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Development of a Numerical Bloch Solver for Low-Field Pulse Sequence Modeling1Department of Physics and Astronomy, Western University, London, ON, Canada, 2xMR Labs, London, ON, Canada
Synopsis
Renewed interest in clinical low-field MR systems has opened up a new design space for MR pulse sequence design. To explore these opportunities, and to better inform hardware design, we are developing a flexible simulation tool based on a numerical simulation of the Bloch equations. This tool will both be able to model pulse sequences under the influence of realistic applied fields, and account for changes in relaxation time due to changes in field strength. This abstract presents our work to date in developing this tool.
Introduction
Research interest in low-field (<1 Tesla) magnetic resonance imaging (MRI) has grown in recent years as a way to reduce the cost of MRI scans, and to make MR more accessible by reducing or removing siting requirements for the magnet1,2. However, as we change field strength, we change how a sample’s physical characteristics translate into MR image contrast due to altered relaxation times3,4. Furthermore, at low-field, changes in applied field due to the activation of modern high strength gradients can alter relaxation times over the course of an MR sequence. This modifies the contrast provided by existing techniques, and opens opportunities for novel, low-field specific contrasts. To account for these effects while designing new MR hardware, we are developing a flexible MR pulse sequence modeling tool capable of modeling the results of an MR experiment. In contrast with many existing solvers, this tool is designed to simulate the system under the influence of arbitrary magnetic fields in order to allow novel hardware configurations and non-idealities to be included in the simulation. This presentation will discuss our development efforts to date, and our ongoing validation work for this tool.Methods
Development of this simulation tool is being done in Python 3. A system of python classes are used to specify the magnetic fields being applied to a sample as time-dependent functions. Once defined, these field functions are used to solve the Bloch equations in the rotating reference frame for each voxel using SciPy’s solve_ivp() function, itself using a Runge-Kutta 853 numerical integration method5. The sample is simulated by dividing the sample volume into voxels, which each contain a defined number of randomly distributed spins. T2* relaxation is simulated by giving each spin a randomly generated field offset calculated based off a tissue specific T2* value6. With this structure, an end user can write a script calling different pulse sequence elements, which will output a simulated signal that can then be processed using existing signal analysis techniques to produce the images or other data desired by the user. To validate this toolset, we recreated a number of basic pulse sequences including a free-induction decay, a CPMG train (TE = 100 ms, 6 echoes), a stimulated echo (TE1 = 50 ms, TE2 = 200 ms), and a simple 1D gradient echo (TE = 8 ms) 3. These sequences were then applied to a virtual phantom with homogenous, user defined properties (T1 = 2 s, T2 = 200 ms, T2* = 30 ms). The resultant output was compared to the initial model used by the simulation for validation. In this initial set of experiments, no noise was simulated.Results
A simple free induction decay experiment was run to test our T2* relaxation results; fitting the signal curve yielded a relaxation time of 34 ± 1 ms. Simulated signal for the CPMG and stimulated echoes are presented in Figures 1 and 2. In the CPMG sequence, the peaks of each echo were used to compute the T2 relaxation time of the resultant signal, giving a result of 188 ± 5 ms. For the stimulated echo sequence, we expected and observed 4 echoes of varying amplitude; the primary stimulated echo at 50 ms after beginning signal acquisition, plus much smaller echoes at 150, 200, and 250 ms. The gradient echo, shown in Figure 3, also yielded the expected peak at the midpoint of the frequency encode gradient.Discussion
At this current stage, our simulation tool is reliably reproducing basic behaviours of an MR experiment while giving results that are roughly in accordance with the physical parameters assigned to the simulated phantom values (with percentage differences between the phantom and simulated experimental values being 13% for T2* and 6.5% for T2 relaxation).Conclusions
Our simulation tool in its current form is able to replicate the fundamental aspects of an MR pulse sequence. Future work will focus on developing simulated imaging experiments, as well as adding features such as field dependent relaxation time calculations, and multithreading to improve simulation speeds. Ultimately we aim for this simulation tool to have the flexibility needed to simulate and optimize pulse sequences for a new generation of low field systems currently in development, novel hardware geometries and experimental techniques such as dreMR7 which violate the fundamental assumptions typical simulation tools rely on for their analyses.Acknowledgements
No acknowledgement found.References
1. Panther, A. et al. A Dedicated Head-Only MRI Scanner for Point-of-Care Imaging. Proc. Annu. Meet. Int. Soc. Magn. Reson. Med. (2019).
2. Wiens, C. N., Harris, C. T., Curtis, A. T., Beatty, P. J. & Stainsby, J. A. Feasibility of Diffusion Tensor Imaging at 0.5T. Proc. Annu. Meet. Int. Soc. Magn. Reson. Med. (2019).
3. Nishimura, D. G. Principles of Magnetic Resonance Imaging. (Stanford University, 2010).
4. DeGraaf, R. A. in vivo NMR Spectroscopy. (John Wiley & Sons, Ltd, 2007).
5. Hairer, E., Norsett, S. P. & Wanner, G. “Solving Ordinary Differential Equations I: Nonstiff Problems”. (1993).
6. Stöcker, T., Vahedipour, K., Pflugfelder, D. & Shah, N. J. High-performance computing MRI simulations. Magn. Reson. Med. 64, 186–193 (2010).
7. Alford, J. K., Rutt, B. K., Scholl, T. J., Handler, W. B. & Chronik, B. A. Delta relaxation enhanced mr: Improving activation - Speeificity of molecular probes through R1 dispersion imaging. Magn. Reson. Med. 61, 796–802 (2009).
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