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Elastic deformation of press-fitted acetabular cups during implantation provides primary stability. Excessive deformation can lead to chipping or improper seating of ceramic inlays and is dictated by cup stiffness, which also affects its vibrational characteristics. Purpose was to investigate the influence of cup design on deformation during press-fitting and on vibration properties.
Methods
Deformation of ten acetabular cups (with and without ceramic inlay) was tested for radial loads clinically occurring during press-fitting (0–2000 N). Eigenfrequencies were measured using experimental modal analysis and related to mass and stiffness.
Findings
The first eigenfrequency of the shells varied greatly (4–9 kHz); insertion of inlays caused an increase (16–33 kHz). The range of shell stiffness was high (2.7–48.4 kN/mm), increasing due to inlay insertion (124.7–376.2 kN/mm). Stiffness and mass were sufficient predictors for eigenfrequencies (p<0.001,R²=0.94).
Interpretation
The cups investigated represent a large stiffness range. Lower cup stiffness can increase primary stability but jeopardize inlay seating, and a suitable balance must be achieved by the designer. Eigenfrequencies also decrease with decreasing stiffness but were all found to lie considerably above clinically observed squeaking frequencies, indicating that these cup designs play no predominant role in the squeaking phenomenon. The observed relation between eigenfrequencies and the quotient of stiffness and mass might be used in the development of new thin walled cup designs so that their contribution to system vibrations is prevented. Presently, surgeons should be aware of the deformation characteristics of cups in order to select a suitable press-fit magnitude.
Uncemented acetabular cup press-fit fixation has become widely accepted as the method of choice for the anchorage of hip replacements, especially in younger patients. This is founded by the advantages compared to cemented systems with regard to survival time and preservation of bone stock (
). The combination of press-fit acetabular cup shells with ceramic articulations has been shown to provide a long-lasting, low friction and low wear arthroplasty (
). The implantation of press-fit shells in the hemi-spherically under-reamed acetabulum leads to high stresses in the pelvic bone in radial direction. Simultaneously the shell is deformed into a non-spherical form, since the stiffness of the acetabulum's bone is not homogeneous but highest along the Illium–Ischium axis (
Contemporary acetabular cup designs vary considerably with respect to material and geometry. This influences cup deformation during press-fit implantation. Large shell deformations due to low stiffness can result in incomplete seating of hard inlays (i.e. ceramic) (
). On the other hand, shells with lower stiffness are supposed to be advantageous for the development of a homogeneously distributed radial press-fit stresses, thereby increasing stability and bone ingrowth (
The stiffness of the acetabular cup also affects its dynamic vibration behaviour, represented by its eigenfrequencies. Those are the specific frequencies in which a structure preferably vibrates—similar to the frequency of a guitar string. Greater structural stiffness generally leads to higher eigenfrequencies while greater mass decreases the eigenfrequencies. The eigenfrequencies, however, are decisive for the possible contribution of the cup component to the vibration characteristics of the dynamic system of an assembled total hip replacement. This is currently discussed with regard to the noise emission problem of artificial hips (
). It is currently unknown whether this is due to the cup's specific vibrational properties and whether these differ between cup designs. It is also unknown if any contemporary cup designs exhibit eigenfrequencies in the squeaking frequency range. This knowledge would help to clarify the contribution of the cup to the squeaking phenomenon.
The purpose of this study was to investigate the influence of individual cup design parameters on their deformation characteristics during press-fit implantation and their eigenfrequencies.
