# 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

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

Intermolecular potential; Absorption; Scattering; CH4–inert gases

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

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

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

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

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

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

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

Since scattered photons carry degraded spatial information, scatter is typically considered a source of contamination in SPECT. However, with the advent of scatter modeling methods and reconstruction-based scatter compensation (RBSC), it may be possible to utilize scattered data in a productive manner. In this work we analyze the reconstructibility of scattered photon projection data and investigate the potential for using scattered photons to reduce the noise levels of SPECT images. We have simulated projection data for an elliptical phantom containing three cold rods in a uniform background of Tc-99m activity. A variety of photopeak and scatter energy windows were formed, as well as corresponding RBSC transfer matrices. Each statistically weighted matrix was decomposed using SVD and analyzed in terms of reconstructibility and noise properties. Results indicate that scattered photons contain sufficient information to reconstruct the source activity, but the scatter-only matrices are very poorly conditioned. We have also evaluated several methods of utilizing scattered events via RBSC, and compared them with other, idealized methods of handling scatter. It was found that scattered photons can be used productively when photopeak and non-photopeak data are separated through the use of multiple energy windows. The RBSC methods outperformed ideal scatter subtraction, but fell short of methods which assume perfect discrimination between scattered and primary events. The knowledge gained by this study may help guide future research and lead to better approaches to handling scatter in SPECT.

PMCID: PMC2804957
PMID: 9434303

The physical properties of nanostructures strongly depend on their structures, and planar defects in particular could significantly affect the behavior of the nanowires. In this work, planar defects (twins or stacking faults) in boron carbide nanowires are extensively studied by transmission electron microscopy (TEM). Results show that these defects can easily be invisible, i.e., no presence of characteristic defect features like modulated contrast in high-resolution TEM images and streaks in diffraction patterns. The simplified reason of this invisibility is that the viewing direction during TEM examination is not parallel to the (001)-type planar defects. Due to the unique rhombohedral structure of boron carbide, planar defects are only distinctive when the viewing direction is along the axial or short diagonal directions ([100], [010], or 1¯10) within the (001) plane (in-zone condition). However, in most cases, these three characteristic directions are not parallel to the viewing direction when boron carbide nanowires are randomly dispersed on TEM grids. To identify fault orientations (transverse faults or axial faults) of those nanowires whose planar defects are not revealed by TEM, a new approach is developed based on the geometrical analysis between the projected preferred growth direction of a nanowire and specific diffraction spots from diffraction patterns recorded along the axial or short diagonal directions out of the (001) plane (off-zone condition). The approach greatly alleviates tedious TEM examination of the nanowire and helps to establish the reliable structure–property relations. Our study calls attention to researchers to be extremely careful when studying nanowires with potential planar defects by TEM. Understanding the true nature of planar defects is essential in tuning the properties of these nanostructures through manipulating their structures.

doi:10.1186/1556-276X-9-30

PMCID: PMC3898527
PMID: 24423258

Boron carbide nanowires; Rhombohedral crystal system; Transmission electron microscopy; Planar defects

Accurate scatter compensation in SPECT can be performed by modeling the scatter response function during the reconstruction process. This method is called reconstruction-based scatter compensation (RBSC). It has been shown that RBSC has a number of advantages over other methods of compensating for scatter, but using RBSC for fully 3D compensation has resulted in prohibitively long reconstruction times. In this work we propose two new methods that can be used in conjunction with existing methods to achieve marked reductions in RBSC reconstruction times. The first method, Coarse-Grid Scatter Modeling, significantly accelerates the scatter model by exploiting the fact that scatter is dominated by low frequency information. The second method, Intermittent RBSC, further accelerates the reconstruction process by limiting the number of iterations during which scatter is modeled. The fast implementations were evaluated using a Monte Carlo simulated experiment of the 3D MCAT phantom with Tc-99m tracer, and also using experimentally acquired data with Tl-201 tracer. Results indicated that these fast methods can reconstruct, with fully 3D compensation, images very similar to those obtained using conventional RBSC methods, and in reconstruction times that are an order of magnitude shorter. Using these methods, fully 3D iterative reconstruction with RBSC can be performed well within the realm of clinically realistic times (under 10 minutes for 64 × 64 × 24 image reconstruction).

