Friction properties of the interface between porous-surfaced metals and tibia1 cancellous bone D. Rancourt,, A. Shirazi-Adl,*,+and G . Drouin: *Department of Mechanical Engineering and %Institute of Biomedical Engineering, Ecole Polytechnique, Montriaal, Que’bec, Canada H3C 3A7
G. Paiement Sacrk-Coeur Hospital, Montrial, Qw%ec, Canada Friction tests between cancellous bone cubes and porous-surfaced metal plates were conducted in order to determine the mechanical properties of the interface in a knee porous-surfaced metal implant. Bone specimens were obtained from fresh frozen amputated tibiae and three metal plates were chosen: titanium bead porous-surfaced, titanium fiber mesh porous-surfaced, and smooth stainless steel. Results show that the friction curve is highly nonlinear. Friction coefficients measured vary between 0.3 and 1.3. The friction coefficient of the interface is in-
dependent of the excision site of the bone cubes and of the magnitude of the rate of relative displacement at the interface. The friction coefficient appears to vary slightly with the normal contact pressure for all the metal surfaces. Both porous surfaces have statistically a higher friction coefficient than the smooth surface. This is likely due to the presence of surface asperities whereby the metal ploughs the bone surface. However, no significant difference is observed between bead and fiber mesh types.
INTRODUCTION
Adequate fixation of an implant to the host bone is essential for the satisfactory long-term performance of a knee arthroplasty. When noncemented implants are used, biological fixation by bone ingrowth is the primary mechanism of implant attachment and provides a means to transfer the stress at the bone-prosthesis interface. Bone ingrowth into the surface pores of an implant has been reported to depend, among other factors, on relative movements at the bone-metal interface,’-4 on the pore on the intimacy of bone-implant apposition,”*and on weight bearing.’ These factors imply that success of noncemented implants is related to the capability of the boneimplant interface to sustain shear as well as normal stresses present after the arthroplasty. Evaluation of the interface shear resistance under various stress conditions is possible through the determination of its mechanical characterNo benefit of any kind will be received either directly or indirectly by the authors. ‘To whom correspondence should be addressed. Journal of Biomedical Materials Research, Vol. 24,1503-1519 (1990) 0 1990 John Wiley & Sons, Inc. CCC 0021-9304/90/111503-17$04.00
RANCOURT ET AL.
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istics, that is the stress-deformation behavior, in the tangential direction of the interface. These characteristics are essential in order to both understand and improve the mechanism of load transfer. Presently, such data are not available in the literature and would be of great help in realistic model studies of cementless prostheses. For example, in a recent study by Shirazi-Ad1 and Ahmed" on the finite element computation of the interface motions in porous-surfaced tibial implants, the frictional properties at the interface between the bone and the porous-surfaced metal were not considered due to the lack of data. The objective of the present study was to experimentally evaluate the interface shear resistance using friction tests between trabecular bone cubes of proximal resurfaced tibiae and porous-surfaced metal plates. An experimental apparatus was first developed and validated to perform the friction tests. It was then used to determine the frictional properties between the cancellous bone, excised from different regions of the tibia, and a number of metal surfaces, i.e., smooth, porous beads and porous fiber mesh. In addition to the bone excision site and metal surface type, effects of the magnitude of interface normal stress as well as displacement rate on the interface friction characteristics were studied. MATERIAL A N D METHOD
(A) Specimens
The two commonly used porous-surfaced metal plates chosen for this study were obtained from Zimmer Inc. Similar to the commercially available ones, the plates were made of titanium with bead (diameter of about 0.7 mm) or fiber mesh (diameter of about 0.3 mm) porous surfaces as shown in Figure 1. The former was fabricated by a sintering process. A third plate, of smooth stainless steel (0.12 pm cla), was used for the sake of comparison. Trabecular bone cubes were obtained from seven amputated tibiae which were frozen within 30 min from the operation. The tibiae were stored at -40°C in plastic bags for 2 to 3 days. The donors, aged from 35 to 65 years, suffered mainly from vascular complications due to diabetes. The resulting gangrene was localized in the feet. Frozen tibial epiphyses were transversely resected, 3 mm below the articular surface, with a diamond saw under constant irrigation with water. Alignment of each tibia was visually verified in order to cut parallel to the articular surface. A second cut, parallel to the first one at 10 mm below, was then executed. From the trabecular bone plate obtained, bone parallelepipeds (20 x 15 x 10 mm) were cut in five different regions as shown in Figure 2. The bone specimens were then stored at 4°C for a maximum of 1 to 2 days in sealed plastic containers filled with Ringers solution. Prior to testing, specimens were maintained in the sealed containers at room temperature for an hour.
FRICTION AT THE BONE-METAL INTERFACE
1505
Figure 1. Porous-surfaced metal plates used in the experimental study. B: beads; F fiber mesh. SURFACE FROM F I R S T CUT TO BE TESTED I N FRICTION
BONE PLATE
Figure 2. The excision sites of the bone specimens on the top of the resurfaced tibia: (1)lateral, (2) medial, (3) anterior, (4) central, ( 5 ) posterior.
(B) Experimental apparatus The friction experimental apparatus was designed based on an existing system used to measure the friction between plastics and metals." The
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apparatus, shown in Figures 3 and 4, was mounted on an MTS hydraulic universal machine equipped with a 5 K N load cell [3] at 10% capacity. The porous-surfaced metal [5] was fixed to the MTS piston [4]. The bone cube [6], shown in Figure 5, was fixed by four setting blocks [7], tightened with screws [8], in a free rotating cage [9]. Vertical translation of the cage was prevented by a support [lo] connected to the load cell [3], During a test, the cube was pressed against the porous surface by an adjustable normal force (Fn), produced by a pneumatic system [ll].The normal force (F,) was distributed uniformly over the cube surface in order to prevent any moment component at the interface and it was kept constant during the experiment. Relative displacement at the interface was initiated by the piston while the bone cube was fixed. Displacement of the piston (which is equivalent to the relative displacement occurring at the interface) was measured with a linear transducer (SINGAMO brand) [12] (Fig. 3). Friction resistance (Ft: tangential force at the interface) was measured with the load cell [3] aligned directly in the plane of the interface, and the normal force was measured with a homemade gauge system. The fixation system of the bone cube was three-axis moment-free to prevent any moment force on the specimen at the interface. The relative displacement measuring system was calibrated with standard metal shims inserted between the piston and the transducer. The accuracy of the system was found to be of the order of 10 pm. Using standard weights, calibration of the load cell [3] and the normal force pneumatic system were per-
Figure 3. Experimental set-up: [l] Data acquisition system, [2] MTS controller, [3] load cell, [4] MTS piston, [lo] support, [12] SINGAMO transducer.
FRICTION AT THE BONE-METAL INTERFACE
Figure 4. Experimental apparatus, top view: [4] MTS piston, [5] Poroussurfaced metal plate, [6] bone cube, [9] rotative cage, [lo] support, [ll]pneumatic system.
Figure 5. Bone cube fixed in rotative cage: [6] Hone cube, 171 setting blocks, [8] screws, [9] rotative cage, [lo] support.
