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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.

White matter (WM) consists of bundles of long axons embedded in a glial matrix, which lead to anisotropic mechanical properties of brain tissue, and this complicates direct numerical simulations of WM viscoelastic response. The detailed axonal geometry contains scales that range from axonal diameter (microscale) to many diameters (mesoscale) imposing an additional challenge to numerical simulations. Here we describe the development of a 3D homogenization model for the central nervous system (CNS) that accounts for the anisotropy introduced by the axon/neuroglia composite, the axonal trace curvature, and the tissue dynamic response in the frequency domain. Homogenized models that allow the incorporation of all the above factors are important for accurately simulating the tissue's mechanical behavior, and this in turn is essential in interpreting non-invasive elastography measurements. Geometric and material parameters affect the material properties and thus the response of the brain tissue. More complex, orthotropic, or anisotropic material properties are to be considered as necessitated by the 3D tissue structure. An assembly of micro-scale 3D representative elemental volumes (REVs) is constructed, leading to an integrated mesoscale WM finite element model. Assemblies of microscopic REVs, with orientations based on geometrical reconstructions driven by confocal microscopy data are employed to form the elements of the WM model. Each REV carries local material properties based on a finite element model of biphasic (axon-glial matrix) unidirectional composite. The viscoelastic response of the microscopic REVs is extracted based on geometric information and fiber volume fractions calculated from the relative distance between the local elements and global axonal trace. The response of the WM tissue model is homogenized by averaging the shear moduli over the total volume (thus deriving effective properties) under realistic external loading conditions. Under harmonic shear loading, it is proven that that the effective transverse shear moduli are higher than the axial moduli when the axon moduli are higher than the glial. Methodologically, the process of using micro-scale 3D REVs to describe more complex axon geometries avoids the partition process in traditional composite finite element methods (based on partition of finite element grids) and constitutes a robust algorithm to automatically build a WM model based on available axonal trace information. Analytically, the model provides unmatched simulation flexibility and computational power as the position, orientation, and the magnitude of each tissue building block is calculated using real tissue data, as are the training and testing processes at each level of the multiscale WM tissue., Competing Interests: Declaration of competing interest The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper., (Copyright © 2022 Elsevier Inc. All rights reserved.)

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.

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.

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, λ 1 , λ 2 , λ 3 ) 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 T 2 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., (© 2019 International Society for Magnetic Resonance in Medicine.)

Insufficient vascularization limits the volume and complexity of engineered tissue. The formation of new blood vessels (neovascularization) is regulated by a complex interplay of cellular interactions with biochemical and biophysical signals provided by the extracellular matrix (ECM) necessitating the development of biomaterial approaches that enable systematic modulation in matrix properties. To address this need poly(ethylene) glycol-based hydrogel scaffolds were engineered with a range of decoupled and combined variations in integrin-binding peptide (RGD) ligand concentration, elastic modulus and proteolytic degradation rate using free-radical polymerization chemistry. The modularity of this system enabled a full factorial experimental design to simultaneously investigate the individual and interaction effects of these matrix cues on vascular sprout formation in 3 D culture. Enhancements in scaffold proteolytic degradation rate promoted significant increases in vascular sprout length and junction number while increases in modulus significantly and negatively impacted vascular sprouting. We also observed that individual variations in immobilized RGD concentration did not significantly impact 3 D vascular sprouting. Our findings revealed a previously unidentified and optimized combination whereby increases in both immobilized RGD concentration and proteolytic degradation rate resulted in significant and synergistic enhancements in 3 D vascular spouting. The above-mentioned findings would have been challenging to uncover using one-factor-at-time experimental analyses.

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.

Magnetic resonance elastography (MRE) has shown promise in noninvasively capturing changes in mechanical properties of the human brain caused by neurodegenerative conditions. MRE involves vibrating the brain to generate shear waves, imaging those waves with MRI, and solving an inverse problem to determine mechanical properties. Despite the known anisotropic nature of brain tissue, the inverse problem in brain MRE is based on an isotropic mechanical model. In this study, distinct wave patterns are generated in the brain through the use of multiple excitation directions in order to characterize the potential impact of anisotropic tissue mechanics on isotropic inversion methods. Isotropic inversions of two unique displacement fields result in mechanical property maps that vary locally in areas of highly aligned white matter. Investigation of the corpus callosum, corona radiata, and superior longitudinal fasciculus, three highly ordered white matter tracts, revealed differences in estimated properties between excitations of up to 33%. Using diffusion tensor imaging to identify dominant fiber orientation of bundles, relationships between estimated isotropic properties and shear asymmetry are revealed. This study has implications for future isotropic and anisotropic MRE studies of white matter tracts in the human brain., (Copyright © 2016 Elsevier Ltd. All rights reserved.)

