# Related Articles

Three-dimensional reciprocal space mapping by X-ray and electron diffraction [namely grazing-incidence X-ray diffraction (GIXD), reflection high-energy electron diffraction (RHEED) and grazing-incidence small-angle X-ray scattering (GISAXS)] was used to explore the internal structure and shape of differently oriented epitaxial Co/CaF2 facetted nanoparticles.

In this work epitaxial growth of cobalt on CaF2(111), (110) and (001) surfaces has been extensively studied. It has been shown by atomic force microscopy that at selected growth conditions stand-alone faceted Co nanoparticles are formed on a fluorite surface. Grazing-incidence X-ray diffraction (GIXD) and reflection high-energy electron diffraction (RHEED) studies have revealed that the particles crystallize in the face-centered cubic lattice structure otherwise non-achievable in bulk cobalt under normal conditions. The particles were found to inherit lattice orientation from the underlying CaF2 layer. Three-dimensional reciprocal space mapping carried out using X-ray and electron diffraction has revealed that there exist long bright 〈111〉 streaks passing through the cobalt Bragg reflections. These streaks are attributed to stacking faults formed in the crystal lattice of larger islands upon coalescence of independently nucleated smaller islands. Distinguished from the stacking fault streaks, crystal truncation rods perpendicular to the {111} and {001} particle facets have been observed. Finally, grazing-incidence small-angle X-ray scattering (GISAXS) has been applied to decouple the shape-related scattering from that induced by the crystal lattice defects. Particle faceting has been verified by modeling the GISAXS patterns. The work demonstrates the importance of three-dimensional reciprocal space mapping in the study of epitaxial nanoparticles.

doi:10.1107/S0021889813008777

PMCID: PMC3769055
PMID: 24046491

cobalt-on-fluorite nanoparticles; grazing-incidence X-ray diffraction (GIXD); reflection high-energy electron diffraction (RHEED); grazing-incidence small-angle X-ray scattering (GISAXS); epitaxial growth; three-dimensional reciprocal space mapping

The high-resolution temperature-dependent diffuse X-ray scattering from an Na0.5Bi0.5TiO3 perovskite-based single crystal is measured on the approach to the polymorphic phase transition. The previously unseen topological features of the diffuse scattering and their temperature evolution are reported.

The results of high-resolution measurements of the diffuse X-ray scattering produced by a perovskite-based Na0.5Bi0.5TiO3 ferroelectric single crystal between 40 and 620 K are reported. The study was designed as an attempt to resolve numerous controversies regarding the average structure of Na0.5Bi0.5TiO3, such as the mechanism of the phase transitions between the tetragonal, P4bm, and rhombohedral | monoclinic, R3c | Cc, space groups and the correlation between structural changes and macroscopic physical properties. The starting point was to search for any transformations of structural disorder in the temperature range of thermal depoling (420–480 K), where the average structure is known to remain unchanged. The intensity distribution around the {032} pseudocubic reflection was collected using a PILATUS 100K detector at the I16 beamline of the Diamond Light Source (UK). The data revealed previously unknown features of the diffuse scattering, including a system of dual asymmetric L-shaped diffuse scattering streaks. The topology, temperature dependence, and relationship between Bragg and diffuse intensities suggest the presence of complex microstructure in the low-temperature R3c | Cc phase. This microstructure may be formed by the persistence of the higher-temperature P4bm phase, built into a lower-temperature R3c | Cc matrix, accompanied by the related long-range strain fields. Finally, it is shown that a correlation between the temperature dependence of the X-ray scattering features and the temperature regime of thermal depoling is present.

doi:10.1107/S160057671501571X

PMCID: PMC4747085
PMID: 26877721

single-crystal diffuse X-ray scattering; lead-free ferroelectrics; high-resolution X-ray diffraction; perovskites; Na0.5Bi0.5TiO3

Acoustic form factors have been used to model the frequency dependence of acoustic scattering in phantoms and tissues. This work demonstrates that a broad range of scatterer sizes, individually well represented by Faran theory or a Gaussian form factor is not accurately described by a single effective scatterer from either of these models. Contributions from a distribution of discrete scatterer sizes for two different form factor functions (Gaussian form factors and scattering functions from Faran’s theory) were calculated and linearly combined. Composite form factors created from Gaussian distributions of scatterer sizes centered at 50 µm with standard deviations of up to σ = 40µm were fit to each scattering model between 2 MHz and 12 MHz. Scatterer distributions were generated using one of two assumptions: the number density of the scatterer diameter distribution was Gaussian distributed, or the volume fraction of each scatterer diameter in the distribution was Gaussian distributed. Each simulated form factor was fit to a single diameter form factor model for Gaussian and exponential form factors. The mean squared error (MSE) between the composite simulated data and the best-fit single diameter model was smaller with an exponential form factor model, compared to a Gaussian model, for distributions with standard deviations larger than 30% of the centroid value. In addition, exponential models were shown to have better ability to distinguish between Faran scattering model-based distributions with varying center diameters than the Gaussian form factor model. The evidence suggests that when little is known about the scattering medium, an exponential scattering model provides a better first approximation to the scattering correlation function for a broad distribution of spherically symmetric scatterers than when a Gaussian form factor model is assumed.

doi:10.1177/0161734614534399

PMCID: PMC4237706
PMID: 24831300

Conspectus

Organic–inorganic semiconductors, which
adopt the perovskite
crystal structure, have perturbed the landscape of contemporary photovoltaics
research. High-efficiency solar cells can be produced with solution-processed
active layers. The materials are earth abundant, and the simple processing
required suggests that high-throughput and low-cost manufacture at
scale should be possible.

