Robust and fast Monte Carlo Markov Chain sampling of diffusion MRI microstructure models

Abstract

In diffusion MRI analysis, advances in biophysical multi-compartment modeling have gained popularity over the conventional Diffusion Tensor Imaging (DTI), because they possess greater specificity in relating the dMRI signal to underlying cellular microstructure. Biophysical multi-compartment models require parameter estimation, typically performed using either Maximum Likelihood Estimation (MLE) or using Monte Carlo Markov Chain (MCMC) sampling. Whereas MLE provides only a point estimate of the fitted model parameters, MCMC recovers the entire posterior distribution of the model parameters given the data, providing additional information such as parameter uncertainty and correlations. MCMC sampling is currently not routinely applied in dMRI microstructure modeling because it requires adjustments and tuning specific to each model, particularly in the choice of proposal distributions, burn-in length, thinning and the number of samples to store. In addition, sampling often takes at least an order of magnitude more time than non-linear optimization. Here we investigate the performance of MCMC algorithm variations over multiple popular diffusion microstructure models to see whether a single well performing variation could be applied efficiently and robustly to many models. Using an efficient GPU-based implementation, we show that run times can be removed as a prohibitive constraint for sampling of diffusion multi-compartment models. Using this implementation, we investigated the effectiveness of different adaptive MCMC algorithms, burn-in, initialization and thinning. Finally we apply the theory of Effective Sample Size to diffusion multi-compartment models as a way of determining a relatively general target for the number of samples needed to characterize parameter distributions for different models and datasets. We conclude that robust and fast sampling is achieved in most diffusion microstructure models with the Adaptive Metropolis-Within-Gibbs (AMWG) algorithm initialized with an MLE point estimate, in which case 100 to 200 samples are sufficient as a burn-in and thinning is mostly unnecessary. As a relatively general target for the number of samples, we recommend a multivariate Effective Sample Size of 2200.