Moment Closure - A Brief Review

Moment closure methods appear in myriad scientific disciplines in the modelling of complex systems. The goal is to achieve a closed form of a large, usually even infinite, set of coupled differential (or difference) equations. Each equation describes the evolution of one "moment", a suitable coarse-grained quantity computable from the full state space. If the system is too large for analytical and/or numerical methods, then one aims to reduce it by finding a moment closure relation expressing "higher-order moments" in terms of "lower-order moments". In this brief review, we focus on highlighting how moment closure methods occur in different contexts. We also conjecture via a geometric explanation why it has been difficult to rigorously justify many moment closure approximations although they work very well in practice.Comment: short survey paper (max 20 pages) for a broad audience in mathematics, physics, chemistry and quantitative biolog

Spondylodiscitis following endovascular abdominal aortic aneurysm repair: imaging perspectives from a single centre's experience.

OBJECTIVE: Very few reports have previously described spondylodiscitis as a potential complication of endovascular aortic aneurysm repair (EVAR). We present to our knowledge the first case series of spondylodiscitis following EVAR based on our institution's experience over an 11-year period. Particular attention is paid to the key imaging features and challenges encountered when performing spinal imaging in this complex patient group. MATERIALS AND METHODS: Of 1,847 patients who underwent EVAR at our institution between January 2006 and January 2017, a total of 9 patients were identified with imaging features of spondylodiscitis (0.5%). All cross-sectional studies before and after EVAR were assessed by a Consultant Musculoskeletal Radiologist and a Musculoskeletal Radiology Fellow to evaluate for features of spondylodiscitis. RESULTS: All 9 patients had single-level spondylodiscitis involving lumbosacral levels adjacent to the aortic/iliac stent graft. Eight out of nine patients had an extensive anterior paravertebral phlegmon/abscess that was contiguous with the infected stent graft and native aneurysm sac ± anterior vertebral body erosion. Epidural disease was present in only 3 out of 9 patients and was a minor feature. MRI was non-diagnostic in 3 out of 9 patients owing to susceptibility artefact. 18F-FDG PET/CT accurately depicted the spinal level involved and adjacent paravertebral disease in patients with non-diagnostic MRI and was adopted as the follow-up modality in 3 out of 5 surviving patients. CONCLUSION: Spondylodiscitis is a rare complication post-EVAR. Imaging features of disproportionate anterior paravertebral disease and anterior vertebral body bony involvement suggest direct spread of infection posteriorly to the adjacent vertebral column. Use of MRI versus 18F-FDG PET/CT as the optimal imaging modality should be directed by the type of stent graft deployed

Development and characterisation of a large diameter decellularised vascular allograft

The aims of this study were to develop a biological large diameter vascular graft by decellularisation of native human aorta to remove the immunogenic cells whilst retaining the essential biomechanical, and biochemical properties for the ultimate benefit of patients with infected synthetic grafts. Donor aortas (n = 6) were subjected to an adaptation of a propriety decellularisation process to remove the cells and acellularity assessed by histological analysis and extraction and quantification of total DNA. The biocompatibility of the acellular aortas was determined using standard contact cytotoxicity tests. Collagen and denatured collagen content of aortas was determined and immunohistochemistry was used to determine the presence of specific extracellular matrix proteins. Donor aortas (n = 6) were divided into two, with one half subject to decellularisation and the other half retained as native tissue. The native and decellularised aorta sections were then subject to uniaxial tensile testing to failure [axial and circumferential directions] and suture retention testing. The data was compared using a paired t-test. Histological evaluation showed an absence of cells in the treated aortas and retention of histoarchitecture including elastin content. The decellularised aortas had less than 15 ng mg¯¹ total DNA per dry weight (mean 94% reduction) and were biocompatible as determined by in vitro contact cytotoxicity tests. There were no gross changes in the histoarchitecture [elastin and collagen matrix] of the acellular aortas compared to native controls. The decellularisation process also reduced calcium deposits within the tissue. The uniaxial tensile and suture retention testing revealed no significant differences in the material properties (p > 0.05) of decellularised aorta. The decellularisation procedure resulted in minimal changes to the biological and biomechanical properties of the donor aortas. Acellular donor aorta has excellent potential for use as a large diameter vascular graft

Dynamics of spherically symmetric spacetimes: hydrodynamics and radiation

Using the 3+1 formalism of general relativity we obtain the equations governing the dynamics of spherically symmetric spacetimes with arbitrary sources. We then specialize for the case of perfect fluids accompanied by a flow of interacting massless or massive particles (e.g. neutrinos) which are described in terms of relativistic transport theory. We focus in three types of coordinates: 1) isotropic gauge and maximal slicing, 2) radial gauge and polar slicing, and 3) isotropic gauge and polar slicing.Comment: submitted to Phys. Rev. D, 46 pages, RevTex file, no figure

Hand osteoarthritis: clinical phenotypes, molecular mechanisms and disease management

Osteoarthritis (OA) is a highly prevalent condition and the hand is the most commonly affected site. Patients with hand OA frequently report symptoms of pain, functional limitations, and frustration in undertaking everyday activities. The condition presents clinically with changes to the bone, ligaments, cartilage and synovial tissue, which can be observed using radiography, ultrasonography or MRI. Hand OA is a heterogeneous disorder and is considered to be multifactorial in aetiology. This review provides an overview of the epidemiology, presentation and burden of hand OA, including an update on hand OA imaging (including the development of novel techniques), disease mechanisms and management. In particular, areas for which new evidence has substantially changed the way we understand, consider and treat hand OA are highlighted. For example, genetic studies, clinical trials and careful prospective imaging studies from the past 5 years are beginning to provide insights into the pathogenesis of hand OA that might uncover new therapeutic targets in disease