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formed and precisions of respectively +/- 0.5 N and +/- 3 N were found. Validity of the friction apparatus has been verified by a friction test between a plastic cube (UHMWPE) against a smooth stainless-steelplate. Figure 6 illustrates the friction curve obtained. Successive tests showed good repeatability with friction coefficient of about 0.12, which is comparable with the values reported in the literature.I2 (C) Data acquisition During the experiment, the normal force (F,), the friction resistance (F,) and the relative displacement (A) were continuously monitored by an IBM compatible microcomputer supported by a Labmaster card and the software UNKELSCOPE. The rate of relative displacement at the interface was set equal to 0.05 cm/min. (8 pm/s) under which preliminary tests at high sampling rate did not show any abrupt changes in the friction resistance curve. Sampling rate was therefore set equal to 1 Hz for practical reasons. (D) Experimental procedure The bone cube was fixed in the rotative cage by tightening the screws manually, without damaging the bone. Once the porous-surfaced metal was fixed and set in contact with the bone surface, as shown in Figure 4, the normal force (F,) was adjusted in order to create a 0.25 MPa normal contact pres-
I
0 -0 A-
0
2
4
6
8
10
TIME
Friction Resistance A Relative Displacement
12
14
16
18
20
(9)
Figure 6. A typical friction curve between a UHMPWE cube and a smooth stainless-steel surface (displacement control test, F , = 110 N).
FRICTION AT THE BONE-METAL INTERFACE
1509
sure. The required force F, is computed using the apparent contact surface area of the bone specimen. About 60 s were necessary to stabilize the force and the bone deformation. The rotative cage was then locked in this position since preliminary studies demonstrated that better repeatability is achieved in this manner. At this point, the relative displacement was initiated by controlling the motion of the MTS piston. Three cycles of relative displacement were realized, as illustrated in Figure 7. Preconditioning of the interface was done during the first two cycles. In fact, preliminary results indicated that the friction behavior stabilized at the second cycle. Each of the three cycles consisted of a ramp with a velocity of 0.15 cm/min for the first two cycles, and 0.05 cm/min for the last cycle. During a cycle, motion of the piston was reversed when the friction resistance encountered a plateau. After completion of the second preconditioning cycle, the friction resistance curve was measured and the cube was taken out and stored at -7°C. Finally, the porous-surfaced metal specimen was cleaned with acetone for the next test.
(E)Protocol Three different experiments were performed in order to determine the relative influence of certain variables on the friction resistance. The variables considered were: the site of excision of the bone (Exp’t. #1), the porous surface type and the magnitude of the normal contact force (Exp’t. #2), and the relative interface velocity (Exp’t. #3). Each experimental protocol is summarized in Table I.
cycles 1,2
cycle 3
III,
.
Relative Displacement
-Friction Resistance
TIME
Figure 7. Motion cycles realized during one test.
RANCOURT ET AL.
1510 TABLE I Protocols of Experiments 1-3 Normal Contact Pressure u,, (MPa)
Rate of Displacement (cm/min)
Bone Excision Site
Expt. #
Metal Plate
No. of Samples
1
B
35 (7 cubes/ region)
0.25
0.05
Lateral Medial Anterior Central Posterior
2
B F
(6 cubes/ each u,)
0.1 0.15 0.2 0.25 0.3 0.4
0.0s
Lateral Medial (same tibia)
B
7
0.2s
0.05 0.1 0.15 0.55 1.1
Lateral Medial Anterior Central Posterior
ss
3
B: bead porous surface; F: fiber mesh porous surface; SS: polished stainless steel.
Since the bone porosity and mechanical properties are known to vary with location in the tibia, Experiment #1 was designed to identify the influence of the bone excision site on the friction characteristics of the interface. Bead porous-surfaced metal was the only surface used in this experiment. Each bone cube was tested only once and the curve F, vs A was recorded. Experiment #2 was set to determine the effects of the normal contact pressure u,,and the metal surface type on the friction resistance. For each metal surface (in order of testing: beads, fiber mesh and then smooth), six bone cubes were tested in friction under various normal contact pressures, and the curves F, vs. A were recorded again. Finally, Experiment #3 studied the possible influence of the rate of relative displacement on the interface frictional properties. The experiments were done at different displacement rates varying from 0.05 to 1.1 cm/min, and curves F, vs. A were recorded. The bead porous-surfaced metal was the only one used in this experiment. RE SU LTS
A typical friction curve ( F , vs. A) is illustrated in Figure 8. The friction resistance is plotted against the relative displacement at the interface. For all metal surfaces, the shape of friction curves displays a similar pattern: a non-
1511
FRICTION AT THE BONE-METAL INTERFACE 100
. . . Normal Force
0-
0
Friction Resistance
80
- --
FM
60
Z
z w
+
.cycle 2
40
- 0
= g 2
20
2 i
0
w
z!w
I 2-20 W
O
O F
2-40
E
-60 -80
-100
I
-10
0
I
10
20
30
40
I
I
50
60
70
I
I
80
90
I
100
110
RELATIVE DISPLACEMENT ( x 10 microns )
Figure 8. A typical friction curve obtained with the experimental apparatus (fiber mesh porous surface, u, = 0.25 MPa).
linear behavior with large hysteresis. A curve can be characterized by the friction coefficient p , of the interface defined as:
F,
ps = -
Fn
F,: maximum friction resistance reached during the test F,: normal force present during the test Preliminary studies have suggested that F , should be estimated by the following equation in order to eliminate the initial offsets of the apparatus:
In Figure 8, when the displacement is initiated, the friction resistance increases up to a maximum FM+.As the displacement direction is reversed, the friction resistance decreases to FM-. Based on the friction coefficient p scomputed from the displacement control curves, such as those shown in Figure 8, it is possible to compare the relative influence of different variables. Results of Experiment #1, summarized in Table 11, reveal that the bone excision site does not have a noticeable effect on the friction coefficient. Results of Experiment #2 are illustrated in Figure 9. The friction coefficient is plotted against the magnitude of the normal contact pressure, for each metal surface type. Results are also presented in Table I11 as the average value of the six cubes tested. Since the bone excision
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TABLE I1 Experiment #1: Variation of the Friction Coefficient with the Bone Excision Site for the Bead Porous Surface No. of Samples
Bone Excision Site ~~
s,”
~
0.3 0.3 0.2 0.1 0.1
0.8 0.8 0.9 0.8 0.9
Lateral Medial Anterior Central Po sterior ~
‘Sp: standard deviation of friction coefficient p s .
1.o
0.9
0.8
-
I-
z w
0.7 -
I I 0.6 LL w
0
z
sI-
‘ r!
