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The Role of Synovial Fluid in Joint Lubrication
Lubricants and Lubrication / D. Dowson et al. (Editors) B.V. All rights reserved.
0 1995 Elsevier Science
65
The Role of Synovial Fluid in Joint Lubrication by K.Ikeuchi Research Center for Biomedical Engineering, Kyoto University Kyoto 606-01, Japan This paper reviews some of the recent trends in lubrication 0, natural and artificial joints focusing the functions of synovial fluid. While elasto-hydrodynamic lubrication is the major mechanism in human joints, they operate with adaptive multimode lubrication. Though the effect of cartilage porosity is small in fluid film lubrication condition, fluid may be pressed out from the cartilage to the gap in mixed lubrication region and it lubricates cartilage effectively. Cushion form joint proved to result better lubrication condition. However, it needs the assistance of supplemental lubrications at start up. 1. INTRODUCTION
In a leg joint, fluid film may be formed due to hydraulic wedge effect during swing phase of a walking cycle. Then, the film of synovial fluid survives for a while due to squeeze film effect. As articular cartilage is compliant, elasto-hydrodynamic lubrication (EHL) makes the fluid film more reliable. Therefore, it would be reasonable to conclude that a gap in a human joint is almost in hydrodynamic lubrication condition.
\Elasto- hy drodynamic Lubrication\
On the other hand, articular cartilage inevitably contacts with the mating cartilage because a joint keeps stationary state under heavy load, and sliding velocity is sometimes too low for sufficient fluid film formation. When direct contact arises, supplemental lubrication acts to prevent wear of cartilage (Fig. 1). This mechanism [1,2] is called adaptive multiple lubrication. The life of an artificial joint is usually much shorter than human life, because the lubrication condition is much severer than that in a natural joint. However, it would be possible to form fluid film in an artificial joint, if the sliding surface is as compliant as articular cartilage. According to this concept [3,4], cushion form bearing of compliant material was proposed and investigated. However, supplemental lubrication seems to be necessary in a compliant joint as in a natural joint. 2. NATURAL JOINTS
Figure 1. Schematic representation of lubrication in natural joint.
2.1 Elasto-hydrodynamic lubrication As sliding surface of a natural joint is covered with cartilage, its lubrication condition is analyzed by soft-EHL theory [5,6]. According to computer simulation,
66
squeeze film effect is predominant at the moments of heel strike and toe off due to rapid change of joint load. Hydraulic wedge effect takes place with slide-roll motion during swing phase and stance phase. According to micro-EHL theory [7], fluctuation of film pressure caused by surface waviness flattens the cartilage surface and forms fluid film between almost smoothed surfaces, if the cartilage is compliant enough and the wavelength is long. As synovial fluid is non-Newtonian liquid, its viscosity decreases with an increase in shear rate. Consequently, for pressure induced flow, shear rate decreases, viscosity increases and flow rate decreases with a decrease of film thickness. In contrast, for shear induced flow, shear rate increases and viscosity decreases with a decrease of film thickness. Therefore, in a gap lubricated with non-Newtonian fluid, fluid film is maintained principally due to squeeze film effect, as film thickness approaches the lower limit for non-contacting condition.
2.2 Flow through cartilage Water which flows through porous articular cartilage may affect the lubrication condition. McCutchen [8] described that, as fluid escapes from the load-bearing region, fluid is wept into the crack to supply the crack flow. On the other hand, Walker, et al. [9] reported, concerning to their boosted lubrication theory, that water flows from the gap into the cartilage in response to pressure gradient. As macromolecule protein and hyaluronic acid cannot pass through the cartilage, they are left in the gap. Consequently, the thickened synovial fluid lubricates the cartilage more effectively. Figure 2 shows that the two models predict different flow directions in cartilage. Recently, Jin, et al., [lo] analyzed squeeze film effect between a flat cartilage and a spherical thruster. The result shows that water flows from the pressurized region of the gap into the cartilage, while water flows
out of the cartilage at the surrounding low pressure zone. As the flow through the cartilage is added to the flow through the gap, total outward flow increases and hence the film thickness decreases more rapidly. However, this disadvantageous effect on fluid film is acceptably small because the permeability of the cartilage is very low. Hou, et al. [ll] obtained similar result by biphasic theory. The both numerical results show that the flow through the cartilage does not contribute to squeeze film lubrication.
