Estimating Particle Shape and Orientation Using Volume Tensors

We develop statistical procedures for estimating shape and orientation of arbitrary three-dimensional particles. We focus on the case where particles cannot be observed directly, but only via sections. Volume tensors are used for describing particle shape and orientation, and we derive stereological estimators of the tensors. These estimators are combined to provide consistent estimators of the moments of the so-called particle cover density. The covariance structure associated with the particle cover density depends on the orientation and shape of the particles. For instance, if the distribution of the typical particle is invariant under rotations, then the covariance matrix is proportional to the identity matrix. We develop a non-parametric test for such isotropy. A flexible Lévy-based particle model is proposed, which may be analysed using a generalized method of moments in which the volume tensors enter. The developed methods are used to study the cell organization in the human brain cortex.

Stereological estimation of particle shape and orientation from volume tensors

In the present paper, we describe new robust methods of estimating cell shape and orientation in 3D from sections. The descriptors of 3D cell shape and orientation are based on volume tensors which are used to construct an ellipsoid, the Miles ellipsoid, approximating the average cell shape and orientation in 3D. The estimators of volume tensors are based on observations in several optical planes through sampled cells. This type of geometric sampling design is known as the optical rotator. The statistical behaviour of the estimator of the Miles ellipsoid is studied under a flexible model for 3D cell shape and orientation. In a simulation study, the lengths of the axes of the Miles ellipsoid can be estimated with CVs of about 2% if 100 cells are sampled. Finally, we illustrate the use of the developed methods in an example, involving neurons in the medial prefrontal cortex of rat.

Wetting and spreading of a surfactant film on solid particles: influence of sharp edges and surface irregularities

In addition to particle size and surface chemistry, the shape of particles plays an important role in their wetting and displacement by the surfactant film in the lung. The role of particle shape was the subject of our investigations using a model system consisting of a modified Langmuir-Wilhelmy surface balance. We measured the influence of sharp edges (lines) and other highly curved surfaces, including sharp corners or spikes, of different particles on the spreading of a dipalmitoylphosphatidyl (DPPC) film. The edges of cylindrical sapphire plates (circular curved edges, 1.65 mm radius) were wetted at a surface tension of 10.7 mJ/m2 (standard error (SE) = 0.45, n = 20) compared with that of 13.8 mJ/m2 (SE = 0.20, n = 20) for cubic sapphire plates (straight linear edges, edge length 3 mm) (p < 0.05). The top surfaces of the sapphire plates (cubic and cylindrical) were wetted at 8.4 mJ/m2 (SE = 0.54, n = 20) and 9.1 mJ/m2 (SE = 0.50, n = 20), respectively, but the difference was not significant (p > 0.05). The surfaces of the plates showed significantly higher resistance to spreading compared to that of the edges, as substantially lower surface tensions were required to initiate wetting (p < 0.05). Similar results were found for talc particles, were the edges of macro- and microcrystalline particles were wetted at 7.2 mJ/m2 (SE = 0.52, n = 20) and 8.2 mJ/m2 (SE = 0.30, n = 20) (p > 0.05), respectively, whereas the surfaces were wetted at 3.8 mJ/m2 (SE = 0.89, n = 20) and 5.8 mJ/m2 (SE = 0.52, n = 20) (p < 0.05), respectively. Further experiments with pollen of malvaceae and maize (spiky and fine knobbly surfaces) were wetted at 10.0 mJ/m2 (SE = 0.52, n = 10) and 22.75 mJ/m2 (SE = 0.81, n = 10), respectively (p < 0.05). These results show that resistance to spreading of a DPPC film on various surfaces is dependent on the extent these surfaces are curved. This is seen with cubic sapphire plates which have at their corners a radius of curvature of about 0.75 microm, spiky malvaceae pollen with an even smaller radius on top of their spikes, or talc with various highly curved surfaces. These highly curved surfaces resisted wetting by the DPPC film to a higher degree than more moderately curved surfaces such as those of cylindrical sapphire plates, maize pollens, or polystyrene spheres, which have a surface free energy similar to that of talc but a smooth surface. The macroscopic plane surfaces of the particles demonstrated the greatest resistance to spreading. This was explained by the extremely fine grooves in the nanometer range, as revealed by electron microscopy. In summary, to understand the effects of airborne particles retained on the surfaces of the respiratory tract, and ultimately their pathological potential, not only the particle size and surface chemistry but also the particle shape should be taken in consideration.

Measurement of charged-particle event shape variables in inclusive √(s)=7 TeV proton-proton interactions with the ATLAS detector

The measurement of charged-particle event shape variables is presented in inclusive inelastic pp collisions at a center-of-mass energy of 7 TeV using the ATLAS detector at the LHC. The observables studied are the transverse thrust, thrust minor, and transverse sphericity, each defined using the final-state charged particles' momentum components perpendicular to the beam direction. Events with at least six charged particles are selected by a minimum-bias trigger. In addition to the differential distributions, the evolution of each event shape variable as a function of the leading charged-particle transverse momentum, charged-particle multiplicity, and summed transverse momentum is presented. Predictions from several Monte Carlo models show significant deviations from data.