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Femoral strain changes after total hip arthroplasty — patient-specific finite element analyses 12 years after operation
Medical Engineering & Physics 27 (2005) 649–654
Femoral strain changes after total hip arthroplasty — patient-specific finite element analyses 12 years after operation Markus Lengsfeld a, b, ∗ , Rene Burchard a , Daniel G¨unther a , Thomas Pressel a , Jan Schmitt a , Ronald Leppek c , Peter Griss a a b
Clinic of Orthopaedic Surgery and Traumatology, Hessisch Lichtenau, Germany Department of Orthopaedic Surgery, Philipps-University of Marburg, Germany c Department of Radiology, Philipps-University of Marburg, Germany
Received 28 May 2004; received in revised form 14 September 2004; accepted 13 December 2004
Abstract Periprosthetic stress-shielding after total hip arthroplasty (THA) is a well-known phenomenon. Many authors have used the finite element (FE) method to show the effects of THA on animal or human femora. In most cases they have performed cadaver experiments. The current project is a FE analysis based on a retrospective computerized tomography (CT) in vivo data set of 11 patients 12 years after THA. In order to control the analysis, a computationally created stem was implanted at the femur model of the not operated contralateral side. In comparison to the not operated side, there was a significant reduction of the strain energy density (SED) values in all regions of interest (ROI) with the greatest effect near the distal tip of the stem. Only zone 1 showed no clear trend which may be due to load application at the greater trochanter causing local strain peaks. The median SED values changed by −31.65% (ROI 1), −25.64% (ROI 2), −30.82% (ROI 3), −12.35% (ROI 4), −40.10% (ROI 5), −30.37% (ROI 6) and −43.38% (ROI 7). As far as we are aware, the current combination of in vivo CT density data with FE strain analyses after THA is based on the largest number of patients and the longest follow-up period. This combination enables analysis and prediction of the influence of implantation upon bone and can be compared with of remodelling theories. The assessment of mechanical strain data during a follow-up trial could be a new approach for analyzing different hip stems in clinical biomechanics. © 2005 IPEM. Published by Elsevier Ltd. All rights reserved. Keywords: Total hip arthroplasty; Periprosthetic stress-shielding; In vivo strain analysis
1. Introduction Periprosthetic stress-shielding is recognized as one of the bone reactions after the implantation of a femoral stem and may be a factor influencing implant survival time [1–3]. Femoral FE bone remodelling analyses were based on animal experiments [4,5] or human specimen after death [6,7]. Kerner et al. [7] used the proximal part of a “typical” femur, which was described by Huiskes and van Rietbergen [8]. They modelled only the distal parts of the femora specimen specifically. Remodelling simulations were conducted by these and other authors, who combine bone remodelling theories with ∗
Corresponding author. Tel.: +49 5602 83 1201; fax: +49 5602 83 1980. E-mail address: [email protected] (M. Lengsfeld).
FE analysis. The project presented here combines clinical long term bone density data with FE analysis. It is a comparison of a 12-year THA follow-up with the not operated contralateral side. Similar to the methodological approach of Kerner et al. [7], the not operated femur is considered to represent the initial situation of the operated side 12 years before. The FE calculations are based on patient-specific CT density data and provide patterns of strain energy density (SED). The objective of the study presented here is an evaluation of femoral strain 12 years after THA.
2. Method Eleven post-menopausal female patients with unilateral THA and a press-fit cemented titanium alloy stem (Marburg
1350-4533/$ – see front matter © 2005 IPEM. Published by Elsevier Ltd. All rights reserved. doi:10.1016/j.medengphy.2004.12.016
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Table 1 Clinical data of all patients Patient number
Age OP
Age CT
Height (cm)
Weight OP (kg)
Weight CT (kg)
Side OP
Anteversion angle
Stem size
Walking distance (km)
Pain: preop./12 years
Flex/Ext: preop.
Flex/Ext: 12 years
11 12 13 14 15 16 17 18 19 20 21
53 60 51 40 53 63 55 56 58 63 57
65 72 63 52 65 74 68 67 71 75 71
168 162 158 164 168 154 154 159 158 161 148
67 83 60 64 75 63 62 75 71 81 90
75 70 77 81 79 75 70 72 78 75 79
Left Right Right Left Right Right Left Right Left Left Left
R: 22–L: 12 R: 19–L: 5 R: 15–L: 14 R: 15–L: 26 R: 27–L: 11 R: 30–L: 21 R: 19–L: 27 R: 25–L: 27 R: 26–L: 33 R: 16–L: 29 R: 30–L: 21
S L S S L M S S S L Dysplasia
>5 2–5 2–5 2–5 2–5 0.5–1 1–2 2–5 2–5 >5 0.5
3/5 3/6 3/6 3/4 3/5 3/6 2/6 3/5 3/6 4/6 3/6
90/10/0 80/0/0 105/0/0 100/0/0 Missing Missing 120/0/5 90/0/0 50/5/0 90/0/0 Missing
100/0/0 100/0/0 100/0/0 Missing Missing 100/0/0 110/0/0 110/5/0 100/5/0 110/0/10 110/0/0
Pain scale according to Merle’Aubign´e from 0 (extreme pain) to 6 (no pain).