Condknsed fluid
Boosted 191 Lubrication
Weeping PI Lubrication
Figure 2. Flow directions in joint. On the other hand, Ikeuchi and Oka [12] considered direct contact on the cartilage surface and non-Newtonian viscosity of synovial fluid in the analysis of squeeze film effect in a human hip joint. According to the computer analysis, cartilage contacts in 0.1s after step loading because the viscosity of synovial fluid is low in the early thick fluid film. Then, water is pressed out from the cartilage into the gap, and it contributes to keeping contact pressure low. To verify this theoretical prediction, Ikeuchi, et al. [13] pressed articular cartilage with saline or porous solid, and measured time dependent surface deflection. At the experiment with saline which simulated fluid film lubrication, no deformation was detected. In contrast, considerable creep deformation was measured when it was pressed by cloth in the experiment which simulated solid contact.
67
In summary, when complete fluid film is kept, water flows from the pressurized region of the gap to the low pressure region through the cartilage. However, the rate of this additional outward flow is much smaller than the flow through the gap, because permeability of the cartilage is very low. On the other hand, when cartilage contacts directly, fluid pressure rises in the cartilage, and water is pressed out from the cartilage to the gap (Fig. 3). As fluid pressure changes only in the very thin region beneath the cartilage surface in a short time after loading, pressure gradient may become high even if contact pressure is low. Thus, water is pressed out to the gap in mixed lubrication condition, lubricates the cartilage surface and reduces contact pressure.
Poro-Elastic Lubrication Long Path and low (Fluid film lubrication)\ pressure gradient
Recently, Higaki, et al. [15] used synthetic lubricants with constituents which are contained in natural synovial fluid. According to their oscillating friction test, only the water solution of hyaluronic acid and y-Globulin lubricated cartilage as well as natural synovial fluid. On the other hand, synthetic fluid with similar constituents as natural synovial fluid resulted high friction coefficient. The effect of lipid (phosphatidylcholine) contained in synovial fluid on boundary lubrication was investigated [16].
3. ARTIFICIAL JOINTS Figure 4 shows the schematic representation of lubrication in an artificial joint. Synovial fluid lubricates articular cartilage well, but it scarcely contributes to lubrication and surface protection from wear. However, we are obliged to use existing synovial fluid as lubricant. Lubrication condition of an artificial joint depends on the materials in the term of compliance.
High pressure zone
Push out lubrication (Mixed lubrication region) Figure 3. Flow directions corresponding to lubrication conditions.
2.3 Boundary lubrication The roles of the constituents of synovial fluid in lubrication have been investigated. According to friction test with synovial fluid in which hyaluronic acid or protein was digested by enzyme, protein lubricated cartilage while hyaluronic acid did not [14].
synovial fluid as lubricant.
Figure 4. Schematic representation of lubrication in artificial joint.
68
3.1 Joint materials In a joint of ceramic or metal, stress concentration and resultant abrasive wear may arise due to the high elastic modulus of the materials in spite of their high wear resistance, Therefore, a hard joint should be designed to have highly conformed geometry and should be finished very precisely. Further tribological study seems to be necessary, because the lubrication condition of a hard joint is entirely deferent from that in a natural joint. Most of the artificial joints are composed of ultra-high molecular weight polyethylene (UHMWPE) and stainless steel, chromium alloy or alumina ceramic. Due to high wear resistance, compliance and biocompatibility, UHMWPE is an excellent material for artificial joints. However, the effect of fluid film lubrication is limited in a joint of UHMWPE, because its elastic modulus is significantly higher than that of articular cartilage. We may think that a joint of more compliant material (cushion form bearing) leads to fluid film lubrication condition as easily as natural joint does [3,4]. Therefore, computer analyses and experimental studies of lubrication condition in compliant joints have been practiced to confirm the idea of cushion form bearing. However, as direct contact is inevitable even in a compliant joint at start up after a long standstill, mixed lubrication condition in artificial joints was studied [17,18]. On the other hand, we probably need to make use of the effect of supplemental lubrication like poro-elastic lubrication, boundary lubrication or solid lubrication. Sliding friction was measured between a non porous polyurethane layer and a porous hydrogel layer [19]. When contact zone moved on the porous layer, coefficient of friction was significantly lower than the ones with contact zone fixed to the porous layer. They proved that good lubrication condition
is realized when load moves on a porous layer. Oka et al. [20] have developed a new surface replacement prosthesis of polyvinyl alcohol hydrogel. (Fig. 5). They attached a gel layer to canine knees by titanium fiber mesh. The prostheses are under in vivo endurance test now.
