201

A simulator study of friction in total replacement hip joints V Saikko, MSc Laboratory of Machine Design, Helsinki University of Technology, Espoo, Finland Frictional behaviour of 22 diflerent femoral head-acetabular cup combinations was studied on a new servo-hydraulic microcomputercontrolled hip joint simulator using various jlexion-extension angle and superior-inferior load set value waveforms and using distilled wuter at 37 f 1°C as lubricant. Six different head materials were included in the study, whereas all cups were ultra-high molecular weight polyethylene ( U H M WPE).Most head-cup combinations studied are commercially available. N o distinctly superior joint design can be pointed out, but the frictional behaviour of alumina ceramic against U H M W P E proved overall most,favourable (pminwas 0.02), whereas that of non-ion-implanted titanium alloy T i 4 A l H V against UIJM W P E proved strikingly poor (p, was 0.15). The lowest frictional torque was in 22 mm joints, but frictional torque did not always increase straightforwardly with increasing diameter of the ,femoral head. The measurements form an extensive comparison between a wide variety of head-cup combinations. The simulator is apparently a useful instrument in the study of frictional behaviour of new designs, materials, surface treatments and coatings that are frequently introduced.

NOTATION

diameter of the flatter area at the apex of acetabular cups with toroidal shape (m) error of the torque signal due to the weight of the cradle (N m) error of the torque signal due to the moment of inertia of the cradle (N m) error of the torque signal due to the torsional vibration of the cradle (N m) error of the torque signal due to the frictional torque of the support bearings of the cradle (N m) error of the torque signal due to the lateral misalignment of the femoral head (N m) error of the torque signal due to the vertical misalignment of the femoral head (N m) load applied to the hip joint (N) contact pressure between articulating surfaces (Pa) radius of the bearing balls used in the measurement of rc (m) internal radius of the acetabular cup (m) radius of the femoral head (m) parameter of surface roughness; the arithmetic mean of the departures of the profile from the mean line (pm) frictional torque of the hip joint (N m) sliding velocity = rHda/dt (m/s) height diil'erence in the three-ball method for measurement of rc (m) flexion-extension angle of the cradle (rad) viscosity of the lubricant (Pa s) coefficient of friction of the hip joint 1 INTRODUCTION

One of the complications in total replacement of the hip joint that still remains unresolved is late loosening. The tribological behaviour of the femoral head-acetabular cup articulation may be a major factor determining the overall performance of the prosthesis, because it is likely that the replacement of bone at the bone-implant interThe M S was received on 22 May I992 and was accepted for publication on 16 November 19Y2.

H02492 @ IMechE 1992

face with soft tissue is a biological response to the wear and corrosion products of the implant. Unsworth et al. (1) reported that the coefficient of friction ( p ) in total replacement hip joints is distinctly higher than in normal joints. High frictional torque ( T )may accelerate the loosening of the acetabular component, as it probably induces shear stresses at the bone-implant interface high enough to lead eventually to fatigue failure of the fixation, as discussed by Simon et al. (2). Davidson et al. (3)suggested that elevated temperatures from frictional heat can increase wear, creep and degradation rates of ultra-high molecular weight polyethylene (UHMWPE). Unsworth et al. (1) and Walker and Gold (4) studied lubrication mechanisms occurring in normal and artificial joints, and Weightman et al. (5) in artificial joints. It seems that momentary full fluid film lubrication in total hip joints is possible, but usually boundary or mixed lubrication prevails. Unsworth et al. (6)studied the very low friction in total hips incorporating a compliant layer on a stainless steel cup, on the Durham hip function simulator. It is obvious that wear cannot be completely prevented unless a fluid film separates the articulating surfaces during loaded articulation. Davidson et al. (3) concentrated on frictional heat, which indeed is a topic previously overlooked. In the present study the emphasis is on the comparison of frictional behaviour of a wide variety of femoral headUHMWPE acetabular cup combinations. The measurements were made on a new hip joint simulator at Helsinki University of Technology. The motion and load waveforms can be modified easily and independently, as they are implemented servo-hydraulically. The quest for joint implants with lower friction and wear is definitely justified and it necessitates experimental studies with joint simulators. It is hoped that the present study for its part will promote understanding of friction in total replacement hip joints. 2 MATERIALS

The femoral heads, acetabular cups and acetabular shells used in the tests are presented in Tables 1, 2 and 3 respectively. The information was obtained from the

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V SAIKKO

Table 1 Femoral heads

Specimen

Description on package

Manufacturer1 vendor

Catalogue number

HI H2 H3 H4 H5 H6 H7 H8 H9 H10 HI1

Elite modular head Charnley ceramic head Femoral head component Ceramic head SP 11-Prothesenkopf SP 11-Prothesenkopf Modular head component Modular head component Modular head component Modular head component Muller modular head

Thackray Thackray Howmedica Howmedica Waldemar Link Waldemar Link Biomet Biomet Biomet Biomet Protek

62-5671 62-6392 6284-0-132 6290-1-032 128-705 128-709 163662 163669 163185 131407 35.32.01

H12 H13 HI4 Hi5 H16 H17 H18 H19 H20 H21 H22

Muller modular head Femoral head Femoral head Femoral head component Femoral head component Femoral head component Ball

Protek Zimmer Zimmer Kirschner Kirschner Kirschner Kirschner

12.32.06 9026-029 9026-033 5406-00-000 5408-0@000 5403-00-000 1010-13

Wagner resurface Wagner resurface

Aesculap Aesculap

NA 396 NA 400

packages, manufacturers and vendors. All heads and cups were new. They had been manufactured for implantation, except the experimental H19 and H20, and were received in their original packages. The heads and the load-bearing surface of the cups were not modified in any way prior to the tests. UHMWPE was the only cup material studied. It has proved its superiority indisputably in clinical practice and therefore it will not be easily replaced. Designs with hard materials articulating against themselves (for example alumina on alumina), being tribologically unsound, were excluded. One of each head-cup combination was studied.