2. Methods
Ten contemporary press-fit acetabular cup designs were investigated. Most of the cups were provided by the respective manufacturers, one was bought on the free market (S0) (Table 1). The cups were selected to cover a wide range of geometries and materials of the clinically used cups. Stiffness and eigenfrequency measurements were made for the metal shells alone and for the shells assembled with the respective ceramic inlay; one design (S3) is a pre-assembled monoblock design and was only examined in the assembled state. All shells are made from various titanium alloys with one exception (S6), which is a CoCr-alloy. Shells varied with respect to diameter, weight and number of screw holes. Eight of the ten shells had an outside diameter of 52 mm (S1, S2, S4, S5, S6, S8, S9, and S0), one of 48 mm (S7) and one of 42 mm (S3). Seven cups had alumina ceramic inlays (Biolox Forte, Ceramtec, Plochingen, Germany: S1, S2, S4, S6, S8, S9, and S0). One of the inlays was a hybrid construction with an alumina ceramic inlay press-fitted into a titanium cladding by the manufacturer (S0). Three inlays were made of composite ceramics: One is made of a zirconium-alumina composite (ATZ, Mathys, Bettlach, Switzerland; S7) and two made of a zirconium-alumina and other materials composite (Biolox Delta, Ceramtec; S3 and S5). One cup was a monoblock cup pre-assembled by the manufacturer (S3). Nominal bearing diameter was 28 mm in eight cases (S1, S2, S4, S5, S6, S8, and S9) and 32 mm in two cases (S3 and S7).
Table 1The 10 acetabular components investigated. The inner and outer diameters of the metal shell are represented by dOutside and dInside, the nominal diameter of the articulation by dBearing. The inlay wall thickness is represented by t. The inner shell diameter of S3 is not specified since this cup is a pre-assembled monoblock design. The number of screw holes in brackets indicates that respective holes were closed by threaded screw hole covers. The mass of the shell and the cup system are indicated by mShell and mSystem respectively.
Each specimen was weighed with and without inlay (excluding the pre-assembled cup) using a digital scale (16520, Maul, Bad Koenig, Germany). The inlays were implanted into the metal shells using a device for defined impaction condition (Conifix, Eska, Luebeck, Germany). Pilot measurements showed that the impaction device provided a reproducible peak impaction force of 1.19±0.26 kN (mean±standard deviation; n=3; 208C05 force sensor, PCB, Depew, NY, USA).
2.1 Experimental modal analysis
Experimental modal analysis was performed to determine the eigenfrequencies of each cup with and without ceramic inlay. The acetabular cups were suspended super-critically from 3 equally spaced elastic bands tied to fine wire loops glued onto the open face of each metal shell (Fig. 1). This allows free oscillations of the cups. The cups were excited using the roving hammer method: Four excitation points were defined, evenly distributed around the upper outside circumference of the shell. Excitation was performed at each point in the radial direction using a high frequency impulse hammer equipped with a force transducer for the detection of time-dependent transmission of force to the structure during the excitation (086D80 impulse hammer, 480E09 signal conditioner, PCB). The transient response of the cup was detected in the radial direction using a laser vibrometer with the sampling point located in the proximity of one of the excitation points (OFV-505 sensor head, OFV-5000 controller, Polytec, Waldbronn, Germany; Fig. 1). The laser vibrometer determined the surface velocity utilizing a decoder (VD-02) which analyzes the Doppler shift of the reflected wave. The sensitivity of the decoder was set to 5(s/mm)/V and an analog low pass filter with a cut-off frequency of 1.5 MHz was used. Data were collected at a sampling rate of 100 kHz using a data acquisition card and custom-coded software (PCI MIO 16 E 1, Lab View 7.1, National Instruments, Austin, TX, USA). Each cup design was excited ten times at each of the four excitation points.
Fig. 1Set-up for the experimental modal analysis of the super-critically suspended acetabular shell. The impulse hammer for excitation, and the placement of the laser vibrometer for the detection of the structural response are indicated.