While these materials bear considerable
similarity to traditional
inorganic semiconductors, there are notable differences in their optoelectronic
behavior. A key distinction of these materials is that they are physically
soft, leading to considerable thermally activated motion.

In
this Account, we discuss the internal motion of methylammonium
lead iodide (CH3NH3PbI3) and formamidinium
lead iodide ([CH(NH2)2]PbI3), covering:
(i) molecular rotation-libration in the cuboctahedral cavity; (ii)
drift and diffusion of large electron and hole polarons; (iii) transport
of charged ionic defects. These processes give rise to a range of
properties that are unconventional for photovoltaic materials, including
frequency-dependent permittivity, low electron–hole recombination
rates, and current–voltage hysteresis. Multiscale simulations,
drawing from electronic structure, ab initio molecular dynamic and
Monte Carlo computational techniques, have been combined with neutron
diffraction measurements, quasi-elastic neutron scattering, and ultrafast
vibrational spectroscopy to qualify the nature and time scales of
the motions. Electron and hole motion occurs on a femtosecond time
scale. Molecular libration is a sub-picosecond process. Molecular
rotations occur with a time constant of several picoseconds depending
on the cation. Recent experimental evidence and theoretical models
for simultaneous electron and ion transport in these materials has
been presented, suggesting they are mixed-mode conductors with similarities
to fast-ion conducting metal oxide perovskites developed for battery
and fuel cell applications. We expound on the implications of these
effects for the photovoltaic action.

The temporal behavior displayed
by hybrid perovskites introduces
a sensitivity in materials characterization to the time and length
scale of the measurement, as well as the history of each sample. It
also poses significant challenges for accurate materials modeling
and device simulations. There are large differences between the average
and local crystal structures, and the nature of charge transport is
too complex to be described by common one-dimensional drift-diffusion
models. Herein, we critically discuss the atomistic origin of the
dynamic processes and the associated chemical disorder intrinsic to
crystalline hybrid perovskite semiconductors.

doi:10.1021/acs.accounts.5b00431

PMCID: PMC4794704
PMID: 26859250

In 131I SPECT, image quality and quantification accuracy are degraded by object scatter as well as scatter and penetration in the collimator. The characterization of energy and spatial distributions of scatter and penetration performed in this study by Monte Carlo simulation will be useful for the development and evaluation of techniques that compensate for such events in 131I imaging.

Methods

First, to test the accuracy of the Monte Carlo model, simulated and measured data were compared for both a point source and a phantom. Next, simulations to investigate scatter and penetration were performed for four geometries: point source in air, point source in a water-filled cylinder, hot sphere in a cylinder filled with nonradioactive water, and hot sphere in a cylinder filled with radioactive water. Energy spectra were separated according to order of scatter, type of interaction, and γ-ray emission energy. A preliminary evaluation of the triple-energy window (TEW) scatter correction method was performed.

Results

The accuracy of the Monte Carlo model was verified by the good agreement between measured and simulated energy spectra and radial point spread functions. For a point source in air, simulations show that 73% of events in the photopeak window had either scattered in or penetrated the collimator, indicating the significance of collimator interactions. For a point source in a water-filled phantom, the separated energy spectra showed that a 20% photopeak window can be used to eliminate events that scatter more than two times in the phantom. For the hot sphere phantoms, it was shown that in the photopeak region the spectrum shape of penetration events is very similar to that of primary (no scatter and no penetration) events. For the hot sphere regions of interest, the percentage difference between true scatter counts and the TEW estimate of scatter counts was <12%.

Conclusion

In 131I SPECT, object scatter as well as collimator scatter and penetration are significant. The TEW method provides a reasonable correction for scatter, but the similarity between the 364-keV primary and penetration energy spectra makes it difficult to compensate for these penetration events using techniques that are based on spectral analysis.

PMCID: PMC2811856
PMID: 10647615

scatter correction; penetration; 131I imaging; SPECT; Monte Carlo simulated data

An approximate empirical isotropic interatomic potentials for CH4–inert gas mixtures are developed by simultaneously fitting the Exponential-Spline-Morse-Spline-van der Waals (ESMSV) potential form to viscosity, thermal conductivity, thermal diffusion factors, diffusion coefficient, interaction second pressure virial coefficient and scattering cross-section data. Quantum mechanical lineshapes of collision-induced absorption (CIA) at different temperatures for CH4–He and at T = 87 K for CH4–Ar are computed using theoretical values for overlap, octopole and hexadecapole mechanisms and interaction potential as input. Also, the quantum mechanical lineshapes of collision-induced light scattering (CILS) for the mixtures CH4–Ar and CH4–Xe at room temperature are calculated. The spectra of scattering consist essentially of an intense, purely translational component which includes scattering due to free pairs and bound dimers, and the other is due to the induced rotational scattering. These spectra have been interpreted by means of pair-polarizability terms, which arise from a long-range dipole-induced-dipole (DID) with small dispersion corrections and a short-range interaction mechanism involving higher-order dipole–quadrupole A and dipole–octopole E multipole polarizabilities. Good agreement between computed and experimental lineshapes of both absorption and scattering is obtained when the models of potential, interaction-induced dipole and polarizability components are used.

