Identification of clinical phenotypes in knee osteoarthritis: a systematic review of the literature

Background: Knee Osteoarthritis (KOA) is a heterogeneous pathology characterized by a complex and multifactorial nature. It has been hypothesised that these differences are due to the existence of underlying phenotypes representing different mechanisms of the disease.Methods: The aim of this study is to identify the current evidence for the existence of groups of variables which point towards the existence of distinct clinical phenotypes in the KOA population. A systematic literature search in PubMed was conducted. Only original articles were selected if they aimed to identify phenotypes of patients aged 18 years or older with KOA. The methodological quality of the studies was independently assessed by two reviewers and qualitative synthesis of the evidence was performed. Strong evidence for existence of specific phenotypes was considered present if the phenotype was supported by at least two high-quality studies.Results: A total of 24 studies were included. Through qualitative synthesis of evidence, six main sets of variables proposing the existence of six phenotypes were identified: 1) chronic pain in which central mechanisms (e.g. central sensitisation) are prominent; 2) inflammatory (high levels of inflammatory biomarkers); 3) metabolic syndrome (high prevalence of obesity, diabetes and other metabolic disturbances); 4) Bone and cartilage metabolism (alteration in local tissue metabolism); 5) mechanical overload characterised primarily by varus malalignment and medial compartment disease; and 6) minimal joint disease characterised as minor clinical symptoms with slow progression over time.Conclusions: This study identified six distinct groups of variables which should be explored in attempts to better define clinical phenotypes in the KOA population

Analytical continuum mechanics \`a la Hamilton-Piola: least action principle for second gradient continua and capillary fluids

In this paper a stationary action principle is proven to hold for capillary fluids, i.e. fluids for which the deformation energy has the form suggested, starting from molecular arguments, for instance by Cahn and Hilliard. Remark that these fluids are sometimes also called Korteweg-de Vries or Cahn-Allen. In general continua whose deformation energy depend on the second gradient of placement are called second gradient (or Piola-Toupin or Mindlin or Green-Rivlin or Germain or second gradient) continua. In the present paper, a material description for second gradient continua is formulated. A Lagrangian action is introduced in both material and spatial description and the corresponding Euler-Lagrange bulk and boundary conditions are found. These conditions are formulated in terms of an objective deformation energy volume density in two cases: when this energy is assumed to depend on either C and grad C or on C^-1 and grad C^-1 ; where C is the Cauchy-Green deformation tensor. When particularized to energies which characterize fluid materials, the capillary fluid evolution conditions (see e.g. Casal or Seppecher for an alternative deduction based on thermodynamic arguments) are recovered. A version of Bernoulli law valid for capillary fluids is found and, in the Appendix B, useful kinematic formulas for the present variational formulation are proposed. Historical comments about Gabrio Piola's contribution to continuum analytical mechanics are also presented. In this context the reader is also referred to Capecchi and Ruta.Comment: 52 page

On the well posedness of static boundary value problem within the linear dilatational strain gradient elasticity

AbstractIn this paper, it is proven an existence and uniqueness theorem for weak solutions of the equilibrium problem for linear isotropic dilatational strain gradient elasticity. Considered elastic bodies have as deformation energy the classical one due to Lamé but augmented with an additive term that depends on the norm of the gradient of dilatation: only one extra second gradient elastic coefficient is introduced. The studied class of solids is therefore related to Korteweg or Cahn–Hilliard fluids. The postulated energy naturally induces the space in which the aforementioned well-posedness result can be formulated. In this energy space, the introduced norm does involve the linear combination of some specific higher-order derivatives only: it is, in fact, a particular example of anisotropic Sobolev space. It is also proven that aforementioned weak solutions belongs to the space $$H^1(div,V)$$ H 1 ( d i v , V ) , i.e. the space of $$H^1$$ H 1 functions whose divergence belongs to $$H^1$$ H 1 . The proposed mathematical frame is essential to conceptually base, on solid grounds, the numerical integration schemes required to investigate the properties of dilatational strain gradient elastic bodies. Their energy, as studied in the present paper, has manifold interests. Mathematically speaking, its singularity causes interesting mathematical difficulties whose overcoming leads to an increased understanding of the theory of second gradient continua. On the other hand, from the mechanical point of view, it gives an example of energy for a second gradient continuum which can sustain externally applied surface forces and double forces but cannot sustain externally applied surface couples. In this way, it is proven that couple stress continua, introduced by Toupin, represent only a particular case of the more general class of second gradient continua. Moreover, it is easily checked that for dilatational strain gradient continua, balance of force and balance of torques (or couples) are not enough to characterise equilibrium: to this aim, externally applied surface double forces must also be specified. As a consequence, the postulation scheme based on variational principles seems more suitable to study second gradient continua. It has to be remarked finally that dilatational strain gradient seems suitable to model the experimentally observed behaviour of some material used in 3D printing process