Frequency response functions (FRFs) and eigenfrequencies of the acetabular cups were calculated from the raw temporal velocity data (Matlab R2007a, Mathworks, Natick, MA, USA). Erroneous measurements due to multiple contacts between hammer and implant were excluded from further processing. Data were digitally filtered using a 5th order Butterworth high pass filter without phase shift with a cut-off frequency of 500 Hz. A rectangular window over the impaction duration was used for the impaction data; an exponential window was applied to the data of the structural response. FRFs were calculated for each impaction and averaged for each excitation point. Modes were identified from the FRF data, defined as a peak of the FRF amplitudes and a simultaneous 180° phase shift.
2.2 Deformation and stiffness measurements
Deformation measurements of both the shells and the assembled cup systems were performed at loads of 0 N, 1000 N and 2000 N applied diametrically using a loading frame equipped with a load cell (8524 load cell, Burster, Gernsbach, Germany; Picas signal conditioner, Peekel, Bochum, Germany) (Fig. 2). The components were clamped in the loading frame between two parallel plane jaws. The inner geometries of the shell as well as the articulation surface of the assembled cup system were measured prior to loading and after each load application 1.5 mm below the equator plane of the specimen. Measurement points with tangential distances of 2 mm were acquired around the circumference using a coordinate measuring machine (CMM, BHN-305, Mitutoyo, Kawasaki, Japan; TP200 probe, Renishaw, Gloucestershire, UK; mean accuracy 2.2 μm). Since differences in stiffness were expected due to the asymmetric shape of some shells caused by screw holes, measurements were made both in the symmetry plane of the shell (0°) and perpendicularly to it (90°). Each shell was tested three times in each of the loading directions (0° and 90°). The unfavorable signal-to-noise ratio caused by the small expected deformations of the assembled cup systems was accounted for by repeating the deformation measurements five times for each test.
Fig. 2Custom built load frame with load cell for diametrical loading of acetabular cups. The probe of the coordinate measurement machine (CMM) for geometry measurement is also shown.
Maximum diametral deformation (Δd) was calculated from the cup geometry measurements (Matlab, R2007a, Mathworks). First the centroid of all data points was determined. The radial distance of each point was then calculated with respect to the undeformed distance to the centroid. Some deformations approached the accuracy of the measuring method (particularly for the assembled cup systems) making the data rather sensitive to micron-scale deviations and noise. A 5th order Butterworth low pass filter without phase shift was used to smooth the data. Two minimum radii were found for each measurement. The diametral deformation was calculated by summing the respective radial deformations.
Linear regression analysis (SPSS, version 15.0, Chicago, IL, USA) was performed for the different applied loads (Fa) as independent variables (0 N, 1000 N, and 2000 N) and the deformation (Δd) as dependent variable to determine the stiffness (c) (Eq. (1)).
(1)
Stiffness values were averaged over the repeated deformation measurements for each test. The influence of the loading direction (0° and 90°) was investigated using a non-parametric Mann–Whitney test. Linear regression analysis was performed to investigate the relationship between the first eigenfrequency (ω) and the theoretical behavior of an undamped oscillator (square root of the ratio of stiffness and mass (m), Eq. (2)):
(2)
The type I error probability for all tests was set to α=0.05.
3. Results
3.1 Experimental modal analysis
The first eigenfrequencies of the metal shells alone ranged from 4.3 kHz to 9.2 kHz (Fig. 3). Insertion of the ceramic inlay at least doubled these frequencies to 16.1 kHz up to 32.5 kHz. Most of the eigenfrequencies of the assembled cup systems were considerably higher than the audible frequency range (<20 kHz).
Fig. 3First eigenfrequencies of the different cup designs. The frequencies of the shells alone are indicated on the right, the frequencies for the assembled cup systems on the left scale. No error bars are displayed if the variation does not exceed the spectral resolution (~10 Hz).
