The closest elastic tensor of arbitrary symmetry to an elasticity tensor of lower symmetry

The closest tensors of higher symmetry classes are derived in explicit form for a given elasticity tensor of arbitrary symmetry. The mathematical problem is to minimize the elastic length or distance between the given tensor and the closest elasticity tensor of the specified symmetry. Solutions are presented for three distance functions, with particular attention to the Riemannian and log-Euclidean distances. These yield solutions that are invariant under inversion, i.e., the same whether elastic stiffness or compliance are considered. The Frobenius distance function, which corresponds to common notions of Euclidean length, is not invariant although it is simple to apply using projection operators. A complete description of the Euclidean projection method is presented. The three metrics are considered at a level of detail far greater than heretofore, as we develop the general framework to best fit a given set of moduli onto higher elastic symmetries. The procedures for finding the closest elasticity tensor are illustrated by application to a set of 21 moduli with no underlying symmetry.Comment: 48 pages, 1 figur

People in different age groups show different hip-joint morphology

It has been suggested that the distribution of the subchondral bone density may be regarded as the expression of the long-term effective stress in a joint, and previous results indicate the regularity of the distribution of subchondral bone density as a function of the passing demands made upon a joint. Computed tomography-osteoabsorptiometry has been developed to visualize the area distribution of subchondral mineralization in the major joints in vivo. The purpose of this study was to display the distribution of subchondral bone density in the acetabular cup of patients of different ages. Computer tomography data files of hip joints of 27 patients (18–89 years) were used. Density ranges, image analysis, and area presentation of the distribution of subchondral mineralization are presented. The maximal subchondral mineralization in young persons is found both in the ventral and dorsal part of the acetabular roof. In older people, however, the densest areas are most often found at the zenith of the acetabulum. These morphological results could be well explained by the experimental results of other authors who found a joint incongruity in young persons with contact areas in the ventral and dorsal part of the acetabulum. With advancing age a decrease in incongruence is found, leading to an increased stress in the dome, i.e. in the area where degenerative changes are often found

Multiscale Bone Remodelling with Spatial P Systems

Many biological phenomena are inherently multiscale, i.e. they are characterized by interactions involving different spatial and temporal scales simultaneously. Though several approaches have been proposed to provide "multilayer" models, only Complex Automata, derived from Cellular Automata, naturally embed spatial information and realize multiscaling with well-established inter-scale integration schemas. Spatial P systems, a variant of P systems in which a more geometric concept of space has been added, have several characteristics in common with Cellular Automata. We propose such a formalism as a basis to rephrase the Complex Automata multiscaling approach and, in this perspective, provide a 2-scale Spatial P system describing bone remodelling. The proposed model not only results to be highly faithful and expressive in a multiscale scenario, but also highlights the need of a deep and formal expressiveness study involving Complex Automata, Spatial P systems and other promising multiscale approaches, such as our shape-based one already resulted to be highly faithful.Comment: In Proceedings MeCBIC 2010, arXiv:1011.005

Morphogenesis of growing soft tissues

Recently, much attention has been given to a noteworthy property of some soft tissues: their ability to grow. Many attempts have been made to model this behaviour in biology, chemistry and physics. Using the theory of finite elasticity, Rodriguez has postulated a multiplicative decomposition of the geometric deformation gradient into a growth-induced part and an elastic one needed to ensure compatibility of the body. In order to fully explore the consequences of this hypothesis, the equations describing thin elastic objects under finite growth are derived. Under appropriate scaling assumptions for the growth rates, the proposed model is of the Foppl-von Karman type. As an illustration, the circumferential growth of a free hyperelastic disk is studied.Comment: 4 pages, 3 figure

Transmembrane protein PERP is a component of tessellate junctions and of other junctional and non-junctional plasma membrane regions in diverse epithelial and epithelium-derived cells