doi:10.1016/j.jare.2012.08.013

PMCID: PMC4294793
PMID: 25685458

Intermolecular potential; Absorption; Scattering; CH4–inert gases

A user-friendly open-source Monte Carlo regression package (McSAS) is presented, which aids in the analysis of scattering patterns from uncorrelated, shape-similar scatterers. The Monte Carlo nature necessitates an assumption on the elementary shape of the scatterer, but can resolve the shape-defining parameter distributions without restrictions on the mathematical form of the distribution.

A user-friendly open-source Monte Carlo regression package (McSAS) is presented, which structures the analysis of small-angle scattering (SAS) using uncorrelated shape-similar particles (or scattering contributions). The underdetermined problem is solvable, provided that sufficient external information is available. Based on this, the user picks a scatterer contribution model (or ‘shape’) from a comprehensive library and defines variation intervals of its model parameters. A multitude of scattering contribution models are included, including prolate and oblate nanoparticles, core–shell objects, several polymer models, and a model for densely packed spheres. Most importantly, the form-free Monte Carlo nature of McSAS means it is not necessary to provide further restrictions on the mathematical form of the parameter distribution; without prior knowledge, McSAS is able to extract complex multimodal or odd-shaped parameter distributions from SAS data. When provided with data on an absolute scale with reasonable uncertainty estimates, the software outputs model parameter distributions in absolute volume fraction, and provides the modes of the distribution (e.g. mean, variance etc.). In addition to facilitating the evaluation of (series of) SAS curves, McSAS also helps in assessing the significance of the results through the addition of uncertainty estimates to the result. The McSAS software can be integrated as part of an automated reduction and analysis procedure in laboratory instruments or at synchrotron beamlines.

doi:10.1107/S1600576715007347

PMCID: PMC4453982
PMID: 26089769

small-angle scattering; Monte Carlo; data analysis software; disperse samples

Abstract.

The feasibility of spatial frequency domain imaging (SFDI) for breast surgical margin assessment was evaluated in tissue-simulating phantoms and in fully intact lumpectomy specimens at the time of surgery. Phantom data was evaluated according to contrast-detail resolution, quantitative accuracy and model-data goodness of fit, where optical parameters were estimated by minimizing the residual sum of squares between the measured modulation amplitude and its solutions, modeled according to diffusion and scaled-Monte Carlo simulations. In contrast-detail phantoms, a 1.25-mm-diameter surface inclusion was detectable for scattering contrast >28%; a fraction of this scattering contrast (7%) was detectable for a 10 mm surface inclusion and at least 33% scattering contrast was detected up to 1.5 mm below the phantom surface, a probing depth relevant to breast surgical margin assessment. Recovered hemoglobin concentrations were insensitive to changes in scattering, except for overestimation at visible wavelengths for total hemoglobin concentrations <15 μM. The scattering amplitude increased linearly with scattering concentration, but the scattering slope depended on both the particle size and number density. Goodness of fit was comparable for the diffusion and scaled-Monte Carlo models of transport in spatially modulated, near-infrared reflectance acquired from 47 lumpectomy tissues, but recovered absorption parameters varied more linearly with expected hemoglobin concentration in liquid phantoms for the scaled-Monte Carlo forward model. SFDI could potentially reduce the high secondary excision rate associated with breast conserving surgery; its clinical translation further requires reduced image reconstruction time and smart inking strategies.

doi:10.1117/1.JBO.18.3.036012

PMCID: PMC3605471
PMID: 23525360

spatial frequency domain imaging; modulated imaging, near-infrared spectroscopy; tissue scattering; pathology discrimination; breast conserving surgery; margin assessment

We explore the use of Monte-Carlo-model-based approaches for the analysis of fluorescence and diffuse reflectance spectra measured ex vivo from breast tissues. These models are used to extract the absorption, scattering, and fluorescence properties of malignant and nonmalignant tissues and to diagnose breast cancer based on these intrinsic tissue properties. Absorption and scattering properties, including β-carotene concentration, total hemoglobin concentration, hemoglobin saturation, and the mean reduced scattering coefficient are derived from diffuse reflectance spectra using a previously developed Monte Carlo model of diffuse reflectance. A Monte Carlo model of fluorescence described in an earlier manuscript was employed to retrieve the intrinsic fluorescence spectra. The intrinsic fluorescence spectra were decomposed into several contributing components, which we attribute to endogenous fluorophores that may present in breast tissues including collagen, NADH, and retinol/vitamin A. The model-based approaches removes any dependency on the instrument and probe geometry. The relative fluorescence contributions of individual fluorescing components, as well as β-carotene concentration, hemoglobin saturation, and the mean reduced scattering coefficient display statistically significant differences between malignant and adipose breast tissues. The hemoglobin saturation and the reduced scattering coefficient display statistically significant differences between malignant and fibrous/benign breast tissues. A linear support vector machine classification using (1) fluorescence properties alone, (2) absorption and scattering properties alone, and (3) the combination of all tissue properties achieves comparable classification accuracies of 81 to 84% in sensitivity and 75 to 89% in specificity for discriminating malignant from nonmalignant breast tissues, suggesting each set of tissue properties are diagnostically useful for the discrimination of breast malignancy.