Material

Nominal diameter mm

Material standard

Stainless steel ORTRON 90 Alumina Co-Cr-Mo Vitallium Alumina Co-Cr-Mo Alumina BIOLOX Co-Cr-Mo Co-Cr-Mo Ti-6A1-4V ion implanted Alumina Stainless steel 316L PROTEMA-42 Alumina BIOLOX Co-Cr-Mo ZIMALOY C1 Co- Cr-Mo ZIMALOY C1 Ti-6A1-4V ELI Ti-6A1-4V ELI Ti-6A1-4V ELI Alumina Silicon nitride Zirconia Co-Cr-Mo CeCr-Mo

IS0 IS0 IS0 IS0 IS0 IS0 IS0 IS0 IS0 IS0 IS0

5832/9, BS 725219 6474, BS 725312 5832/4, ASTM F 75 6474 5832/4 6474, DIN 58 835 5832/4, ASTM F 799 583214, ASTM F 799 5832/3, ASTM F 136 6474 5832/1, ASTM F 138

I S 0 6474, ASTM F 603 I S 0 583214, ASTM F 75 I S 0 5832/4, ASTM F 75 ASTM F 136 ASTM F 136 ASTM F 136 ASTM F 603 I S 0 5832/4 I S 0 583214

22.25 22.25 32 32 32 32 28 32 32 32 32 32 28 32 26 28 32 32 32 32 42 46

3 APPARATUS AND EXPERIMENTAL PROCEDURE

In the study of friction of total hip joints, a machine that simulates the conditions of the hip joint in regard to motion, load, lubrication and temperature is a prerequisite. Such machines are commonly referred to as hip joint simulators (7). Although descriptions of hip joint simulators used in frictional torque studies (3, 5, 6, 8-16) are usually rather general, it is obvious that new information about the tribology of total hip joints could be obtained with an apparatus, the motion and load of which could be independently and easily modified so

Table 2 Acetabular cups

Specimen

Description on package

Manufacturer/ vendor

Catalogue number

UHMWPE material standard

C8

C9 c10 c11 c12 C13

Charnley PCA acetabular insert Lubinus Modular acetabular liner Modular acetabular liner Full profile cup Liner Liner Polyethylene liner Polyethylene liner Polyethylene liner Wagner resurface Wagner resurface

T hackray Howmedica Waldemar Link Biomet Biomet Protek Zimmer Zimmer Kirschner Kirschner Kirschner Aesculap Aesculap

62-3717 6285-@525 102-110 104346 104352 62.32.50 6728-87 6732-87 2426-56-104 2428-56-104 2432-56-105 NA 397 NA 401

Nominal 0.d.

mm

mm

Shell number if or

metal-backed (Table 3)

-~~

~~

c1 c2 c3 c4 c5 C6 c7

Nominal i.d.

I S 0 5834/1+2, BS 7253/4+ 5 I S 0 5834/2, BS 725314 I S 0 5834/2, DIN 58 834 I S 0 5834/1, ASTM F 648 I S 0 5834/1, ASTM F 648 I S 0 5834/1+2, ASTM F 648 I S 0 5834/2, ASTM F 648 I S 0 5834/2, ASTM F 648 ASTM F 648 ASTM F 648 ASTM F 648

22.25 32 32.5 28 32 32 28 32 26 28 32 42 46

43 51

52

52 53

50 54 54 55 55 55

50 54

Table 3 Acetabular shells Description on Specimen

package

s1

PCA Mallory/Head Mallory/Head H G P 11 KM-4

s2 S3 s4 s5

Manufacturer/ vendor Howmedica Biomet Biomet Zimmer Kirschner

Catalogue

Nominal 0.d.

number

Material

mm

6289-5-052 11-104252 11-104256 6610-56-01 2400-56-105

Co-Cr-Mo Vitallium Ti-6A1-4V Ti-6AI-4V Titanium Ti-6A1-4V ELI

52 52 56 56 56

Part H : Journal of Engineering in Medicine

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A SIMULATOR STUDY OF FRICTION IN TOTAL REPLACEMENT HIP JOINTS

that various published angle and load waveforms could be readily realized. A single-station servo-hydraulic microcomputer-controlled hip joint simulator was designed and constructed. The layout of the apparatus is depicted in Fig. 1 and Fig. 2 is a general view of the apparatus. The motion of the apparatus is uniaxial and simulates the flexion-extension of the hip joint. In level walking, which is the most important activity to simulate, the abduction-adduction and the internakxternal rotation are distinctly smaller than the flexionextension. Only flexion-extension is simulated to avoid excessive complexity of the apparatus. Consequently, the measured frictional torque about the axis of flexionextension is probably slightly higher than in the case of all three motions being included. The range of motion is about + ~ / 6rad, depending on the depth of the cup. The angle between the horizontal plane and the plane of the rim of the cup is 4 4 . The femoral head (1) (see Fig. 1) is attached to a pole (2) by taper-fit or press-fit, or with polymethylmethacrylate. The pole is firmly locked to a cradle (4). The eccentric part of the cradle allows space for the hip joint. It is located between the two low-friction ( p about 0,001) support bearings (6). The head is carefully aligned with the axis of swinging. The position of the head can be adjusted in two directions which are perpendicular to each other and to the axis of swinging. The alignment is checked with displacement indicators as the cradle is swung manually f x / 6 rad.

203

The adjustment is continued until the motion of the head in the vertical and lateral directions is 0.02 mm at most. The motion is implemented servo-hydraulically. The actuator is an axial piston hydraulic motor (8) on which a servo-valve (9) and a feedback transducer (10) are mounted. The simulator is a real-time microcomputer system. The angle waveforms are stored on the hard disc of the personal computer (PC) as lists of discrete set value voltages. The PC supplies the set value, updated at 1/64 s intervals, via an input/output (I/O) board to a servo-control module. The current that the servo-control module supplies to the servo-valve is proportional to the difference between the set value and the feedback transducer real value, resulting in a close reproduction of the set value waveform by the cradle. Perhaps the principal advantage that the servohydraulic system offers is that various waveforms found in the biomechanical literature can be realized with extraordinary ease. The tasks of the PC software also include the load set value supply, and the angle, load, frictional torque and temperature data acquisition, and frictional torque data processing. The load is also uniaxial and simulates the superiorinferior component of the hip joint contact force. The reasons for omitting the anterior-posterior and the medial-lateral force components are similar to the reasons for omitting the abduction-adduction and the internal-external rotations. Maximum load of the simulator is about 5 kN. The loading arrangement consists

