Coronary artery stent geometry and in-stent contrast attenuation with 64-slice computed tomography

We aimed at assessing stent geometry and in-stent contrast attenuation with 64-slice CT in patients with various coronary stents. Twenty-nine patients (mean age 60 +/- 11 years; 24 men) with 50 stents underwent CT within 2 weeks after stent placement. Mean in-stent luminal diameter and reference vessel diameter proximal and distal to the stent were assessed with CT, and compared to quantitative coronary angiography (QCA). Stent length was also compared to the manufacturer's values. Images were reconstructed using a medium-smooth (B30f) and sharp (B46f) kernel. All 50 stents could be visualized with CT. Mean in-stent luminal diameter was systematically underestimated with CT compared to QCA (1.60 +/- 0.39 mm versus 2.49 +/- 0.45 mm; P < 0.0001), resulting in a modest correlation of QCA versus CT (r = 0.49; P < 0.0001). Stent length as given by the manufacturer was 18.2 +/- 6.2 mm, correlating well with CT (18.5 +/- 5.7 mm; r = 0.95; P < 0.0001) and QCA (17.4 +/- 5.6 mm; r = 0.87; P < 0.0001). Proximal and distal reference vessel diameters were similar with CT and QCA (P = 0.06 and P = 0.03). B46f kernel images showed higher image noise (P < 0.05) and lower in-stent CT attenuation values (P < 0.001) than images reconstructed with the B30f kernel. 64-slice CT allows measurement of coronary artery in-stent density, and significantly underestimates the true in-stent diameter compared to QCA.

Regional structural characteristics of bovine periodontal ligament samples and their suitability for biomechanical tests

Mechanical testing of the periodontal ligament requires a practical experimental model. Bovine teeth are advantageous in terms of size and availability, but information is lacking as to the anatomy and histology of their periodontium. The aim of this study, therefore, was to characterize the anatomy and histology of the attachment apparatus in fully erupted bovine mandibular first molars. A total of 13 teeth were processed for the production of undecalcified ground sections and decalcified semi-thin sections, for NaOH maceration, and for polarized light microscopy. Histomorphometric measurements relevant to the mechanical behavior of the periodontal ligament included width, number, size and area fraction of blood vessels and fractal analysis of the two hard-soft tissue interfaces. The histological and histomorphometric analyses were performed at four different root depths and at six circumferential locations around the distal and mesial roots. The variety of techniques applied provided a comprehensive view of the tissue architecture of the bovine periodontal ligament. Marked regional variations were observed in width, surface geometry of the two bordering hard tissues (cementum and alveolar bone), structural organization of the principal periodontal ligament connective tissue fibers, size, number and numerical density of blood vessels in the periodontal ligament. No predictable pattern was observed, except for a statistically significant increase in the area fraction of blood vessels from apical to coronal. The periodontal ligament width was up to three times wider in bovine teeth than in human teeth. The fractal analyses were in agreement with the histological observations showing frequent signs of remodeling activity in the alveolar bone - a finding which may be related to the magnitude and direction of occlusal forces in ruminants. Although samples from the apical root portion are not suitable for biomechanical testing, all other levels in the buccal and lingual aspects of the mesial and distal roots may be considered. The bucco-mesial aspect of the distal root appears to be the most suitable location.

Rotational integral geometry of tensor valuations

We derive a new rotational Crofton formula for Minkowski tensors. In special cases, this formula gives (1) the rotational average of Minkowski tensors defined on linear subspaces and (2) the functional defined on linear subspaces with rotational average equal to a Minkowski tensor. Earlier results obtained for intrinsic volumes appear now as special cases.

Foundations of stochastic geometry and theory of random sets

The first section of this chapter starts with the Buffon problem, which is one of the oldest in stochastic geometry, and then continues with the definition of measures on the space of lines. The second section defines random closed sets and related measurability issues, explains how to characterize distributions of random closed sets by means of capacity functionals and introduces the concept of a selection. Based on this concept, the third section starts with the definition of the expectation and proves its convexifying effect that is related to the Lyapunov theorem for ranges of vector-valued measures. Finally, the strong law of large numbers for Minkowski sums of random sets is proved and the corresponding limit theorem is formulated. The chapter is concluded by a discussion of the union-scheme for random closed sets and a characterization of the corresponding stable laws.

Analysis of fractal electrodes for efficient neural stimulation

Planar electrodes are increasingly used in therapeutic neural stimulation techniques such as functional electrical stimulation, epidural spinal cord stimulation (ESCS), and cortical stimulation. Recently, optimized electrode geometries have been shown to increase the efficiency of neural stimulation by increasing the variation of current density on the electrode surface. In the present work, a new family of modified fractal electrode geometries is developed to enhance the efficiency of neural stimulation. It is shown that a promising approach in increasing the neural activation function is to increase the "edginess" of the electrode surface, a concept that is explained and quantified by fractal mathematics. Rigorous finite element simulations were performed to compute electric potential produced by proposed modified fractal geometries. The activation of 256 model axons positioned around the electrodes was then quantified, showing that modified fractal geometries required a 22% less input power while maintaining the same level of neural activation. Preliminary in vivo experiments investigating muscle evoked potentials due to median nerve stimulation showed encouraging results, supporting the feasibility of increasing neural stimulation efficiency using modified fractal geometries.

Characterization of granite matrix porosity and pore-space geometry by in situ and laboratory methods

Most available studies of interconnected matrix porosity of crystalline rocks are based on laboratory investigations; that is, work on samples that have undergone stress relaxation and were affected by drilling and sample preparation. The extrapolation of the results to in situ conditions is therefore associated with considerable uncertainty, and this was the motivation to conduct the ‘in situ Connected Porosity’ experiment at the Grimsel Test Site (Central Swiss Alps). An acrylic resin doped with fluorescent agents was used to impregnate the microporous granitic matrix in situ around an injection borehole, and samples were obtained by overcoring. The 3-D structure of the porespace, represented by microcracks, was studied by U-stage fluorescence microscopy. Petrophysical methods, including the determination of porosity, permeability and P -wave velocity, were also applied. Investigations were conducted both on samples that were impregnated in situ and on non-impregnated samples, so that natural features could be distinguished from artefacts. The investigated deformed granites display complex microcrack populations representing a polyphase deformation at varying conditions. The crack population is dominated by open cleavage cracks in mica and grain boundary cracks. The porosity of non-impregnated samples lies slightly above 1 per cent, which is 2–2.5 times higher than the in situ porosity obtained for impregnated samples. Measurements of seismic velocities (Vp ) on spherical rock samples as a function of confining pressure, spatial direction and water saturation for both non-impregnated and impregnated samples provide further constraints on the distinction between natural and induced crack types. The main conclusions are that (1) an interconnected network of microcracks exists in the whole granitic matrix, irrespective of the distance to ductile and brittle shear zones, and (2) conventional laboratory methods overestimate the matrix porosity. Calculations of contaminant transport through fractured media often rely on matrix diffusion as a retardation mechanism.