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

Improved quantification in CEST-MRI by joint spatial total generalized variation

PURPOSE

In this work, the use of joint Total Generalized Variation (TGV) regularization to improve Multipool-Lorentzian fitting of chemical exchange saturation transfer (CEST) Spectra in terms of stability and parameter signal-to-noise ratio (SNR) was investigated.

THEORY AND METHODS

The joint TGV term was integrated into the nonlinear parameter fitting problem. To increase convergence and weight the gradients, preconditioning using a voxel-wise singular value decomposition was applied to the problem, which was then solved using the iteratively regularized Gauss-Newton method combined with a Primal-Dual splitting algorithm. The TGV method was evaluated on simulated numerical phantoms, 3T phantom data and 7T in vivo data with respect to systematic errors and robustness. Three reference methods were also implemented: The standard nonlinear fitting, a method using a nonlocal-means filter for denoising and the pyramid scheme, which uses downsampled images to acquire accurate start values.

RESULTS

The proposed regularized fitting method showed significantly improved robustness (compared to the reference methods). In testing, over a range of SNR values the TGV fit outperformed the other methods and showed accurate results even for large amounts of added noise. Parameter values found were closer or comparable to the ground truth. For in vivo datasets, the added regularization increased the parameter map SNR and prevented instabilities.

CONCLUSION

The proposed fitting method using TGV regularization leads to improved results over a range of different data-sets and noise levels. Furthermore, it can be applied to all Z-spectrum data, with different amounts of pools, where the improved SNR and stability can increase diagnostic confidence.

PhoenixMR: A GPU-based MRI simulation framework with runtime-dynamic code execution

BACKGROUND

Simulations of physical processes and behavior can provide unique insights and understanding of real-world problems. Magnetic Resonance Imaging (MRI) is an imaging technique with several components of complexity. Several of these components have been characterized and simulated in the past. However, several computational challenges prevent simulations from being simultaneously fast, flexible, and accurate.

PURPOSE

The simulation of MRI experiments is underutilized by medical physicists and researchers using currently available simulators due to reasons including speed, accuracy, and extensibility constraints. This paper introduces an innovative MRI simulation engine and framework that aims to overcome these issues making available realistic and fast MRI simulation.

METHODS

Using the CUDA C/C++ programing language, an MRI simulation engine (PhoenixMR), incorporating a Turing-complete virtual machine (VM) to simulate abstract spatiotemporal complexities, was developed. This engine solves a set of time-discrete Bloch equations using the symmetric operator splitting technique. An extensible front-end framework package (written in Python) aids the use of PhoenixMR to simplify simulation development.

RESULTS

The PhoenixMR library and front-end codes have been developed and tested. A set of example simulations were performed to demonstrate the ease of use and flexibility of simulation components such as geometrical setup, pulse sequence design, phantom design, and so forth. Initial validation of PhoenixMR is performed by comparing its accuracy and performance against a widely used MRI simulator using identical simulation parameters. Validation results show PhoenixMR simulations are three orders of magnitude faster. There is also strong agreement between models.

CONCLUSIONS

A novel MRI simulation platform called PhoenixMR has been introduced. This research tool is designed to be usable by physicists and engineers interested in performing MRI simulations. Examples are shown demonstrating the accuracy, flexibility, and usability of PhoenixMR in several key areas of MRI simulation.

CMRsim-A python package for cardiovascular MR simulations incorporating complex motion and flow

PURPOSE

To present an open-source MR simulation framework that facilitates the incorporation of complex motion and flow for studying cardiovascular MR (CMR) acquisition and reconstruction.

METHODS

CMRsim is a Python package that allows simulation of CMR images using dynamic digital phantoms with complex motion as input. Two simulation paradigms are available, namely, numerical and analytical solutions to the Bloch equations, using a common motion representation. Competitive simulation speeds are achieved using TensorFlow for GPU acceleration. To demonstrate the capability of the package, one introductory and two advanced CMR simulation experiments are presented. The latter showcase phase-contrast imaging of turbulent flow downstream of a stenotic section and cardiac diffusion tensor imaging on a contracting left ventricle. Additionally, extensive documentation and example resources are provided.

RESULTS

The Bloch simulation with turbulent flow using approximately 1.5 million particles and a sequence duration of 710 ms for each of the seven different velocity encodings took a total of 29 min on a NVIDIA Titan RTX GPU. The results show characteristic phase contrast and magnitude modulation present in real data. The analytical simulation of cardiac diffusion tensor imaging with bulk-motion phase sensitivity took approximately 10 s per diffusion-weighted image, including preparation and loading steps. The results exhibit the expected alteration of diffusion metrics due to strain.

