Presence Of Inhomogeneous Field Research Articles

Quantification of the rotating frame relaxation time T2ρ: Comparison of balanced spin-lock and continuous-wave Malcolm-Levitt preparations.

For the quantification of rotating frame relaxation times, the T2ρ relaxation pathway plays an essential role. Nevertheless, T2ρ imaging has been studied only to a small extent compared with T1ρ, and preparation techniques for T2ρ have so far been adapted from T1ρ methods. In this work, two different preparation concepts are compared specifically for the use of T2ρ mapping. The first approach involves transferring the balanced spin-locking (B-SL) concept of T1ρ imaging. The second and newly proposed approach is a continuous-wave Malcolm-Levitt (CW-MLEV) pulse train with zero echo times and was motivated from T2 preparation strategies. The modules are tested in Bloch simulations for their intrinsic sensitivity to field inhomogeneities and validated in phantom experiments. In addition, myocardial T2ρ mapping was performed in mice as an exemplary application. Our results demonstrate that the CW-MLEV approach provides superior robustness and thus suggest that established methods of T1ρ imaging are not best suited for T2ρ experiments. In the presence of field inhomogeneities, the simulations indicated an increased banding compensation by a factor of 4.1 compared with B-SL. Quantification of left ventricular T2ρ time in mice yielded more consistent results, and values in the range of 59.2-61.1 ms (R2= 0.986-0.992) were observed at 7 T.

Balanced spin-lock preparation for B1 -insensitive and B0 -insensitive quantification of the rotating frame relaxation time T1ρ.

Accurate and artifact-free T1ρ quantification is still a major challenge due to a susceptibility of the spin-locking module to B0 and/or B1 field inhomogeneities. In this study, we present a novel spin-lock preparation module (B-SL) that enables an almost full compensation of both types of inhomogeneities. The new B-SL module contains a second 180° refocusing pulse to compensate each pulse in the preparation block by a corresponding pulse with opposite phase. For evaluation and validation of B-SL, extensive simulations as well as phantom measurements were performed. Furthermore, the new module was compared to three common established compensation methods. Both simulations and measurements demonstrate a much lower susceptibility to artifacts for the B-SL module, therefore providing an improved accuracy in T1ρ quantification. In the presence of field inhomogeneities, measurements revealed an increased banding compensation by 79% compared with the frequently used composite module. The goodness of the mono-exponential T1ρ fitting procedure was improved by 58%. The B-SL preparation enables the generation of accurate relaxation maps with significantly reduced artifacts, even in the case of large field imperfections. Therefore, the B-SL module is suggested to be highly beneficial for in vivo T1ρ quantification.

Analysis and correction of off-resonance artifacts in echo-planar cardiac diffusion tensor imaging.

Cardiac diffusion tensor imaging using EPI readout is prone to image distortions in the presence of field inhomogeneities. In this work, a framework to analyze and correct image distortions in cardiac diffusion tensor imaging is presented. A multi-coil reconstruction framework was implemented to enable field map-based off-resonance correction. Numerical simulations were used to examine reconstruction performance for EPI phase-encode directions blip up-down and down-up for different degrees of off-resonance gradients and varying field map resolution. The impact of coil encoding was analyzed using the g-factor and normalized RMSE. Finally, the proposed method was tested on free-breathing in vivo cardiac diffusion tensor imaging data acquired in healthy subjects at 3 Tesla. Depending on the local field map gradient strength and polarity and the selected phase-encode direction, field inhomogeneities lead to either local spatial compression or stretching with standard image reconstruction. Although spatial compression results in loss of image resolution upon field map-based reconstruction, spatial stretching can be recovered once multiple receive coils are utilized. Multi-coil reconstruction was found to reduce the normalized RMSE from 34.3% to 8.1% for image compression, and 33.6% to 1.8% for image stretching, with resulting average g-factors 14.7 ± 2.9 and 1.2 ± 0.1, respectively. In vivo, multi-coil field map-based reconstruction yielded improved alignment of angle maps with anatomical cine data. Multi-coil, field map-based image reconstruction for echo-planar cardiac diffusion tensor imagingallows accurate image reconstruction provided that the phase-encode direction and polarity is chosen to principally align with the direction and polarity of the prominent gradients of field inhomogeneities.

