In vitro studies of the wear of articular cartilage II. Characteristics of the wear of articular cartilage when worn against stainless steel plates having characterized surfaces

Wear, 52 (1979) 297 - 339 0 Elsevier Sequoia S.A., Lausanne

297 - Printed

in the Netherlands

IiV VITRO STUDIES OF THE WEAR OF ARTICULAR CARTILAGE II. CHARACTERISTICS OF THE WEAR OF ARTICULAR CARTILAGE WHEN WORN AGAINST STAINLESS STEEL PLATES HAVING CHARACTERIZED SURFACES

HAROLD

LIPSHITZ

and MELVIN

J. GLIMCHER

Department of Orthopaedic Surgery, Harvard Medical School, Children’s Hospital Medical Center, Boston, Mass. 02115 (U.S.A.) (Received

June 16,1978)

Summary As part of an attempt to elucidate the physical parameters that govern the wear of articular cartilage, its wear properties were studied with the tissue interfaced against stainless steel plates having characterized surface profiles. The studies were carried out in apparatus that was designed and constructed for these purposes. In addition measurements were made of (1) the geometric contact areas between the tissue and the plates as functions of time and load, (2) the changes with time and load of the average fluid contents of the cartilage, (3) the changes in dimension and profile of the surface of the tissue after it had been worn under various conditions and equilibrated for different times with dilute neutral buffered solutions, and (4) the fraction of the hexosamine and hydroxyproline contents of the debris that dissolved during the wear in the dilute neutral buffer used as a lubricant. Wear rates were found to be sensitive functions of the surface profile of the metal. The tissue initially wore against “smooth” surfaces at rates that ‘decreased with time until a final rate, characteristic for a given surface and pressure, was attained. The extent of wear in this region of the wear-time curve could be described by linear functions of the pressure, plate speed and time. The data are interpreted as follows: (1) network breakdown and reorientation of the domains of the macromolecules and their aggregates towards the wear direction occur within a surface region of the tissue as it wears, and such reorientation is responsible for the initial decrease of the wear rates; (2) the rate of crack initiation governs the overall wear rate of the tissue in the linear region of the wear-time curve; (3) the formation of wear particles is accompanied by chain scission.

1. Introduction Although the pathogenesis of the various arthritides has not been completely elucidated, the wear of articular cartilage (i.e. the amount and rate at

298

which the organic phase of the tissue is lost from joint surfaces) in pathological states probably depends in some way on the mechanical properties of the tissue [l] . As part of an effort to assess the influence of various mechanical factors on the wear of the tissue, some of the characteristics of its wear when worn against stainless steel plates with different surface profiles have been studied. Numerous factors affect to varying extents the measured wear rates of any material [ 2 - 43 , e.g. (1) the load under which one material is compressed against the other, (2) the frictional forces between the articulating surfaces, (3) the area of contact between the articulating surfaces, (4) the nature and mode of action of the lubricant used, (5) the mechanical and ultrastructural properties of each of the materials, (6) the characteristics of the contacting surfaces and (7) the mechanism by which wear is achieved. The wear of articular cartilage in any environment other than that of a living intact joint will consequentIy be in~uenced by factors that probably differ considerably from those found under in uiuo conditions. This is especially so because of the unique surface contour of each mating partner of each joint. Attempts were therefore made to simulate natural joint articulation in previous studies of the in vitro wear of the tissue [5]. While these studies proved useful, the experimental configuration used did not permit an assessment of the geometric contact areas, could not assure that the contact areas of repeated experiments under the same load were the same and in the last analysis did not duplicate in uiuo conditions. Furthermore, under these conditions the mechanism of wear could not be clearly delineated. These deficiencies, together with other factors, made it very difficult, if not impossible, to assess qu~titatively the influence of various parameters on the wear of the tissue. To try to overcome some of these problems a simpler experimental configuration was adopted. Small circular cylindrical plugs of cartilage and underlying bone with ffat surfaces were worn in a specially designed apparatus against stainless steel plates whose surface profiles were characterized. The principal advantages of this experimental configuration were that the geometric contact areas between the tissue and the plate could be measured and reproduced as a function of load, the surface features of the plate could be independently varied and deformational or plowing effects could be minimized as a contributing factor to the wear of the tissue. It is recognized, however, that the cartilage was worn against surfaces quite different from that of the tissue, and the frictional forces that it was subjected to as well as the pressure variance on it were obviously not the same as those existing under in uiuo conditions. Nevertheless, it is felt that an understanding of the wear characteristics of articular cartilage under these conditions, where each of a number of variables can be independently varied, will be helpful in understanding the effect of various factors on the wear behavior of the tissue under in uiuo conditions. This paper describes (I) the extent of wear of cartilage with time under various pressures, (2) changes in its wear behavior when worn against plates

having different surface profiles, (3) the relation of the wear rate of the tissue to the average applied pressure and plate speed, (4) the changes in its average fluid content with time and the relation between its equilibrium fluid content and the applied pressure, (5) the geometric contact area between the tissue and the plate as a function of time and load, (6) the ratios of the amounts of hydroxyproline and the hexosamines dissolved in the lubricant to their content in the wear debris and their variance with pressure and time, and (7) the surface characteristics of the tissue following its wear and equilibration with dilute neutral buffer.

2. Experimental

procedures

2.1. Studies of the wear of the tissue with time 2.1 .l. Source and form of the cartilage used in the wear studies The studies were carried out with cylindrical plugs of cartilage (5.7 mm in diameter) and underlying subchondral bone that were cut from the parapatellar region of the medial femoral condyles of adult steers (about two years old). The plugs were prepared by a technique, described elsewhere [6] , that ensured that the surface of the cartilage capping the cylindrical shaft of underlying bone was flat and perpendicular to its axis. The use of such plugs ensured that the contact areas between the tissue and the wearing plate were similar for repeated experiments at each pressure. Except for one series of experiments, the joints were obtained from a local packing house that normally received steers slaughtered approximately four days earlier. During this time the intact animals were kept in refrigerated rooms at around 5 “C. On receipt the joints were immediately dissected and frozen until ready for use. When needed, rectangular sections measuring approximately 2 cm X 4 cm were cut from each femoral condyle [6] . These were then equilibrated with 0.03 M phosphate buffer* (pH 7.4) for around 4 h at 5 “C and circular cylindrical plugs were prepared from them [6] . 2.1.2. Procedure for wearing the tissue The cartilage was worn in a specially designed and constructed apparatus. The instrument, which will be described in greater detail elsewhere [12] (Fig. l), consists in part of a round stainless steel plate (Type 302 non*Phenyl methyl sulfonyl fluoride (PMSF) was dissolved (to a concentration of 1 x lo-* M) in the phosphate buffer to serve as a proteolytic enzyme inhibitor. In one series of experiments, however, other known proteolytic enzyme inhibitors were additionally dissolved. These, as described by Oegema et al. [ 7 1, Byers et al. [ 81 and other workers [ 9 - 111, consisted of 0.2 M ethylenediaminetetraacetic acid (EDTA), 0.05 M sodium acetate, 0.1 M 6-aminohexanoic acid and 0.005 M benzamidine hydrochloride. The results of wear experiments in which the lubricant contained all of these reagents were identical to those where it contained only PMSF. Their use was therefore discontinued. PMSF is sparingly soluble in aqueous media. Its dissolution to a concentration of lo-* M was achieved by initially dissolving the compound in a small volume of 95% ethanol and then adding the ethanol solution to the phosphate buffer with vigorous stirring.

(a)

(b)

Fig. 1. (a) Overall view of the apparatus used to study the wear of the cartilage. The compressor A served as the air source to the pneumatic actuators B; the plate C was driven by the attached lever arm at D. This was spring loaded at E against the cam F which was driven by the motor G. H is the speed control for the motor. The loads on the tissue were monitored by a load ceil I, the output potentials of which were measured by an electrometer J or a strip chart recorder K. L is the control box for the apparatus. The rest of the instrumentation is for programmed load patterns and temperature control. (b) Closeup view of the plate. Note the concentric circular troughs to contain the lubricant. The outer trough was compartmentalized as seen at A. The plugs were secured in plug holders B which were held in place by guides C. The plug holders were attached to the pneumatic actuators through chucks D. The loads were monitored by the load cell positioned at E. F is a displacement transducer that was used to monitor the displacement in the axial direction in other studies.

magnetic stainless steel) the surface of which (against which the tissue was worn) was highly polished. Concentric circular troughs, 2.5 cm wide and 0.6 cm deep, were accurately machined into the plate to contain the lubricant (Fig. l(b)). The outer trough, in which the experimental work reported here was done, was divided into six compartments (Fig. l(b)) so that multiple experiments could be run simultaneously. To affect the wear of the tissue, the plate was made to move in a reciprocating sinusoidal motion by an attached lever arm that was spring loaded against an off-center cam driven by a variable-speed motor. The speed, or rate of reciprocation, was varied by regulating the motor speed. The average plate speed was determined by multiplying the number of reciprocations per given time period by the distance travelled in each reciprocation (1.27 cm).

301

The tissue was interfaced with the plate as follows. The plugs, as described, were machined to fit snugly into stainless steel holders that were part of the wear apparatus (Fig. l(b)). They were prevented from rotating in their holders during a wear experiment by set screws that penetrated their bony part. Adjustable back-up screws within the holders further precluded the plugs from receding into them under load. Pressure was applied to the tissue by means of pneumatic actuators, which were connected through attached chucks to the plug holders (Fig. l(b)). The plugs, in their holders, were forced onto the plate through guides (Fig. l(b)), whereupon the loads were adjusted to the desired level of each experiment. The loads were measured by a calibrated load cell (model U2M1, RLH Inc., Waltham, Mass.) positioned between the chuck and the piston of the actuator (Fig. l(b)), the output potentials of which were continuously monitored by a strip chart recorder or electrometer. With the tissue compressed against the plate, the plate was made to move in the reciprocating sinusoidal motion described above to achieve its wear. Each compartment of the trough contained around 9 - 10 ml of 0.03 M phosphate buffer (pH 7.4) which served as the lubricant and maintained the tissue in its hydrated state during the experiment. The following variations were made in the experimental procedure to study their effect on the wear of the tissue. 2.1.2.1. Compression of the cartilage prior to wearing it. The average fluid content of the tissue changed with time during an initial period of the wear experiments until an equilibrium fluid content, characteristic for each pressure, was attained (see Section 2.3). To assess the effect of such changes on the initial wear of the tissue, the cartilage was first compressed, but not worn, against the metal plate (Surface A, see Section 2.1.3) until its average fluid content prior to wearing it was the same as it normally would have been after some 180 min of wear (see Section 2.3). The compression was done under a load of 5.4 kg with the tissue in contact with the 0.03 M phosphate buffer. Under this load (which corresponded to a final average pressure on the tissue of 1.9 X 10’ dyn cme2 (276 lbf in2) (see Section 2.2) 300 min were required for the tissue to attain a fluid content that was the same as the equilibrium fluid content normally attained at that pressure while being worn. 2.1.2.2. Reswelling of the cartilage during wear. The effect of relieving the pressure on the tissue and allowing it to reimbibe fluid on its subsequent wear was studied. This was done when the tissue was wearing at a constant rate and had attained its equilibrium fluid content (see Section 3). In this series the cartilage was worn for 180 min under a pressure of 1.65 X 10’ dyn cme2 (240 lbf in2), the pressure was relieved and the tissue was reswollen to its equilibrium fluid content. The wear of the cartilage was resumed after about 18 h under the same pressure with the tissue oriented in the same direction.