Diametral loading of the cup resulted in non-spherical deformation of both the shell and the assembled cup system (Fig. 4). Maximum diametral deformation ranged from 41 μm to 730 μm for shells alone and from 5 μm to 52 μm for assembled cup systems (Fig. 5). Shell stiffness ranged from 2.7 kN/mm to 48.4 kN/mm (Table 2). Eight of the shells exhibited stiffness below 12 kN/mm, while two designs’ stiffness exceeded 40 kN/mm (Table 2). Assembly of the cup systems with the ceramic inlay tripled the stiffness of each design at least compared to the shells alone. System stiffness ranged from 124.7 kN/mm to 376.2 kN/mm (Table 2). The percentage increase in stiffness due to the insertion of the ceramic inlay was highly variable between the different designs (Table 2).
Fig. 4Example for a shell deformation (2000 N). The maximum diametral deformation in this case was 731 μm. The deviations from the undeformed state are shown 20 times magnified.
Table 2Stiffness of the shells and the assembled systems (mean (SD)). The stiffness ratio as percentage of the shell alone to the assembled cup system highlights the different responses to the ceramic inlay insertion of the respective cup system. No shell stiffness and stiffness ration is given for S3 due to its monoblock design.
No significant differences were observed between directional stiffness neither for the metal shells alone nor for the assembled cup systems. One design (S9) showed a strong tendency for difference in directional stiffness (0°: 8680.4±25.8 N/mm (mean±standard deviation); 90°: 8611.1±22.7 N/mm; P=0.05). This result is due to a very small variation between the repeated measurements and has no relevance for the clinical application.
3.3 Relationship between stiffness and frequency
A strong linear correlation between the first eigenfrequency and the square root of the quotient between radial stiffness and mass was found for the shells alone (P<0.001, corrected R²=0.84) and also the assembled cup systems (P<0.001, corrected R²=0.91). This relationship was confirmed for the analysis of all measurement data together (shells alone and assembled cup systems; P<0.001, corrected R²=0.94; Fig. 6).
Fig. 6Linear fit of the first eigenfrequency vs. the square root of stiffness and mass (representation of an undamped oscillator). The regression is based on the entire data set containing shells and assembled cup systems. Data points in the shaded area represent the values for the shells alone, data points outside the shaded area represent the respective assembled cup systems. Components are identified in Table 1.
). Forces of this magnitude were shown in this study to cause highly design-specific shell deformations ranging up to considerable 547 μm for the shell alone and small 37 μm for the assembled cup systems (Fig. 5). Shell deformations of this magnitude can explain improper seating of the ceramic inlay as observed in other studies (
). It is unclear, how the inlay implantation forces are affected by the deformation of the acetabular shell and whether the surgeon can still achieve proper seating without damaging the inlay at greater deformations. Prosthesis manufacturers advise the surgeon to implant the inlays with limited impaction forces (e. g. using force limiting impaction devices, Eska Conifix). The magnitude of the applied seating force has an influence on the taper lock of the inlay (
). Improper inlay seating, either due to excessive shell deformation or insufficient implantation force, can cause changes in the specific contact conditions between shell, ceramic inlay and also the articulating femoral head. A greatly deformed bearing surface can change the tribological system due to a modification in contact area and effective clearance of the ceramic–ceramic articulation, which might also influence the fluid film lubrication.
No significant differences in stiffness between the loading directions of the acetabular cups were found, indicating that the screw holes have little influence on the overall mechanical characteristics. This allows elimination of directional measurements from further studies.
The increase in stiffness caused by the insertion of the ceramic inlay was not systematic for the different designs. This is due to the differences in thickness and material of the ceramic inlay (Table 1). Since ceramics have a higher Young's modulus than the metal of the shells, the stiffness of the assembled cup system is dominated by the stiffness of the ceramic inlay, thus explaining how the system with the thickest inlay exhibited the highest system stiffness (S8, Table 2). Thin shells with thin inlays are desirable since they are able to accommodate larger heads (which improve resistance against dislocation and also hydrodynamic lubrication) and simultaneously require less bone removal. Although thinner-walled designs are more sensitive to excessive deformation during press-fit implantation, a certain deformation is advantageous since bone damage under lower shear loads during insertion is reduced. The radial expansion of the metal shell due to subsequent inlay insertion was shown to provide an improved anchorage (
Primary stability of uncemented femoral resurfacing implants for varying interface parameters and material formulations during walking and stair climbing.
