This article was downloaded by: [Selcuk Universitesi] On: 17 January 2015, At: 10:48 Publisher: Taylor & Francis Informa Ltd Registered in England and Wales Registered Number: 1072954 Registered office: Mortimer House, 37-41 Mortimer Street, London W1T 3JH, UK
Computer Methods in Biomechanics and Biomedical Engineering Publication details, including instructions for authors and subscription information: http://www.tandfonline.com/loi/gcmb20
Comparison between mechanical stress and bone mineral density in the femur after total hip arthroplasty by using subject-specific finite element analyses a
a
a
a
a
Hiroyuki Ike , Yutaka Inaba , Naomi Kobayashi , Yasuhide Hirata , Yohei Yukizawa , Chie a
a
a
Aoki , Hyonmin Choe & Tomoyuki Saito a
Click for updates
Department of Orthopaedic Surgery, Yokohama City University, 3-9, Fukuura, Kanazawaku, Yokohama, Kanagawa 236-0004, Japan Published online: 24 Mar 2014.
To cite this article: Hiroyuki Ike, Yutaka Inaba, Naomi Kobayashi, Yasuhide Hirata, Yohei Yukizawa, Chie Aoki, Hyonmin Choe & Tomoyuki Saito (2015) Comparison between mechanical stress and bone mineral density in the femur after total hip arthroplasty by using subject-specific finite element analyses, Computer Methods in Biomechanics and Biomedical Engineering, 18:10, 1056-1065, DOI: 10.1080/10255842.2013.869320 To link to this article: http://dx.doi.org/10.1080/10255842.2013.869320
PLEASE SCROLL DOWN FOR ARTICLE Taylor & Francis makes every effort to ensure the accuracy of all the information (the “Content”) contained in the publications on our platform. However, Taylor & Francis, our agents, and our licensors make no representations or warranties whatsoever as to the accuracy, completeness, or suitability for any purpose of the Content. Any opinions and views expressed in this publication are the opinions and views of the authors, and are not the views of or endorsed by Taylor & Francis. The accuracy of the Content should not be relied upon and should be independently verified with primary sources of information. Taylor and Francis shall not be liable for any losses, actions, claims, proceedings, demands, costs, expenses, damages, and other liabilities whatsoever or howsoever caused arising directly or indirectly in connection with, in relation to or arising out of the use of the Content. This article may be used for research, teaching, and private study purposes. Any substantial or systematic reproduction, redistribution, reselling, loan, sub-licensing, systematic supply, or distribution in any form to anyone is expressly forbidden. Terms & Conditions of access and use can be found at http:// www.tandfonline.com/page/terms-and-conditions
Computer Methods in Biomechanics and Biomedical Engineering, 2015 Vol. 18, No. 10, 1056– 1065, http://dx.doi.org/10.1080/10255842.2013.869320
Comparison between mechanical stress and bone mineral density in the femur after total hip arthroplasty by using subject-specific finite element analyses Hiroyuki Ike, Yutaka Inaba*, Naomi Kobayashi, Yasuhide Hirata, Yohei Yukizawa, Chie Aoki, Hyonmin Choe and Tomoyuki Saito Department of Orthopaedic Surgery, Yokohama City University, 3-9, Fukuura, Kanazawa-ku, Yokohama, Kanagawa 236-0004, Japan
Downloaded by [Selcuk Universitesi] at 10:48 17 January 2015
(Received 7 February 2013; accepted 21 November 2013) The mechanism underling bone mineral density (BMD) loss that occurs in the femur after total hip arthroplasty (THA) remains unknown. We compared the equivalent stress and strain energy density (SED) to BMD in the femur after THA using subject-specific finite element analyses. Twenty-four patients who had undergone primary cementless THA were analysed. BMD was measured using dual-energy X-ray absorptiometry (DEXA) at 1 week and 3, 6 and 12 months after THA. Seven regions of interest (ROIs) were defined in accordance with Gruen’s system (ROIs 1 – 7). Computed tomography images of the femurs were acquired pre- and postoperatively, and the images were converted into three-dimensional finite element (FE) models. Equivalent stress and SED were analysed and compared with DEXA data. BMD was maintained 1 year after THA in ROIs 3, 4, 5 and 6, whereas BMD decreased in ROIs 1, 2 and 7. FE analysis revealed that equivalent stress in ROIs 3, 4, 5 and 6 was much higher than that in ROIs 1, 2 and 7. A significant correlation was observed between the rate of changes in BMD and equivalent stress. Reduction of equivalent stress may contribute to decrease in BMD in the femur after THA. Keywords: finite element analysis; bone mineral density; total hip arthroplasty
1.
