Imaging the femoral cortex: thickness, density and mass from clinical CT.

There is growing evidence that focal thinning of cortical bone in the proximal femur may predispose a hip to fracture. Detecting such defects in clinical CT is challenging, since cortices may be significantly thinner than the imaging system's point spread function. We recently proposed a model-fitting technique to measure sub-millimetre cortices, an ill-posed problem which was regularized by assuming a specific, fixed value for the cortical density. In this paper, we develop the work further by proposing and evaluating a more rigorous method for estimating the constant cortical density, and extend the paradigm to encompass the mapping of cortical mass (mineral mg/cm(2)) in addition to thickness. Density, thickness and mass estimates are evaluated on sixteen cadaveric femurs, with high resolution measurements from a micro-CT scanner providing the gold standard. The results demonstrate robust, accurate measurement of peak cortical density and cortical mass. Cortical thickness errors are confined to regions of thin cortex and are bounded by the extent to which the local density deviates from the peak, averaging 20% for 0.5mm cortex.

Imaging the femoral cortex: Thickness, density and mass from clinical CT

There is growing evidence that focal thinning of cortical bone in the proximal femur may predispose a hip to fracture. Detecting such defects in clinical CT is challenging, since cortices may be significantly thinner than the imaging system's point spread function. We recently proposed a model-fitting technique to measure sub-millimetre cortices, an ill-posed problem which was regularized by assuming a specific, fixed value for the cortical density. In this paper, we develop the work further by proposing and evaluating a more rigorous method for estimating the constant cortical density, and extend the paradigm to encompass the mapping of cortical mass (mineral mg/cm 2) in addition to thickness. Density, thickness and mass estimates are evaluated on sixteen cadaveric femurs, with high resolution measurements from a micro-CT scanner providing the gold standard. The results demonstrate robust, accurate measurement of peak cortical density and cortical mass. Cortical thickness errors are confined to regions of thin cortex and are bounded by the extent to which the local density deviates from the peak, averaging 20% for 0.5mm cortex. © 2012 Elsevier B.V.

Proposal for a novel and simple WDM NRZ-DPSK system

A novel and simple non-return-to-zero differential phase shift keying (NRZ-DPSK) wavelength division multiplexing (WDM) system, which can simultaneously demultiplex and demodulate multiple wavelengths, is proposed and investigated in this paper. The phase-to-intensity demodulation principle is based on detuned filtering, which is achieved by using a single commercial array waveguide grating (AWG) in our scheme. By properly choosing appropriate AWG channels at the transmitter, the AWG at the receiver can act as both the demultiplexer and the demodulator of the DPSK signals. Simulations at 10, 20, and 40 Gbit/s show good flexibility and performance for the proposed system. © 2009 Higher Education Press and Springer-Verlag GmbH.

Cortical thickness mapping to identify focal osteoporosis in patients with hip fracture.

BACKGROUND: Individuals with osteoporosis are predisposed to hip fracture during trips, stumbles or falls, but half of all hip fractures occur in those without generalised osteoporosis. By analysing ordinary clinical CT scans using a novel cortical thickness mapping technique, we discovered patches of markedly thinner bone at fracture-prone regions in the femurs of women with acute hip fracture compared with controls. METHODS: We analysed CT scans from 75 female volunteers with acute fracture and 75 age- and sex-matched controls. We classified the fracture location as femoral neck or trochanteric before creating bone thickness maps of the outer 'cortical' shell of the intact contra-lateral hip. After registration of each bone to an average femur shape and statistical parametric mapping, we were able to visualise and quantify statistically significant foci of thinner cortical bone associated with each fracture type, assuming good symmetry of bone structure between the intact and fractured hip. The technique allowed us to pinpoint systematic differences and display the results on a 3D average femur shape model. FINDINGS: The cortex was generally thinner in femoral neck fracture cases than controls. More striking were several discrete patches of statistically significant thinner bone of up to 30%, which coincided with common sites of fracture initiation (femoral neck or trochanteric). INTERPRETATION: Femoral neck fracture patients had a thumbnail-sized patch of focal osteoporosis at the upper head-neck junction. This region coincided with a weak part of the femur, prone to both spontaneous 'tensile' fractures of the femoral neck, and as a site of crack initiation when falling sideways. Current hip fracture prevention strategies are based on case finding: they involve clinical risk factor estimation to determine the need for single-plane bone density measurement within a standard region of interest (ROI) of the femoral neck. The precise sites of focal osteoporosis that we have identified are overlooked by current 2D bone densitometry methods.

On the application of differential geometry to MDO

Multidisciplinary Design Optimization (MDO) is a methodology for optimizing large coupled systems. Over the years, a number of different MDO decomposition strategies, known as architectures, have been developed, and various pieces of analytical work have been done on MDO and its architectures. However, MDO lacks an overarching paradigm which would unify the field and promote cumulative research. In this paper, we propose a differential geometry framework as such a paradigm: Differential geometry comes with its own set of analysis tools and a long history of use in theoretical physics. We begin by outlining some of the mathematics behind differential geometry and then translate MDO into that framework. This initial work gives new tools and techniques for studying MDO and its architectures while producing a naturally arising measure of design coupling. The framework also suggests several new areas for exploration into and analysis of MDO systems. At this point, analogies with particle dynamics and systems of differential equations look particularly promising for both the wealth of extant background theory that they have and the potential predictive and evaluative power that they hold. © 2012 by the American Institute of Aeronautics and Astronautics, Inc. All rights reserved.

Differential equation based length scales to improve DES and RANS simulations

Surprisingly expensive to compute wall distances are still used in a range of key turbulence and peripheral physics models. Potentially economical, accuracy improving differential equation based distance algorithms are considered. These involve elliptic Poisson and hyperbolic natured Eikonal equation approaches. Numerical issues relating to non-orthogonal curvilinear grid solution of the latter are addressed. Eikonal extension to a Hamilton-Jacobi (HJ) equation is discussed. Use of this extension to improve turbulence model accuracy and, along with the Eikonal, enhance Detached Eddy Simulation (DES) techniques is considered. Application of the distance approaches is studied for various geometries. These include a plane channel flow with a wire at the centre, a wing-flap system, a jet with co-flow and a supersonic double-delta configuration. Although less accurate than the Eikonal, Poisson method based flow solutions are extremely close to those using a search procedure. For a moving grid case the Poisson method is found especially efficient. Results show the Eikonal equation can be solved on highly stretched, non-orthogonal, curvilinear grids. A key accuracy aspect is that metrics must be upwinded in the propagating front direction. The HJ equation is found to have qualitative turbulence model improving properties. © 2003 by P. G. Tucker.