Fatigue failure in the cement mantle of a simplified acetabular replacement model

Abstract

Although the role of fatigue failure in aseptic loosening of cemented total hip replacements has been extensively studied in femoral components, studies of fatigue failure in cement mantle of acetabular replacements have yet to be reported, despite that the long-term failure rate in the latter is about three times that of femoral components. Part of the reason may be that a complex pelvic bone structure does not land itself readily for a 2D representation as that of a femur.

In this work, a simple multilayer model has been developed to reproduce the stress distributions in the cement mantle of an acetabular replacement from a plane strain finite element pelvic bone model. The experimental multilayer model was subjected to cyclic loading up to peak hip contact force during normal walking. Radial fatigue cracks were observed in the vicinity of the maximum tangential and compressive stresses, as predicted by the FE models. Typical fatigue striations were also observed on the fracture surfaces post cyclic testing. The results were examined in the context of retrieval studies, 3D FE analysis and in vitro experimental results using full-sized hemi-pelvic bone models.

1. Introduction

Late failure of implants in the absence of infection, known as “aseptic loosening”, has been identified as the most common cause for long-term instability leading to gross migration of the implants and failure of total hip replacements (THRs) [1,2]. Fig. 1 shows a schematic of a cemented THR, where the femoral head and acetabular cup are fixed with bone cement. The role of fatigue failure in aseptic loosening of cemented THRs has been studied extensively in femoral components [3-12]. Maloney et al. [3] observed cracks in retrieved cement mantles; Topoleski et al. [4] reported a fractographic study of ex vivo cement mantles and showed remarkable similarity in fracture surfaces between in vivo and in vitro specimens. Jasty et al. [5] observed fatigue striations in femora retrieved at postmortem from otherwise satisfactory total hip arthroplasties. The significance of this latter work lies in the evidence of fatigue failure from symptom free patients at periods of between 2 weeks to 17 years post-operation, suggesting fatigue as one of the possible failure mechanisms that initiates the failure of the cement fixation. In addition to retrieval studies [3-6], in vitro fatigue testing of femoral implants has also been carried out [7-9]. An experimental model [7,8] was developed to represent a cemented femoral implantation with “windows” that permit monitoring of fatigue crack growth in situ. Multiple microcracks were observed with over 80% in the cement mantle. Radial cracks were observed in transverse cross-sections of implanted femora [9]. Finite element methods have also been used to simulate the fatigue damage accumulation in the cement mantle [10-12]. Stolk et al. [10] developed a finite element algorithm that simulated creep and fatigue damage accumulation in acrylic bone cement. Damage development in tubular cement specimens and cement mantles around femoral implants was successfully simulated. Although numerous experimental studies of micro-cracking in bulk cement provide essential information on the crack initiation and growth in cement specimens, the conclusions drawn from these experiments are often difficult to apply to the cement mantle in cemented joint replacements, as the stress state in a cement mantle is inevitably multiaxial and variable, could not be adequately represented by material testing of cement specimens. Consequently, in vitro fatigue experiments of cemented implants are preferred, as the loading conditions are closer to those in vivo.

Fig. 1.

A schematic of a cemented acetabular replacement in a total hip replacement [10].

Evidence from retrieval studies and in vitro experiments seems to support the hypothesis that cement mantles fail by fatigue. For femoral components, the accumulated damage failure scenario is thought to be one of the most prominent ones in cemented THRs [13]. Mechanical damage in the form of microcracks accumulates under cyclic loading conditions, cracks coalesce and form macrocracks, leading to disintegrition of the cement mantle and eventually to gross loosening of the implant. Although the late loosening rate of acetabular cups has been reported to be three times that of femoral components 20 years after operation [14], mechanistic studies of fatigue failure in the cement mantle of acetabular replacements have yet to be reported. Structurally, an acetabulum is more complex than a femur, in that the 3D structure of pelvic bone does not permit a ready 2D representation as that of a femur [15].

In this work, we present a simple multilayer model that would reproduce similar cement stress distributions as those in the cement mantle of an acetabular replacement from a plane strain FE pelvic bone model. Cyclic loading was applied to the experimental multilayer model where a dominant radial crack was grown, as predicted by the FE analysis. Crack morphologies were also examined using microscopy post fatigue testing. The results were discussed with regard to retrieval studies, in vitro experimental results, as well as 3D FE analyses.