I
t
Penetratipn at mo9lding I
-t
t
Bone ingrowth after replacement Titanium fiber Subchondral bone Figure 5. New surface replacement prosthesis
3.2 Sealed joint with artificial joint capsule Wear particles formed in an artificial joint may result tissue response, bone absorption and loosening of the joint. Figure 6 shows a new prosthesis with an artificial joint capsule of compliant membrane in which synthetic lubricant is sealed [21]. Extremely low wear rate is expected with artificial synovial fluid which lubricates joint materials well. As small amounts of wear particles are trapped in the capsule, they result no biological response. The most important point of this joint is high reliability of the capsule for many years. The capsules of silicon rubber survived in fatigue test for 3x10’ cycles, which corresponded to more than 20 years use. Further environmental fatigue tests and in vivo tests will be necessary before the clinical application.
69 4. SUMMARY Articular cartilage is lubricated principally by hydrodynamic lubricating film, with supplemental lubrication mechanisms. Although a modern artificial joint which applies high technology is one of the most successful artificial organs, its life time is usually shorter than the life of a natural joint. Further contribution of tribology is hence required to develop a prosthesis of new generation for permanent use. However, we must remind that a basic study about what happens in the gap is generally more useful than a superficial knowledge of tribology . REFERENCES 1. Dowson, D., Proc. IME, 181, Pt. 35 (1967) 45. 2. T. Murakami, JSME International J., Ser. 3,33,4 (1990) 465. 3. D. Dowson, J. Fisher, Z,M. Jin, D.D. Auger and B. Jobbins, Proc. IME, Pt. H, 205 (1991) 59. 4. D.D. Auger, D. Dowson and J. Fisher, Proc. 19th Leeds-Lyon Symp. on Trib. (1993) 683. 5. K. Ikeuchi, H. Mori, T. Ohkubo and S. Ichi, Bulletin of JSME, 25,202 (1982) 646. 6. J.B. Medley and D. Dowson, ASLE Trans., 27,3 (1984) 243. 7. D. Dowson and Z.M. Jin, Engineering in Medicine, 15,2 (1986) 63. 8. C.W. McCutchen, Proc. IME, 181, Pt. 35 (1967) 55. 9. P.S. Walker, D. Dowson, M.D. Longfield and V. Wright, Ann. Rheum. Dis., 27 (1968) 364. 10. Z.M. Jin, D. Dowson and J. Fisher, Proc. IME, Pt. H, 206 (1992) 117. 11. J.S.Hou, V.C. Mow, W.M. Lai and M.H. Holmes, J. Biomechanics, 25, 3 (1992) 247.
\
Socket
A' c/'
Femoral head
Joint capsule
Stem
Figure 6. Cross sectional view of sealed joint. 12. K. Ikeuchi and M. Oka, Proc. 19th Leeds Lyon Symp. on Trib. (1993) 513. 13. K. Ikeuchi, M. Oka and S. Kubo, Proc. 20th Leeds-Lyon Symp. on Trib. (1994) 247. 14. H. Chikama, J. Japanese Orthop. Ass., 59 (1985) 559 (in Japanese). 15. H. Higaki, T. Murakami and H. Ando, Proc. JAST Trib. Conf. Nagoya (1993) 607 (in Japanese). 16. P.S. Williams, G.L.Powell and M. LaBerge, Proc. IME, Pt. H, 207 (1993) 59. 17. K. Ikeuchi, H. Mori and Y.Murai, Japanese J.Tribology, 34,9 (1989) 1067. 18. K. Ikeuchi, Y. Kusuyama, N. Shibata and T. Ohsumi, Japanese J. Tribologist, 38,4 (1993) 533. 19. L. Calavia, D. Dowson, J. Fisher, P.H. Corkhill and B.J. Tighe, Proc. 19th Leeds-Lyon Symp. on Trib. (1993) 529. 20. M. Oka, et al., Biomech. in Orthop. (1992) 282, Springer-Verlag. 21. K. Ikeuchi, et al., Proc. Japanese SOC. Orth. Biomech., 14 (1993) 221 (in Japanese).
