RESOLVING POWER OF MODIFIED IMAGE RECONSTRUCTION METHOD IN SPIN DENSITY PROJECTIONS IN MAGNETIC RESONANCE IMAGING

Abstract

The well-known method of image reconstruction by projections in magnetic resonance imaging uses spin echo excited by two sinc pulses. The further processing involves forming of the spin echo signal two quadrature components converting them into a digital format and the subsequent Fourier transform. The proposed modified method is based on the second sinc radio pulse substitution for the linear FM pulse. In this case, the mentioned projections are formed by amplitude detection of the spin echo envelope, which significantly simplifies the processing procedure. The aim of the research is to analyze the modified method resolution. The mathematical model is based on Bloch equations. Their solution is carried out on the basis of the device of the spin system state transition matrices. For their calculation, the stepped approximation of the excitation pulse complex envelopes is used. It makes possible to convert the system of linear differential equations with variable coefficients (Bloch equations) to the system of linear differential equations with piecewise constant coefficients. In this case, the equations have analytical solution. Following the obtained solution, the analysis of the method resolution not previously investigated, is performed by means of modeling the spin echo excitation. The conditions are specified when no dynamic distortions influencing received image quality exist. It is shown that resolution is determined by the size of the scan area, the magnitude of the gradient of the applied magnetic field, the pulse duration with linear frequency modulation, as well as gyromagnetic ratio of the core type used. The developed method eliminates the need for Fourier transform over the spin echo signal and pro-vides resolution comparable to the conventional one.