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1.  A look inside epitaxial cobalt-on-fluorite nanoparticles with three-dimensional reciprocal space mapping using GIXD, RHEED and GISAXS 
Journal of Applied Crystallography  2013;46(Pt 4):874-881.
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
2.  Characterization of Scatter and Penetration Using Monte Carlo Simulation in 131I Imaging 
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
3.  Diagnosis of breast cancer using fluorescence and diffuse reflectance spectroscopy: a Monte-Carlo-model-based approach 
Journal of biomedical optics  2008;13(3):034015.
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
4.  Small field-of-view dedicated cardiac SPECT systems: impact of projection truncation 
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
5.  Imaging cortical absorption, scattering, and hemodynamic response during ischemic stroke using spatially modulated near-infrared illumination 
Journal of biomedical optics  2009;14(2):024033.
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
6.  Formulation of photon diffusion from spherical bioluminescent sources in an infinite homogeneous medium 
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
7.  Alamethicin aggregation in lipid membranes 
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
8.  Quantitative, depth-resolved determination of particle motion using multi-exposure, spatial frequency domain laser speckle imaging 
Biomedical Optics Express  2013;4(12):2880-2892.
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
9.  Diffusive Dynamics of Vesicles Tethered to a Fluid Supported Bilayer by Single Particle Tracking 
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
10.  Diffuse scattering provides material parameters and electron density profiles of biomembranes 
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
11.  Curvature Effect on the Structure of Phospholipid Bilayers 
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
12.  Bayesian reconstruction of P(r) directly from two-dimensional detector images via a Markov chain Monte Carlo method 
Journal of Applied Crystallography  2013;46(Pt 2):404-414.
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
13.  Observation of ‘hidden’ planar defects in boron carbide nanowires and identification of their orientations 
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
14.  Analysis of the Reconstructibility and Noise Properties of Scattered Photons in Tc-99m SPECT 
Physics in medicine and biology  1997;42(12):2493-2516.
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
15.  Fast Implementations of Reconstruction-Based Scatter Compensation in Fully 3D SPECT Image Reconstruction 
Physics in medicine and biology  1998;43(4):857-873.
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
16.  Spillover Compensation in the Presence of Respiratory Motion Embedded in SPECT Perfusion Data 
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
17.  Activated ERK2 is a Monomer in vitro with or without Divalent Cations and when Complexed to the Cytoplasmic Scaffold PEA15 
Biochemistry  2011;50(21):4568-4578.
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
18.  Novel scatter compensation of list-mode PET data using spatial and energy dependent corrections 
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
19.  Experimental Electron Density and Neutron Diffraction Studies on the Polymorphs of Sulfathiazole 
Crystal Growth & Design  2014;14(3):1227-1239.
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
20.  Interactions between Ether Phospholipids and Cholesterol as Determined by Scattering and Molecular Dynamics Simulations 
The journal of physical chemistry. B  2012;116(51):14829-14838.
Cholesterol and ether lipids are ubiquitous in mammalian cell membranes, and their interactions are crucial in ether lipid mediated cholesterol trafficking. We report on cholesterol’s molecular interactions with ether lipids as determined using a combination of small-angle neutron and X-ray scattering, and all-atom molecular dynamics (MD) simulations. A scattering density profile model for an ether lipid bilayer was developed using MD simulations, which was then used to simultaneously fit the different experimental scattering data. From the analysis of the data the various bilayer structural parameters were obtained. Surface area constrained MD simulations were also performed to reproduce the experimental data. This iterative analysis approach resulted in good agreement between the experimental and simulated form factors. The molecular interactions taking place between cholesterol and ether lipids were then determined from the validated MD simulations. We found that in ether membranes, cholesterol primarily hydrogen bonds with the lipid headgroup phosphate oxygen, while in their ester membrane counterparts, cholesterol hydrogen bonds with the backbone ester carbonyls. This different mode of interaction between ether lipids and cholesterol induces cholesterol to reside closer to the bilayer surface, dehydrating the headgroup’s phosphate moiety. Moreover, the three-dimensional lipid chain spatial density distribution around cholesterol indicates anisotropic chain packing, causing cholesterol to tilt. These insights lend a better understanding of ether lipid mediated cholesterol trafficking and the roles that the different lipid species have in determining the structural and dynamical properties of membrane associated biomolecules.
doi:10.1021/jp310345j
PMCID: PMC3539752  PMID: 23199292
lipid bilayer; lipid area; bilayer thickness; ether linkage; spatial density distribution; hydrogen bonding
21.  Improvements and considerations for size distribution retrieval from small-angle scattering data by Monte Carlo methods 
Journal of Applied Crystallography  2013;46(Pt 2):365-371.
