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

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.

Assessment of Mechanically Induced Changes in Helical Fiber Microstructure Using Diffusion Tensor Imaging

Noninvasive methods to detect microstructural changes in collagen-based fibrous tissues are necessary to differentiate healthy from damaged tissues in vivo but are sparse. Diffusion Tensor Imaging (DTI) is a noninvasive imaging technique used to quantitatively infer tissue microstructure with previous work primarily focused in neuroimaging applications. Yet, it is still unclear how DTI metrics relate to fiber microstructure and function in musculoskeletal tissues such as ligament and tendon, in part because of the high heterogeneity inherent to such tissues. To address this limitation, we assessed the ability of DTI to detect microstructural changes caused by mechanical loading in tissue-mimicking helical fiber constructs of known structure. Using high-resolution optical and micro-computed tomography imaging, we found that static and fatigue loading resulted in decreased sample diameter and a re-alignment of the macro-scale fiber twist angle similar with the direction of loading. However, DTI and micro-computed tomography measurements suggest microstructural differences in the effect of static versus fatigue loading that were not apparent at the bulk level. Specifically, static load resulted in an increase in diffusion anisotropy and a decrease in radial diffusivity suggesting radially uniform fiber compaction. In contrast, fatigue loads resulted in increased diffusivity in all directions and a change in the alignment of the principal diffusion direction away from the constructs' main axis suggesting fiber compaction and microstructural disruptions in fiber architecture. These results provide quantitative evidence of the ability of DTI to detect mechanically induced changes in tissue microstructure that are not apparent at the bulk level, thus confirming its potential as a noninvasive measure of microstructure in helically architected collagen-based tissues, such as ligaments and tendons.

Intravoxel Incoherent Motion Magnetic Resonance Imaging in Skeletal Muscle: Review and Future Directions

Throughout the body, muscle structure and function can be interrogated using a variety of noninvasive magnetic resonance imaging (MRI) methods. Recently, intravoxel incoherent motion (IVIM) MRI has gained momentum as a method to evaluate components of blood flow and tissue diffusion simultaneously. Much of the prior research has focused on highly vascularized organs, including the brain, kidney, and liver. Unique aspects of skeletal muscle, including the relatively low perfusion at rest and large dynamic range of perfusion between resting and maximal hyperemic states, may influence the acquisition, postprocessing, and interpretation of IVIM data. Here, we introduce several of those unique features of skeletal muscle; review existing studies of IVIM in skeletal muscle at rest, in response to exercise, and in disease states; and consider possible confounds that should be addressed for muscle-specific evaluations. Most studies used segmented nonlinear least squares fitting with a b-value threshold of 200 sec/mm2 to obtain IVIM parameters of perfusion fraction (f), pseudo-diffusion coefficient (D*), and diffusion coefficient (D). In healthy individuals, across all muscles, the average ± standard deviation of D was 1.46 ± 0.30 × 10-3  mm2 /sec, D* was 29.7 ± 38.1 × 10-3  mm2 /sec, and f was 11.1 ± 6.7%. Comparisons of reported IVIM parameters in muscles of the back, thigh, and leg of healthy individuals showed no significant difference between anatomic locations. Throughout the body, exercise elicited a positive change of all IVIM parameters. Future directions including advanced postprocessing models and potential sequence modifications are discussed. LEVEL OF EVIDENCE: 2 TECHNICAL EFFICACY: Stage 2.

Varying diffusion time to discriminate between simulated skeletal muscle injury models using stimulated echo diffusion tensor imaging

PURPOSE

Evaluate the relationship between muscle microstructure, diffusion time (Δ), and the diffusion tensor (DT) to identify the optimal Δ where changes in muscle fiber size may be detected.

METHODS

The DT was simulated in models with histology informed geometry over a range of Δ with a stimulated echo DT imaging (DTI) sequence using the numerical simulation application DifSim. The difference in the DT at each Δ between healthy and injured skeletal muscle models was calculated, to identify the optimal Δ at which changes in muscle fiber size may be detected. The random permeable barrier model (RPBM) was used to estimate muscle microstructure from the simulated DT measurements, which were compared to the ground truth.