Introduction
Periprosthetic bone loss, i.e. decrease in bone mineral density (BMD) around an implant, is a major concern following total hip arthroplasty (THA) (Malchau et al. 1993; Dorr et al. 1997). Severe periprosthetic bone loss may contribute to aseptic loosening of the prosthesis or the risk of periprosthetic fracture (Bougherara et al. 2007) and presents serious problems if revision surgery becomes necessary (Kerner et al. 1999). Several studies have reported that BMD decreases following THA, particularly in the proximal femur (Kroger et al. 1996; Kim et al. 2007). Most changes in BMD occur during the first postoperative year, after which BMD is maintained (Nishii et al. 1997; Kroger et al. 1998; Rosenthall et al. 1999). This phenomenon may be an adaptive remodelling response of the bone structure to significantly alter its stress environment due to the implantation. Therefore, mechanical stress may be associated with the patterns in BMD changes. In particular, in cementless THA, an optimal fit of the stem into the metaphyseal region of the femur reportedly leads to a reduction in periprosthetic bone loss (Ostbyhaug et al. 2009). A major cause of this phenomenon may be that the fit-and-fill type of prosthesis was designed to improve proximal fixation and physiological load transfer in the proximal femur. Wolff (1892) proposed that trabecular bone in the proximal femur adapts to external mechanical loads. This structural change is caused by bone remodelling, which
*Corresponding author. Email: [email protected] q 2014 Taylor & Francis
couples bone resorption by osteoclasts and bone formation by osteoblasts (Jaworski 1984). It is generally accepted that bone tissue can detect and respond to its mechanical environment, but there is no consensus regarding how bone cells detect mechanical loads (Turner et al. 1995). Various biomechanical parameters have been investigated as the remodelling stimulus. Huiskes et al. (1987) examined whether strain energy density (SED) controls bone remodelling. Carter et al. (1996) examined the stress and Stulpner et al. (1997) examined the equivalent strain as signals. Adachi et al. (1997) proposed that the driving force of the remodelling is the local nonuniformity of the scalar function of stress. The existence of various theories indicates that the mechanism of bone remodelling is not well understood. Several simulation models based on the micro-scale bone remodelling theory have reproduced some characteristics of the trabecular bone or BMD in the human femur (Adachi et al. 1997). Kwon et al. (2013) proposed a method to predict a change in bone structure, based on a trabecular bone remodelling model. They concluded that mechanical remodelling simulation could effectively estimate bone resorption and the occurrence of the stress shielding after THA. Jang and Kim (2010) developed a micro finite element (FE) model to represent the full trabecular architecture in the human proximal femur. They showed that the external shape of the cortical bone and internal morphology of the trabecular bone adapted to the surrounding mechanical environment.
Downloaded by [Selcuk Universitesi] at 10:48 17 January 2015
Computer Methods in Biomechanics and Biomedical Engineering
1057
Subject-specific FE models based on geometry and mechanical properties derived from computed tomography (CT) have been described in several studies (Keyak et al. 1998; Taddei et al. 2007; Pettersen et al. 2009). Furthermore, relationships between results of subjectspecific FE analyses and bone density have been investigated. Cody et al. (1999) carried out subjectspecific FE analyses and bone density measurements for predicting the fracture load of femurs. Tawara et al. (2010) evaluated the vertebral strength using the subject-specific FE models and BMD. However, few studies have focused on the validity of subject-specific FE analyses in assessing BMD changes in the femur after THA. In this study, we constructed subject-specific FE models of femurs and assessed changes in equivalent stress and SED using clinical samples before and after THA. Therefore, the purpose of this study was to investigate the equivalent stress and SED using subject-specific FE analyses and to compare the results of the FE analyses with changes in BMD in the femur after fit-and-fill type cementless THA. 2. Materials and methods This study was approved by our Institutional Review Board. Informed consent was obtained from all individuals before enrollment. Twenty-four patients (16 women and 8 men) who underwent primary cementless THA using the same fit-and-fill type of prosthesis (collarless Versys Fiber Metal MidCoat; Zimmer, Inc., Warsaw, IN) were enrolled in this prospective study. Collarless Versys Fiber Metal MidCoat is a fit-and-fill type femoral component composed of titanium alloy with a fibre metal porous coating on the proximal region of the implant (Figure 1). Patients treated with bisphosphonate, vitamin D or systemic oestrogen were excluded from the study. The mean age of the patients at the time of THA was 63 ^ 11 years (range 44– 82). After surgery, all patients were allowed to transfer from the bed to a wheelchair with full weight bearing on postoperative day 1 followed by gait exercise as soon as possible. 2.1
Figure 1. Collarless Versys Fiber Metal MidCoat.
