Monte Carlo Simulations of Diffusion Weighted MRI in Myocardium: Validation and Sensitivity Analysis

Abstract

A model of cardiac microstructure and diffusion MRI is presented, and compared with experimental data from ex vivo rat hearts. The model includes a simplified representation of individual cells, with physiologically correct cell size and orientation, as well as intra- to extracellular volume ratio. Diffusion MRI is simulated using a Monte Carlo model and realistic MRI sequences. The results show good correspondence between the simulated and experimental MRI signals. Similar patterns are observed in the eigenvalues of the diffusion tensor, the mean diffusivity (MD), and the fractional anisotropy (FA). A sensitivity analysis shows that the diffusivity is the dominant influence on all three eigenvalues of the diffusion tensor, the MD, and the FA. The area and aspect ratio of the cell cross-section affect the secondary and tertiary eigenvalues, and hence the FA. Within biological norms, the cell length, volume fraction of cells, and rate of change of helix angle play a relatively small role in influencing tissue diffusion. Results suggest that the model could be used to improve understanding of the relationship between cardiac microstructure and diffusion MRI measurements, as well as in testing and refinement of cardiac diffusion MRI protocols.

Novel insights into in‐vivo diffusion tensor cardiovascular magnetic resonance using computational modelling and a histology‐based virtual microstructure

“…Convergence tests in in Supporting Information Figure S1 show that 10 repetitions per data point using N P = 10 4 and N T = 10 3 is sufficient to reliably compute DT‐CMR parameters while keeping the simulation within an acceptable runtime. These findings are consistent with the observations in simulations of cardiac and brain tissue . The normally‐distributed step lengths aid convergence and a rejection threshold of ±5σ is sufficient for accuracy (Supporting Information Figure S2).…”

“…These included both short and long diffusion times (M2‐SE and STEAM) and we compared the results to those from a PGSE sequence for reference. This extends recent work simulating ex‐vivo DT‐CMR, where the authors simulated a Stejskal–Tanner PGSE sequence in a cuboid‐based simulation substrate with 200 μm isotropic voxel size.…”

“…However, these studies lack the long diffusion times and microstructural architecture characteristic of DT‐CMR. Another approach is to use available packages to simulate the motion of molecules (Smoldyn as done by, or MCell as done by) and synthesise the MR signal by applying the pulse sequence during post‐processing. This may come at a large overhead in computation or software development.…”

“…identified two compartments in rat hearts through ex‐vivo experiments at 37 ∘ C. The observed values were 1.2 and 3.0μm 2 /ms, presumably intra‐ and extra‐cellular diffusivities respectively. used constant D IC = D EC when modelling cardiac tissue, and varied the ratio of D and compared results to the Kärger model for simulations of white matter.…”

“…Both continuum solutions of the Bloch–Torrey Equations and Monte Carlo random walk methods, which are significantly more efficient for complex geometries, can be used to synthesise DT‐CMR data in a known microstructure. Previous studies have reported DTI simulations in a number of organs, often modelling geometries using ordered or random arrays of cuboids or cylinders. These investigations lack the long mixing times and large voxels that are typical for DT‐CMR and the simplified shapes may not be adequate to represent the complicated architecture of cardiac muscle tissues.…”