Axis of loading

L

0.1 m

7 1 Femoral head 2 Attachment pole of the femoral head 3a, 3h Fastening nut of the attdchment pole 4 Cradle 5 Adjustment \crew 6 Support bedring 7 Gear coupling 8 Hydraulic motor 9 Servo-valve 10 Anglc transducer 1 I Acetabular cup 12 Acetabular cup holder 13 Bone cement

14 Support plate ISa, b Beam ofthe loading frame 16 Connecting rod of the loading frame 17 Guide of the connecting rod 18 Hydraulic cylinder 19 Force transducer 20a, b Knuckle joint 2 1 Joint capsule 22 Lubricant inlet connection 23 Lubricant outlet connection 24 Strain gauge rosette 25 Cover of the torque transducer

Fig. 1 General layout of servo-hydraulic hip joint simulator from anteriorposterior (left) and from medial-lateral view (right) 0 IMechE 1992

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used in the present study was distilled, deionized water at 37 f 1"C, the viscosity of which was c. l o p 3 Pa s. The end of the cradle which is located outside the support bearings and is coupled to the hydraulic motor forms a torque transducer. It is a cylindrical neck in the cradle on which a full bridge strain gauge rosette (24) is cemented. The Wheatstone bridge coupling of the rosette is done so that the transducer is sensitive to torsion only. The shear strain on the neck is 1.9 x at 10 N m torque. The signal of the torque transducer is the sum of several parts. One of them is the frictional torque of the hip joint, T . All others are considered errors and the signal is carefully purged of them. The noteworthy error torques, attributable to the structure of the apparatus, can be divided into five categories, according to their origins E l : weight of the cradle. E , is equal to the product of

Fig. 2 General view of hip joint simulator

of an upper and a lower horizontal beam (15a and 15b), two vertical rods (16), a hydraulic cylinder (18), force feedback transducer (19) and two three-degree-offreedom knuckle joints (20a and 20b). Regardless of the position of the cradle, the axis of loading (vertical) is perpendicular to the axis of swinging (horizontal) and it is practically stationary with respect to the acetabular cup, slight leaning being due to frictional force. The acetabular cup is self-centring on the femoral head. The cup holder (12) is machined of polymethylmethacrylate. The thickness of the acrylic wall at the point of the load axis is 5 mm. Excessive turning of the loading arrangement due to the frictional torque of the hip joint is prevented by two guides (17) that permit transverse motion of about kO.1 mm. Hence a slight lag from the reversal of the cradle to the beginning of sliding in the hip joint remains. The load control is also servo-hydraulic and it is very similar to the angle control. It is implemented using a servo-control module and a servo-valve of the same kind as the angle control. The joint is surrounded by a flexible capsule (21) filled with lubricant. The lubricant is circulated by a peristaltic pump at a rate of about 50 ml/min. The pump sucks lubricant from a container and pumps it through a filter and a duct in the cup holder into the joint capsule. Another duct in the cup holder operates as an outlet. The temperature of the lubricant is maintained at 37 f 1°C. The lubricant container also serves as a heat exchanger. It stands in the jet of a hot-air fan that is switched on and off by a relay. The lubricant

the weight of the cradle, distance between the axis of swinging and the mass centre of the cradle, and sin a. E,: torsional inertia of the cradle. E , is equal to the product of the moment of inertia of the cradle and d2a/dt2. E , : single-degree-of-freedom torsional vibration of the cradle-torque transducer system. It is excited by a drop of T , concomitant with the commencement of sliding, if the coeficicnt of kinetic friction is less than the coeficient of static friction. The cradle represents the moment of inertia and the transducer represents the torsional spring. E , : frictional torque of the support bearings, which is assumed to be 1.52 x lo-' x L N m ( L in newtons), according to the information of the manufacturer. E5*: lateral misalignment of the femoral head in the neutral position of the cradle. If there is no vertical misalignment, a simple geometrical examination shows that the greatest possible lateral misalignment is 0.02 mm, since the permissible vertical displacement of the dial indicator in the alignment procedure is kO.01 mm as the cradle is swung f n / 6 rad. E,, is equal to lateral misalignment x L x cos a. vertical misalignment of the femoral head in the neutral position of the cradle. If there is no lateral misalignment, the greatest possible vertical misalignment is 0.02 mm. E , , is equal to vertical misalignment x L x sin a.

E l , E , and E , , and also other possible errors, for example the effect of the joint capsule and the cable of the torque transducer, are eliminated by the PC software. The ramp function generator of the angle servocontrol module, which the set value signal must first pass, is also needed to eliminate E,. The slope of the ramp is adjusted so that the set value update does not cause too quick a change in the output current of the servo-module, and consequently excessive angular acceleration of the hydraulic motor. Nevertheless, the elimination is not complete and some oscillation remains in the torque signal attributable to the set value update. E , proved insignificant. E5A is eliminated as the measurements are made in both directions. In order to minimize E,,, all angle waveforms are positioned symmetrically with respect to

Part H . Journal of Engineering in Medicine

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A SIMULATOR STUDY OF FRICTION IN TOTAL REPLACEMENT HIP JOINTS

+

0.027 c

0.007

1

N 0

8 1 S

0.020 S AXISof \winging F Centre of femoral head

Fig. 3 Illustration of greatest permissible lateral and vertical misalignment of femoral head. (Units in millimetres)

the neutral position, for example, fx/9, *x/S and fx/6 rad. The lateral and vertical misalignments usually coexist. The worst possible situation is such that the lateral and vertical misalignments are both 0.02 mm. A simple geometrical examination shows that the displacements of the dial indicators in that case are 0.02 mm in the vertical and lateral directions as the cradle is swung f x / 6 rad (Fig. 3). The moment arm (the horizontal projection of the misalignment SF) that causes the error torque then varies between 0.007 and 0.027 mm. The operation of the simulator control, data acquisition and data processing PC software can be divided into three modes: Mode J : p with constant angular velocity and constant load. The absolute values of da/dt are 0.6, 1.2, 1.8, 2.4 and 3.0 rad/s and the loads are 1, 2, 3, 4 and 5 kN, resulting in 25 different combinations. The range of motion is f z / 9 rad and so the cycle lengths are 2.327, 1.164, 0.776, 0.582 and 0.465 seconds respectively. p is calculated from the simple equation p = T/(LrH).The equation is naturally true for point contact only, but it was used because the contact pressure distribution is unknown. The torque measurement is made in the neutral position of the cradle (a= 0), at which time E , , E , and E,, are negligible. A mode I measurement consists of ten consecutive cycles. The mean of the 20 calculated values is taken to represent p . E , , is eliminated when the mean is calculated, because the torque is measured in both directions in turn. A few minutes is allowed for the hip joint to cool down before the next measurement. Thc highest velocity and load were not used in the tests and so the parameter rpr,/L varied between 0.15 x x r i a n d 2.4 x x r$. Mode 11: T waveform in the simulation. Various angle and load waveforms are converted into lists of 64 discrete set values, which are stored on the hard disc of the PC. An inverse waveform is also created from each angle waveform, that is it is inverted about the time axis, for the elimination of E,A. The length of a