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.

Purpose: To develop an acquisition scheme for generating MR elastography (MRE) displacement data with whole-brain coverage, high spatial resolution, and adequate signal-to-noise ratio (SNR) in a short scan time., Theory and Methods: A 3D multislab, multishot acquisition for whole-brain MRE with 2.0 mm isotropic spatial resolution is proposed. The multislab approach allowed for the use of short repetition time to achieve very high SNR efficiency. High SNR efficiency allowed for a reduced acquisition time of only 6 min while the minimum SNR needed for inversion was maintained., Results: The mechanical property maps estimated from whole-brain displacement data with nonlinear inversion (NLI) demonstrated excellent agreement with neuroanatomical features, including the cerebellum and brainstem. A comparison with an equivalent 2D acquisition illustrated the improvement in SNR efficiency of the 3D multislab acquisition. The flexibility afforded by the high SNR efficiency allowed for higher resolution with a 1.6 mm isotropic voxel size, which generated higher estimates of brainstem stiffness compared with the 2.0 mm isotropic acquisition., Conclusion: The acquisition presented allows for the capture of whole-brain MRE displacement data in a short scan time, and may be used to generate local mechanical property estimates of neuroanatomical features throughout the brain., (Copyright © 2013 Wiley Periodicals, Inc.)

The noninvasive measurement of the mechanical properties of brain tissue using magnetic resonance elastography (MRE) has emerged as a promising method for investigating neurological disorders. To date, brain MRE investigations have been limited to reporting global mechanical properties, though quantification of the stiffness of specific structures in the white matter architecture may be valuable in assessing the localized effects of disease. This paper reports the mechanical properties of the corpus callosum and corona radiata measured in healthy volunteers using MRE and atlas-based segmentation. Both structures were found to be significantly stiffer than overall white matter, with the corpus callosum exhibiting greater stiffness and less viscous damping than the corona radiata. Reliability of both local and global measures was assessed through repeated experiments, and the coefficient of variation for each measure was less than 10%. Mechanical properties within the corpus callosum and corona radiata demonstrated correlations with measures from diffusion tensor imaging pertaining to axonal microstructure., (Copyright © 2013 Elsevier Inc. All rights reserved.)

Tissue displacements required for mechanical property reconstruction in magnetic resonance elastography (MRE) are acquired in a magnetic resonance imaging (MRI) scanner, therefore, anatomical information is available from other imaging sequences. Despite its availability, few attempts to incorporate prior spatial information in the MRE reconstruction process have been reported. This paper implements and evaluates soft prior regularization (SPR), through which homogeneity in predefined spatial regions is enforced by a penalty term in a nonlinear inversion strategy. Phantom experiments and simulations show that when predefined regions are spatially accurate, recovered property values are stable for SPR weighting factors spanning several orders of magnitude, whereas inaccurate segmentation results in bias in the reconstructed properties that can be mitigated through proper choice of regularization weighting. The method was evaluated in vivo by estimating viscoelastic mechanical properties of frontal lobe gray and white matter for five repeated scans of a healthy volunteer. Segmentations of each tissue type were generated using automated software, and statistically significant differences between frontal lobe gray and white matter were found for both the storage modulus and loss modulus . Provided homogeneous property assumptions are reasonable, SPR produces accurate quantitative property estimates for tissue structures which are finer than the resolution currently achievable with fully distributed MRE.

