Q-space Analysis Research Articles

The fractal characteristics of atmospheric coated soot: Implication for morphological analysis

In this work, we have numerically investigated the variation of fractal characteristics of soot particles as soot is coated. We found that the ideal fractal law can fit the morphologies of coated soot only when the radius of gyration (Rg) of coated soot is identical to that of the soot core. In that case, the fractal dimension (Df) of coated soot is close to that of the soot core, which can explain why the unchanged fractal dimension was observed by the previous study as soot was evenly coated. As the voids among monomers is commonly filled firstly, the Rg of coated soot obtained from the two-dimensional (2D) method would be close to that of the soot core, so the measured fractal dimension would be close to that of the soot core. Our results also show that the fractal parameters of coated soot at different size scales can be varied, so the ideal fractal law is difficult to fit the structures of unevenly coated soot universally. Besides, we also found that the effective fractal dimension can increase as soot is unevenly coated. The results of the Q-space analysis show that as soot particles are unevenly coated, the power-law exponent of the structure factor (S(q)) versus the scattering wave vector (q) tends to -4 for heavily coated soot. This means that heavily, unevenly coated soot exhibits the characteristics of nearly spherical particles.

Three-dimensional tomography reveals distinct morphological and optical properties of soot aggregates from coal-fired residential stoves in China

Electron tomography (ET) is used to reconstruct the exact 3-dimensional morphologies of fractal-like soot aggregates sampled from a household heating stove commonly used in China. Conventional ET techniques suffer from “the missing wedge” problem caused by unreachable tilt angles, leading to noisy reconstructed tomograms. We overcame this problem by implementing a high-resolution object-edge identification method coupled with a novel voxel-filling algorithm to improve the reconstruction quality. Our reconstructed micron-length aggregates highlight the local non-idealities present throughout a particle's surface; these characteristics are almost impossible to account for in existing computational simulation exercises. Q-space analysis predicts the fractal dimension of our ET reconstructed aggregates to be in the range between 2.2 and 2.6, which deviates significantly from the universal value of 1.8 obtained using the widely adopted diffusion limited cluster-cluster aggregation (DLCA) model. The optical properties of our ET reconstructed aggregates are compared with those built with a DLCA model and equivalent spheres . The most striking optical characteristics of the ET reconstructed aggregates are their wavelength invariant mass absorption cross-sections of ~3.5 m2/g and single scattering albedo of ~0.5. The sample size investigated in this work is constrained by the extremely time-consuming object-edge identification process of electron tomography. This issue necessitates the development of more efficient computer vision algorithms for future research.

Detecting white matter alterations in multiple sclerosis using advanced diffusion magnetic resonance imaging.

Multiple sclerosis is a neurodegenerative and inflammatory disease, a hallmark of which is demyelinating lesions in the white matter. We hypothesized that alterations in white matter microstructures can be non-invasively characterized by advanced diffusion magnetic resonance imaging. Seven diffusion metrics were extracted from hybrid diffusion imaging acquisitions via classic diffusion tensor imaging, neurite orientation dispersion and density imaging, and q-space imaging. We investigated the sensitivity of the diffusion metrics in 36 sets of regions of interest in the brain white matter of six female patients (age 52.8 ± 4.3 years) with multiple sclerosis. Each region of interest set included a conventional T2-defined lesion, a matched perilesion area, and normal-appearing white matter. Six patients with multiple sclerosis (n = 5) or clinically isolated syndrome (n = 1) at a mild to moderate disability level were recruited. The patients exhibited microstructural alterations from normal-appearing white matter transitioning to perilesion areas and lesions, consistent with decreased tissue restriction, decreased axonal density, and increased classic diffusion tensor imaging diffusivity. The findings suggest that diffusion compartment modeling and q-space analysis appeared to be sensitive for detecting subtle microstructural alterations between perilesion areas and normal-appearing white matter.

