This course provides insight into practical implementation of computer simulations based on classical MR physics. Analytical solutions versus numerical implementations will be discussed. Based on pictorial examples, an introduction to various MRI simulator software packages will be given. Some code snippets will be presented in order to implement MRI physics simulation from scratch
Introduction
There exist many approaches to computer simulations of MR physics, based on different assumptions of the underlying physical model. This talk will solely discuss classical MR physics, which is accurately described by the phenomenological Bloch Equations (i.e. spin interactions and higher-order quantum coherences are not considered). However, also in case of classical MR, there exists no explicit analytical expression of the MR signal for a general driving field – the RF and gradient pulses of the MRI sequence. Therefore, many approaches take advantage of simplifying assumptions, e.g. instantaneous RF pulses or ideal spoiling, in order to utilize closed-form solutions.
The talk will first give several examples for analytical or semi-analytical solutions of the Bloch Equation and their field of application. Then, more general but computationally much more demanding approaches are discussed, which utilize numerical solutions of the Bloch Equation followed by subsequent isochromat averaging to simulate the MR signal. One possibility is to approximate the driving field by a piece-wise constant field. In this case individual closed-form solutions exist in terms of rotation operators. This approach typically requires a dense time discretization, which is on the one hand time consuming but on the other hand well-suited for parallelization on modern GPU hardware. The other approach is to utilize a variable time-stepping differential equation solver, which is very efficient for a single isochromat but more difficult to parallelize. It will be shown that realistic MRI simulations may require a large ensemble of isochromats, e.g. to accurately simulate intra-voxel dephasing, while the actual required number of simulated isochromats strongly depends on the problem.
There exist many excellent and freely available tools for MRI simulation. Without claiming to be complete, several software packages will be presented and some example applications will be shown in the lecture. Some references to existing tools are given in the list below. In addition, important extensions of the Bloch Equation will be briefly discussed. For instance, the Bloch-Torrey Equation describes diffusion and flow of isochromats while multi-pool exchange is governed by the Bloch-McConnel equation. The according computational costs are much higher than for the basic Bloch Equation and again several solver strategies exist. In addition to the Bloch Equation solver, a general-purpose MRI simulation software needs to provide a flexible and efficient definition of the sequence as well as the in silico phantom. Both problems and several proposed solutions will be discussed.
Besides the educational value of performing basic MR physics simulations, the actual implementation itself provides great insight too. Therefore, the course presents basic code snippets, which can be easily used and extended to start implementing your own MRI simulator.
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Drobnjak, I., Gavaghan, D., Süli, E., Pitt-Francis, J., & Jenkinson, M. (2006). Development of a functional magnetic resonance imaging simulator for modeling realistic rigid-body motion artifacts. Magnetic Resonance in Medicine, 56(2), 364–80. Hanson L. G. (2007) A Graphical Simulator for Teaching Basic and Advanced MR Imaging Techniques, RadioGraphics, 27(6):e27
Jochimsen, T. H., Schäfer, A., Bammer, R., & Moseley, M. E. (2006) Efficient simulation of magnetic resonance imaging with Bloch-Torrey equations using intra-voxel magnetization gradients. Journal of Magnetic Resonance, 180(1), 29–38.
Liu, F., Velikina, J. V., Block, W. F., Kijowski, R., & Samsonov, A. A. (2017). Fast Realistic MRI Simulations Based on Generalized Multi-Pool Exchange Tissue Model. IEEE Transactions on Medical Imaging, 36(2), 527–537.
Stöcker, T., Vahedipour, K., Pflugfelder, D., & Shah, N. J. (2010). High-performance computing MRI simulations. Magnetic Resonance in Medicine, 64(1), 186–93.
Xanthis, C. G., Venetis, I. E., & Aletras, A. H. (2014). High performance MRI simulations of motion on multi-GPU systems. Journal of Cardiovascular Magnetic, 16(1).