PMCID: PMC2808130
PMID: 9572510

Spillover from adjacent significant accumulations of extra-cardiac activity decreases diagnostic accuracy of SPECT perfusion imaging in especially the inferior/septal cardiac region. One method of compensating for the spillover at some location outside of a structure is to estimate it as the counts blurred into this location when a template (3D model) of the structure undergoes simulated imaging followed by reconstruction. The objective of this study was to determine what impact uncorrected respiratory motion has on such spillover compensation of extra-cardiac activity in the right coronary artery (RCA) territory, and if it is possible to use manual segmentation to define the extra-cardiac activity template(s) used in spillover correction. Two separate MCAT phantoms (1283 matrices) were simulated to represent the source and attenuation distributions of patients with and without respiratory motion. For each phantom the heart was modeled: 1) with a normal perfusion pattern and 2) with an RCA defect equal to 50% of the normal myocardium count level. After Monte Carlo simulation of 64 × 64 × 120 projections with appropriate noise, data were reconstructed using the rescaled block iterative (RBI) algorithm with 30 subsets and 5 iterations with compensation for attenuation, scatter and resolution. A 3D Gaussian post-filter with a sigma of 0.476 cm was used to suppress noise. Manual segmentation of the liver in filtered emission slices was used to create 3D binary templates. The true liver distribution (with and without respiratory motion included) was also used as binary templates. These templates were projected using a ray-driven projector simulating the imaging system with the exclusion of Compton scatter and reconstructed using the same protocol as for the emission data, excluding scatter compensation. Reconstructed templates were scaled using reconstructed emission count levels from the liver, and spillover subtracted outside the template. It was evident from the polar maps that the manually segmented template reconstructions were unable to remove all the spillover originating in the liver from the inferior wall. This was especially noticeable when a perfusion defect is present. Templates based on the true liver distribution appreciably improved spillover correction. Thus the emerging combined SPECT/CT technology may play a vital role in identifying and segmenting extra-cardiac structures more reliably thereby facilitating spillover correction. This study also indicates that compensation for respiratory motion might play an important role in spillover compensation.

doi:10.1109/TNS.2007.912874

PMCID: PMC2774930
PMID: 19907675

Cardiac SPECT; partial volume; respiratory motion; spillover compensation

Kaoud, Tamer S. | Devkota, Ashwini K. | Harris, Richard | Rana, Mitra S. | Abramczyk, Olga | Warthaka, Mangalika | Lee, Sunbae | Girvin, Mark E. | Riggs, Austen F. | Dalby, Kevin N.
The extracellular signal-regulated protein kinase, ERK2, fully activated by phosphorylation and without a His6-tag, shows little tendency to dimerize with or without either calcium or magnesium ions when analyzed by light scattering or analytical ultracentrifugation. Light scattering shows that ~ 90% of ERK2 is monomeric. Sedimentation equilibrium data (obtained at 4.8–11.2 μM ERK2) with or without magnesium (10 mM) are well described by an ideal one-component model with a fitted molar mass of 40,180 ± 240 Da (- Mg2+ ions) and 41,290 ± 330 Da (+ Mg2+ ions). These values, close to the sequence-derived mass of 41,711 Da, indicate that no significant dimerization of ERK2 occurs in solution. Analysis of sedimentation velocity data for a 15 μM solution of ERK2 with an enhanced van Holde-Weischet method determined the sedimentation coefficient (s) to be ~ 3.22 S for activated ERK2 with or without 10 mM MgCl2. The frictional coefficient ratio (f/f0) of 1.28 calculated from the sedimentation velocity and equilibrium data is close to that expected for a globular protein of ~ 42 kDa. The translational diffusion coefficient of ~ 8.3 × 10-7 cm2s-1 calculated from the experimentally determined molar mass and sedimentation coefficient agrees with the value determined by dynamic light scattering in the absence and presence of calcium or magnesium ions and a value determined by NMR spectrometry. ERK2 has been proposed to homodimerize and bind only to cytoplasmic but not nuclear proteins. Our light scattering data show, however, that ERK2 forms a strong 1:1 complex of ~ 57 kDa with the cytoplasmic scaffold protein PEA-15. Thus ERK2 binds PEA-15 as a monomer. Our data provide strong evidence that ERK2 is monomeric under physiological conditions. Analysis of the same ERK2 construct with the non-physiological His6-Tag shows substantial dimerization under the same ionic conditions.