AXONAL DENSITY IS ASSOCIATED WITH SUBJECTIVE COGNITIVE DECLINE (SCD) IN OLDER ADULTS ASSESSED USING THE COGNITIVE CHANGE INDEX

Converging evidence suggests that the pathophysiologic processes in the brains of Alzheimer's disease (AD) patients begin decades before symptoms occur1–3. Individuals in the preclinical stages of AD often report self-perceived decline in cognitive functions. The self-perception of cognitive decline can be assessed via the cognitive change index (CCI)4,5, a recently proposed measure of perceived neuropsychological function focusing on the memory, executive, and language domains from both self and informant perspectives. In this study, we examine the association of CCI with a novel diffusion metric for axonal density. The axonal density metric is derived via a three-compartmental model, Neurite Orientation Distribution and Density Imaging (NODDI)6. Sixty-one participants with cognitively normal (CN, N=21), subjective cognitive decline (SCD, N=23) and mild cognitive impairment (MCI, N=17) underwent Hybrid Diffusion Imaging (HYDI)7,8 that consists of five b-value shells. Diffusion images were corrected for motion, eddy and geometric distortion9 prior to nonlinear transformation to standard MNI space using ANTS registration10. Median values of diffusion metrics including DTI, NODDI, and q-space analysis were extracted from skeletonized 48 white matter (WM) ROIs provided in the JHU atlas11. General linear regression analyses were performed to test associations between diffusion metrics and CCI scores adjusted for age, sex, and education. For comparisons of demographic and cognitive variables, ANOVAs were employed with Tukey's tests followed by post-hoc t-tests. The three groups did not differ significantly in age, sex, and education distribution (Table 1). Strong associations (p<0.001) between CCI and diffusion metrics were found in ROIs belonging to the limbic system. Specifically, fractional anisotropy (FA) of DTI in the right stria terminalis had negative correlation with CCI-12 (i.e., episodic memory) (p<0.001, Figure 1). Axonal density in the right uncinate fasciculus negatively correlated with both CCI-12 and CCI-TOT (20 item) (p<0.001, Figure 2). Other ROIs had no significant correlations. These results suggest that lower axonal density and fiber coherence are risk factors for self-perceived memory decline. The two most vulnerable white matter tracts - the right stria terminalis and uncinate fasciculus, connect between the amygdala and hippocampus - two of the areas that show the earliest disease-associated changes. ROI map and scatter plot of CCI score and fractional anisotropy (FA). A. The ROI in red denotes the right stria terminalis. B. FA of diffusion tensor imaging (DTI) negatively correlated with CCI-12 (episodic memory) with p=0.0007. Age, sex and education were adjusted in the linear regression analysis. Green dots denote cognitively normal (CN); blue dots denote subjective cognitive decline (SCD); red dots denote mild cognitive impairment (MCI); and the black solid line denotes the regression line. ROI map and scatter plot of CCI score and axonal density. A. The ROI in red denotes the right uncinate fasciculus. B. Axonal density negatively correlated with both CCI-12 (episodic memory) with p=0.00009 and CCI-TOT (20 items) with p=0.0002. Age, sex and education were adjusted in the linear regression analysis. Green dots denote cognitively normal (CN); blue dots denote subjective cognitive decline (SCD); red dots denote mild cognitive impairment (MCI); and the black solid line denotes the regression line.

Q-Space Analysis of the Light Scattering Phase Function of Particles with Any Shape

Q-space analysis is applied to the light scattering phase function of a wide variety of non-spherical and irregularly shaped particles including a great many types of dusts, fractal aggregates, spheroids, irregular spheres, Gaussian random spheres, thickened clusters and nine types of ice crystals. The phase functions were either experimental data or calculations. This analysis method uncovers many specific and quantitative similarities and differences between the scattering by various shapes and also when compared to spheres. From this analysis a general description for scattering by a particle of any shape emerges with specific details assigned to various shapes.

Q-space analysis of light scattering by ice crystals

Q-space analysis is applied to extensive simulations of the single-scattering properties of ice crystals with various habits/shapes over a range of sizes. The analysis uncovers features common to all the shapes: a forward scattering regime with intensity quantitatively related to the Rayleigh scattering by the particle and the internal coupling parameter, followed by a Guinier regime dependent upon the particle size, a complex power law regime with incipient two dimensional diffraction effects, and, in some cases, an enhanced backscattering regime. The effects of significant absorption on the scattering profile are also studied. The overall features found for the ice crystals are similar to features in scattering from same sized spheres.