doi:10.1117/1.2931078

PMCID: PMC2791791
PMID: 18601560

fluorescence; diffuse reflectance; spectroscopy; intrinsic fluorescence; optical property; Monte Carlo; breast cancer

Numerous theoretical and experimental efforts have been paid to describe and understand the dislocation and void nucleation processes that are fundamental for dynamic fracture modeling of strained metals. To date an essential physical picture on the self-organized atomic collective motions during dislocation creation, as well as the essential mechanisms for the void nucleation obscured by the extreme diversity in structural configurations around the void nucleation core, is still severely lacking in literature. Here, we depict the origin of dislocation creation and void nucleation during uniaxial high strain rate tensile processes in face-centered-cubic (FCC) ductile metals. We find that the dislocations are created through three distinguished stages: (i) Flattened octahedral structures (FOSs) are randomly activated by thermal fluctuations; (ii) The double-layer defect clusters are formed by self-organized stacking of FOSs on the close-packed plane; (iii) The stacking faults are formed and the Shockley partial dislocations are created from the double-layer defect clusters. Whereas, the void nucleation is shown to follow a two-stage description. We demonstrate that our findings on the origin of dislocation creation and void nucleation are universal for a variety of FCC ductile metals with low stacking fault energies.

doi:10.1038/srep06981

PMCID: PMC4225538
PMID: 25382029

Thermal ablation is a minimally invasive cancer treatment which has been rapidly gaining clinical acceptance. It is well known that thermal ablation increases the acoustic attenuation and shear modulus of tissue. In this work, we examine changes to the spatial distribution of scatterers in liver tissue following thermal ablation. Acoustic scatterers within liver tissue have frequently been modeled as pseudo-periodic. The positions of pseudo-periodic scatterers have been Gamma distributed along the beam dimension, and these scatterers are characterized by their mean scatterer spacing (MSS). Prior work have demonstrated significant changes in MSS due to diffuse liver disease, such as steatosis progressing to cirrhosis. However, relatively few results have been reported regarding changes in MSS following thermal ablation. In this study, we estimated MSS in ex vivo bovine liver by detecting local maxima in spectral coherence functions calculated using Thomson's multi-taper method. We examined a large number of uncorrelated regions of interest recorded from five normal bovine livers (~300 images from each animal). We also examined a large number of ROI's from five bovine livers following thermal coagulation. All bovine livers were obtained from a commercial meat production facility immediately following animal sacrifice and imaged within 12 hours. Thermal coagulation was induced by heating liver in saline water baths at 80° C for 45 minutes. For normal, unheated liver an MSS of approximately 1.5 mm was estimated. Following thermal ablation, an MSS of approximately 0.5 mm in thermally coagulated tissue was obtained. Frequently, studies estimating MSS in liver tissue provide an MSS estimate regardless of the state of tissue. Authors rarely present what their MSS estimation algorithm would produce if it were applied to tissue which is better modeled as a collection of uniformly, randomly distributed scatterers lacking periodicity. In this study, we found that thermal coagulation results in a loss of periodicity. The MSS of 0.5 mm corresponds to the value that a spectral coherence-based MSS algorithm would produce if presented with a signal that was generated from uniform, randomly distributed scatterers.

doi:10.1109/ULTSYM.2014.0473

PMCID: PMC4500940
PMID: 26185596

MSS; thermal ablation; spectral coherence

In this paper, we demonstrate that a scanning MEMS mirror can be employed to create a linear gradient line source that is equivalent to a planar source. This light source setup facilitates the use of diffusion models of increased orders of approximation having closed form solution, and thus enhance the efficiency and accuracy in sample optical properties recovery. In addition, compared with a regular planar light source, the linear gradient line source occupies much less source area and has an elevated measurement efficiency. We employed a δ-P1 diffusion equation with a closed form solution and carried out a phantom study to understand the performance of this new method in determining the absorption and scattering properties of turbid samples. Moreover, our Monte Carlo simulation results indicated that this geometry had probing depths comparable to those of the conventional diffuse reflectance measurement geometry with a source-detector separation of 3 mm. We expect that this new source setup would facilitate the investigating of superficial volumes of turbid samples in the wavelength regions where tissue absorption coefficients are comparable to scattering coefficients.

doi:10.1364/BOE.5.003628

PMCID: PMC4206330
PMID: 25360378

(170.5280) Photon migration; (170.3660) Light propagation in tissues; (170.7050) Turbid media; (170.2945) Illumination design

Amorphous thin-film oxygen evolving catalysts, OECs, of first-row transition metals show promise to serve as self-assembling materials in solar-driven, photoelectrochemical ‘artificial leaf’ devices. This report demonstrates the ability to use high-energy X-ray scattering and atomic pair distribution function analyses, PDF, to resolve structure in amorphous metal oxide catalysts films, and is applied here to resolve domain structure differences induced by oxyanion substitution during the electrochemical assembly of amorphous cobalt oxide catalyst films.