302

During the time that the cartilage was not worn the surface of the plate was recleaned as if the experiment were begun anew (see Section 2.1.3). For control experiments the plate was likewise stopped when the tissue was wearing at a constant rate, but the pressure was maintained for 18 h before the experiment was resumed.

.Zf.2.3. The effect of different o~~e~tatio~s of the tissue with respect to the wear direction prior to and during the experiment. A series of experiments was done to compare the wear of tissue worn parallel or perpendicular to its natural articulating direction within the intact joints. A series of experiments was also done to evaluate the effect of wearing the tissue either parallel or perpendicular to the split-line direction [13], The split-line patterns in the vicinity of the region from which the plugs were cut were determined by a procedure described by Hultkrantz [ 13 3 and Kempson [14]. The procedure consisted of pricking the surface of t&e tissue (outside the plug region) with a pin and visualizing the split-line pattern with the aid of India ink. The split-line pattern across the plug was determined by connecting imaginary lines between the split lines on one side of the area to those on the other. Unfortunately the region of the condyle from which our plugs could be prepared had a split-line pattern that curved across its surface. The plugs were therefore worn either perpendicular to a tangent to the curved lines or as parallel as possible to the curved lines. The plugs in this series were worn under a pressure of 1.90 X 10’ dyn cms2 (276 lbf in-- 2). The effect of changing the orientation of the tissue during a run was also studied. For these experiments the cartilage samples were initially randomly oriented with respect to the wear direction. After they had been worn for 300 min at a pressure of 1.90 X lo7 dyn crnme2(276 lbf in-2) the pressure was momentarily relieved, the samples were turned through 90” and the wear experiments were resumed with the tissue worn perpendicular to the previous orientation. For control experiments, the pressure was likewise momentarily relieved but the wear was resumed with the tissue oriented in the same direction as before. 2.1.2.4. The effect of an abrasive on the wear characteristics of the tissue. The effect of having small amounts of abrasive suspended in the lubricating fluid on the wear characteristics of the tissue were studied, For this series, 10 - 15 mg of a calcium phosphate salt were placed in each ~ompa~ment and the tissue was worn for 90 min under an average pressure of 1.65 X 10’ dyn cmP2 (240 lbf inU2). 2.1.2.5. The effect of temperature on the wear of the tissue. For these studies, the plate and lubricant were maintained at around 5 “C throughout the experiments. This was done by placing ice at the center of the plate. The tissue in this series was worn against surface A (see Section 2.1.3) under a pressure of 1.9 X lo7 dyn crne2 (276 lbf irm2).

303

2.1.3.

Preparation of the surface of the plate of the wear studies were done against one of two surfaces. One, designated surface B, was very smooth but somewhat rougher than the other (surface A) where the plate was polished to a virtual mirror finish.* Additional surfaces were obtained by securing to the main plate stainless steel plates that had been polished with emery cloth having different degrees of coarseness (grades 600,400,220). These are designated surfaces C, D and E. The polishing procedure used to prepare these surfaces consisted in using alternate strokes in the wear direction and perpendicular to it. These plates were secured to the master plate by C clamps. Prior to the start of every experiment the stainless steel surfaces were cleaned with warm alkali (about 8 M NaOH) until a minimum wetting angle was attained between a drop of water and the plate, after it had been washed free of residual alkali. This procedure removed adsorbed organic films that may have initially been present (ref. 4, pp. 71 - 72) and ensured that the surface was the same at the beginning of each experiment. Failure to do this resulted in increased experimental scatter and higher average wear rates for tissue worn against that surface under the same loads. The majority

2.1.4. Surface characterization of the plates The surface features were characterized by viewing gold-coated silastic replicas by stereoscopic scanning electron microscopy (Cambridge Stereoscan, model Mark 2A, Cambridge, England) at 20 kV excitation energy. The depths of the surface depressions were determined by viewing the specimens at two angles of tilt (15”, 413 and applying the equations described by Boyde [ 151 to calculate their depths. 2.1.5. Measurement of wear At selected intervals of time the instrument was stopped and, with pressure on the tissue maintained, the lubricating fluid in each compartment (containing the suspended wear debris and its dissolved constituents) was quantitatively aspirated out. The time required to obtain samples did not affect the subsequent wear of the tissue. (When the sampling time was varied between 0 and 15 min no effect on the curve of wear uersus time was seen.) *The mirror finish was achieved by using a very fine silicone carbide abrasive (Clover compound, grade 3A grit no. 500. Clover Manufacturine Co.. Norwalk. Corm.)., The abrasive could not, however, be used as supplied becauseqts petroleum-based suspending fluid coated the surface of the metal and prevented its wetting by the aqueous buffer used as a lubricant. This caused the tissue to wear at considerably higher rates. Furthermore, once on it was not easily removed with either ordinary organic solvents or by washing with hot alkali. To remove it, it was necessary to polish the plate further with dry emery cloth. The grits were therefore separated from the suspending fluid by diluting the suspension with ethyl ether, which caused the grits to settle out. The supernatant was decanted off and the process was repeated from four to six times until no trace of extracted suspending fluid was detectable in the ether. (Its presence was easily seen by a yellowing of the ethyl ether.) The grits were then air dried and used as an aqueous suspension. After polishing the plate was washed free of grits by wiping several times with a soft damp cloth.

304

After the lubricating fluid was removed fresh buffer was placed in each compartment and the experiment was resumed. The wear debris and its dissolved constituents were quantitatively removed from each compartment by using a thin piece of flexible plastic tubing attached to a suction flask under partial vacuum. It was necessary to rub the bottom of each compartment throughout its area while aspirating to remove the wear debris qu~ti~tively. With this technique, particles that adhered to the bottom of the plate were removed. This was followed by several washings with water using the same procedure. Quantitative removal was ensured by placing solutions containing known amounts of tissue wear debris and its dissolved constituents in several comp~tments and recovering between 98 and 100% of the material so placed. The solutions containing the suspended wear debris were concentrated by gentle evaporation over a hot plate to a final volume of around 1 - 2 ml. They were then qu~titatively transferred to Pyrex glass t&bes and hydrolyzed by adding HCl to a final concentration of 6 N. The tubes were sealed and placed in a 100 “C oven overnight, following which the HCl was evaporated off with an Evapo-Mix (Beuchler Instrument Co., Fort Lee, NJ.). The residues were dissolved in a known volume of water and their hydroxyproline contents were determined by the procedure described by Grant [ 161. The use of the dilute buffer (0.03 M phosphate) as lubricant ensured that, despite concentration, the final salt concentrations of the solutions assayed were less than 0.2 M. The calorimetric assay of hydroxyproline by Grant’s method was not affected by salt concentrations that were equal to or less than this. The ratio of the hydroxyproline content of the tissue to its dry weight was shown to be constant with depth for bovine articular cartilage, except for a small surface region of approximately 25 pm [ 171. Hence the hydroxyproline content of the worn tissue could be used as a marker to measure sensitively the extent of wear of the cartilage during a given time period.* There is, however, anatural variance of the percentage of hydroxyproline by weight from sample to sample [ 171. It was therefore necessary to determine a calibration factor for each individual specimen by analyzing a sample of tissue immediately adjacent to the region from which the plug was cut for its hydroxyproline content.

*With 0.03 M phosphate buffer (pH 7.4) as Iubricant, the extent of dissolution of the constituents of intact cartilage was negligible during a wear experiment [ 171. The overall hydroxyproline and hexosamine contents of the intact cartilage at the end of the experiments were identical to those at the beginning 1171. Thus any significant dissolution of the constituents of the intact cartilage during its wear (if it occurred at all) woutd have to have been limited to a thin superficial surface region such that losses would only negligibly affect the overall composition. Such dissolution would be a part of the mechanism of wear of the tissue under these conditions. A significant fraction of the hexosamlne- and hydroxyproline-containing molecules of the wear debris did, however, dissolve in the lubricant (see Section 2.5). It was therefore necessary to measure the hydroxyproline content of both the lubricant and the solid wear debris to determine the total amount of cartilage worn during a given time interval.

The surface region of articular cartilage contains a higher percentage of hydroxyproline by weight [ 171. Nevertheless, the experimentally determined factor for the bulk tissue was used to compute the amount of cartilage worn, even during the initial periods of the experiment when presumably the thin collagen-rich regions were being worn. This was done because the probable pressure distribution across the surface of the tissue (in this experimental configuration [18] ) made it doubtful that the tissue wore evenly across its surface (i.e. solely from the collagen-rich region) at any time except the very earliest moments, i.e. since the local pressures at the central areas of the plug were most probably higher [ 181 than those at the periphery, the tissue at the center wore at greater rates. Hence, even after the first few minutes the worn tissue most probably came from cartilage that was initially at different depths from the surface. Furthermore, even if we assumed that the first few micrograms of hydroxyproline came solely from the coll~en-~ch region and multiplied these values by the appropriately lower conversion factors 1171, there was substantially no change in the shape of the wear-time curve. The compression of the tissue prior to wearing often caused small loose pieces of cartilage to fall off. The amount lost ranged from 0 to 60 I.tg, as was determined by analyzing the buffer for its hydroxyproline content at zero time (i.e. after the tissue was compressed but prior to its wear). The usual amount was around 10 E.tg.Therefore, after the tissue was compressed but before the reciprocating motion of the plate was started the buffer was aspirated out and the trough was refilled with fresh buffer. 2.2. The ~e~ure~~nt of the geu~et~ic contuct areu between the curt~~uge and wearing plate as a function of the load on the tissue The wear of the cylindrical plugs of cartilage and bone against the plate caused the tissue to spread at its surface while its thickness diminished (Fig. 2(a)). It was therefore necessary to determine the geometric contact areas* between the tissue and the plate as a function of load in order to be able to calculate the average pressure on it at each load. The geometric contact areas were measured against surfaces A and B as functions of both time and load. The change of contact areas with time, under given loads, was determined by wearing different samples of the tissue against either of the surfaces for various periods of uninterrupted time and measuring their contact areas by the procedures that are described below. The equilibrium or asymptotic contact areas under different loads were determined after the tissue had been worn for 180 min. This period was found to be sufficient to reach asymptotic values. *The geometric contact area Ag is defined as the area of the surface that makes contact with the plate. This is distinguished from the actual area of contact A,, which consists of the total area of the tips of the asperities within the geometric boundary that actually make contact with the plate. Thus A, < A,. With a relatively compliant material like cartilage, the geometric contact area is probably not far removed from the actual contact area when the tissue is compressed against a smooth flat hard surface (Fig. 2) [ 21.

