To understand the effects of muscle microstructure on the diffusion tensor.

We hypothesize 1) decreased fiber size decreases λ₂ and λ₃, with no effect on λ₁, 2) fibrosis has little effect on the diffusion tensor, and 3) when edema is present, multi-echo DTI is required to resolve microstructural changes of muscle tissue.

Simplified models of muscle microstructure were integrated into diffusion simulation software (see below) to study the relationship between muscle fiber size, fibrosis, and edema on the diffusion tensor using single- and multi-echo DT-MRI techniques. The MRI simulation tool DifSim¹ was used to model DTI experiments within complex structures. DifSim employs MCell, a Monte Carlo simulator for cellular microphysiology, to simulate the diffusion of particles, and tracks particle location, signal amplitude and phase, within a user defined arbitrarily complex model. DifSim is capable of supporting boundary interactions, particle interactions, and multiple molecular species with different diffusion coefficients and T2-relaxation constants. MRI pulse sequence parameters were as follows: diffusion-weighted multi-spin-echo, TE=21.76ms, b=500s/mm², voxel size=200μmx200μmx200μm, number of echoes=16, echo spacing=10ms. Data was analyzed using a custom Matlab program, using the equations outlined by Fan et al².

Muscle fibers were approximated as tightly packed hexagons, surrounded by ECM as shown in Figure 1. Fiber diameter, fibrosis, and increased extra-cellular water content due to edema were varied across a range of physiologically relevant dimensions and concentrations, (Table 1). Model inputs for diffusion coefficients and T2-relaxation rates are reported in Table 2. To relate diffusion measurements to individual features of muscle microstructure, we used linear or non-linear regression (when appropriate).

To test our hypothesis that multi-echo DTI is required to measure fiber size changes in the presence of edema, we compared diffusion measurements taken by single-echo and multi-echo DTI in normal (4% volume fraction extracellular water) and edematous (40% volume fraction extracellular water) muscle, across a range of fiber sizes. Non-linear regression was used to describe the relationship between fiber size and diffusion in non-edematous muscle using single-echo DTI. Coefficient of variation from this regression was used to determine which DTI technique is most closely related to single echo DTI of normal muscle.

As fiber diameter decreases below 60μm, a nonlinear decrease of λ₂ and λ₃ and a nonlinear increase in fractional anisotropy was found, while λ₁ remained constant (Figures 2A,C). Small linear changes were observed in all diffusion measurements except λ₁ as diffusion increased (Figures 2B,D). There was an exponential relationship between mean diffusivity and fractional anisotropy and fiber size in non-edematous muscle (r²=0.996 mean diffusivity; r²=0.995 fractional anisotropy) using single-echo DTI (Figure 3). Similarly, an exponential relationship was observed for intracellular diffusion measured with multi-echo DTI in the presence of edema (r² = 98.8% mean diffusivity; r² 97.9% fractional anisotropy). However, this relationship did not explain the variance in mean diffusivity or fractional anisotropy when measured with single-echo DTI in edematous muscle.

In this study, we have described, with a series of highly controlled simulations, the direct relationship between muscle microstructure and the diffusion tensor. We identified a plateau in diffusion measurements as muscle fiber diameter increases to 60μm. Since average skeletal muscle fiber diameter is around 50μm, DTI is a suitable technique to determine if fibers have a decreased diameter. However, DTI is likely not a good tool to measure hypertrophic changes in muscle, or study animals with larger muscle fiber diameters.

As the sarcolemma (membrane) is thought to be the primary barrier to diffusion, decreased fractional anisotropy is thought to be indicative of fiber hypertrophy³. However, less restricted diffusion is also observed as a result of edema, likely due to increased extra-cellular water volume or membrane damage, even in injuries where fiber atrophy is known to occur. Multi-echo DTI has been used to separate the diffusion signal coming from short (intracellular) and long (extracellular) T2 species in muscle^{2, 4, 5}. However, multi-echo DTI has not been used to validate underlying microstructural changes that cause the restricted diffusion signal. Our results demonstrate that, in the presence of edema, traditional single-echo DTI is biased by increased extracellular water, regardless of underlying fiber atrophy. Using multi-echo DTI, we can resolve microstructural changes from the diffusion tensor of the short T2 species. Future work will investigate the effect of fiber permeability, fiber shape, and interactions between multiple microstructural changes in muscle and the resulting diffusion profile.

These findings describe the relationship between microstructural features of fiber size, and fibrosis to diffusion measured with DTI. We demonstrate in the presence of edema, multi-echo DTI must be used in order to measure underlying microstructural changes.