system, Sulzer Orthopedics Ltd., Baar, Switzerland) were scanned in vivo 12 years (range 11 years and 3 months to 13 years and 8 months) after implantation. The scanner setting (Somatom Plus-4, Siemens, Erlangen, Germany) was 140 kV, 206 mA, 17 s, spiral algorithm with a recalculated slice thickness of 2 mm and a 512 × 512 pixel resolution. Clinical and CT density data of the patients have already been published [9]. A summary is shown in Table 1. On a scale of 1:1 CT voxels were transferred to finite element voxels (eight node brick elements) except for patient no. 1 with an enlarged scale because of a meshing-failure. Subsequently, the full CT information was used for automatic generation of the femoral FE models with an identical CT and FE voxel resolution of 0.66 mm × 0.66 mm × 2 mm. The number of elements is approximately 250 000 for each femur (bone and stem). The press-fit implantation technique is based on no size difference between the final rasp and the stem, thus causing a very thin cement layer (<2 mm). Therefore, no separate cement layer was modelled, neither at the operated nor at the computational implanted side (see below). Periprosthetic regions of interest (ROI) according to Gruen et al. [10] were defined around the stem. The CT Hounsfield values (HU) were linearly converted into elastic moduli [11,12]. Bone was defined between 170 and 1799 HU and was linearly related to elastic moduli between 1500 and 15 000 MPa. It is recognized that various relationships between apparent density and the modulus have been investigated [11,13–16]. Weinans et al. [17] demonstrated that the differences in stress-shielding results are independent of the density–modulus relationship used and can be examined as long as one uses the same relationship intraindividually or for each subject. In this study the same method was used at the operated side and at the contralateral side. The CT density of titanium has the maximum technical value of 3072 HU and was related to a modulus of 110 000 MPa. In order to investigate the effect of a 12-year THA survival time on femoral strain, the SED distribution was compared to the SED distribution of the contralateral femur (still not operated). The analysis of the anatomical contralateral femur would not be a suitable control for a 12-year comparison
with the postoperative situation. In order to make the results comparable, a computationally created stem was “implanted” into the contralateral femur model. A matrix of the stem size values was generated. An automatic algorithm [18] selected all bone, or bone marrow, elements that belong to the matrix and assigns to them an elastic modulus value of titanium alloy. The alignment and anteversion angle of the stem was equal to the stem’s position at the operated side (Fig. 1). In contrast to this methodology, a real contralateral implantation after death was conducted in the post-mortem study by Kerner et al. [7]. Loads were applied weight-dependent with a prosthesis head force, and an abductor force was applied at the greater trochanter [19,20]. Force magnitudes of 347% bodyweight (hip joint force) and 270% bodyweight (abductor force) were used. The vertical axis (z) of the coordinate system was defined by the hip and knee joint centre and the frontal axis (x) by the dorsal aspect of the femoral condyles. The joint force of a right hip was multiplied by −sin(15◦ ) to obtain the x-, by −sin(13◦ ) to obtain the y- and by cos(15◦ ) to obtain the z-component. The factors for the right abductor force were sin(19.5◦ ), sin(13◦ ) and −cos(19.5◦ ), respectively. Selection of these values was anticipated by an earlier sensitivity study in our group [21]. The trochanter force was divided into 40
Fig. 1. Method of computational hip stem implantation: femoral FE model of patient no. 9 (A) and after computational implantation (B). The model of patient no. 9 after computational implantation is again displayed (sections) (C) and compared with the surgical operated contralateral one (D).
0.07893 0.00476 0.01047 0.01504 0.01097 0.00545 0.00239
S.D. Mean
0.00785 −0.00506 −0.00986 −0.00604 −0.01171 −0.00524 −0.00189 −0.03740 −0.01385 −0.01206 −0.01070 −0.01478 −0.00552 −0.00904
No. 11 No. 10
−0.02752 −0.00722 −0.01984 −0.02715 −0.02042 −0.00762 −0.00020 −0.07378 −0.00966 −0.02350 −0.02208 −0.02089 −0.00896 −0.00174
No. 9 No. 8
0.00794 −0.00110 −0.00843 0.00905 −0.00807 −0.00556 −0.00138 −0.01366 0.00222 0.01412 0.02559 0.01574 0.00309 −0.00176
No. 7 No. 6
0.24142 −0.00309 −0.00406 −0.00298 −0.01084 −0.00123 −0.00066 0.00130 −0.00196 −0.00541 −0.00296 −0.00868 −0.00295 −0.00041
No. 5 No. 4
0.03266 −0.00164 −0.00687 0.00267 −0.00479 −0.00104 0.00011 −0.00221 −0.01090 −0.02629 −0.02696 −0.02635 −0.01009 −0.00250 0.00228 −0.00130 −0.00824 −0.00615 −0.00794 −0.00021 −0.00115
No. 3 No. 2
The calculated intraindividual strain energy density differences between operated and non-operated side (SED(operated) − SED(not operated)) of all 11 cases are shown in Table 2. The median SED values (Fig. 3) changed by −31.65% (ROI 1), −25.64% (ROI 2), −30.82% (ROI 3), −12.35% (ROI 4), −40.10% (ROI 5), −30.37% (ROI 6) and −43.38% (ROI 7). The reduction of SED was greatest in the ROI 3 and 5 which are around the tip of the stem. ROI 1, where the abductor’s forces were applied, shows no clear trend with varying results from positive to negative SED adaptation. Generally, a reduction of the SED increasing from proximal to distal is observed. Distal of the stem (ROI 4) the SED difference regains. The absolute strain energy density values are summarized in Fig. 4.
