Suitability of poroelastic and viscoelastic mechanical models for high and low frequency MR elastography.

PURPOSE: Descriptions of the structure of brain tissue as a porous cellular matrix support application of a poroelastic (PE) mechanical model which includes both solid and fluid phases. However, the majority of brain magnetic resonance elastography (MRE) studies use a single phase viscoelastic (VE) model to describe brain tissue behavior, in part due to availability of relatively simple direct inversion strategies for mechanical property estimation. A notable exception is low frequency intrinsic actuation MRE, where PE mechanical properties are imaged with a nonlinear inversion algorithm. METHODS: This paper investigates the effect of model choice at each end of the spectrum of in vivo human brain actuation frequencies. Repeat MRE examinations of the brains of healthy volunteers were used to compare image quality and repeatability for each inversion model for both 50 Hz externally produced motion and ≈1 Hz intrinsic motions. Additionally, realistic simulated MRE data were generated with both VE and PE finite element solvers to investigate the effect of inappropriate model choice for ideal VE and PE materials. RESULTS: In vivo, MRE data revealed that VE inversions appear more representative of anatomical structure and quantitatively repeatable for 50 Hz induced motions, whereas PE inversion produces better results at 1 Hz. Reasonable VE approximations of PE materials can be derived by equating the equivalent wave velocities for the two models, provided that the timescale of fluid equilibration is not similar to the period of actuation. An approximation of the equilibration time for human brain reveals that this condition is violated at 1 Hz but not at 50 Hz. Additionally, simulation experiments when using the "wrong" model for the inversion demonstrated reasonable shear modulus reconstructions at 50 Hz, whereas cross-model inversions at 1 Hz were poor quality. Attenuation parameters were sensitive to changes in the forward model at both frequencies, however, no spatial information was recovered because the mechanisms of VE and PE attenuation are different. CONCLUSIONS: VE inversions are simpler with fewer unknown properties and may be sufficient to capture the mechanical behavior of PE brain tissue at higher actuation frequencies. However, accurate modeling of the fluid phase is required to produce useful mechanical property images at the lower frequencies of intrinsic brain motions.

Multiresolution MR elastography using nonlinear inversion.

PURPOSE: Nonlinear inversion (NLI) in MR elastography requires discretization of the displacement field for a finite element (FE) solution of the "forward problem", and discretization of the unknown mechanical property field for the iterative solution of the "inverse problem". The resolution requirements for these two discretizations are different: the forward problem requires sufficient resolution of the displacement FE mesh to ensure convergence, whereas lowering the mechanical property resolution in the inverse problem stabilizes the mechanical property estimates in the presence of measurement noise. Previous NLI implementations use the same FE mesh to support the displacement and property fields, requiring a trade-off between the competing resolution requirements. METHODS: This work implements and evaluates multiresolution FE meshes for NLI elastography, allowing independent discretizations of the displacements and each mechanical property parameter to be estimated. The displacement resolution can then be selected to ensure mesh convergence, and the resolution of the property meshes can be independently manipulated to control the stability of the inversion. RESULTS: Phantom experiments indicate that eight nodes per wavelength (NPW) are sufficient for accurate mechanical property recovery, whereas mechanical property estimation from 50 Hz in vivo brain data stabilizes once the displacement resolution reaches 1.7 mm (approximately 19 NPW). Viscoelastic mechanical property estimates of in vivo brain tissue show that subsampling the loss modulus while holding the storage modulus resolution constant does not substantially alter the storage modulus images. Controlling the ratio of the number of measurements to unknown mechanical properties by subsampling the mechanical property distributions (relative to the data resolution) improves the repeatability of the property estimates, at a cost of modestly decreased spatial resolution. CONCLUSIONS: Multiresolution NLI elastography provides a more flexible framework for mechanical property estimation compared to previous single mesh implementations.

Removal of olefinic fat chemical shift artifact in diffusion MRI.

Diffusion-weighted (DW) MRI has emerged as a key tool for assessing the microstructure of tissues in healthy and diseased states. Because of its rapid acquisition speed and insensitivity to motion, single-shot echo-planar imaging is the most common DW imaging technique. However, the presence of fat signal can severely affect DW-echo planar imaging acquisitions because of the chemical shift artifact. Fat suppression is usually achieved through some form of chemical shift-based fat saturation. Such methods effectively suppress the signal originating from aliphatic fat protons, but fail to suppress the signal from olefinic protons. Olefinic fat signal may result in significant distortions in the DW images, which bias the subsequently estimated diffusion parameters. This article introduces a method for removing olefinic fat signal from DW images, based on an echo time-shifted acquisition. The method is developed and analyzed specifically in the context of single-shot DW-echo-planar imaging, where image phase is generally unreliable. The proposed method is tested with phantom and in vivo datasets, and compared with a standard acquisition to demonstrate its performance.

Differential ion transport induced electroosmosis and internal recirculation in heterogeneous osmosis membranes.

Water and ion transport through a heterogeneous membrane separating two electrolyte solutions at different concentrations is investigated by using molecular dynamics simulations. The membrane features pairs of oppositely charged pores with identical diameters. Simulation results indicate that the differential transport of K(+) and Cl(-) ions through the membrane pores creates an electrical potential difference across the membrane, which then induces an electroosmotic water flux. The induced electroosmosis creates an internal recirculation loop of water between adjacent pores. The implications of these new observations are discussed.