Nuclear signature effect on spatial distribution of molecular harmonic in the presence of spatial inhomogeneous field

Spatial distribution of the molecular harmonic spectra from in the presence of inhomogeneous field has been theoretically investigated. It shows that (i) the harmonic intensities from the negative-H nucleus play the dominating role in harmonic emission spectra. (ii) Through the investigations of the nuclear signature effect on the spatial distribution of the molecular harmonic spectra, the differences of the harmonic intensities between the negative-H nucleus and the positive-H nucleus can be enhanced and reduced with the introduction of the higher vibrational state and the heavy nucleus (i.e. ), respectively. The time-frequency analyses of the harmonic spectra, the time-dependent wave function and the electron localization have been shown to explain the harmonic spatial distribution and the electron motion. (iii) Due to the plasmon-resonance-enhancement near the metallic nanostructure, the harmonic cutoff can be remarkably enhanced as the spatial position of the inhomogeneous field moving away from the gap center. The ionization probabilities have been shown to explain the harmonic cutoff extension.

Myocardial T1 mapping with spectrally-selective inversion pulse to reduce the influence of fat

Background Changes in the longitudinal relaxation time (T1) of the myocardium are considered an important imaging-based biomarker to detect and quantify diffuse fibrosis. Several sequences have been suggested to measure myocardial T1 values [1]. However, T1 measurements are often influenced by the presence of intramyocardial or epicardial fat [2,3,4]. The aim of this study was to minimize the effect of fat in T1 mapping by the use of a water selective inversion pulse and to investigate the impact of this spectrally-selective inversion pulse on T1 measurements in the presence of field inhomogeneities.

Interaction of a two-dimensional electromagnetic pulse with an electron inhomogeneity in an array of carbon nanotubes in the presence of field inhomogeneity

In this study, we address the challenging problem of propagation of infrared electromagnetic two-dimensional bipolar pulses of extremely short duration in a heterogeneous array of semiconductor carbon nanotubes. Heterogeneity is defined here as a region of high electron density. The evolutions of the electromagnetic field and charge density in the sample are described by Maxwell’s equations and the continuity equation respectively, wherein the inhomogeneity of the field along the nanotube axis is integrated and incorporated into the modeling framework. Our numerical solution to this problem shows the possibility of a stable propagation of two-dimensional electromagnetic pulses through a heterogeneous array of carbon nanotubes. This propagation of electromagnetic pulses is accompanied by a redistribution of the electron density in the sample. For the first time to the best of our knowledge, this latter effect is fully accounted for in our study. Specifically, we demonstrate that depending on the initial speed of the electromagnetic pulse two possible outcomes might ensue: either (i) the pulse overcomes the region of increased electron concentration, or alternatively (ii) it is reflected therefrom. As a result, a near-infrared pulse is transmitted, while the long-wavelength infrared pulse is reflected, on an obstacle that is much smaller than its wavelength.

A fully flow-compensated multiecho susceptibility-weighted imaging sequence: The effects of acceleration and background field on flow compensation.

To present a fully flow-compensated multiecho gradient echo sequence that can be used for MR angiography (MRA), susceptibility weighted imaging (SWI), and quantitative susceptibility mapping (QSM) and to study the effects of flow acceleration and background field gradients on flow compensation. The quality of flow compensation was evaluated using the data from eight volunteers. The effects of flow acceleration were studied by changing the polarities of the readout gradients in two consecutive scans. The background field was used to estimate the phase errors of flow compensation in the presence of field inhomogeneities. SWI and QSM data were generated with confounding arterial phase removed. T2 * maps were obtained from the multiecho data to estimate T2 * of arterial blood. Reasonable flow compensation was achieved. Nevertheless, background field gradients and acceleration-induced phase errors were found to be as large as π/2 and π/3, respectively, both in agreement with theory. T2 * was measured as 82 ± 4 ms and 74 ± 9 ms for arteries inside and outside the brain, respectively, at 3T. High-quality MRA, SWI, and QSM data can be obtained simultaneously. Masking out the arteries to remove the phase due to flow acceleration and background field gradients improves the quality of both SWI and QSM data. Magn Reson Med 76:478-489, 2016. © 2015 Wiley Periodicals, Inc.

