Effect of the friction coefficient between bone cement and polished stem on subsidence of the stem in total hip arthroplasty

Yuta Nakajo; Ayumi Kaneuji; Noriyuki Takano

doi:10.1016/j.jor.2025.03.055

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62 (); 148-151

doi:

10.1016/j.jor.2025.03.055

Effect of the friction coefficient between bone cement and polished stem on subsidence of the stem in total hip arthroplasty

Yuta Nakajo^a, Ayumi Kaneuji^b, Noriyuki Takano^c,

a Graduate Program in Mechanical Engineering, 3-1Yatsukaho, Hakusan, Ishikawa, 924-0838, Japan

b Department of Orthopaedic Surgery, Kanazawa Medical University, 1-1 Uchinada, Kahoku-gun, 920-0293, Ishikawa, Japan

c Integrated Technology Research Center of Medical Science and Engineering, 3-1 Yatsukaho, Hakusan, Ishikawa, 924-0838, Japan

⁎Corresponding author: Noriyuki Takano. ntakano@neptune.kanazawa-it.ac.jp

Received: 2025-3-18, Accepted: 2025-3-25, Published: 2025-3-26

Professor P K Surendran Memorial Education Foundation

Disclaimer:
This article was originally published by Reed Elsevier India Pvt. Ltd. and was migrated to Scientific Scholar after the change of Publisher.

Abstract

The effect of the friction coefficient between bone cement and polished stems on stem subsidence was investigated in total hip arthroplasty (THA) using nonlinear finite element analysis. Stem subsidence results from both stem slip and shear deformation of the cement. On the lateral side, subsidence is mainly caused by stem slip, while on the medial side, cement deformation is involved. With low friction coefficients, "Reverse subsidence" occurs after load release, where the stem moves upward, and compressive stress is transmitted to the cement. On the other hand, with high friction coefficients, more significant shear deformation of the cement mantle occurs, and residual strain accumulates in the proximal region. The present study implies a trade-off relationship: high friction increases the risk of periprosthetic fractures (PPFs) in the proximal region, while low friction increases the risk in the distal region.

Keywords

Cemented stem

Bone cement

Subsidence

Shear deformation

THA

Friction coefficient

Finite element analysis

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1 Introduction

In recent years, cementless stems have been widely used in THA. Still, a higher probability of periprosthetic fractures (PPFs) of hip arthroplasties has been reported compared with cemented stems.¹^,² The likelihood of PPFs differs for the cemented stems' material, shape, and surface roughness. Several studies show that the probability of PPFs with collarless polished tapered stems (PTS) is higher than composite beam-type stems.³^,⁴ On the other side, many studies show that the prolonged survival of PTS is better than that of a rough-surfaced stem.⁵^,⁶ Lee⁷ suggested that a rough stem gave mainly tensile and shear force to bone cement, but a polished stem gave compression force. The compressive force may have a lower risk of cement fracture than the tensile or shear force. Kaneuji et al.⁸ indicated that the subsidence induced compressive force on the bone cement in PTS through in vitro experiments. However, shear force was not estimated in their study. The subsidence is a crucial factor in both stem and cement stability.

It is influenced by the friction between the stem and cement, a variable that hinges on their materials and surface condition. Thus, the effect of the surface roughness on the stem on the force component or type of deformation in bone cement is interesting. Surface roughness on a stem highly correlates with the friction coefficient between the stem and cement.⁹ Mann et al.¹⁰ reported that the friction condition lead the sizeable tensile stress to the proximal region of cement compared with the glue condition using finite element analyses (FEA). However, the details of the effect of friction between stem and cement have not been clarified, while it has been reported between bone and stem.¹¹^,¹² The present work employs the nonlinear finite element analysis and focuses solely on the impact of the friction coefficient on the subsidence of cement mantles.

2 Numerical method

We used a femur model truncated femoral head from CT data of a female patient with hip osteoarthritis, assuming a polished tapered stem made of titanium alloys (E = 110 GPa, ν = 0.3). The shape of the stem was modeled based on the C2 stem in Lima Corp, although it was a tapered rectangular cementless stem, not a cemented stem. Young's cortical and cancellous bone modulus were set to 17 GPa and 1 GPa, respectively, with Poisson's ratios of 0.3; the bone density was assumed to be uniform. A cement mantle layer was carefully placed between the stem and the femur model, with a thickness of about 1.9 mm. The cement layer and the femur were securely glued, assuming the cement was interlocked with the bone.¹³ The friction coefficient μ between the stem and the cement mantle was varied by 0.01, 0.1, 0.2, 0.3, 0.4, 0.6, and 0.9 (0.2–0.7 in actual THA). It is known that stem subsidence increases with cyclic loading.¹⁴^,¹⁵ It indicates that the cement deforms inelastically. In the present work, a non-linear stress-strain relation between bone cement and stem, obtained by Kurz et al.,¹⁶ was used in our non-linear FEA. Its solver is the advanced non-linear analysis SOL601 in NX NASTRAN.

