The influence of the acetabular labrum seal, intact articular superficial zone and synovial fluid thixotropy on squeeze-film lubrication of a spherical synovial joint.

A model of synovial fluid (SF) filtration by articular cartilage (AC) in a step-loaded spherical synovial joint at rest is presented. The effects of joint pathology (such as a depleted acetabular labrum, a depleted cartilage superficial zone consistent with early osteoarthritis and an inflammatory SF) on the squeezed synovial film are also investigated. Biphasic mixture models for AC (ideal fluid and elastic porous transversely isotropic two-layer matrix) and for SF (ideal and thixotropic fluids) are applied and the following results are obtained. If the acetabular labrum is able to seal the pressurised SF between the articular surfaces (as in the normal hip joint), the fluid in the synovial film and in the cartilage within the labral ring is homogeneously pressurised. The articular surfaces remain separated by a fluid film for minutes. If the labrum is destroyed or absent and the SF can escape across the contact edge, the fluid pressure is non-homogeneous and with a small jump at the articular surface at the very moment of load application. The ensuing synovial film filtration by porous cartilage is lower for the normal cartilage (with the intact superficial zone) than if this zone is already depleted or rubbed off as in the early stage of primary osteoarthritis. Compared with the inflammatory (Newtonian) SF, the normal (thixotropic) fluid applies favourably in the squeezed film near the contact centre only, yielding a thicker SF film there, but not affecting the minimum thickness in the fluid film profile at a fixed time. For all that, in the unsealed case for both the normal and pathological joint, the macromolecular concentration of the hyaluronic acid-protein complex in the synovial film quickly increases due to the filtration in the greater part of the contact. A stable synovial gel film, thick on the order of 10(-7)m, protecting the articular surfaces from the intimate contact, is formed within a couple of seconds. Boundary lubrication by the synovial gel is established if sliding motion follows until a fresh SF is entrained into the contact. This theoretical prediction is open for experimental verifications.

The thixotropic effect of the synovial fluid in squeeze-film lubrication of the human hip joint.

The thixotropic (shear-thinning) effect of the synovial fluid in squeeze-film lubrication of the human hip joint is evaluated, taking into account filtration of the squeezed synovial film by biphasic articular cartilage. A porous, homogeneous, elastic cartilage matrix filled with the interstitial ideal fluid, with the intact superficial zone (of lower permeability and stiffness in compression) already disrupted or worn away, models an early stage of arthritis. Due to a high viscosity of the normal synovial fluid at very low shear rates, the squeezed synovial film at a fixed time after the application of a steady load is found to be much thicker in a small central part of the lubricated contact area. In the remaining part, the film is thin as it corresponds to the Newtonian fluid with the same high-shear-rate viscosity. Filtration is lower for the normal cartilage with the intact superficial zone due to its lower permeability and compression stiffness. But even in the fictitious case of zero filtration, calculations show that the effect of thixotropy on the increase of the minimum synovial film thickness would manifest itself as late as after several tens of seconds since the physiologic load application. At that time, this thickness would be as low as about 0.3 microm. It follows that thixotropy of the normal synovial fluid (and so much more of the inflammatory fluid) is irrelevant in squeeze-film lubrication of both the normal and arthritic human hip joints.

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

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

Lubrication of the human ankle joint in walking with the synovial fluid filtrated by the cartilage with the surface zone worn out: steady pure sliding motion.

A mixture model of synovial fluid filtration by cartilage in the human ankle joint during walking is presented for steady sliding motion of the articular surfaces. In the paper the cartilage surface zone is assumed worn out. The same model has been recently applied to the squeeze-film problem for the human hip joint loaded by the body weight during standing (Hlavácek, Journal of Biomechanics 26, 1145-1150, 1151-1160, 1993; Hlavácek and Novák, Journal of Biomechanics 28, 1193-1198, 1199-1205, 1995). The linear biphasic model for cartilage (elastic porous matrix + ideal fluid) due to Prof. V. C. Mow and his co-workers and the biphasic model for synovial fluid (viscous fluid + ideal fluid), as used in the above-mentioned squeeze-film problem, are applied. For the physiologic parameters of the ankle joint during walking, a continuous synovial fluid film about 1 microm thick is maintained under steady entraining motion according to the classical model without the fluid transport across the articular surface. This is not the case in the filtration model with the cartilage surface zones worn out. On the contrary, this filtration model indicates that synovial fluid is intensively filtrated by such cartilage, so that no continuous fluid film is maintained and a synovial gel layer, about 10(-8) m thick, develops over the majority of the contact. Thus, if the cartilage surface zones are worn out, boundary lubrication should prevail in the ankle joint under steady sliding motion for the mean values of loading and the sliding velocity encountered in walking cycle.