A light-scattering study of Al2O3 abrasives of various grit sizes

We report light scattering phase function measurements for irregularly shaped Al2O3 abrasive powders of various grit sizes. Q-space analysis is applied to the angular scattering to reveal a forward scattering regime, Guinier regime, power law regime with quantifiable exponents, and an enhanced backscattering regime. The exponents of the power laws for Al2O3 abrasives decrease with increasing internal coupling parameter ρ′, which is in agreement with previous observations for other irregular particles. Unlike other dust particles previously studied showing single power laws under Q-space analysis, the largest three abrasives, for which ρ′≳100, showed a kink in the power law, which is possibly due to the higher degree of symmetry for the abrasives than for all the particles studied previously. Direct comparison of the 1200, 1000, and 800 grit abrasive scattering to scattering by corresponding spheres shows that the scatterings approximately coincide at the spherical particle qR≃ρ′ crossover point. Furthermore, the scattering at the maximum qR=2kR by the irregularly shaped abrasives is close to the geometric centers of the glories of the spheres.

Q-space analysis of light scattering by Gaussian Random Spheres

Q-space analysis is applied to the scattered intensity from Gaussian Random Spheres (GRSs). Q-space analysis involves plotting the scattered intensity vs. the magnitude of the scattering wave vector q=2ksinθ2 where k=2π/λ with λ the wavelength and θ is the scattering angle, on a log–log plot. The light scattering properties of GRSs were calculated using a discrete dipole approximation algorithm. The GRSs had σ=0.2 and ν=3, where σ is the relative standard deviation in the radial direction, and ν describes fluctuations in the angular direction. Calculations were systematically performed with size parameters ranging from 10 to 30, and with a relative index of refraction, m, ranging from 1.01 to 1.5. The results show quantifiable, power law descriptions of the scattered intensity and a Rayleigh functionality of the forward scattered intensity that depend upon the phase shift parameter ρ=2kReq|m−1| where Req is an equivalent radius. Similar functionalities have been observed in both spheres and other irregularly shaped particles. These results continue the implication that there is a comprehensive description of light scattering for all particles that can be uncovered with the application of Q-space.

Effect of the imaginary part of the refractive index on light scattering by spheres.

For spheres of arbitrary radius R and complex index of refraction n+iκ, we identify a new parameter that indicates when the imaginary part κ seriously affects the scattering by a sphere. The parameter is κkR, where k is the wave vector magnitude, such that when κkR grows larger than one, the scattering is affected and, when κkR>3, the effects saturate. The effects are uncovered and demonstrated with Q-space analysis. The physical basis for κkR lies in the fact that it is the ratio of the radius to the optical skin depth.

A light-scattering study of the scattering matrix elements of Arizona Road Dust

We report measurements of the light scattering matrix elements of Arizona Road Dust, which has irregular shapes. Our experimental apparatus used photodiode arrays to detect scattered light simultaneously at many angles including small angles that are necessary for accurate characterization of large particles. The setup was calibrated with single slit diffraction and water droplet scattering. Guinier analysis yielded the dust particle size. Q-space analysis of the dust scattering yielded a comprehensive description of scattering in terms of power laws with quantifiable exponents.

Dynamic state of water molecular displacement of the brain during the cardiac cycle in idiopathic normal pressure hydrocephalus

The predictive accuracy of iNPH diagnoses could be increased using a combination of supplemental tests for iNPH. To evaluate the dynamic state of water displacement during the cardiac cycle in idiopathic normal pressure hydrocephalus (iNPH), we determined the change in water displacement using q-space analysis of diffusion magnetic resonance image. ECG-triggered single-shot diffusion echo planar imaging was used. Water displacement was obtained from the displacement probability profile calculated by Fourier transform of the signal decay fitted as a function of the reciprocal spatial vector q. Then maximum minus minimum displacement (delta-displacement), of all cardiac phase images was calculated. We assessed the delta-displacement in white matter in patients with iNPH and atrophic ventricular dilation (atrophic VD), and in healthy volunteers (control group). Delta-displacement in iNPH was significantly higher than those in the atrophic VD and control. This shows that water molecules of the white matter in iNPH are easily fluctuated by volume loading of the cranium during the cardiac cycle, due to the decrease in intracranial compliance. There was no significant correlation between delta-displacement and displacement. The delta-displacement and the displacement do not necessarily yield the same kind of information. Delta-displacement demonstrated to obtain biophysical information about fluctuation. This analysis may be helpful in the understanding physiology and pathological condition in iNPH and the assisting in the diagnosis.

Crossover from spherical particle Mie scattering to circular aperture diffraction.

This paper demonstrates the manner in which the Mie results for light scattering by a three-dimensional sphere of arbitrary size and refractive index crosses over to Fraunhofer diffraction by a two-dimensional circular aperture of the same radius in the limit of very large radius. Demonstration is feasible only because the graphical results are plotted in the manner of the Q-space analysis that plots scattered intensity versus the logarithm of the magnitude of the scattering wave vector rather than linear versus the scattering angle.