No. 1
3. Results
−0.04468 −0.00716 −0.00791 −0.00478 −0.02175 −0.01749 −0.00207
components being separately applied at 40 different superficial nodes at the greater trochanter region. The 25 components were associated with the gluteus medius and 15 with the gluteus minimus muscle insertion area. The sensitivity of this method of force separation was examined in case no. 2 by applying 20, 30 and 40 nodal forces. Each application was done three times with coincidental selected nodes at the greater trochanter. Lowest averaged SED value of every ROI was subtracted from highest of the three calculations. In the case of 40 components, the difference between the three coincidental loads became less than 5% (Fig. 2) except of ROI 1. Solutions were performed with the gradient solver (default setting) of the FE software ANSYS® 5.3. Statistical analysis was performed for the group of 11 as a sample size, recognising the low number of patients. The two-way Wilcoxon test (signed-rank-test) was applied with a level of statistical significance at 5%. The study was approved by the ethics commission of the Philipps University of Marburg. Informed consent is documented.
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ROI 1 ROI 2 ROI 3 ROI 4 ROI 5 ROI 6 ROI 7
Fig. 2. Deviation of the SED reduction results by three coincidental load applications using one time 20 nodes at the greater trochanter, one time 30 and one time 40 nodes (from left to right). Lowest averaged SED value of every ROI was subtracted from highest of the three calculations. In case of 40 components, the difference between the three coincidental loads became less than 5% except of ROI 1.
Table 2 The calculated intraindividual strain energy density differences between operated and non-operated femur (SED(operated) − SED(not operated)) of all 11 cases are shown including mean values and standard deviations (S.D.)
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Fig. 5. Median SED differences (MPa) between the operated and not operated femur of all 11 patients with respect to the ROI.
Fig. 3. Median SED differences (%) between the operated and not operated femur of all 11 patients with respect to the ROI.
Fig. 4. The mean SED values of the operated (white columns) and computationally operated (black columns) side is given with respect to the Gruen zones.
In Fig. 5 the medians of all SED differences (ROI 1–7) are presented. The results of all regions except of ROI 1 and ROI 4 demonstrated a statistically significant decreased SED at the operated side with p-values: ROI 1 (p = 0.2676), ROI 2 (p = 0.0064), ROI 3 (p = 0.0132), ROI 4 (p = 0.0655), ROI 5 (p = 0.0104), ROI 6 (p = 0.0064) and ROI 7 (p = 0.0022).
4. Discussion The combination of bone remodelling theories with FE analysis (e.g. [8]) represents a valuable tool in order to analyze and to predict the influence of an implant upon bone. Unfortunately, remodelling theory [22–26] is still not defined as a quantitative mathematical law. Hence, FE remodelling
results are based on phenomenological descriptions of the reality and not of quantitative-mechanistic models. As Wolff’s law is still not finally formulated, it is reasonable to combine FE analyses not with calculated, but with clinically available bone remodelling data. Bone mineral density changes after THA are clinically measurable by dual X-ray absorptiometry (DEXA), cf. [27,28]. However, DEXA has rather low resolution, measures only two-dimensionally and does not provide complete circumferential information. The striking advantage of the CT scans is the acquisition of fully 3D density values while providing also geometric data, which can be easily postprocessed by a variety of 3D finite element meshing techniques [29,30]. FE models of the current study are therefore based on a CT data source [9]. The mesh density in the current FE simulation project strictly depends on the voxel/pixel resolution of the CT data set. Hence, the FE mesh has the identical density than the CT mesh without information loss during the transfer process. Of course, multiple CT scanning in order to test different voxel resolutions would have given further information but could not be done for ethical reasons. A higher in-plane pixel resolution was not possible during in vivo scanning with this scanner setting, anyway. Using the maximum FE mesh density under these circumstances, a mesh density sensitivity study is not possible and was not done. Several relationships have been published in order to transfer bone density to elastic modulus accurately [11,13–16,31]. In this study a direct linear transfer from HU to elastic modulus was used, an approach which can be traced back to Ciarelli et al. [11]. Weinans et al. [17] demonstrated that subjectspecific FE models provide consistent stress-shielding patterns in the bone, independent of the choice of the bone density–modulus relationship used in the computer model. As Pauwels [19] convincingly demonstrated, forces were applied weight-dependent at the FE models with a femoral head force and an abductor force to simulate the one legged stance, a method, which was again tested and confirmed by Stolk et al. [20]. The resultant hip force being implemented is verified by telemetric hip force measurements in vivo [32]. The certainty