205

cycle can be adjusted from 0.6 to 1.3 seconds. The torque, angle and load data acquisition is performed at the set value update frequency. A mode TI measurement also consists of ten cycles. Each point in the resulting T waveform is a mean of ten measurements. El and E , are eliminated as the measurement is made first without load and then the same angle waveform is run together with a load waveform. Finally, the former torque waveform is subtracted from the latter. A few minutes is allowed for the hip joint to cool down and then the same measurements are made using an inverse angle waveform. The resulting torque waveform is then inverted. The mean of this inverted waveform and the one measured using the original angle waveform is the outcome, purged of E,,. Three different combinations of set value waveforms were used, They are shown in Figs. 4a, b and c together with the resulting T waveform of joint H3-C2. The angle and load feedback values are not shown but the waveforms are practically identical to the set value waveforms with a lag of 15-25 ms. The flexion-extension of waveform combination 1 (Fig. 4a) is taken from Johnston and Smidt (17) and the load from Crowninshield et al. (18). The sinusoidal waveform combinations 2 (Fig. 4b) and 3 (Fig. 4c) were used to study the effect of maximum load coinciding with maximum angular velocity 2.2 rad/s versus with zero angular velocity. Mode 111: continuous simulation with 1-10 torque measurements per cycle. The length of a cycle can be adjusted from 0.6 to 1.3 seconds. This mode may be used for wear tests, for which, however, a singlestation servo-hydraulic apparatus is not suitable. Mode I11 is useful in the study of the effect of frictional heat. Set value waveform combination 2 was used in the tests. The duration of the test was 1000 cycles and the torque was measured once a cycle during the maximum load. Since CI = 0 at that moment, El, E , and E,, were negligible. A couple of hours was allowed for the hip joint to cool down and then the test was repeated with an inverse angle waveform. In the final graph, which is the variation of T with the number of cycles, each point is a mean of two measurements, in opposite sliding directions, and so E,, is eliminated. For each combination, mode TI1 measurements were made first, then mode I1 and last mode I. Altogether, the values of ,u and T reported in this paper are estimated to be accurate within i10 per cent. The estimate is based on the above theoretical considerations, calibration of the load, angle and torque transducers, accuracy of the amplifiers, study of the signals with an oscilloscope and repetition of measurements. The magnitude of the error depends on p and on the set value waveforms, and it varies with position in the cycle. 4 RESULTS

The mode I results are presented in Table 4. The maxima of the mode I1 T waveforms are presented in Table 5 together with concomitant ,u. The mode I11 results are shown in Fig. 5. In mode 111, T usually decreased exponentially with time, apparently due to frictional heat. The drop during

0 IMechE 1992

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206

A

+

0

a set value L set value TinH3-C2

A

+

0.1 0.2 0.3 0.4 0.5-0.6

a set value L set value TinH3-C2

0.7 0.8 0.9 1.0

Time

Time

S

S

(b) Combination 2

(a) Combination 1 0 a

set value

L set value + Tin H3-C2 A

0

0.1 0.2 0.3 0.4 0 s 0.6 0.7

0.8 0.9 1.0

Time b

(c) Combination 3

Fig. 4

Flexion+xtension angle and superior-inferior load set value waveform combinations and resulting T in joint H3-C2

the first few cycles was often steep. The surface of titanium heads H15, H16 and H17 was damaged soon after the start, which resulted in a steep rise of T . Due to the exceptional behaviour, these three curves are from the first measurement only, unlike the others, which are means of two, as described above. The R, values of the damaged load-bearing areas, measured perpendicular to the direction of sliding, were 0.197, 0.133, and 0.144 pm respectively. Large areas of the articulating surface of cups C9, C10 and C11 were covered by transferred titanium (Fig. 6). Mode I1 and mode I measurements for these three joints are naturally strongly affected by this damage. All the other heads, including ion-implanted

H9, proved undamaged after the tests and there was no change in the R , value of the load-bearing area compared with the non-load-bearing area. All cups, except C9, C10 and C11, proved undamaged after the tests in visual examination (H18-Cll was studied prior to H17-C11). In mode 11, there was joint-to-joint variation in the position of the maximum T in the cycle. The coefficient of friction ,u was distinctly smaller with waveform combinations 1 and 2 than in mode I, and smaller with combination 2 than with combination 3, indicating that a lubricant of low viscosity can effectively reduce frictional resistance. In combination 1 there was usually a

Part H: Journal of Engineering in Medicine

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A SIMULATOR STUDY OF FRICTION IN TOTAL REPLACEMENT HIP JOINTS

Table 4 Coefficients of friction p obtained using measurement mode I Angular velocity Load rad/s ’ kN Head-cup

0.6, 1 0.6, 2

0.6, 3

0.6, 4

1.2, 1

1.2, 2

1.2, 3

1.2, 4

1.8, 1

1.8, 2

1.8, 3

1.8, 4

2.4, 1

2.4, 2

2.4, 3

2.4, 4

Mean

H1-C1 H2-Cl H3 x 2 H4X2 H543 H6 C3 H7-C4 H8-C5 H9 C5 H10-C5 H11LC6 H1 2 x 6 H 13-C7 H14C8 H 1 5-C9 H16-Cl0 H17-Cll H18-Cll H 19-C5 H20GC5 H21-Cl2 H22-Cl3

0.051 0.032 0.058 0.043 0.065 0.067 0.057 0.075 0.069 0.05 1 0.069 0.029 0.090 0.082 0.140 0.124 0.150 0.056 0.066 0.063 0.086 0.105

