A framework for accurate determination of the T₂ distribution from multiple echo magnitude MRI images

Measurement of the T₂ distribution in tissues provides biologically relevant information about normal and abnormal microstructure and organization. Typically, the T₂ distribution is obtained by fitting the magnitude MR images acquired by a multi-echo MRI pulse sequence using an inverse Laplace transform (ILT) algorithm. It is well known that the ideal magnitude MR signal follows a Rician distribution. Unfortunately, studies attempting to establish the validity and efficacy of the ILT algorithm assume that these input signals are Gaussian distributed. Violation of the normality (or Gaussian) assumption introduces unexpected artifacts, including spurious cerebrospinal fluid (CSF)-like long T₂ components; bias of the true geometric mean T₂ values and in the relative fractions of various components; and blurring of nearby T₂ peaks in the T₂ distribution. Here we apply and extend our previously proposed magnitude signal transformation framework to map noisy Rician-distributed magnitude multi-echo MRI signals into Gaussian-distributed signals with high accuracy and precision. We then perform an ILT on the transformed data to obtain an accurate T ₂ distribution. Additionally, we demonstrate, by simulations and experiments, that this approach corrects the aforementioned artifacts in magnitude multi-echo MR images over a large range of signal-to-noise ratios.