A sound and efficient measure of joint congruence

In the medical world, the term “congruence” is used to describe by visual inspection how the articular surfaces mate each other, evaluating the joint capability to distribute an applied load from a purely geometrical perspective. Congruence is commonly employed for assessing articular physiology and for the comparison between normal and pathological states. A measure of it would thus represent a valuable clinical tool. Several approaches for the quantification of joint congruence have been proposed in the biomechanical literature, differing on how the articular contact is modeled. This makes it difficult to compare different measures. In particular, in previous articles a congruence measure has been presented which proved to be efficient and suitable for the clinical practice, but it was still empirically defined. This article aims at providing a sound theoretical support to this congruence measure by means of the Winkler elastic foundation contact model which, with respect to others, has the advantage to hold also for highly conforming surfaces as most of the human articulations are. First, the geometrical relation between the applied load and the resulting peak of pressure is analytically derived from the elastic foundation contact model, providing a theoretically sound approach to the definition of a congruence measure. Then, the capability of congruence measure to capture the same geometrical relation is shown. Finally, the reliability of congruence measure is discussed.

[1]  S. Dekel,et al.  Joint changes after overuse and peak overloading of rabbit knees in vivo. , 1978, Acta orthopaedica Scandinavica.

[2]  R. Putz,et al.  The effects of exercise on human articular cartilage , 2006, Journal of anatomy.

[3]  P. Bullough,et al.  The geometry of diarthrodial joints, its physiologic maintenance, and the possible significance of age-related changes in geometry-to-load distribution and the development of osteoarthritis. , 1981, Clinical orthopaedics and related research.

[4]  Michele Conconi,et al.  Joint Kinematics from Functional Adaptation: An Application to the Human Ankle , 2012 .

[5]  Susan Standring PhD DSc Gray's Anatomy: The Anatomical Basis of Clinical Practice , 2005 .

[6]  Robert L Spilker,et al.  A Lagrange multiplier mixed finite element formulation for three-dimensional contact of biphasic tissues. , 2007, Journal of biomechanical engineering.

[7]  J. Li,et al.  Trabecular angle of the human talus is associated with the level of cartilage degeneration. , 2007, Journal of musculoskeletal & neuronal interactions.

[8]  B B Seedhom,et al.  Thickness of human articular cartilage in joints of the lower limb , 1999, Annals of the rheumatic diseases.

[9]  R Frayne,et al.  Analysis techniques for congruence of the patellofemoral joint. , 2009, Journal of biomechanical engineering.

[10]  Cyril B Frank,et al.  Congruency Effects on Load Bearing in Diarthrodial Joints , 2004, Computer methods in biomechanics and biomedical engineering.

[11]  M. Holmes,et al.  An analysis of the squeeze-film lubrication mechanism for articular cartilage. , 1992, Journal of biomechanics.

[12]  W M Lai,et al.  An asymptotic solution for the contact of two biphasic cartilage layers. , 1994, Journal of biomechanics.

[13]  R M Rose,et al.  Effect of repetitive impulsive loading on the knee joints of rabbits. , 1978, Clinical orthopaedics and related research.

[14]  V. Mow,et al.  Curvature characteristics and congruence of the thumb carpometacarpal joint: differences between female and male joints. , 1992, Journal of biomechanics.

[15]  T. Fukubayashi,et al.  Load-bearing mode of the knee joint: physical behavior of the knee joint with or without menisci. , 1980, Clinical orthopaedics and related research.

[16]  Mads Nielsen,et al.  Automatic Quantification of Tibio-Femoral Contact Area and Congruity , 2012, IEEE Transactions on Medical Imaging.

[17]  K. Johnson Contact Mechanics: Frontmatter , 1985 .

[18]  J. A. Greenwood,et al.  Analysis of elliptical Hertzian contacts , 1997 .