306

--CARTILAGE

0 LOAD ON CARTILAGE SURFACE AREA = 25.5 mm2

(a)

LOAD = 2.7 KGms. CONTACT AREA. 3Omnl2

LOAD = 13 h CONTACT AREA33mm2

(b)

Fig. 2. (a) Schematic drawing (drawn to scale) showing the changes of thickness and contact area between the tissue and the plate with load. (b) Drawing of the apparatus used to measure the geometric contact areas of worn and unworn tissue in contact with fluids against glass as a function of load. A represents the dissection microscope that was fitted with an eyepiece having a calibrated grid. B is a light source. C is the sleeve (sealed at the end by glass plate) from which screws protruded at D. The sleeve fitted over the plug holder E which contained the circular cylindrical plugs. The set-up was secured in a base F. Weights G were hung from the screws.

The procedure was as follows. The plate was stopped at midcycle and, with the pressure maintained on the tissue, the surrounding buffer was aspirated out. The cartilage was rapidly frozen by pouring liquid nitrogen into the compartmentalized troughs of the plate. Before the tissue could thaw, the plugs were rapidly removed from the apparatus and the major and minor axes of their surface areas making contact with the plate (the geometry was slightly elliptical) were measured by viewing them under a dissection microscope fitted with a calibrated grid. Repeated measurements of a given surface area resulted in values that varied by no more than 3 - 5%. When viewing the frozen surface, it was important to distinguish between a ring of frozen water that frequently surrounded the cartilage and the tissue itself. Failure to do this naturally gave erroneously high contact area measurements. The water ring, when sufficiently large, was easily distinguishable from the tissue by its transparency. If, however, the ring was very small, as was the case if almost all the water (or buffer) was removed before the tissue was frozen, it was difficult to see where the tissue ended and the water began. A little water was therefore deliberately left around each plug before freezing it. The geometric contact areas of both worn and unworn tissue were also determined against glass as a function of load. The experimental procedure consisted of wearing the tissue samples against the metal plate in the manner described for 180 min. The plugs in their holders were then removed from the wear apparatus. A sleeve, sealed at one end by a glass plate and machined to fit loosely around the metal plug holder, was filled with buffer (0.03 M

307

phosphate buffer, pH 7.4) and the plug in its holder was inserted into it. A heavy coating of silicone grease applied to the side of the plug holder (stopcock grease, Dow Corning Co., Midland, Michigan) contained the fluid in the sleeve while the entire set-up was righted. This was then inserted into an aluminum block that served as a base (Fig. 2(b)). Appropriate weights were hung from two long screws that protruded from the bottom of the sleeve (Fig. 2(b)), and the area of contact between the tissue and the glass plate was measured by viewing it through the dissection microscope. For these measurements the plugs of cartilage and bone were secured in their holders such that their surfaces were at least 0.6 cm above the height of the holder. This ensured that the tissue was free to deform under load. With worn cartilage 10 - 20 min elapsed before the tissue crept to its equilibrium or asymptotic contact area, This was taken as the contact area for that load. Tissue that had not been worn, however, spread almost instantaneously to its equilibrium contact area on the application of a load. In the presence of fluid barrelling of the tissue against the glass was probably minimal since the interfacial forces between it and the glass were very small. Thus the contact areas measured were probably very close to those of the true geometric contact area. 2.3. Determination of theaverage* fluid content of the cartilage as a function of pressure and time Changes of the average fluid content of the tissue during wear were determined as a function of pressure and time. For these studies, groups of plugs were worn against the metal plate (surfaces A or B), each under different pressures+, for various intervals of time. The plate was stopped and, with the pressure maintained, the fluid in the trough was quickly and completely aspirated out. The pressure was rapidly relieved, the plugs were removed and the cartilage was quickly cut off from the underlying bone just above the tidemark. The samples were lightly blotted, placed in preweighed bottles, weighed and put in a vacuum oven at 50 “C until constant weights were attained. This usually took about a week. The difference between the wet and dry weights was equated with the loss of fluid from the tissue. Two series of determinations were done: in one the fluid contents of all the cartilage of each plug was measured. In the other measurements were made only for the tissue that was directly under the cylindrical shaft of bone when under pressure (see Fig. 2(a)). This was done by carefully removing the ring of cartilage that spread beyond the area of the underlying bone on compression with a surgical scalpel before the rest of the tissue was cut off. The equilibrium fluid content at each pressure was determined after 150 min of wear. This time was sufficient for it to reach asymptotic values. *Articular cartilage is not a homogeneous material. Its fluid content and composition have been shown to vary as a function of depth [ 191. Since the fluid content was determined for its entire thickness we can therefore speak only of its average content. +The pressure on the tissue means the average pressure across its surface. As stated, the pressure at the periphery of the plug was probably minimal while at its center it was maximal [ 181.

308

For the studies described in Section 2.1.2.1, it was necessary to determine the changes of fluid content with time when the cartilage was compressed against the metal plate (in contact with excess buffer) but not worn. This was done by compressing different samples under an average pressure of 1.65 X lo7 dyn cm-’ for various time periods and determining their average fluid contents by the procedure described above. 2.4. HistofogicaE staining for Eight microscopy After the samples were worn, under a pressure of 1.65 X lo7 dyn cm-’ (about 240 lbf in-‘) each for varying periods of time, blocks of cartilage and underlying bone were cut from them. The sections were fixed in neutral formalin, decalcified in either 2 N formic acid or in 0.5 M EDTA at pH 8.3 and embedded in paraffin, Sections of thickness 6 pm cut perpendicular to the joint surface were stained with Safranin-0 [ 20 ] or Van Gieson’s stain. 2.5. The ratios of the hexosamines and hydroxyproline dissolved in the lubricant to that in the wear debris as a function of pressure and suspension time The dissolution of the constituents of intact articular cartilage below a certain particle size [ 171 is negligibly small in the dilute buffer used as a lubricant. However, with small particles of tissue, the fractions of hexosamineand hydroxyproline-~ont~ning molecules (i.e. the proteoglycans, breakdown products of the proteoglycans, collagen and breakdown products of collagen) dissolved are functions of the tissue particle size [17]. The extents of dissolution of both groups of constituents were shown to increase with smaller particle size. To investigate this further, batches of powdered cartilage having different average particle sizes were prepared and the dissolution of their hexosamine- and hydroxyproline-containing constituents in the dilute buffer were studied. The powders were prepared by grinding slices of hydrated cartilage for about 30 min in a mortar and pestle. During the grinding the tissue was kept frozen under liquid nitrogen. The powdered sample was then separated into coarse, medium and fine fractions by sequentially passing it through no. 35 and no. 60 sieves having pore sizes of 500 and 250 pm. Particles that passed through the no. 60 sieve were then ground under liquid nitrogen for a further 20 min. Particles that did not pass through the no. 35 sieve constituted the coarse fraction; particles that passed through the no. 35 but not the no. 60 sieve constituted the medium fraction; particles that passed through the no. 60 sieve constituted the fine fraction. The fractions were characterized with respect to their average particle size in the fully hydrated state. This was done by photographing through a microscope samples of each fraction suspended in buffer. Photographs of particles of known dimension were similarly made. These served as calibration standards. The tissue particles prepared in this manner had irregular shapes. However, their Iargest dimensions were not grossly different from their smallest dimensions. Therefore it was possible to characterize the relative

309

sizes of the particles of each fraction with respect to their largest dimension as seen on the photomicro~aphs. The third dimension (not seen) was thus assumed to be similar. A considerable effort was made to obtain particle size dist~but~on measurements of the tissue particles and wear debris by other means. However, these efforts were not fruitful. To measure the extent of dissolution of the hexosamine- and hydroxyproline-containing molecules of each fraction, approximately 1 g of each of the powdered samples was weighed and suspended by stirring in 100 cm3 of 0.03 M phosphate buffer (pH 7.4) at room temperature. Duplicate 5 cm3 aliquots of the suspension were withdrawn 2 min after the aqueous buffer was added to the powdered cartilage and at selected times thereafter. They were immediately filtered through 0.45 pm Millipore filters six times and the supernatant solutions were analyzed for their hexosamine and hydroxyproline contents by the procedures of Cessi and Piliego [Zl] and Grant [16]. The filtration procedure was previously shown by Coulter counter analysis to yield particle-free solutions [ 171. Since the weight and the hexosamine and hydroxyproline contents of the powdered cartilage samples prior to suspension were known (by analysis), .the fraction of each constituent dissolved in the buffer could easily be computed as a function of time. The fractions of the hexosamine- and hydroxyproli~e-cont~ning constituents of the wear debris that dissolved were determined for samples of debris generated under different pressures. As will be described later (see Section 3), after about 150 - 180 min of wear against surface A the cartilage wore at a constant rate at each of the pressures studied. The determinations described here were made only for debris generated while the tissue was wearing at a constant rate. Hence after the tissue was worn for about 200 min the lubricating fluid in each trough was qu~titatively removed and the trough was filled with fresh buffer. This time was defined as zero time for the remainder of the experiment. The dissolved fractions of the hexosamines and hydroxyproline contents of the debris were determined as a function of time. For these studies, the tissue was worn under an average pressure of 1.9 X lo7 dyn cm-’ (276 lbf inm2). The procedure used was the same as that previously described [ 171. After 30,100,300 and 1000 min of continuous wear the fluid in each trough (containing the debris) was quickly aspirated out. It was necessary to pool the fluid contents of four troughs for each determination for each time period. The pooling ensured that sufficient material was available for duplicate assays of the hexosamine and hydroxyproline contents of both the debris and the solution. The contents in each fraction were determined by dividing the pooled solutions in two. One half was filtered through Millipore filters (average pore size, 0.45 pm) six times and the hexosamine and hydroxyproline contents of both the filtered and unfiltered solutions were determined by the procedures described previously. From these determinations the amount of hexosamines and hydroxyproline dissolved and that contained in the debris were calculated. Four to six determinations were made for each time period.

310

The effect of the pressure that the tissue was worn under on the fraction of each of the two groups of constituents that dissolved was determined for tissue worn for 300 min under pressures of 0.91 X lo’, 1.69 X lo7 and 2.98 X lo7 dyn cm .2. Six determinations were made for each pressure. 2.6. Measurement of the surface characteristics of the tissue after it has been resw~~~enwith dilute neu traEbuffer following its wear Following their wear the plugs were equilibrated with the phosphate buffer at 5 “C for different times. The surfaces were examined at selected times under a dissection microscope equipped with a calibrated grid and camera attachment and by a light section microscope (Carl Zeiss, F.R.G.). With the light section microscope, the peak-to-valley heights and the number and width of the ridges seen on the surface of the tissue were measured. Dimensional changes of the surface area with time were measured with the dissection microscope.