Geometric distortion evaluation using a multi-orientated water-phantom at 0.2 T MRI.

Magnetic Resonance Imaging (MRI) has been one of the most revolutionary medical imaging modalities in the past three decades. It has been recognized as a potential technique in the clinical diagnosis of diseases as well as tumor differentiation. Although MRI has now become the preferred choice in many clinical examinations, there are some drawbacks, which still limit its applications. One of the crucial issues of MRI is the geometric distortion caused by magnetic field inhomogeneity and susceptibility effects. The farther the lesion from the center of a magnetic field (off-center field), the more severe the distortion becomes, especially in low-field MRI. Hence, it might hinder the diagnosis and characterization of lesions in the presence of field inhomogeneity. In this study, an innovative multi-orientated water-phantom was used to evaluate the geometric distortion. The correlations between the level of image distortion and the relative off-center positions, as well as the variation of signal intensities, were both investigated. The image distortion ratios of axial, coronal and sagittal images were calculated.

Geometrically undistorted MRI in the presence of field inhomogeneities using compressed sensing accelerated broadband 3D phase encoded turbo spin-echo imaging

In this study, we explore the potential of compressed sensing (CS) accelerated broadband 3D phase-encoded turbo spin-echo (3D-PE-TSE) for the purpose of geometrically undistorted imaging in the presence of field inhomogeneities. To achieve this goal 3D-PE-SE and 3D-PE-TSE sequences with broadband rf pulses and dedicated undersampling patterns were implemented on a clinical scanner. Additionally, a 3D multi-spectral spin-echo (ms3D-SE) sequence was implemented for reference purposes. First, we demonstrated the influence of susceptibility induced off-resonance effects on the spatial encoding of broadband 3D-SE, ms3D-SE, 3D-PE-SE and 3D-PE-TSE using a grid phantom containing a titanium implant (Δχ = 182 ppm) with x-ray CT as a gold standard. These experiments showed that the spatial encoding of 3D-PE-(T)SE was unaffected by susceptibility induced off-resonance effects, which caused geometrical distortions and/or signal hyper-intensities in broadband 3D-SE and, to a lesser extent, in ms3D-SE frequency encoded methods. Additionally, an SNR analysis was performed and the temporally resolved signal of 3D-PE-(T)SE sequences was exploited to retrospectively decrease the acquisition bandwidth and obtain field offset maps. The feasibility of CS acceleration was studied retrospectively and prospectively for the 3D-PE-SE sequence using an existing CS algorithm adapted for the reconstruction of 3D data with undersampling in all three phase encoded dimensions. CS was combined with turbo-acceleration by variable density undersampling and spherical stepwise T2 weighting by randomly sorting consecutive echoes in predefined spherical k-space layers. The CS-TSE combination resulted in an overall acceleration factor of 60, decreasing the original 3D-PE-SE scan time from 7 h to 7 min. Finally, CS accelerated 3D-PE-TSE in vivo images of a titanium screw were obtained within 10 min using a micro-coil demonstrating the feasibility of geometrically undistorted MRI near severe field inhomogeneities.

Simultaneous fat saturation and magnetization transfer contrast imaging with steady-state incoherent sequences.