0.043 0.034 0.061 0.046 0.061 0.065 0.054 0.069 0.066 0.055 0.046 0.026 0.076 0.054 0.137 0.133 0.142 0.058 0.066 0.064 0.077 0.090

0.037 0.034 0.061 0.044 0.057 0.064 0.050 0.064 0.062 0.057 0.039 0.025 0.068 0.043 0.134 0.134 0.136 0.058 0.065 0.064 0.070 0.076

0.032 0.032 0.058 0.044 0.054 0.064 0.048 0.061 0.058 0.059 0.034 0.024 0.065 0.039 0.129 0.131 0.133 0.058 0.065 0.062 0.062 0.066

0.039 0.023 0.062 0.034 0.063 0.061 0.053 0.079 0.065 0.051 0.053 0.023 0.081 0.052 0.122 0.126 0.139 0.047 0.066 0.059 0.078 0.09 5

0.035 0.029 0.062 0.039 0.061 0.062 0.052 0.072 0.063 0.055 0.041 0.02 1 0.067 0.041 0.129 0.134 0.138 0.051 0.067 0.061 0.072 0.082

0.032 0.030 0.058 0.038 0.057 0.062 0.049 0.066 0.059 0.057 0.035 0.021 0.059 0.035 0.127 0.131 0.133 0.052 0.066 0.060 0.066 0.070

0.029 0.029 0.055 0.039 0.053 0.06 1 0.047 0.06 1 0.054 0.059 0.03 1 0.022 0.052 0.032 0.121 0.124 0.129 0.052 0.065 0.058 0.060 0.060

0.035 0.021 0.060 0.033 0.061 0.059 0.054 0.080 0.060 0.049 0.049 0.022 0.071 0.042 0.119 0.125 0.135 0.042 0.066 0.060 0.071 0.085

0.033 0.029 0.059 0.035 0.061 0.061 0.053 0.074 0.059 0.055 0.037 0.022 0.060 0.033 0.127 0.133 0.135 0.046 0.068 0.059 0.068 0.076

0.03 1 0.028 0.057 0.036 0.057 0.060 0.05 1 0.067 0.055 0.056 0.033 0.02 1 0.053 0.030 0.123 0.128 0.130 0.048 0.067 0.057 0.063 0.064

0.028 0.026 0.053 0.036 0.054 0.060 0.049 0.064 0.051 0.058 0.030 0.022 0.047 0.028 0.1 14 0.121 0.126 0.048 0.066 0.056 0.058 0.056

0.030 0.023 0.059 0.024 0.061 0.067 0.060 0.080 0.056 0.055 0.038 0.018 0.065 0.026 0.114 0.122 0.136 0.048 0.065 0.055 0.061 0.073

0.035 0.023 0.055 0.032 0.060 0.059 0.054 0.075 0.052 0.053 0.038 0.017 0.056 0.028 0.119 0.126 0.131 0.044 0.066 0.058 0.060 0.061

0.029 0.028 0.051 0.032 0.056 0.056 0.052 0.067 0.050 0.054 0.031 0.023 0.048 0.025 0.112 0.118 0.121 0.042 0.064 0.054 0.054 0.056

0.028 0.024 0.049 0.032 0.052 0.056 0.048 0.062 0.046 0.053 0.028 0.02 1 0.044 0.023 0.108 0.109 0.120 0.044 0.061 0.052 0.052 0.052

0.034 0.028 0.057 0.037 0.058 0.062 0.052 0.070 0.058 0.055 0.040 0.022 0.063 0.038 0.123 0.126 0.133 0.050 0.066 0.059 0.066 0.073

sharp T peak soon after the extension-flexion reversal, similar to that observed by O’Kelly et aE. (19) in a Charnley joint with 2 x 10 Pa s fluid. In mode I, p usually gradually increased with each measurement from number 1 to 20. Sometimes, however, p decreased. Drying of the contact area apparently increases p and frictional heat decreases it. Which one of them has the greater effect varies from joint to joint, and they may also be naturally interactive. The drying is a consequence of the constant load, which hampers lubrication. The coefficient of friction p usually decreased with increasing L and with increasing u in ~

Table 5 Maximum frictional torques obtained using mea-

metal-head joints. In the ceramic-head joints the behaviour was more obscure. Average p was lowest (0.022) in H12-C6 and highest (0.133) in damaged H17-Cll. Against a particular cup, alumina heads generated lower p than metallic, except against C3. Experimental silicon nitride (Si,N,) H19 generated distinctly higher and zirconia (ZrO,) H20 (both yttria-stabilized) slightly higher p against C5 than alumina H10, and Co-Cr H8 higher than ion-implanted Ti-6A1-4V H9. The diameter, roundness and surface roughness measurements of the femoral heads are presented in Table 6. They were done in an outside laboratory. The diameter was measured at the equator using a micrometer. The roundness was measured along the equator in accord-

surement mode 11, and concomitant l~

Table 6 Measured diameter, roundness and surface finish of femoral heads

Set value waveform combination Combination 1 (Fig. 4a)

Combination 2 (Fig. 4b)

Combination 3 (Fig. 4c)

Head-cup

T __ Nm

T Nm

T -

/I

p

Nm

p

Specimen

nun

Pm

Surface roughness R, vm

Hl-Cl H2-CI H3-C2 H4-C2 H5-C3 H6-C3 H7-C4 H8-C5 H9-C5 H10-C5 HllLC6 H12-C6 H13 C7 H14-C8 H15-C9 H16-ClO H17 C11 HI%Cll H19-C5 H20-C5 H21-Cl2 H22-Cl3

0.7 1 0.71 2.34 1.79 2.50 2.90 1.88 2.50 2.46 1.98 1.28 1.10 1.39 0.96 3.75 4.51 6.27 1.55 2.87 2.39 2.21 2.58

0.019 0.020 0.046 0.033 0.047 0.054 0.040 0.047 0.046 0.037 0.030 0.021 0.030 0.019 0.091 0.101 0.123 0.029 0.054 0.045 0.033 0.036

0.73 0.78 2.45 1.71 2.48 2.98 1.89 2.59 2.53 2.01 1.44 1.15 1.88 1.21 4.43 4.85 6.24 1.66 2.87 2.35 2.53 2.83

0.019 0.025 0.045 0.032 0.047 0.054 0.043 0.048 0.047 0.037 0.028 0.02 1 0.040 0.028 0.105 0.106 0.127 0.030 0.052 0.043 0.037 0.038

