A Method of Estimation for Magnetic Resonance Spectroscopy Using Complex-Valued Neural Networks

A Method of Estimation for Magnetic Resonance Spectroscopy Using Complex-Valued Neural Networks

Naoyuki Morita
DOI: 10.4018/978-1-60566-214-5.ch011
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The author proposes an automatic estimation method for nuclear magnetic resonance (NMR) spectra of the metabolites in the living body by magnetic resonance spectroscopy (MRS) without human intervention or complicated calculations. In the method, the problem of NMR spectrum estimation is transformed into the estimation of the parameters of a mathematical model of the NMR signal. To estimate these parameters, Morita designed a complex- valued Hopfield neural network, noting that NMR signals are essentially complex-valued. In addition, we devised a technique called sequential extension of section (SES) that takes into account the decay state of the NMR signal. Morita evaluated the performance of his method using simulations and shows that the estimation precision on the spectrum improves when SES is used in combination the neural network, and that SES has an ability to avoid the local minimum solution on Hopfield neural networks.
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Magnetic resonance imaging (MRI) systems, which produce medical images using the nuclear magnetic resonance (NMR) phenomenon, have recently become popular. Additional technological innovations, such as high-speed imaging technologies (Feinberg & Oshio, 1991; Henning, Nauerth, & Fnedburg, 1986; Mansfield, 1977; Melki, Mulkern, Panych, & Joles, 1991; Meyer, Hu, Nishimura, & Macovski, 1992) and imaging of brain function using functional MRI (Belliveau et al., 1991; Kwong et al., 1992; Ogawa, Lee, Nayak, & Glynn, 1990), are also rapidly progressing. Currently, the above-mentioned imaging technologies mainly take advantage of the NMR phenomena of protons. The atomic nuclei used for analyzing metabolism in the living body include proton, phosphorus-31, carbon-13, fluorine-19 and sodium-22. Phosphorus-31 NMR spectroscopy has been widely used for measurement of the living body, because it is able to track the metabolism of energy.

NMR was originally developed and used in the field of analytical chemistry. In that field, NMR spectra are used to analyze the chemical structure of various materials. This is called NMR spectroscopy. In medical imaging, it is also possible to obtain NMR spectra. In this case, the technique is called magnetic resonance spectroscopy (MRS), and it can be used to collect the spectra of metabolites in organs such as the brain, heart, liver and muscle. The difference between NMR spectroscopy and MRS is that in MRS, we collect spectra from the living body in a relatively low magnetic field (usually, about 1.5 Tesla); in NMR spectroscopy, small chemical samples are measured in a high magnetic field.

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