A.V. Protopopov – Post-graduate Student, Moscow Institute of Physics and Technology (State University), FSCC after the name of Dmitri Rogachev E-mail: email@example.com
The technique of a gradient recalled echo (GRE) became a powerful tool for sensing tiniest heterogeneities of magnetic field inside a human body. GRE sequences are used to depict hemorrhage, calcification, iron deposition in various tissues and lesions, to measure capillary dimensions and densities, for characterization of bone structure, mapping of brain iron content, and are the basis of the blood oxygen level dependent (BOLD) technique. Traditionally, in GRE magnetic resonance imaging (MRI), the image is formed by variations of an echo signal, which may be considered as some type of rendering but not as a map of a certain measured parameter. Such a rendering, whatever helpful it is for visual perception, does not answer the question what exactly physical parameter we see. Therefore, in GRE MRI, an important problem is identification of physical parameters that make an echo signal, and mapping them in a form of an image. The GRE signal evolves as a combined result of irreversible transverse relaxation processes T2, determined by spin-spin interactions on a quantum-mechanical level, and heterogeneities in the static magnetic field described by classical electrodynamics. Once separated, T2 and background gradients are two clear physical parameters that may be used for creating independent GRE images, thus providing additional information for diagnostics. Commonly used techniques for separating contribution of T2 relaxation from contribution by background gradients are based on one-dimensional models and fitting known decay functions into experimental relaxation curves. Namely, the T2 relaxation is always assumed to be monoexponential and contribution of the background gradient is represented by sinc function. However, in the one-dimensional model, the sinc function oscillates, which happens in reality only on rare occasions of newly installed scanners with uncompensated coils. In all other practical cases the experimental relaxation curves do not show oscillations. To cope with this artificial problem, the fitting procedures are usually limited to the first zero of sinc function, thus preserving only positive values. This results in ignoring information from longer echo intervals, making the measurement inaccurate. There are also other drawbacks of the fitting algorithms. In the present publication, we introduce: the three-dimensional relaxation model consistent with experiments; fittingless algorithms for separating T2 relaxation from background gradients.
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