Robust T2 Relaxometry With Hamiltonian MCMC for Myelin Water Fraction Estimation

Abstract

We present a voxel-wise Bayesian multi-compartment $T_{2}$ relaxometry fitting method based on Hamiltonian Markov Chain Monte Carlo (HMCMC) sampling. The $T_{2}$ spectrum is modeled as a mixture of truncated Gaussian components, which involves the estimation of parameters in a completely data-driven and voxel-based fashion, i.e. without fixing any parameters or imposing spatial regularization. We estimate each parameter as the expectation of the corresponding marginal distribution drawn from the joint posterior obtained with Hamiltonian sampling. We validate our scheme on synthetic and ex vivo data for which histology is available. We show that the proposed method enables a more robust parameter estimation than a state of the art point estimate based on differential evolution. Moreover, the proposed HMCMC-based myelin water fraction calculation reveals high spatial correlation with the histological counterpart.