RESULTS

Across all models, fractional anisotropy provided greater contrast between injured and control models than diffusivity measurements. Compared to control models, in atrophic injury models, the greatest difference in the DT was found between 90 ms and 250 ms. In models with acute edema, the contrast between injured and control muscle increased with increasing diffusion time, although these models had smaller mean fiber areas. RPBM systematically underestimated fiber size but accurately estimated surface area-to-volume ratio of simulated models.

CONCLUSION

These findings may better inform pulse sequence parameter selection when performing DTI experiments in vivo. If only a single diffusion experiment can be performed, the selected Δ should be ~170 ms to maximize the ability to discriminate between different injury models. Ideally several diffusion times between 90 ms and 500 ms should be sampled in order to maximize diffusion contrast, particularly when the disease process is unknown.

Sensitivity analysis of effective transverse shear viscoelastic and diffusional properties of myelinated white matter

Motivated by the need to interpret the results from a combined use of in vivo brain Magnetic Resonance Elastography (MRE) and Diffusion Tensor Imaging (DTI), we developed a computational framework to study the sensitivity of single-frequency MRE and DTI metrics to white matter microstructure and cell-level mechanical and diffusional properties. White matter was modeled as a triphasic unidirectional composite, consisting of parallel cylindrical inclusions (axons) surrounded by sheaths (myelin), and embedded in a matrix (glial cells plus extracellular matrix). Only 2D mechanics and diffusion in the transverse plane (perpendicular to the axon direction) was considered, and homogenized (effective) properties were derived for a periodic domain containing a single axon. The numerical solutions of the MRE problem were performed with ABAQUS and by employing a sophisticated boundary-conforming grid generation scheme. Based on the linear viscoelastic response to harmonic shear excitation and steady-state diffusion in the transverse plane, a systematic sensitivity analysis of MRE metrics (effective transverse shear storage and loss moduli) and DTI metric (effective radial diffusivity) was performed for a wide range of microstructural and intrinsic (phase-based) physical properties. The microstructural properties considered were fiber volume fraction, and the myelin sheath/axon diameter ratio. The MRE and DTI metrics are very sensitive to the fiber volume fraction, and the intrinsic viscoelastic moduli of the glial phase. The MRE metrics are nonlinear functions of the fiber volume fraction, but the effective diffusion coefficient varies linearly with it. Finally, the transverse metrics of both MRE and DTI are insensitive to the axon diameter in steady state. Our results are consistent with the limited anisotropic MRE and co-registered DTI measurements, mainly in the corpus callosum, available in the literature. We conclude that isotropic MRE and DTI constitutive models are good approximations for myelinated white matter in the transverse plane. The unidirectional composite model presented here is used for the first time to model harmonic shear stress under MRE-relevant frequency on the cell level. This model can be extended to 3D in order to inform the solution of the inverse problem in MRE, establish the biological basis of MRE metrics, and integrate MRE/DTI with other modalities towards increasing the specificity of neuroimaging.

Lattice Boltzmann method for simulation of diffusion magnetic resonance imaging physics in multiphase tissue models

We report an implementation of the lattice Boltzmann method (LBM) to integrate the Bloch-Torrey equation, which describes the evolution of the transverse magnetization vector and the fate of the signal of diffusion magnetic resonance imaging (dMRI). Motivated by the need to interpret dMRI experiments in biological tissues, and to offset the small time-step limitation of classical LBM, a hybrid LBM scheme is introduced and implemented to solve the Bloch-Torrey equation. A membrane boundary condition is presented which is able to accurately represent the effects of thin curvilinear membranes typically found in biological tissues. As implemented, the hybrid LBM scheme accommodates piece-wise uniform transport, dMRI parameters, periodic and mirroring outer boundary conditions, and finite membrane permeabilities on non-boundary-conforming inner boundaries. By comparing with analytical solutions of limiting cases, we demonstrate that the hybrid LBM scheme is more accurate than the classical LBM scheme. The proposed explicit LBM scheme maintains second-order spatial accuracy, stability, and first-order temporal accuracy for a wide range of parameters. The parallel implementation of the hybrid LBM code in a multi-CPU computer system, as well as on GPUs, is straightforward and efficient. Along with offering certain advantages over finite element or Monte Carlo schemes, the proposed hybrid LBM constitutes a flexible scheme that can by easily adapted to model more complex interfacial conditions and physics in heterogeneous multiphase tissue models and to accommodate sophisticated dMRI sequences.