Amorphous thin film oxygen evolving catalysts, OECs, of first-row transition metals show promise to serve as self-assembling photoanode materials in solar-driven, photoelectrochemical ‘artificial leaf’ devices. This report demonstrates the ability to use high-energy X-ray scattering and atomic pair distribution function analysis, PDF, to resolve structure in amorphous metal oxide catalyst films. The analysis is applied here to resolve domain structure differences induced by oxyanion substitution during the electrochemical assembly of amorphous cobalt oxide catalyst films, Co-OEC. PDF patterns for Co-OEC films formed using phosphate, Pi, methylphosphate, MPi, and borate, Bi, electrolyte buffers show that the resulting domains vary in size following the sequence Pi < MPi < Bi. The increases in domain size for CoMPi and CoBi were found to be correlated with increases in the contributions from bilayer and trilayer stacked domains having structures intermediate between those of the LiCoOO and CoO(OH) mineral forms. The lattice structures and offset stacking of adjacent layers in the partially stacked CoMPi and CoBi domains were best matched to those in the LiCoOO layered structure. The results demonstrate the ability of PDF analysis to elucidate features of domain size, structure, defect content and mesoscale organization for amorphous metal oxide catalysts that are not readily accessed by other X-ray techniques. PDF structure analysis is shown to provide a way to characterize domain structures in different forms of amorphous oxide catalysts, and hence provide an opportunity to investigate correlations between domain structure and catalytic activity.

doi:10.1107/S2052520615022180

PMCID: PMC4669998
PMID: 26634728

water-splitting catalysts; amorphous metal oxides; pair distribution function analysis; high-energy X-ray scattering; cobalt oxide

Purpose

Small field-of-view (FOV) dedicated cardiac SPECT systems suffer from truncated projection data. This results in (1) neglect of liver activity that otherwise could be used to estimate (and subsequently correct) the amount of scatter in the myocardium by model-based scatter correction, and (2) distorted attenuation maps. In this study, we investigated to what extent truncation impacts attenuation correction and model-based scatter correction in the cases of 99mTc, 201Tl, and simultaneous 99mTc/201Tl studies. In addition, we evaluated a simple correction method to mitigate the effects of truncation.

Methods

Digital thorax phantoms of different sizes were used to simulate the full FOV SPECT projections for 99mTc, 201Tl, and simultaneous 99mTc/201Tl studies. Small FOV projections were obtained by artificially truncating the full FOV projections. Deviations from ideal heart positioning were simulated by axially shifting projections resulting in more severe liver truncation. Effects of truncation on SPECT images were tested for ordered subset (OS) expectation maximization reconstruction with (1) attenuation correction and detector response modelling (OS-AD), and (2) with additional Monte-Carlo-based scatter correction (OS-ADS). To correct truncation-induced artefacts, we axially extended truncated projections on both sides by duplicating pixel values on the projection edge.

Results

For both 99mTc and 201Tl, differences in the reconstructed myocardium between full FOV and small FOV projections were negligible. In the nine myocardial segments, the maximum deviations of the average pixel values were 1.3% for OS-AD and 3.5% for OS-ADS. For the simultaneous 99mTc/201Tl studies, reconstructed 201Tl SPECT images from full FOV and small FOV projections showed clearly different image profiles due to truncation. The maximum deviation in defected segments was found to be 49% in the worst-case scenario. However, artificially extending projections reduced deviations in defected segments to a few percent.

Conclusion

Our results indicate that, for single isotope studies, using small FOV systems has little impact on attenuation correction and model-based scatter correction. For simultaneous 99mTc/201Tl studies, artificial projection extension almost fully eliminates the adverse effects of projection truncation.

doi:10.1007/s00259-009-1223-9

PMCID: PMC2822234
PMID: 19722106

Cardiac SPECT; Truncation; Attenuation correction; Scatter correction; Small field-of-view

We describe a technique that uses spatially modulated near-infrared (NIR) illumination to detect and map changes in both optical properties (absorption and reduced scattering parameters) and tissue composition (oxy- and deoxyhemoglobin, total hemoglobin, and oxygen saturation) during acute ischemic injury in the rat barrel cortex. Cerebral ischemia is induced using an open vascular occlusion technique of the middle cerebral artery (MCA). Diffuse reflected NIR light (680 to 980 nm) from the left parietal somatosensory cortex is detected by a CCD camera before and after MCA occlusion. Monte Carlo simulations are used to analyze the spatial frequency dependence of the reflected light to predict spatiotemporal changes in the distribution of tissue absorption and scattering properties in the brain. Experimental results from seven rats show a 17±4.7% increase in tissue concentration of deoxyhemoglobin and a 45±3.1, 23±5.4, and 21±2.2% decrease in oxyhemoglobin, total hemoglobin concentration and cerebral tissue oxygen saturation levels, respectively, 45 min following induction of cerebral ischemia. An ischemic index (Iisch=ctHHb/ctO2Hb) reveals an average of more then twofold contrast after MCAo. The wavelength-dependence of the reduced scattering (i.e., scatter power) decreased by 35±10.3% after MCA occlusion. Compared to conventional CCD-based intrinsic signal optical imaging (ISOI), the use of structured illumination and model-based analysis allows for generation of separate maps of light absorption and scattering properties as well as tissue hemoglobin concentration. This potentially provides a powerful approach for quantitative monitoring and imaging of neurophysiology and metabolism with high spatiotemporal resolution.