2. Finite element studies

2.1. The pelvic bone finite element model

The plane strain finite element model of a natural hip joint was adapted from Rapperport et al. [16]. Generated from a roentgenogram of a 4 mm slice normal to the acetabulum through the pubic and ilium, the model was divided into 24 regions of different elastic constants with isotropic material properties assumed in each region. The main regions were cortical bone, subchondral bone, trabecular bone and cartilage. The trabecular bone region was further divided into smaller regions to account for the different densities of the bone in different areas within the region. A standard ultra high molecular weight polyethylene (UHWMPE) cup was secured with bone cement and the cup was in articulation with a spherical femoral head of Co-Cr alloy. The diameter of the replacement head was 28 mm while the thickness of the UHWMPE cup was 10 mm. The cement mantle was assumed to be uniform with a thickness of 3 mm. The interfaces between the cement and the cup, the cement and the subchondral bone were assumed to be fully bonded, while the articulating femoral and cup surfaces were assumed to be frictionless. This configuration was chosen to be representative of a cemented THR. The model was meshed using quadrilateral and triangular plane strain elements. A total of 3673 elements and 3265 nodes were used for the model (Fig. 2). The size of the smallest element on the articulating surfaces was 0.5 mm. The bone properties were taken from Rapperport et al. [16], properties for acrylic cement were from [17] and properties of Co-Cr alloy and UHMWPE were from [18].

Fig. 2.

The meshed plane strain pelvic bone model with a cemented acetabular implant.

The hip contact force during normal walking was adopted from Bergmann et al. [19]. The components of the hip contact force relative to the cup co-ordinates were used. Transformation was performed to project the hip contact force onto the model plane. Fig. 3 shows the magnitude and direction of the projected hip contact force during gait. At a single-legged stance, a peak hip contact force of 2300 N was assumed acting at an angle of 38.5° from the vertical plane. The load was applied on the extreme distal femoral neck nodes. The sacroiliac joint was fully fixed while the pubic joint was allowed to move in the sagittal plane, a boundary condition considered to be representative of anatomic configuration [16]. The contact was assumed to be frictionless under small sliding condition, and the contact analyses were carried out using the algorithm built in ABAQUS 6.5. The accuracy of the contact analysis and mesh sensitivity was evaluated using a simple cup/ball configuration and the results were compared favourably with published work [18] and classic Hertz theory.

Fig. 3.

The magnitude and the direction of the projected hip contact force during gait, the five load cases selected are marked with circles.

The stress distributions in the mid-plane of the cement mantle were analysed at five selected load cases, as shown in Fig. 3, during normal walking, and the results are presented in a local polar coordinate system with the origin at the centre of the femoral head, as shown in Fig. 4. It is evident that the cement mantle experienced variable loads during gait. Generally, high tangential tensile stresses were balanced by compressive radial stresses, while the shear stresses remain small in comparison with the other two components. The maximum tangential stress appears to be at load case 2, i.e. the single-legged stance. The variation of the stresses during gait at an angular position of 70° is illustrated in Fig. 5, where the maximum tangential stress range is over 8 MPa, while compressive radial stress range is about 6 MPa. These stresses are to have the most significant influence on the integrity of the cement mantle.

Fig. 4.

Local stress distributions in the cement mantle at selected load cases during gait. (a) Load case 1, 7% gait cycle; (b) load case 2, 17% gait cycle; (c) load case 3, 36% gait cycle; (d) load case 4, 45% gait cycle; and (e) load case 5, 64% gait cycle.

Fig. 5.

Variation of local stress distributions at ∼70° angular position during gait.

2.2. The simple multilayer model

A simple multilayer finite element model was developed to simulate the essential features of the stress distributions in a cemented acetabular replacement (Section 2.1), with a view of experimental studies using the same configuration. The model consists of a cylindrical rod of 10 mm diameter, as a simplified femoral head, articulating acetabular cup as semi-cylindrical tube of 10 mm thickness, a cement layer of 3 mm contained in a rectangular sawbone block of 40 mm × 65 mm with a thickness of 10 mm, as shown in Fig. 6. Perfect bonding was assumed between the cement and the sawbone, while frictionless contact surfaces were assumed between the femoral head and the cup. The sawbone block was fully constrained at the base and a load of 2 kN was applied through the centre of the semi-cylindrical rod. Eight-noded brick elements were used throughout the model and the total number of elements was 10,260. The materials properties used were the same as those used in Section 2.1, and the model was analysed using ABAQUS 6.5.