0.98 0.67 2.55 2.20 2.86 3.1 3 2.24 2.97 2.80 2.51 1.59 1.46 1.96 1.52 4.23 4.84 5.92 1.95 3.20 2.71 2.46 3.08

0.028 0.027 0.056 0.047 0.063 0.057 0.054 0.069 0.062 0.055 0.031 0.029 0.049 0.030 0.127 0.136 0.145 0.041 0.058 0.060 0.041 0.047

H1 H2 H3 H4 H5 H6 H7 H8 H9 H10 H11 HI2 H13 H14 H1S H16 H17 H18 H19 H20 H21 H22

22.19 22.2 1 31.97 32.00 32.02 31.94 27.92 31.92 31.92 31.95 31.94 31.95 27.96 31.83 25.95 27.98 31.95 31.99 32.00 3 1.95 41.96 45.92

0.25 0.54 1.67 0.52 1.Do 0.41 0.20 0.20 5.26 0.44 0.86 0.45 0.76 0.55 0.95 1.80 4.02 0.36 3.41 0.54 8.59 2.23

0.021 0.009 0.027 0.024 0.028 0.026 0.010 0.022 0.025 0.008 0.009 0.012 0.034 0.031 0.028 0.020 0.015 0.017 0.028 0.022 0.020 0.037

Diameter

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208

6’01

HI?-CII

5.5 -

4.5

h E lb

3.0

2.5

2.0

I .5

t

0

I

0

100

200

100

500 600 Number of cycles

400

I

I

I

700

800

900

loo0

Fig. 5 Variation of T with number of cycles in 22 different head-cup combinations. Measurement mode I11 and set value waveform combination 2 were used. T was measured once a cycle during maximum

load

Fig. 6 Damaged titanium-head joints, from left to right ~ 1 7 - c l 1 H16-ClO , and H15p-9, c11 is in acetabular CUP holder, to which acetabular shell s5 is cemented. Far right attachment pole of femoral head together with its fastening nuts

ance with the minimum zone centre (MZC) method using a Rank Taylor Hobson Talyrond M51 112/843-75 apparatus. The surface roughness was measured using a Rank Taylor Hobson Form Talysurf 112/1825-776 apparatus. The stylus tip radius was 2 pm, cut-off length 0.25 mm and positions of measurement the polar and equatorial areas. Fifteen parameters were obtained, but only R, is presented here. as it is the most used. The uncertainty at 95 per cent confidence level of the measurements of diameter, roundness and surface roughness are f0.01 mm, f0.2 pm and f20 per cent respectively. Total hip joint heads met the requirements of I S 0 7206-2 (20) with one exception: the diameter of H5 was 0.02 mm larger than its nominal diameter. The measurements of internal radius, surface roughness and thickness of the acetabular cups are presented in Table 7. The Form Talysurf apparatus was used in rc and Surface roughness measurements (uncertainty k0.05 mm and 15 per cent respectively), done by the same outside laboratory; rC was measured in one plane,

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A SIMULATOR STUDY OF FRICTION IN TOTAL REPLACEMENT HIP JOINTS

Table 7 Measured internal radius, surface finish and thickness of acetabular cups Radius (Farm Talysurf) Specimen

nun

Radius (three-ball) mm

c1 c2 c3 c4 c5 C6 c7 C8 c9 c10 c11 c12 C13

11.199 16.165 16.633 13.610 15.290 15.857 14.032 15.980 12.988 13.887 15.897 21.126 23.041

11.23 16.31 16.34 13.84 15.82 16.11 14.09 16.03 13.02 13.97 16.06 21.28 23.07

Surface roughness R, -

wn

0.897 1.285 1.743 1.216 3.671 0.715 0.569 0.317 2.115 1.012 0.846 0.360 0.279

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Table 8 Relative clearances of joints at 20°C Relative clearance

Thickness mm 10.7 5.6 11.0 9.4 9.5 7.2 8.1 6.3 11.2 10.2

8.2 3.8 3.6

in the medial-lateral direction, across the load-bearing area. The stylus tip radius was 0.397 mm and traverse length 10 mm. The direction of measurement of surface roughness was perpendicular to machining grooves, if any were perceived. The stylus tip radius was 2 pm, cut-off length 0.8 mm and position of measurement away from the load-bearing area. C5 clearly exceeded the R , requirement of I S 0 7206-2 (maximum 2 pm). Radius rc was also measured in-house using a rigidly attached digital displacement indicator with a disc-like head and three bearing balls (Fig. 7) to obtain a threedimensional estimate. The ratio rs/rc was c. 1/4. The cup was held stationary and one ball was first put into the cup, the disc was lowered on to it (dashed lines) and the indicator was reset. Two more balls were then put into the cup so that the three balls formed a triangle and the height difference z was recorded. Assuming that

Head-cup

per cent

Hi-Cl H2-Cl H3-C2 H4-C2 H5-C3 H6-C3 H7-C4 H8-C5 H9-C5 H10-C5 H11-C6 H 12-C6 H13-C7 H1448 H1 5 x 9 H16-CIO H17-Cll H18-Cll H 19-C5 H20-C5 H21-Cl2 H22ZC13

1.20 1.11 1.99 1.90 2.02 2.26 -0.87 -0.88 -0.88 -0.98 0.87 0.84 0.78 0.72 0.35 -0.14 0.53 0.40 - 1.14 -0.98 1.41 0.48

the concave surface is spherical, a geometrical examination shows that r, = rB + 212 + 2rg/3z. The contact angle is c. 23". These rc values (accuracy c. k0.05 mm) were used in the calculation of relative clearances (rC - rH)/rC of the head-cup combinations (Table 8). The geometry of C4, C5 and C6 proved somewhat toroidal, which is exaggeratedly illustrated in Fig. 7. Only in H16-Cl0 was there a real, albeit slight, pressfit. However, due to the non-spherical geometry of some cups and the low creep resistance of UHMWPE, the very concept of clearance is not readily applicable. The thickness was measured in-house so that the spherical tip of a rigidly attached digital displacement indicator was first put in contact with the bearing surface a t the point of the load axis, the armature being parallel with the load axis and then with the base of the cup, after the removal of the cup from below the indicator. Accuracy was c. kO.1 mm. The surface roughness and the form of the heads and cups were measured after the simulator tests. 5 DISCUSSION