0.5
T
-
-
Iaw I
X
Bead Porous Surface
-b
A Fiber Mesh Porous Surface 0 Smooth Surface
d
0.4 0.3
-
J T
0.2 0.1
-
0.0
I
1
I
I
I
site was identified to have nearly no effect on the friction coefficient, the results of the cubes from different sites were lumped together. As the variances alter substantially between samples, it is preferable to use a Student t-test, based on the Welch formula^.'^ Using the average values of the friction coefficients of Table 111, statistical analysis indicates, with an error of 0.05 (that is 1 - (1 - 0.01)3),that porous-surfaced metals (bead and fiber mesh) have significantly higher friction coefficient than the smooth surface for any value of normal contact pressure. However, no statistical difference is computed between the results of the bead and fiber mesh surfaces. Using a one-way ANOVA test, assuming constant variance for each surface type regardless of the normal contact pressure, no significant variation of the friction coef-
1513
FRICTION AT THE BONE-METAL INTERFACE
TABLE 111 Average Values and Standard Deviation of Friction Coefficients for Experiment #2
Type of Surface Beads
Average
Standard Deviation
0.1 0.15 0.2 0.25 0.3 0.4
0.63 0.56 0.55 0.53 0.47 0.45
0.15 0.09 0.12 0.14 0.07 0.05
6 6 6 6 6
0.1 0.15 0.2 0.25 0.3 0.4
0.52 0.46 0.45 0.45 0.47 0.44
0.07 0.03 0.04
6 6 6 6 6 6
0.1 0.15 0.2 0.25 0.3 0.4
0.32 0.32 0.29 0.28 0.30 0.28
0.04 0.04 0.03 0.03 0.03 0.03
No. of Samples
6" 6 6 6 6 6
Fiber mesh
Smooth
Friction Coefficient
Contact Pressure (MW
6
0.05 0.04 0.07
"The same six cubes were tested in all experiments.
ficient with the normal pressure was found (test was only positive for p = 0.25, for the three surface types). Finally, results of Experiment #3, summarized in Table IV, show that the rate of relative displacement does not affect the friction resistance of the interface. Other tests similar to the displacement control tests, such as that in Figure 8, were performed under force control of the piston to better analyze the TABLE IV Results of Experiment #3: Variation of the Friction Coefficient with the Magnitude of the Relative Displacement Rate (Bead Porous Surface, Contact Pressure = 0.25 MPa)
Bone Excision Site (1samule by sitej
Relative Displacement Rate (cm/min) .05
0.1
0.15
0.55
1.1 1.1 1.3 1.1 0.7 0.9 0.9 1.2
Lateral . Medial Anterior Central Posterior
1.1 1.2 1.2 0.5 0.9
1.0 1.3 1.1 0.9 0.9
0.9 1.2
0.9 0.8 0.6
1.0 1.2 1.2 0.8 0.6
Lateral Medial
0.9 1.2
0.9 1.1
0.9 1.1
0.9 1.1
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stress-deformation behavior of the interface. A typical friction curve, in force control, is presented in Figure 10. For this test, the interface was subjected to a cyclic tangential force, with increasing amplitude, until gross sliding occurred. As the tangential force was initially applied, the interface exhibited a nonlinear behavior. When the tangential force was then diminished to zero, a permanent nonzero displacement (Ap) remained. As the tangential force was increased again, the interface presented an almost elastic behavior up to the point where the previous maximal tangential force was reached. Afterwards, it presented a nonlinear characteristic and the accumulated permanent displacement further increased. The slope of the cyclic parts of the friction curve remained nearly constant irrespective of the tangential force resisted. DISCUSSION
Friction curves
The friction curves obtained in the present work are markedly different from those which conform to the Coulombs friction law where no displacement occurs before the maximum resistance force F, is reached. In fact, the friction curves at the bone-metal interface are highly nonlinear. There is no pronounced "peak of the friction resistance as that expected in a system that
100
. . . Normal Force A
-A Friction Resistance
'60 OI
20
30
40
50
60
70
80
90
100
110
120
Figure 10. A typical friction curve obtained under force control test (bead porous surface, (T, = 0.25 MPa).
FRICTION AT THE BONE-METAL INTERFACE
1515
passes from static to dynamic friction in dry condition (i.e., when gross sliding starts). Moreover, large relative displacements (about 100 to 500 pm) occur before F, is reached (Fig. 8). In Figure 8, it can be observed that the initial tangential force F , is not zero at zero tangential displacement. That is, prior to the application of interface relative displacement, a tangential force Fti is generated as a normal interface pressure is applied. This deviation can be attributed to offsets of the apparatus and inadequate geometry of the bone specimens. As this initial force Ft, varied from one test to the other, it was important to eliminate it before further analysis of the curves to determine the nonlinear response as well as the friction coefficient. That is why cyclic displacement was used to perform the friction test. Assuming the interface to be uniform, the friction resistance is the same in any two opposite directions of motion. The maximum friction resistance F, can then be evaluated by computing the arithmetic mean of the maximum resistant forces measured in the two opposite directions (see Eq. (2)). Thus, the initial nonzero tangential force did not affect the magnitude of F,. However, to use this technique, it was necessary to ensure that the maximum friction resistance F, was reached in the two opposite directions. Therefore, in this study, the motion of the piston was reversed as soon as the friction resistance F, reached a plateau. The interface was then displaced back toward its initial undeformed position. Friction coefficient
In this study, for the sake of comparison, each nonlinear friction relationship is solely characterized by a single friction coefficient p 5 ,computed from Eq. (1). The friction coefficient was evaluated based on the third cycle of displacement, at which point the friction phenomenon is found to be stabilized. This cyclic technic to measure the friction coefficient has also been used by other investigator^,'^ studying the platinum-platinum interface. Values of p , measured at the bone-metal interface vary from 0.3 to 1.3. In other words, there exists a shear resistance of 0.03 to 0.52 MPa for normal stresses of 0.1 to 0.4 MPa. Coefficients of friction measured in the present study are of the same order of magnitude as those between common metals (steel, aluminum, copper) and ~tee1.l~ They can also be compared with those of Maniatopoulos et a1.16 who carried out pull-out tests of porous-surfaced tooth implants in trabecular bone. Immediately after insertion of the implants, they measured shear strength of 0.5 MPa. However, the normal contact pressure present in their study is unknown. The results of this study indicate that the friction coefficient p s does not noticeably vary with the alteration in either the bone excision site on the resurfaced tibia or the magnitude of displacement rate considered in this work. However, it markedly increases as the metal surface becomes porous.