This work combines an n-dimensional fat sat(uration) radiofrequency (RF) pulse with steady-state incoherent (SSI) pulse sequences, e.g., spoiled gradient-echo sequence, to simultaneously produce B0 insensitive fat suppression and magnetization transfer (MT) contrast. This pulse is then referred to as "fat sat and MT contrast pulse." We discuss the features of the fat sat and MT contrast pulse and the MT sensitivities of the SSI sequences when combining with fat sat. Moreover, we also introduce an adapted RF spoiling scheme for SSI sequences with fat sat. Simulations and phantom experiments were conducted to demonstrate the adapted RF spoiling. Fat suppression and MT effects are shown in 3T phantom experiments and in vivo experiments, including brain imaging, cartilage imaging, and angiography. To ensure that the sequence reaches steady state, the adapted RF spoiling is required for fat sat SSI sequences. Fat sat and MT contrast pulse works robustly with field inhomogeneity and also produces MT contrasts. SSI sequences with fat sat and MT contrast pulse and adapted RF spoiling can robustly produce fat suppressed and MT contrast images in the presence of field inhomogeneity.

Accelerated phase-cycled SSFP imaging with compressed sensing.

Balanced steady-state free precession (SSFP) imaging suffers from irrecoverable signal losses, known as banding artifacts, in regions of large B0 field inhomogeneity. A common solution is to acquire multiple phase-cycled images each with a different frequency sensitivity, such that the location of banding artifacts are shifted in space. These images are then combined to alleviate signal loss across the entire field-of-view. Although high levels of artifact suppression are viable using a large number of images, this is a time costly process that limits clinical utility. Here, we propose to accelerate individual acquisitions such that the overall scan time is equal to that of a single SSFP acquisition. Aliasing artifacts and noise are minimized by using a variable-density random sampling pattern in k-space, and by generating disjoint sampling patterns for separate acquisitions. A sparsity-enforcing method is then used for image reconstruction. Demonstrations on realistic brain phantom images, and in vivo brain and knee images are provided. In all cases, the proposed technique enables robust SSFP imaging in the presence of field inhomogeneities without prolonging scan times.

Chemical shift encoding‐based water–fat separation methods

The suppression of signal from fat constitutes a basic requirement in many applications of magnetic resonance imaging. To date, this is predominantly achieved during data acquisition, using fat saturation, inversion recovery, or water excitation methods. Postponing the separation of signal from water and fat until image reconstruction holds the promise of resolving some of the problems associated with these methods, such as failure in the presence of field inhomogeneities or contrast agents. In this article, methods are reviewed that rely on the difference in chemical shift between the hydrogen atoms in water and fat to perform such a retrospective separation. The basic principle underlying these so-called Dixon methods is introduced, and some fundamental implementations of the required chemical shift encoding in the acquisition and the subsequent water-fat separation in the reconstruction are described. Practical issues, such as the selection of key parameters and the appearance of typical artifacts, are illustrated, and a broad range of applications is demonstrated, including abdominal, cardiovascular, and musculoskeletal imaging. Finally, advantages and disadvantages of these Dixon methods are summarized, and emerging opportunities arising from the availability of information on the amount and distribution of fat are discussed.

On the utility of spectroscopic imaging as a tool for generating geometrically accurate MR images and parameter maps in the presence of field inhomogeneities and chemical shift effects

Lack of spatial accuracy is a recognized problem in magnetic resonance imaging (MRI) which severely detracts from its value as a stand-alone modality for applications that put high demands on geometric fidelity, such as radiotherapy treatment planning and stereotactic neurosurgery. In this paper, we illustrate the potential and discuss the limitations of spectroscopic imaging as a tool for generating purely phase-encoded MR images and parameter maps that preserve the geometry of an object and allow localization of object features in world coordinates.Experiments were done on a clinical system with standard facilities for imaging and spectroscopy. Images were acquired with a regular spin echo sequence and a corresponding spectroscopic imaging sequence. In the latter, successive samples of the acquired echo were used for the reconstruction of a series of evenly spaced images in the time and frequency domain. Experiments were done with a spatial linearity phantom and a series of test objects representing a wide range of susceptibility- and chemical-shift-induced off-resonance conditions.In contrast to regular spin echo imaging, spectroscopic imaging was shown to be immune to off-resonance effects, such as those caused by field inhomogeneity, susceptibility, chemical shift, f0 offset and field drift, and to yield geometrically accurate images and parameter maps that allowed object structures to be localized in world coordinates.From these illustrative examples and a discussion of the limitations of purely phase-encoded imaging techniques, it is concluded that spectroscopic imaging offers a fundamental solution to the geometric deficiencies of MRI which may evolve toward a practical solution when full advantage will be taken of current developments with regard to scan time reduction. This perspective is backed up by a demonstration of the significant scan time reduction that may be achieved by the use of compressed sensing for a simple phantom.