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of muscle forces are not that clear as the amounts of these forces have been never confirmed by in vivo measurements. The data given by Duda et al. [33] are based on purely theoretical calculations. The “classical” load configuration in the current study could be justified by the fact that always right-to-left comparisons with identical constraints were performed and analyzed. Moreover, Stolk et al. [20] state that additional inclusion of the iliotibial tract, the adductors and the vastii produced relatively small effects during all gait phases. Their most prominent effect was a slight reduction of bone strains at the level of the stem tip during heel-strike. Their results suggest that a loading configuration including the hip joint contact force and the abductor forces can adequately reproduce in vivo loading of cemented total hip reconstructions in pre-clinical tests. Apparently, there is no striking effect after inclusion of further muscles, while this effect is counterbalanced in a rightto-left comparison, anyway. Therefore we decided to choose the “classical” load configurations at the hip joint. The accuracy was enhanced by dividing the trochanter force into 40 components being separately applied at 40 different superficial nodes at the muscular insertion area. In accordance with Weinans et al. [17] the same loading was used within each subject in the study. The known limitations of the CT approach used here (partial volume effect, fat error, metal artifacts) have only a minor influence upon density data [9] and would not markedly influence the right-to-left comparison presented in this study. Zannoni et al. [34] demonstrated that the presence of a titanium alloy implant creates an apparent increase in crosssectional bone density of 71–85 HU. They found this increase within a distance of 4–8 pixels from the metal implant, with a pixel size being 0.3 mm × 0.3 mm, this means a distance of 1–2.5 mm. Within this interface zone the average density increase was 1100 HU in the first, 400 in the second, 100 in the third and zero in the fourth pixel crown surrounding the stem. They conducted their in vitro experiments without bone cement and selected a higher image resolution. In the in vivo study presented here, the CT/FE pixel size is 0.66 mm × 0.66 mm × 2 mm causing a higher partial volume effect. The upper threshold value is 1600 HU in order to separate bone from metal voxels, while the CT density of titanium is the maximum technical value of 3072 HU. As a result of this difference, interface voxels containing both metal and cement have an averaged HU value above 1600 and are deleted. In addition, pure cement voxels at the interface above 1600 HU due to a metal induced enhancement are deleted. Using this procedure the artifacts caused by the implant could be minimised. After converting the HU values in elastic moduli, Zannoni et al. [34] concluded that apart from a 2 mm thick region around the implant, the CT images could be used to derive the mechanical properties of bone tissue. As regards the geometry they estimated average error of 0.45 mm in the reconstruction of titanium hip stem cross-section geometry. Previously, Sutherland and Gayou [35] concluded
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from their composite phantom tests that intramedullary titanium is not a deterrent to obtaining accurate measurements of cortical bone dimensions and properties. When using cemented titanium implants, as in the current study, the artifacts are primarily located within the cement layer and they hardly influence the bone density values. Evidently, the artifacts are greater at the proximal stem, where this type has a larger extension of width and the surrounding bone a lower density. Cross-sectional evaluations at the greater trochanter region may show no clear results at the greater trochanter region. The deletion of a second voxel crown around the interface could further diminish the artifacts in the trochanter part of the femur. This was previously tested by deleting a voxel crown around the implant [9]: a density enhancement up to 40 HU was seen around the greater trochanter region, while no difference was measured distally. Titanium artifacts are primarily located near the interface within the cement layer [34], which was not separately modelled. Evidently, the artifacts are greater at ROI 1, where this type of endoprosthesis has a larger extension of width and the surrounding bone is of lower density. Furthermore, abductor force components applied at ROI 1 could cause local strain peaks. This could be the reason for the unclear, statistically not significant, results at ROI 1. The certainty of the current retrospective CT/FE study is limited because of a comparison with the contralateral side only. To date prospective, longitudinal 12-year CT follow-up studies are not available. These would provide useful additional data. Our results demonstrate a clear, statistically significant, SED reduction being caused by bone loss at the operated side in individual patients 12 years after surgery. This observation increases from proximal to distal. The reduction of SED was greatest in the ROI 3 and 5 which are around the tip of the stem. If the statistical test was done without the data of no. 7, the p-value of ROI 4 became also significant (p = 0.0183). Kr¨oger et al. [36] reported that a restoration of bone density around the implants may occur in some cases, which could explain almost no stress-shielding in one particular patient (no. 7). As the stress-shielding results presented here do not depend on a mechanical bone adaptation hypothesis, they are probably close to reality and might serve as reference data for purely theoretical simulations. As far as we are aware, this in vivo collection of patientspecific stress-shielding information after THA is based on the highest case number and the longest follow-up period. The method could be a new approach for analyzing different hip stems in clinical biomechanics.