3. Resufts Wear as a function of time and pressure Against surfaces A or B, the articular cartilage wore initially at rates that decreased with time until a final constant rate* characteristic for each pressure and surface was attained. The times needed to reach the final rates were a function of the surface characteristics of the plate, but were independent of the applied pressure for each surface. Against surface A the weartime curves became Iinear after about 150 - 180 min, but against surface I3 only about 40 min elapsed before the tissue began to wear at a constant rate. The wear of the tissue against each of the surfaces under different pressures is plotted as a function of time in Figs. 3 and 4. The final rates, once attained, were constant for at least 24 h {Fig. 5) and frequently for longer. Against surface C, which was relatively smooth but had depressions whose long dimension was on average preferentially oriented perpendicular to the wear direction (see Fig. 9(c)), the cartilage still initially wore at higher rates than the final constant rate attained at that pressure (1.9 X 10’ dyn cm 2). However, the final rate in thi? case was higher than when the tissue was worn against surface A, which had no prevalent orientation of its surface features (see Fig. 7(a)). Against the much rougher surfaces D and E the tissue wore at the same rate throughout the experiment. Under each load, however, the rates were greater against surface E, the depressions of which were deeper than those of surface D. A comparison of the wear-time curves of cartilage worn against each of these surfaces under a load of 14.6 kg is shown in Fig. 6. 3.1.

*The rates are given in micrograms of cartifage worn per minute (on a dry weight basis). Since the average plate speed was the same for all the experiments (52 cm min-l), except those where the plate speed itself was the variable, the rates can be converted to micrograms of cartilage worn per centimeter traversed by multiplying by 0.019.

311

0

40

60

120

160 TIME

200

240

260

320

360

400

lminutd

Fig. 3. The wear of articular cartilage function of time. The mean values of are plotted: curve 1 ressure, 5.24 x 3.24 x 10’ dyn cm- *B (470 lbf inP2); 276 lbf inP2); curve 4, pressure, 6.62

against surface A under different pressures as a 12 runs at each pressure + 1 standard deviation 10’ dyn cmP2 (760 lbf inP2j; curve 2Lgressure, curve 3, pressure, 1.90 x 10 dyn cm (about x lo6 dyn cmd2 (96 lbf in?).

1.2 -

T

1.0 -

E z

0.6-

8 8 4

0.6-

F %

w-

0

40

so

120 TIME

160

2w

240

260

320

(minuted

Fig. 4. The wear of articular cartilage as a function of time when worn against surface B. Each point represents the mean value of 12 - 15 runs. The scatter, similar to that shown in Fig. 3, was left out for clarity. Curve 1, pressure, 4.62 X 10’ dyn cm-2 (670 lbf in-‘); curve 2, pressure, 2.96 X 10’ dyn crnm2 (about 430 lbf ind2); curve 3, pressure, 1.65 X 10’ dyn cmh2 (about 240 lbf inW2); curve 4, pressuy% 1.03 x 10’ dyn crne2 (about 150 lbf inP2); curve 5, pressure, 6.62 x lo6 dyn cm (96 lbf inP2); curve 6, pressure, 3.45 x lo6 dyn cmP2 (50 lbf in-‘).

TIME

(hrr)

Fig. 5. The wear of articular cartilage for a prolonged period of time against surface B. The mean values of eight runs are plotted.

TIME

hinutod

Fig. 6. The wear of articular cartilage a#ainst rougher surfaces. The pressure in all cases was 1.65 x 10’ dyn cm-’ (240 lbf in- f. +rve A, surface A; curve C, surface C; curve D, surface D; curve E, surface E. The points and mean values of four runs against each of the surfaces.

The wear characteristics of the tissue under these conditions were the same, whether the tissue was worn just 3 h after death without being frozen or whether it was obtained from our usual source. The wear behavior of fresh and stored tissue is plotted in Fig. 7. Against surface A the slopes of the linear portion of the wear-time curves were a linear function of the applied pressure. This was also true against surface B, but at around 2.07 X 10’ dyn cmW2 (300 lbf inb2) a somewhat abrupt change in the wear rate-pressure relation occurred (Fig. 8).

313

7 ? f -

.6 1

0

20

40

SO

80

140 TIME

180

200

220

240

~minutes)

Fig. 7. Comparison of the wear of fresh and stored tissue against surface: pressure, 1.82 x 10’ dyn cmW2; l , frozen and thawed cartilage; A, m, fresh cartilage.

AVERAGE

PRESSURE

kIynsa/cm2x 106,

Fig. 8. The final wear rates of articular cartilage as functions of pressure when worn against surfaces A and 3. The mean values of 12 - 15 runs f 1 standard deviation are plotted.

The linear regions of the wear-time following equations: W = (1.40 x lo-12)VR

curves can be described

by the

+ 0.11

(1)

where 0 < V =G52 cm min- l, 0 Q P < 5.34 X 10’ dyn crnm2 (775 Ibf iS2) and 150 < t < 1440 min for surface A; W = (2.25 X 10-12)VPt

+ 0.075

(2a)

where 0 < V < 52 cm min- 2, 0 G P < 2.07 X 10’ dyn cmp2 (300 lbf in -2) and 40 < t G 1440 min, and

314

W= ((1.35X lo-12)VP+ 1.08 X 10 3}t+ 0.124

(2b)

where 0 < V < 52 cm min. l, 2.07X lo7 dyn crn~ 2 (about 300 lbf in- 2, G P < 5.3 X lo7 dyn cmd2 (about 775 lbf in 2, and 40 G t < 1440 min for surface B. Here W is the amount of cartilage worn (on a dry weight basis) in milligrams, V is the average plate speed in centimeters per minute (see Section 3.1.8), P is the average pressure on the tissue in dynes per square centimeter and t is the time in minutes. The constants can be considered as wear coefficients (in units of mg cm dyn- ‘) that are characteristic of the surface against which the tissue was worn and, in the case of surface B, the range of pressures under which it was worn. The average initial wear rate (i.e. the mean rate for each load prior to the time that the tissue wore at a constant rate) increased, but not linearly, with increasing load when the tissue was interfaced with surface A. Against surface B, however, the average initial rates were not simply related to the load on the tissue (Fig. 4). 31.1. Surface ch~r~cter~~ticsof the plate Surface A (Fig. 9(a)), which was the smoothest surface, was characterized by randomly oriented depressions, which were 0.2 - 0.3 pm deep and 6 - 10 pm long and spaced about 4 - 8 (*rn apart. Surface 3 (Fig. 9(b)) had ridges running in the wear direction which were about 0.5 pm deep, 1.1 pm wide and 1 - 2.6 pm apart. Surface C (Fig. 9(c)) had a pebble-like surface profile with craters about 1 pm apart and 0.3 I.trn deep, the long dimension of which was preferenti~ly oriented approximately perpendicular to the direction in which the tissue was worn. Surface D (Fig. 9(d)) had large valleys about 0.5 pm deep in which were superimposed sharp-edged depressions that criss-crossed the surface. These depressions were 0.7 - 1.5 pm deep and were spaced 4 - 8 pm apart. Surface E (Fig. 9(e)) also had valleys or craters about 0.5 Mm deep with irregular sharp-edged depressions that crisscrossed the surface superimposed on them. These depressions were 1 - 2 pm deep and were about 5 -10 pm apart. 3.1.2. The effect of co~~pre§~i~g the tissue prior to wearing The compression of the tissue prior to wearing resulted in its average fluid content being the same at the beginning of the experiment as it normally would have been after 150 - 180 min of wear (see Section 3.1.3). Nevertheless its wear-time curve was similar in form to that of tissue worn without precompression, i.e. it initially wore at rates that decreased with time until a constant rate was attained. Furthermore, the time that elapsed before it began to wear at a constant rate was about the same. However, the final average wear rate was greater than that normally attained at that pressure when worn against surface A. The wear of the tissue

(b)

(d)

(e) Fig. 9. Scanning electron micrographs of silastic replicas of the metal surfaces against which the tissue was worn: (a) surface A, magnification, 13 500x ; (b) surface B, magnification, 13 500~ ; (c) surface C, magnification, 13 500~ ; (d) surface D, magnification, 1000x ; (e) surface E, magnification, 1000X.

as a function

of time for this series of experiments

is plotted

in Fig. 10.

3.1.3. The effect of reswelling the cartilage after the tissue was wearing at a constant rate on its subsequent wear Once the tissue was wearing at a constant rate, relieving the pressure and allowing it to equilibrate with fluid overnight caused no change in its

316

0

loo

200

300

400

500

TIME (minutes)

Fig. 10. The wear of articular cartilage that was compressed prior to its being worn such that its average fluid content (47%) at the beginning of the experiment was the same as it normally would have been after 180 min of wear. The tissue was worn under a pressure of 1.9 X 10’ dyn ems2 (276 Ibf ine2). The mean values of 10 runs I: 1 standard deviation are plotted.

rate of wear when the experiment was resumed (Fig. 11) provided that the tissue remained oriented in the same direction. The tissue immediately began to wear at the same constant rate at which it was wearing before it was allowed to reimbibe fluid. The initial higher wear rates seen with unworn tissue were totally absent. This was so whether the plate was recleaned, such that its surface was identical to that when the experiment was begun (i.e. the wetting angle of water on the plate was minimal), or whether the plate was left intact.

OY 0

I

25

50

7s

I

,

100

125

TIME

150

,

,

175

200

I

225

t

250

(minuted

Fig. 11. The effect of relieving the pressure on the tissue and ahowing it to reimbibe fluid overnight on its subsequent wear. The broken lines represent the wear of the tissue after it had been reswollen. The tissue was worn against surface 8 under a pressure of 165 x 10’ dyn cm-_2 (240 lbf inW2). The mean values of 8 runs f 1 standard deviation are plotted.

317

When the plate was stopped and the pressure on the tissue was maintained overnight, the tissue also continued to wear at the same constant rate as before.

3.1.4. The effect of orientation with respect to the direction of wear prior to and during the experiment The wear-time curves of the cartilage were the same whether the samples were oriented with the wear direction parallel or perpendicular to its natural articulating direction within the joints. There was also no difference in the rates at which the tissue wore whether the wear direction was parallel (as possible) or perpendicular to the split-line direction (Fig. 12). Once the tissue was wearing at a constant rate, however, releasing the pressure on it momentarily and reorienting it perpendicular to the direction in which it was wearing resulted in its wearing at an increased rate for about 30 - 40 min, after which it continued to wear at the same constant rate as before (Fig. 13). If the pressure was momentarily released without reorientation the cartilage wore throughout at the same constant rate.

3.1.5. The effects of a small amount of abrasive in the lubricating fluid on the wear characteristics of the tissue When 10 - 15 mg calcium phosphate were suspended in the lubricating fluid, the tissue wore from the beginning at rates that increased with time. Within approximately 2 - 2.5 h the cartilage was worn to the bone. The results of these studies are shown in Fig. 14.

TIME

(minutes)

Fig. 12. Comparison of the wear of articular cartilage when worn either parallel or perpendicular to the split-line direction. For these studies the tissue was worn against surface A under a pressure of 1.9 x 10’ dyn crne2 (276 lbf ine2). The mean values of 12 runs * 1 standard deviation are plotted: l , worn parallel to split-line direction; l , worn perpendicular to split-line direction.

318

036

;

036

/

(

034

,’

/

022

020 I

040 0

/ IS0

200

2YJ

300

350

400

450

500

TlME hn”Dsl

Fig. 13. The effect of reorienting the tissue perpendicular to its previous direction (after it was wearing at a constant rate) on its subsequent wear. The tissue was worn against surface A under a pressure of 1.9 x 10’ dyn cm-’ (276 lbf inP2). The points are mean values of 12 runs.

