Robust Monte-Carlo Simulations in Diffusion-MRI: Effect of the Substrate Complexity and Parameter Choice on the Reproducibility of Results.

Jonathan Rafael-Patino,David Romascano,Gabriel Girard,Erick Jorge Canales-Rodríguez,Jean-Philippe Thiran,Alonso Ramirez-Manzanares

doi:10.3389/fninf.2020.00008

Abstract

Monte-Carlo Diffusion Simulations (MCDS) have been used extensively as a ground truth tool for the validation of microstructure models for Diffusion-Weighted MRI. However, methodological pitfalls in the design of the biomimicking geometrical configurations and the simulation parameters can lead to approximation biases. Such pitfalls affect the reliability of the estimated signal, as well as its validity and reproducibility as ground truth data. In this work, we first present a set of experiments in order to study three critical pitfalls encountered in the design of MCDS in the literature, namely, the number of simulated particles and time steps, simplifications in the intra-axonal substrate representation, and the impact of the substrate's size on the signal stemming from the extra-axonal space. The results obtained show important changes in the simulated signals and the recovered microstructure features when changes in those parameters are introduced. Thereupon, driven by our findings from the first studies, we outline a general framework able to generate complex substrates. We show the framework's capability to overcome the aforementioned simplifications by generating a complex crossing substrate, which preserves the volume in the crossing area and achieves a high packing density. The results presented in this work, along with the simulator developed, pave the way toward more realistic and reproducible Monte-Carlo simulations for Diffusion-Weighted MRI.

Highlights

Diffusion-Weighted Magnetic Resonance Imaging (DW-MRI) is a non-invasive technique with enormous potential for the study of the brain’s microstructure by measuring the diffusion properties of biological tissue
This paper outlines and investigates a set of pitfalls encountered on the parameter selection and substrates’ design for Monte-Carlo simulations
We found that for experiments with parameters in the range used in this study—which are in the range of interest in the literature— simulations with less than 5 × 105 particles and 1 × 104 steps carried a significant variance between the computed signals for both, the intra- and extra-axonal compartments

Summary

Introduction

Diffusion-Weighted Magnetic Resonance Imaging (DW-MRI) is a non-invasive technique with enormous potential for the study of the brain’s microstructure by measuring the diffusion properties of biological tissue. Analytical solutions of the signal attenuation can be derived for simple geometrical shapes such as impermeable planes, cylinders, and spheres (Neuman, 1974). For applications where the signal attenuation of complex cellular structures or non-homogeneous media is needed, e.g., to generate ground truth data, an analytical solution is no longer feasible to pursue due to its inherent complexity. Simplifications of the diffusion media have been used as the backbone of most of the microstructure models in the literature (Bammer, 2003; Panagiotaki et al, 2012; Zhang et al, 2012; Ferizi et al, 2015)

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Conclusion