Acknowledgements The authors express gratitude for the funding received from the Deutsche Forschungsgemeinschaft (DFG Le-
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1065/1-1). We wish to thank Dr. Helen Steele for discussing the text. [18]
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Femoral strain changes after total hip arthroplasty — patient-specific finite element analyses 12 years after operation Markus Lengsfeld a, b, ∗ , Rene Burchard a , Daniel G¨unther a , Thomas Pressel a , Jan Schmitt a , Ronald Leppek c , Peter Griss a a b
Clinic of Orthopaedic Surgery and Traumatology, Hessisch Lichtenau, Germany Department of Orthopaedic Surgery, Philipps-University of Marburg, Germany c Department of Radiology, Philipps-University of Marburg, Germany
Received 28 May 2004; received in revised form 14 September 2004; accepted 13 December 2004
Abstract Periprosthetic stress-shielding after total hip arthroplasty (THA) is a well-known phenomenon. Many authors have used the finite element (FE) method to show the effects of THA on animal or human femora. In most cases they have performed cadaver experiments. The current project is a FE analysis based on a retrospective computerized tomography (CT) in vivo data set of 11 patients 12 years after THA. In order to control the analysis, a computationally created stem was implanted at the femur model of the not operated contralateral side. In comparison to the not operated side, there was a significant reduction of the strain energy density (SED) values in all regions of interest (ROI) with the greatest effect near the distal tip of the stem. Only zone 1 showed no clear trend which may be due to load application at the greater trochanter causing local strain peaks. The median SED values changed by −31.65% (ROI 1), −25.64% (ROI 2), −30.82% (ROI 3), −12.35% (ROI 4), −40.10% (ROI 5), −30.37% (ROI 6) and −43.38% (ROI 7). As far as we are aware, the current combination of in vivo CT density data with FE strain analyses after THA is based on the largest number of patients and the longest follow-up period. This combination enables analysis and prediction of the influence of implantation upon bone and can be compared with of remodelling theories. The assessment of mechanical strain data during a follow-up trial could be a new approach for analyzing different hip stems in clinical biomechanics. © 2005 IPEM. Published by Elsevier Ltd. All rights reserved. Keywords: Total hip arthroplasty; Periprosthetic stress-shielding; In vivo strain analysis
1. Introduction Periprosthetic stress-shielding is recognized as one of the bone reactions after the implantation of a femoral stem and may be a factor influencing implant survival time [1–3]. Femoral FE bone remodelling analyses were based on animal experiments [4,5] or human specimen after death [6,7]. Kerner et al. [7] used the proximal part of a “typical” femur, which was described by Huiskes and van Rietbergen [8]. They modelled only the distal parts of the femora specimen specifically. Remodelling simulations were conducted by these and other authors, who combine bone remodelling theories with ∗
Corresponding author. Tel.: +49 5602 83 1201; fax: +49 5602 83 1980. E-mail address: [email protected] (M. Lengsfeld).
FE analysis. The project presented here combines clinical long term bone density data with FE analysis. It is a comparison of a 12-year THA follow-up with the not operated contralateral side. Similar to the methodological approach of Kerner et al. [7], the not operated femur is considered to represent the initial situation of the operated side 12 years before. The FE calculations are based on patient-specific CT density data and provide patterns of strain energy density (SED). The objective of the study presented here is an evaluation of femoral strain 12 years after THA.
2. Method Eleven post-menopausal female patients with unilateral THA and a press-fit cemented titanium alloy stem (Marburg
1350-4533/$ – see front matter © 2005 IPEM. Published by Elsevier Ltd. All rights reserved. doi:10.1016/j.medengphy.2004.12.016
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Table 1 Clinical data of all patients Patient number
Age OP
Age CT
Height (cm)
Weight OP (kg)
Weight CT (kg)
Side OP
Anteversion angle
Stem size
Walking distance (km)
Pain: preop./12 years
Flex/Ext: preop.
Flex/Ext: 12 years
11 12 13 14 15 16 17 18 19 20 21
53 60 51 40 53 63 55 56 58 63 57
65 72 63 52 65 74 68 67 71 75 71
168 162 158 164 168 154 154 159 158 161 148
67 83 60 64 75 63 62 75 71 81 90
75 70 77 81 79 75 70 72 78 75 79
Left Right Right Left Right Right Left Right Left Left Left
R: 22–L: 12 R: 19–L: 5 R: 15–L: 14 R: 15–L: 26 R: 27–L: 11 R: 30–L: 21 R: 19–L: 27 R: 25–L: 27 R: 26–L: 33 R: 16–L: 29 R: 30–L: 21
S L S S L M S S S L Dysplasia
>5 2–5 2–5 2–5 2–5 0.5–1 1–2 2–5 2–5 >5 0.5
3/5 3/6 3/6 3/4 3/5 3/6 2/6 3/5 3/6 4/6 3/6
90/10/0 80/0/0 105/0/0 100/0/0 Missing Missing 120/0/5 90/0/0 50/5/0 90/0/0 Missing
100/0/0 100/0/0 100/0/0 Missing Missing 100/0/0 110/0/0 110/5/0 100/5/0 110/0/10 110/0/0
Pain scale according to Merle’Aubign´e from 0 (extreme pain) to 6 (no pain).