1.6 r 1.4 -

I

’

ci4LClUM WIOSPNATE

I 1.2 I

J

0.0 0.6

0

20

40

60 TIME

00

loo

120

140

160

hinutd

Fig. 14. The effect of suspending small amounts of abrasive (calcium phosphate crystals) in a lubricating fluid on the wear of the tissue. The tissue was worn against surface B under a pressure of 1.65 x 10’ dyn cme2 (240 lbf inV2). The points are the mean values of eight runs.

319

3.1.6. The effect of temperature on the wear of the tissue The wear-time curves of cartilage that was cooled to 5 “C and worn

under conditions where the plate and lubricant were maintained throughout the experiment at 5 “C were not significantly different from that of cartilage worn at room temperature. It is noted, however, that while the overall temperature of the tissue was considerably lower than that of cartilage worn at room temperature, the difference in the interfacial regions might not have been large. 3.1.7. The effect of changing the pressure on the tissue after it was wearing at a constant rate Once the tissue was wearing at a constant rate against either surface A or B, increasing or decreasing the pressure caused it to wear at the rate corresponding to the new pressure almost immediately. The rapid change of wear rate can be seen in Fig. 15. In these experiments the pressure was dropped from 3.76 X 10’ dyn crnF2 (545 lbf in2) to 1.31 X 10’ dyn cmP2 (190 lbf in2). The rates under the new pressures were the same as if the tissue had worn from the beginning at those pressures. 3.1.8. The effect of plate speed on the wear of the tissue The average wear rates (in micrograms cartilage worn per minute) for the linear portion of the wear-time curves were directly proportional to the average plate speed against either surface A or B up to around 50 cm min-’ . At speeds greater than that the rates against surface A were greater than the proportional increase of plate speed, whereas plate speeds greater than 50 cm mine1 against surface B resulted in wear rates that increased proportionally less than the increase of the plate speed (Fig. 16).

m

a00 TIME

xx)

400

600

600

(rninu~~)

Fig. 15. The effect of changing the pressure on the tissue, once it was wearing at a constant rate, on its subsequent wear. For these studies the tissue was worn against surface B. The points are the mean values of eight runs.

320

ZOO-

Fig. 16. The effect of plate speed on the final wear rates of articular cartilage when worn against surfaces A + B. The points plotted are the mean values of 8 - 12 runs t 1 standard deviation.

Prior to its wearing at a constant rate, higher plate speeds also caused the tissue to wear at greater rates. However, these changes, in contrast to the constant wear rate region, were not directly proportional to the changes of speed. Changing the plate speed did not noticeably change the time at which the tissue began to wear at a constant rate. 3.2. The geometric contact area between the cartilage and the wearing plate as a function of time and load During an initial period of each experiment the tissue gradually spread at its surface while its thickness diminished until a constant time-invariant contact area was attained between the cartilage and the wearing plate (Fig. Z(a)). When worn (i.e. when the tissue was subjected to both compressive and shear stresses) the time to reach a constant contact area decreased with increasing load but was the same for each load regardless of whether it was worn against surface A or surface B (Fig. 17). Thus under load the average pressure on the tissue decreased with time during an initial period of the experiment until a constant value for that load was attained (Fig. 18). If the tissue was not worn but merely compressed, it spread to its equilibrium contact area at each load almost immediately (Fig. 19). These contact areas were, however, considerably fess than those attained when the tissue was worn. The final time-invest contact areas for this size plug are plotted as a function of load in Fig. 19. Using these data, a calibration curve relating the applied load to the final average pressure on the tissue was drawn (Fig. 20). When the tissue was compressed against glass in the presence of fluid after it had been worn for a specified time, it crept within about 20 min to the identical contact area for that load that it had had when it was frozen in situ against the metal plate.

321

2 T

LOAD= 5.4 Km.

OY

0

6

20

40

60

80

too

I20

140

160

180

200

TIME (minutes)

Fig. 17. Changes in the geometric contact area with time when worn against either surface A or B under two different loads. The points are the mean values of 10 - 12 determinations 2 1 standard deviation. 014-

20.7

20.0

a.3

% 2.3 loo

TIME fminutr)

Fig. 18. Comparison of the calculated wear (that would have occurred during an initial period if the constant wear rates found for each pressure against surface A were operative throughout the experiment) with that actually found. (The experimental curve is of tissue worn under a final pressure of 1.9 x lo7 dyn cme2.) The broken curve is a plot of the initial changes of the average pressure on the tissue with time caused by the increasing contact area between it and the plate.

3.2.1. Changes in the geometry of the con tatting surface during wear As the tissue wore, what was initially a circular contact area became more elliptical. The major axis was in the direction of wear. The ratio of the major to minor axes became constant at about the time the contact area became constant (up to 3.6 X lo7 dyn cmT2 (about 525 lbf ine2)).

322

25

4

.

,

,

(

,

,

,

,

2

4

6

8

IO

I2

14

16

0 0

LOAD

_I 18

(Kant)

Fig. 19. The equilibrium (asymptotic) contact areas of worn and unworn tissue as a function of Ioad. The points plotted are the mean values of 10 - 12 determinations r 1 standard deviation.

43 1 42I= ‘0

0

2

4

6 LOAO

8

IO

12

I4

16

~kilogroms)

Fig. 20. Calibration curve relating the load to the final average pressure on the tissue taking into account the change of contact area with load.

323

32.2. ~~mensionul changes of the contacting surface following its wear and re-equilibration with buffer When cartilage that was worn was equilibrated with 0.03 M phosphate buffer (pH 7.4) at 4 “C, complete dimensional recovery of the surface region occurred within 96 h, provided that it was worn for times shorter than that required to reach a constant wear rate (i.e. less than about 150 - 180 min) and at pressures less than 2.9 X 10’ dyn cmP2 (425 lbf inV2). The actual recovery time depended on the pressure and the length of time that the tissue was worn. If, however, it was worn for longer periods or under higher pressures, dimensional recovery did not occur even when it was equilibrated for two weeks. Thus, as a result of its wear under these conditions, the surface region, with the tissue fully hydrated, was “permanently” set in a slight elliptical geometry (Table 1). TABLE 1 The times needed to attain dimensional recovery of the cartilage while being equilibrated with 0.03 M phosphate buffer at 4 “C after it was worn for different time periods under different pressures against surface A Pressure (x 10’ dyn cmm2)

Time of wear (min)

Recovery time (h)

2.85 0.91 2.85 2.85 4.70

10-40 80 80 300 80

o-3 3 - 24 ‘72 - 96 Not recovered Not recovered

3.2.3. Loss of the superficial zone of the tissue during wear us determined histologically The Safranin-0 negative surface region of cartilage, corresponding to the collagen-rich zone 1171, was worn off 10 - 20 min after the experiment started when the tissue was worn against surface B under a pressure of 1.65 X 10’ dyn cmV2 (240 lbf inw2). This region of the tissue was therefore removed before the tissue began to wear at its constant rate. Histological cross-sections of normal cartilage and cartilage worn for 20 min can be seen in Fig. 21. Histograms of cartilage worn for 10 min at that pressure still had a Safranin-0 negative surface region. Cartilage that was worn for long periods of time did not decrease its Safranin-0 stainability. 3.2.4. Characterization of the ridges on the surface of the cartilage following its wear and equilibration with buffer When the cartilage was equilibrated with 0.03 M phosphate buffer (pH 7.4) for 16 h at 5 “C after it had been worn against either surface (A or B) for periods sufficiently long to ensure a constant wear rate, the surface of

(al

@I

Fig. 21. (a) Histograms of normal articular cartilage stained with Safranin-0 and counterstained with methyl green, The characteristic collagen-rich Safranin-0 negative surface region is seen as a dark band. (b) The same histogram of tissue that ha a been worn for 20 min against surface B. Note the absence of the Safranin-0 negative surface region.

the tissue had ridges running the length of the plug in the wear direction (Fig. 22). The numbers and average depth of the ridges varied with the applied pressure and the surface characteristics of the plate. Cartilage worn against surface B had fewer ridges on reswelling then cartilage worn against surface A but their peak-to-valley heights were much larger. The surface of the tissue worn under higher pressures had more ridges on reswelling but smaller peak-to-valley heights. The number and depth of the ridges were a function of the time of wear. If worn for short periods of time (less than 150 min for surface A and less than 40 min for surface B) few if any ridges were evident upon reswelling, Longer periods of wear, however, resulted in more ridges. The m~imum number of ridges were seen after the tissue was worn for 40 - 100 min against surface B and for 150 - 225 min against surface A. Illustrative drawings (to

(4

(b)

Fig. 22. Photographs of the surfaces of worn and unworn cartilage after the samples were equilibrated with 6.03 M phosphate buffer (pH 7.4) at 5 “C for 18 h. The tissue was worn against surface B for 4 h under a pressure of 1.65 x 10’ dyn cmL2 (about 240 lbf ine2). Note the deep ridges running the full length of the pfug in the wear direction. However, these do not correspond to regions of greater wear (see pp. 335 and 336).

325

(a)

(b)

Fig. 23. (a) Drawing to scale of the surface profile of the cartilage perpendicular to the wear direction after it had been worn against surface B for 2 h under different pressures and equilibrated with 0.03 M phosphate buffer (pH 7.4) for 16 h at 5 “C. Measurements of the number and size of the ridges as well as the general concavity of the surface were obtained by light section microscopy. The broken lines represent the original dimensions of the hydrated tissue rior to wear. The tissue was worn under the following pressures: -sl I, 0.34 x 10’ d;l’n cm (about 50 lbf inme2);‘$1.65 x 10’ dyn cmm2 (about 240 lbf ine2); III, 3.10 X 10 dyn crne2 (about 450 lbf in-’ ); IV, 4.62 x 10’ dyn crnm2 (670 Ibf ine2). (b) Changes of the surface profile of cartilage after wear as a function of the time of equilibration with 0.03 M phosphate buffer at 5 “C. The tissue was worn against surface A for 200 min under a pressure of 1.9 x 10’ dyn cmP2 (276 lbf inP2). The periods of equilibration were A, 2.5 h, B, 24 h, C, 48 h and D, 72 h. Note that, while there was almost complete recovery of the shape of the sample and the depths of the surface ridges were reduced, some ridges still remained even after 72 h of equilibration.

scale) of the surface profiles of cartilage worn under different conditions and equilibrated for 16 h at 5 “C are shown in Fig. 23(a). When the cartilage was equilibra~d with the buffer for longer periods of time, the depth of the ridges diminished with time and eventually completely disappeared provided the tissue was worn for periods of less than 80 min and at pressures that were equal to or less than 2.9 X 10’ dyn cme2 (about 425 lbf in2). If, however, the tissue was worn for longer periods of time or at higher pressures, the ridges were still evident even after two weeks of equilibration. Representative drawings (to scale) of changes of the surface profile with equilibration time are shown in Fig. 23(b). 3.3. Changes of the average fluid content of the tissue during its wear under different pressures 3.3.1. Changes with time when interfaced with surfaces A or B Although the tissue was always in contact with excess fluid, its average fluid content decreased during an initial period of the experiment as it was worn. The rate of decrease was a function of the surface profile of the plate. Against surface B, 40 - 80 min elapsed before the tissue reached an equilibri-

326

urn fluid content at a given pressure (Fig. time-invariant content was attained only times were roughly the same as the times to wear at a constant rate. Furthermore, applied pressure.