doi:10.1117/1.3116709

PMCID: PMC2868516
PMID: 19405762

stroke; brain ischemia; structured light; tissue optical properties; diffuse optical imaging; cerebral hemodynamics

Stacking fault tetrahedra (SFTs) are ubiquitous defects in face-centered cubic metals. They are produced during cold work plastic deformation, quenching experiments or under irradiation. From a dislocation point of view, the SFTs are comprised of a set of stair-rod dislocations at the (110) edges of a tetrahedron bounding triangular stacking faults. These defects are extremely stable, increasing their energetic stability as they grow in size. At the sizes visible within transmission electron microscope they appear nearly immobile. Contrary to common belief, we show in this report, using a combination of molecular dynamics and temperature accelerated dynamics, how small SFTs can diffuse by temporarily disrupting their structure through activated thermal events. More over, we demonstrate that the diffusivity of defective SFTs is several orders of magnitude higher than perfect SFTs, and can be even higher than isolated vacancies. Finally, we show how SFTs can coalesce, forming a larger defect in what is a new mechanism for the growth of these omnipresent defects.

doi:10.1038/srep09084

PMCID: PMC4357870
PMID: 25765711

Background

The bioluminescent enzyme firefly luciferase (Luc) or variants of green fluorescent protein (GFP) in transformed cells can be effectively used to reveal molecular and cellular features of neoplasia in vivo. Tumor cell growth and regression in response to various therapies can be evaluated by using bioluminescent imaging. In bioluminescent imaging, light propagates in highly scattering tissue, and the diffusion approximation is sufficiently accurate to predict the imaging signal around the biological tissue. The numerical solutions to the diffusion equation take large amounts of computational time, and the studies for its analytic solutions have attracted more attention in biomedical engineering applications.

Methods

Biological tissue is a turbid medium that both scatters and absorbs photons. An accurate model for the propagation of photons through tissue can be adopted from transport theory, and its diffusion approximation is applied to predict the imaging signal around the biological tissue. The solution to the diffusion equation is formulated by the convolution between its Green's function and source term. The formulation of photon diffusion from spherical bioluminescent sources in an infinite homogeneous medium can be obtained to accelerate the forward simulation of bioluminescent phenomena.

Results

The closed form solutions have been derived for the time-dependent diffusion equation and the steady-state diffusion equation with solid and hollow spherical sources in a homogeneous medium, respectively. Meanwhile, the relationship between solutions with a solid sphere source and ones with a surface sphere source is obtained.

Conclusion

We have formulated solutions for the diffusion equation with solid and hollow spherical sources in an infinite homogeneous medium. These solutions have been verified by Monte Carlo simulation for use in biomedical optical imaging studies. The closed form solution is highly accurate and more computationally efficient in biomedical engineering applications. By using our analytic solutions for spherical sources, we can better predict bioluminescent signals and better understand both the potential for, and the limitations of, bioluminescent tomography in an idealized case. The formulas are particularly valuable for furthering the development of bioluminescent tomography.

doi:10.1186/1475-925X-3-12

PMCID: PMC421737
PMID: 15125780

Diffusion equation; Green's function; analytical solution; Monte Carlo simulation; bioluminescent imaging

X-ray scattering features induced by aggregates of alamethicin (Alm) were obtained in oriented stacks of model membranes of DOPC(diC18:1PC) and diC22:1PC. The first feature obtained near full hydration was Bragg rod in-plane scattering near 0.11 Å-1 in DOPC and near 0.08 Å-1 in diC22:1PC at 1:10 Alm:lipid ratio. This feature is interpreted as bundles consisting of N Alm monomers in a barrel-stave configuration surrounding a water pore. Fitting the scattering data to previously published MD simulations indicates that the number N of peptides per bundle is N=6 in DOPC and N≥9 in diC22:1PC. The larger bundle size in diC22:1PC is explained by hydrophobic mismatch of Alm with the thicker bilayer. A second diffuse scattering peak located at qr≈0.7 Å-1 is obtained for both DOPC and diC22:1PC at several peptide concentrations. Theoretical calculations indicate that this peak can not be caused by the Alm bundle structure. Instead, we interpret it as due to two-dimensional hexagonally packed clusters in equilibrium with Alm bundles. As the relative humidity was reduced, interactions between Alm in neighboring bilayers produced more peaks with three dimensional crystallographic character that do not index with the conventional hexagonal space groups.

doi:10.1007/s00232-009-9199-8

PMCID: PMC2813886
PMID: 19789905

alamethicin; aggregation; hydrophobic mismatch; water pore; helix bundle; ion channel