system, Sulzer Orthopedics Ltd., Baar, Switzerland) were scanned in vivo 12 years (range 11 years and 3 months to 13 years and 8 months) after implantation. The scanner setting (Somatom Plus-4, Siemens, Erlangen, Germany) was 140 kV, 206 mA, 17 s, spiral algorithm with a recalculated slice thickness of 2 mm and a 512 × 512 pixel resolution. Clinical and CT density data of the patients have already been published [9]. A summary is shown in Table 1. On a scale of 1:1 CT voxels were transferred to finite element voxels (eight node brick elements) except for patient no. 1 with an enlarged scale because of a meshing-failure. Subsequently, the full CT information was used for automatic generation of the femoral FE models with an identical CT and FE voxel resolution of 0.66 mm × 0.66 mm × 2 mm. The number of elements is approximately 250 000 for each femur (bone and stem). The press-fit implantation technique is based on no size difference between the final rasp and the stem, thus causing a very thin cement layer (<2 mm). Therefore, no separate cement layer was modelled, neither at the operated nor at the computational implanted side (see below). Periprosthetic regions of interest (ROI) according to Gruen et al. [10] were defined around the stem. The CT Hounsfield values (HU) were linearly converted into elastic moduli [11,12]. Bone was defined between 170 and 1799 HU and was linearly related to elastic moduli between 1500 and 15 000 MPa. It is recognized that various relationships between apparent density and the modulus have been investigated [11,13–16]. Weinans et al. [17] demonstrated that the differences in stress-shielding results are independent of the density–modulus relationship used and can be examined as long as one uses the same relationship intraindividually or for each subject. In this study the same method was used at the operated side and at the contralateral side. The CT density of titanium has the maximum technical value of 3072 HU and was related to a modulus of 110 000 MPa. In order to investigate the effect of a 12-year THA survival time on femoral strain, the SED distribution was compared to the SED distribution of the contralateral femur (still not operated). The analysis of the anatomical contralateral femur would not be a suitable control for a 12-year comparison
with the postoperative situation. In order to make the results comparable, a computationally created stem was “implanted” into the contralateral femur model. A matrix of the stem size values was generated. An automatic algorithm [18] selected all bone, or bone marrow, elements that belong to the matrix and assigns to them an elastic modulus value of titanium alloy. The alignment and anteversion angle of the stem was equal to the stem’s position at the operated side (Fig. 1). In contrast to this methodology, a real contralateral implantation after death was conducted in the post-mortem study by Kerner et al. [7]. Loads were applied weight-dependent with a prosthesis head force, and an abductor force was applied at the greater trochanter [19,20]. Force magnitudes of 347% bodyweight (hip joint force) and 270% bodyweight (abductor force) were used. The vertical axis (z) of the coordinate system was defined by the hip and knee joint centre and the frontal axis (x) by the dorsal aspect of the femoral condyles. The joint force of a right hip was multiplied by −sin(15◦ ) to obtain the x-, by −sin(13◦ ) to obtain the y- and by cos(15◦ ) to obtain the z-component. The factors for the right abductor force were sin(19.5◦ ), sin(13◦ ) and −cos(19.5◦ ), respectively. Selection of these values was anticipated by an earlier sensitivity study in our group [21]. The trochanter force was divided into 40
Fig. 1. Method of computational hip stem implantation: femoral FE model of patient no. 9 (A) and after computational implantation (B). The model of patient no. 9 after computational implantation is again displayed (sections) (C) and compared with the surgical operated contralateral one (D).
0.07893 0.00476 0.01047 0.01504 0.01097 0.00545 0.00239
S.D. Mean
0.00785 −0.00506 −0.00986 −0.00604 −0.01171 −0.00524 −0.00189 −0.03740 −0.01385 −0.01206 −0.01070 −0.01478 −0.00552 −0.00904
No. 11 No. 10
−0.02752 −0.00722 −0.01984 −0.02715 −0.02042 −0.00762 −0.00020 −0.07378 −0.00966 −0.02350 −0.02208 −0.02089 −0.00896 −0.00174
No. 9 No. 8
0.00794 −0.00110 −0.00843 0.00905 −0.00807 −0.00556 −0.00138 −0.01366 0.00222 0.01412 0.02559 0.01574 0.00309 −0.00176
No. 7 No. 6
0.24142 −0.00309 −0.00406 −0.00298 −0.01084 −0.00123 −0.00066 0.00130 −0.00196 −0.00541 −0.00296 −0.00868 −0.00295 −0.00041
No. 5 No. 4
0.03266 −0.00164 −0.00687 0.00267 −0.00479 −0.00104 0.00011 −0.00221 −0.01090 −0.02629 −0.02696 −0.02635 −0.01009 −0.00250 0.00228 −0.00130 −0.00824 −0.00615 −0.00794 −0.00021 −0.00115
No. 3 No. 2
The calculated intraindividual strain energy density differences between operated and non-operated side (SED(operated) − SED(not operated)) of all 11 cases are shown in Table 2. The median SED values (Fig. 3) changed by −31.65% (ROI 1), −25.64% (ROI 2), −30.82% (ROI 3), −12.35% (ROI 4), −40.10% (ROI 5), −30.37% (ROI 6) and −43.38% (ROI 7). The reduction of SED was greatest in the ROI 3 and 5 which are around the tip of the stem. ROI 1, where the abductor’s forces were applied, shows no clear trend with varying results from positive to negative SED adaptation. Generally, a reduction of the SED increasing from proximal to distal is observed. Distal of the stem (ROI 4) the SED difference regains. The absolute strain energy density values are summarized in Fig. 4.
