Parallel Cross Sections Research Articles

Structure simulation of concentrated suspensions of hard spherical particles

AbstractA monte Carlo technique is applied to simulate the structure of concentrated suspensions of hard spherical particles that obey lognormal distribution. With this technique, the random loose packing, with packing density Φm is obtained first, and then the particles in the packing are randomly separated to achieve a specified solid‐volume fraction Φ. The simulated structure is evaluated both in the microscale, the neighboring number distribution, and the distribution of gaps between neighboring particles; and in the macroscale, the distribution of the solid‐area fractions on a series of parallel cross sections. Results show that, at the same solid‐volume fraction, the increase in the standard deviation of particle diameters leads to the decrease in the mean neighboring number and leads to the increase in the mean gap. The mean relative gap obtained from the simulation is larger than that from theoretical prediction, δ=[(Φm/Φ)1/3−1]. With particles of lognormal distribution, both the gap sizes and the neighboring numbers distributed over broader ranges than that with equal particles. Results also show that, with equal particles and particles of lognormal distribution, there is no significant differenence between the distributions of the solid‐area fractions on the cross sections. The structures obtained in this study are shown to be completely random, homogeneous, and isotropic by statistical tests.

Surface Rendering for Multi-axial Cross Sections

This study presents, for the first time, an automatic algorithm for surface rendering of a volume consisting of multi-axial cross sections. In computer graphics, although a medical volume is usually considered to consist of sequential parallel cross sections, multi-axial parallel sections that constitute a multi-axial volume have also been frequently used in recent clinical cases. Herein, a multi-axial volume is assumed to consist of multiple one-axial subvolumes occupying the same space. The discrete ray tracing algorithm that searches for only a hit vowel in a conventional one-axial volume is extended to search for multiple hit vowels in a multi-axial volume. Quadratic isosurfaces reconstructed from the hit vowels are used to approximate the object surface. The rendering results, applied to clinical cases to improve diagnostic rates, indicate that 3D images obtained by applying our methods to multi-axial volumes are more clinically useful than those obtained from one-axial volumes.

Spline subdivision schemes for convex compact sets

The application of spline subdivision schemes to data consisting of convex compact sets, with addition replaced by Minkowski sums of sets, is investigated. These methods generate in the limit set-valued functions, which can be expressed explicitly in terms of linear combinations of integer shifts of B-splines with the initial data as coefficients. The subdivision techniques are used to conclude that these limit set-valued spline functions have shape-preserving properties similar to those of the usual spline functions. This extension of subdivision methods from the scalar setting to the set-valued case has application in the approximate reconstruction of 3-D bodies from finite collections of their parallel cross-sections.

MATCHING AND CHOICE OF PARAMETER IN SECTIONAL INTERPOLATION

An overview is given of a method for constructing a C1 surface which interpolates data given on parallel cross-sections. It is envisaged that the data is relatively sparse and so the data on each cross-section is interpolated by a scheme which is shape-preserving, i.e. it does not introduce any unnecessary inflections. These curves are then blended to form the surface. We concentrate on describing how the interpolation curves are parameterised so that points with the same parameter value at different levels correspond in a way suitable for the blending procedure.

Evaluation of regional systolic function in hypertrophic cardiomyopathy and hypertensive heart disease: A three-dimensional echocardiographic study

