Magnetic Resonance Imaging (MRI) detects signal from hydrogen nuclei in biological tissue. MRI requires a homogeneous static magnetic field to generate artifact-free images. The subject is spatially encoded with magnetic field gradients. The signal is acquired in the frequency domain and the image is reconstructed by inverse Fourier transform. Objects with high magnetic susceptibility, such as MRI-safe metallic implants, distort the surrounding magnetic field. This leads to severe artifacts that appear as signal voids in the conventional MRI images, due to rapid intravoxel dephasing, in addition to misregistration of frequencies to position.
Pure phase encoding techniques with short encoding times are largely immune to magnetic field inhomogeneity artifacts. This is because the constant signal evolution times can be sufficiently short that no appreciable dephasing has occurred. High quality artifact-free MRI images were acquired with pure phase encoding techniques, from which the magnetic field distribution around the metal was derived. This approach was compared with conventional MRI methods, which failed to map the magnetic field in high susceptibility regions. Although it is challenging to apply the proposed method in a routine clinical MRI scan, the measured magnetic field distribution could enable the development of novel nonlinear encoding techniques, where the metal induced magnetic field distortion is exploited to provide spatial information.

Mapping Magnetic Field Around Metal with Pure Phase Encoding Magnetic Resonance Imaging

Magnetic resonance imaging (MRI) is widely used as a non-invasive diagnostic technique to visualize the internal structure of biological systems. Quantitative analysis of magnetic resonance signal lifetimes, i.e., relaxation times, can reveal molecular scale information and has significance in the study of brain, spinal cord, articular cartilage, and cancer discrimination. Determination of MR relaxation spectra (relaxometry) is an inherently ill-posed problem. Conventional methods to extract MR relaxation spectra are computationally intensive, requiring high quality data and generally lacking the spectrum peak width information. A novel computationally efficient signal analysis method, based on neural networks (NN), has been developed to provide accurate real-time quantitative MR relaxation spectrum analysis. 
Deep learning with NN is a technique for solving complex nonlinear problems. NN have been optimized to determine 1D and 2D MR relaxation spectra. Simulated signals with Rician noise were employed for training the neural networks. The network performance was evaluated with simulated and experimental data, and compared with the traditional inverse Laplace transform (ILT) method. NN outperformed ILT. The 1D spectrum peak widths, generally considered not reliable with the traditional approach, could be determined accurately by the NN, noise permitting. 
The proposed exponential analysis method is not restricted to magnetic resonance. It is readily applicable in other areas with exponential analysis, such as fluorescence decay and radioactive decay. The method could be extended to higher dimensional spectra and adopted to solve other ill-posed problems.

Magnetic Resonance Relaxometry with Neural Networks

Magnetic resonance imaging (MRI) is widely used as a non-invasive diagnostic technique to visualize the internal structure of biological systems. MRI has limited spatial resolution and the microscopic behaviour within an image voxel cannot be visualized with qualitative images. Quantitative analysis of molecular diffusion provides insights into the microscopic structure beyond the MRI image resolution. It is challenging to analytically derive the MR diffusion signals for complex microscopic environments, particularly with susceptibility effects. In this work, an easy to use open-source Monte Carlo algorithm has been developed to simulate MR diffusion measurements under arbitrary conditions.
The self diffusion of water molecules can be described by Brownian motion. The Monte Carlo method was applied to simulate the Brownian motion in a user-defined microscopic environment. The fast simulation can be performed on any MRI experiments with user-defined magnetic field distribution. The method has been applied to predict nanoparticle configuration. Magnetic nanoparticles, serving as biosensors, distort the local magnetic field leading to changes in the MR diffusion signals. The simulation agreed with the experimental results. The nanoparticle concentration in water can be determined with MR diffusion measurements. 
We have developed an efficient, easy to use algorithm for rapid diffusion simulation in different microscopic environments with arbitrary magnetic fields. This simulation will be employed to optimize the nanoparticle biosensor systems for a wide range of targets, including cancer cells and COVID virus.

Monte Carlo Simulation for Magnetic Resonance Diffusion Measurements

M3-3 MR and PET Imaging - Part 1 (DPMB) / Imagerie RM et TEP - Partie 1 (DPMB)

technical paper

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Dan Xiao

3

Presentations

Mapping Magnetic Field Around Metal with Pure Phase Encoding Magnetic Resonance Imaging

Magnetic Resonance Relaxometry with Neural Networks

Monte Carlo Simulation for Magnetic Resonance Diffusion Measurements

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