0 1995 Elsevier Science
65
The Role of Synovial Fluid in Joint Lubrication by K.Ikeuchi Research Center for Biomedical Engineering, Kyoto University Kyoto 606-01, Japan This paper reviews some of the recent trends in lubrication 0, natural and artificial joints focusing the functions of synovial fluid. While elasto-hydrodynamic lubrication is the major mechanism in human joints, they operate with adaptive multimode lubrication. Though the effect of cartilage porosity is small in fluid film lubrication condition, fluid may be pressed out from the cartilage to the gap in mixed lubrication region and it lubricates cartilage effectively. Cushion form joint proved to result better lubrication condition. However, it needs the assistance of supplemental lubrications at start up. 1. INTRODUCTION
In a leg joint, fluid film may be formed due to hydraulic wedge effect during swing phase of a walking cycle. Then, the film of synovial fluid survives for a while due to squeeze film effect. As articular cartilage is compliant, elasto-hydrodynamic lubrication (EHL) makes the fluid film more reliable. Therefore, it would be reasonable to conclude that a gap in a human joint is almost in hydrodynamic lubrication condition.
\Elasto- hy drodynamic Lubrication\
On the other hand, articular cartilage inevitably contacts with the mating cartilage because a joint keeps stationary state under heavy load, and sliding velocity is sometimes too low for sufficient fluid film formation. When direct contact arises, supplemental lubrication acts to prevent wear of cartilage (Fig. 1). This mechanism [1,2] is called adaptive multiple lubrication. The life of an artificial joint is usually much shorter than human life, because the lubrication condition is much severer than that in a natural joint. However, it would be possible to form fluid film in an artificial joint, if the sliding surface is as compliant as articular cartilage. According to this concept [3,4], cushion form bearing of compliant material was proposed and investigated. However, supplemental lubrication seems to be necessary in a compliant joint as in a natural joint. 2. NATURAL JOINTS
Figure 1. Schematic representation of lubrication in natural joint.
2.1 Elasto-hydrodynamic lubrication As sliding surface of a natural joint is covered with cartilage, its lubrication condition is analyzed by soft-EHL theory [5,6]. According to computer simulation,
66
squeeze film effect is predominant at the moments of heel strike and toe off due to rapid change of joint load. Hydraulic wedge effect takes place with slide-roll motion during swing phase and stance phase. According to micro-EHL theory [7], fluctuation of film pressure caused by surface waviness flattens the cartilage surface and forms fluid film between almost smoothed surfaces, if the cartilage is compliant enough and the wavelength is long. As synovial fluid is non-Newtonian liquid, its viscosity decreases with an increase in shear rate. Consequently, for pressure induced flow, shear rate decreases, viscosity increases and flow rate decreases with a decrease of film thickness. In contrast, for shear induced flow, shear rate increases and viscosity decreases with a decrease of film thickness. Therefore, in a gap lubricated with non-Newtonian fluid, fluid film is maintained principally due to squeeze film effect, as film thickness approaches the lower limit for non-contacting condition.
2.2 Flow through cartilage Water which flows through porous articular cartilage may affect the lubrication condition. McCutchen [8] described that, as fluid escapes from the load-bearing region, fluid is wept into the crack to supply the crack flow. On the other hand, Walker, et al. [9] reported, concerning to their boosted lubrication theory, that water flows from the gap into the cartilage in response to pressure gradient. As macromolecule protein and hyaluronic acid cannot pass through the cartilage, they are left in the gap. Consequently, the thickened synovial fluid lubricates the cartilage more effectively. Figure 2 shows that the two models predict different flow directions in cartilage. Recently, Jin, et al., [lo] analyzed squeeze film effect between a flat cartilage and a spherical thruster. The result shows that water flows from the pressurized region of the gap into the cartilage, while water flows
out of the cartilage at the surrounding low pressure zone. As the flow through the cartilage is added to the flow through the gap, total outward flow increases and hence the film thickness decreases more rapidly. However, this disadvantageous effect on fluid film is acceptably small because the permeability of the cartilage is very low. Hou, et al. [ll] obtained similar result by biphasic theory. The both numerical results show that the flow through the cartilage does not contribute to squeeze film lubrication.