Fig. 7 Three-ball method for measurement of internal radius of acetabular cups

Davidson and Lynch (21) observed that in a swivelmotion simulator T decreased with increasing temperature above 29°C in a 32 mm Co-Cr on UHMWPE joint. Elevated temperature is otherwise likely to be detrimental, as discussed by Davidson et al. (3). They observed that, against UHMWPE, alumina generated significantly less heat than Co-Cr. In the present study only the mean temperature of the reservoir of the water circulation system was measured (and maintained at 37 & l°C) but no explicit difference in the decrease of T with time could be seen between head materials. Davidson and Lynch also observed that synovial fluid aspirated from two patients with reconstructed hip joints had little effect on T compared with water. In swivel-motion tests by Davidson (22), alumina and zirconia generated significantly lower friction than Co-Cr, Ti-6A1-4V and 316L stainless steel. Alumina generated lower friction

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V SAIKKO

than zirconia, as in the present study. In Davidson’s simulator the axes of motion and load coincided and the loaded area was at the apex of the cup, while in the simulator used in the present study the axes are perpendicular to each other and the direction of loading is n/4 rad from the apex. Measured T is likely to be lower in swivel motion due to a lower effective moment arm. This may explain why T values reported by Davidson et al. (3) are lower than those of the present study. The alumina heads were superior to metallic in the present study, too, excepting H5-C3 and H6-C3. The superiority of alumina has been related to its better wettability, which may be an important feature, especially in boundary lubrication between asperity contacts. Since the decrease of p with increasing L in mode 1 was not observed in all joints, it is hardly attributable to the decrease of the effective moment arm of the shear stress distribution between the articulating surfaces, as the extent of contact increases with L. The decrease of p with increasing L suggests fluid film lubrication, but the measured p values are too high for that. They are rather typical of mixed lubrication, which is further suggested by the decrease of p with increasing u. The decrease of p with increasing L is typical of the dry friction behaviour of polymers, but the values of p are too low for dry contact. The drop in T at the beginning of mode I11 measurements suggests that the L dependence is rather due to the increase of temperature, which apparently decreases shear stresses at asperity contacts. Similar L dependence was observed by Unsworth (23) in pendulum tests. Weightman et al. (5) explained their similar results in terms of a constant force that is required to shear the lubricant layer. The theoretical study by Fricker (24), assuming constant p and predicting increasing ratio T/(pLrH)from 1 to 1.27 as the angular extent of contact increases from 0 to n/2 rad, seems too simplified, since p is apparently highly variable. From Table 8, it is interesting to compare H7-C4 with H8-C5, H21-Cl2 with H22-Cl3, and H13-C7 with H14-CS. The thickness of C4 and C5 is about the same and so is the thickness of C12 and C13, whereas the outside diameter of C7 is the same as that of C8. Surprisingly, T decreased with increasing rII when the outside diameter of the cup was constant, whereas it increased with increasing rH when the thickness of the cup was constant. It is possible that in H13-C7 the creep deformation of UHMWPE becomes important and the resulting large extent of contact effectively hampers lubrication. The resurface prostheses were included in the study because it was thought that their clinical failure could have been partly due to high T. However, their T proved no higher than that of common 32 mm total hip joints, for example of H5-C3 and H6-C3. This may be attributable to the exceptionally smooth surfaces of C12 and C13, compared with which C3 was much rougher. The result is inconsistent with the study by Ma et al. (16), in which, however, only low constant loads up to 890 N were used. So the common belief that small rH always means low T , and vice versa, is not consolidated by the present study. As rH increases, u increases and p,,, decreases, and so T does not necessarily increase, if the decreasing effect of increasing u on p outweighs the opposite effect of decreasing p,,,. T was still lowest in H 1 4 1 and H2-C1, not only

because of the small rH but also due to very low p ; only in H12-C6 was p lower. Higher T in cups with pronounced machining grooves seems logical since a greater proportion of the load is apparently carried by asperity contacts, at which the boundary lubrication mechanism, at best, prevails. Hydrodynamic pressure is not likely to be generated in the grooves if their geometry enables the lubricant to be vented to the atmosphere from the contact area. If hydrodynamic lubrication is to be promoted by slots, they should naturally be designed so that they are not vented to the atmosphere. Circumferential machining grooves were pronounced in C2, C3, C4 and C5, and none of them had notably low T . High T in H5-C3 and H6-C3 may partly be duc to high relative clearance, which further hampers hydrodynamic lubrication. According to a personal communication by a representative of the manufacturer of C3, the machining grooves are to improve lubrication, but apparently they are not beneficial. In a test arrangement described by Davidson et al. (3), lubricant is not so easily vented if the grooves are circumferential, and subsequently measured T may be lower. The grooves at the contact area are likely to be smoothed sooner or later in oizio though, which surely affects frictional behaviour. The deviations from roundness and R , values of the femoral heads (Table 4) were all so low that they hardly explain differences in frictional behaviour. The performance of all three non-ion-implanted Ti6A1-4V heads H15, H16 and H17 was strikingly poor. The poor performance of the material has been observed also by Galante and Rostoker (25) in disc-onplate tests and Sioshansi et al. (26) in pin-on-disc tests. The performance of nitrogen ion-implanted Ti-6A1-4V head H9 was quite satisfactory. The improvement achieved by ion implantation has been related to increased surface hardness. 6 CONCLUSIONS

1. The lowest frictional torques were in 22 mm joints; p was also very low in them. The name ‘low-friction arthroplasty’ indeed seems justified. 2. A large femoral head diameter does not always mean high frictional torque. The head material, surface finishes, deviations from sphericity, relative clearance, thickness of the cup and stiffness of its backing are obviously very important parameters, to all of which the frictional behaviour may be highly sensitive, and they may outweigh the head diameter. 3. No distinctly superior head-cup combination can be pointed out from the 22 tested, but the combination of alumina head-UHMWPE cup seems to have overall the most favourable frictional properties. 4. The performance of non-ion-implanted Ti-6A1-4V was extremely poor. Its wear resistance proved inadequatc, even for relatively short frictional tests. 5. The simulator is apparently a useful instrument in the study of frictional behaviour of new designs, materials, surface treatments and coatings that are frequently introduced. ACKNOWLEDGEMENTS