CONCLUSION

CMRsim is the first simulation framework that allows one to feasibly incorporate complex motion, including turbulent flow, to systematically study advanced CMR acquisition and reconstruction approaches. The open-source package features modularity and transparency, facilitating maintainability and extensibility in support of reproducible research.

Enhanced and robust contrast in CEST MRI: Saturation pulse shape design via optimal control

PURPOSE

To employ optimal control for the numerical design of Chemical Exchange Saturation Transfer (CEST) saturation pulses to maximize contrast and stability againstB 0 $$ {\mathrm{B}}_0 $$ inhomogeneities.

THEORY AND METHODS

We applied an optimal control framework for the design pulse shapes for CEST saturation pulse trains. The cost functional minimized both the pulse energy and the discrepancy between the corresponding CEST spectrum and the target spectrum based on a continuous radiofrequency (RF) pulse. The optimization is subject to hardware limitations. In measurements on a 7 T preclinical scanner, the optimal control pulses were compared to continuous-wave and Gaussian saturation methods. We conducted a comparison of the optimal control pulses with Gaussian, block pulse trains, and adiabatic spin-lock pulses.

RESULTS

The optimal control pulse train demonstrated saturation levels comparable to continuous-wave saturation and surpassed Gaussian saturation by up to 50 % in phantom measurements. In phantom measurements at 3 T the optimized pulses not only showcased the highest CEST contrast, but also the highest stability against field inhomogeneities. In contrast, block pulse saturation resulted in severe artifacts. Dynamic Bloch-McConnell simulations were employed to identify the source of these artifacts, and underscore theB 0 $$ {\mathrm{B}}_0 $$ robustness of the optimized pulses.

CONCLUSION

In this work, it was shown that a substantial improvement in pulsed saturation CEST imaging can be achieved by using Optimal Control design principles. It is possible to overcome the sensitivity of saturation to B0 inhomogeneities while achieving CEST contrast close to continuous wave saturation.

Robust dual-angle T 1 $$ {T}_1 $$ measurement in magnetization transfer spectroscopy by time-optimal control

Magnetization transfer spectroscopy relies heavily on the robust determination ofT 1 $$ {T}_1 $$ relaxation times of nuclei participating in metabolic exchange. Challenges arise due to the use of surface RF coils for transmission (highB 1 + $$ {B}_1^{+} $$ variation) and the broad resonance band of most X nuclei. These challenges are particularly pronounced when fastT 1 $$ {T}_1 $$ mapping methods, such as the dual-angle method, are employed. Consequently, in this work, we develop resonance offset andB 1 + $$ {B}_1^{+} $$ robust excitation RF pulses for 31P magnetization transfer spectroscopy at 7T through ensemble-based time-optimal control. In our approach, we introduce a cost functional for designing robust pulses, incorporating the full Bloch equations as constraints, which are solved using symmetric operator splitting techniques. The optimal control design of the RF pulses developed demonstrates improved accuracy, desired phase properties, and reduced RF power when applied to dual-angleT 1 $$ {T}_1 $$ mapping, thereby improving the precision of exchange-rate measurements, as demonstrated in a preclinical in vivo study quantifying brain creatine kinase activity.

Dynamic and rapid deep synthesis of chemical exchange saturation transfer and semisolid magnetization transfer MRI signals

Model-driven analysis of biophysical phenomena is gaining increased attention and utility for medical imaging applications. In magnetic resonance imaging (MRI), the availability of well-established models for describing the relations between the nuclear magnetization, tissue properties, and the externally applied magnetic fields has enabled the prediction of image contrast and served as a powerful tool for designing the imaging protocols that are now routinely used in the clinic. Recently, various advanced imaging techniques have relied on these models for image reconstruction, quantitative tissue parameter extraction, and automatic optimization of acquisition protocols. In molecular MRI, however, the increased complexity of the imaging scenario, where the signals from various chemical compounds and multiple proton pools must be accounted for, results in exceedingly long model simulation times, severely hindering the progress of this approach and its dissemination for various clinical applications. Here, we show that a deep-learning-based system can capture the nonlinear relations embedded in the molecular MRI Bloch-McConnell model, enabling a rapid and accurate generation of biologically realistic synthetic data. The applicability of this simulated data for in-silico, in-vitro, and in-vivo imaging applications is then demonstrated for chemical exchange saturation transfer (CEST) and semisolid macromolecule magnetization transfer (MT) analysis and quantification. The proposed approach yielded 63-99% acceleration in data synthesis time while retaining excellent agreement with the ground truth (Pearson's r > 0.99, p < 0.0001, normalized root mean square error < 3%).

KomaMRI.jl: An open-source framework for general MRI simulations with GPU acceleration

PURPOSE

To develop an open-source, high-performance, easy-to-use, extensible, cross-platform, and general MRI simulation framework (Koma).

