Articular human joint modelling

Copyright @ Cambridge University Press 2009.The work reported in this paper encapsulates the theories and algorithms developed to drive the core analysis modules of the software which has been developed to model a musculoskeletal structure of anatomic joints. Due to local bone surface and contact geometry based joint kinematics, newly developed algorithms make the proposed modeller different from currently available modellers. There are many modellers that are capable of modelling gross human body motion. Nevertheless, none of the available modellers offer complete elements of joint modelling. It appears that joint modelling is an extension of their core analysis capability, which, in every case, appears to be musculoskeletal motion dynamics. It is felt that an analysis framework that is focused on human joints would have significant benefit and potential to be used in many orthopaedic applications. The local mobility of joints has a significant influence in human motion analysis, in understanding of joint loading, tissue behaviour and contact forces. However, in order to develop a bone surface based joint modeller, there are a number of major problems, from tissue idealizations to surface geometry discretization and non-linear motion analysis. This paper presents the following: (a) The physical deformation of biological tissues as linear or non-linear viscoelastic deformation, based on spring-dashpot elements. (b) The linear dynamic multibody modelling, where the linear formulation is established for small motions and is particularly useful for calculating the equilibrium position of the joint. This model can also be used for finding small motion behaviour or loading under static conditions. It also has the potential of quantifying the joint laxity. (c) The non-linear dynamic multibody modelling, where a non-matrix and algorithmic formulation is presented. The approach allows handling complex material and geometrical nonlinearity easily. (d) Shortest path algorithms for calculating soft tissue line of action geometries. The developed algorithms are based on calculating minimum ‘surface mass’ and ‘surface covariance’. An improved version of the ‘surface covariance’ algorithm is described as ‘residual covariance’. The resulting path is used to establish the direction of forces and moments acting on joints. This information is needed for linear or non-linear treatment of the joint motion. (e) The final contribution of the paper is the treatment of the collision. In the virtual world, the difficulty in analysing bodies in motion arises due to body interpenetrations. The collision algorithm proposed in the paper involves finding the shortest projected ray from one body to the other. The projection of the body is determined by the resultant forces acting on it due to soft tissue connections under tension. This enables the calculation of collision condition of non-convex objects accurately. After the initial collision detection, the analysis involves attaching special springs (stiffness only normal to the surfaces) at the ‘potentially colliding points’ and motion of bodies is recalculated. The collision algorithm incorporates the rotation as well as translation. The algorithm continues until the joint equilibrium is achieved. Finally, the results obtained based on the software are compared with experimental results obtained using cadaveric joints

The Two Roads to "Intrinsic Charm" in B Decays

We describe two complementary ways to show the presence of higher order effects in the 1/m_Q expansion for inclusive B decays that have been dubbed "Intrinsic Charm". Apart from the lessons they can teach us about QCD's nonperturbative dynamics their consideration is relevant for precise extractions of |V_{cb}|: for they complement the estimate of the potential impact of 1/m_Q^4 contributions. We draw semiquantitative conclusions for the expected scale of Weak Annihilation in semileptonic B decays, both for its valence and non-valence components.Comment: 17 pages, 3 figure

The Aerodynamic Performance of the Houck Configuration Flow Guides

In an effort to explore efficient wing designs for UAV\u27s, the Air Force is investigating the patented Houck Aircraft Configuration, which is a joined-wing aircraft with curved flow guides of varying camber connecting the upper and lower wingtips. Models were drawn in three-dimensions using Solidworks® with upper and lower wings drawn as identical NACA 2412 airfoil sections for all models. A variety of airfoil sections between the upper and lower wingtips were drawn and rotated to achieve a combination of cant and angle of attack variation. Subsequently, a solid part was lofted through these sections and merged with the upper and lower wings. Each model was built by a rapid prototype machine. A six-component balance in the AFIT low-speed wind tunnel provided measurements yielding the aerodynamic data of each model. Comparisons are made to the same basic planform area without flow guides and to a case where the wingtips are joined with a flat plate. At a Reynolds number of 38K, the increase in skin friction drag outweighed any possible reduction of induced drag. However for Reynolds numbers in the 57K to 120K range, improvements in L/Dmax of about 2-5% over the no flow guide case were measured