A method is presented and applied, capable of retrieving form-free particle size distributions complete with uncertainties from small-angle scattering patterns. Special attention is paid to particle observability in the scattering patterns, accurate estimation of data uncertainty and the effect of uncertainty on the resulting size distribution statistics.
Monte Carlo (MC) methods, based on random updates and the trial-and-error principle, are well suited to retrieve form-free particle size distributions from small-angle scattering patterns of non-interacting low-concentration scatterers such as particles in solution or precipitates in metals. Improvements are presented to existing MC methods, such as a non-ambiguous convergence criterion, nonlinear scaling of contributions to match their observability in a scattering measurement, and a method for estimating the minimum visibility threshold and uncertainties on the resulting size distributions.
doi:10.1107/S0021889813001295
PMCID: PMC3627408  PMID: 23596341
structure analysis; small-angle scattering; Monte Carlo methods; particle size distribution
22.  Stacking faults and superstructures in a layered brownmillerite 
Stacking faults in Ca4Fe2Mn0.5Ti0.5O9 have been examined using X-ray diffraction and high-resolution transmission electron microscopy. Electron diffraction revealed two superstructures with ordered stacking sequences.
Single crystals of Ca4Fe2Mn0.5Ti0.5O9 have been synthesized using a flux method. The structural characterization using single-crystal X-ray diffraction revealed the space group Amma and unit-cell dimensions of a = 5.3510 (6), b = 26.669 (3), c = 5.4914 (6) Å. The structure is isotypic with Sr3NdFe3O9 [Barrier et al. (2005 ▶). Chem. Mater. 17, 6619–6623] and exhibits separated brownmillerite-type layers. One-dimensional diffuse scattering shows that the unit cell is doubled along c by alternating the intra-layer order of tetrahedral chains, causing stacking faults along the b direction. A computer simulation was performed, proving that the observed intensity variations along the diffuse scattering rods originates from two different local structures depending on the configuration of the tetrahedral chains. Selected-area electron diffraction experiments exhibit well ordered regions characterized by satellite reflections corresponding to two different superstructures. Both superstructures can be described using the superspace group A21/m(0βγ)0s, with γ = 0.5 and β ≃ 0.27 or β = 0.
doi:10.1107/S0108768111042005
PMCID: PMC3222140  PMID: 22101537
layered brownmillerite; diffuse scattering; stacking faults; modulated structure
23.  Real-Time Optical Diagnosis of the Rat Brain Exposed to a Laser-Induced Shock Wave: Observation of Spreading Depolarization, Vasoconstriction and Hypoxemia-Oligemia 
PLoS ONE  2014;9(1):e82891.
Despite many efforts, the pathophysiology and mechanism of blast-induced traumatic brain injury (bTBI) have not yet been elucidated, partially due to the difficulty of real-time diagnosis and extremely complex factors determining the outcome. In this study, we topically applied a laser-induced shock wave (LISW) to the rat brain through the skull, for which real-time measurements of optical diffuse reflectance and electroencephalogram (EEG) were performed. Even under conditions showing no clear changes in systemic physiological parameters, the brain showed a drastic light scattering change accompanied by EEG suppression, which indicated the occurrence of spreading depression, long-lasting hypoxemia and signal change indicating mitochondrial energy impairment. Under the standard LISW conditions examined, hemorrhage and contusion were not apparent in the cortex. To investigate events associated with spreading depression, measurement of direct current (DC) potential, light scattering imaging and stereomicroscopic observation of blood vessels were also conducted for the brain. After LISW application, we observed a distinct negative shift in the DC potential, which temporally coincided with the transit of a light scattering wave, showing the occurrence of spreading depolarization and concomitant change in light scattering. Blood vessels in the brain surface initially showed vasodilatation for 3–4 min, which was followed by long-lasting vasoconstriction, corresponding to hypoxemia. Computer simulation based on the inverse Monte Carlo method showed that hemoglobin oxygen saturation declined to as low as ∼35% in the long-term hypoxemic phase. Overall, we found that topical application of a shock wave to the brain caused spreading depolarization/depression and prolonged severe hypoxemia-oligemia, which might lead to pathological conditions in the brain. Although further study is needed, our findings suggest that spreading depolarization/depression is one of the key events determining the outcome in bTBI. Furthermore, a rat exposed to an LISW(s) can be a reliable laboratory animal model for blast injury research.
