Numerical Simpson’s Rule for Real Time and Accurate T2* maps generation Using 3D Quantitative GRE

Abstract

T2* plays an important role in the quantitative evaluation of brain function and tissue iron content. Conventional approaches for quantitative T2* maps generation use linear or nonlinear least square curve fitting. Nevertheless, these methods are very time consuming and could not be used in real time T2* computation. Hagberg et al (2002) proposed a numerical method that relies on trapezoidal integration of signal decay. This method is faster than conventional methods and provides an accurate T2* value. However, this approach is valid for small echo spacing and low noise level. In this work, we propose an alternative numerical integration relying on Simpson’s rule that generates an accurate T2* maps even in the presence of large echo spacing and high noise value. The proposed method yields T2* values comparable to NumART2* in the presence of small echo spacing and high SNR and provides better results in the opposite case.