Mathematical Modeling and Numerical Simulation of Magnetic Susceptibility Artifacts in Magnetic Resonance IMAGING*

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Abstract
The technique used to recognise information in Magnetic Resonance Imaging (MRI) is based on electromagnetic fields. A linearly varying field (around 10−2 Tesla per meter) is added to a strong homogeneous magnetic field (order of magnitude of approximately one Tesla). When these fields are disturbed by the presence of a paramagnetic material, in the sample for instance, the resulting image is usually distorted, these distortions being termed artifacts. Our goal is to present a method, assuming the field disturbances are known, to construct the resulting images. A mathematical model of the MRI process is developed. The way the images are distorted in intensity and shape is explained and an algorithm to simulate magnetic susceptibility artifacts is deduced.