2.2 Finite element analysis CT scans (Sensation16; SiemensAG, Erlangen, Germany) of the femurs of all patients were acquired pre- and postoperatively (1 week after surgery). Scanner settings were approximately 140 kV and 300 mA, with a slice thickness of 2 mm, 512 £ 512 pixel resolution and a 0.70 mm £ 0.70 mm £ 2 mm voxel size. We calibrated the Hounsfield unit values in the CT using a water phantom once a day.
BMD measurement
BMD was measured 1 week after THA as reference baseline, with subsequent measurements taken at 3, 6 and 12 months postoperatively. BMD measurement was carried out with dual-energy X-ray absorptiometry (DEXA) on the Hologic Discovery system (Hologic, Inc., Waltham, MA). Patients were placed in the supine position with the affected leg in 208 internal rotation for limiting measurement errors. The BMD was measured using the ‘Array prosthetic mode’ in which metal was excluded from analysis of regions of interest (ROIs). ROIs were defined in accordance with the system established by Gruen et al. (1979) (Figure 2). Pixel size was 1.1 mm £ 0.56 mm.
Figure 2. ROIs for BMD measurements in accordance with the system established by Gruen.
Downloaded by [Selcuk Universitesi] at 10:48 17 January 2015
1058
H. Ike et al.
FE models of the femur and stem were obtained from pre- and postoperative CT data using Mechanical Finder ver. 6.0 (Research Center of Computational Mechanics, Inc., Tokyo, Japan), which is a software that creates FE models showing individual bone shape and density distribution (Bessho et al. 2007). A global threshold algorithm was used to extract the bone area with a threshold of 200 mg/cm3 with manual correction if necessary. For extracting the bone area when the density was extremely low, we used a closing algorithm in addition to the global threshold algorithm (Bessho et al. 2007). A global threshold algorithm was used to extract the stem area with a threshold of 2000 Hounsfield Units. Three-dimensional FE models, using 1 – 4 mm tetrahedral elements for the trabecular and inner cortical bone and 3-nodal-point shell elements with a thickness of 0.3 mm for the outer surface of the cortical bone, were constructed for each patient (Figure 3). FE models of the femur consisted of approximately 600,000 elements in addition to 200,000 elements for the stem. The bone density was determined on the basis of CT density values, using the calibration equation (Table 1). The elastic modulus of the bone was determined on the basis of bone density values, using the equations proposed by Keyak et al. (1994, 1998) and Keller (1994) (Table 1). The Poisson’s ratio of the bone was 0.40. The stem was an isotropic titanium alloy with an elastic modulus of 109.0 GPa and a Poisson’s ratio of 0.28. The models assumed a completely bonded interface between the stem and the bone. The onelegged standing condition was simulated. The femoral shaft was fully restrained, and force was applied to the femoral head and greater trochanter. A load of 2400 N was applied to the femoral head at an angle of 158 relative to the femoral axis, and a load of 1200 N was applied to the greater trochanter at an angle of 208 (Bergmann et al. 2001; Herrera et al. 2009) (Figure 4). Linear FE analysis was carried out. Equivalent stress and SED were analysed in ROIs 1– 7 and compared with the DEXA data. Average equivalent stress and SED in a sphere with a radius of 3 mm, the centre of
which was on the surface of the femur, were measured for each ROI. We adopted the Drucker – Prager equivalent stress (Appendix A). Stem alignment was measured on postoperative anteroposterior radiographs by measuring the angle formed between the long axis of the stem and the long axis of the femur. Stem alignment of less than 28 was considered neutral (Gonzalez Della Valle et al. 2005). The Wilcoxon signed-rank test was used to analyse changes in BMD. Correlations between BMD and other values were analysed using Pearson’s product-moment correlation coefficient. p-Values , 0.05 were considered significant. All data are expressed as the mean ^ standard deviation.
3.