Quantification of T1ρ relaxation by using rotary echo spin-lock pulses in the presence of B0 inhomogeneity

T1ρ relaxation is traditionally described as a mono-exponential signal decay with spin-lock time. However, T1ρ quantification by fitting to the mono-exponential model can be substantially compromised in the presence of field inhomogeneities, especially for low spin-lock frequencies. The normal approach to address this issue involves the development of dedicated composite spin-lock pulses for artifact reduction while still using the mono-exponential model for T1ρ fitting. In this work, we propose an alternative approach for improved T1ρ quantification with the widely-used rotary echo spin-lock pulses in the presence of B0 inhomogeneities by fitting to a modified theoretical model which is derived to reveal the dependence of T1ρ-prepared magnetization on T1ρ, T2ρ, spin-lock time, spin-lock frequency and off-resonance, without involving complicated spin-lock pulse design. It has potentials for T1ρ quantification improvement at low spin-lock frequencies. Improved T1ρ mapping was demonstrated on phantom and in vivo rat spin-lock imaging at 3 T compared to the mapping using the mono-exponential model.

Simultaneous fat suppression and band reduction with large‐angle multiple‐acquisition balanced steady‐state free precession

Balanced steady-state free precession (bSSFP) MRI is a rapid and signal-to-noise ratio-efficient imaging method, but suffers from characteristic bands of signal loss in regions of large field inhomogeneity. Several methods have been developed to reduce the severity of these banding artifacts, typically involving the acquisition of multiple bSSFP datasets (and the accompanying increase in scan time). Fat suppression with bSSFP is also challenging; most existing methods require an additional increase in scan time, and some are incompatible with bSSFP band-reduction techniques. This work was motivated by the need for both robust fat suppression and band reduction in the presence of field inhomogeneity when using bSSFP for flow-independent peripheral angiography. The large flip angles used in this application to improve vessel conspicuity and contrast lead to specific absorption rate considerations, longer repetition times, and increased severity of banding artifacts. In this work, a novel method that simultaneously suppresses fat and reduces bSSFP banding artifact with the acquisition of only two phase-cycled bSSFP datasets is presented. A weighted sum of the two bSSFP acquisitions is taken on a voxel-by-voxel basis, effectively synthesizing an off-resonance profile at each voxel that puts fat in the stop band while keeping water in the pass band. The technique exploits the near-sinusoidal shape of the bSSFP off-resonance spectrum for many tissues at large (>50°) flip angles.

Defeating Radiation Damping and Magnetic Field Inhomogeneity with Spatially Encoded Noise

A simple NMR experiment capable of providing well resolved spectra under conditions where either radiation damping or static magnetic field inhomogeneity would broaden otherwise high-resolution NMR spectra is introduced. The approach involves using a strong pulsed magnetic field gradient and a selective radio-frequency pulse to encode a predetermined noise pattern into the spatial distribution of magnetization. Following readout in a much smaller field gradient, the noise sequence may be deconvolved from the acquired data and a high-resolution spectrum is obtained, eliminating the effects of either radiation damping or the static field inhomogeneity. In the presence of field inhomogeneity a field map is also obtained from the same single transient. A quasi-two-dimensional version of the experiment eliminates the need for deconvolution and produces improved results with simplified processing, but without requiring a full two-dimensional experiment. Example spectra are shown for both radiation damping and one-dimensional field inhomogeneity with improvement in linewidths of more than a factor of 40.