A pulse sequence optimization method for assessment of nucleus size in q-space analysis of idealized cells

To adjust pulse sequences that produce diffusion-weighted MRI signals for increased sensitivity to nucleus size, the impulse-propagator method in q-space is applied to a spherical geometry that would describe each member of a collection of cells and their nuclei, with several possible representations of the extracellular space. The method is extended to allow propagation between nucleus, cytoplasm, and extracellular space through semi-permeable membranes, using an approximate adjustment of intra-compartment propagators. Diffraction patterns are first calculated for the three compartments separately, for PGSE and OGSE pulse sequences, and verified by comparison with Monte Carlo simulations. The detailed patterns from the separate compartments determine the q value for maximum contrast in the total signal between large and small nuclei, an optimization that is not accurate in a Gaussian Phase Distribution (GPD) approximation. Then diffraction patterns are calculated for the case of linked compartments with semi-permeable membranes. The treatment of permeability adequately estimates pulse-sequence parameters for maximum contrast in calculated signal as nucleus size varies.

Q-space analysis of scattering by small irregular particles

This paper applies the Q-space analysis method to the scattering phase function of small irregular particles. Q-space analysis involves plotting the scattered intensity versus the magnitude of the scattering wave vector q=(4π/λ) sin(θ/2) on a double log plot. Four types of irregularly shaped particles were studied: strongly damaged spheres, rough surface spheres, pocked spheres, and agglomerated debris particles. The angular scattering phase function was calculated using the discrete dipole approximation (DDA). The Q-space analysis uncovered power law descriptions of the scattering as it has previously for aggregates, spheres and dusts, although in some situations the description is marginal. It also showed that the forward scattering lobe has Rayleigh functionalities on size and refractive index. These results imply that Q-space analysis can yield a comprehensive description of scattering in terms of power laws with quantifiable exponents for a wide variety of particle shapes. However, a theoretical explanation of the power laws and the values of the numerical exponents is lacking.

Spectral and angular light-scattering from silica fractal aggregates

This work applies a new model based on the discrete dipole approximation to simulate the scattering of coherent broadband light from fixed and randomly oriented silica fractal aggregates. Two classes of aggregate morphology are considered; the standard aggregate with a single fractal dimension and superaggregates with two dimensions, both of which are generated from a Diffusion-Limited Cluster-Aggregation model. Light scattering from these aggregates is simulated over the short wave infrared to ultraviolet spectral range. We find features in the distribution of the spectral and angular scattered-intensities that do not disappear after orientation averaging and are seen for both types of aggregates. The important role played by the wavelength in q-space analysis is observed and we report the utility of a spectral q-space analysis for multi-dimensional objects like superaggregates with spectrally dependent refractive index.

Q-space analysis of scattering by particles: A review

This review describes and demonstrates the Q-space analysis of light scattering by particles. This analysis involves plotting the scattered intensity versus the scattering wave vector q=(4π/λ)sin(θ/2) on a double log plot. The analysis uncovers power law descriptions of the scattering with length scale dependent crossovers between the power laws. It also systematically describes the magnitude of the scattering and the interference ripple structure that often underlies the power laws. It applies to scattering from dielectric spheres of arbitrary size and refractive index (Mie scattering), fractal aggregates and irregularly shaped particles such as dusts. The benefits of Q-space analysis are that it provides a simple and comprehensive description of scattering in terms of power laws with quantifiable exponents; it can be used to differentiate scattering by particles of different shapes, and it yields a physical understanding of scattering based on diffraction.

Q-space analysis of scattering by dusts

This note applies Q-space analysis, wherein the scattered intensity is plotted versus the scattering wave vector q=(4π/λ) sin(θ/2) on a double log plot, to phase function data for scattering from irregularly shaped dusts. This analysis yields a power law description of the dust scattering as it has for aggregates and spheres. This implies that Q-space analysis can yield a simple and comprehensive description of scattering in terms of power laws with quantifiable exponents for a wide variety of shapes. It also calls for an explanation of the power law for irregular dust particles and the numerical exponent.

