Local quantum control of Heisenberg spin chains

Motivated by some recent results of quantum control theory, we discuss the feasibility of local operator control in arrays of interacting qubits modeled as isotropic Heisenberg spin chains. Acting on one of the end spins, we aim at finding piecewise-constant control pulses that lead to optimal fidelities for a chosen set of quantum gates. We analyze the robustness of the obtained results f or the gate fidelities to random errors in the control fields, finding that with faster switching between piecewise-constant controls the system is less susceptible to these errors. The observed behavior falls into a generic class of physical phenomena that are related to a competition between resonance- and relaxation-type behavior, exemplified by motional narrowing in NMR experiments. Finally, we discuss how the obtained optimal gate fidelities are altered when the corresponding rapidly-varying piecewise-constant control fields are smoothened through spectral filtering.Comment: final, published versio

Controlling qubit arrays with anisotropic XXZ Heisenberg interaction by acting on a single qubit

We investigate anisotropic $XXZ$ Heisenberg spin-1/2 chains with control fields acting on one of the end spins, with the aim of exploring local quantum control in arrays of interacting qubits. In this work, which uses a recent Lie-algebraic result on the local controllability of spin chains with "always-on" interactions, we determine piecewise-constant control pulses corresponding to optimal fidelities for quantum gates such as spin-flip (NOT), controlled-NOT (CNOT), and square-root-of-SWAP ($\sqrt{\textrm{SWAP}}$). We find the minimal times for realizing different gates depending on the anisotropy parameter $\Delta$ of the model, showing that the shortest among these gate times are achieved for particular values of $\Delta$ larger than unity. To study the influence of possible imperfections in anticipated experimental realizations of qubit arrays, we analyze the robustness of the obtained results for the gate fidelities to random variations in the control-field amplitudes and finite rise time of the pulses. Finally, we discuss the implications of our study for superconducting charge-qubit arrays.Comment: 6 pages, 4 figure

Rapid whole-brain quantitative MT imaging

PURPOSE To provide a robust whole-brain quantitative magnetization transfer (MT) imaging method that is not limited by long acquisition times. METHODS Two variants of a spiral 2D interleaved multi-slice spoiled gradient echo (SPGR) sequence are used for rapid quantitative MT imaging of the brain at 3 T. A dual flip angle, steady-state prepared, double-contrast method is used for combined B$_{1}$ and-T$_{1}$ mapping in combination with a single-contrast MT-prepared acquisition over a range of different saturation flip angles (50 deg to 850 deg) and offset frequencies (1 kHz and 10 kHz). Five sets (containing minimum 6 to maximum 18 scans) with different MT-weightings were acquired. In addition, main magnetic field inhomogeneities (ΔB$_{0}$) were measured from two Cartesian low-resolution 2D SPGR scans with different echo times. Quantitative MT model parameters were derived from all sets using a two-pool continuous-wave model analysis, yielding the pool-size ratio, F, their exchange rate, k$_{f}$, and their transverse relaxation time, T$_{2r}$. RESULTS Whole-brain quantitative MT imaging was feasible for all sets with total acquisition times ranging from 7:15 min down to 3:15 min. For accurate modeling, B$_{1}$-correction was essential for all investigated sets, whereas ΔB$_{0}$-correction showed limited bias for the observed maximum off-resonances at 3 T. CONCLUSION The combination of rapid B$_{1}$-T$_{1}$ mapping and MT-weighted imaging using a 2D multi-slice spiral SPGR research sequence offers excellent prospects for rapid whole-brain quantitative MT imaging in the clinical setting

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

Accelerated MRI at 9.4 T with electronically modulated time-varying receive sensitivities