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Friction mechanism Due to the expected role of friction in load transfer, an improvement in the friction properties could lead to better prosthesis stabilization. Understanding the mechanism of friction would help to identify factors affecting interface friction and hence, implant performance. It has been shown that the structure of boneI7-l9varies significantly with the site of excision in the tibia. The real contact surface of the bone-metal complex is therefore expected to vary with the excision site and to influence the friction coefficient. However, Experiment #1 revealed that the friction coefficient is independent of the bone excision site. This possibly indicates that the bone marrow could be a factor in the friction resistance. In fact, the marrow, which has a similar viscosity as a medium motor oil?’ acts as a lubricant. The marked increase in the friction resistance for the porous metal surfaces, in comparison with the smooth metal surface, points to a distinct mechanism of friction generation. Asperities on the metal surfaces plough the bone specimen whereby a larger resistance to the relative motion is generated. The observation of a number of broken individual beads in the bone specimens and grooves in the bone surface further support this mechanism of load transfer. The type of the metal asperity does not seem to change the friction resistance as the friction coefficients of the bead and of the fiber mesh surfaces have similar values. states that friction resistance is made by ”juncThe adhesion tions” at the interface (chemical links such as hydrogen bonds between the organic substances and the oxides of the metallic plates). It is proposed that when the surfaces are brought into contact, a certain amount of junctions are created under the normal contact pressure. When a tangential force is then applied at the interface, more junctions are created due to the motion. If the tangential force is then brought back to zero, the interface motion will reverse but the interface will not return to its initial position and a permanent displacement appears as seen in Figure 10. Then, if the tangential force is increased again, the interface will exhibit an elastic behavior due to the presence of the junctions which produce mainly a deformation of the bone specimens. Identification of the relative contribution of the foregoing two distinct mechanisms of “adhesion” and “ploughing” in the interface frictional response, however, needs further studies. Results for model studies
A purpose of this study was to quantify the mechanical properties of the bone-porous metal interface to incorporate in finite element models of knee implants. Based on friction curves such as that in Figure 8, tangential stressdeformation curves for the interface can be identified. The force-displacement relationship between points A and B of Figure 8 is the only portion of the friction curve necessary to completely define the interface behavior. How-
1517
FRICTION AT THE BONE-METAL INTERFACE
ever, the friction curve has to be modified by subtracting the elastic component of the interface deformation caused mainly by the flexibility of the bone specimens. This elastic component is evaluated by estimating the rigidity of the interface from the displacement control curves by drawing a straight line between points B and C (Fig. 8). These points correspond respectively to the maximum force and zero force conditions obtained under the reversal of the interface displacement as shown in Figure 8. Such elastic deformation of the specimens is not unusual and has been eliminated by a similar procedure in a smooth platinum friction test by Bowden et al.14as well. The new friction curve obtained, shown for one case in Figure 11, is nonlinear and suitable to be employed in a biomechanical model study of the interface. It describes the deformation of the interface subjected to shear stress. It has been reported that bone ingrowth is possible in the presence of micromotion at the bone-metal interface of up to about 28 pm, while excess motion of about 150 pm or more may result in attachment by fibrous tissue ingrowth.3 Therefore, in the normal in vivo conditions, the interface friction resistance may only be partially utilized if the interface motion should remain well below 150 pm. The presence of force-fit is expected, even for a temporary period, to enhance the shear resistance of the interface. A quantitative evaluation of the effect of the presence of friction, with and without force-fit, on the biomechanics of an implanted joint, however, requires a detailed nonlinear stress analysis which is currently under way.
, ""
80
1 0
. . . Measured Friction Curve Modified Friction Curve
A-A
10
20
30
40
50
60
RELATIVE DISPLACEMENT ( X 10 microns )
Figure 11. A modified curve representing section A-B of Figure 8 0.25 MPa).
(0,
=
RANCOURT ET AL.
1518 CONCLUSIONS
An experimental set-up was designed in order to measure the friction properties of the tibia1 cancellous bone-metal prosthesis interface. In addition to the excision site of the bone and the metal surface, the effects of the normal pressure and displacement rate on the interface friction properties were studied. Some of the salient findings of this experimental work are as follows. (1) The tangential stress-deformation relationship of the bone-metal interface is nonlinear and a relatively large displacement of about 100 to 500 pm is necessary before the maximal resistance is reached. (2) The friction coefficient appears to be independent of the bone excision site of the resurfaced tibia. Friction coefficient is also independent of the rate of relative displacement. (3) The friction coefficient of the bead porous metal-bone interface slightly diminishes ( p = 0.25) with increase in the normal contact pressure. Almost no similar variation is observed for the other metal surfaces. (4)In comparison with the smooth metal surface, the porous surfaces markedly increase the interface friction properties. There is, however, no significant differences between the two porous surfaces used in this study. This study is supported by the IRSST and the FCAR (Quebec) and the NSERC (Canada, Grant OGP0005596). Special thanks to Zimmer Inc. for providing the poroussurfaced metal samples.
References 1. H.U. Cameron, R.M. Pilliar, and I. Macnab, ”The effect of movement on the bonding of porous metal to bone,” J. Biomed. Muter. Res., 7,301311 (1973). 2. P. Ducheyne, P. DeMeester, E. Aernoudt, M. Martens, and C. Mulier, “Influence of a functional dynamic loading on bone ingrowth into surface pores of orthopedic implants,” J. Biomed. Muter. Res., 11,811-838 (1977). 3. R. M. Pilliar, J. M. Lee, and C. Maniatopoulos, ”Observations on the effect of movement on bone ingrowth into porous-surfaced implants,” Clin. Orthop. Rel. Res., 208, 109-113 (1986). 4. R. M. Pilliar, H.U. Cameron, R. P. Welsh, and A.G. Binnington, ”Radiographic and morphologic studies of load-bearing porous-surfaced structured implants,” Clin.Orthop. Rel. Res., 156, 249-257 (1981). 5. J. D. Bobyn, R. M. Pilliar, H.U. Cameron, and G.C. Weatherly, ”The optimum pore size for the fixation of porous-surfaced metal implants by the ingrowth of bone,” Clin. Orthop. Rel. Res., 150, 263-270 (1980). 6. A. J.T. Clemow, A.M. Weinstein, J. J. Klawitter, J. Koeneman, and J. Anderson, ”Interface mechanics of porous titanium implants,” J. Biomed. Muter. Res., 15, 73-82 (1981). 7. H.U. Cameron, R.M. Pilliar, and 1. Macnab, ”The rate of bone ingrowth into porous metal,” J. Biomed. Muter. Res., 10,295-302 (1976). 8. P.M. Sandborn, S.D. Cook, R.C. Anderson, W.P. Spires, and M. A. Kester, ”The effect of surgical fit on bone growth into porous coated implants,” Trans. 33th Annual Meeting, Orthopaedic Research Society, San Francisco, January 19-22, 1987, p. 217.
FRICTION AT THE BONE-METAL INTERFACE 9.
10. 11.
12. 13.
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16. 17.
18. 19. 20.
21. 22. 23.