Assessment of regional left ventricular (LV) function in patients with asymmetric LV hypertrophy is difficult with two-dimensional echocardiography mainly because of factors such as LV geometry, structure, regional wall stress, and ischemia. Multiplane transesophageal echocardiography with three-dimensional reconstruction of cross-sectional images was used for quantitative evaluation of regional wall thickness and fractional thickening. Fifteen patients (56 ± 13 years old) with hypertrophic cardiomyopathy (LV ejection fraction 71% ± 4%), 15 (62 ± 13 years) with hypertensive heart disease (ejection fraction 66% ± 8%) and 15 (53 ± 11 years) healthy control subjects (ejection fraction 61% ± 5%) were included in the analysis. Regional function was studied in four parallel equidistant short-axis cross sections from base to apex of the reconstructed left ventricle. In 15 degree intervals, 24 wall thickness measurements in each cross section were made at end-diastole and end-systole after endocardial and epicardial border tracing. A total of 192 measurements were obtained in each patient, and absolute wall thickening and fractional thickening were calculated. Absolute and fractional wall thickening showed a significant inverse relation to end-diastolic wall thickness in all heart conditions ( r = 0.71, p < 0.0001). Regions of normal wall thickness in diseased patients were not hyperdynamic when compared with normal control subjects. Significant impairment in fractional thickening at identical end-diastolic thickness was observed in the septum compared with the lateral free wall in both hypertrophic cardiomyopathy and hypertensive heart disease. Thus regional systolic function is inversely related to end-diastolic wall thickness. The decrease in regional systolic function with increasing LV hypertrophy was similar in idiopathic and hypertensive cardiomyopathy. In both types of hypertrophy, significant differences in systolic function were observed in septal and lateral wall segments of similar wall thickness. This indicates that factors other than end-diastolic wall thickness influence myocardial thickening in patients with hypertrophy and preserved global function. (J Am Soc Echocardiogr 1998;11:778-86.)

A new unsupervised cube-based algorithm for iso-surface generation

This paper introduces a new algorithm which automatically produces polygonal representations of 3D structures within a volume data set built from a stack of parallel cross-sections. Several methods of 3D surface reconstruction have already been proposed ranging from heuristic approaches for constructing 3D surfaces from 2D contours to the Marching Cubes (MC) approach where the different configurations are checked systematically. Instead, we define a cube-to-cube connection based upon geometrical closeness provided by convex hulls computation. We further evaluate the precision of 3D models reconstructed from synthetic and real data obtained in confocal microscopy and compare it with the conventional MC algorithm. We also discuss improvements that allow to reduce the number of generated surface patches and the ability to be used in 3D quantitative tasks.

In vitro 3D reconstruction of long bones using B-scan image processing.

An echographic image processing method has been developed, and validated by in vitro experiments, for the 3D reconstruction of the long bones of the newborn. The reconstruction of successive parallel cross-sections is obtained by a 2D reconstruction technique using radial B-scan image processing. The automatic segmentation of all the calculated images allows the extraction of the external contours of the skeleton. After structuring the explored volume using a contour association method, a contour interpolation step is required to solve the anisotropy problem, to obtain a 3D representation with cubic voxel lists. The results are encouraging, and a new mechanical part prototype of the acquisition system is under test for in vivo experiments. The main originality of the paper lies in the combination of different steps to obtain a practical solution to a clinical problem.

Accurate assessment of mitral valve area in patients with mitral stenosis by three-dimensional echocardiography

The accuracy of measurements of mitral valve orifice area (MVA) from three-dimensional echocardiographic (3DE) image data sets obtained by a transthoracic or transesophageal rotational imaging probe was studied in 15 patients with native mitral stenosis. The smallest MVA was identified from a set of eight parallel short-axis cut planes of the mitral valve between the anulus and the tips of leaflets (paraplane echocardiography) and measured by planimetry. In addition, MVA was measured from the two-dimensional short-axis view (2DE). Values of MVA measured by 3DE and 2DE were compared with those calculated from Doppler pressure half-time (PHT) as a gold standard. Observer variabilities were studied for 3DE. MVA measured from PHT ranged between 0.55 and 3.19 cm 2 (mean ± SD 1.57 ± 0.73 cm 2), from 3DE between 0.83 and 3.23 cm 2 (mean ± SD 1.55 ± 0.67 cm 2), and from 2DE between 1.27 and 4.08 cm 2 (mean ± SD 1.9 ± 0.7 cm 2). The variability of intraobserver and interobserver measurements for 3DE measurements was not significantly different ( p = 0.79 and p = 0.68, respectively); for interobserver variability, standard error of the estimate = 0.25. There was excellent correlation, close limits of agreement (mean difference ± 2 SD), and nonsignificant differences between 3DE and PHT for MVA measurements ( r = 0.98 [0.02 ± 0.3] and p = 0.6), respectively. There was moderate correlation, wider limits of agreement, and significant difference between 2DE and PHT for MVA measurements ( r = 0.89 [0.32 ± 0.66] and p = 0.002), respectively. This may be related to the difficulties in visualization of the smallest orifice in precordial short-axis views. This study suggests that three-dimensional image data sets, by providing the possibility of “computer slicing” to generate equidistant parallel cross sections of the mitral valve independently from physically dictated ultrasonic windows, allow accurate and reproducible measurement of the MVA. (J Am Soc Echocardiogr 1997;10:133-40.)