Results
The relative BMD values in the femur at 1 week and 3, 6 and 12 months after THA are shown in Figure 5. Relative BMD values are expressed as percentage of the baseline measurement. Similarly, equivalent stress and SED are expressed as percentage of the preoperative values. BMD was maintained 12 months after THA in ROIs 3, 4, 5 and 6, whereas it decreased significantly by 19%, 11% and 27% in ROIs 1, 2 and 7, respectively, 12 months after THA. Stem alignment was neutral in 20 subjects (83%), 28 of the varus in 2 subjects (8%), 38 of the varus in 1 subject (4%) and 28 of the valgus in 1 subject (4%). No valgus or varus stem alignment greater than 38 was observed. The elastic modulus, equivalent stress and SED in preand postoperative models are shown in Figure 6. FE analyses revealed that equivalent stress and SED were maintained in ROIs 3, 4 and 5 after THA, whereas both decreased in ROIs 1, 2, 6 and 7 (Figure 7). In particular, in ROI 7, equivalent stress, SED and relative BMD values exhibited the lowest values of all regions examined ( p , 0.05). A significant correlation was observed between the rate of changes in BMD and equivalent stress
Figure 3. Diagram of mesh model. Trabecular bone and the inner portion of cortical bone were modelled using 1 –4 mm tetrahedral elements, while the outer cortex was modelled using 3-nodal-point shell elements with a thickness of 0.3 mm.
Computer Methods in Biomechanics and Biomedical Engineering Table 1. bone.
Equations used to calculate the elastic modulus of the
Bone density
r¼0 0 , r # 0.27 0.27 , r , 0.6 0.6 # r
Elastic modulus (MPa) 0.001 33,900r 2.20 5307r þ 469 10,200r 2.01
Notes: r(g/cm3) ¼ (HU þ 1.4246) £ 0.001/1.058 (HU . 2 1) ¼ 0.0 (HU # 2 1), where HU represents CT density values in Hounsfield Units. The elastic modulus of the bone is determined on the basis of CT density values, using the equations proposed by Keyak et al. and Keller.
Downloaded by [Selcuk Universitesi] at 10:48 17 January 2015
(R ¼ 0.426, p , 0.01). However, no significant correlation was observed between the rate of changes in BMD and SED (R ¼ 0.183, p ¼ 0.053) (Figure 8). 4. Discussion Postoperative BMD loss, which can occur around implants after THA, may be related to changes in mechanical stress conditions. This loss is an important issue, which requires a multifactorial approach. The goal of this study was to reveal the relationship between BMD loss and changes in mechanical stress conditions after cementless THA involving fit-and-fill type stems using subject-specific FE analyses. The present subject-specific analyses of the femurs of 24 subjects before and after THA revealed a significant correlation between changes in BMD and equivalent stress.
Figure 4. Diagram of loading and restriction conditions. The femoral shaft is fully restrained, and force is applied to the femoral head and the greater trochanter. A load of 2400 N is applied to the femoral head at an angle of 158 relative to the femoral axis, and a load of 1200 N is applied to the greater trochanter at an angle of 208.
1059
Previous investigations have predominantly used changes in SED for bone adaptation remodelling. However, the results obtained from our preliminary analysis indicated that the SED variation in the femur was relatively large, and there was a very weak correlation between the rate of changes in BMD and SED. In contrast, the equivalent stress decreased in the proximal femur and was maintained in the distal femur, in most cases, after THA. The changes in equivalent stress showed similar patterns compared with the changes in BMD. From a previous report, a good correlation was reported between the results of equivalent stress and DEXA (Herrera et al. 2007). Therefore, we focused on SED and equivalent stress in this study. After THA, the stress load is transferred to the distal femur through the stem rather than to the periprosthetic bone due to the high elastic modulus of the stem (Maistrelli et al. 1991; Decking et al. 2006). Therefore, equivalent stress in the proximal femur may decrease after stem implantation. These results were consistent with those of previous studies (Herrera et al. 2009; Pettersen et al. 2009). We assessed the effect on bone remodelling of the collarless Versys Fiber Metal MidCoat, a porouscoated titanium-alloy fit-and-fill type stem. Although this implant is meant to provide proximal fixation, BMD and equivalent stress in the proximal femur decreased postoperatively. These results indicate that stress transfer to the proximal femur may be insufficient for maintaining BMD. Our results showed that BMD decreased by 19%, 11% and 27% in ROIs 1, 2 and 7, respectively, 12 months after THA. The changes in BMD noted in this study were similar to those reported by others (Aldinger et al. 2003; Boden and Adolphson 2004).
Figure 5. Bar graph of changes in BMD 1 week and 3, 6 and 12 months after THA in each ROI. Changes in BMD are calculated as percent decreases of the status at 1 week. BMD significantly decreased by 19%, 11% and 27% in ROIs 1, 2 and 7, respectively, 12 months after THA (*p , 0.05, which was significantly different from the 1-week value with a Wilcoxon signed-rank test). BMD was maintained 12 months after THA in ROIs 3, 4, 5 and 6.