High‐resolution MRS in the presence of field inhomogeneity via intermolecular double‐quantum coherences on a 3‐T whole‐body scanner

Signals from intermolecular double-quantum coherences (iDQCs) have been shown to be insensitive to macroscopic field inhomogeneities and thus enable acquisition of high- resolution MR spectroscopy in the presence of large inhomogeneous fields. In this paper, localized iDQC (1)H spectroscopy on a whole-body 3-T MR scanner is reported. Experiments with a brain metabolite phantom were performed to quantify characteristics of the iDQC signal under different conditions. The feasibility of in vivo iDQC high-resolution MR spectroscopy in the presence of large intrinsic and external field inhomogeneity (in the order of hundreds of hertz) was demonstrated in the whole cerebellum of normal volunteers in a scan time of about 6.5 min. Major metabolite peaks were well resolved in the reconstructed one-dimensional spectra projected from two-dimensional iDQC acquisitions. Investigations on metabolite ratios, signal-to-noise ratio, and line width were performed and compared with results obtained with conventional point-resolved spectroscopy/MR spectroscopy in homogeneous fields. Metabolite ratios from iDQC results showed excellent consistency under different in vitro and in vivo conditions, and they were similar to those from point-resolved spectroscopy with small voxel sizes in homogeneous fields. MR spectroscopy with iDQCs can be applied potentially for quantification of gross metabolite changes due to diseases in large brain volumes with high field inhomogeneity.

Sodium MRI using a density‐adapted 3D radial acquisition technique

A density-adapted three-dimensional radial projection reconstruction pulse sequence is presented which provides a more efficient k-space sampling than conventional three-dimensional projection reconstruction sequences. The gradients of the density-adapted three-dimensional radial projection reconstruction pulse sequence are designed such that the averaged sampling density in each spherical shell of k-space is constant. Due to hardware restrictions, an inner sphere of k-space is sampled without density adaption. This approach benefits from both the straightforward handling of conventional three-dimensional projection reconstruction sequence trajectories and an enhanced signal-to-noise ratio (SNR) efficiency akin to the commonly used three-dimensional twisted projection imaging trajectories. Benefits for low SNR applications, when compared to conventional three-dimensional projection reconstruction sequences, are demonstrated with the example of sodium imaging. In simulations of the point-spread function, the SNR of small objects is increased by a factor 1.66 for the density-adapted three-dimensional radial projection reconstruction pulse sequence sequence. Using analytical and experimental phantoms, it is shown that the density-adapted three-dimensional radial projection reconstruction pulse sequence allows higher resolutions and is more robust in the presence of field inhomogeneities. High-quality in vivo images of the healthy human leg muscle and the healthy human brain are acquired. For equivalent scan times, the SNR is up to a factor of 1.8 higher and anatomic details are better resolved using density-adapted three-dimensional radial projection reconstruction pulse sequence.

Self-Consistent Multiscale Modeling in the Presence of Inhomogeneous Fields

Molecular dynamics (MD) simulations of a Lennard–Jones fluid in an inhomogeneous external field generate steady-state profiles of density and pressure with nanoscopic heterogeneities. The continuum level of mass, momentum, and energy transport balances is capable of reproducing the MD profiles only when the equation of state for pressure as a function of density is extracted directly from the molecular level of description. We show that the density profile resulting from simulation is consistent with both a molecular-level theoretical prediction from statistical mechanics as well as the solution of the continuum-level set of differential equations describing the conservation of mass and momentum.