No. 1
3. Results
−0.04468 −0.00716 −0.00791 −0.00478 −0.02175 −0.01749 −0.00207
components being separately applied at 40 different superficial nodes at the greater trochanter region. The 25 components were associated with the gluteus medius and 15 with the gluteus minimus muscle insertion area. The sensitivity of this method of force separation was examined in case no. 2 by applying 20, 30 and 40 nodal forces. Each application was done three times with coincidental selected nodes at the greater trochanter. Lowest averaged SED value of every ROI was subtracted from highest of the three calculations. In the case of 40 components, the difference between the three coincidental loads became less than 5% (Fig. 2) except of ROI 1. Solutions were performed with the gradient solver (default setting) of the FE software ANSYS® 5.3. Statistical analysis was performed for the group of 11 as a sample size, recognising the low number of patients. The two-way Wilcoxon test (signed-rank-test) was applied with a level of statistical significance at 5%. The study was approved by the ethics commission of the Philipps University of Marburg. Informed consent is documented.
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ROI 1 ROI 2 ROI 3 ROI 4 ROI 5 ROI 6 ROI 7
Fig. 2. Deviation of the SED reduction results by three coincidental load applications using one time 20 nodes at the greater trochanter, one time 30 and one time 40 nodes (from left to right). Lowest averaged SED value of every ROI was subtracted from highest of the three calculations. In case of 40 components, the difference between the three coincidental loads became less than 5% except of ROI 1.
Table 2 The calculated intraindividual strain energy density differences between operated and non-operated femur (SED(operated) − SED(not operated)) of all 11 cases are shown including mean values and standard deviations (S.D.)
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Fig. 5. Median SED differences (MPa) between the operated and not operated femur of all 11 patients with respect to the ROI.
Fig. 3. Median SED differences (%) between the operated and not operated femur of all 11 patients with respect to the ROI.
Fig. 4. The mean SED values of the operated (white columns) and computationally operated (black columns) side is given with respect to the Gruen zones.
In Fig. 5 the medians of all SED differences (ROI 1–7) are presented. The results of all regions except of ROI 1 and ROI 4 demonstrated a statistically significant decreased SED at the operated side with p-values: ROI 1 (p = 0.2676), ROI 2 (p = 0.0064), ROI 3 (p = 0.0132), ROI 4 (p = 0.0655), ROI 5 (p = 0.0104), ROI 6 (p = 0.0064) and ROI 7 (p = 0.0022).
4. Discussion The combination of bone remodelling theories with FE analysis (e.g. [8]) represents a valuable tool in order to analyze and to predict the influence of an implant upon bone. Unfortunately, remodelling theory [22–26] is still not defined as a quantitative mathematical law. Hence, FE remodelling
results are based on phenomenological descriptions of the reality and not of quantitative-mechanistic models. As Wolff’s law is still not finally formulated, it is reasonable to combine FE analyses not with calculated, but with clinically available bone remodelling data. Bone mineral density changes after THA are clinically measurable by dual X-ray absorptiometry (DEXA), cf. [27,28]. However, DEXA has rather low resolution, measures only two-dimensionally and does not provide complete circumferential information. The striking advantage of the CT scans is the acquisition of fully 3D density values while providing also geometric data, which can be easily postprocessed by a variety of 3D finite element meshing techniques [29,30]. FE models of the current study are therefore based on a CT data source [9]. The mesh density in the current FE simulation project strictly depends on the voxel/pixel resolution of the CT data set. Hence, the FE mesh has the identical density than the CT mesh without information loss during the transfer process. Of course, multiple CT scanning in order to test different voxel resolutions would have given further information but could not be done for ethical reasons. A higher in-plane pixel resolution was not possible during in vivo scanning with this scanner setting, anyway. Using the maximum FE mesh density under these circumstances, a mesh density sensitivity study is not possible and was not done. Several relationships have been published in order to transfer bone density to elastic modulus accurately [11,13–16,31]. In this study a direct linear transfer from HU to elastic modulus was used, an approach which can be traced back to Ciarelli et al. [11]. Weinans et al. [17] demonstrated that subjectspecific FE models provide consistent stress-shielding patterns in the bone, independent of the choice of the bone density–modulus relationship used in the computer model. As Pauwels [19] convincingly demonstrated, forces were applied weight-dependent at the FE models with a femoral head force and an abductor force to simulate the one legged stance, a method, which was again tested and confirmed by Stolk et al. [20]. The resultant hip force being implemented is verified by telemetric hip force measurements in vivo [32]. The certainty