H. Ike et al.
Downloaded by [Selcuk Universitesi] at 10:48 17 January 2015
1060
Several previous studies have described the application of FE analysis in investigating bone remodelling patterns around implants. However, most of these models were not subject specific. For example, mechanical properties of the bone were homogeneous (Herrera et al. 2009) or parts of the bone model were based on the geometry of a typical femur (Kerner et al. 1999). Weinans et al. (2000) reported that subject-specific FE models may be useful for explaining variations in bone adaptation responsiveness between different subjects. In our study, CT scans were obtained from all patients pre- and postoperatively, and subject-specific FE models were constructed to investigate bone heterogeneity by using the
equations proposed by Keyak et al. (1994, 1998) and Keller (1994). Variations in equivalent stress and SED between patients resulted from the subject-specific geometry and mechanical properties of the femur. DEXA is a precise method for quantifying bone mass and density changes during follow-up after THA. Kroger et al. (1996) reported that the average precision error of DEXA is 2.3% for the uncemented stem and concluded that small changes in the bone can be measured. Changes in BMD are influenced by the size, coating, design and stiffness of the stem, initial bone density, focal osteolysis and timing of weight bearing (Engh et al. 1987; Nishii et al. 1997; Boden and Adolphson 2004). Varus or valgus
1061
Downloaded by [Selcuk Universitesi] at 10:48 17 January 2015
Computer Methods in Biomechanics and Biomedical Engineering
stem alignment leads to changes in the stress distribution of the femur, which may affect the BMD changes. In this study, no valgus or varus stem alignment greater than 38 was observed. Therefore, the effects of stem alignment on stress distribution and BMD changes are considered negligible. This study demonstrated that equivalent stress correlates to changes in BMD in the femur in the 12 months following THA. Our results suggest that the rate of changes in equivalent stress could be an important factor for changes in BMD; however, the determination coefficient was only 18%. Therefore, equivalent stress alone was insufficient for predicting changes in BMD. The
strain-adaptive bone remodelling theory was used to simulate changes in BMD after THA; Huiskes et al. (1987) reported that the SED distribution represents the regions where resorption and apposition is expected. However, other studies have shown that stress parameters, rather than strain parameters, are better predictors of bone remodelling. The clinical data and simulation results showed a correlation between average equivalent stress and BMD (Herrera et al. 2007; Kwon et al. 2013). As these examples suggest, controversy still exists with regard to whether equivalent stress or SED is an appropriate parameter for evaluating bone remodelling. Our results suggest that the decrease in equivalent stress caused the
H. Ike et al.
Downloaded by [Selcuk Universitesi] at 10:48 17 January 2015
1062
Figure 6. Distributions of (a) elastic modulus, (b) equivalent stress and (c) SED in the femur. Pre- and postoperative elastic modulus showed similar patterns, suggesting that changes of bone density after implantation of the femoral stems were small. Equivalent stress and SED were maintained in the distal femur after THA, whereas both decreased in the proximal femur.
decrease in BMD in the proximal femur after THA. Furthermore, no significant correlation was observed between the rate of changes in BMD and SED. This result might be explained by the considerable dispersion in SED. Figure 7 shows relatively large values of standard deviation in SED. Another possible explanation is that the equivalent stress more strongly influences the bone tissue in sensing the surrounding mechanical environment than does the SED. In this study, equivalent stress and SED were measured in the cortex of the femur around the
stem, because the stem was inserted into the femur using the press-fit technique in which the femoral canal was filled with the stem. Equivalent stress rather than SED may be an appropriate parameter for analysing bone remodelling in the cortex bone. There are several limitations to this study. First, all analyses were carried out using only one static-loading condition, and the patients’ age, gender and activity levels, which might affect the changes in BMD, were not taken into account. Second, in the FE analysis, we did not
Computer Methods in Biomechanics and Biomedical Engineering
1063
Downloaded by [Selcuk Universitesi] at 10:48 17 January 2015
Figure 7. Bar graph of the results of SED, equivalent stress and BMD 12 months after THA. In ROI 7, equivalent stress, SED and relative BMD values showed the lowest values.