A note on an asymptotic solution for the contact of two biphasic cartilage layers in a loaded synovial joint at rest.

Retaining the first terms of asymptotic expansions and assuming zero gradient of the contact pressure at the contact edge in the perpendicular direction to the edge, Ateshian et al. (1994, J. Biomechanics 27, 1347-1360; 1992, Adv. Bioeng. ASME 22, 191-194) have presented an asymptotic axially symmetric and plane strain solutions to the contact problems of the two thin biphasic cartilage layers in the synovial joint (with the synovial fluid film in between already depleted), subjected to a sudden normal load. Both the immediate and an early time response to a step loading have been analysed. The present note shows that the contact width thus obtained immediately after the load application differs from the numerical values for a dry frictionless contact of incompressible single-phase elastic layers available in the literature. The difference increases with the decreasing contact width-to-layer thickness ratio. It is proposed to improve the above solutions by releasing zero pressure gradient condition at the contact edge and calculating the instantaneous contact widths from the equations proposed for the corresponding case by Matthewson (1981, J. Mech. Phys. Solids 29, 89-113) and Meijers (1967, Appl. Sci. Res. 18, 353-383) that approximate better the numerical values. The instantaneous rate of change in the contact width is then obtained for a step load varying in time.

The influence of articular surface incongruity on lubrication and contact pressure distribution of loaded synovial joints.

In the model intended for short-term loading (such as during the walking cycle) of a human synovial joint in the lower extremities, cartilage lubricated by Newtonian synovial fluid is considered to be incompressible elastic and subchondral bone is considered to be rigid. The model is non-diffusional, i.e. no interstitial fluid flow occurs across the articular surfaces. A simple plane strain case of the human ankle joint is considered. For high steady loading applied in the centre of the stationary tibial arc and for steady sliding of the talar arc, this model shows that individual physiological variations in the geometry of the articular surfaces have only a small effect on the contact stress distribution and the fluid film thickness. If this load is applied eccentrically in the tibial arc, the contact pressure distribution varies more with surface geometry, but the minimum fluid film thickness differs little from that for symmetric loading. The maximum contact pressure is placed eccentrically in this case, but its value is changed only little when compared to the central loading of the same value. In order to explain different distribution patterns of subchondral bone mineralization, it is anticipated that the total load peaks of periodic time-dependent loads are transmitted centrally in some incongruent joints and eccentrically in others.

The role of synovial fluid filtration by cartilage in lubrication of synovial joints--III. Squeeze-film lubrication: axial symmetry under low loading conditions.

A mixture model of synovial fluid filtration and synovial gel formation at normal approach of cartilage surfaces in the human synovial joints loaded by a compressive force has been recently presented in Parts I and II of this paper (Hlavácek, 1993, J. Biomechanics 26, 1145-1150; 1151-1160). In the model synovial fluid is taken as a mixture of two incompressible fluids (ideal and Newtonian viscous), while the biphasic model of Mow et al. (1980, J. Biomech. Engng 102, 73-84) is used for cartilage. A system of partial differential equations for the normal approach of axially symmetric cartilage surfaces in the human hip joint obtained in Part II is solved numerically for low loads. A shallow pocket-type configuration of the synovial film is formed shortly after the load application at time t = 0. For constant loads the fluid film pressure profile follows very closely that in a dry frictionless contact. To this approximation and with the exception of a close vicinity of the squeeze-film edge the flux of the ideal fluid across the synovial fluid-cartilage interface varies quadratically with the radial distance r and decreases as t-1/2 with time. The ideal fluid is forced into cartilage at the central region and out of cartilage at the low-pressure periphery of the squeezed synovial film. The maximum gel-forming concentration (the 20-fold of the original value) of the hyaluronic acid-protein macromolecular complex of the synovial fluid is reached at the film centre first, then the gel film starts spreading quickly sideways. Later, the process slows down approaching the value r/2 1/2 where r is the radius of a dry frictionless contact. The final gel-film thickness decreases very slowly with the increasing r for 0 < or = r < r/2 1/2.

The role of synovial fluid filtration by cartilage in lubrication of synovial joints--IV. Squeeze-film lubrication: the central film thickness for normal and inflammatory synovial fluids for axial symmetry under high loading conditions.