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of muscle forces are not that clear as the amounts of these forces have been never confirmed by in vivo measurements. The data given by Duda et al. [33] are based on purely theoretical calculations. The “classical” load configuration in the current study could be justified by the fact that always right-to-left comparisons with identical constraints were performed and analyzed. Moreover, Stolk et al. [20] state that additional inclusion of the iliotibial tract, the adductors and the vastii produced relatively small effects during all gait phases. Their most prominent effect was a slight reduction of bone strains at the level of the stem tip during heel-strike. Their results suggest that a loading configuration including the hip joint contact force and the abductor forces can adequately reproduce in vivo loading of cemented total hip reconstructions in pre-clinical tests. Apparently, there is no striking effect after inclusion of further muscles, while this effect is counterbalanced in a rightto-left comparison, anyway. Therefore we decided to choose the “classical” load configurations at the hip joint. The accuracy was enhanced by dividing the trochanter force into 40 components being separately applied at 40 different superficial nodes at the muscular insertion area. In accordance with Weinans et al. [17] the same loading was used within each subject in the study. The known limitations of the CT approach used here (partial volume effect, fat error, metal artifacts) have only a minor influence upon density data [9] and would not markedly influence the right-to-left comparison presented in this study. Zannoni et al. [34] demonstrated that the presence of a titanium alloy implant creates an apparent increase in crosssectional bone density of 71–85 HU. They found this increase within a distance of 4–8 pixels from the metal implant, with a pixel size being 0.3 mm × 0.3 mm, this means a distance of 1–2.5 mm. Within this interface zone the average density increase was 1100 HU in the first, 400 in the second, 100 in the third and zero in the fourth pixel crown surrounding the stem. They conducted their in vitro experiments without bone cement and selected a higher image resolution. In the in vivo study presented here, the CT/FE pixel size is 0.66 mm × 0.66 mm × 2 mm causing a higher partial volume effect. The upper threshold value is 1600 HU in order to separate bone from metal voxels, while the CT density of titanium is the maximum technical value of 3072 HU. As a result of this difference, interface voxels containing both metal and cement have an averaged HU value above 1600 and are deleted. In addition, pure cement voxels at the interface above 1600 HU due to a metal induced enhancement are deleted. Using this procedure the artifacts caused by the implant could be minimised. After converting the HU values in elastic moduli, Zannoni et al. [34] concluded that apart from a 2 mm thick region around the implant, the CT images could be used to derive the mechanical properties of bone tissue. As regards the geometry they estimated average error of 0.45 mm in the reconstruction of titanium hip stem cross-section geometry. Previously, Sutherland and Gayou [35] concluded
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from their composite phantom tests that intramedullary titanium is not a deterrent to obtaining accurate measurements of cortical bone dimensions and properties. When using cemented titanium implants, as in the current study, the artifacts are primarily located within the cement layer and they hardly influence the bone density values. Evidently, the artifacts are greater at the proximal stem, where this type has a larger extension of width and the surrounding bone a lower density. Cross-sectional evaluations at the greater trochanter region may show no clear results at the greater trochanter region. The deletion of a second voxel crown around the interface could further diminish the artifacts in the trochanter part of the femur. This was previously tested by deleting a voxel crown around the implant [9]: a density enhancement up to 40 HU was seen around the greater trochanter region, while no difference was measured distally. Titanium artifacts are primarily located near the interface within the cement layer [34], which was not separately modelled. Evidently, the artifacts are greater at ROI 1, where this type of endoprosthesis has a larger extension of width and the surrounding bone is of lower density. Furthermore, abductor force components applied at ROI 1 could cause local strain peaks. This could be the reason for the unclear, statistically not significant, results at ROI 1. The certainty of the current retrospective CT/FE study is limited because of a comparison with the contralateral side only. To date prospective, longitudinal 12-year CT follow-up studies are not available. These would provide useful additional data. Our results demonstrate a clear, statistically significant, SED reduction being caused by bone loss at the operated side in individual patients 12 years after surgery. This observation increases from proximal to distal. The reduction of SED was greatest in the ROI 3 and 5 which are around the tip of the stem. If the statistical test was done without the data of no. 7, the p-value of ROI 4 became also significant (p = 0.0183). Kr¨oger et al. [36] reported that a restoration of bone density around the implants may occur in some cases, which could explain almost no stress-shielding in one particular patient (no. 7). As the stress-shielding results presented here do not depend on a mechanical bone adaptation hypothesis, they are probably close to reality and might serve as reference data for purely theoretical simulations. As far as we are aware, this in vivo collection of patientspecific stress-shielding information after THA is based on the highest case number and the longest follow-up period. The method could be a new approach for analyzing different hip stems in clinical biomechanics.
Acknowledgements The authors express gratitude for the funding received from the Deutsche Forschungsgemeinschaft (DFG Le-
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1065/1-1). We wish to thank Dr. Helen Steele for discussing the text. [18]
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