Condknsed fluid
Boosted 191 Lubrication
Weeping PI Lubrication
Figure 2. Flow directions in joint. On the other hand, Ikeuchi and Oka [12] considered direct contact on the cartilage surface and non-Newtonian viscosity of synovial fluid in the analysis of squeeze film effect in a human hip joint. According to the computer analysis, cartilage contacts in 0.1s after step loading because the viscosity of synovial fluid is low in the early thick fluid film. Then, water is pressed out from the cartilage into the gap, and it contributes to keeping contact pressure low. To verify this theoretical prediction, Ikeuchi, et al. [13] pressed articular cartilage with saline or porous solid, and measured time dependent surface deflection. At the experiment with saline which simulated fluid film lubrication, no deformation was detected. In contrast, considerable creep deformation was measured when it was pressed by cloth in the experiment which simulated solid contact.
67
In summary, when complete fluid film is kept, water flows from the pressurized region of the gap to the low pressure region through the cartilage. However, the rate of this additional outward flow is much smaller than the flow through the gap, because permeability of the cartilage is very low. On the other hand, when cartilage contacts directly, fluid pressure rises in the cartilage, and water is pressed out from the cartilage to the gap (Fig. 3). As fluid pressure changes only in the very thin region beneath the cartilage surface in a short time after loading, pressure gradient may become high even if contact pressure is low. Thus, water is pressed out to the gap in mixed lubrication condition, lubricates the cartilage surface and reduces contact pressure.
Poro-Elastic Lubrication Long Path and low (Fluid film lubrication)\ pressure gradient
Recently, Higaki, et al. [15] used synthetic lubricants with constituents which are contained in natural synovial fluid. According to their oscillating friction test, only the water solution of hyaluronic acid and y-Globulin lubricated cartilage as well as natural synovial fluid. On the other hand, synthetic fluid with similar constituents as natural synovial fluid resulted high friction coefficient. The effect of lipid (phosphatidylcholine) contained in synovial fluid on boundary lubrication was investigated [16].
3. ARTIFICIAL JOINTS Figure 4 shows the schematic representation of lubrication in an artificial joint. Synovial fluid lubricates articular cartilage well, but it scarcely contributes to lubrication and surface protection from wear. However, we are obliged to use existing synovial fluid as lubricant. Lubrication condition of an artificial joint depends on the materials in the term of compliance.
High pressure zone
Push out lubrication (Mixed lubrication region) Figure 3. Flow directions corresponding to lubrication conditions.
2.3 Boundary lubrication The roles of the constituents of synovial fluid in lubrication have been investigated. According to friction test with synovial fluid in which hyaluronic acid or protein was digested by enzyme, protein lubricated cartilage while hyaluronic acid did not [14].
synovial fluid as lubricant.
Figure 4. Schematic representation of lubrication in artificial joint.
68
3.1 Joint materials In a joint of ceramic or metal, stress concentration and resultant abrasive wear may arise due to the high elastic modulus of the materials in spite of their high wear resistance, Therefore, a hard joint should be designed to have highly conformed geometry and should be finished very precisely. Further tribological study seems to be necessary, because the lubrication condition of a hard joint is entirely deferent from that in a natural joint. Most of the artificial joints are composed of ultra-high molecular weight polyethylene (UHMWPE) and stainless steel, chromium alloy or alumina ceramic. Due to high wear resistance, compliance and biocompatibility, UHMWPE is an excellent material for artificial joints. However, the effect of fluid film lubrication is limited in a joint of UHMWPE, because its elastic modulus is significantly higher than that of articular cartilage. We may think that a joint of more compliant material (cushion form bearing) leads to fluid film lubrication condition as easily as natural joint does [3,4]. Therefore, computer analyses and experimental studies of lubrication condition in compliant joints have been practiced to confirm the idea of cushion form bearing. However, as direct contact is inevitable even in a compliant joint at start up after a long standstill, mixed lubrication condition in artificial joints was studied [17,18]. On the other hand, we probably need to make use of the effect of supplemental lubrication like poro-elastic lubrication, boundary lubrication or solid lubrication. Sliding friction was measured between a non porous polyurethane layer and a porous hydrogel layer [19]. When contact zone moved on the porous layer, coefficient of friction was significantly lower than the ones with contact zone fixed to the porous layer. They proved that good lubrication condition
is realized when load moves on a porous layer. Oka et al. [20] have developed a new surface replacement prosthesis of polyvinyl alcohol hydrogel. (Fig. 5). They attached a gel layer to canine knees by titanium fiber mesh. The prostheses are under in vivo endurance test now.