The femur's mesh size was 1–2 mm based on the mesh convergence test performed by Oba et al.¹⁷ The stem and cement mesh sizes were 0.9–1.1 mm and 0.4–0.7 mm, respectively. Consequently, the number of tetrahedral elements is about 882000.

As shown in Fig. 1a, the distal end of the femur was fully constrained. The proximal end surface of the stem was subjected to an articulating force equivalent to 1817 N in a downward direction of 15° relative to the femoral axis. An abductor force of 1189 N was subjected to the circular region on the greater trochanter of the femur, which radius was almost 10 mm, in an upward direction of 17.5° relative to the femoral axis as an abductor muscle force. These values assumed a body weight of 68 kgf and were based on the condition presented by Gesso.¹⁸

FEA Model and analysis conditions (a). These figures are section cut. The load induces bending of bone axis. These figures are section cut. The load induces the bending of the bone axis. As a result, points A, B, and C move to A′, B,' and C′ by the load (b).

This THA model bends in a medial direction to rotate around the femoral end under loading conditions, as shown in Fig. 1b. Since its magnitude is different between friction conditions, it is difficult to compare the magnitude of the subsidence and deformation on the deformed coordinate. Therefore, the settlement concerning the initial shape was assessed as follows. Nodes A and B on the edge of the femoral bone at the initial configuration (Fig. 1a) move to A′ and B′ by load (Fig. 1b). They are related by equations(1)A′=RAand(2)B′=RBwhere R is transition matrix. The R can be determined from these two equations since translations of nodes in the vicinity of the center of the femoral bone can be neglected along the front-back body direction under the present load condition. Then, the coordinate C″ of the reduction to the initial configuration corresponds to a node C′ is obtained by(3)C″=R−1C′

The displacement along the bone axis (z direction in Fig. 1) is estimated by the difference between the vertical component of the reduction coordinate C″ and the original coordinate C at the initial configuration, that is(4)(C″−C)z

3 Results

The node displacements were evaluated using Eq. (4). The difference between node displacements facing each other on the bone and stem surfaces indicates the magnitude of the shear deformation of the cement mantle. The difference between node displacement on the cement surface at the stem side and the stem surface at the cement side indicates subsidence due to the stem slip. These nodes were selected for the nearest neighbor, and the cement was glued to the bone; the cement nodes on the bone side were fixed on the femoral bone.

Table 1 shows the results near the distal of the stem (around point C in Fig. 1a). The stem slip decreased with the friction coefficient at maximum load conditions. It was smaller at the lateral than the medial and small over 0.4 friction coefficient. On the other hand, the shear deformation of the cement at the medial was small, and almost 10 μm over the deformation were observed in whole friction conditions at the lateral.

Table 1 Component of the subsidence of stem under each load condition with each coefficient of friction μ. It consists of shear deformation of the cement mantle and stem slip.

	μ	Cement deformation/μm		Stem slip/μm
	μ	Medial	Lateral	Medial	Lateral
Max. Load	0.01	1.10	14.75	52.55	28.40
	0.1	−0.96	15.36	41.90	14.32
	0.2	−1.89	16.73	38.39	7.96
	0.3	−2.13	17.27	33.41	2.42
	0.4	−2.33	16.62	30.74	0.19
	0.6	−2.56	13.47	27.18	0.10
	0.9	−2.78	11.90	25.42	0.06

70 % release	0.01	0.20	4.52	16.90	9.01
	0.1	0.87	4.90	22.19	14.46
	0.2	0.33	6.87	19.80	9.06
	0.3	−0.10	7.35	15.86	4.29
	0.4	−0.43	8.60	15.01	1.24
	0.6	−0.64	6.74	12.06	0.20
	0.9	−0.65	5.02	9.32	0.11

100 % release	0.01	−0.00	−0.00	−24.32	−24.35
	0.1	−0.00	−0.00	−12.28	−12.30
	0.2	−0.00	−0.00	−0.48	−0.51
	0.3	−0.00	−0.00	−0.80	−0.82
	0.4	−0.00	−0.00	−1.17	−1.18
	0.6	−0.00	−0.00	−0.82	−0.82
	0.9	−0.00	−0.00	−2.28	−2.28

After the load was released, the stem moved upwards with a low friction coefficient, and the cement deformation was almost released. However, the stem did not move upward when the load drop stayed at 70 % released condition.