doi:10.1371/journal.pone.0082891
PMCID: PMC3885400  PMID: 24416150
24.  Cementoblast Delivery for Periodontal Tissue Engineering 
Journal of periodontology  2004;75(1):154-161.
Background
Predictable periodontal regeneration following periodontal disease is a major goal of therapy. The objective of this proof of concept investigation was to evaluate the ability of cementoblasts and dental follicle cells to promote periodontal regeneration in a rodent periodontal fenestration model.
Methods
The buccal aspect of the distal root of the first mandibular molar was denuded of its periodontal ligament (PDL), cementum, and superficial dentin through a bony window created bilaterally in 12 athymic rats. Treated defects were divided into three groups: 1) carrier alone (PLGA polymer sponges), 2) carrier + follicle cells, and 3) carrier + cementoblasts. Cultured murine primary follicle cells and immortalized cementoblasts were delivered to the defects via biodegradable PLGA polymer sponges, and mandibulae were retrieved 3 weeks and 6 weeks post-surgery for histological evaluation. In situ hybridization, for gene expression of bone sialoprotein (BSP) and osteocalcin (OCN), and histomorphometric analysis were further done on 3-week specimens.
Results
Three weeks after surgery, histology of defects treated with carrier alone indicated PLGA particles, fibrous tissue, and newly formed bone scattered within the defect area. Defects treated with carrier + follicle cells had a similar appearance, but with less formation of bone. In contrast, in defects treated with carrier + cementoblasts, mineralized tissues were noted at the healing site with extension toward the root surface, PDL region, and laterally beyond the buccal plate envelope of bone. No PDL-bone fibrous attachment was observed in any of the groups at this point. In situ hybridization showed that the mineralized tissue formed by cementoblasts gave strong signals for both BSP and OCN genes, confirming its nature as cementum or bone. The changes noted at 3 weeks were also observed at 6 weeks. Cementoblast-treated and carrier alone-treated defects exhibited complete bone bridging and PDL formation, whereas follicle cell-treated defects showed minimal evidence of osteogenesis. No new cementum was formed along the root surface in the above two groups. Cementoblast-treated defects were filled with trabeculated mineralized tissue similar to, but more mature, than that seen at 3 weeks. Furthermore, the PDL region was maintained with well-organized collagen fibers connecting the adjacent bone to a thin layer of cementum-like tissue observed on the root surface. Neoplastic changes were observed at the superficial portions of the implants in two of the 6-week cementoblast-treated specimens, possibly due in part to the SV40-transformed nature of the implanted cell line.
Conclusions
This pilot study demonstrates that cementoblasts have a marked ability to induce mineralization in periodontal wounds when delivered via polymer sponges, while implanted dental follicle cells seem to inhibit periodontal healing. These results confirm the selective behaviors of different cell types in vivo and support the role of cementoblasts as a tool to better understand periodontal regeneration and cementogenesis.
PMCID: PMC2596890  PMID: 15025227
Animal studies; biomimetics; cementoblasts; cementogenesis; dental follicle/anatomy and histology; periodontal regeneration; wound healing
25.  Three dimensional multiphoton imaging of fresh and whole mount developing mouse mammary glands 
BMC Cancer  2013;13:373.