24). Against surface A, however, a after 150 - 200 min (Fig. 24). These that elapsed before the tissue began they were independent of the

60

k

04 0

20

40

60

60 TIME

100

120

140

WI

160

hnutsr)

Fig. 24. Changes of the average fluid content of cartilage with time when worn against surfaces A and B. For curves I and III the cartilage was worn against surface B under pressures of 1.15 x 10’ and 2.24 X 10’ dyn cmm~2 respectively (167 and 325 lbf iK2). Forgurve II the tissue was worn against surface A under a pressure of 1.15 x lo7 dyn cm

.

If the tissue was compressed against the plate but not worn (i.e. there was no movement of the plate) the time to reach an equilibrium fluid content under a given load was considerably longer. The fluid contents of the cartilage were not the same across its surface. As stated in connection with the contact area measurements, the tissue spread under load beyond the area of the underlying shaft of subchondral bone (Fig. 2). The fluid contents of the ring of cartilage that spread beyond the diameter of the bone decreased with pressure up to about 6.89 X lo6 dyn cm-2 (about 100 lbf in2), but remained unchanged with further increases of pressure. 3.3.2. Changes of the asymptotic fluid contents with pressure The equilibrium or asymptotic fluid contents of the tissue decreased monotonically with pressure. The changes with pressure are plotted in Fig. 25.

327

I-

0% 0

IO

20 PRESSURE

t

30

, 40

SO

60

70

(dynes/cm2 x IO61

Fig. 25. The equilibrium in the asymptotic fluid content of the tissue (in contact with fluid) as a function of pressure.

3.4. Changes in the fraction of the hydroxyproline and hexosamine content of the wear debris dissolved in the lubricant when the tissue was worn under different pressures 3.4.1. Changes of dissolution of the hexosamine and hydroxyproline contents of carti~~e in 0.03 M phosphate differ(pH 7.4) as Qfunction of the average particle size of the tissue The three batches of powdered cartilage consisted of particles the sizes of which were characterized as follows. The coarse fraction was made up of particles with a longest dimension of, on average, 500 - 600 pm, the longest dimension of the particle of the middle fraction ranged between 200 and 300 pm and those making up the fine fraction had longest dimensions between 55 and 80 pm. The fraction of the hydroxyprolineand hexos~ine-cont~ning molecules that dissolved increased with decreasing tissue particle size (Table 2). However, the fraction of hexosamines dissolved increased considerably more with decreasing particle size than did the fraction of hydroxyproline (Table 2). With each fraction, the percentage of both groups of constituents dissolved was the same whether the particles were suspended for 10 - 15 min or for 2 h. 3.42. The dissoiu tion of hexosamine- and hydroxyproiine-con taining molecules of the wear debris in the lubricant The dissolved fraction of the hydroxyprolineand hexosamine-containing molecules of the wear debris increased when the tissue was worn under higher pressures (Table 3). The wear particles that could be seen under

328 TABLE 2 The fraction of the hydroxyproline and hexosamine content dissolved in 0.03 M phosphate buffer (pH 7.4) of different sized particles of articular cartilage Fraction

Hydroxyproline (W)

Coarse (500 - 600 pm) Intermediate

0.003 + 0.001

(200 - 300 pm) Small (50 - 80 pm)

dissolveda

Hexosamine dissolvedb (%) 0.8 t 0.1

0.009 f 0.002

-

0.025 t 0.009

11.2 f 0.8

aThe mean values of seven experiments i 1 standard deviation are reported. bThe mean values of four experiments f the average deviation are reported.

TABLE 3 The fraction of the hydroxyproline and hexosamine content of the wear debris dissolved in the lubricant (0.03 M phosphate buffer, pH 7.4) when the tissue was worn against surface A for 300 min under different pressures Pressure (X 10’ dyn cm-2)

Hydroxyproline (%)

0.92

8.4 f 2.ga

1.69 2.99

9.6 * 3.6b 38.7 + 9.4b

dissolved

Hexosamine dissolved (%) _ 58.7 i 13.3b 81.7 t 11.6b

aMean value of three experiments t the average deviation. bMean value of six experiments t 1 standard deviation.

microscope examination ranged from barely visible specks to particles with a longest dimension that was no greater than about 35 I.tm. Assuming, as was shown earlier, that the fraction of each group of constituents dissolved is inversely related to the tissue particle size for this smaller particle size range, the debris generated at higher pressures was, on average, smaller than that generated at lower pressures. In the linear region of the wear-time curve the dissolution of hydroxyproline- and hexosamine-containing molecules from the debris was rapid, if not instantaneous. The fraction of hydroxyproline dissolved increased linearly with time when the tissue was worn against surface A (at a pressure of 1.9 X 10’ dyn cme2 (276 lbf inW2)) (Fig. 26), but the fraction of hexosamines dissolved was constant with time. The intercepts, on extrapolation to zero time were taken as the fraction of each group of constituents that dissolved “instantaneously”.

329

$1

t

200

400 TIME

600

800

loo0

1200

fminutes)

Fig. 26. The ratio of the contents of hydroxyproline and the hexosamines dissolved in the lubricant to that contained within the wear debris as a function of time. The tissue was worn under a pressure of 1.9 x lo7 dyn cm-’ (276 lbf inP2) against surface A.

4. Discussion When worn against the “smooth” metal surfaces (i.e. surface A, B or C) the articular cartilage initially wore at higher rates than the final constant rate that was characteristic for each surface and pressure. Among the factors that could conceivably have caused or contributed to this effect were (1) the average pressure on the tissue decreased during the initial period owing to the concomitant changes of contact area between it and the plate (Fig. 18), (2) the surface region of the tissue had properties different from the bulk (owing, perhaps, to surface flaws or incipient cracks, or to some structural entity) which, when worn away, resulted in its wearing at reduced rates, (3) the initially higher fluid content of the tissue made it more plasticized which caused it to wear during this period at higher rates or (4) the surface of the metal changed during the course of the experiment possibly because of the adsorption of constituents of the tissue onto its surface. Such changes could have altered the nature of the interfacial interactions between it and the cartilage and thus caused it to wear at reduced rates. None of these possibilities can, however, explain the changes of rate for the following reasons, The pressure changes during the initial period were insufficient to explain the magnitude of the rate changes that were obsenred. If we assume that the wear rate-pressure relations described by eqns. (1) and (2) held throughout the experiment and that no factors other than pressure changes were operative, the calculated wear-time curves turn out to be grossly different from those observed (Fig. 18). Obviously then the wear ratepressure relation during the initial experimental period must be different. Hence pressure changes by themselves cannot account for the initial decrease of the wear rates. Furthermore, under loads equal to or greater than 3 kg the equilibrium or asymptotic contact areas (and hence the final average

330

pressures) were attained long before the tissue began to wear at its constant rate (Fig. 18). The possibility that the removal of a surface region that was less wear resistant or flawed during the initial period was the cause of the decrease of the wear rates is also precluded. The time that elapsed before the tissue began to wear at a constant rate was independent of the applied pressure (Figs. 3 and 4). Surface flaws inherent in the tissue would have been expected to have been worn away more rapidly under higher pressures. If this were the case, the time elapsing before the tissue began to wear at a constant rate should have been inversely related to the average pressure. This was not observed. The same is true if a less wear resistant surface region, inherent to the structure of the tissue, is postulated. Under higher loads more cartilage was initially worn away (Figs. 3 and 4) prior to the wear rates becoming constant. Again, since the time required for the tissue to wear at a constant rate was independent of the pressure, the change of rate cannot be attributed to the removal of a characteristic region of the tissue. The surface region of cartilage normally seen in histograms (Fig. 21) was worn away before the tissue began to wear at its constant rate. The decrease of the average fluid content during the initial period (Fig. 24) also cannot explain the reduction of the rates during the initial period. When the cartilage was compressed prior to its being worn such that its average fluid content at the beginning of the experiment was the same as its equilibrium fluid content for that load, the initial wear rates were still higher than that finally attained under that load (Fig. 10). Furthermore, when the tissue was reswollen after it had been wearing at a constant rate, it immediately wore at the same rate, at that load, when the experiment was resumed (Fig. 11). We cannot, however, preclude the possibility that there is some relation between the reduction of the average fluid content of the tissue and the lowering of the rates. It may be more than coincidence that the tissue attained its final fluid content against both surfaces A and B at about the same time that it began to wear at a constant rate. Finally, the redked wear rates could not have been brought about as a result of changes of the surface properties of the metal. Some changes of the metallic surface undoubtedly occurred during the course of the experiment. The wetting angle between the metal and a drop of water was always somewhat greater at the end of the experiment than it was at the beginning. However, these changes apparently had no effect on the wear rate of the tissue. When the pressure on the cartilage was relieved during a run and the tissue was reswollen, it still continued to wear at the same constant rate despite the fact that the plate was recleaned during the interim such that the wetting angle of water on its surface was once again minimal. Furthermore, extensive contamination of the metallic surface caused an increase rather than a decrease of the wear rates. It was precisely for this reason that the plate had to be meticulously cleaned prior to the start of each experiment. What we would therefore propose as the primary cause of the decrease of the initial rates is that partial orientation of the macromolecules and their

331

aggregates in domains of the surface region towards the direction of wear took place as a consequence of the stress field to which the tissue was subjected. This, we shall try to explain, caused the tissue to wear at reduced rates provided the wear direction remained unchanged. Furthermore, it is suggested that, since the final rates were constant for at least 24 h, the oriented surface region was maintained throughout the experiment by the continuous subsequent orientation of domains of the macromolecules at some depth below the contacting surface as the tissue wore. The above contention is supported by the fact that when the cartilage was wearing at a constant rate and was reoriented perpendicular to its previous direction, it wore for a period of time at higher rates before it resumed its previous wear rate (Fig. 13). When the same experiments were conducted without reorientation, no change of rate occurred. The resumption of the previous rate is interpreted as having been due to a further reorientation of the macromolecules of the surface region towards the new wear direction. Evidence that network rearrangement, accompanied most likely by network breakdown, occurred during the initial phase of the wear experiments is as follows. (1) When the tissue was worn for a period long enough to ensure a constant wear rate (or for a somewhat shorter period at higher pressures), the surface region was permanently set. * This was maintained even after the tissue was equilibrated with buffer for two weeks.+ In contrast, when it was worn for shorter periods under the same pressures, dimensional recovery was complete within at most 96 h and usually after shorter times (Table 1). The time for dimensional recovery of the surface region (or whether it recovered at all) when equilibrated with dilute buffer was thus dependent on the time and pressure under which the tissue had been worn. This can probably be explained by network breakdown and/or macromolecular rearrangement of the surface region and subsequent network reformation, as has been shown for other systems (ref. 22, pp. 334 - 336). (2) The contact area between the tissue and the plate increased, under a given load, during the initial wear period such that its final value was significantly larger than that of unworn tissue (Fig. 19). Furthermore, when the pressure on the tissue was relieved (which caused the surface region to contract) and the tissue was re-equilibrated with fluid overnight, application of the same load caused the cartilage to creep to the same contact area that it had had while previously under that load. In contrast, unworn tissue assumed its equilibrium or asymptotic contact area almost instantaneously when a load was applied and this was considerably less than that of worn tissue (Fig. 19).