consider the surface properties of the implant (e.g. hydroxyapatite coatings), which affect fixation of the implant in the femur and may influence bone remodelling around the implant (Boe et al. 2011). The surface texture, localisation and magnitude of the surface material can facilitate bone ingrowth (Baad-Hansen et al. 2011). The fibre metal porous coating, which was applied to the proximal portion of the collarless Versys Fiber Metal MidCoat, exhibited high levels of osseointegration (Rahbek et al. 2005). Our models assumed a completely bonded interface, which did not allow micromotion between the stem and bone. Consideration of the surface properties of the implant and degree of stem fixation would be useful to construct more realistic models. Third, CT scans were acquired without the calibration phantom. Quantitative CT-based FE models can improve the prediction of the bone mechanical properties. A reference phantom is typically used to standardise measurements to a mineral reference and correct for potential analytical errors arising from beam hardening and radiation scattering (Habashy et al. 2011). The calibration of Hounsfield unit values, using a reference phantom, improves the model accuracy and may affect the SED and equivalent stress results. In addition, the effect of metal artefacts caused by implants is a major concern in CT-based FE analysis. During CT scanning, metallic objects absorb and scatter radiant energy at various sites, causing metal artefacts. Titanium is recognised as having fewer artefacts on CT (Lawton et al. 1996). In this study, the stems were composed of titanium alloy and small artefacts were observed in the vicinity of the stems in CT images. We used a moderately high peak voltage to acquire images with fewer artefacts. Barrett and Keat (2004) reported that increasing the peak voltage increases the likelihood that radiation energy will penetrate the metallic hardware; thus, artefacts are expected to be diminished with higher peak voltages (Lee et al. 2007).
Figure 8. Scatter plot of the relationship (a) between BMD and equivalent stress and (b) between BMD and SED. BMD values 1 year after THA were expressed as percentage of the baseline measurements (1 week after THA). Postoperative equivalent stress and SED, which were analysed using the CT data 1 week after THA, were expressed as percentage of the preoperative values. (a) A significant correlation was observed between the rate of changes in BMD and equivalent stress (R ¼ 0.426, p , 0.01). (b) No significant correlation was observed between the rate of changes in BMD and SED (R ¼ 0.183, p ¼ 0.053).
Finally, the maximum length of the tetrahedral elements (4 mm) was relatively large and might straddle the boundary between the cortical and cancellous area in the FE models. Therefore, the elastic modulus of the element straddling the boundary would contain some errors. Chen et al. (2010) reported that the distribution of bone density becomes smoother as the element size decreases. A smaller element size provides more accurate results in the FE analysis. To overcome this limitation, we adopted triangular shell elements on the outer surface of the cortical area to represent the thin cortical shell for reproducing the cortical area (Bessho et al. 2007). Furthermore, the number of elements in our FE models is larger than that of other recent reports (Perez and SeralGarcia 2013; van der Ploeg et al. 2012). Further studies involving these factors are necessary to more accurately simulate postoperative conditions.
1064
H. Ike et al.
5. Conclusion We confirmed a correlation between changes in BMD and equivalent stress through subject-specific FE analysis before and after THA. BMD and equivalent stress decreased in the proximal femur after THA. The rate of changes in equivalent stress could be an important factor for changes in BMD after THA.
Downloaded by [Selcuk Universitesi] at 10:48 17 January 2015
References Adachi T, Tomita Y, Sakaue H, Tanaka M. 1997. Simulation of trabecular surface remodeling based on local stress uniformity. Jpn Soc Mech Eng. 40:782 – 792. Aldinger PR, Sabo D, Pritsch M, Thomsen M, Mau H, Ewerbeck V, Breusch SJ. 2003. Pattern of periprosthetic bone remodeling around stable uncemented tapered hip stems: a prospective 84-month follow-up study and a median 156month cross-sectional study with DXA. Calcif Tissue Int. 73:115 – 121. Baad-Hansen T, Kold S, Olsen N, Christensen F, Soballe K. 2011. Excessive distal migration of fiber-mesh coated femoral stems. Acta Orthop. 82:308– 314. Barrett JF, Keat N. 2004. Artifacts in CT: recognition and avoidance. Radiographics. 24:1679 – 1691. Bergmann G, Deuretzbacher G, Heller M, Graichen F, Rohlmann A, Strauss J, Duda GN. 2001. Hip contact forces and gait patterns from routine activities. J Biomech. 34:859 – 871. Bessho M, Ohnishi I, Matsuyama J, Matsumoto T, Imai K, Nakamura K. 2007. Prediction of strength and strain of the proximal femur by a CT-based finite element method. J Biomech. 40:1745– 1753. Boden H, Adolphson P. 2004. No adverse effects of early weight bearing after uncemented total hip arthroplasty: a randomized study of 20 patients. Acta Orthop Scand. 75:21– 29. Boe BG, Rohrl SM, Heier T, Snorrason F, Nordsletten L. 2011. A prospective randomized study comparing electrochemically deposited hydroxyapatite and plasma-sprayed hydroxyapatite on titanium stems. Acta Orthop. 82:13 – 19. Bougherara H, Bureau M, Campbell M, Vadean A, Yahia L. 2007. Design of a biomimetic polymer-composite hip prosthesis. J Biomed Mater Res. 82:27 – 40. Carter DR, Van Der Meulen MC, Beaupre GS. 1996. Mechanical factors in bone growth and development. Bone. 18:5S – 10S. Chen G, Schmutz B, Epari D, Rathnayaka K, Ibrahim S, Schuetz MA, Pearcy MJ. 2010. A new approach for assigning bone material properties from CT images into finite element models. J Biomech. 43:1011– 1015. Cody DD, Gross GJ, Hou FJ, Spencer HJ, Goldstein SA, Fyhrie DP. 1999. Femoral strength is better predicted by finite element models than QCT and DXA. J Biomech. 32:1013 – 1020. Decking R, Puhl W, Simon U, Claes LE. 2006. Changes in strain distribution of loaded proximal femora caused by different types of cementless femoral stems. Clin Biomech (Bristol, Avon). 21:495– 501. Dorr LD, Lewonowski K, Lucero M, Harris M, Wan Z. 1997. Failure mechanisms of anatomic porous replacement I cementless total hip replacement. Clin Orthop Relat Res. 334:157 – 167. Engh CA, Bobyn JD, Glassman AH. 1987. Porous-coated hip replacement. The factors governing bone ingrowth, stress shielding, and clinical results. J Bone Joint Surg Br. 69:45 – 55.