I
t
Penetratipn at mo9lding I
-t
t
Bone ingrowth after replacement Titanium fiber Subchondral bone Figure 5. New surface replacement prosthesis
3.2 Sealed joint with artificial joint capsule Wear particles formed in an artificial joint may result tissue response, bone absorption and loosening of the joint. Figure 6 shows a new prosthesis with an artificial joint capsule of compliant membrane in which synthetic lubricant is sealed [21]. Extremely low wear rate is expected with artificial synovial fluid which lubricates joint materials well. As small amounts of wear particles are trapped in the capsule, they result no biological response. The most important point of this joint is high reliability of the capsule for many years. The capsules of silicon rubber survived in fatigue test for 3x10’ cycles, which corresponded to more than 20 years use. Further environmental fatigue tests and in vivo tests will be necessary before the clinical application.
69 4. SUMMARY Articular cartilage is lubricated principally by hydrodynamic lubricating film, with supplemental lubrication mechanisms. Although a modern artificial joint which applies high technology is one of the most successful artificial organs, its life time is usually shorter than the life of a natural joint. Further contribution of tribology is hence required to develop a prosthesis of new generation for permanent use. However, we must remind that a basic study about what happens in the gap is generally more useful than a superficial knowledge of tribology . REFERENCES 1. Dowson, D., Proc. IME, 181, Pt. 35 (1967) 45. 2. T. Murakami, JSME International J., Ser. 3,33,4 (1990) 465. 3. D. Dowson, J. Fisher, Z,M. Jin, D.D. Auger and B. Jobbins, Proc. IME, Pt. H, 205 (1991) 59. 4. D.D. Auger, D. Dowson and J. Fisher, Proc. 19th Leeds-Lyon Symp. on Trib. (1993) 683. 5. K. Ikeuchi, H. Mori, T. Ohkubo and S. Ichi, Bulletin of JSME, 25,202 (1982) 646. 6. J.B. Medley and D. Dowson, ASLE Trans., 27,3 (1984) 243. 7. D. Dowson and Z.M. Jin, Engineering in Medicine, 15,2 (1986) 63. 8. C.W. McCutchen, Proc. IME, 181, Pt. 35 (1967) 55. 9. P.S. Walker, D. Dowson, M.D. Longfield and V. Wright, Ann. Rheum. Dis., 27 (1968) 364. 10. Z.M. Jin, D. Dowson and J. Fisher, Proc. IME, Pt. H, 206 (1992) 117. 11. J.S.Hou, V.C. Mow, W.M. Lai and M.H. Holmes, J. Biomechanics, 25, 3 (1992) 247.
\
Socket
A' c/'
Femoral head
Joint capsule
Stem
Figure 6. Cross sectional view of sealed joint. 12. K. Ikeuchi and M. Oka, Proc. 19th Leeds Lyon Symp. on Trib. (1993) 513. 13. K. Ikeuchi, M. Oka and S. Kubo, Proc. 20th Leeds-Lyon Symp. on Trib. (1994) 247. 14. H. Chikama, J. Japanese Orthop. Ass., 59 (1985) 559 (in Japanese). 15. H. Higaki, T. Murakami and H. Ando, Proc. JAST Trib. Conf. Nagoya (1993) 607 (in Japanese). 16. P.S. Williams, G.L.Powell and M. LaBerge, Proc. IME, Pt. H, 207 (1993) 59. 17. K. Ikeuchi, H. Mori and Y.Murai, Japanese J.Tribology, 34,9 (1989) 1067. 18. K. Ikeuchi, Y. Kusuyama, N. Shibata and T. Ohsumi, Japanese J. Tribologist, 38,4 (1993) 533. 19. L. Calavia, D. Dowson, J. Fisher, P.H. Corkhill and B.J. Tighe, Proc. 19th Leeds-Lyon Symp. on Trib. (1993) 529. 20. M. Oka, et al., Biomech. in Orthop. (1992) 282, Springer-Verlag. 21. K. Ikeuchi, et al., Proc. Japanese SOC. Orth. Biomech., 14 (1993) 221 (in Japanese).