Accelerated, Physics-Inspired Inference of Skeletal Muscle Microstructure From Diffusion-Weighted MRI

Abstract

Muscle health is a critical component of overall health and quality of life. However, current measures of skeletal muscle health take limited account of microstructural variations within muscle, which play a crucial role in mediating muscle function. To address this, we present a physics-inspired, machine learning-based framework for the non-invasive estimation of microstructural organization in skeletal muscle from diffusion-weighted MRI (dMRI) in an uncertainty-aware manner. To reduce the computational expense associated with direct numerical simulations of dMRI physics, a polynomial meta-model is developed that accurately represents the input/output relationships of a high-fidelity numerical model. This meta-model is used to develop a Gaussian process (GP) model that provides voxel-wise estimates and confidence intervals of microstructure organization in skeletal muscle. Given noise-free data, the GP model accurately estimates microstructural parameters. In the presence of noise, the diameter, intracellular diffusion coefficient, and membrane permeability are accurately estimated with narrow confidence intervals, while volume fraction and extracellular diffusion coefficient are poorly estimated and exhibit wide confidence intervals. A reduced-acquisition GP model, consisting of one-third the diffusion-encoding measurements, is shown to predict parameters with similar accuracy to the original model. The fiber diameter and volume fraction estimated by the reduced GP model is validated via histology, with both parameters accurately estimated, demonstrating the capability of the proposed framework as a promising non-invasive tool for assessing skeletal muscle health and function.

Fig. 1:. In-silico experiments of skeletal muscle dMRI.

(a) Schematic of the generalized diffusion sequence used to represent the diffusion-encoding sequence. (b) Schematic of numerical model of skeletal muscle as periodically packed hexagonal cylinders. (c) Overview of numerical simulation process with the generation of a pulse sequence and microstructural domain, the independent simulation of multiple diffusion directions, construction of diffusion tensors, and finally estimation of dMRI metrics. (d) Overview of meta-model approach where the microstructural and pulse sequence parameters are directly mapped to the dMRI metrics. Here standard DTI metrics are used, but more complex diffusion models can be straightforwardly included.

Fig. 2:. Meta-model acceleration of dMRI simulations.

(a) Density plots of meta-model error for dMRI metrics of FA, MD, RD, ${\text{λ}}_1,{\text{λ}}_2$, and ${\text{λ}}_3$. Solid colors denote a polynomial meta-model while dashed lines are for a feed-forward neural network meta-model. As the order of the polynomial basis set increases, the meta-model accuracy improves. (b) Global sensitivity indices of the 7^th-order meta-model (solid color) and LBM numerical model (white) demonstrating the meta-model captures the global behavior of parameter variation. Results for ${\text{λ}}_2$ and ${\text{λ}}_3$ and not shown as they are nearly identical to RD results. (c) The computational cost of meta-model evaluation increases with polynomial order but remains lower than the numerical model in all cases. The 7^th-order meta-model has a mean evaluation time three orders of magnitude (1000x) faster than the numerical model and a maximum evaluation time five orders of magnitude faster. All models were evaluated on a machine with an Intel Xeon W-2265 processor.

Fig. 3:. Gaussian process inverse mapping.

(a) Error density of GP model when evaluating synthetic, noise-free dMRI measurements. (b) Error density of GP model when evaluating noisy dMRI measurements with a diffusion-to-noise ratio of 30. (c) GP model results for dMRI measurements (DNR=30) when a single microstructural parameter is varied at a time. For each column, 200 meta-model evaluations were made as the varied microstructure parameter was linearly increased. Results are organized column-wise with vertical alignment relating to the same dMRI measurement and the dashed line denoting the true microstructural value.

Fig. 4:. Optimized diffusion-encoding sequence selection.

(a) Convergence of CMA-ES algorithm’s maximization of the objective function over 2000 iterations to select a compact set of ten diffusion-encoding sequences. (b) Map of the variance between the 1024 different microstructural parameters used for different diffusion time and b-value combinations. The locations of the sequence used for the full GP model (black boxes; b=1200 s/mm2 not visualized) and ten sequences selected by the CMA-ES algorithm (red circles) are overlaid. (c) Comparisons of the relative error histograms of the full and reduced sequence GP models for all microstructural parameters shows limited loss in accuracy when the reduced set of sequences are used.

Fig. 5:. Experimental estimates of microstructure organization.

(a) Voxel-wise estimates of all five microstructural parameters for a single slice of the bovine biceps femoris dMRI data (top row); histograms of the distribution of the five microstructural parameters over the entire 3D domain after thresholding to exclude outliers related to edge voxels (middle row); and distribution of 95% confidence intervals from GP model over entire 3D domain (bottom row). (b) GP estimates and 95% confidence intervals of all five microstructural parameters and RPBM estimates of three microstructural parameters for two ROIs.