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S. F. Hulbert, J. R. Matthews, J. J. Klawitter, B.W. Sauer, and R. 8. Leonard, “Effects of stress on tissue ingrowth into porous aluminum oxide,” J. Biomed. Muter. Res. Symp., 5 (Part 11, 85-97 (1974). A. Shirazi-Ad1 and A. M. Ahmed, “A parametric axisymmetric model study on the interface motions in porous-surfaced tibial implants,” Ann. Biomed. Eng., in press. S. M. Benabdallah and J.-P. Chalifoux,“Computer-aidedfriction tester,” Int. Tribol., in press. , S. M. Benabdallah, “Etude du frottement de glissement alterpatif thermoplastique-m6tal en contact plan-plan,” Doctoral Thesis, Ecole Polytechnique de Montreal, 1987. G.V. Glass and K. D. Hopkins, Statistical Methods in Education and Psychology, 2nd Ed., Prentice-Hall Inc., Engelwood Cliffs, N.J., 1984. F. P. Bowden and D. Tabor, The Friction and Lubrication of Solids, Part 11, Clarendon Press, Oxford, 1964. E. O’Berg, F. D. Jones, and H. L. Horton, Machinery’s Handbook, Industrial Press Inc., New York (1980). C. Maniatopoulos, R. M. Pilliar, and D.C. Smith, “Threaded versus porous-surfaced designs for implant stabilization in bone-endodontic implant model,” J. Biomed. Muter. Res., 20, 1309-1333 (1986). R. M. Henshaw, T. P. Harrigan, M. Jasty, R. Mann, and W.H. Harris, “Three dimensional map of trabecular architecture of the proximal and distal human femur and proximal human tibia,” Proc. Orthop. Res. Soc., 41 (1986). M. H. Pope and J.O. Outwater, ”Mechanical properties of bone as a function of position and orientation,” J. Biomech., 7, 61-66 (1974). J. L. Williams and J. L. Lewis, “Properties and an anisotropic model of cancellous bone from the proximal tibial epiphysis,” ASME, 104, 50-56 (1982). S. A.V. Swanson and M. A. R. Freeman, “Is bone hydraulically strengthened?,” Med. Bid. Eng., 4, 433-438 (1966). E P. Bowden and D. Tabor, The Fricfion and Lubrication of Solids, Part 1, Clarendon Press, Oxford, 1958. A. Dorinson and K.C. Ludema, Mechanics and Chemistry in Lubrication, Tribology Series Vol. 9, Elsevier, New York, 1985. N. C. Barford, Experimental Measurements: Precision, Error and Truth, 2nd Ed., John Wiley & Sons, Toronto, 1985.
Received September 1, 1989 Accepted May 15,1990
G. Paiement Sacrk-Coeur Hospital, Montrial, Qw%ec, Canada Friction tests between cancellous bone cubes and porous-surfaced metal plates were conducted in order to determine the mechanical properties of the interface in a knee porous-surfaced metal implant. Bone specimens were obtained from fresh frozen amputated tibiae and three metal plates were chosen: titanium bead porous-surfaced, titanium fiber mesh porous-surfaced, and smooth stainless steel. Results show that the friction curve is highly nonlinear. Friction coefficients measured vary between 0.3 and 1.3. The friction coefficient of the interface is in-
dependent of the excision site of the bone cubes and of the magnitude of the rate of relative displacement at the interface. The friction coefficient appears to vary slightly with the normal contact pressure for all the metal surfaces. Both porous surfaces have statistically a higher friction coefficient than the smooth surface. This is likely due to the presence of surface asperities whereby the metal ploughs the bone surface. However, no significant difference is observed between bead and fiber mesh types.
INTRODUCTION
Adequate fixation of an implant to the host bone is essential for the satisfactory long-term performance of a knee arthroplasty. When noncemented implants are used, biological fixation by bone ingrowth is the primary mechanism of implant attachment and provides a means to transfer the stress at the bone-prosthesis interface. Bone ingrowth into the surface pores of an implant has been reported to depend, among other factors, on relative movements at the bone-metal interface,’-4 on the pore on the intimacy of bone-implant apposition,”*and on weight bearing.’ These factors imply that success of noncemented implants is related to the capability of the boneimplant interface to sustain shear as well as normal stresses present after the arthroplasty. Evaluation of the interface shear resistance under various stress conditions is possible through the determination of its mechanical characterNo benefit of any kind will be received either directly or indirectly by the authors. ‘To whom correspondence should be addressed. Journal of Biomedical Materials Research, Vol. 24,1503-1519 (1990) 0 1990 John Wiley & Sons, Inc. CCC 0021-9304/90/111503-17$04.00
RANCOURT ET AL.
1504
istics, that is the stress-deformation behavior, in the tangential direction of the interface. These characteristics are essential in order to both understand and improve the mechanism of load transfer. Presently, such data are not available in the literature and would be of great help in realistic model studies of cementless prostheses. For example, in a recent study by Shirazi-Ad1 and Ahmed" on the finite element computation of the interface motions in porous-surfaced tibial implants, the frictional properties at the interface between the bone and the porous-surfaced metal were not considered due to the lack of data. The objective of the present study was to experimentally evaluate the interface shear resistance using friction tests between trabecular bone cubes of proximal resurfaced tibiae and porous-surfaced metal plates. An experimental apparatus was first developed and validated to perform the friction tests. It was then used to determine the frictional properties between the cancellous bone, excised from different regions of the tibia, and a number of metal surfaces, i.e., smooth, porous beads and porous fiber mesh. In addition to the bone excision site and metal surface type, effects of the magnitude of interface normal stress as well as displacement rate on the interface friction characteristics were studied. MATERIAL A N D METHOD
(A) Specimens
The two commonly used porous-surfaced metal plates chosen for this study were obtained from Zimmer Inc. Similar to the commercially available ones, the plates were made of titanium with bead (diameter of about 0.7 mm) or fiber mesh (diameter of about 0.3 mm) porous surfaces as shown in Figure 1. The former was fabricated by a sintering process. A third plate, of smooth stainless steel (0.12 pm cla), was used for the sake of comparison. Trabecular bone cubes were obtained from seven amputated tibiae which were frozen within 30 min from the operation. The tibiae were stored at -40°C in plastic bags for 2 to 3 days. The donors, aged from 35 to 65 years, suffered mainly from vascular complications due to diabetes. The resulting gangrene was localized in the feet. Frozen tibial epiphyses were transversely resected, 3 mm below the articular surface, with a diamond saw under constant irrigation with water. Alignment of each tibia was visually verified in order to cut parallel to the articular surface. A second cut, parallel to the first one at 10 mm below, was then executed. From the trabecular bone plate obtained, bone parallelepipeds (20 x 15 x 10 mm) were cut in five different regions as shown in Figure 2. The bone specimens were then stored at 4°C for a maximum of 1 to 2 days in sealed plastic containers filled with Ringers solution. Prior to testing, specimens were maintained in the sealed containers at room temperature for an hour.
FRICTION AT THE BONE-METAL INTERFACE
1505
Figure 1. Porous-surfaced metal plates used in the experimental study. B: beads; F fiber mesh. SURFACE FROM F I R S T CUT TO BE TESTED I N FRICTION
BONE PLATE
Figure 2. The excision sites of the bone specimens on the top of the resurfaced tibia: (1)lateral, (2) medial, (3) anterior, (4) central, ( 5 ) posterior.
(B) Experimental apparatus The friction experimental apparatus was designed based on an existing system used to measure the friction between plastics and metals." The
1506
RANCOURT ET AL.
apparatus, shown in Figures 3 and 4, was mounted on an MTS hydraulic universal machine equipped with a 5 K N load cell [3] at 10% capacity. The porous-surfaced metal [5] was fixed to the MTS piston [4]. The bone cube [6], shown in Figure 5, was fixed by four setting blocks [7], tightened with screws [8], in a free rotating cage [9]. Vertical translation of the cage was prevented by a support [lo] connected to the load cell [3], During a test, the cube was pressed against the porous surface by an adjustable normal force (Fn), produced by a pneumatic system [ll].The normal force (F,) was distributed uniformly over the cube surface in order to prevent any moment component at the interface and it was kept constant during the experiment. Relative displacement at the interface was initiated by the piston while the bone cube was fixed. Displacement of the piston (which is equivalent to the relative displacement occurring at the interface) was measured with a linear transducer (SINGAMO brand) [12] (Fig. 3). Friction resistance (Ft: tangential force at the interface) was measured with the load cell [3] aligned directly in the plane of the interface, and the normal force was measured with a homemade gauge system. The fixation system of the bone cube was three-axis moment-free to prevent any moment force on the specimen at the interface. The relative displacement measuring system was calibrated with standard metal shims inserted between the piston and the transducer. The accuracy of the system was found to be of the order of 10 pm. Using standard weights, calibration of the load cell [3] and the normal force pneumatic system were per-
Figure 3. Experimental set-up: [l] Data acquisition system, [2] MTS controller, [3] load cell, [4] MTS piston, [lo] support, [12] SINGAMO transducer.