4 Discussion

The present results show the different behavior between medial and lateral. The stem subsidence is caused by both the stem slip and the cement deformation at the lateral, but mainly by the stem slip at the lateral. Since the stem bends forward the medial, the contact force between the stem and cement is considered high at the lateral. Even if the friction coefficient is the same, the friction force is more significant at the lateral than at the medial. Of course, the slip occurs at the lateral if the friction coefficient is small.

Dropping the load, slip, and deformation is decreasing. However, the stem moved upwards for a low friction coefficient, and the cement deformation was almost released. Its stem's motion was observed experimentally in vitro by Kaneuji et al.,¹⁹ who called it 'reverse subsidence'. It is considered to be due to the plastic deformation of the cement and a reduction in its width. Table 2 shows the change in the width of the cement mantle, that is, the length of the cement mantle perpendicular to the paper surface after the load was released. The reduction of the width is significant for low friction coefficients in proximal. The cement mantle is extended along the horizontal direction in Fig. 1 by bending so that the width of the cement mantle may be shortened.

Table 2 Change of width of cement mantle due to the coefficient of friction μ.

μ	Proximal/μm	Distal/μm
0.01	−1.08	0.01
0.1	−0.54	−0.00
0.2	−0.01	−0.00
0.3	−0.01	0.00
0.4	−0.03	−0.00
0.6	−0.01	−0.01
0.9	−0.08	0.00

The load cannot be released entirely clinically. Table 2 corresponds to this condition. Namely, the stem did not move upward when the load drop stayed at 70 % released condition.

The stem's subsidence due to slip is considered to compress the cement mantle, but the subsidence with the shear deformation of cement does not lead to compressive stress. Fig. 2 shows the section-cut diagrams of the Von Mieses stress distribution in the cement mantle. Stress at the proximal and the stem top was high, with a low friction coefficient. It agrees with Lee's results.⁷ The former may decrease the risk of stress shielding, but the latter may induce the PPF. Furthermore, residual strain remained in the proximal area, as shown in Fig. 3. This tendency is more significant due to the shear deformation of the cement mantle with more significant friction coefficients. The immense friction coefficient may induce PPF in the proximal area due to storage residual strain caused by the cyclic load. Therefore, the risk of PPF is high at the proximal region with the high friction coefficient and at the distal region with the low friction coefficient. They are trade-off relations.

Von Mieses stress distribution at maximum load condition. These figures are section cut. The friction coefficient is 0.01 (a), 0.4 (b) and 0.9 (c).

Von Mieses strain distribution after load released. These figures are section cut. The friction coefficient is 0.01 (a), 0.4 (b) and 0.9 (c).

The quantitative discussion has limitations in the present work: First, it assumes uniform bone density. Second, pseudoelastic behavior is not considered in the present calculation. Third, numerical results may change according to bone and stem shape. In particular, we did not use a regular PTS model. However, the qualitative behavior of the cement mantle is believed to be similar.

5 Conclusions

The stem subsidence contributes to the stem slip and the shear deformation of cement. Its ratio varied with the friction coefficient between stem and bone cement. Considerable friction between the stem and cement induces shear deformation at the lateral. Slight friction leads to slip but does not induce the shear deformation of cement. The slip causes compressive stress on the cement, but the shear deformation does not. On the other hand, significant friction induces residual strain in the proximal region. Moreover, the slight friction causes reverse subsidence after the released load. The effect of cyclic load and stem shape will be researched.

CRediT authorship contribution statement

Yuta Nakajo: Formal analysis, Investigation, Writing – original draft. Ayumi Kaneuji: Conceptualization, Writing – review & editing. Noriyuki Takano: Methodology, Data curation, Writing – review & editing, Visualization, Supervision.

Ethical statement

This study is computational only and does not raise ethical issues.

Funding

This research did not receive any specific grant.

References

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Yates P.J., Burston B.J., Whitley E., Bannister G.C., . Collarless polished tapered stem CLINICAL AND RADIOLOGICAL RESULTS AT A MINIMUM OF TEN. J Bone Joint Surg. 2008;90:16-22.
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Introduction

Numerical method

Results

Discussion

Conclusions

CRediT authorship contribution statement

Patient consent

Ethical statement

Funding

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[1] Abdel M.P., Watts C.D., Houdek M.T., Lewallen D.G., Berry D.J., . Epidemiology of periprosthetic fracture of the femur in 32 644 primary total hip arthroplasties: a 40-year experience. Bone Joint Lett J. 2016;98-B:461-467.
[Google Scholar]