Gonzalez Della Valle A, Slullitel G, Piccaluga F, Salvati EA. 2005. The precision and usefulness of preoperative planning for cemented and hybrid primary total hip arthroplasty. J Arthroplasty. 20:51– 58. Gruen TA, McNeice GM, Amstutz HC. 1979. “Modes of failure” of cemented stem-type femoral components: a radiographic analysis of loosening. Clin Orthop Relat Res. 334:157– 167. Habashy AH, Yan X, Brown JK, Xiong X, Kaste SC. 2011. Estimation of bone mineral density in children from diagnostic CT images: a comparison of methods with and without an internal calibration standard. Bone. 48:1087– 1094. Herrera A, Panisello JJ, Ibarz E, Cegonino J, Puertolas JA, Gracia L. 2007. Long-term study of bone remodelling after femoral stem: a comparison between DEXA and finite element simulation. J Biomech. 40:3615 – 3625. Herrera A, Panisello JJ, Ibarz E, Cegonino J, Puertolas JA, Gracia L. 2009. Comparison between DEXA and finite element studies in the long-term bone remodeling of an anatomical femoral stem. J Biomech Eng. 131:041013. doi: 10.1115/1. 3072888. Huiskes R, Weinans H, Grootenboer HJ, Dalstra M, Fudala B, Slooff TJ. 1987. Adaptive bone-remodeling theory applied to prosthetic-design analysis. J Biomech. 20:1135 – 1150. Jang IG, Kim IY. 2010. Computational simulation of simultaneous cortical and trabecular bone change in human proximal femur during bone remodeling. J Biomech. 43:294– 301. Jaworski ZF. 1984. Coupling of bone formation to bone resorption: a broader view. Calcif Tissue Int. 36:531– 535. Keller TS. 1994. Predicting the compressive mechanical behavior of bone. J Biomech. 27:1159 – 1168. Kerner J, Huiskes R, van Lenthe GH, Weinans H, van Rietbergen B, Engh CA, Amis AA. 1999. Correlation between preoperative periprosthetic bone density and post-operative bone loss in THA can be explained by strain-adaptive remodelling. J Biomech. 32:695 – 703. Keyak JH, Lee IY, Skinner HB. 1994. Correlations between orthogonal mechanical properties and density of trabecular bone: use of different densitometric measures. J Biomed Mater Res. 28:1329 – 1336. Keyak JH, Rossi SA, Jones KA, Skinner HB. 1998. Prediction of femoral fracture load using automated finite element modeling. J Biomech. 31:125 – 133. Kim YH, Yoon SH, Kim JS. 2007. Changes in the bone mineral density in the acetabulum and proximal femur after cementless total hip replacement: alumina-on-alumina versus alumina-on-polyethylene articulation. J Bone Joint Surg Br. 89:174– 179. Kroger H, Miettinen H, Arnala I, Koski E, Rushton N, Suomalainen O. 1996. Evaluation of periprosthetic bone using dual-energy X-ray absorptiometry: precision of the method and effect of operation on bone mineral density. J Bone Miner Res. 11:1526 –1530. Kroger H, Venesmaa P, Jurvelin J, Miettinen H, Suomalainen O, Alhava E. 1998. Bone density at the proximal femur after total hip arthroplasty. Clin Orthop Relat Res. 352:66 – 74. Kwon JY, Naito H, Matsumoto T, Tanaka M. 2013. Estimation of change of bone structures after total hip replacement using bone remodeling simulation. Clin Biomech (Bristol, Avon). 28:514 – 518. Lawton MT, Ho JC, Bichard WD, Coons SW, Zabramski JM, Spetzler RF. 1996. Titanium aneurysm clips. Part I. Mechanical, radiological, and biocompatibility testing. Neurosurgery. 38:1158– 1164. Lee MJ, Kim S, Lee SA, Song HT, Huh YM, Kim DH, Han SH, Suh JS. 2007. Overcoming artifacts from metallic
Downloaded by [Selcuk Universitesi] at 10:48 17 January 2015
