Background and Purpose—: Traditional vascular risk factors do not completely explain the asymmetry, racial, and sex differences in carotid artery disease. Carotid anatomy and geometry may play a role in the pathogenesis of internal carotid artery (ICA) stenosis, but their effects are unknown. We hypothesized that carotid artery anatomy and geometry would be independently associated with ICA stenosis. Method—: This is a retrospective study of patients with CT angiography at Monash Medical Centre, 2006 to 2007. Carotid arteries were segmented using semiautomated methods to estimate measures of carotid anatomy and geometry. Measurements of carotid artery geometry were performed according to the recent article by Thomas and colleagues. ICA stenosis was dichotomized as <30% or ≥30% stenosis. Cluster logistic regression was used to examine the associations of anatomy and geometry with stenosis accounting for the paired arteries within subjects, adjusting for age, sex, and vascular risk factors. Results—: Mean age of the sample (n=178) was 68.4 years (SD, 14 years). The following were independently associated with ICA stenosis: ICA radius at the bifurcation (OR, 0.20; 95% CI, 0.14–0.29), ICA angle (OR, 1.05 per degree increment; 95% CI, 1.04–1.07), age (OR, 1.05 per year increment; 95% CI, 1.03–1.07), male sex (OR, 1.72; 95% CI, 1.08–2.8), and ever-smoker (OR, 1.85; 95% CI, 1.15–2.96). Conclusions—: Carotid anatomy and geometry may enhance the risk of stenosis independent of traditional vascular risk factors and may be of help in very early identification of patients at high risk of developing carotid artery atherosclerosis for aggressive intervention.

Granular material freely discharging from a hopper under gravity is one of the oldest and most widely studied problems in granular flow. Despite the apparent simplicity of the system, expressions relating the discharge rate of the hopper to the properties of the individual grains are difficult to determine and typically empirical in nature. A mathematical model for discharge from a hopper is derived based on the dynamics of individual particles just within the outlet. In contrast to previous models, this analysis derives a flow rate from granular dynamics, rather than dimensional arguments. The model, therefore, uses no assumptions about the form of the stress distribution within the hopper, or the addition of empirical factors or fitting parameters. Our model gives a flow rate identical in form to a well-known empirical expression, showing that an experimentally determined constant used in this expression is purely geometry-dependent. Our analysis is also extended to derive an expression for the flow rate incorporating gas drag, which becomes dominant at small grain sizes, significantly reducing the outflow rate. The resulting expression shows excellent agreement with a range of computational simulations using a coupled discrete element and Navier-Stokes method. These simulations also show that the gas flow is much more complex than previously assumed in this region, and simplified assumptions used in prior hopper flow models do not hold.

The concept of ``random loose packing'' (RLP) has evolved through extensive study of loose packings of spheres, which has resulted in an accepted definition as the loosest packing that can be obtained by pouring grains. We extend this consideration to packings of nonspherical grains (ellipsoids) formed by slow settling in a viscous liquid, and perform a detailed analysis of the structural properties of the resulting packings. We find that as in the case of spheres the loosest ellipsoid packings are generated for grains with high interparticle friction. However, unlike spheres, these packings cannot be considered random as they have a significant degree of orientational ordering that increases with the grain's aspect ratio. This demonstrates that applying sedimentation or pouring techniques that have become part of the commonly held definition of RLP, will not generate random packings of ellipsoids. The consequences for the accepted definition of RLP and its applicability to nonspherical grains is discussed.