Background
The applications of multiphoton microscopy for deep tissue imaging in basic and clinical research are ever increasing, supplementing confocal imaging of the surface layers of cells in tissue. However, imaging living tissue is made difficult by the light scattering properties of the tissue, and this is extraordinarily apparent in the mouse mammary gland which contains a stroma filled with fat cells surrounding the ductal epithelium. Whole mount mammary glands stained with Carmine Alum are easily archived for later reference and readily viewed using bright field microscopy to observe branching architecture of the ductal network. Here, we report on the advantages of multiphoton imaging of whole mount mammary glands. Chief among them is that optical sectioning of the terminal end bud (TEB) and ductal epithelium allows the appreciation of abnormalities in structure that are very difficult to ascertain using either bright field imaging of the stained gland or the conventional approach of hematoxylin and eosin staining of fixed and paraffin-embedded sections. A second advantage is the detail afforded by second harmonic generation (SHG) in which collagen fiber orientation and abundance can be observed.
Methods
GFP-mouse mammary glands were imaged live or after whole mount preparation using a Zeiss LSM510/META/NLO multiphoton microscope with the purpose of obtaining high resolution images with 3D content, and evaluating any structural alterations induced by whole mount preparation. We describe a simple means for using a commercial confocal/ multiphoton microscope equipped with a Ti-Sapphire laser to simultaneously image Carmine Alum fluorescence and collagen fiber networks by SHG with laser excitation set to 860 nm. Identical terminal end buds (TEBs) were compared before and after fixation, staining, and whole mount preparation and structure of collagen networks and TEB morphologies were determined. Flexibility in excitation and emission filters was explored using the META detector for spectral emission scanning. Backward scattered or reflected SHG (SHG-B) was detected using a conventional confocal detector with maximum aperture and forward scattered or transmitted SHG (SHG-F) detected using a non-descanned detector.
Results
We show here that the developing mammary gland is encased in a thin but dense layer of collagen fibers. Sparse collagen layers are also interspersed between stromal layers of fat cells surrounding TEBs. At the margins, TEBs approach the outer collagen layer but do not penetrate it. Abnormal mammary glands from an HAI-1 transgenic FVB mouse model were found to contain TEBs with abnormal pockets of cells forming extra lumens and zones of continuous lateral bud formation interspersed with sparse collagen fibers.
Parameters influencing live imaging and imaging of fixed unstained and Carmine Alum stained whole mounts were evaluated. Artifacts induced by light scattering of GFP and Carmine Alum signals from epithelial cells were identified in live tissue as primarily due to fat cells and in whole mount tissue as due to dense Carmine Alum staining of epithelium. Carmine Alum autofluorescence was detected at excitation wavelengths from 750 to 950 nm with a peak of emission at 623 nm (~602-656 nm). Images of Carmine Alum fluorescence differed dramatically at emission wavelengths of 565–615 nm versus 650–710 nm. In the latter, a mostly epithelial (nuclear) visualization of Carmine Alum predominates. Autofluorescence with a peak emission of 495 nm was derived from the fixed and processed tissue itself as it was present in the unstained whole mount. Contribution of autofluorescence to the image decreases with increasing laser excitation wavelengths. SHG-B versus SHG-F signals revealed collagen fibers and could be found within single fibers, or in different fibers within the same layer. These differences presumably reflected different states of collagen fiber maturation. Loss of SHG signals from layer to layer could be ascribed to artifacts rendered by light scattering from the dense TEB structures, and unless bandpass emissions were selected, contained unfiltered non-SHG fluorescence and autofluorescent emissions. Flexibility in imaging can be increased using spectral emission imaging to optimize emission bandwidths and to separate SHG-B, GFP, and Carmine Alum signals, although conventional filters were also useful.
Conclusions
Collagen fibril arrangement and TEB structure is well preserved during the whole mount procedure and light scattering is reduced dramatically by extracting fat resulting in improved 3D structure, particularly for SHG signals originating from collagen. In addition to providing a bright signal, Carmine Alum stained whole mount slides can be imaged retrospectively such as performed for the HAI-1 mouse gland revealing new aspects of abnormal TEB morphology. These studies demonstrated the intimate contact, but relatively sparse abundance of collagen fibrils adjacent to normal and abnormal TEBS in the developing mammary gland and the ability to obtain these high resolution details subject to the discussed limitations. Our studies demonstrated that the TEB architecture is essentially unchanged after processing.
doi:10.1186/1471-2407-13-373
PMCID: PMC3750743  PMID: 23919456

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