FRICTION AT THE BONE-METAL INTERFACE
Figure 4. Experimental apparatus, top view: [4] MTS piston, [5] Poroussurfaced metal plate, [6] bone cube, [9] rotative cage, [lo] support, [ll]pneumatic system.
Figure 5. Bone cube fixed in rotative cage: [6] Hone cube, 171 setting blocks, [8] screws, [9] rotative cage, [lo] support.
1507
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1508
formed and precisions of respectively +/- 0.5 N and +/- 3 N were found. Validity of the friction apparatus has been verified by a friction test between a plastic cube (UHMWPE) against a smooth stainless-steelplate. Figure 6 illustrates the friction curve obtained. Successive tests showed good repeatability with friction coefficient of about 0.12, which is comparable with the values reported in the literature.I2 (C) Data acquisition During the experiment, the normal force (F,), the friction resistance (F,) and the relative displacement (A) were continuously monitored by an IBM compatible microcomputer supported by a Labmaster card and the software UNKELSCOPE. The rate of relative displacement at the interface was set equal to 0.05 cm/min. (8 pm/s) under which preliminary tests at high sampling rate did not show any abrupt changes in the friction resistance curve. Sampling rate was therefore set equal to 1 Hz for practical reasons. (D) Experimental procedure The bone cube was fixed in the rotative cage by tightening the screws manually, without damaging the bone. Once the porous-surfaced metal was fixed and set in contact with the bone surface, as shown in Figure 4, the normal force (F,) was adjusted in order to create a 0.25 MPa normal contact pres-
I
0 -0 A-
0
2
4
6
8
10
TIME
Friction Resistance A Relative Displacement
12
14
16
18
20
(9)
Figure 6. A typical friction curve between a UHMPWE cube and a smooth stainless-steel surface (displacement control test, F , = 110 N).
FRICTION AT THE BONE-METAL INTERFACE
1509
sure. The required force F, is computed using the apparent contact surface area of the bone specimen. About 60 s were necessary to stabilize the force and the bone deformation. The rotative cage was then locked in this position since preliminary studies demonstrated that better repeatability is achieved in this manner. At this point, the relative displacement was initiated by controlling the motion of the MTS piston. Three cycles of relative displacement were realized, as illustrated in Figure 7. Preconditioning of the interface was done during the first two cycles. In fact, preliminary results indicated that the friction behavior stabilized at the second cycle. Each of the three cycles consisted of a ramp with a velocity of 0.15 cm/min for the first two cycles, and 0.05 cm/min for the last cycle. During a cycle, motion of the piston was reversed when the friction resistance encountered a plateau. After completion of the second preconditioning cycle, the friction resistance curve was measured and the cube was taken out and stored at -7°C. Finally, the porous-surfaced metal specimen was cleaned with acetone for the next test.
(E)Protocol Three different experiments were performed in order to determine the relative influence of certain variables on the friction resistance. The variables considered were: the site of excision of the bone (Exp’t. #1), the porous surface type and the magnitude of the normal contact force (Exp’t. #2), and the relative interface velocity (Exp’t. #3). Each experimental protocol is summarized in Table I.
cycles 1,2
cycle 3
III,
.
Relative Displacement
-Friction Resistance
TIME
Figure 7. Motion cycles realized during one test.
RANCOURT ET AL.
1510 TABLE I Protocols of Experiments 1-3 Normal Contact Pressure u,, (MPa)
Rate of Displacement (cm/min)
Bone Excision Site
Expt. #
Metal Plate
No. of Samples
1
B
35 (7 cubes/ region)
0.25
0.05
Lateral Medial Anterior Central Posterior
2
B F
(6 cubes/ each u,)
0.1 0.15 0.2 0.25 0.3 0.4
0.0s
Lateral Medial (same tibia)
B
7
0.2s
0.05 0.1 0.15 0.55 1.1
Lateral Medial Anterior Central Posterior
ss
3
B: bead porous surface; F: fiber mesh porous surface; SS: polished stainless steel.
Since the bone porosity and mechanical properties are known to vary with location in the tibia, Experiment #1 was designed to identify the influence of the bone excision site on the friction characteristics of the interface. Bead porous-surfaced metal was the only surface used in this experiment. Each bone cube was tested only once and the curve F, vs A was recorded. Experiment #2 was set to determine the effects of the normal contact pressure u,,and the metal surface type on the friction resistance. For each metal surface (in order of testing: beads, fiber mesh and then smooth), six bone cubes were tested in friction under various normal contact pressures, and the curves F, vs. A were recorded again. Finally, Experiment #3 studied the possible influence of the rate of relative displacement on the interface frictional properties. The experiments were done at different displacement rates varying from 0.05 to 1.1 cm/min, and curves F, vs. A were recorded. The bead porous-surfaced metal was the only one used in this experiment. RE SU LTS
A typical friction curve ( F , vs. A) is illustrated in Figure 8. The friction resistance is plotted against the relative displacement at the interface. For all metal surfaces, the shape of friction curves displays a similar pattern: a non-
1511
FRICTION AT THE BONE-METAL INTERFACE 100
. . . Normal Force
0-
0
Friction Resistance
80
- --
FM
60
Z
z w
+
.cycle 2
40
- 0
= g 2
20
2 i
0
w
z!w
I 2-20 W
O
O F
2-40
E
-60 -80
-100
I
-10
0
I
10
20
30
40
I
I
50
60
70
I
I
80
90
I
100
110
RELATIVE DISPLACEMENT ( x 10 microns )
Figure 8. A typical friction curve obtained with the experimental apparatus (fiber mesh porous surface, u, = 0.25 MPa).
linear behavior with large hysteresis. A curve can be characterized by the friction coefficient p , of the interface defined as:
F,
ps = -
Fn
F,: maximum friction resistance reached during the test F,: normal force present during the test Preliminary studies have suggested that F , should be estimated by the following equation in order to eliminate the initial offsets of the apparatus:
In Figure 8, when the displacement is initiated, the friction resistance increases up to a maximum FM+.As the displacement direction is reversed, the friction resistance decreases to FM-. Based on the friction coefficient p scomputed from the displacement control curves, such as those shown in Figure 8, it is possible to compare the relative influence of different variables. Results of Experiment #1, summarized in Table 11, reveal that the bone excision site does not have a noticeable effect on the friction coefficient. Results of Experiment #2 are illustrated in Figure 9. The friction coefficient is plotted against the magnitude of the normal contact pressure, for each metal surface type. Results are also presented in Table I11 as the average value of the six cubes tested. Since the bone excision
RANCOURT ET AL.