[2] Heu J.-Y., Kim J.-Y., Lee S.-W., . Periprosthetic fracture around a cemented stem in total hip arthroplasty. Hip Pelvis. 2022;34:140-149.
[Google Scholar]

[3] Scott T., Salvatore A., Woo P., et al . Cemented stems for primary hip arthroplasty may exhibit high rate of periprosthetic fracture at short-term follow-up. J Arthroplast. 2018;33:1120-1125.
[Google Scholar]

[4] Mellner C., Mohammed J., Larsson M., et al . Increased risk for postoperative periprosthetic fracture in hip fracture patients with the Exeter stem than the anatomic SP2 Lubinus stem. Eur J Trauma Emerg Surg. 2021;47:803-809.
[Google Scholar]

[5] Dall D.M., Learmonth I.D., Solomon M.I., Miles A.W., Davenport J.M., . Fracture and loosening of Charnley femoral stems. Comparison between first-generation and subsequent designs. J Bone Joint Surg. 1993;75:259-265.
[Google Scholar]

[6] Collis D.K., Mohler C.G., . Comparison of clinical outcomes in total hip arthroplasty using rough and polished cemented stems with essentially the same geometry. J Bone Joint Surg. 2002;84:586-592.
[Google Scholar]

[7] Lee A.J.C., . The time-dependent properties of polymethylmethacrylate bone cement: the interaction of shape of femoral stems surface finish and bone cement. 1990:11-19.
[Google Scholar]

[8] Kaneuji A., Yamada K., Hirosaki K., Takano T., Matsumoto T., . Stem subsidence of polished and rough double-taper stems: in vitro mechanical effects on the cement-bone interface. Acta Orthop. 2009;80(3):270-276.
[Google Scholar]

[9] Hirata M., Oe K., Kaneuji A., Uozu R., Shintani K., Saito T., . Relationship between the surface roughness of material and bone cement: an increased “polished” stem may result in the excessive taper-slip. Materials. 2021;14
[Google Scholar]

[10] Mann K.A., Bartel D.L., Wright T.M., Burstein A.H., . Coulomb frictional interfaces in modeling cemented total HIP replacements: a more realistic model. J Biomech. 1995;28(9):1062-1078.
[Google Scholar]

[11] Raffa M.L., Nguyen V.-H., Hernigou P., Flouzat‐Lachaniette C.-H., Haiat G., . Stress shielding at the bone‐implant interface: influence of surface roughness and of the bone‐implant contact ratio. J Orthop Res. 2021;39:1174-1183.
[Google Scholar]

[12] Immel K., Nguyen V.-H., Haïat G., Sauer R.A., . Modeling the debonding process of osseointegrated implants due to coupled adhesion and friction. Biomech Model Mechanobiol. 2023;22:133-158.
[Google Scholar]

[13] Jensen D., Mann K.A., Verdonschot N., . Micromechanical modeling of the cement-bone interface: the effect of friction, morphology and material properties on the micromechanical response. J Biomech. 2008;41(15):3158-3163.
[Google Scholar]

[14] Yates P.J., Burston B.J., Whitley E., Bannister G.C., . Collarless polished tapered stem CLINICAL AND RADIOLOGICAL RESULTS AT A MINIMUM OF TEN. J Bone Joint Surg. 2008;90:16-22.
[Google Scholar]

[15] Numata Y., Kaneuji A., Kerboull L., et al . Biomechanical behaviour of a French femoral component with thin cement mantle: the ‘French paradox’ may not be a paradox after all. Bone Joint Res. 2018;7:485-493.
[Google Scholar]

[16] Kurz S.M., Villarraga M.L., Zhao K., Edidin A.A., . Static and fatigue mechanical behavior of bone cement with elevated barium sulfate content for treatment of vertebral compression fractures. Biomaterials. 2005;26:3699-3712.
[Google Scholar]

[17] Oba M., Inaba Y., Kobayashi N., Ike H., Tezuka T., Saito T., . Effect of femoral canal shape on mechanical stress distribution and adaptive bone remodeling around a cementless tapered-wedge stem. Bone & Joint Research. 2016;5(9):362-369.
[Google Scholar]

[18] Gesso H., . Bone density equation in the future. Jpn J Clinic Biomech. 1995;16:213-216.
[Google Scholar]

[19] Kaneuji A., Chen M., Takahashi E., et al . Collarless polished tapered stems of identical shape provide differing outcomes for stainless steel and cobalt chrome: a biomechanical study. J Funct Biomater. 2023;14
[Google Scholar]

Effect of the friction coefficient between bone cement and polished stem on subsidence of the stem in total hip arthroplasty

Abstract