doi:10.1021/bi200202y

PMCID: PMC3401516
PMID: 21506533

Light scattering during optical imaging of electrical activation within the heart is known to significantly distort the optically-recorded action potential (AP) upstroke, as well as affecting the magnitude of the measured response of ventricular tissue to strong electric shocks. Modeling approaches based on the photon diffusion equation have recently been instrumental in quantifying and helping to understand the origin of the resulting distortion. However, they are unable to faithfully represent regions of non-scattering media, such as small cavities within the myocardium which are filled with perfusate during experiments. Stochastic Monte Carlo (MC) approaches allow simulation and tracking of individual photon “packets” as they propagate through tissue with differing scattering properties. Here, we present a novel application of the MC method of photon scattering simulation, applied for the first time to the simulation of cardiac optical mapping signals within unstructured, tetrahedral, finite element computational ventricular models. The method faithfully allows simulation of optical signals over highly-detailed, anatomically-complex MR-based models, including representations of fine-scale anatomy and intramural cavities. We show that optical action potential upstroke is prolonged close to large subepicardial vessels than further away from vessels, at times having a distinct “humped” morphology. Furthermore, we uncover a novel mechanism by which photon scattering effects around vessels cavities interact with “virtual-electrode” regions of strong de-/hyper-polarized tissue surrounding cavities during shocks, significantly reducing the apparent optically-measured epicardial polarization. We therefore demonstrate the importance of this novel optical mapping simulation approach along with highly anatomically-detailed models to fully investigate electrophysiological phenomena driven by fine-scale structural heterogeneity.

doi:10.3389/fphys.2014.00338

PMCID: PMC4164003
PMID: 25309442

optical mapping; photon scattering; cardiac modeling; Monte Carlo; bidomain

Digital tomosynthesis of the breast is being investigated as one possible solution to the problem of tissue superposition present in planar mammography. This imaging technique presents various advantages that would make it a feasible replacement for planar mammography, among them similar, if not lower, radiation glandular dose to the breast; implementation on conventional digital mammography technology via relatively simple modifications; and fast acquisition time. One significant problem that tomosynthesis of the breast must overcome, however, is the reduction of x-ray scatter inclusion in the projection images. In tomosynthesis, due to the projection geometry and radiation dose considerations, the use of an antiscatter grid presents several challenges. Therefore, the use of postacquisition software-based scatter reduction algorithms seems well justified, requiring a comprehensive evaluation of x-ray scatter content in the tomosynthesis projections. This study aims to gain insight into the behavior of x-ray scatter in tomosynthesis by characterizing the scatter point spread functions (PSFs) and the scatter to primary ratio (SPR) maps found in tomosynthesis of the breast. This characterization was performed using Monte Carlo simulations, based on the Geant4 toolkit, that simulate the conditions present in a digital tomosynthesis system, including the simulation of the compressed breast in both the cranio-caudal (CC) and the medio-lateral oblique (MLO) views. The variation of the scatter PSF with varying tomosynthesis projection angle, as well as the effects of varying breast glandular fraction and x-ray spectrum, was analyzed. The behavior of the SPR for different projection angle, breast size, thickness, glandular fraction, and x-ray spectrum was also analyzed, and computer fit equations for the magnitude of the SPR at the center of mass for both the CC and the MLO views were found. Within mammographic energies, the x-ray spectrum was found to have no appreciable effect on the scatter PSF and on the SPR. Glandular fraction and compressed breast size were found to have a small effect, while compressed breast thickness and projection angle, as expected, introduced large variations in both the scatter PSF and SPR. The presence of the breast support plate and the detector cover plate in the simulations introduced important effects on the SPR, which are also relevant to the scatter content in planar mammography.

