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.

Global sensitivity analysis of skeletal muscle dMRI metrics: Effects of microstructural and pulse parameters.

PURPOSE: Estimating microstructural parameters of skeletal muscle from diffusion MRI (dMRI) signal requires understanding the relative importance of both microstructural and dMRI sequence parameters on the signal. This study seeks to determine the sensitivity of dMRI signal to variations in microstructural and dMRI sequence parameters, as well as assess the effect of noise on sensitivity. METHODS: Using a cylindrical myocyte model of skeletal muscle, numerical solutions of the Bloch-Torrey equation were used to calculate global sensitivity indices of dMRI metrics (FA, RD, MD, λ1 , λ2 , λ3 ) for wide ranges of microstructural and dMRI sequence parameters. The microstructural parameters were: myocyte diameter, volume fraction, membrane permeability, intra- and extracellular diffusion coefficients, and intra- and extracellular T2 times. Two separate pulse sequences were examined, a PGSE and a generalized diffusion-weighted sequence that accommodates a larger range of diffusion times. The effect of noise and signal averaging on the sensitivity of the dMRI metrics was examined by adding synthetic noise to the simulated signal. RESULTS: Among the examined parameters, the intracellular diffusion coefficient has the strongest effect, and myocyte diameter is more influential than permeability for FA and RD. The sensitivity indices do not vary significantly between the two pulse sequences. Also, noise strongly affects the sensitivity of the dMRI signal to microstructural variations. CONCLUSIONS: With the identification of key microstructural features that affect dMRI measurements, the reported sensitivity results can help interpret dMRI measurements of skeletal muscle in terms of the underlying microstructure and further develop parsimonious dMRI models of skeletal muscle.

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

Clinical diffusion MRI (dMRI) is sensitive to micrometer scale spin displacements, but the image resolution is ∼mm, so the biophysical interpretation of the signal relies on establishing appropriate subvoxel tissue models. A class of two-compartment exchange models originally proposed by Kärger have been used successfully in neural tissue dMRI. Their use to interpret the signal in skeletal muscle dMRI is challenging because myocyte diameters are comparable to the root-mean-square of spin displacement and their membrane permeability is high. A continuum tissue model consisting of the Bloch-Torrey equation integrated by a hybrid lattice Boltzmann scheme is used for comparison. The validity domain of a classical two-compartment tissue model is probed by comparing it with the prediction of the continuum model for a 2D unidirectional composite continuum model of myocytes embedded in a uniform matrix. This domain is described in terms of two dimensionless parameters inspired by mass transfer phenomena, the Fourier (F) and Biot (B) numbers. The two-compartment model is valid when [Formula: see text] and [Formula: see text], or when [Formula: see text] and [Formula: see text]. The model becomes less appropriate for muscle dMRI as the cell diameter and volume fraction increase, with the primary source of error associated with modeling diffusion in the extracellular matrix.