A Finite Element Formulation and Program to Study Transient Swelling and Load-carriage in Healthy and Degenerate Articular Cartilage

The theory of poroelasticity is extended to include physico-chemical swelling and used to predict the transient responses of normal and degenerate articular cartilage to both chemical and mechanical loading; with emphasis on isolating the influence of the major parameters which govern its deformation. Using a new hybrid element, our mathematical relationships were implemented in a purpose-built poroelastic finite element analysis algorithm (u–π–c fortran program) which was used to resolve the nature of the coupling between the mechanical and chemical responses of cartilage when subjected to ionic transport across its membranous skeleton. Our results demonstrate that one of the roles of the strain-dependent matrix permeability is to limit the rate of transmission of stresses from the fluid to the collagen-proteoglycan solid skeleton in the incipient stages of loading, and that the major contribution of the swelling pressure is that of preventing any excessive deformation of the matrix.

[1]  M. Biot.  General Theory of Three‐Dimensional Consolidation , 1941 .

[2]  W M Lai,et al.  A continuum theory and an experiment for the ion-induced swelling behavior of articular cartilage. , 1984, Journal of biomechanical engineering.

[3]  A. Maroudas,et al.  Balance between swelling pressure and collagen tension in normal and degenerate cartilage , 1976, Nature.

[4]  P. M. Naghdi,et al.  A MIXTURE OF VISCOUS ELASTIC MATERIALS WITH DIFFERENT CONSTITUENT TEMPERATURES , 1970 .

[5]  A. Grodzinsky,et al.  Swelling of articular cartilage and other connective tissues: Electromechanochemical forces , 1985, Journal of orthopaedic research : official publication of the Orthopaedic Research Society.

[6]  P. Torzilli,et al.  Transient solute diffusion in articular cartilage. , 1987, Journal of biomechanics.

[7]  Ogston Ag.  On water binding. , 1966 .

[8]  B. Simon,et al.  Multiphase Poroelastic Finite Element Models for Soft Tissue Structures , 1992 .

[9]  A. Ogston.  On water binding. , 1966, Federation proceedings.

[10]  A. Maroudas,et al.  Measurement of swelling pressure in cartilage and comparison with the osmotic pressure of constituent proteoglycans. , 1981, Biorheology.

[11]  J. Urban.  Solute Transport in Articular Cartilage and the Intervertebral Disc , 1990 .

[12]  V C Mow,et al.  The significance of electromechanical and osmotic forces in the nonequilibrium swelling behavior of articular cartilage in tension. , 1981, Journal of biomechanical engineering.

[13]  Paula A. Revell,et al.  The Composition of Normal and Osteoar-thritic Articular Cartilage from Human Knee Joints , 1984 .

[14]  J Mizrahi,et al.  The "instantaneous" deformation of cartilage: effects of collagen fiber orientation and osmotic stress. , 1986, Biorheology.

[15]  W M Lai,et al.  Fluid transport and mechanical properties of articular cartilage: a review. , 1984, Journal of biomechanics.

[16]  V. Mow,et al.  Biphasic creep and stress relaxation of articular cartilage in compression? Theory and experiments. , 1980, Journal of biomechanical engineering.

[17]  A Oloyede,et al.  Complex nature of stress inside loaded articular cartilage. , 1994, Clinical biomechanics.

[18]  A Oloyede,et al.  Is classical consolidation theory applicable to articular cartilage deformation? , 1991, Clinical biomechanics.

[19]  M A Freeman,et al.  The composition of normal and osteoarthritic articular cartilage from human knee joints. With special reference to unicompartmental replacement and osteotomy of the knee. , 1984, The Journal of bone and joint surgery. American volume.

[20]  H. Nötzli,et al.  Deformation of articular cartilage collagen structure under static and cyclic loading , 1998, Journal of orthopaedic research : official publication of the Orthopaedic Research Society.

[21]  D Pflaster,et al.  A poroelastic finite element formulation including transport and swelling in soft tissue structures. , 1996, Journal of biomechanical engineering.

[22]  S Olsen,et al.  A Finite Element Analysis Methodology for Representing the Articular Cartilage Functional Structure , 2002, Computer methods in biomechanics and biomedical engineering.

[23]  F. Young.  Biochemistry , 1955, The Indian Medical Gazette.

[24]  M. Tombs,et al.  The osmotic pressure of biological macromolecules , 1974 .

[25]  Gerard A. Ateshian,et al.  Interstitial Fluid Pressurization During Confined Compression Cyclical Loading of Articular Cartilage , 2000, Annals of Biomedical Engineering.

[26]  E B Hunziker,et al.  Optical and mechanical determination of Poisson's ratio of adult bovine humeral articular cartilage. , 1997, Journal of biomechanics.

[27]  K. Terzaghi.  Theoretical Soil Mechanics , 1943 .

[28]  N. Broom,et al.  Abnormal softening in articular cartilage: its relationship to the collagen framework. , 1982, Arthritis and rheumatism.

[29]  W M Lai,et al.  A triphasic theory for the swelling and deformation behaviors of articular cartilage. , 1991, Journal of biomechanical engineering.