Magnetic resonance elastography (MRE) has been introduced in clinical practice as a possible surrogate for mechanical palpation, but its application to study the human brain in vivo has been limited by low spatial resolution and the complexity of the inverse problem associated with biomechanical property estimation. Here, we report significant improvements in brain MRE data acquisition by reporting images with high spatial resolution and signal-to-noise ratio as quantified by octahedral shear strain metrics. Specifically, we have developed a sequence for brain MRE based on multishot, variable-density spiral imaging, and three-dimensional displacement acquisition and implemented a correction scheme for any resulting phase errors. A Rayleigh damped model of brain tissue mechanics was adopted to represent the parenchyma and was integrated via a finite element-based iterative inversion algorithm. A multiresolution phantom study demonstrates the need for obtaining high-resolution MRE data when estimating focal mechanical properties. Measurements on three healthy volunteers demonstrate satisfactory resolution of gray and white matter, and mechanical heterogeneities correspond well with white matter histoarchitecture. Together, these advances enable MRE scans that result in high-fidelity, spatially resolved estimates of in vivo brain tissue mechanical properties, improving upon lower resolution MRE brain studies that only report volume averaged stiffness values., (© 2012 Wiley Periodicals, Inc.)

Hydrogels have gained wide usage in a range of biomedical applications because of their biocompatibility and the ability to finely tune their properties, including viscoelasticity. The use of hydrogels on the microscale is increasingly important for the development of drug delivery techniques and cellular microenvironments, though the ability to accurately characterize their micromechanical properties is limited. Here we demonstrate the use of microelectromechanical systems (MEMS) resonant sensors to estimate the properties of poly(ethylene glycol) diacrylate (PEGDA) microstructures over a range of concentrations. These microstructures are integrated on the sensors by deposition using electrohydrodynamic jet printing. Estimated properties agree well with independent measurements made using indentation with atomic force microscopy.

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.

In magnetic resonance elastography (MRE), shear waves at a certain frequency are encoded through bipolar gradients that switch polarity at a controlled encoding frequency and are offset in time to capture wave propagation using a controlled sampling frequency. In brain MRE, there is a possibility that the mechanical actuation frequency is different from the vibration frequency, leading to a mismatch with encoding and sampling frequencies. This mismatch can occur in brain MRE from causes both extrinsic and intrinsic to the brain, such as scanner bed vibrations or active damping in the head. The purpose of this work was to investigate how frequency mismatch can affect MRE shear stiffness measurements. Experiments were performed on a dual-medium agarose gel phantom, and the results were compared with numerical simulations to quantify these effects. It is known that off-frequency encoding alone results in a scaling of wave amplitude, and it is shown here that off-frequency sampling can result in two main effects: (1) errors in the overall shear stiffness estimate of the material on the global scale and (2) local variations appearing as stiffer and softer structures in the material. For small differences in frequency, it was found that measured global stiffness of the brain could theoretically vary by up to 12.5% relative to actual stiffness with local variations of up to 3.7% of the mean stiffness. It was demonstrated that performing MRE experiments at a frequency other than that of tissue vibration can lead to artifacts in the MRE stiffness images, and this mismatch could explain some of the large-scale scatter of stiffness data or lack of repeatability reported in the brain MRE literature., (Copyright © 2012 Elsevier Inc. All rights reserved.)

Background: The purpose of this double-blind randomized clinical trial was to compare the relative effectiveness of a higher protein and conventional carbohydrate intake during weight loss on body composition and physical function in older women., Methods: Thirty-one overweight or obese, postmenopausal women (mean ± SD: age 65.2 ± 4.6 years, body mass index 33.7 ± 4.9 kg/m(2)) were prescribed a reduced calorie diet (1,400 kcal/day; 15%, 65%, 30% energy from protein, carbohydrate, and fat, respectively) and randomly assigned to 2 × 25 g/day whey protein (PRO n = 15) or maltodextrin (CARB n = 16) supplementation for 6 months. Lean soft tissue (LST) via dual-energy X-ray absorptiometry; thigh muscle, subcutaneous adipose tissue (SAT), and intermuscular adipose tissue with magnetic resonance imaging; knee strength with isokinetic dynamometry; balance and physical function with a battery of performance tests., Results: PRO lost more weight than CARB (-8.0% ± 6.2%, -4.1% ± 3.6%, p = .059; respectively). Changes in LST, %LST, and strength, balance, or physical performance measures did not differ between groups (all p > .05). Weight to leg LST ratio improved more in PRO versus CARB (-4.6 ± 3.6%, -1.8 ± 2.6%, p = .03). PRO lost 4.2% more muscle (p = .01), 10.9% more SAT (p = .02), and 8.2% more intermuscular adipose tissue (p = .03) than CARB. Relative to thigh volume changes, PRO gained 5.8% more muscle (p = .049) and lost 3.8% greater SAT (p = .06) than CARB. Weight to leg LST ratio (r(2) = .189, p = .02) and SAT (r(2) = .163, p = .04) predicted improved up and go, relative muscle (r(2) = .238, p = .01) and SAT (r(2) = .165, p = .04) predicted improved transfer test, and %LST predicted improved balance (r(2) = .179, p = .04)., Conclusions: A higher protein intake during caloric restriction maintains muscle relative to weight lost, which in turn enhances physical function in older women.