The author thanks the Academy of Finland, the Emil Aaltonen Foundation and the Foundation of Tech-

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A SIMULATOR STUDY OF FRICTION IN TOTAL REPLACEMENT HIP JOINTS

nology for financial support; Mr I. Pajamaki and his associates in the workshop of the Machine Laboratory Building, Helsinki University of Technology, for the machining of the numerous components of the simulator; engineering student K. Hiekkanen for developing the software; the Orthopaedic Hospital of the Invalid Foundation (Helsinki), Kirschner International, Chas. F. Thackray Limited-DePuy International Limited, Howmedica-a Division of Pfizer Oy Finland, Waldemar Link GmbH and Company, Biomet Limited and Protek A G for the donation of the specimens; and Dr P. Paavolainen for reviewing the manuscript. REFERENCES 1 Unsworth, A., Dowson, D. and Wright, V. The frictional behaviour of human synovial joints-Part I : natural joints, and Part 11: artificial joints. J . Luhric. Technol., 1975,97(3), 369-382. 2 Simon, S. R., Paul, I. L., Rose, R. M. and Radin, E. L. ‘Stictionfriction’ of total hip prostheses and its relationship to loosening. J. Bone Jt Surg., 1975,57A(2), 226-230. 3 Davidson, J. A., Schwartz, G., Lynch, G . and Gir, S. Wear, creep and frictional heating of femoral implant articulating surfaces and the effect on long-term performanccPart 11, friction, heating, and torque. J . Biomed. Mater. Rex Appl. Biomater., 1988, 22(A1), 69-91. 4 Walker, P. S. and Gold, B. L. Comparison of the bearing performance of normal and artificial human joints. J . Luhric. Technol., 1973,95(3), 333-341. 5 Weightman, B., Simon, S., Paul, I., Rose, R. and Radin, E. Lubrication mechanism of hip joint replacement prostheses. J . Lubric. Technol., 1972,94(2), 131-135. 6 Unsworth, A., Pearcy, M. J., White, E. F. T. and White, G. Frictional properties of artificial hip joints. Engng in Medicine, 1988, 17(3), 101-104. 7 1SO TR 9325 Implants for surgery-partial and total hip joint prostheses-recommendations ,fiw simulators .for evaluation uf hip joint prostheses, 1989 (International Standardization Organization). 8 Swanson, S. A. V., Freeman, M. A. R. and Heath, J. C. Laboratory tests on total joint replacement prostheses. J . Bone Jt Surg., 1973, 55B(4), 759-773. 9 Walker, P. S. and Salvati, E. The measurement and effects of friction and wear in artificial hip joints. Journal of Biomedical Materials Research, Biomedical Materials Symposium No. 4 on Materials and design considerations for the attachment of prostheses to the musculo-skeletal system, Clemson, South Carolina, 1972, pp. 327-342 (John Wiley, New York). 10 Beutler, H., Lehmann, M. and Stahli, G. Wear behaviour of medical engineering materials. Wear, 1975,33(2), 337-350.

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11 Swikert, M. A. and Johnson, R. L. Simulated studies of wear and friction in total hip prosthesis components with various ball sizes and surface finishes. N A S A TN D-8174, 1976 (National Aeronautics and Space Administration, Washington, D.C.). 12 Ungethiim, M. Requirements of operational tests and test results in total hip and knee arthroplasty. International Symposium on Advances in artijicial hip and knee joint technology, Erlangen, 1975, pp. 493-518 (Springer-Verlag, Berlin and Heidelberg). 13 O’Kelly, J., Unsworth, A, Dowson, D., Jobbins, B. and Wright, V. Pendulum and simulator for studies of friction in hip joints. In Evaluation of artiJcial joints, 1977, pp. 19-29 (The Biological Engineering Society, London). 14 Cappozzo, A., Chi, L., Pizzoferrato, A., Trentani, C. and Cortesi, S. S. Evaluation of hip arthroprostheses by means of body environment simulators. J. Biomed. Mater. Rex, 1977, 11(5), 657669. 15 Dumbleton, J. H. Tribology of natural and artificial joints, 1981, pp. 263-267 (Elsevier Scientific Publishing Company, Amsterdam). 16 Ma, S. M., Kabo, J. M. and Amstutz, H. C. Frictional torque in surface and conventional hip replacement. J . Bone J t Surg., 1983, 65A(3), 366-370. 17 Johnston, R. C. and Smidt, G. L. Measurement of hip-joint motion during walking. J . Hone Jt Surg., 1969,51A(6), 1083-1094. 18 Crowninshield, R. D., Johnston, R. C., Andrews, J. G. and Brand, R. A. A biomechanical investigation of the human hip. J . Biomechanics, 1978, 11(2), 75-85. 19 O’Kelly, J., Unsworth, A., Dowson, D. and Wright, V. An experimental study of friction and lubrication in hip prostheses. Engng in Medicine, 1979,8(3), 153-159. 20 I S 0 7206-2 Implants for surgery-partial and total hip joint prostheses-Part 2 : hearing surfaces made of metallic and plastic materials, 1987 (International Standardization Organization). 21 Davidson, J. A. and Lynch, G. E. The effect of human synovial lubricant and temperature on in-vitro friction and torque of the prosthetic hip. Proceedings of Twelfth Annual Meeting, American Society of Biomechanics, University of Illinois at Urbana, 28-30 September 1988. 22 Davidson, J. A. The effect of femoral head size and hardness on the frictional moment during articulation. Proceedings of ASME Winter Meeting Symposium on The mechanics of joints, San Francisco, 10-15 December 1989. 23 Unsworth, A. The effects of lubrication in hip joint prostheses. Phys. Med. Biol., 1978,23(2), 253-268. 24 Fricker, D. C. Friction when femoral prosthesis heads slide in acetabular cups. In Ceramics in substitutive and reconstructive surgery (Ed. P. Vincenzini), 1991, pp. 207-215 (Elsevier Science Publishers, Amsterdam). 25 Galante, J. 0. and Rostoker, W. Wear in total hip prostheses. Acta Orthopaedica Scandinavica, 1973, Suppl. 145. 26 Sioshansi, P., Oliver, R. W. and Matthews, F. D. Wear improvement of surgical titanium alloys by ion implantation. J . Vacuum Sci. Technol., 1985, A3(6), 2670-2674.

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