Fig. 6.

A simple multilayer model including a femoral head, an acetabular cup, cement and sawbone block.

The stress components at the mid-plane of the cement mantle were obtained and presented in a polar coordinate system, and comparison was made between the results from the pelvic bone model and the simple multilayer model. Fig. 7 shows the stress components of tangential, radial and shear at peak hip contact force during gait from both models. The simple multilayer model appears to reproduce well the three stress components in the cement mantle as obtained from the replaced pelvic bone model, although the angular locations of the maxima differ slightly due to the direction of the load. We hypothesise that the high tangential stresses would favour radial crack growth, facilitated by the high compressive radial stresses. This hypothesis was tested using the following experiment.

Fig. 7.

Comparison of local stress distribution at the peak hip contact force from the pelvic bone (P) and the simple multilayer (S) models.

3. Experimental studies

3.1. Experimental methods

The above simple multilayer model was made to the same dimensions as in Section 2.2. Blocks of saw bone were machined to size in height and width, and the semi-cylindrical cut was made with a router to a diameter of 36 mm and finished off by hand. A polyethylene cup was made of an UHMWP rod of 30 mm diameter. The rod was cut in half and semi-cylindrical cut-out of 10 mm was made with a router and finished of again by hand. Standard cementing technique was utilised to prepare and apply two mixes of CMW 1 (DePuy International) into the cut-out in the sawbone block. Short metal rods with a diameter of 3 mm were used as spacers to guarantee a cement layer of an uniform thickness. The finished multilayer blocks were left to set for 24 h, before specimens were cut to a thickness of 10 mm and polished prior to testing.

Cyclic tests were carried out on a servo-hydraulic testing machine (Si-Plan Electronics Research Ltd., UK), as shown in Fig. 8. Sinusoidal waveforms were applied and the load was fully compressive from −0.2 to −2.0 kN at a frequency of 10 Hz. The specimens were inspected periodically (10⁴ to 10⁵ cycles) for crack initiation and growth. A total of six experiments were carried out. After mechanical testing, the fracture surfaces were coated with platinum gold and examined using scanning electron microscopy.

Fig. 8.

Experimental set up for the simple multilayer model.

3.2. Experimental results

All specimens showed similar crack growth behaviour in that a dominant radial crack was initiated at the bone-cement interface at between half to one million cycles. The crack would travel in the radial direction across the thickness of the cement mantle, and then grew across the thickness of the specimen. Table 1 shows a summary of the experimental results. For majority of the cases, the average number of cycles for crack initiation was about 5 × 10⁵ and the time taken for the crack to travel across the thickness of the specimens was recorded with an average crack growth rate of approximately 2.9 × 10⁻⁵ mm/cycle. A frontal view of a fractured cement mantle is shown in Fig. 9a, while Fig. 9b shows the details of the crack path. There are pores in the cement mantle, although the crack trajectory does not appear to be overly affected. The fracture surface of the cement mantle is shown in Fig. 10, where the initiation of the crack was from the bone-cement interface (Fig. 10a), and the stable crack growth is evidenced by fatigue striations, as shown in Fig. 10b.

Table 1.

Summary of the in vitro fatigue experimental results

Specimen	Load (kN)	Crack initiation (cycles)	Grown to full size (cycles)
1	2.0	0.54 × 106	0.87 × 106
2	2.0	0.49 × 106	0.71 × 106
3	2.0	0.61 × 106	0.93 × 106
4	2.0	0.51 × 106	-
5	2.0	0.72 × 106	1.16 × 106
6	2.0	1.21 × 106	1.81 × 106

Fig. 9.

A radial fatigue crack developed at the location of the maximum tangential stress (a); and the details of the radial crack (b).

Fig. 10.

Fatigue crack growth across the thickness of the specimen (a); and the details of the fatigue striations (b).

4. Discussion

Using a simple multilayer model, the variable multiaxial stress state in the cement mantle of an implanted acetabulum has been reproduced. The predominant stress components are tangential and radial stresses, while shear stresses remain small during a normal walking cycle. Cyclic tests of the experimental model confirm that high combined tangential and radial stresses seem to be the source in promoting radial crack growth under peak hip contact force during normal walking. Initiation of the fatigue cracks occurred at 5-10 × 10⁵ cycles in this experimental configuration, and crack grew across the thickness of the cement mantle and the thickness of the specimen, where typical fatigue striations were observed during stable crack growth. Further testing after the first radial crack had fully grown generated additional radial cracks, although these rarely grew into sizes of significance before failures of the bone-cement interface and/or bone matrix set in.