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., (Copyright © 2010 Wiley-Liss, Inc.)

Purpose: To propose a reformulation of the intravoxel incoherent motion (IVIM) technique exploiting the low b-value diffusion-weighted imaging regime that can characterize microcirculation of tissues perfused with partially coherent blood flow., Materials and Methods: The new methodology, termed intravoxel partially coherent motion (IVPCM) technique, is suitable for probing microcirculation in tissues with ordered microvasculature, such as skeletal muscle. We employ a subvoxel model utilizing a randomly oriented bundle of straight vessels whose orientation statistics are characterized by a Fisher axial distribution with concentration parameter K quantifying the anisotropy of the distribution (K = 0 indicates isotropic capillary orientation). The methodology is first validated with a proof-of-principle phantom experiment and is then applied to analyze the microvasculature of human calf muscle at rest., Results: The microcirculatory part of the diffusion-weighted signal at b < 200 s/mm(2) is anisotropic. The variation of the diffusion-weighted signal with b-value exhibits stronger deviation from the expected monoexponential decay when the diffusion encoding gradient is applied parallel to the mean myofiber direction in the calf muscle of three healthy volunteers. The application of the model to data from the medial gastrocnemius and the soleus of the three volunteers gives results within the expected range for the mean microvascular volume fraction, the mean microflow velocity, and the parameter K., Conclusion: The proposed methodology has the capability of characterizing the anisotropy of the capillary network in vivo in a manner analogous to the capability of high b-value diffusion to characterize the anisotropy of muscle fibers., ((c) 2010 Wiley-Liss, Inc.)

Due to its unique non-invasive microstructure probing capabilities, diffusion tensor imaging (DTI) constitutes a valuable tool in the study of fiber orientation in skeletal muscles. By implementing a DTI sequence with judiciously chosen directional encoding to quantify in vivo the microarchitectural properties in the calf muscles of three healthy volunteers at rest, we report that the secondary eigenvalue is significantly higher than the tertiary eigenvalue, a phenomenon corroborated by prior DTI findings. Toward a physics-based explanation of this phenomenon, we propose a composite medium model that accounts for water diffusion in the space within the muscle fiber and the extracellular space. The muscle fibers are abstracted as cylinders of infinite length with an elliptical cross section, the latter closely approximating microstructural features well documented in prior histological studies of excised muscle. The range of values of fiber ellipticity predicted by our model agrees with these studies, and the spatial orientation of the cross-sectional ellipses is consistent with local muscle strain fields and the putative direction of lateral transmission of stress between fibers in certain regions in three antigravity muscles (Tibialis Anterior, Soleus, and Gastrocnemius), as well as independent measurements of deformation in active calf muscles. As a metric, fiber cross-sectional ellipticity may be useful for quantifying morphological changes in skeletal muscle fibers with aging, hypertrophy, or sarcopenia.