*The term “permanent set” is used here as defined by Bueche (ref. 22, pp. 334 - 336) as the non-recoverable dimensional change exhibited by a network after it is released from a strained position. ‘The equilibration times could not be practically extended beyond this period as tissue degeneration due to a variety of factors was frequently evident after longer periods.

332 (3) Even the slightly elliptical geometry of the contacting surface (where the major axis was in the direction of wear) was maintained when the tissue was reswollen and the same load was applied. Unworn tissue always had circular contact areas. The rates at which the tissue wore did not change as a result of orienting the wear direction with respect to the split-line direction. This could have been due to experimental difficulty. The split-line pattern was curved across the region of the condyle from which our plugs could be cut. It was therefore difficult to orient the specimens exactly parallel or perpendicular to the splitline pattern. macromolecule o~entation in the stress direction has long been recognized as a primary factor governing the moduli and strength of polymeric materials (see ref. 23, pp. 143 - 158, and ref. 24). In the simplest sense, such orientation results in the stress being shared at any instant by more macromolecular chains and aggregates of these chains per unit cross-section. The net result is to reduce the fraction of the total stress borne by each individual chain fragment. Furthermore, orientation causes a greater share of the stress to be borne by the stronger covalent bonds of the chain backbone and less by the weaker in~rmolecul~ bonds (see ref. 23, pp. 143 - 158). The rate of bond breakage* during fracture (which we shall attempt to show governs the rate of wear of the tissue under these conditions) has been shown to obey an Arrhenius type of exponential equation for a variety of polymeric as well as non-polymeric materials (refs. 30, 31, 32 and ref. 23, pp. 38 - 51). Furthermore, the activation energies for bond rupture were shown experimentally (refs. 30 and 32 and ref. 23, pp. 38 - 51) to decrease linearly with increasing stress on each bond*, i.e.

dc dtaexp

--u kT C-1

where U = U, - yo. Here dcldt is the rate of bond rupture (which we assume to be proportional to the rate of crack initiation), U is the Anhenius activation energy which is equal to the difference between U,, the activation energy for bond rupture with no stress on the material, and the product of a proportionally constant y and the stress cr on the bond,? k is the Roltzman constant and T is the absolute temperature. Obviously lower stresses (on average) borne by each chain fragment would result in higher activation energies and *The rate of bond rupture may not, of course, be equivafent to the rate of formation of cracks capable of propagation, since these must attain a critical size [ 25 1. Furthermore, a variety of elementary molecular processes, in addition to chain scission (e.g. slip of chains, segment rotation etc. [ 261) can initiate events that will lead to crack initiation. However, for a highly interacting or cross-Iinked system such as cartilage [ 271 it is reasonable to assume that a proportionality exists between the rates of crack initiation and chain scission [ 28,291 (see the extensive theoretical treatment of fracture processes of polymers by Knauss [28, 291 and others (refs. 30 - 32 and ref. 23, pp. 38 - 51) where a theoytical rationale for such a proportionality is demonstrated). The average stress per bond in a given direction has been taken as being equal to the stress divided by the number of bonds in a cross section perpendicular to the stress

1301.

333

hence lower bond rupture rates. The concept of a probability factor governing chain s&ion, inherent in the use of an Arrhenius-type equation to predict the rates of bond rupture and crack initiation, obviates the need to assume maximum chain or fiber extension as a precondition to chain fracture within the tissue as has been suggested [33]. When the tissue was worn against the rougher scratched surfaces, the wear-time curves were linear from the start, the slopes remained constant throughout the experiment, the rates were proportional to the degree of surface roughness (i.e. the depth of the scratches) and the tissue debris was larger. The mechanism of wear in these cases was clearly abrasive. The rates appeared to be a function of the extent of penetration of the metal into the tissue as it slid across its surface. The wear mechanism thus apparently shifted from a primarily adhesive one when the tissue was interfaced against the smooth metal surfaces to a predominantly abrasive one against. the rougher ones. It is thought that under these conditions the surface regions were worn away too rapidly to allow macromolecular orientation to occur. Consequently no change of rates was observed. It is thought that, once the tissue wore at a constant rate (against surfaces A or B), it was the properties of its surface region and not its bulk mechanical properties that governed its wear behavior. The average fluid contents of the tissue decreased significantly with increasing pressure (Fig. 25). Such decreases would have been expected to cause significant changes to properties of the tissue (e.g. greatly increased moduli etc.) that would affect its wearability. As such, the linear relations* between its wear rates and the average applied pressure (Fig. 8 and eqns. (1) and (2)) should not have been expected. Therefore what is thought to have occurred is that, although the average fluid content decreased with pressure, the fluid content of the surface region (i.e. some thin region from the contacting surface inward) did not change significantly. The implication of this is that there is a gradient of fluid content from the contacting surface inward under all pressures. If such were the case, the material properties of the surface region would not. have varied greatly with pressure and the direct proportionality between the wear rates of the tissue and pressure could more easily be explained. When small amounts of a calcium phosphate salt acting as an abrasive were suspended in the lubricant, the wear rates increased continuously with time (Fig. 14). This could be explained by the abrasive particles puncturing or cutting the tissue as it wore, which caused increasing numbers of secondary cracks to be formed in its interior. On coalescence of these cracks larger and more wear particles would have been formed per unit, time, and the wear rates would consequently increase with time. The ridges seen on reswelling cannot be categorically interpreted. However, they do not correspond to regions of wear and their depth and geometry are not consistent with the surface profile of the plate. Furthermore, *Similar relations were found to describe the wear of a variety of homogeneous polymers that were slid, unlubricated, against metal surfaces [ 341.

334

their peak-to-valley heights are greatest after being equilibrated with buffer for 24 h and diminish with longer equilibration times. It is plausible that the ridges were caused by different extents of swelling in alternate regions of the surface, perpendicular to the wear direction. It is proposed that the more oriented regions, with presumably lower free energies of stretch perpendicular to the predominant chain or fiber direction, would swell more in that direction. If neighboring less oriented regions swelled to a lesser extent in that direction, the more swollen regions would have to “pucker” to absorb their equilibrium fluid content and consequently ridges would appear. When the tissue was reoriented perpendicular to its original direction during a run, the predominant ridges on reswelling were parallel to the new direction. However, ridges of lower average height perpendicular to the dominant ones in a cross pattern were alsq observed if the experiment was stopped within an hour or two after reorientation. If, however, the experiment was run for a more extended period of time, the only ridges on reswelling were parallel to the new wear direction. When the tissue was equilibrated with buffer for times sufficiently long that network reformation could have taken place, the ridges began to disappear. As to why some regions of the surface should have been more oriented than others, we can only speculate that this could have been caused by the channelling of the lubricant between the tissue and the plate. If this did occur, there would have been regular variations of interfacial forces across the surface of the tissue and hence regularly spaced periodic orientations of the surface region of the tissue. During the course of this investigation we attempted to obtain measurements of the particle size distributions of the wear debris by Coulter counter analysis and light microscopy. These, however, were not successful because we could not distinguish using either method artifactual dust and minute particles of fat (that originated from the underlying bone) from the actual wear debris itself. Of more importance, however, was the fact that we could not prevent the partial dissolution of constituents of the formed wear particles themselves. Unlike the wear debris of metals and other materials, the volume of each of the particles formed in this case would be a function of its state of hydration. This would vary with the fixed charge and interaction densities of the particles [ 191. The formation of wear particles, however, was shown in this investigation to be accompanied by the dissolution of hexosaminecontaining molecules among others (see later). It is known that these can be directly correlated with the fixed electrokinetic charge density within the tissue [ 351. It is therefore most probable that the state of hydration of the wear particles was quite different from that of the bulk tissue in equilibrium with the same solvent and so the relation of their size to the mass of solid organic material contained within them is indeterminate. However, we had previously observed that the fraction of hydroxyproline and hexosamines dissolved in the dilute buffer used as a lubricant throughout this investigation increased with decreasing tissue particle size

335

[ 171. This qualitative relation was confirmed in the present investigation (Table 2) (i.e. for different size particles prior to the dissolution of any Of their constituten~). The ratio of each constituent dissolved to that contained within the debris increased when the tissue was worn under higher pressures (Table 3). If the same qualitative relation as was shown earlier, i.e. that the smaller the tissue particles, the greater is the fraction of each constituent dissolved (Table 21, holds for the range of particle sizes making up the debris, then the wear debris generated under higher pressures was on average smaller than that generated under lower pressures. The average size of particles is defined as the average volume of particles formed during the wear of the tissue if none were dissolved and if there was no dissolution of any of their constituents. It does not mean an average of the particle size distribution of the actual debris suspended in the lubricant that would be obtained in the experiments since those have been affected by dissolution and hydration processes. The overall wear rate dw/dt is clearly equal to the product of the number of wear particles formed per unit time dn/dt, the mean particle volume u (in the sense as described above) and a propo~ionality factor 0 relating u to the mass of the solid organic material contained within it, i.e. dw -= dt

dn zVP

However, the wear rates dw/dt increase linearly with pressure (Fig. 8). Since u decreases with increasing pressure and p is constant at all pressures, the rates of particle generation increase more than the proportions increase of pressure and the crack propagation paths leading to particle formation are smaller with increasing pressure. For the linear portion of the wear-time curve the rates at which particles are formed must therefore be either greater than or, more likely, proportional to the rates of crack initiation. This can be seen from the following reasoning. The formation of a wear particle can be caused either by the coalescence of a number of existing cracks or by the propagation of an initiated crack to failure. In any case, each particle formed, in the absence of other processes, results in the crack population, or the number of cracks per unit volume of the material, being reduced. If the rate of particle formation were faster than the rate of crack initiation, eventually all existing cracks within the affected volume of tissue would have been eliminated. Under these conditions, the wear mechanisms would require every initiated crack to terminate rapidly into a wear particle. If, however, a steady state population of cracks within the affected volume is presumed, then the rate of particle formation would have to be directly proportional to the rate of crack initiation to maintain the steady state. If this were not so (i.e. if the rates of crack initiation were faster than the rates of particle fo~ation~, then the number of cracks within the volume would consequently increase with time and at some critical point these