One limitation of this study is the insertion of the inlay into an undeformed shell. This does not represent the clinical situation, since the inlay is actually inserted into the shell deformed by press-fitting (
). The approach to deform the assembled cup system rather than inserting the inlay in a deformed cup was chosen in order to estimate the mechanical properties without biasing the result by inlay implantation condition, which varies with the amount of shell deformation.
Depending on the shell design, different magnitudes of underreaming of the acetabulum are clinically possible without deforming the shell to a critical extent.
The deformation experiments accomplished in this study simplify the true in vivo conditions but produced deformations, which are similar to deformations found in vivo (
The lowest eigenfrequency of each acetabular shell alone attained the audible range (Fig. 3). However, clinically the characteristics of the assembled cup system are of higher interest. The vibrational and stiffness properties are considerably influenced by the ceramic inlay. Just three of the assembled cup systems investigated (Fig. 3) had a first eigenfrequency in the audible range (<20 kHz). However, these eigenfrequency clearly outrange the squeaking frequency range which was found in vivo (1 to 5 kHz). For this reason it is unlikely that the eigenmodes of the investigated acetabular cups are responsible of the squeaking noises observed clinically. It has to be considered that the eigenmodes represent the vibrational characteristics of structures unaffected by the environment. In the implanted in vivo situation, the vibrational behaviour of the cup is influenced by the surrounding bone stock as well as the applied joint load and orientation. However, the detuning effect does not compensate the differences between squeaking frequencies and cup eigenfrequencies that were determined in this study. It could be possible that the assembled cup systems do not vibrate elastically but as rigid bodies in the elastic bone suspension. Femoral stem design has been shown to be most likely the responsible oscillator of a total hip replacement (THR) system during squeaking (
). This goes along with the results of this study.
A lower cup stiffness, which is advantageous for the preservation of bone stock and primary stability of the prosthesis, results in a lower cup eigenfrequency. Due to this trend towards thin and elastic cup designs, the contribution of the cup design on the vibrational properties of THR systems has to be considered in the future although a direct contribution of the eigenfrequencies of the cups tested in this study is unlikely.
The eigenfrequencies of the shells and the assembled cup systems were shown to be well estimated by their mass and stiffness. This allows the estimation of eigenfrequencies based on mass and radial stiffness of the cups during the design process without any experimental vibration measurements. Especially for the development of rather soft shells which might be favorable with regard to bone anchorage this relation enables to stay in a low-risk region with regard to vibrations.
The stiffness and vibration characteristics of contemporary acetabular cup systems show large differences between the designs. These differences play an important role for the cup deformation during press-fitting. At a given amount of underreaming, the deformation is larger for a soft shell than for a stiff shell. This has direct consequences for possible inlay chipping and seating, a problem, which has become more and more recognized in recent years. On the other side, a softer shell will cause less bone abrasion and more elastic radial bone deformation during insertion, which has been shown to be advantageous for primary stability. Further studies to determine the optimal compromise between the amount of underreaming, the stiffness of the metal shell and the resulting primary stability are required. Presently the surgeons should be made aware of the big variations between implant systems and the possible requirement to change their implantation procedure (i.e. amount of underreaming) when changing to a different acetabular system.
Acknowledgements
Financial funding was kindly received by Ceramtec. Components were provided by Aesculap, Biomet, DePuy, Eska, Mathys, Plus and Smith & Nephew. The support of Nicholas Bishop, Malte Steiner and Christoph Materne is deeply appreciated.
References
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Friction of total hip replacements with different bearings and loading conditions.
Primary stability of uncemented femoral resurfacing implants for varying interface parameters and material formulations during walking and stair climbing.
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