRI, mutual coupling, mutual inductance, mutually coupled gradient array coils

“…Thus, they require high-precision high-cost current sensors because any error in the current measurements results in an output error. The recently introduced gradient array systems, [3][4][5] multi-coil technique, [6][7][8] and matrix gradient coils, 9,10 which are capable of generating dynamically controllable magnetic field profiles, use multiple gradient coils and, hence, need many current sensors for the feedback loop, which significantly increases the system cost (>$600 per sensor). Therefore, to avoid the need for measurement data and expensive current sensors, feedforward controllers might be preferable.…”

Section: Introductionmentioning

confidence: 99%

Nonlinear droop compensation for current waveforms in MRIgradient systems

Babaloo

Atalar

2022

Self Cite

Providing accurate gradient currents is challenging due to the gradient chain nonlinearities, arising from gradient power amplifiers and power supply stages. This work introduces a new characterization approach that takes the amplifier and power supply into account, resulting in a nonlinear model that compensates for the current droop. Methods:The gradient power amplifier and power supply stage were characterized by a modified state-space averaging technique. The resulting nonlinear model was inverted and used in feedforward to control the gradient coil current. A custom-built two-channel z-gradient coil was driven by high-switching (1 MHz), low-cost amplifiers (<$200) using linear and nonlinear controllers.High-resolution (<80 ps) pulse-width-modulation signals were used to drive the amplifiers. MRI experiments were performed to validate the nonlinear controller's effectiveness. Results:The simulation results validated the functionality of the state-space averaging method in characterizing the gradient system. The performance of linear and nonlinear controllers in generating a trapezoidal current waveform was compared in simulations and experiments. The integral errors between the desired waveform and waveforms generated by linear and nonlinear controllers were 1.9% and 0.13%, respectively, confirming the capability of the nonlinear controller to compensate for the current droop. Phantom images validated the nonlinear controller's ability to correct droop-induced distortions. Conclusion: Benchtop measurements and MRI experiments demonstrated that the proposed nonlinear characterization and digitally implemented feedforward controller could drive gradient coils with droop-free current waveforms (without a feedback loop). In experiments, the nonlinear controller outperformed the linear controller by a 14-fold reduction in the integral error of a test waveform.