Non-destructive quantification of tissue scaffolds and augmentation implants using X-ray microtomography

A three dimensional (3D), interconnected, porous structure is essential for bone tissue engineering scaffolds and skeletal augmentation implants. Current methods of characterising these structures, however, are limited to average properties such as percentage porosity. More accurate quantitative properties, such as pore and interconnect size distributions, are required. Once measured, these parameters need to be correlated to tissue regeneration and integration criteria, including solute transport, blood vessel regeneration, bone ingrowth, and mechanical properties. Ideally, these techniques would work in vitro and in vivo, and hence allow evaluation of osteoconduction and osseointegration after implantation. This thesis will focus on developing and applying algorithms for use with X-ray microtomography (micro-CT or μCT) which can non-destructively image internal structure at the micron scale. The technique will be demonstrated on two separate materials: bioactive glass scaffolds and titanium (Ti) augmentation devices. Using the developed techniques, the structural and compositional evolutions of bioactive glass scaffolds in a simulated body fluid (SBF) flow environment were quantified using micro-CT scans taken at different dissolution stages. Results show that 70S30C bioactive scaffolds retain favourable 3D structures during a 28 d dissolution experiment, with a modal equivalent pore diameter of 682 μm staying unchanged, and a modal equivalent interconnect diameter decreasing from 252 μm to 209 μm. The techniques were then applied to porous Ti augmentation scaffolds. These scaffolds, produced by selective laser melting have very different pore networks with graded randomness and unit size. They present new challenges when applying the developed micro-CT quantification techniques. Using a further adapted methodology, the interconnecting pore sizes, strut thickness, and surface roughness were measured. This demonstrated the robustness of the methodologies and their applicability to a range of tissue scaffolds and augmentation devices

Distributed linear regression by averaging

Distributed statistical learning problems arise commonly when dealing with large datasets. In this setup, datasets are partitioned over machines, which compute locally, and communicate short messages. Communication is often the bottleneck. In this paper, we study one-step and iterative weighted parameter averaging in statistical linear models under data parallelism. We do linear regression on each machine, send the results to a central server, and take a weighted average of the parameters. Optionally, we iterate, sending back the weighted average and doing local ridge regressions centered at it. How does this work compared to doing linear regression on the full data? Here we study the performance loss in estimation, test error, and confidence interval length in high dimensions, where the number of parameters is comparable to the training data size. We find the performance loss in one-step weighted averaging, and also give results for iterative averaging. We also find that different problems are affected differently by the distributed framework. Estimation error and confidence interval length increase a lot, while prediction error increases much less. We rely on recent results from random matrix theory, where we develop a new calculus of deterministic equivalents as a tool of broader interest.Comment: V2 adds a new section on iterative averaging methods, adds applications of the calculus of deterministic equivalents, and reorganizes the pape

Preparation and Characterization of High-Temperature Thermally Stable Alumina Composite Membrane

A crack- and pinhole-free composite membrane consisting of an α-alumina support and a modified γ-alumina top layer which is thermally stable up to 1100°C was prepared by the sol–gel method. The supported thermally stable top layer was made by dipcoating the support with a boehmite sol doped with lanthanum nitrate. The temperature effects on the microstructure of the (supported and unsupported) La-doped top layers were compared with those of a common γ-alumina membrane (without doping with lanthanum), using the gas permeability and nitrogen adsorption porosimetry data. After sintering at 1100°C for 30 h, the average pore diameter of the La-doped alumina top layer was 17 nm, compared to 109 nm for the common alumina top layer. Addition of poly(vinyl alcohol) to the colloid boehmite precursor solution prevented formation of defects in the γ-alumina top layer. After sintering at temperatures higher than 900°C, the common alumina top layer with addition of poly(vinyl alcohol) exhibits a bimodal pore distribution. The La-doped alumina top layer (also with addition of poly(vinyl alcohol)) retains a monopore distribution after sintering at 1200°C

Rational Solutions of the Painlev\'e-II Equation Revisited

The rational solutions of the Painlev\'e-II equation appear in several applications and are known to have many remarkable algebraic and analytic properties. They also have several different representations, useful in different ways for establishing these properties. In particular, Riemann-Hilbert representations have proven to be useful for extracting the asymptotic behavior of the rational solutions in the limit of large degree (equivalently the large-parameter limit). We review the elementary properties of the rational Painlev\'e-II functions, and then we describe three different Riemann-Hilbert representations of them that have appeared in the literature: a representation by means of the isomonodromy theory of the Flaschka-Newell Lax pair, a second representation by means of the isomonodromy theory of the Jimbo-Miwa Lax pair, and a third representation found by Bertola and Bothner related to pseudo-orthogonal polynomials. We prove that the Flaschka-Newell and Bertola-Bothner Riemann-Hilbert representations of the rational Painlev\'e-II functions are explicitly connected to each other. Finally, we review recent results describing the asymptotic behavior of the rational Painlev\'e-II functions obtained from these Riemann-Hilbert representations by means of the steepest descent method

Anisotropic emission of thermal dielectrons from Au+Au collisions at sNN=200\sqrt{s_{NN}}=200~GeV with EPOS3

Dileptons, as an electromagnetic probe, are crucial to study the properties of a Quark-Gluon Plasma (QGP) created in heavy ion collisions. We calculated the invariant mass spectra and the anisotropic emission of thermal dielectrons from Au+Au collisions at the Relativistic Heavy Ion Collider (RHIC) energy $\sqrt{s_{NN}}=200$~GeV based on EPOS3. This approach provides a realistic (3+1)-dimensional event-by-event viscous hydrodynamic description of the expanding hot and dense matter with a very particular initial condition, and a large set of hadron data and direct photons (besides $v_{2}$ and $v_{3}$ !) can be successfully reproduced. Thermal dilepton emission from both the QGP phase and the hadronic gas are considered, with the emission rates based on Lattice QCD and a vector meson model, respectively. We find that the computed invariant mass spectra (thermal contribution + STAR cocktail) can reproduce the measured ones from STAR at different centralities. Different compared to other model predictions, the obtained elliptic flow of thermal dileptons is larger than the STAR measurement referring to all dileptons. We observe a clear centrality dependence of thermal dilepton not only for elliptic flow $v_{2}$ but also for higher orders. At a given centrality, $v_{n}$ of thermal dileptons decreases monotonically with $n$ for $2\leq n\leq5$.Comment: 10pages, 12fig