Magnetic and Gravity Modelling of the Renison Tin Mine, Tasmania

Tin mineralisation occurs at Renison Bell, near Zeehan in Tasmania, as a group of cassiterite-bearing massive pyrrhotite bodies in Cambrian sedimentary rocks. Mineralising fluids from the underlying Pine Hill Granite have replaced carbonate rocks with massive sulphides and cassiterite. The discrete blocks of massive pyrrhotite have high density and high magnetic susceptibility contrasts with the comparatively barren country rock. They are strongly remanently magnetised and are excellent geophysical targets.A detailed geophysical model of the mine was created from a database comprising 1:2500 scale geological mapping and geological logs of approximately 4000 drill-cores. The model comprises 93 parallel cross-sections, each 1.5 km long, spaced 20 m apart. Each cross-section is comprised of up to 150 polygons which represent all known individual rock types and ore bodies. The magnetic response of the model was computed and the residual between the model and the observed response, measured by a low-level helicopter magnetic survey, revealed several anomalies unaccounted for by the model. Drill testing of these anomalies led to the discovery of several hitherto unknown massive sulphide occurrences.Surface gravity data of the mine and surrounding district were enhanced by applying digital terrain corrections. The corrected Bouguer anomaly revealed a hitherto unknown positive anomaly associated with the ore zones of the Renison mine. The gravity anomaly of the model was also computed. Unfortunately, the limited resolution of the observed data prevented the delineation of ore targets.The terrain-corrected Bouguer gravity data were also used to model the shape of the underlying non-magnetic Pine Hill Granite. A computer inversion method was implemented to build a 3-D block model of the granite. Results agreed with previous conventional 3-D modelling techniques but yielded improved resolution of the granite form.The project involved development of new computer software to build and edit the large and complex 3-D geophysical model of the mine, and to compute the model’s magnetic and gravity responses. Software was also developed to build and compute the gravity response of a 3D block model of the underlying granite.

Surface study of cross-linking gradients in photopolymers by acoustic microscopy

Acoustic techniques use the propagation of ultrasonic waves a few microns under the sample surface and their interaction with the material structure to characterize sample surface properties. The aim of this work is to apply these investigation methods to display cross-linking gradients created in photopolymers by a reticulation process induced by UV light. This method has first been tested on materials exposed through a test target mask. Using 600 and 90 MHz focused lenses, we got fine acoustic images with resolution respectively around 4 μm and 25 μm, where the abrupt variations of elastic properties produced by the optic filter are easily detectable. Next, we tried to locate a more gradual distribution of elastic properties, created via the UV exposure through an apodizing filter with a progressive radial transmission function. This gradient has not been detected with the previous acoustic imaging system, but using the complementary technique of acoustic signature, a quite similar profile has been retrieved from measurements of the longitudinal lateral velocity on small volumes close to the material surface. This sample has then been cut off in two parallel cross-sections to follow, via surface investigation, variations induced inside the material. This study has demonstrated a softening of the cross-linkings gradients close to the surface, responsible for the absence of contrast on previous acoustic images. Moreover, the evolution of the velocities measured inside this sample has shown a special volumic distribution, which agrees with the chemical theories predictions about the reticulation process. Acoustic attenuation measurements are also produced as a possible complementary information on structural changes in photopolymers.