The maximum principle stress of ∼9 MPa at peak hip contact force during gait is comparable with the fatigue strength of CMW cement reported [20]. For load ratio R > 0, and a maximum stress of 15 MPa, the numbers of cycles to failure were reported to be between 3 and 10 × 10³; while for full reversed cycles at ±10 MPa, the numbers of cycles to failure were between 10⁵ and 10⁶ cycles. The fatigue limit (10⁶) of CMW was reported to be 14-17 MPa for fully compressive cycles, and 10 MPa for fully tensile cycles in [21]. The current results are in general agreement with the published results, given that the difference in stress gradient between the present tests and the material characterisation tests.

Radial cracks have been observed in sections of cemented femoral replacements tested in vitro [22], and retrieved samples [5]. Interestingly, Jasty et al. [5] reported that specimens less than 10 years in vivo showed small, incomplete fractures while specimens implanted for more than 10 years all showed large, complete cement mantle fractures, indicative of a progressive nature of fatigue damage accumulation well before gross loosening manifested clinically. The crack growth appears to be associated with little plastic deformation and does not necessarily relate to porosity [22]. Fig. 10 bears striking resemblance to one of the retrieved sample reported in [5], where fatigue striations were observed around a large void in the cement mantle. In contrast to femoral implants, cracks in acetabular implants were observed to initiate from the bone-cement interface, rather than prosthesis-cement interface. This feature was also captured by the current model, where all cracks were initiated at the bone-cement interface.

The effect of loading frequency on fatigue behaviour of PMMA has been the subject of several systematic studies [20,23], and a range of frequencies (1-30 Hz) has been used in the testing of bone cement. Although fatigue life was found to increase with the increase in frequency for smooth specimens, fatigue crack growth rates were found to decrease with increasing frequency for notched specimens, and there is no consensus on the most suitable frequency for fatigue testing of PMMA [20]. The results presented here should be used qualitatively.

Although the simple multiplayer model offers a step forward towards simulation of stress state in acetabular replacements, the lack of 3D features, common with all 2D models, does limit the conclusions drawn with respect to in vivo applications. However, our most recent 3D finite element studies of implanted pelvic bone models [24] seem to indicate that, although the magnitudes of the stress components in the cement mantle of 3D pelvic bone model are much lower than those in the multilayer model (17-25%), the stress distributions are broadly similar in both cases. This evidence is encouraging in that, firstly, parametric studies may be carried out using 2D models with confidence; secondly, the fact that the stress levels in the cement mantle of a 3D model is much lower than that of a 2D model seems to suggest that other failure modes, such as debonding at the bone-cement interface, may take precedence over cement cracking. When the stress level in the cement mantle is well below the fatigue limit of the cement, cracking in the cement mantle may be completely suppressed. Indeed, experimental results from in vitro testing of 3D acetabular reconstructs seem to support this line of argument. In these tests [25], full-sized artificial hemi-pelvic bones were implanted with Charnley cups, and tested under peak hip contact force during gait up to 20 million cycles. Failure at the bone-cement interface was identified in all cases studied, with no apparent cement cracking. The test was recently repeated using an implanted bovine pelvis, a similar result, i.e. bone-cement failure, was also observed.

Complex loading conditions may also result in different failure scenarios, as opposed to the simplified loading condition employed here, where the direction of the load was assumed to be constant, and a sinusoidal waveform was used instead of loading profiles recorded in vivo [19]. A hip simulator for fatigue testing of implanted acetabula has recently been developed in our laboratory. A study is being carried out to examine the effect of variation in both magnitude and direction of the hip contact force, as well as the combined activities, on acetabular fixation. These will be reported in due course.

5. Conclusion

A simple multilayer model is able to reproduce the stress distributions in the cement mantle of acetabular replacements, as obtained from a plane strain finite element model. High tangential stresses combined with high compressive radial stresses prompted radial crack growth in the cement mantle with characteristics of fatigue damage.

Although the stress distributions from these 2D models are similar to those from 3D models, the magnitudes are much greater hence the form of fatigue damage in 2D models may not be necessarily representative of that found 3D models.