Squeeze-film lubrication of the human ankle joint with synovial fluid filtrated by articular cartilage with the superficial zone worn out

Abstract

A squeeze-film lubrication model of the human ankle joint in standing that takes into account the fluid transport across the articular surface is presented. Articular cartilage is a biphasic mixture of the ideal interstitial fluid and an elastic permeable isotropic homogeneous intrinsically incompressible matrix. The simple homogeneous model for articular cartilage models the case of early osteoarthritis, when the intact superficial zone of the normal articular cartilage, much stiffer in tension than the bulk material, has been already disrupted or worn out. The calculations indicate for this case that in normal approach motion the lubricating fluid film is quickly depleted and turned into a synovial gel film that is supposed to serve as a boundary lubricant if sliding motion follows

Introduction

Articular cartilage is a layered medium composed of several structural zones (Lane and Weiss, 1975): superficial, middle and deep. The superficial zone of the normal cartilage is the most distinct and reaches up to 200 μm. Its upper most layer, only about 3 μm thick, is called “lamina splendens” and is made of non-banded, randomly arranged fine collagen filaments 4–12 nm in diameter. Below this layer there are sheets of a well-identified period, each sheet with predominantly parallel, banded collagen fibrils, their diameter increasing with depth. They remind of industrially produced angle-ply laminates. The collagen fibres of the middle zone are randomly oriented and homogeneously dispersed. In the deep zone, the fibres form larger, radially oriented fibre bundles that insert into the calcified zone across the tidemark and furcate to anchor the tissue to the subchondral bone. Proteoglycan occupies the interfibrilar space of the tissue and its concentration increases from the surface to a maximum in the middle zone and then diminishes again. Within each zone, regions of specific cellular organization exist. This composite solid matrix is swollen by water in which a variety of mobile electrolytes are distributed.

The collagen fibres limit the swelling of the proteoglycan gel and experience tensile stresses giving the cartilage its tensile stiffness. Kempson (1973) found that the normal articular cartilage shows large differences in tensile stiffness and strength, depending on the place and orientation. The tensile stiffness and strength are low in the middle zone, independent of orientation parallel to the surface. However, they are high in the superficial zone. A decrease in the tensile stiffness, as well as disruption and disorganization of the collagen network of the superficial zone, have been reported in a canine model of experimental osteoarthritis generated by transection of the anterior cruciate ligament of the knee (Stockwell et al., 1983; Guilak et al., 1994).

It is the surface layer that is much important for synovial fluid filtration by cartilage. For the normal cartilage the surface layer is formed by the intact superficial zone that has mechanical properties quite different from the surface layer of a cartilage in an early stage of osteoarthritis. In the latter case, the intact superficial zone is either already disrupted (with a decreased stiffness in tension when compared to its originally higher value) or even worn out so that the surface layer may be considered with the same stiffness in tension as the bulk material. Thus, an arthritic cartilage might be roughly considered homogeneous throughout, as it is the case in the models analysed so far (Hou et al., 1992; Jin et al., 1992; Hlaváček (1993a), Hlavác̀ek (1993b), Hlaváèek (1995); Hlaváček and Novák, 1995; Ateshian et al (1994), Ateshian and Wang (1995)). However, the homogeneous model can hardly describe lubrication for the intact articular cartilage.

The present paper gives an analysis of the squeeze-film lubrication of the human ankle joint under stationary step loading in normal approach motion and plane strain with the articular cartilage biphasic and homogeneous, i.e. with the superficial zone already disrupted or worn out. As distinct from Hlaváček and Novák (1995) where the fluid-film profiles were obtained for axial symmetry and for very low loading only (calculations for physiologic loading broke), in the present paper the inverse method of elastohydrodynamic lubrication theory (Blok, 1964) is used, with the use of the dry contact pressure profile instead of the fluid pressure of the lubricated contact, in order to obtain the film thickness profile even for high, physiologic loading.