Piecewise-Linear Interpolation between Polygonal Slices

In this paper we present a new technique for piecewise-linear surface reconstruction from a series of parallel polygonal cross sections. This is an important problem in medical imaging, surface reconstruction from topographic data, and other applications. We reduce the problem, as in most previous works, to a series of problems of piecewise-linear interpolation between each pair of successive slices. Our algorithm uses a partial curve matching technique for matching parts of the contours, an optimal triangulation of 3-D polygons for resolving the unmatched parts, and a minimum spanning tree heuristic for interpolating between nonsimply connected regions. Unlike previous attempts at solving this problem, our algorithm seems to handle successfully in practice any kind of data. It allows multiple contours in each slice, with any hierarchy of contour nesting, and avoids the introduction of counterintuitive bridges between contours, proposed in some earlier papers to handle interpolation between multiply connected regions. Experimental results on various complex examples, involving actual medical imaging data, are presented and show the good and robust performance of our algorithm.

Geometry and kinematics of the South Atlas Front, Algeria and Tunisia

The South Atlas Front is the structural boundary between the Sahara platform and the Atlas mountains. It is frequently indicated as a foreland dipping monocline known as the Sahara Flexure. Earlier work generally considered that such a cover structure resulted from direct inversion of basement faults. This assumption is not applicable to the studied area which is situated close to the Algeria-Tunisia border: our study demonstrates a thin-skinned style characterised by ramp-related folds. Ten parallel balanced cross sections give an interpretation for the South Atlas Front from Negrine to Gafsa, about 100 km along strike. The geometry at depth of each cross section is defined by forward modelling of each individual anticline. The depth-to-detachment is defined using the geometric characteristics of the fault-propagation folds well exposed along the deformation front. In all sections, the modelling is consistent with basal décollements located within Cretaceous stratigraphic levels. Lateral changes of the tectonic style accommodated by tear faults are observed. They seem related to lateral variations in the efficiency of the based décollement faults inducing either a jump of the décollement to another level or the development of en-échelon folds. The modelling predicts small rotations of cover sheets separated by large-scale tear faults.

743-3 Initial Quantitative Application of Three-dimensional Voxel Imaging with a Rotating Transducer to the Human Right Ventricle

Three-dimensional echo measurement of right ventricular (RV) volume has recently been validated in experimental models using automated voxel acquisition from rotated 2D echo views. This technique conveniently provides rapid and animated spatial appreciation from multiple perspectives. However, its feasibility and reliability for reconstructing and quantitating RV volume and function in humans is not known, given limitations of acoustic access and the need for ECG and respiratory gating; also, no other method for RV volume by 3D echo has been tested quantitatively in patients. We therefore imaged the RV from a parasternal or subcostal rotation in 18 normal subjects (6–19 years old) in order to compare calculated stroke volumes with an independent noninvasive measure in subjects not undergoing catheterization. Endocardial borders in parallel cross-sections derived from the voxel data set were traced and volumes calculated as σ (cavity area x slice height). Stroke volumes were compared with Doppler values (mean of mitral inflow and aortic outflow in the absence of regurgitation). In 13/18 (72%) of subjects, the inflow, outflow and apical portions of the RV could be included in a rotational scan. In these individuals, 3D echo visually reproduced the crescentic RV shape, and 3D stroke volumes agreed well with Doppler values (y = 0.87x + 1.1, r = 0.95, SEE = 5.1 ml. mean error = -5.7 ml, related to mild apical foreshortening). 3D volumetric reconstruction using a rotating transducer can be applied to the human RV and provides convenient gated acquisition and ready spatial appreciation from multiple perspectives, subject to the need for visualizing the RV from a fixed point. It is also quantitatively accurate for RV stroke volume and therefore cardiac output by the transthoracic approach.