[19]  E S Grood,et al.  A joint coordinate system for the clinical description of three-dimensional motions: application to the knee. , 1983, Journal of biomechanical engineering.

[20]  B B Kimia,et al.  Quantitative MR imaging using "LiveWire" to measure tibiofemoral articular cartilage thickness. , 2008, Osteoarthritis and cartilage.

[21]  W Herzog,et al.  Joint contact mechanics in the early stages of osteoarthritis. , 2000, Medical engineering & physics.

[22]  I. Etsion,et al.  A rational human joint friction test using a human cartilage-on-cartilage arrangement , 2006 .

[23]  J. O'Connor,et al.  Incongruent Surfaces in the Human Hip Joint , 1968, Nature.

[24]  Friedrich Pauwels,et al.  Biomechanics of the Locomotor Apparatus , 1980 .

[25]  Gerard A Ateshian,et al.  Finite element algorithm for frictionless contact of porous permeable media under finite deformation and sliding. , 2010, Journal of biomechanical engineering.

[26]  G A Ateshian,et al.  A theoretical solution for the frictionless rolling contact of cylindrical biphasic articular cartilage layers. , 1995, Journal of biomechanics.

[27]  A S Greenwald,et al.  Mathematical model of the human ankle joint. , 1983, Journal of biomechanics.

[28]  N. Shrive The transmission of load through animal joints, with particular reference to the role of the meniscus in the knee , 1974 .

[29]  D. Felson,et al.  The validity of different definitions of radiographic worsening for longitudinal studies of knee osteoarthritis. , 2001, Journal of clinical epidemiology.

[30]  J. Barbera,et al.  Contact mechanics , 1999 .

[31]  Kenneth D Brandt,et al.  Etiopathogenesis of osteoarthritis. , 2009, The Medical clinics of North America.

[32]  Margarita Vergara,et al.  A modified elastic foundation contact model for application in 3D models of the prosthetic knee. , 2008, Medical engineering & physics.

[33]  Robert L. Spilker,et al.  A contact finite element formulation for biological soft hydrated tissues , 1998 .

[34]  Felix Eckstein,et al.  The influence of geometry on the stress distribution in joints — a finite element analysis , 1994, Anatomy and Embryology.

[35]  D. Carter Mechanical loading history and skeletal biology. , 1987, Journal of biomechanics.

[36]  M. Nakatsukasa,et al.  The inner structural variation of the primate tibial plateau characterized by high-resolution microtomography. Implications for the reconstruction of fossil locomotor behaviours , 2010 .

[37]  L. Kamibayashi,et al.  Changes in mean trabecular orientation in the medial condyle of the proximal tibia in osteoarthritis , 1995, Calcified Tissue International.

[38]  W Herzog,et al.  An improved solution for the contact of two biphasic cartilage layers. , 1997, Journal of biomechanics.

[39]  R. Spilker,et al.  Biphasic finite element modeling of hydrated soft tissue contact using an augmented Lagrangian method. , 2011, Journal of biomechanical engineering.

[40]  R. Huiskes,et al.  Proposal for the regulatory mechanism of Wolff's law , 1995, Journal of orthopaedic research : official publication of the Orthopaedic Research Society.

[41]  Toshiaki Hisada,et al.  Development of a Finite Element Procedure of Contact Analysis for Articular Cartilage with Large Deformation Based on the Biphasic Theory , 2005 .

[42]  M. Morris,et al.  Reviewing knee osteoarthritis--a biomechanical perspective. , 2004, Journal of science and medicine in sport.

[43]  L. Sokoloff The Biology of Degenerative Joint Disease , 2015, Perspectives in biology and medicine.

[44]  W Herzog,et al.  Articular joint mechanics with biphasic cartilage layers under dynamic loading. , 1998, Journal of biomechanical engineering.

[45]  J. O'Connor,et al.  Kinematics of the human ankle complex in passive flexion; a single degree of freedom system. , 1999, Journal of biomechanics.