Comparison of two-compartment exchange and continuum models of dMRI in skeletal muscle

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.

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.