METHODS

Koma was developed using the Julia programming language. Like other MRI simulators, it solves the Bloch equations with CPU and GPU parallelization. The inputs are the scanner parameters, the phantom, and the pulse sequence that is Pulseq-compatible. The raw data is stored in the ISMRMRD format. For the reconstruction, MRIReco.jl is used. A graphical user interface utilizing web technologies was also designed. Two types of experiments were performed: one to compare the quality of the results and the execution speed, and the second to compare its usability. Finally, the use of Koma in quantitative imaging was demonstrated by simulating Magnetic Resonance Fingerprinting (MRF) acquisitions.

RESULTS

Koma was compared to two well-known open-source MRI simulators, JEMRIS and MRiLab. Highly accurate results (with mean absolute differences below 0.1% compared to JEMRIS) and better GPU performance than MRiLab were demonstrated. In an experiment with students, Koma was proved to be easy to use, eight times faster on personal computers than JEMRIS, and 65% of test subjects recommended it. The potential for designing acquisition and reconstruction techniques was also shown through the simulation of MRF acquisitions, with conclusions that agree with the literature.

CONCLUSIONS

Koma's speed and flexibility have the potential to make simulations more accessible for education and research. Koma is expected to be used for designing and testing novel pulse sequences before implementing them in the scanner with Pulseq files, and for creating synthetic data to train machine learning models.

A fast and practical computation method for magnetic resonance simulators

PURPOSE

This work aims to develop a fast and practical computation method for MR simulations. The computational cost of MR simulations is often high because magnetizations of many isochromats are updated using a small step size on the order of microseconds. There are two types of subsequences to be processed for the simulations: subsequences with and without RF pulses. While straightforward implementations spend most of their time calculating subsequences with RF pulses, there is a method which efficiently reuses the computation for repetitive RF pulses.

THEORY AND METHODS

A new method for efficiently processing subsequences with RF pulses is proposed. Rather than using an iterative update approach, the proposed method computes the combined transition which combines all transitions applied iteratively for each subsequence with RF pulses. The combined transition is used again when the same subsequence is used later. The combined transitions are cached and managed using a least recently used algorithm.

RESULTS

The proposed method was found to accelerate the simulation by ˜20 times when 3.9 million isochromats were simulated using spin-echo sequences. Even on a laptop computer, the proposed method was able to simulate these sequences in ˜3.5 min.

CONCLUSION

An efficient method for simulating pulse sequences is proposed. The proposed method computes and manages combined transitions, making MR simulation practical on a wide range of computers, including laptops.

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.

Myocardium Assessment by Relaxation along Fictitious Field, Extracellular Volume, Feature Tracking, and Myocardial Strain in Hypertensive Patients with Left Ventricular Hypertrophy

Background

Previous research has shown impaired global longitudinal strain (GLS) and slightly elevated extracellular volume fraction (ECV) in hypertensive patients with left ventricular hypertrophy (HTN LVH). Up to now, only little attention has been paid to interactions between macromolecules and free water in hypertrophied myocardium.

Purpose

To evaluate the feasibility of relaxation along a fictitious field with rank 2 (RAFF2) in HTN LVH patients. Study Type. Single institutional case control.

Subjects

9 HTN LVH (age, 69 ± 10 years) and 11 control subjects (age, 54 ± 12 years). Field Strength/Sequence. Relaxation time mapping (T₁, T_1ρ, and T_RAFF2 with 11.8 μT maximum radio frequency field amplitude) was performed at 1.5 T using a Siemens Aera (Erlangen, Germany) scanner equipped with an 18-channel body array coil. Assessment. ECV was calculated using pre- and postcontrast T₁, and global strains parameters were assessed by Segment CMR (Medviso AB Co, Sweden). The parametric maps of T_1ρ and T_RAFF2 were computed using a monoexponential model, while the Bloch-McConnell equations were solved numerically to model effect of the chemical exchange during radio frequency pulses. Statistical Tests. Parametric maps were averaged over myocardium for each subject to be used in statistical analysis. Kolmogorov-Smirnov was used as the normality test followed by Student's t-test and Pearson's correlation to determine the difference between the HTN LVH patients and controls along with Hedges' g effect size and the association between variables, respectively.

Results

T_RAFF2 decreased statistically (83 ± 2 ms vs 88 ± 6 ms, P < 0.031), and global longitudinal strain was impaired (GLS, −14 ± 3 vs − 18 ± 2, P < 0.002) in HTN LVH patients compared to the controls, respectively. Also, significant negative correlation was found between T_RAFF2 and GLS (r = −0.53, P < 0.05). Data Conclusion. Our results suggest that T_RAFF2 decrease in HTN LVH patients may be explained by gradual collagen accumulation which can be reflected in GLS changes. Most likely, it increases the water proton interactions and consequently decreases T_RAFF2 before myocardial scarring.