Motion during diffusion encodings leads to different phase errors in different shots of multishot diffusion-weighted acquisitions. Phase error incoherence among shots results in undesired signal cancellation when data from all shots are combined. Motion-induced phase error correction for multishot diffusion-weighted imaging (DWI) has been studied extensively and there exist multiple phase error correction algorithms. A commonly used correction method is the direct phase subtraction (DPS). DPS, however, can suffer from incomplete phase error correction due to the aliasing of the phase errors in the high spatial resolution phases. Furthermore, improper sampling density compensation is also a possible issue of DPS. Recently, motion-induced phase error correction was incorporated in the conjugate gradient (CG) image reconstruction procedure to get a nonlinear phase correction method that is also applicable to parallel DWI. Although the CG method overcomes the issues of DPS, its computational requirement is high. Further, CG restricts to sensitivity encoding (SENSE) for parallel reconstruction. In this paper, a new time-efficient and flexible k-space and image-space combination (KICT) algorithm for rigid body motion-induced phase error correction is introduced. KICT estimates the motion-induced phase errors in image space using the self-navigated capability of the variable density spiral trajectory. The correction is then performed in k -space. The algorithm is shown to overcome the problem of aliased phase errors. Further, the algorithm preserves the phase of the imaging object and receiver coils in the corrected k -space data, which is important for parallel imaging applications. After phase error correction, any parallel reconstruction method can be used. The KICT algorithm is tested with both simulated and in vivo data with both multishot single-coil and multishot multicoil acquisitions. We show that KICT correction results in diffusion-weighted images with higher signal-to-noise ratio (SNR) and fractional anisotropy (FA) maps with better resolved fiber tracts as compared to DPS. In peripheral-gated acquisitions, KICT is comparable to the CG method.

Diffusion tensor imaging of localized anatomic regions, such as brainstem, cervical spinal cord, and optic nerve, is challenging because of the existence of significant susceptibility differences, severe physiologic motion in the surrounding tissues, and the need for high spatial resolution to resolve the underlying complex neuroarchitecture. The aim of the methodology presented here is to achieve high-resolution diffusion tensor imaging in localized regions of the central nervous system that is motion insensitive and immune to susceptibility while acquiring a set of two-dimensional images with more than six diffusion encoding directions within a reasonable total scan time. We accomplish this aim by implementing self-navigated, multishot, variable-density, spiral encoding with outer volume suppression. We establish scan protocols for achieving equal signal-to-noise ratio at 1.2 mm and 0.8 mm in-plane resolution for reduced field-of-view diffusion tensor imaging of the brainstem. In vivo application of the technique on the human pons of three subjects shows a clear delineation of the multiple local neural tracts. By comparing scans acquired with varying in-plane resolution but with constant signal-to-noise ratio, we demonstrate that increasing the resolution and reducing the partial volume effect result in higher fractional anisotropy values for the corticospinal tracts., ((c) 2009 Wiley-Liss, Inc.)

One of the most pervasive problems afflicting people throughout the world is inadequate access to clean water and sanitation. Problems with water are expected to grow worse in the coming decades, with water scarcity occurring globally, even in regions currently considered water-rich. Addressing these problems calls out for a tremendous amount of research to be conducted to identify robust new methods of purifying water at lower cost and with less energy, while at the same time minimizing the use of chemicals and impact on the environment. Here we highlight some of the science and technology being developed to improve the disinfection and decontamination of water, as well as efforts to increase water supplies through the safe re-use of wastewater and efficient desalination of sea and brackish water.

Motion during diffusion encodings leads to phase errors in different shots of a multishot acquisition. Phase differences in k-space data among shots result in phase cancellation artifacts in the reconstructed image. Due to aliasing of the phase from under-sampled regions of the shot, correction of the phase error using direct low-resolution phase subtraction is incomplete. We introduce a new k-space and image-space combination (KICT) method for motion artifacts cancellation that avoids incomplete phase error correction. Further, the method preserves the phase of the object, which is important for parallel imaging applications.

Diffusion Tensor Imaging (DTI) of localized anatomical regions (i.e brainstem, cervical spinal cord, and optic nerve) is challenging because of the existence of significant susceptibility differences in the surrounding tissues, their high motion sensitivity and the need for high spatial resolution to resolve the underlying complex histoarchitecture. The aim of the present methodology is to achieve high resolution DTI with motion compensating capability in localized regions of the central nervous system. We accomplish this by implementing self-navigated multi-shot variable density spiral encoding with outer volume suppression. In vivo application of the technique on the human brainstem demonstrates a clear delineation of the multiple local neural tracts. We also investigate the partial volume effect on the extracted diffusion anisotropy metrics by varying the in-plane resolution while maintaining a constant signal-to-noise ratio.