PURPOSE To investigate how electronically modulated time-varying receive sensitivities can improve parallel imaging reconstruction at ultra-high field. METHODS Receive sensitivity modulation was achieved by introducing PIN diodes in the receive loops, which allow rapid switching of capacitances in both arms of each loop coil and by that alter B$_{1}$ $^{-}$ profiles, resulting in two distinct receive sensitivity configurations. A prototype 8-channel reconfigurable receive coil for human head imaging at 9.4T was built, and MR measurements were performed in both phantom and human subject. A modified SENSE reconstruction for time-varying sensitivities was formulated, and g-factor calculations were performed to investigate how modulation of receive sensitivity profiles during image encoding can improve parallel imaging reconstruction. The optimized modulation pattern was realized experimentally, and reconstructions with the time-varying sensitivities were compared with conventional static SENSE reconstructions. RESULTS The g-factor calculations showed that fast modulation of receive sensitivities in the order of the ADC dwell time during k-space acquisition can improve parallel imaging performance, as this effectively makes spatial information of both configurations simultaneously available for image encoding. This was confirmed by in vivo measurements, for which lower reconstruction errors (SSIM = 0.81 for acceleration R = 4) and g-factors (max g = 2.4; R = 4) were observed for the case of rapidly switched sensitivities compared to conventional reconstruction with static sensitivities (SSIM = 0.74 and max g = 3.2; R = 4). As the method relies on the short RF wavelength at ultra-high field, it does not yield significant benefits at 3T and below. CONCLUSIONS Time-varying receive sensitivities can be achieved by inserting PIN diodes in the receive loop coils, which allow modulation of B$_{1}$ $^{-}$ patterns. This offers an additional degree of freedom for image encoding, with the potential for improved parallel imaging performance at ultra-high field

Functional mapping of sensorimotor activation in the human thalamus at 9.4 Tesla

Although the thalamus is perceived as a passive relay station for almost all sensory signals, the function of individual thalamic nuclei remains unresolved. In the present study, we aimed to identify the sensorimotor nuclei of the thalamus in humans using task-based fMRI at a field strength of 9.4T by assessing the individual subject-specific sensorimotor BOLD response during a combined active motor (finger-tapping) and passive sensory (tactile-finger) stimulation. We demonstrate that both tasks increase BOLD signal response in the lateral nuclei group (VPL, VA, VLa, and VLp), and in the pulvinar nuclei group (PuA, PuM, and PuL). Finger-tapping stimuli evokes a stronger BOLD response compared to the tactile stimuli, and additionally engages the intralaminar nuclei group (CM and Pf). In addition, our results demonstrate reproducible thalamic nuclei activation during motor and tactile stimuli. This work provides important insight into understanding the function of individual thalamic nuclei in processing various input signals and corroborates the benefits of using ultra-high-field MR scanners for functional imaging of fine-scale deeply located brain structures

Volumetric measurements of weak current-induced magnetic fields in the human brain at high resolution

PURPOSE Clinical use of transcranial electrical stimulation (TES) requires accurate knowledge of the injected current distribution in the brain. MR current density imaging (MRCDI) uses measurements of the TES-induced magnetic fields to provide this information. However, sufficient sensitivity and image quality in humans in vivo has only been documented for single-slice imaging. METHODS A recently developed, optimally spoiled, acquisition-weighted, gradient echo-based 2D-MRCDI method has now been advanced for volume coverage with densely or sparsely distributed slices: The 3D rectilinear sampling (3D-DENSE) and simultaneous multislice acquisition (SMS-SPARSE) were optimized and verified by cable-loop experiments and tested with 1-mA TES experiments for two common electrode montages. RESULTS Comparisons between the volumetric methods against the 2D-MRCDI showed that relatively long acquisition times of 3D-DENSE using a single slab with six slices hindered the expected sensitivity improvement in the current-induced field measurements but improved sensitivity by 61% in the Laplacian of the field, on which some MRCDI reconstruction methods rely. Also, SMS-SPARSE acquisition of three slices, with a factor 2 CAIPIRINHA (controlled aliasing in parallel imaging results in higher acceleration) acceleration, performed best against the 2D-MRCDI with sensitivity improvements for the and Laplacian noise floors of 56% and 78% (baseline without current flow) as well as 43% and 55% (current injection into head). SMS-SPARSE reached a sensitivity of 67 pT for three distant slices at 2 × 2 × 3 mm$^{3}$ resolution in 10 min of total scan time, and consistently improved image quality. CONCLUSION Volumetric MRCDI measurements with high sensitivity and image quality are well suited to characterize the TES field distribution in the human brain