The bias-extension test for the analysis of in-plane shear properties of textile composite reinforcements and prepregs: a review

The bias-extension test is a rather simple experiment aiming to determine in-plane shear properties of textile composite reinforcements. However the mechanics during the test involves fibrous material at large shear strains and large rotations of the fibres. Several aspects are still being studied and are not yet modeled in a consensual manner. The standard analysis of the test is based on two assumptions: inextensibility of the fibers and rotations at the yarn crossovers without slippage. They lead to the development of zones with constant fibre orientations proper to the bias-extension test. Beyond the analysis of the test within these basic assumptions, the paper presents studies that have been carried out on the lack of verification of these hypothesis (slippage, tension in the yarns, effects of fibre bending). The effects of temperature, mesoscopic modeling and tension locking are also considered in the case of the bias-extension test

On nonlinear dilatational strain gradient elasticity

We call nonlinear dilatational strain gradient elasticity the theory in which the specific class of dilatational second gradient continua is considered: those whose deformation energy depends, in an objective way, on the gradient of placement and on the gradient of the determinant of the gradient of placement. It is an interesting particular case of complete Toupin–Mindlin nonlinear strain gradient elasticity: indeed, in it, the only second gradient effects are due to the inhomogeneous dilatation state of the considered deformable body. The dilatational second gradient continua are strictly related to other generalized models with scalar (one-dimensional) microstructure as those considered in poroelasticity. They could be also regarded to be the result of a kind of “solidification” of the strain gradient fluids known as Korteweg or Cahn–Hilliard fluids. Using the variational approach we derive, for dilatational second gradient continua the Euler–Lagrange equilibrium conditions in both Lagrangian and Eulerian descriptions. In particular, we show that the considered continua can support contact forces concentrated on edges but also on surface curves in the faces of piecewise orientable contact surfaces. The conditions characterizing the possible externally applicable double forces and curve forces are found and examined in detail. As a result of linearization the case of small deformations is also presented. The peculiarities of the model is illustrated through axial deformations of a thick-walled elastic tube and the propagation of dilatational waves

Large deformations of Timoshenko and Euler beams under distributed load

International audienceIn this paper, the general equilibrium equations for a geometrically nonlinear version of the Timoshenko beam are derived from the energy functional. The particular case in which the shear and extensional stiffnesses are infinite, which correspond to the inextensible Euler beam model, is studied under a uniformly distributed load. All the global and local minimizers of the variational problem are characterized, and the relative monotonicity and regularity properties are established

Identification of a geometrically nonlinear micromorphic continuum via granular micromechanics

Describing the emerging macro-scale behavior by accounting for the micro-scale phenomena calls for microstructure-informed continuum models accounting properly for the deformation mechanisms identifiable at the micro-scale. Classical continuum theory, in contrast to the micromorphic continuum theory, is unable to take into account the effects of complex kinematics and distribution of elastic energy in internal deformation modes within the continuum material point. In this paper, we derive a geometrically nonlinear micromorphic continuum theory on the basis of granular mechanics, utilizing grain-scale deformation as the fundamental building block. The definition of objective kinematic descriptors for relative motion is followed by Piola’s ansatz for micro–macro-kinematic bridging and, finally, by a limit process leading to the identification of the continuum stiffness parameters in terms of few micro-scale constitutive quantities. A key aspect of the presented approach is the identification of relevant kinematic measures that describe the deformation of the continuum body and link it to the micro-scale deformation. The methodology, therefore, has the ability to reveal the connections between the micro-scale mechanisms that store elastic energy and lead to particular emergent behavior at the macro-scale