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

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 towards more realistic and reproducible Monte-Carlo simulations for Diffusion-Weighted MRI.

Estimating axial diffusivity in the NODDI model

“…Interestingly, in this simplistic model, undulations with an amplitude of only ~ 2 μm could lower the axial diffusivity from 3 to ~ 2.5 μm 2 /ms, as is seen in the data (Figure 7b). In current literature, the impact of undulations often focuses on the measurement of radial diffusion or axon diameter [32, 75, 33], though the effect of undulations on other diffusion characteristics, such as axial diffusion, deserve further investigation. Future work will benefit greatly from more realistic simulations [76, 34, 33] where, for example, the tissue structure is directly inspired by 3D reconstructed surfaces from microscopy images of real tissue [77, 34, 33].…”

Axon morphology is modulated by the local environment and impacts the non-invasive investigation of its structure-function relationship

“…Still, EM is time demanding and there is a need to combine techniques that bridge different resolutions and volumes; it would be valuable to image a sample by synchrotron XNH, and thereafter image a sub-region of the same sample with 3D EM.Lastly, the axonal trajectory variations and dispersion behavior presented here could act as an axonal "fingerprint" to guide the construction of anatomically informed axonal phantoms for MC simulations. Existing frameworks have been developed to model morphological features such as fiber undulation43,51 (although we do not observe periodic undulations in our data), and diameter variations52,53 . Others allow for the generation of a more complex WM environment with beaded axons and cells54 .…”

“…Finally, the resulting meshes were triangulated and decimated to reduce the computational burden for the simulation. 42 All simulations were performed using the Monte Carlo Diffusion and Collision simulator presented in Rafael-Patino et al (2020) 51 . Each axon in each geometry was simulated separately, and the intra-axonal diffusivity was set to 6.0 ⋅10 -10 m 2 s -1 as measured in Dyrby et al (2013), as is conventional for ex vivo diffusion MRI.…”

“…This confined initialization ensured that virtually no particle was able to diffuse outside the mesh. Perfectly elastic mesh boundaries were implemented, as in 51 . The number of particles and time-step duration (number of steps) were chosen using a bootstrap-based analysis of the convergence of the simulation as explained in 51 .…”

“…Perfectly elastic mesh boundaries were implemented, as in 51 . The number of particles and time-step duration (number of steps) were chosen using a bootstrap-based analysis of the convergence of the simulation as explained in 51 . In this investigation, we studied diffusion times, D_t, between 1-50 ms at intervals of 1 ms.…”