We recently introduced a method to tether intact phospholipid vesicles onto a fluid supported lipid bilayer using DNA hybridization (Yoshina-Ishii, C.; Miller, G. P.; Kraft, M. L; Kool, E. T.; Boxer, S. G. J. Am. Chem. Soc. 2005, 127, 1356–1357). Once tethered, the vesicles can diffuse in two dimensions parallel to the supported membrane surface. The average diffusion coefficient, D, is typically 0.2 μm2/s; this is 3–5 times smaller than individual lipid or DNA-lipid conjugate diffusion in supported bilayers. In this paper, we investigate the origin of this difference in the diffusive dynamics of tethered vesicles by single particle tracking under collision-free conditions. D is insensitive to tethered vesicle size from 30 to 200 nm, as well as a 3 -fold change in viscosity of the bulk medium. Addition of macromolecules such as poly(ethylene glycol) reversibly stops the motion of tethered vesicles without causing the exchange of lipids between the tethered vesicle and supported bilayer. This is explained as a depletion effect at the interface between tethered vesicles and the supported bilayer. Ca ions lead to transient vesicle-vesicle interactions when tethered vesicles contain negatively charged lipids, and vesicle diffusion is greatly reduced upon Ca ion addition when negatively charged lipids are present both in the supported bilayer and tethered vesicles. Both effects are interesting in their own rights, and they also suggest that tethered vesicle-supported bilayer interactions are possible; this may be the origin of the reduction in D for tethered vesicles. In addition, the effects of surface defects which reversibly trap diffusing vesicles, are modeled by Monte Carlo simulations. This shows that a significant reduction in D can be observed while maintaining normal diffusion behavior in the timescale of our experiments.

doi:10.1021/la0534219

PMCID: PMC2527860
PMID: 16768494

Laser Speckle Imaging (LSI) is a simple, noninvasive technique for rapid imaging of particle motion in scattering media such as biological tissue. LSI is generally used to derive a qualitative index of relative blood flow due to unknown impact from several variables that affect speckle contrast. These variables may include optical absorption and scattering coefficients, multi-layer dynamics including static, non-ergodic regions, and systematic effects such as laser coherence length. In order to account for these effects and move toward quantitative, depth-resolved LSI, we have developed a method that combines Monte Carlo modeling, multi-exposure speckle imaging (MESI), spatial frequency domain imaging (SFDI), and careful instrument calibration. Monte Carlo models were used to generate total and layer-specific fractional momentum transfer distributions. This information was used to predict speckle contrast as a function of exposure time, spatial frequency, layer thickness, and layer dynamics. To verify with experimental data, controlled phantom experiments with characteristic tissue optical properties were performed using a structured light speckle imaging system. Three main geometries were explored: 1) diffusive dynamic layer beneath a static layer, 2) static layer beneath a diffuse dynamic layer, and 3) directed flow (tube) submerged in a dynamic scattering layer. Data fits were performed using the Monte Carlo model, which accurately reconstructed the type of particle flow (diffusive or directed) in each layer, the layer thickness, and absolute flow speeds to within 15% or better.

doi:10.1364/BOE.4.002880

PMCID: PMC3862160
PMID: 24409388

(110.6150) Speckle imaging; (170.3660) Light propagation in tissues

Representational analysis is used to characterize correlated short-range order in large atomistic ensembles. This method, analogous to tight-binding methods, enables the extraction of relevant structural parameters in an orthogonal and local basis that permits robust statistical analysis of crystalline disorder.

With the increased availability of high-intensity time-of-flight neutron and synchrotron X-ray scattering sources that can access wide ranges of momentum transfer, the pair distribution function method has become a standard analysis technique for studying disorder of local coordination spheres and at intermediate atomic separations. In some cases, rational modeling of the total scattering data (Bragg and diffuse) becomes intractable with least-squares approaches, necessitating reverse Monte Carlo simulations using large atomistic ensembles. However, the extraction of meaningful information from the resulting atomistic ensembles is challenging, especially at intermediate length scales. Representational analysis is used here to describe the displacements of atoms in reverse Monte Carlo ensembles from an ideal crystallographic structure in an approach analogous to tight-binding methods. Rewriting the displacements in terms of a local basis that is descriptive of the ideal crystallographic symmetry provides a robust approach to characterizing medium-range order (and disorder) and symmetry breaking in complex and disordered crystalline materials. This method enables the extraction of statistically relevant displacement modes (orientation, amplitude and distribution) of the crystalline disorder and provides directly meaningful information in a locally symmetry-adapted basis set that is most descriptive of the crystal chemistry and physics.

doi:10.1107/S1600576715016404

PMCID: PMC4603272
PMID: 26500465

extended disorder; atomistic ensembles; modeling; pair distribution function analysis

A method of simulating X-ray diffuse scattering from multi-model PDB files is presented. Despite similar agreement with Bragg data, different translation–libration–screw refinement strategies produce unique diffuse intensity patterns.