1512
TABLE I1 Experiment #1: Variation of the Friction Coefficient with the Bone Excision Site for the Bead Porous Surface No. of Samples
Bone Excision Site ~~
s,”
~
0.3 0.3 0.2 0.1 0.1
0.8 0.8 0.9 0.8 0.9
Lateral Medial Anterior Central Po sterior ~
‘Sp: standard deviation of friction coefficient p s .
1.o
0.9
0.8
-
I-
z w
0.7 -
I I 0.6 LL w
0
z
sI-
‘ r!
0.5
T
-
-
Iaw I
X
Bead Porous Surface
-b
A Fiber Mesh Porous Surface 0 Smooth Surface
d
0.4 0.3
-
J T
0.2 0.1
-
0.0
I
1
I
I
I
site was identified to have nearly no effect on the friction coefficient, the results of the cubes from different sites were lumped together. As the variances alter substantially between samples, it is preferable to use a Student t-test, based on the Welch formula^.'^ Using the average values of the friction coefficients of Table 111, statistical analysis indicates, with an error of 0.05 (that is 1 - (1 - 0.01)3),that porous-surfaced metals (bead and fiber mesh) have significantly higher friction coefficient than the smooth surface for any value of normal contact pressure. However, no statistical difference is computed between the results of the bead and fiber mesh surfaces. Using a one-way ANOVA test, assuming constant variance for each surface type regardless of the normal contact pressure, no significant variation of the friction coef-
1513
FRICTION AT THE BONE-METAL INTERFACE
TABLE 111 Average Values and Standard Deviation of Friction Coefficients for Experiment #2
Type of Surface Beads
Average
Standard Deviation
0.1 0.15 0.2 0.25 0.3 0.4
0.63 0.56 0.55 0.53 0.47 0.45
0.15 0.09 0.12 0.14 0.07 0.05
6 6 6 6 6
0.1 0.15 0.2 0.25 0.3 0.4
0.52 0.46 0.45 0.45 0.47 0.44
0.07 0.03 0.04
6 6 6 6 6 6
0.1 0.15 0.2 0.25 0.3 0.4
0.32 0.32 0.29 0.28 0.30 0.28
0.04 0.04 0.03 0.03 0.03 0.03
No. of Samples
6" 6 6 6 6 6
Fiber mesh
Smooth
Friction Coefficient
Contact Pressure (MW
6
0.05 0.04 0.07
"The same six cubes were tested in all experiments.
ficient with the normal pressure was found (test was only positive for p = 0.25, for the three surface types). Finally, results of Experiment #3, summarized in Table IV, show that the rate of relative displacement does not affect the friction resistance of the interface. Other tests similar to the displacement control tests, such as that in Figure 8, were performed under force control of the piston to better analyze the TABLE IV Results of Experiment #3: Variation of the Friction Coefficient with the Magnitude of the Relative Displacement Rate (Bead Porous Surface, Contact Pressure = 0.25 MPa)
Bone Excision Site (1samule by sitej
Relative Displacement Rate (cm/min) .05
0.1
0.15
0.55
1.1 1.1 1.3 1.1 0.7 0.9 0.9 1.2
Lateral . Medial Anterior Central Posterior
1.1 1.2 1.2 0.5 0.9
1.0 1.3 1.1 0.9 0.9
0.9 1.2
0.9 0.8 0.6
1.0 1.2 1.2 0.8 0.6
Lateral Medial
0.9 1.2
0.9 1.1
0.9 1.1
0.9 1.1
RANCOURT ET AL.
1514
stress-deformation behavior of the interface. A typical friction curve, in force control, is presented in Figure 10. For this test, the interface was subjected to a cyclic tangential force, with increasing amplitude, until gross sliding occurred. As the tangential force was initially applied, the interface exhibited a nonlinear behavior. When the tangential force was then diminished to zero, a permanent nonzero displacement (Ap) remained. As the tangential force was increased again, the interface presented an almost elastic behavior up to the point where the previous maximal tangential force was reached. Afterwards, it presented a nonlinear characteristic and the accumulated permanent displacement further increased. The slope of the cyclic parts of the friction curve remained nearly constant irrespective of the tangential force resisted. DISCUSSION
Friction curves
The friction curves obtained in the present work are markedly different from those which conform to the Coulombs friction law where no displacement occurs before the maximum resistance force F, is reached. In fact, the friction curves at the bone-metal interface are highly nonlinear. There is no pronounced "peak of the friction resistance as that expected in a system that
100
. . . Normal Force A
-A Friction Resistance
'60 OI
20
30
40
50
60
70
80
90
100
110
120
Figure 10. A typical friction curve obtained under force control test (bead porous surface, (T, = 0.25 MPa).
FRICTION AT THE BONE-METAL INTERFACE
1515
passes from static to dynamic friction in dry condition (i.e., when gross sliding starts). Moreover, large relative displacements (about 100 to 500 pm) occur before F, is reached (Fig. 8). In Figure 8, it can be observed that the initial tangential force F , is not zero at zero tangential displacement. That is, prior to the application of interface relative displacement, a tangential force Fti is generated as a normal interface pressure is applied. This deviation can be attributed to offsets of the apparatus and inadequate geometry of the bone specimens. As this initial force Ft, varied from one test to the other, it was important to eliminate it before further analysis of the curves to determine the nonlinear response as well as the friction coefficient. That is why cyclic displacement was used to perform the friction test. Assuming the interface to be uniform, the friction resistance is the same in any two opposite directions of motion. The maximum friction resistance F, can then be evaluated by computing the arithmetic mean of the maximum resistant forces measured in the two opposite directions (see Eq. (2)). Thus, the initial nonzero tangential force did not affect the magnitude of F,. However, to use this technique, it was necessary to ensure that the maximum friction resistance F, was reached in the two opposite directions. Therefore, in this study, the motion of the piston was reversed as soon as the friction resistance F, reached a plateau. The interface was then displaced back toward its initial undeformed position. Friction coefficient
In this study, for the sake of comparison, each nonlinear friction relationship is solely characterized by a single friction coefficient p 5 ,computed from Eq. (1). The friction coefficient was evaluated based on the third cycle of displacement, at which point the friction phenomenon is found to be stabilized. This cyclic technic to measure the friction coefficient has also been used by other investigator^,'^ studying the platinum-platinum interface. Values of p , measured at the bone-metal interface vary from 0.3 to 1.3. In other words, there exists a shear resistance of 0.03 to 0.52 MPa for normal stresses of 0.1 to 0.4 MPa. Coefficients of friction measured in the present study are of the same order of magnitude as those between common metals (steel, aluminum, copper) and ~tee1.l~ They can also be compared with those of Maniatopoulos et a1.16 who carried out pull-out tests of porous-surfaced tooth implants in trabecular bone. Immediately after insertion of the implants, they measured shear strength of 0.5 MPa. However, the normal contact pressure present in their study is unknown. The results of this study indicate that the friction coefficient p s does not noticeably vary with the alteration in either the bone excision site on the resurfaced tibia or the magnitude of displacement rate considered in this work. However, it markedly increases as the metal surface becomes porous.