336

would eventually coalesce to cause the wear-time curve to sweep up. This was not observed. Thus the rate-determining factor governing the rate of wear of the tissue under these conditions must have been the rate of crack initiation. The possibility of the tissue wearing by a fatigue mechanism involving relatively slow crack growth is thus precluded under these conditions. If such a mech~ism were solely operative there would have been a latent period in the wear-time curve where no wear was observed. This was not observed. If, however, slow crack growth occurred together with the presumed adhesive wear mechanism, there should have been, for the reasons cited, an upsweep in the wear-time curve at some point during the experiment. This also did not occur. Furthermore, surface cracks could not be seen at the end of any of the wear experiments. Hence the fatigue mechanism proposed by Weightman et al. [ 361 for the wear of cartilage does not appear to,have been operative under these conditions. It is unlikely, however, that there is not a steady state crack population within the tissue during its wear. The cleavage of oriented polymeric materials has been shown to involve chain fracture removed from the apparent crack sites [37 - 391. The stress field generated in the vicinity of an advancing crack apparently causes entangled (or otherwise interacting) chains that do not yield in time to rupture. It is therefore highly improbable that a crack initiated within the tissue could propagate to failure without causing numerous other bond ruptures that could serve as the locus of formation of additional incipient cracks as the tissue wears [28,29]. Once the tissue was wearing at a constant rate under a given pressure changing the pressure caused it almost immediately to wear at rates that were identical with that of tissue that was worn continuously at that pressure (Fig. 16), i.e. the wear rates at the new pressure were insensitive to the previous wear history. If the steady state crack population was different at different pressures, changing pressures should have been expected to result in wear rates that were, initially at least, different from that finally attained. That we did not see this probably indicates that new steady state conditions can be rapidly attained. When worn against the “smooth” metal surfaces, it is apparent that the crack propagation paths were short and limited to a surface region. As stated, no gross signs of surface cracks could be seen after any wear period, even when India ink was used to visualize them better. Cracks of any significant depth could usualiy be visualized by this technique [ 14 ] . In addition, the preponderant fraction of the wear fragments suspended in the lubricant was very small (not more than 3 pm). The longest dimensions of even the largest fragments (and there were not many of these) generally did not exceed 35 Brn. The short propagation paths are, no doubt, related to the fibrous nature of the matrix [40]. The ratio of hydroxypr~line and hexosamine dissolved to that contained within the wear debris does not go through the origin when extrapolated to zero time (Fig. 26). On extrapolation, the fraction dissolved can be considered

337

as that which dissolved concomitantly with or immediately after particle formation. Thus, the formation of wear particles is accompanied by the dissolution of molecular fragments from within the wear debris and, most probably, also from the immediate vicinity of the newly formed surfaces within the intact tissue [ 371. This most probably happens as the result of chain scission occurring on both sides of the crack at a distance removed from the crack surface as has been suggested for other polymeric materials [ 371. Such a phenomenon is consistent with the observed increased dissolution of the constituents of the tissue with smaller particle size. Chain scission due to mechanical stress does not ordinarily occur unless the macromolecular network is crosslinked or highly entangled (ref. 22, p. 336). The fact that the glycosaminoglycan content of the debris dissolved to such an extent therefore indicates that the proteoglycans are intermolecularly entangled or crosslinked within the tissue and that they bear a fraction of the stress imposed on it. Furthermore, since the fraction of the hexosamines dissolved is so much greater than that of hydroxyproline, the increased dissolution with decreasing tissue particle size cannot be explained as being due merely to surface energy effects.

Acknowledgment The authors wish to thank Mr. Robert Etheridge, III, for his help during the course of this work, which was supported in part by funds from NIH grant AM 15671, The New England Peabody Home for Crippled Children, Inc., and The John A. Hartford Foundation, Inc.

References 1 L. Sokoloff, Biology of Degenerative Joint Diseases, Univ. Chicago Press, Chicago, Ill., 1969. 2 F. P. Bowden and D. Tabor, Friction and Lubrication of Solids, Vols. 1, 2, Oxford Univ. Press, London, 1954,1964. 3 D. Tabor, Friction, lubrication and wear. In M. Matjevic (ed.), Surface and Colloid Science, Vol. 5, Interscience, New York, 1972, pp. 245 - 312. 4 E. Rabinowicz, Friction and Wear of Materials, Wiley, New York, 1965. 5 E. Radin and I. Paul, Response of joints to impact loading. 1. In vitro wear, Arthritis Rheum., 14 (1971) 356 - 362. 6 H. Lipshitz and M. J. Glimcher, A technique for the preparation of plugs of articular cartilage and subchondral bone, J. Biomech., 7 (1974) 293 - 294. 7 T. R. Oegema, V. C. Hascall and D. D. Dziewiatkowski, Isolation and characterization of proteoglycans from the swarm chondrosarcoma, J. Biol. Chem., 50 (1975) 6151 6159. 8 P. H. Byers, K. H. McKenney, J. P. Lichtenstein and G. P. Martin, Preparation of type II procollagen and collagen from rat skin, Biochemistry, 13 (1974) 5243 - 5248. 9 A. I. Sapolsky, D. S. Howell and J. F. Woessner, Jr., Neutral proteases and cathepsin D in human articular cartilage, J. Clin. Invest., 53 (1974) 1044 - 1053.

338 10 S. Y. Ali, L. Evans, E. Stainthorpe and C. H. Lack, Characterization of cathepsins in cartilage, Biochem. J., 105 (1967) 549 - 557. 11 J. F. Woessner, Jr., Purification of cathepsin D from cartilage and its action on the protein-polysaccharide complex of cartilage, J. Biol. Chem., 248 (1973) 1634 - 1641. 12 H. Lipshitz and M. J. Glimcher, An instrument to study the wear of articular cartilage, in preparation. 13 J. W. Hulthkrantz, uber die Spaltrichtung der Gelen Knorpel, Verh. Anat. Ges., 12 (1898) 248. 14 G. E. Kempson, Mechanical properties of articular cartilage. In M. A. R. Freeman (ed.), Adult Articular Cartilage, Grune and Stratton, New York, 1972, p. 171 (cf. p. 202). 15 A. Boyde, Quantitative photogrammetric analysis and qualitative stereoscopic analysis of SEM images, J. Microsc. (Oxford), 98 (1973) 452 - 471. 16 R. A. Grant, Estimation of hydroxyproline by the auto analyser, J. Clin. Pathol., 17 1964 685 - 686. 17 H. Lipshitz, R. Etheredge and M. J. Glimcher, In uitro wear of articular cartilage. I. Hydroxyproline, hexosamine and amino acid composition of bovine articular cartilage as a function of depth from the surface; hydroxypro&e content of the lubricant and the wear debris as a measure of wear, J. Bone Jt Surg., Am. Vol., 57 (1975) 527 - 534. 18 B. Avitzur, Metal Forming Processes and Analysis, McGraw-Hill, New York, 1968, pp. 102 - 120. 19 H. Lipshitz, R. Etheredge, III, and M. J. Glimcher, Changes in the hexosamine content and swelling ratio of articular cartilage as a function of depth from the surface, J. Bone Jt. Surg. Am. Vol., 58 (1976) 1149 - 1153. 20 L. Rosenberg, Chemical basis for the histological use of Safranin-0 in the study of articular cartilage, J. Bone Jt Surg., Am. Vol., 53 (1971) 69 - 82. 21 C. Cessi and F. Piliego, The determination of amino sugars in the presence of amino acids and glucose, Biochem. J., 71 (1960) 508 - 510. 22 F. Bueche, Physical Properties of High Polymers, Interscience, New York, 1962. 23 G. M. Bartenel and Y. S. Zuyev, The Strength and Failure of Viscoelastic Materials, Pergamon Press, Oxford, 1968. 24 C. C. Hsiao, Theory of the mechanical breakdown and molecular orientation of a model linear high polymer solid, J. Appl. Phys., 30 (1954) 1492 - 1497. 25 B. L. Averbach, Some physical aspects of fracture. In H. Liebowitz (ed.), Fracture: An Advanced Treatise, Vol. 1, Academic Press, New York, 1968, pp. 441 - 472. 26 H. H. Kausch, The role of network orientation and micro structure in fracture initiation, J. Polym. Sci., Part C, 32 (1971) 1 - 44. 27 A. Serafini-Fracassini and J. W. Smith, The Structure and Biochemistry of Cartilage, Churchill Livingstone, Edinburgh, 1974, pp. 101 ff. 28 R. F. Landel and R. F. Fedors, Rupture of amorphous, unfilled polymers. In B. Rosen (ed.), Fracture Processes in Polymeric Solids, Phenomena and Theory, Interscience, New York, 1964, pp. 362 - 485 (cf. pp. 442 - 446). 29 W. G. Knauss, The time-dependent fracture of viscoelastic materials. In T. Yokobori, T. Kawasaki and J. M. Swedlow (eds.), Proc. First Int. Congr. on Fracture, Vol. 2, Sendai, Japan, Sept. 1965, Japanese Society for the Strength and Fracture of Materials, Sendai, pp. 1139 - 1166. 30 K. L. DeVries, B. A. Lloyd and M. L. Williams, Reaction rate model for fracture in polymeric fibers, J. Appl. Phys., 42 (1971) 4644 - 4651. 31 A. Bueche, The ultimate properties of simple elastomers, J. Polym. Sci., 19 (1956) 275 - 284. 32 S. N. Zhurkov and E. E. Tomashevsky, An investigation of fracture processes of polymers by the electron spin resonance method. In A. C. Strickland (ed.), Physical Basis of Yield and Fracture Conf. Proc., Institute of Physics and the Physical Society, Oxford, 1966, pp. 200 - 208.

339 33 I. Redler and V. C. Mow, Biomechanical theories of ultrastructural alteration of articular surfaces of femoral heads. In. W. H. Harris (ed.), Proc. Second Open Scientific Meeting of the Hip Society, C. W. Mosby, St. Louis, MO., 1974, pp. 23 - 59 (cf. pp. 50 - 51). 34 S. K. Rhee, Wear equation for polymers sliding against metal surfaces, Wear, 16 (1970) 431 - 455. 35 A. Maroudas, H. Muir and J. Wingham, The correlation of fixed negative charge with the glycosaminoglycan content of human articular cartilage, Biochim. Biophys. Acta, .177 (1969) 492 - 500. 36 B. 0. Weightman, M. A. R. Freeman and S. A. V. Swanson, Fatigue of articular cartilage, Nature (London), 244 (1973) 303 - 304. 37 F. R. Eirich and T. L. Smith, Molecular mechanical aspects of the isothermal rupture of elastomers. In H. Liebowitz (ed.), Fracture: An Advanced Treatise, Vol. VII, Academic Press, New York, 1972, pp. 351 - 609 (cf. pp. 433 ff.). 38 A. Peterlin, Bond rupture in highly oriented crystalline polymers, J. Polym. Sci., Part A-2,7 (1969) 1151.- 1163. 39 A. Peterlin, Chain scission and plastic deformation in the strained crystalline polymer, J. Polym. Sci., Part C, 32 (1971) 297 - 317. 40 H. J. Corten, Micromechanics and fracture behavior of composites. In L. J. Broutman and R. H. Krock (eds.), Modern Composite Materials, Addison-Wesley, Reading, Mass., 1967, pp. 27 - 105 (cf. pp. 93 - 97).