743-1 Quantitative Transthoracic Three-dimensional Voxel Imaging of the Left Ventricle: Clinical Validation

Recent computational advances have permitted 3-dimensional (3D) reconstruction of echo intensities over the cardiac volume from rotated 2D echo views gated to ECG and respiration. Unlike approaches using selected 2D views, such automated voxel acquisitions conveniently provide rapid spatial appreciation in animated views from multiple perspectives. However, only limited data are available regarding the accuracy of such reconstructions in patients, particularly using the transthoracic approach without the need for TEE. We therefore reconstructed the left ventricles of 10 consecutive patients referred for cardiac gated blood pool scan (GBPS) by transthoracic apical rotation, 5 with abnormal wall motion. LV volume was calculated by summing endocardial areas in parallel cross-sections derived from the voxel data, and compared to GBPS values by validated techniques to normalize counts for attenuation and countstvolume of blood sample. Reconstructed volumes (vol) agreed well with those from GBPS: y = r SEE Mean Error End-diastolic vol 0.85x + 17.2 098 8.66 cc 1.4% End-systolic vol 0.89x + 9.42 099 5.29 cc 4.6% Stroke vol 0.93x + 0.64 095 6.01 cc 2.4% Ejection fraction 0.94x - 0.23 0.99 2.59% 5.5% 3D volumetric reconstruction of the LV not only provides convenient gated acquisition and ready spatial appreciation from multiple perspectives, but is also quantitatively accurate for LV size and function in patients by the transthoracic approach. This study supports the use of this technique to address clinical and research questions.

Surface microsurgery: taper section preparation

Surface microsurgery is the science of preparing surface layers, such as oxide scales and coatings, for characterisation of their microstructure and composition, by conventional surface analytical techniques, such as SEM, EPMA, SIMS etc. A surface microsurgery procedure often employed involves the preparation of a taper section. Using relatively simple equipment, significant improvements have been made to the precision, and thus the effectiveness, of this procedure such that production of uniform, parallel cross sections, with magnifications in excess of 1000, can be achieved readily and consistently. The procedure has enabled the detailed characterisation of 100-5000 A thick interlayers in composite coatings on both metallic and semiconductor substrates and also two-dimensional elemental analysis of micron thick oxide scales

Regional Variations in Formation Water Chemistry: Major and Minor Elements, Frio Formation Fluids, Texas (1)

Spatial variation of major element content (Na, Ca, and Cl) in formation waters in the Oligocene Frio Formation, Texas, show that mixing occurs vertically and that the chemistry of Ca-rich fluids varies from northern coastal to southern Texas. Relative amounts of major and minor elements (Sr, Mg, and K) in Ca-rich fluids from south Texas differ from those in other areas of Texas and also are different from updip Mesozoic fluids. Such differences seem to preclude the known Mesozoic fluids as a source of Ca in the south Texas Frio Formation fluids, barring complicated, nonuniform water-rock alteration changing the Mesozoic-fluid composition. Approximately coast parallel (and strike parallel) cross sections show that Ca-rich fluids in the Frio are usually found at depth. Some anomalies occur where fluids are present near piercement structures and in a relatively large part of south Texas. In the latter region, Ca-rich fluids exist above the top of geopressure, suggesting that they may have been emplaced before geopressure became widespread (2-3 m.y. ago). Because there are no shallow Ca-rich fluids in the vicinity of major river systems in south Texas, meteoric fluids may have flushed Ca-rich fluids out of the areas near the rivers during past pluvial periods. This process does not preclude the dilution of formation water by clay-dehydration reactions, another process that has been proposed to explain deep, dilute formatio waters in Gulf basin reservoirs.