Identifying the intramolecular motions of proteins and nucleic acids is a major challenge in macromolecular X-ray crystallography. Because Bragg diffraction describes the average positional distribution of crystalline atoms with imperfect precision, the resulting electron density can be compatible with multiple models of motion. Diffuse X-ray scattering can reduce this degeneracy by reporting on correlated atomic displacements. Although recent technological advances are increasing the potential to accurately measure diffuse scattering, computational modeling and validation tools are still needed to quantify the agreement between experimental data and different parameterizations of crystalline disorder. A new tool, phenix.diffuse, addresses this need by employing Guinier’s equation to calculate diffuse scattering from Protein Data Bank (PDB)-formatted structural ensembles. As an example case, phenix.diffuse is applied to translation–libration–screw (TLS) refinement, which models rigid-body displacement for segments of the macromolecule. To enable the calculation of diffuse scattering from TLS-refined structures, phenix.tls_as_xyz builds multi-model PDB files that sample the underlying T, L and S tensors. In the glycerophosphodiesterase GpdQ, alternative TLS-group partitioning and different motional correlations between groups yield markedly dissimilar diffuse scattering maps with distinct implications for molecular mechanism and allostery. These methods demonstrate how, in principle, X-ray diffuse scattering could extend macromolecular structural refinement, validation and analysis.

doi:10.1107/S1399004715007415

PMCID: PMC4528799
PMID: 26249347

diffuse scattering; TLS; correlated motion; structural ensemble; structure refinement

Fully hydrated stacks of DOPC lipid bilayer membranes generate large diffuse x-ray scattering that corrupts the Bragg peak intensities that are used in conventional biophysical structural analysis, but the diffuse scattering actually contains more information. Using an efficient algorithm for fitting extensive regions of diffuse data to classical smectic liquid crystalline theory we first obtain the compressional modulus B=1013 erg/cm4, which involves interactions between membranes, and the bending modulus Kc=8×10−13 erg of the membranes. The membrane form factor F(qz) is then obtained for most values of qz up to 0.8 Å−1. The electron density profile ρ(z) is obtained by fitting models to F(qz). Constraining the models to conform to other measurements provides structural quantities such as area A=72.1±0.5 Å2 per lipid at the interface.

PMCID: PMC2761748
PMID: 15169001

87.14.Cc; 61.30.Cz; 87.16.Dg; 87.64.Bx

High-resolution small-angle X-ray scattering (SAXS), complemented by small-angle neutron scattering (SANS) and dynamic light scattering (DLS) experiments, was used to study the effect of curvature on the bilayer structure of dioleoyl-phosphatidylcholine (DOPC) and dioleoyl-phosphatidylserine (DOPS) unilamellar vesicles (ULVs). Bilayer curvature, as a result of finite vesicle size, was varied as a function of vesicle radius and determined by DLS and SANS measurements. Unilamellarity of large DOPC ULVs was achieved by the addition of small amounts (up to 4 mol %) of the charged lipid, DOPS. A comparison of SANS data over the range of 0.02 < q <0.2 Å−1 indicated no change in the overall bilayer thickness as a function of ULV diameter (620 to 1840 Å). SANS data were corroborated by high-resolution (0.06 < q <0.6 Å−1) SAXS data for the same diameter ULVs and data obtained from planar samples of aligned bilayers. Both the inner and outer leaflets of the bilayer were found to be indistinguishable. This observation agrees well with simple geometric models describing the effect of vesicle curvature. However, 1220-Å-diameter pure DOPS ULVs form asymmetric bilayers whose structure can most likely be rationalized in terms of geometrical constraints coupled with electrostatic interactions, rather than curvature alone.

doi:10.1021/la062455t

PMCID: PMC2720570
PMID: 17241048

A new method for reconstruction of the interatomic distance distribution, P(r), directly from two-dimensional detector images of solution scattering data is developed and tested. This method employs Bayesian inference and a Markov chain Monte Carlo method to simultaneously estimate indirect transform coefficients and beam and detector parameters, while also evaluating the covariance among all parameters.

The interatomic distance distribution, P(r), is a valuable tool for evaluating the structure of a molecule in solution and represents the maximum structural information that can be derived from solution scattering data without further assumptions. Most current instrumentation for scattering experiments (typically CCD detectors) generates a finely pixelated two-dimensional image. In continuation of the standard practice with earlier one-dimensional detectors, these images are typically reduced to a one-dimensional profile of scattering intensities, I(q), by circular averaging of the two-dimensional image. Indirect Fourier transformation methods are then used to reconstruct P(r) from I(q). Substantial advantages in data analysis, however, could be achieved by directly estimating the P(r) curve from the two-dimensional images. This article describes a Bayesian framework, using a Markov chain Monte Carlo method, for estimating the parameters of the indirect transform, and thus P(r), directly from the two-dimensional images. Using simulated detector images, it is demonstrated that this method yields P(r) curves nearly identical to the reference P(r). Furthermore, an approach for evaluating spatially correlated errors (such as those that arise from a detector point spread function) is evaluated. Accounting for these errors further improves the precision of the P(r) estimation. Experimental scattering data, where no ground truth reference P(r) is available, are used to demonstrate that this method yields a scattering and detector model that more closely reflects the two-dimensional data, as judged by smaller residuals in cross-validation, than P(r) obtained by indirect transformation of a one-dimensional profile. Finally, the method allows concurrent estimation of the beam center and D
max, the longest interatomic distance in P(r), as part of the Bayesian Markov chain Monte Carlo method, reducing experimental effort and providing a well defined protocol for these parameters while also allowing estimation of the covariance among all parameters. This method provides parameter estimates of greater precision from the experimental data. The observed improvement in precision for the traditionally problematic D
max is particularly noticeable.

doi:10.1107/S002188981300109X

PMCID: PMC3627411
PMID: 23596342

structure analysis; small-angle X-ray scattering; small-angle neutron scattering; Bayesian inference; Markov chain Monte Carlo methods