PMCID: PMC4280187
PMID: 17388174

tomosynthesis; digital mammography; scatter; breast; Monte Carlo

With the widespread use of PET crystals with greatly improved energy resolution (e.g., 11.5% with LYSO as compared to 20% with BGO) and of list-mode acquisitions, the use of the energy of individual events in scatter correction schemes becomes feasible. We propose a novel scatter approach that incorporates the energy of individual photons in the scatter correction and reconstruction of list-mode PET data in addition to the spatial information presently used in clinical scanners. First, we rewrite the Poisson likelihood function of list-mode PET data including the energy distributions of primary and scatter coincidences and show that this expression yields an MLEM reconstruction algorithm containing both energy and spatial dependent corrections. To estimate the spatial distribution of scatter coincidences we use the single scatter simulation (SSS). Next, we derive two new formulae which allow estimation of the 2D (coincidences) energy probability density functions (E-PDF) of primary and scatter coincidences from the 1D (photons) E-PDFs associated with each photon. We also describe an accurate and robust object-specific method for estimating these 1D E-PDFs based on a decomposition of the total energy spectra detected across the scanner into primary and scattered components. Finally, we show that the energy information can be used to accurately normalize the scatter sinogram to the data. We compared the performance of this novel scatter correction incorporating both the position and energy of detected coincidences to that of the traditional approach modeling only the spatial distribution of scatter coincidences in 3D Monte Carlo simulations of a medium cylindrical phantom and a large, non uniform NCAT phantom. Incorporating the energy information in the scatter correction decreased bias in the activity distribution estimation by ~20% and ~40% in the cold regions of the large NCAT phantom at energy resolutions 11.5 and 20% at 511 keV, respectively, compared to when using the spatial information alone.

doi:10.1109/TMI.2010.2095025

PMCID: PMC3120772
PMID: 21118770

absolute quantification; energy information; fully 3D reconstruction; list-mode PET data; scatter correction

High resolution X-ray diffraction
data on forms I–IV of
sulfathiazole and neutron diffraction data on forms II–IV have
been collected at 100 K and analyzed using the Atoms in Molecules
topological approach. The molecular thermal motion as judged by the
anisotropic displacement parameters (adp’s) is very similar
in all four forms. The adp of the thiazole sulfur atom had the greatest
amplitude perpendicular to the five-membered ring, and analysis of
the temperature dependence of the adps indicates that this is due
to genuine thermal motion rather than a concealed disorder. A minor
disorder (∼1–2%) is evident for forms I and II, but
a statistical analysis reveals no deleterious effect on the derived
multipole populations. The topological analysis reveals an intramolecular
S–O···S interaction, which is consistently present
in all experimental topologies. Analysis of the gas-phase conformation
of the molecule indicates two low-energy theoretical conformers, one
of which possesses the same intramolecular S–O···S
interaction observed in the experimental studies and the other an
S–O···H–N intermolecular interaction.
These two interactions appear responsible for “locking”
the molecular conformation. The lattice energies of the various polymorphs
computed from the experimental multipole populations are highly dependent
on the exact refinement model. They are similar in magnitude to theoretically
derived lattice energies, but the relatively high estimated errors
mean that this method is insufficiently accurate to allow a definitive
stability order for the sulfathiazole polymorphs at 0 K to be determined.

High resolution X-ray diffraction data on sulfathiazole
(forms I−IV) and neutron diffraction data have been used to
analyze the polymorphic electron density using Quantum Theory of Atoms
in Molecules. Two low-energy theoretical conformers are found in the
gas phase, one of which possesses an S−O···S
interaction (a) and the other an S−O···H−N
(b) intermolecular interaction. These interactions appear responsible
for “locking” the molecular conformation.

doi:10.1021/cg401757z

PMCID: PMC3963452
PMID: 24672285