Fiber type-specific distribution of parvalbumin in rabbit skeletal muscle

A highly sensitive sandwich ELISA for parvalbumin (PA), based on a fluorometric detection system, was developed. This assay detected PA concentrations as low as 20 pg/ml (2 pg per assay) and was used for measuring PA contents in fragments of single muscle fibers isolated from freeze-dried 100-150 microns thick cross sections. The fibers were typed according to their histochemically assessed mATPase in parallel cross sections. Type I fibers from rabbit tibialis anterior (TA) and vastus lateralis (VL) muscles contained extremely low PA concentrations (2-5 micrograms/g w.wt.). Type IIA fibers displayed slightly higher values with mean values of 17 and 29 micrograms/g w.wt. (range 5-65) in TA and VL, respectively. Much higher PA concentrations were found in type IIB fibers with wide ranges from 75-1150 micrograms/g w.wt. in TA and 440-1370 micrograms/g w.wt. in VL. Whereas the IIB fibers of the TA displayed a continuum, two subgroups were distinguishable according to their PA contents (means of 590 and 1230 micrograms/g w.wt.) in VL. Possibly, the population with the lower PA content which was histochemically defined as type IIB in the present study, corresponds to fiber type IID. The finding that PA is predominantly present in type IIB fibers was also confirmed by the parallel decay of PA and type IIB fibers during chronic low-frequency stimulation. The use of freeze substitution, or alternatively, of freeze-drying, made it possible to demonstrate PA immunohistochemically without artifacts and to evaluate the staining intensity by microphotometry.(ABSTRACT TRUNCATED AT 250 WORDS)

Finding the Volume of an Ellipsoid Using Cross-Sectional Slices

While I was consulting at a major medical complex, a medical researcher asked how he could find the volume of an object from cross-sectional slices through the object. (What actually happened was that foreign objects were imbedded in the lungs of a rat and, after some appropriate time period, a section of lung tissue was removed. Cross-sections were taken of the extracted section and some of the cross-sections contained slices through the mass formed by the body of the rat as it encased the implanted object. The researcher wanted to know the volume of the mass formed by the body when the section of tissue extracted contained only a portion of the mass.) However, the cross-sections of the mass appeared to be elliptical, and the researcher indicated that an ellipsoidal shape for the entire mass was expected. Thus I was led to consider (separate from this particular problem) whether the volume of an ellipsoid can be found exactly from some minimum number of parallel cross-sections. The purpose of this paper is to show how the volume can be calculated from three equally spaced slices. Assume an ellipsoid is positioned in three-dimensional space with the orientation of the ellipsoid unknown. Axes may be chosen so that the ellipsoid is centered at the origin, slices through the ellipsoid are made parallel to the xy-plane, and the x and y axes lie along the principal axes of the equatorial ellipse cut by z = 0. Thus, without loss of generality, we may suppose that the ellipsoid has equation

Parallel cross sections and canonical frames in normal bundles of immersed manifolds in Euclidean space

Article Parallel cross sections and canonical frames in normal bundles of immersed manifolds in Euclidean space was published on July 1, 1990 in the journal Demonstratio Mathematica (volume 23, issue 3).

Elastic and inelastic scattering of electrons by aligned light nuclei

The contribution to the elastic and inelastic scattering cross sections, Δ, due to alignment of nuclei having axial symmetry was calculated for scattering of unpolarized, ultra-relativistic electrons by7Li atoms. This contribution turned out to be on the order of magnitude of the cross section σ0 previously calculated in the absence of nuclear alignment. For various nuclear orientations, the ratios Δ/σo were calculated as a function of the momentum transfer q, which may be useful, for example, in increasing the reliability of identification of quantum numbers of nuclear states and multipole transitions. In contrast with the expression for σo, the expression for Δ contains cross products of reduced matrix elements (RME), along with the squares of their moduli. This permits one, having previously experimentally found σ0 and Δ under various kinematical conditions but for fixed q (the RME depend only on q), to obtain a system of equations for the RME and the statistical tensor g2, which characterizes the degree of alignment of the nuclear target, along with the separation of the parallel and perpendicular cross sections as in the case of unaligned nuclei. Having solved the system of equations, one finds g2 both in terms of the moduli of the RME of each multipole transition individually, and also in terms of their relative phases. The additional information thus obtained for each nuclear transition may serve as a more strict criterion for checking models of nuclei used in calculations than measurement of σ0 alone.