Tomographic study of helical modes in bifurcating Taylor-Couette-Poiseuille flow using magnetic resonance imaging.

The quantitative visualization of flow in a wide-gap annulus (radius ratio 0.5) between concentric cylinders with the inner cylinder rotating and a superimposed axial flow reveals a novel mixed-mode state at relatively high flow rates. A fast magnetic resonance imaging sequence allows the cinematographic dissection and three-dimensional reconstruction of supercritical nonaxisymmetric modes in a regime where stationary helical and propagating toroidal vortices coexist. The findings shed light on symmetry-breaking instabilities, flow pattern selection, and their consequences for hydrodynamic mixing in a complex laminar flow that constitutes a celebrated prototype of many mixing or fractionation processes.

On the use of optical flow methods with spin-tagging magnetic resonance imaging.

Magnetic resonance imaging (MRI) is a versatile noninvasive tool for achieving full-field quantitative visualization of biomedical fluid flows. In this study, two MRI velocimetry techniques (spin tagging and phase contrast) are used to obtain velocity measurements in a Poiseuille flow for Reynolds numbers below 1,000. Spin-tagging MRI velocimetry supplies the displacement of tagged grids of nuclear spins from which the velocity field can be inferred, while phase contrast MRI velocimetry directly provides velocity data for every pixel in the field of view. Although the phase contrast method is more accurate for this flow, this technique is more sensitive to errors from magnetic susceptibility gradients, higher order motions, and has limited dynamic range. Spin-tagging MRI velocimetry is a viable alternative if automatic methods for extracting velocity fields from the tags can be found. Optical flow, a technique originally developed for machine vision applications, is proposed here as a postprocessing step to obtain two-dimensional velocity fields from spin-tagging MRI images. Results with artificially generated grids demonstrate the robustness of the optical flow algorithm to noise and indicate that a 7%-10% average error can be expected from the optical flow calculations alone, independent of MRI image artifacts. Experiments on spin-tagging MRI images for a Re=230 Poiseuille flow gave an average error of 6.41%, which was consistent with the measurement error of the generated (synthetic) images with the same level of random noise superimposed.

On the accuracy of EPI-based phase contrast velocimetry.

For over a decade, echo-planar imaging (EPI) has been used in both the medical and applied sciences to capture velocity fields of fluid flows. However, previous studies have not rigorously confirmed the accuracy of the measurements or sought to understand the limitations of the technique. In this study, a bipolar gradient was added to a flow-compensated EPI pulse sequence to obtain rapid phase contrast images of steady and unsteady flows through two step stenoses. For steady Re = 100 and 258 flows, accuracy was measured through systematic comparisons with CFD simulations, mass flow rate measurements, and spin echo phase contrast images. On average, the EPI image data exhibited velocity errors of 5 to 10 percent, while mass was conserved to within 5.6 percent at each axial position. Compared to spin-echo phase contrast images, the EPI images have 50 percent lower signal-to-noise ratio, larger local velocity errors, and similar mass conservation characteristics. An unsteady flow was then examined by starting a pump and allowing it to reach a steady Re = 100 flow. Accuracy in this case was measured by the consistency between mass flow rate measurements at different axial positions. Images taken at 0.3 s intervals captured the velocity field evolution and showed that 50 to 100 percent errors occur when the flow changes on a time scale faster than the image acquisition time.

Pressure propagation in pulsatile flow through random microvascular networks.

A microvascular network with random dimensions of vessels is built on the basis of statistical analysis of conjunctival beds reported in the literature. Our objective is to develop a direct method of evaluating the statistics of the pulsatile hydrodynamic field starting from a priori statistics which mimic the large-scale heterogeneity of the network. The model consists of a symmetric diverging-converging dentritic network of ten levels of vessels, each level described by a truncated Gaussian distribution of vessel diameters and lengths. In each vascular segment, the pressure distribution is given by a diffusion equation with random parameters, while the blood flow rate depends linearly on the pressure gradient. The results are presented in terms of the mean value and standard deviation of the pressure and flow rate waveforms at two positions along the network. It is shown that the assumed statistical variation of vessel lengths results in flow rate deviations as high as 50 percent of the mean, while the corresponding effect of vessel diameter variation is much smaller. For a given pressure drop, the statistical variation of lengths increases the mean flow while the effect on the mean pressure distribution is negligible.

Computational fluid dynamics of left ventricular ejection.

The present investigation addresses the effects of simple geometric variations on intraventricular ejection dynamics, by methods from computational fluid dynamics. It is an early step in incorporating more and more relevant characteristics of the ejection process, such as a continuously changing irregular geometry, in numerical simulations. We consider the effects of varying chamber eccentricities and outflow valve orifice-to-inner surface area ratios on instantaneous ejection gradients along the axis of symmetry of the left ventricle. The equation of motion for the streamfunction was discretized and solved iteratively with specified boundary conditions on a boundary-fitted adaptive grid, using an alternating-direction-implicit (ADI) algorithm. The unsteady aspects of the ejection process were subsequently introduced into the numerical simulation. It was shown that for given chamber volume and outflow orifice area, higher chamber eccentricities require higher ejection pressure gradients for the same velocity and local acceleration values at the aortic anulus than more spherical shapes. This finding is referable to the rise in local acceleration effects across the outflow axis. This is to be contrasted with the case of outflow orifice stenosis, in which it was shown that it is the convective acceleration effects that are intensified strongly.