NMR q-space analysis of canonical shapes of human erythrocytes: stomatocytes, discocytes, spherocytes and echinocytes

q-Space plots obtained experimentally using pulsed field-gradient stimulated echo (PGSTE) nuclear magnetic resonance (NMR) spectroscopy from water diffusing in red blood cells (RBCs) of different canonical (distinct variant) morphologies have "signature" features. The experimental q-space plots from suspensions of stomatocytes, echinocytes and spherocytes generated chemically had no diffraction features; in contrast a sample of blood from a patient with hereditary spherocytosis showed diffraction minima. To understand the forms of q-space plots, mathematical/geometrical models of discocytes, stomatocytes, echinocytes and spherocytes were used as restricting boundaries in simulations of water diffusion with Monte Carlo random walks. These simulations indicated that diffusion-diffraction minima are expected for each of the cell shapes considered. The absence of diffusion-diffraction minima in stomatocytes generated by dithiothreitol treatment was surmised to be due to non-alignment of the cells with the magnetic field of the NMR spectrometer. Differential interference contrast microscopy images of the chemically generated spherocyte and echinocyte suspensions showed them to be heterogeneous in cell shape. Therefore, we concluded that the shape heterogeneity caused the loss of the diffusion-diffraction features, which were observed in the more homogeneous sample from a patient with hereditary spherocytosis, and in the simulations of homogeneous cell suspensions. This understanding of factors that affect q-space plots from RBC suspensions will assist morphological studies of other cell and tissue types.

Alveolarization Continues during Childhood and Adolescence

The current hypothesis that human pulmonary alveolarization is complete by 3 years is contradicted by new evidence of alveolarization throughout adolescence in mammals.We reexamined the current hypothesis using helium-3 ((3)He) magnetic resonance (MR) to assess alveolar size noninvasively between 7 and 21 years, during which lung volume nearly quadruples. If new alveolarization does not occur, alveolar size should increase to the same extent.Lung volumes were measured by spirometry and plethysmography in 109 healthy subjects aged 7-21 years. Using (3)HeMR we determined two independent measures of peripheral airspace dimensions: apparent diffusion coefficient (ADC) of (3)He at FRC (n = 109), and average diffusion distance of helium (X(rms)) by q-space analysis (n = 46). We compared the change in these parameters with lung growth against a model of lung expansion with no new alveolarization.ADC increased by 0.19% for every 1% increment in FRC (95% confidence interval [CI], 0.13-0.25), whereas the expected change in the absence of neoalveolarization is 0.41% (95% CI, 0.31-0.52). Similarly, increase of (X(rms)) with FRC was significantly less than the predicted increase in the absence of neoalveolarization. The number of alveoli is estimated to increase 1.94-fold (95% CI, 1.64-2.30) across the age range studied.Our observations are best explained by postulating that the lungs grow partly by neoalveolarization throughout childhood and adolescence. This has important implications: developing lungs have the potential to recover from early life insults and respond to emerging alveolar therapies. Conversely, drugs, diseases, or environmental exposures could adversely affect alveolarization throughout childhood.

Mean displacement map of spine and spinal cord disorders using high b-value q-space imaging-feasibility study

Q-space analysis is a new metric that uses multiple, high b-value, diffusion-weighted magnetic resonance (MR) data. This technique shows promising results as a tool to provide information complementary to that of other imaging techniques used on biological tissue in vivo. To investigate the use of a mean displacement (MDP) map of high b-value, q-space imaging (QSI) to characterize spinal and spinal cord lesions in vivo. Eight patients with spine or spinal cord disorders (two neurinomas, one myeloma, three cases of syringohydromyelia, and two cases of cervical spondylosis) were included. The MR imaging protocol consisted of conventional MR sequences, conventional diffusion-weighted imaging (DWI; b = 1000), and high b-value QSI with a maximum q value of 836.9 cm(-1). Apparent diffusion coefficient (ADC) maps of conventional DWI and MDP maps of QSI data were obtained and region-of-interest analyses for the lesions were performed. MDP values of normal spinal cord, cerebrospinal fluid (CSF), and tumor parenchyma were 6.57 ± 0.52, 17.6 ± 2.75, and 8.49 ± 2.09, respectively (µm, mean ± standard deviation). In general, MDP maps were not well correlated with the corresponding ADC maps at the pathologic lesions. Spondylotic lesions tended to have higher MDP values than normal spinal cord, whereas syringohydromyelia produced MDP values slightly lower than those of CSF. The heterogeneous MDP values were probably due to differences in tissues and pathologic structures. This technique has potential to provide additional clinical information to that obtained with conventional MR imaging.