Trust Region Methods for the Estimation of a Complex Exponential Decay Model in MRI With a Single-Shot or Multi-Shot Trajectory

In vivo monitoring of renal tubule volume fraction using dynamic parametric MRI

PURPOSE

The increasing incidence of kidney diseases is a global concern, and current biomarkers and treatments are inadequate. Changes in renal tubule luminal volume fraction (TVF) serve as a rapid biomarker for kidney disease and improve understanding of renal (patho)physiology. This study uses the amplitude of the long T2 component as a surrogate for TVF in rats, by applying multiexponential analysis of the T2-driven signal decay to examine micromorphological changes in renal tissue.

METHODS

Simulations were conducted to identify a low mean absolute error (MAE) protocol and an accelerated protocol customized for the in vivo study of T2 mapping of the rat kidney at 9.4 T. We then validated our bi-exponential approach in a phantom mimicking the relaxation properties of renal tissue. This was followed by a proof-of-principle demonstration using in vivo data obtained during a transient increase of renal pelvis and tubular pressure.

RESULTS

Using the low MAE protocol, our approach achieved an accuracy of MAE < 1% on the mechanical phantom. The T2 mapping protocol customized for in vivo study achieved an accuracy of MAE < 3%. Transiently increasing pressure in the renal pelvis and tubules led to significant changes in TVF in renal compartments: ΔTVFcortex = 4.9%, ΔTVFouter_medulla = 4.5%, and ΔTVFinner_medulla = -14.6%.

CONCLUSION

These results demonstrate that our approach is promising for research into quantitative assessment of renal TVF in in vivo applications. Ultimately, these investigations have the potential to help reveal mechanism in acute renal injury that may lead to chronic kidney disease, which will support research into renal disorders.

In-Situ Efficiency Estimation of Induction Motors Based on Quantum Particle Swarm Optimization-Trust Region Algorithm (QPSO-TRA)

The accuracy estimation of induction motors’ efficiency is beneficial and crucial in the industry for energy savings. The requirement for in situ machine efficiency estimation techniques is increasing in importance because it is the precondition to making the energy-saving scheme. Currently, the torque and speed identification method is widely applied in online efficiency estimation for motor systems. However, the higher precision parameters, such as stator resistance Rs and equivalent resistance of iron losses Rfe, which are the key to the efficiency estimation process with the air gap torque method, are of cardinal importance in the estimation process. Moreover, the computation burden is also a severe problem for the real-time data process. To solve these problems, as for the torque and speed-identification-based efficiency estimation method, this paper presents a lower time burden method based on Quantum Particle Swarm Optimization-Trust Region Algorithm (QPSO-TRA). The contribution of the proposed method is to transform the disadvantages of former algorithms to develop a reliable hybrid algorithm to identify the crucial parameters, namely, Rs and Rfe. Sensorless speed identification based on the rotor slot harmonic frequency (RSHF) method is adopted for speed determination. This hybrid algorithm reduces the computation burden by about 1/3 compared to the classical genetic algorithm (GA). The proposed method was validated by testing a 5.5 kW motor in the laboratory and a 10 MW induction motor in the field.

SUPER: A blockwise curve-fitting method for accelerating MR parametric mapping with fast reconstruction

PURPOSE

To investigate Shift Undersampling improves Parametric mapping Efficiency and Resolution (SUPER), a novel blockwise curve-fitting method for accelerating parametric mapping with very fast reconstruction.

METHODS

SUPER uses interleaved k-space undersampling, which enables a blockwise decomposition of the otherwise large-scale cost function to improve the reconstruction efficiency. SUPER can be readily combined with SENSE to achieve at least 4-fold acceleration. D-factor, a parametric-mapping counterpart of g-factor, was proposed and formulated to compare spatially heterogeneous noise amplification because of different acceleration methods. As a proof-of-concept, SUPER/SUPER-SENSE was validated using T1 mapping, by comparing them to alternative model-based methods, including MARTINI and GRAPPATINI, via simulations, phantom imaging, and in vivo brain imaging (N = 5), over criteria of normalized root-mean-squares error (NRMSE), average d-factor, and computational time per voxel (TPV). A novel SUPER-SENSE MOLLI cardiac T1 -mapping sequence with improved resolution (1.4 mm × 1.4 mm) was compared to standard MOLLI (1.9 mm × 2.5 mm) in 8 healthy subjects.

RESULTS

In brain imaging, 2-fold SUPER achieved lower NRMSE (0.04 ± 0.02 vs. 0.11 ± 0.02, P < 0.01), lower average d-factor (1.01 ± 0.002 vs. 1.12 ± 0.004, P < 0.001), and lower TPV (4.6 ms ± 0.2 ms vs. 79 ms ± 3 ms, P < 0.001) than 2-fold MARTINI. Similarly, 4-fold SUPER-SENSE achieved lower NRMSE (0.07 ± 0.01 vs. 0.13 ± 0.03, P = 0.02), lower average d-factor (1.15 ± 0.01 vs. 1.20 ± 0.01, P < 0.001), and lower TPV (4.0 ms ± 0.1 ms vs. 72 ms ± 3 ms, P < 0.001) than 4-fold GRAPPATINI. In cardiac T1 mapping, SUPER-SENSE MOLLI yielded similar myocardial T1 (1151 ms ± 63 ms vs. 1159 ms ± 32 ms, P = 0.6), slightly lower blood T1 (1643 ms ± 86 ms vs. 1680 ms ± 79 ms, P = 0.004), but improved spatial resolution compared with standard MOLLI in the same imaging time.

CONCLUSION

SUPER and SUPER-SENSE provide fast model-based reconstruction methods for accelerating parametric mapping and improving its clinical appeal.

An Efficient Reconstruction Algorithm Based on the Alternating Direction Method of Multipliers for Joint Estimation of ${R}_{{2}}^{*}$ and Off-Resonance in fMRI

R*₂ mapping is a useful tool in blood-oxygen-level dependent fMRI due to its quantitative-nature. However, like T*₂-weighted imaging, standard R*₂ mapping based on multi-echo EPI suffers from geometric distortion, due to strong off-resonance near the air-tissue interface. Joint mapping of R*₂ and off-resonance can correct the geometric distortion and is less susceptible to motion artifacts. Single-shot joint mapping of R*₂ and off-resonance is possible with a rosette trajectory due to its frequent sampling of the k-space center. However, the corresponding reconstruction is nonlinear, ill-conditioned, large-scale, and computationally inefficient with current algorithms. In this paper, we propose a novel algorithm for joint mapping of R*₂ and off-resonance, using rosette k-space trajectories. The new algorithm, based on the alternating direction method of multipliers, improves the reconstruction efficiency by simplifying the original complicated cost function into a composition of simpler optimization steps. Compared with a recently developed trust region algorithm, the new algorithm achieves the same accuracy and an acceleration of threefold to sixfold in reconstruction time. Based on the new algorithm, we present simulation and in vivo data from single-shot, double-shot, and quadruple-shot rosettes and demonstrate the improved image quality and reduction of distortions in the reconstructed R*₂ map.