The axially symmetric problem of synovial film filtration and synovial gel formation at normal approach of cartilage surfaces in the human hip joint loaded by a compressive force has been solved numerically in Part III of this paper [Hlavácek and Novák, J. Biomechanics 28, 1193-1198 (1995)] for the Newtonian viscous phase of the biphasic synovial fluid and for low loads only. Because of a high non-linearity of the problem the method used there breaks down for higher loads. On anticipating that for a high step loading the fluid pressure in the central part of the squeezed synovial film is close to the pressure in a dry frictionless contact, the synovial film filtration at the film centre is governed by two ordinary differential equations that are easy to solve. The central gel film thickness thus obtained, i.e. the film thickness at the moment, when the filtered fluid turns into a stable gel is about 1 micron for the normal synovial fluid (with a non-Newtonian viscous phase of the synovial fluid) and changes very little if the geometric, material and loading parameters of the problem vary within the physiological range. The inflammatory case (with a more or less Newtonian viscous phase) yields values by one order lower at least. The results of stress analysis in the cartilage for this mixture model suggest the reason for vertical cracking at the free cartilage surface and horizontal splitting at the tide mark observed in osteoarthritic joints.

The role of synovial fluid filtration by cartilage in lubrication of synovial joints--I. Mixture model of synovial fluid.

A mathematical model of lubrication of human synovial joints under squeeze-film conditions is presented in this several-part paper. Squeeze-film action leads to a concentration of hyaluronic-acid-protein macromolecular complex in the synovial fluid between the approaching cartilage surfaces as a result of the diffusion of water and low molecular weight substances through the cartilage surfaces or along the gap. Increasing viscosity of synovial fluid delays the approach of these surfaces and the formation of stable gels then protects cartilage, if sliding motion ensues, before fluid film lubrication is restored. In Part I of the present paper synovial fluid is considered as a mixture of two incompressible fluids. The material parameters of this mixture of fluids are found using previously published experimental results. Squeeze-film analysis is carried out for the axially symmetric synovial film.

The role of synovial fluid filtration by cartilage in lubrication of synovial joints--II. Squeeze-film lubrication: homogeneous filtration.

A mathematical model of synovial film filtration and synovial gel formation at normal approach of cartilage surfaces in the human hip joint is presented. The biphasic mixture model presented in Part I of this paper [Hlavácek, J. Biomechanics 26, (1993)] for synovial fluid and that of Mow and his collaborators [J. Biomech. Engng 102, 73-84 (1980)] for cartilage are used. A general analysis of filtration of an axially symmetric synovial squeeze-film between two cartilage layers at normal approach is given. The geometrically simple case much idealising the human hip joint is also considered: two cartilage discs with a synovial film in between are compressed by the steady loading of the half human weight. The homogeneous film filtration process where the synovial gap remains parallel and the macromolecular concentration in the gap is spatial homogeneous (to the thin-film approximation) and time-dependent is numerically analysed. If the hyaluronic acid concentration of the synovial gel at equilibrium is 50 mg/ml at least, the resulting stable gel layer thickness for the homogeneous filtration in the human hip joint and for normal synovial fluids is about 0.1 micron, being almost independent of the loading. Inflammatory synovial fluid shows values several times lower.

The mormyrid brainstem. I. Distribution of brainstem neurones projecting to the spinal cord in Gnathonemus petersii. An HRP study.

The sources of the descending spinal tracts were identified in the teleost fish Gnathonemus petersii by retrograde HRP transport. HRP injections were made at two spinal levels, either at level of the caudal end of the dorsal fin, anterior to the electric organ, or at the pectoral fin. In both cases all labeled cells were found in the rhombencephalon and the mesencephalic tegmentum. No labeled cells were observed either in the cerebellum and lateral line lobes or in the dorsal mesencephalon i.e. torus semicircularis and mesencephalic tectum or in the telencephalon. Following caudal spinal injections, the majority of the labeled cells were grouped in a median and a ventrolateral column of the rhombencephalic reticular formation. The latter is composed of three parts corresponding to the nucleus reticularis inferior, medius and superior. Both Mauthner cells, all the cells in the medullary relay nucleus controlling the electric organ discharge and a few cells in the posterior part of the magnocellular octaval nucleus were labeled. In the mesencephalon, four nuclei were identified by HRP labeling: the nucleus of the medial longitudinal fasciculus, the nucleus reticularis mesencephali and the anterior and posterior tegmental mesodiencephalic nuclei. The rostral injections revealed several additional spinal projections from the descending vestibular and tangential nuclei, from the medial part of the magnocellular nucleus and, finally, from the rostral periventricular gray of the mesencephalon. Also, after such injections, a greater number of cells were labeled in the reticular formation, especially in the median column and in the inferior reticular nucleus. The results suggest that the rostral spinal cord has a larger connection with the acoustico-vestibular area and the medullary reticular formation than the caudal spinal cord. In contrast, the mesencephalic nuclei, probably linked to the mesencephalic tectum and the pretectal area, appears to be a coordinating apparatus between the visual system and the trunk/tail musculature. Thus, it appears that teleost fish possess the same basic equipment of descending spinal pathways as higher vertebrates.