Numerical simulation of Bloch equations for dynamic magnetic resonance imaging

Hazra, Arijit; Lube, Gert; Raumer, Hans-Georg

doi:10.1016/j.apnum.2017.09.007

Cited by 7 publications

(7 citation statements)

References 23 publications

(44 reference statements)

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“…During the latter, the excitation fields are nulled:

{B}_x={B}_y=0

in Equation (). In the precession regime, the operator splitting method gives an exact solution, whereas during the excitation regime the method has

O\left(\Delta {t}^3\right)

convergence 30 …”

Section: Methodsmentioning

confidence: 99%

“…In the precession regime, the operator splitting method gives an exact solution, whereas during the excitation regime the method has O ( Δt 3 ) convergence. 30 From this point forward, we will drop the vectorial notation for M and B 1 , and we will use M xy = M x + iM y and B 1 = B 1,x + iB 1,y to describe the simplifications made in each regime.…”

Section: F I G U R Ementioning

confidence: 99%

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

Castillo-Passi

Coronado

Varela-Mattatall

et al. 2023

Magnetic Resonance in Med

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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.

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“…During the latter, the excitation fields are nulled:

{B}_x={B}_y=0

in Equation (). In the precession regime, the operator splitting method gives an exact solution, whereas during the excitation regime the method has

O\left(\Delta {t}^3\right)

convergence 30 …”

Section: Methodsmentioning

confidence: 99%

Section: F I G U R Ementioning

confidence: 99%

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

Castillo-Passi

Coronado

Varela-Mattatall

et al. 2023

Magnetic Resonance in Med

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“…The configuration proposed by Yuan et al [ 31 ] and reproduced in [ 20 ] was tested to validate the implementation of the Bloch equations solver. The evolution of the magnetization vector of isochromats flowing along a 1-D segment (see Fig 7a ) under a simple 90° slice-selection pulse sequence (see Fig 7(b) was simulated and compared to the results obtained in [ 31 ].…”

Section: Verification and Validationmentioning

confidence: 99%

“…A classical approach often adopted in the literature consists in solving the Eulerian formulation of the Bloch equations [ 18 – 20 ]. In this case, the CFD velocity ( u ) is used to transport the magnetization vector and a convection term is explicitly added to the time rate of change of the magnetization vector ( M ), which becomes: …”

Section: Introductionmentioning

confidence: 99%

“…As discussed by Shkarin & Spencer [ 25 ], at least 3 isochromats/direction/voxel are necessary to reduce the MR signal error to 1.5%: this may require high computational resources depending on the image spatial resolution (450 million particles for a 256 × 256 × 256 image). Since homogeneous particle repartition within the domain is also required to avoid zones with spurious MR signals [ 24 ], the existing studies are most often limited to simulations in simple geometries [ 18 , 20 , 26 ]. Moreover, in the usual procedure [ 15 , 21 – 24 , 26 , 27 ], a prior CFD simulation is performed to store all the particle positions during the entire simulation.…”

Section: Introductionmentioning

confidence: 99%

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Numerical simulation of time-resolved 3D phase-contrast magnetic resonance imaging

Puiseux

Sewonu²,

Moreno

et al. 2021

PLoS ONE

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A numerical approach is presented to efficiently simulate time-resolved 3D phase-contrast Magnetic resonance Imaging (or 4D Flow MRI) acquisitions under realistic flow conditions. The Navier-Stokes and Bloch equations are simultaneously solved with an Eulerian-Lagrangian formalism. A semi-analytic solution for the Bloch equations as well as a periodic particle seeding strategy are developed to reduce the computational cost. The velocity reconstruction pipeline is first validated by considering a Poiseuille flow configuration. The 4D Flow MRI simulation procedure is then applied to the flow within an in vitro flow phantom typical of the cardiovascular system. The simulated MR velocity images compare favorably to both the flow computed by solving the Navier-Stokes equations and experimental 4D Flow MRI measurements. A practical application is finally presented in which the MRI simulation framework is used to identify the origins of the MRI measurement errors.

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

Duncan‐Gelder,

O'Keeffe,

Bones

et al. 2024

Medical Physics

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BackgroundSimulations 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.PurposeThe 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.MethodsUsing 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.ResultsThe 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.ConclusionsA 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.

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Numerical simulation of Bloch equations for dynamic magnetic resonance imaging

Cited by 7 publications

References 23 publications

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

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

Numerical simulation of time-resolved 3D phase-contrast magnetic resonance imaging

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

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