MRI lung lobe segmentation in pediatric cystic fibrosis patients using a recurrent neural network trained with publicly accessible CT datasets

PURPOSE To introduce a widely applicable workflow for pulmonary lobe segmentation of MR images using a recurrent neural network (RNN) trained with chest CT datasets. The feasibility is demonstrated for 2D coronal ultrafast balanced SSFP (ufSSFP) MRI. METHODS Lung lobes of 250 publicly accessible CT datasets of adults were segmented with an open-source CT-specific algorithm. To match 2D ufSSFP MRI data of pediatric patients, both CT data and segmentations were translated into pseudo-MR images that were masked to suppress anatomy outside the lung. Network-1 was trained with pseudo-MR images and lobe segmentations and then applied to 1000 masked ufSSFP images to predict lobe segmentations. These outputs were directly used as targets to train Network-2 and Network-3 with non-masked ufSSFP data as inputs, as well as an additional whole-lung mask as input for Network-2. Network predictions were compared to reference manual lobe segmentations of ufSSFP data in 20 pediatric cystic fibrosis patients. Manual lobe segmentations were performed by splitting available whole-lung segmentations into lobes. RESULTS Network-1 was able to segment the lobes of ufSSFP images, and Network-2 and Network-3 further increased segmentation accuracy and robustness. The average all-lobe Dice similarity coefficients were 95.0 ± 2.8 (mean ± pooled SD [%]) and 96.4 ± 2.5, 93.0 ± 2.0; and the average median Hausdorff distances were 6.1 ± 0.9 (mean ± SD [mm]), 5.3 ± 1.1, 7.1 ± 1.3 for Network-1, Network-2, and Network-3, respectively. CONCLUSION Recurrent neural network lung lobe segmentation of 2D ufSSFP imaging is feasible, in good agreement with manual segmentations. The proposed workflow might provide access to automated lobe segmentations for various lung MRI examinations and quantitative analyses

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

MRI lung lobe segmentation in pediatric cystic fibrosis patients using a recurrent neural network trained with publicly accessible CT datasets.

PURPOSE To introduce a widely applicable workflow for pulmonary lobe segmentation of MR images using a recurrent neural network (RNN) trained with chest CT datasets. The feasibility is demonstrated for 2D coronal ultrafast balanced SSFP (ufSSFP) MRI. METHODS Lung lobes of 250 publicly accessible CT datasets of adults were segmented with an open-source CT-specific algorithm. To match 2D ufSSFP MRI data of pediatric patients, both CT data and segmentations were translated into pseudo-MR images that were masked to suppress anatomy outside the lung. Network-1 was trained with pseudo-MR images and lobe segmentations and then applied to 1000 masked ufSSFP images to predict lobe segmentations. These outputs were directly used as targets to train Network-2 and Network-3 with non-masked ufSSFP data as inputs, as well as an additional whole-lung mask as input for Network-2. Network predictions were compared to reference manual lobe segmentations of ufSSFP data in 20 pediatric cystic fibrosis patients. Manual lobe segmentations were performed by splitting available whole-lung segmentations into lobes. RESULTS Network-1 was able to segment the lobes of ufSSFP images, and Network-2 and Network-3 further increased segmentation accuracy and robustness. The average all-lobe Dice similarity coefficients were 95.0 ± 2.8 (mean ± pooled SD [%]) and 96.4 ± 2.5, 93.0 ± 2.0; and the average median Hausdorff distances were 6.1 ± 0.9 (mean ± SD [mm]), 5.3 ± 1.1, 7.1 ± 1.3 for Network-1, Network-2, and Network-3, respectively. CONCLUSION Recurrent neural network lung lobe segmentation of 2D ufSSFP imaging is feasible, in good agreement with manual segmentations. The proposed workflow might provide access to automated lobe segmentations for various lung MRI examinations and quantitative analyses