Protein PERP (p53 apoptosis effector related to PMP-22) is a small (21.4 kDa) transmembrane polypeptide with an amino acid sequence indicative of a tetraspanin character. It is enriched in the plasma membrane and apparently contributes to cell-cell contacts. Hitherto, it has been reported to be exclusively a component of desmosomes of some stratified epithelia. However, by using a series of newly generated mono- and polyclonal antibodies, we show that protein PERP is not only present in all kinds of stratified epithelia but also occurs in simple, columnar, complex and transitional epithelia, in various types of squamous metaplasia and epithelium-derived tumors, in diverse epithelium-derived cell cultures and in myocardial tissue. Immunofluorescence and immunoelectron microscopy allow us to localize PERP predominantly in small intradesmosomal locations and in variously sized, junction-like peri- and interdesmosomal regions (“tessellate junctions”), mostly in mosaic or amalgamated combinations with other molecules believed, to date, to be exclusive components of tight and adherens junctions. In the heart, PERP is a major component of the composite junctions of the intercalated disks connecting cardiomyocytes. Finally, protein PERP is a cobblestone-like general component of special plasma membrane regions such as the bile canaliculi of liver and subapical-to-lateral zones of diverse columnar epithelia and upper urothelial cell layers. We discuss possible organizational and architectonic functions of protein PERP and its potential value as an immunohistochemical diagnostic marker

Tissue Microenvironments Define and Get Reinforced by Macrophage Phenotypes in Homeostasis or during Inflammation, Repair and Fibrosis

Current macrophage phenotype classifications are based on distinct in vitro culture conditions that do not adequately mirror complex tissue environments. In vivo monocyte progenitors populate all tissues for immune surveillance which supports the maintenance of homeostasis as well as regaining homeostasis after injury. Here we propose to classify macrophage phenotypes according to prototypical tissue environments, e.g. as they occur during homeostasis as well as during the different phases of (dermal) wound healing. In tissue necrosis and/or infection, damage- and/or pathogen-associated molecular patterns induce proinflammatory macrophages by Toll-like receptors or inflammasomes. Such classically activated macrophages contribute to further tissue inflammation and damage. Apoptotic cells and antiinflammatory cytokines dominate in postinflammatory tissues which induce macrophages to produce more antiinflammatory mediators. Similarly, tumor-associated macrophages also confer immunosuppression in tumor stroma. Insufficient parenchymal healing despite abundant growth factors pushes macrophages to gain a profibrotic phenotype and promote fibrocyte recruitment which both enforce tissue scarring. Ischemic scars are largely devoid of cytokines and growth factors so that fibrolytic macrophages that predominantly secrete proteases digest the excess extracellular matrix. Together, macrophages stabilize their surrounding tissue microenvironments by adapting different phenotypes as feed-forward mechanisms to maintain tissue homeostasis or regain it following injury. Furthermore, macrophage heterogeneity in healthy or injured tissues mirrors spatial and temporal differences in microenvironments during the various stages of tissue injury and repair. Copyright (C) 2012 S. Karger AG, Base

New Suggestions for the Mechanical Control of Bone Remodeling

Bone is constantly renewed over our lifetime through the process of bone (re)modeling. This process is important for bone to allow it to adapt to its mechanical environment and to repair damage from everyday life. Adaptation is thought to occur through the mechanosensitive response controlling the bone-forming and -resorbing cells. This report shows a way to extract quantitative information about the way remodeling is controlled using computer simulations. Bone resorption and deposition are described as two separate stochastic processes, during which a discrete bone packet is removed or deposited from the bone surface. The responses of the bone-forming and -resorbing cells to local mechanical stimuli are described by phenomenological remodeling rules. Our strategy was to test different remodeling rules and to evaluate the time evolution of the trabecular architecture in comparison to what is known from μ-CT measurements of real bone. In particular, we tested the reaction of virtual bone to standard therapeutic strategies for the prevention of bone deterioration, i.e., physical activity and medications to reduce bone resorption. Insensitivity of the bone volume fraction to reductions in bone resorption was observed in the simulations only for a remodeling rule including an activation barrier for the mechanical stimulus above which bone deposition is switched on. This is in disagreement with the commonly used rules having a so-called lazy zone