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Friction mechanism Due to the expected role of friction in load transfer, an improvement in the friction properties could lead to better prosthesis stabilization. Understanding the mechanism of friction would help to identify factors affecting interface friction and hence, implant performance. It has been shown that the structure of boneI7-l9varies significantly with the site of excision in the tibia. The real contact surface of the bone-metal complex is therefore expected to vary with the excision site and to influence the friction coefficient. However, Experiment #1 revealed that the friction coefficient is independent of the bone excision site. This possibly indicates that the bone marrow could be a factor in the friction resistance. In fact, the marrow, which has a similar viscosity as a medium motor oil?’ acts as a lubricant. The marked increase in the friction resistance for the porous metal surfaces, in comparison with the smooth metal surface, points to a distinct mechanism of friction generation. Asperities on the metal surfaces plough the bone specimen whereby a larger resistance to the relative motion is generated. The observation of a number of broken individual beads in the bone specimens and grooves in the bone surface further support this mechanism of load transfer. The type of the metal asperity does not seem to change the friction resistance as the friction coefficients of the bead and of the fiber mesh surfaces have similar values. states that friction resistance is made by ”juncThe adhesion tions” at the interface (chemical links such as hydrogen bonds between the organic substances and the oxides of the metallic plates). It is proposed that when the surfaces are brought into contact, a certain amount of junctions are created under the normal contact pressure. When a tangential force is then applied at the interface, more junctions are created due to the motion. If the tangential force is then brought back to zero, the interface motion will reverse but the interface will not return to its initial position and a permanent displacement appears as seen in Figure 10. Then, if the tangential force is increased again, the interface will exhibit an elastic behavior due to the presence of the junctions which produce mainly a deformation of the bone specimens. Identification of the relative contribution of the foregoing two distinct mechanisms of “adhesion” and “ploughing” in the interface frictional response, however, needs further studies. Results for model studies
A purpose of this study was to quantify the mechanical properties of the bone-porous metal interface to incorporate in finite element models of knee implants. Based on friction curves such as that in Figure 8, tangential stressdeformation curves for the interface can be identified. The force-displacement relationship between points A and B of Figure 8 is the only portion of the friction curve necessary to completely define the interface behavior. How-
1517
FRICTION AT THE BONE-METAL INTERFACE
ever, the friction curve has to be modified by subtracting the elastic component of the interface deformation caused mainly by the flexibility of the bone specimens. This elastic component is evaluated by estimating the rigidity of the interface from the displacement control curves by drawing a straight line between points B and C (Fig. 8). These points correspond respectively to the maximum force and zero force conditions obtained under the reversal of the interface displacement as shown in Figure 8. Such elastic deformation of the specimens is not unusual and has been eliminated by a similar procedure in a smooth platinum friction test by Bowden et al.14as well. The new friction curve obtained, shown for one case in Figure 11, is nonlinear and suitable to be employed in a biomechanical model study of the interface. It describes the deformation of the interface subjected to shear stress. It has been reported that bone ingrowth is possible in the presence of micromotion at the bone-metal interface of up to about 28 pm, while excess motion of about 150 pm or more may result in attachment by fibrous tissue ingrowth.3 Therefore, in the normal in vivo conditions, the interface friction resistance may only be partially utilized if the interface motion should remain well below 150 pm. The presence of force-fit is expected, even for a temporary period, to enhance the shear resistance of the interface. A quantitative evaluation of the effect of the presence of friction, with and without force-fit, on the biomechanics of an implanted joint, however, requires a detailed nonlinear stress analysis which is currently under way.
, ""
80
1 0
. . . Measured Friction Curve Modified Friction Curve
A-A
10
20
30
40
50
60
RELATIVE DISPLACEMENT ( X 10 microns )
Figure 11. A modified curve representing section A-B of Figure 8 0.25 MPa).
(0,
=
RANCOURT ET AL.
1518 CONCLUSIONS
An experimental set-up was designed in order to measure the friction properties of the tibia1 cancellous bone-metal prosthesis interface. In addition to the excision site of the bone and the metal surface, the effects of the normal pressure and displacement rate on the interface friction properties were studied. Some of the salient findings of this experimental work are as follows. (1) The tangential stress-deformation relationship of the bone-metal interface is nonlinear and a relatively large displacement of about 100 to 500 pm is necessary before the maximal resistance is reached. (2) The friction coefficient appears to be independent of the bone excision site of the resurfaced tibia. Friction coefficient is also independent of the rate of relative displacement. (3) The friction coefficient of the bead porous metal-bone interface slightly diminishes ( p = 0.25) with increase in the normal contact pressure. Almost no similar variation is observed for the other metal surfaces. (4)In comparison with the smooth metal surface, the porous surfaces markedly increase the interface friction properties. There is, however, no significant differences between the two porous surfaces used in this study. This study is supported by the IRSST and the FCAR (Quebec) and the NSERC (Canada, Grant OGP0005596). Special thanks to Zimmer Inc. for providing the poroussurfaced metal samples.
References 1. H.U. Cameron, R.M. Pilliar, and I. Macnab, ”The effect of movement on the bonding of porous metal to bone,” J. Biomed. Muter. Res., 7,301311 (1973). 2. P. Ducheyne, P. DeMeester, E. Aernoudt, M. Martens, and C. Mulier, “Influence of a functional dynamic loading on bone ingrowth into surface pores of orthopedic implants,” J. Biomed. Muter. Res., 11,811-838 (1977). 3. R. M. Pilliar, J. M. Lee, and C. Maniatopoulos, ”Observations on the effect of movement on bone ingrowth into porous-surfaced implants,” Clin. Orthop. Rel. Res., 208, 109-113 (1986). 4. R. M. Pilliar, H.U. Cameron, R. P. Welsh, and A.G. Binnington, ”Radiographic and morphologic studies of load-bearing porous-surfaced structured implants,” Clin.Orthop. Rel. Res., 156, 249-257 (1981). 5. J. D. Bobyn, R. M. Pilliar, H.U. Cameron, and G.C. Weatherly, ”The optimum pore size for the fixation of porous-surfaced metal implants by the ingrowth of bone,” Clin. Orthop. Rel. Res., 150, 263-270 (1980). 6. A. J.T. Clemow, A.M. Weinstein, J. J. Klawitter, J. Koeneman, and J. Anderson, ”Interface mechanics of porous titanium implants,” J. Biomed. Muter. Res., 15, 73-82 (1981). 7. H.U. Cameron, R.M. Pilliar, and 1. Macnab, ”The rate of bone ingrowth into porous metal,” J. Biomed. Muter. Res., 10,295-302 (1976). 8. P.M. Sandborn, S.D. Cook, R.C. Anderson, W.P. Spires, and M. A. Kester, ”The effect of surgical fit on bone growth into porous coated implants,” Trans. 33th Annual Meeting, Orthopaedic Research Society, San Francisco, January 19-22, 1987, p. 217.
FRICTION AT THE BONE-METAL INTERFACE 9.
10. 11.
12. 13.
14. 15.
16. 17.
18. 19. 20.
21. 22. 23.
1519
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Received September 1, 1989 Accepted May 15,1990