Efforts to adapt and extend graphic arts printing techniques for demanding device applications in electronics, biotechnology and microelectromechanical systems have grown rapidly in recent years. Here, we describe the use of electrohydrodynamically induced fluid flows through fine microcapillary nozzles for jet printing of patterns and functional devices with submicrometre resolution. Key aspects of the physics of this approach, which has some features in common with related but comparatively low-resolution techniques for graphic arts, are revealed through direct high-speed imaging of the droplet formation processes. Printing of complex patterns of inks, ranging from insulating and conducting polymers, to solution suspensions of silicon nanoparticles and rods, to single-walled carbon nanotubes, using integrated computer-controlled printer systems illustrates some of the capabilities. High-resolution printed metal interconnects, electrodes and probing pads for representative circuit patterns and functional transistors with critical dimensions as small as 1 mum demonstrate potential applications in printed electronics.

Skeletal muscles are highly organized hierarchical structures characterized by an anisotropic arrangement of muscle fibers (myocytes) in fascicles. Due to its unique non-invasive microstructure probing capabilities, diffusion-weighted Magnetic Resonance Imaging (DW-MRI) constitutes a valuable non-invasive tool in the study of such fibrous biological tissues. We have implemented a DW-MRI sequence with highly sensitive directional encoding to quantify the microarchitectural properties of human calf muscles at rest. We have specifically focused on a composite model-based analysis of diffusion tensor MRI measurements to quantify in vivo the cross-sectional asymmetry of muscle fiber geometry, which is a microstructural feature well documented in prior histological studies.

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.

Magnetic Resonance Imaging methods sensitive to individual molecular displacements (q-space MRI) provide a convenient means of measuring dispersion in complex interstitial spaces. Pressure-driven flow experiments through a water-saturated packed bed phantom have been conducted to prove the feasibility of using q-space MRI to measure the coherence length associated with the interstitial velocity field. The method involves measuring the dependence of the apparent dispersion coefficient on the distance along the mean flow by repeating a small number of pulsed-gradient stimulated-echo experiments with increasing gradient pulse separation times. Assuming homogeneous interstitial flow statistics inside the averaging volume, an integral spatial scale characterizing the Eulerian velocity auto-correlation coefficient is extracted via a stochastic convective model. The validity of the a priori statistical description of interstitial flow is verified by comparing with an independent MRI measurement of the Eulerian velocity field using phase contrast methods in the same phantom with pore-level resolution. The integral length scale obtained via q-space MRI agrees with the mean pore size in the present as well as in similar phantoms found in the literature. This method has direct applicability in the quantification of the interstitial morphology of fluid-saturated porous media with resolution independent of voxel size, assuming "perfectly reflecting pore walls" (no surface relaxation) and no contribution to the MR signal from outside the pore space.

We propose a computational technique to reconstruct internal physiological flows described by sparse point-wise MRI velocity measurements. Assuming that the viscous forces in the flow are negligible, the incompressible flow field can be obtained from a velocity potential that satisfies Laplace's equation. A set of basis functions each satisfying Laplace's equation with appropriately defined boundary data is constructed using the finite-element method. An inverse problem is formulated where higher resolution boundary and internal velocity data are extracted from the point-wise MRI velocity measurements using a least-squares method. From the results we obtained with approximately 100 internal measurement points, the proposed reconstruction method is shown to be effective in filtering out the experimental noise at levels as high as 30%, while matching the reference solution within 2%. This allows the reconstruction of a high-resolution velocity field with limited MRI encoding.

Notwithstanding its widespread use in cardiovascular and functional MRI studies, Echo Planar Imaging (EPI) has only recently been subjected to systematic validation studies. Most velocity measurement studies employing such ultrafast MRI methods involve the use of phantoms characterized by rigid or deformable solid motion. The current implementation involves a rotating phantom (angular velocity up to 10.5 rpm) with a superimposed swirling liquid flow (with axial velocities ranging between 0.145 and 0.27 cm/s) of water doped with copper sulfate. The standard implementation of single-shot EPI with phase contrast velocity encoding allows the complete mapping of the Eulerian velocity field in slices perpendicular to the rotation axis following a subtractive procedure requiring the synchronized acquisition of each velocity component on each selected transverse slice during two revolutions of the rotor. The image acquisition time is 100 ms (per velocity component) at each 64 x 64 slice. In addition to acquiring full-field velocity data for future direct comparisons with other techniques, EPI is employed here for the first time to reconstruct the three-dimensional flow field between the blades of a partitioned pipe mixer.

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.

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.

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.

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.

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.