Special Section on Multiscale Materials Modeling

Materials modeling is intrinsically multiscale and has motivated much of the development of multiscale methods for both analysis and simulation. Multiscale features of materials can originate from a variety of sources, including multiple physics, atomistic effects, defects, multiscale continuum structures, and multiscale behavior of the PDEs or other elements of mathematical models. The following special section on multiscale materials modeling was motivated by the Fourth International Conference on Multiscale Materials Modeling (MMM-2008), which was held in Tallahassee, Florida, October 27–31, 2008. Anter El-Azab, Max Gunzberger, and Sidney Yip served as guest editors for this special section. Molecular dynamics using effective potentials is an appropriate model for the mechanical properties of fluids and solids at the atomistic scale. The most basic multiscale issue is the connection between molecular dynamics and continuum mechanics, and analysis of this connection is one of the most important goals of mathematical materials science. Besides its basic scientific importance, a practical outcome of this analysis can be a molecular-based determination of the constitutive equations for the material. In “Self-Consistent Multiscale Modeling in the Presence of Inhomogeneous Fields” by Ruichang Xiong, Rebecca L. Empting, Ian C. Morris, and David J. Keffer, computational results from molecular dynamics for an isothermal fluid are averaged to directly evaluate the equation of state for fluid pressure using a novel thermostat to keep the system at a fixed temperature. An alternative approach to relating atomistic and continuum mechanics is taken by Pablo Seleson, Michael L. Parks, Max Gunzberger, and Richard B. Lehoucq in their article “Peridynamics as an Upscaling of Molecular Dynamics.” Peridynamics is a continuum model for solid mechanics involving nonlocal interactions, as in molecular dynamics. This article shows that peridynamics can be interpreted as an upscaling of molecular dynamics. A principal computational difficulty with molecular dynamics is the large number of atoms required for realistic systems and the resulting large computational complexity. For materials with defects, molecular dynamics may be necessary near the defects, but far from the defects a coarse grained description may be adequate and much more computationally efficient. “Multiscale Analysis across Atoms/Continuum by a Generalized Particle Dynamics Method” by Jinghong Fan develops a new multiscale computational approach for particle/continuum mechanics, in which the spatial domain is divided into different regions. In each region the material is represented as a system of particles, but the size and spacing of the particles are different in different regions. Large molecules, such as peptides and proteins, can arrange themselves in various spatial configurations or conformations. The dynamics of these conformations are difficult to directly represent and simulate, because of the large size of the molecules. In their paper “Mean Field Approximation in Conformation Dynamics,” Gero Friesecke, Oliver Junge, and Péter Koltai develop a mean field description of conformation dynamics, based on molecular dynamic simulations over short times and an assumption of statistical independence of the eigenfunctions of the related transfer operators. At macroscopic scales, the most natural theory is a continuum description based on partial differential equations (PDEs). This can already require a multiscale description due to spontaneous formation of multiscale phenomena such as fluid turbulence or mechanical shear bands, or inherent multiscale structures as composite materials or porous media. These phenomena lead to multiscale analysis of the PDEs for the continuum theory. The Hamilton–Jacobi equation is a canonical equation for transport of material or other quantities. In “Homogenization of Metric Hamilton–Jacobi Equations,” Adam M. Oberman, Ryo Takei, and Alexander Vladimirsky derive a new approach to homogenization for static Hamilton–Jacobi equations. They relate the Hamilton–Jacobi solution to a distance function for a corresponding metric and show that the homogenized equation also induces a metric. This provides a simplified description of the homogenization. For materials with microscopic heterogeneity, a stochastic description of the heterogeneities is a useful mathematical model. In their article “A Bounded Random Matrix Approach for Stochastic Upscaling,” Sonjoy Das and Roger Ghanem develop a maximum entropy approach to probabilistic construction of the matrices of coefficients for the constitutive laws, taking advantage of the energy bounds on the constitutive coefficients. Bone is a particularly complex and important multiscale material. The article “Micromechamical Modeling of the Anisotropy of Elastic Biological Composites” by Jamila Rahmoun, Fahmi Chaari, Eric Markiewicz, and Pascal Drazetic derives a mathematical model for the effective elastic parameters of trabecular bone, based on micromechanical modeling and using the multiscale geometry obtained from x-ray microtomography. In summary, this collection of seven papers provides a sampling of some of the most important issues in multiscale modeling and simulation for materials. It shows the range of issues and results in this field of great current interest.