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Numerical simulation of Bloch equations for dynamic magnetic resonance imaging. (English) Zbl 1378.78033

Summary: Magnetic resonance imaging (MRI) is a widely applied non-invasive imaging modality based on non-ionizing radiation which gives excellent images and soft tissue contrast of living tissues. We consider the modified Bloch problem as a model of MRI for flowing spins in an incompressible flow field. After establishing the well-posedness of the corresponding evolution problem, we analyze its spatial semi-discretization using discontinuous Galerkin methods. The high frequency time evolution requires a proper explicit and adaptive temporal discretization. The applicability of the approach is shown for basic examples.

MSC:

78M10 Finite element, Galerkin and related methods applied to problems in optics and electromagnetic theory
78A25 Electromagnetic theory (general)
65N40 Method of lines for boundary value problems involving PDEs
65M60 Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs
65L06 Multistep, Runge-Kutta and extrapolation methods for ordinary differential equations
92C55 Biomedical imaging and signal processing
78M20 Finite difference methods applied to problems in optics and electromagnetic theory

Software:

COMSOL; SIMRI
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References:

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