Computer Methods in Biomechanics and Biomedical Engineering orthopedic implants at high-field-strength MR imaging and multi-detector CT. Radiographics. 27:791 – 803. Maistrelli GL, Fornasier V, Binnington A, McKenzie K, Sessa V, Harrington I. 1991. Effect of stem modulus in a total hip arthroplasty model. J Bone Joint Surg Br. 73:43– 46. Malchau H, Herberts P, Ahnfelt L. 1993. Prognosis of total hip replacement in Sweden. Follow-up of 92,675 operations performed 1978– 1990. Acta Orthop Scand. 64:497 – 506. Nishii T, Sugano N, Masuhara K, Shibuya T, Ochi T, Tamura S. 1997. Longitudinal evaluation of time related bone remodeling after cementless total hip arthroplasty. Clin Orthop Relat Res. 339:121 – 131. Ostbyhaug PO, Klaksvik J, Romundstad P, Aamodt A. 2009. An in vitro study of the strain distribution in human femora with anatomical and customised femoral stems. J Bone Joint Surg Br. 91:676 –682. Perez MA, Seral-Garcia B. 2013. A finite element analysis of the vibration behaviour of a cementless hip system. Comput Methods Biomech Biomed Engin. 9:1022 – 1031. Pettersen SH, Wik TS, Skallerud B. 2009. Subject specific finite element analysis of stress shielding around a cementless femoral stem. Clin Biomech (Bristol, Avon). 24:196– 202. Rahbek O, Kold S, Zippor B, Overgaard S, Soballe K. 2005. The influence of surface porosity on gap-healing around intraarticular implants in the presence of migrating particles. Biomaterials. 26:4728 – 4736. Rosenthall L, Bobyn JD, Brooks CE. 1999. Temporal changes of periprosthetic bone density in patients with a modular noncemented femoral prosthesis. J Arthroplasty. 14:71 – 76. Stulpner MA, Reddy BD, Starke GR, Spirakis A. 1997. A threedimensional finite analysis of adaptive remodelling in the proximal femur. J Biomech. 30:1063 – 1066. Taddei F, Schileo E, Helgason B, Cristofolini L, Viceconti M. 2007. The material mapping strategy influences the accuracy of CT-based finite element models of bones:
1065
an evaluation against experimental measurements. Med Eng Phys. 29:973 – 979. Tawara D, Sakamoto J, Murakami H, Kawahara N, Oda J, Tomita K. 2010. Mechanical evaluation by patient-specific finite element analyses demonstrates therapeutic effects for osteoporotic vertebrae. J Mech Behav Biomed Mater. 3:31 –40. Turner CH, Owan I, Takano Y. 1995. Mechanotransduction in bone: role of strain rate. Am J Physiol. 269:E438 – E442. van der Ploeg B, Tarala M, Homminga J, Janssen D, Buma P, Verdonschot N. 2012. Toward a more realistic prediction of peri-prosthetic micromotions. J Orthop Res. 30:1147 –1154. Weinans H, Sumner DR, Igloria R, Natarajan RN. 2000. Sensitivity of periprosthetic stress-shielding to load and the bone density– modulus relationship in subject-specific finite element models. J Biomech. 33:809 –817. Wolff J. 1892. Das Gesettz Der Transformation Der Knochen. Berlin: Hirschwald.
Appendix A. Drucker –Prager equivalent stress
pffiffiffiffiffi aJ 1 þ J 2 Drucker – Prager equivalent stress ¼ pffiffiffiffiffiffiffiffiffiffiffi ; ð1=3Þ 2 a J 1 ¼ sx þ sy þ sz ;
1 J 2 ¼ ðs2x þ s2y þ s2z 2 sx sy 2 sy sz 2 sz sx Þ þ t2xy þ t2yz þ t2zx ; 3 where s is the normal stress, t is the shear stress, J1 is the first invariant of stress, J2 is the second invariant of deviatoric stress and a is the constant value. a is a parameter that reflects the dilative potential of the material and it is related to the proportions of the volumetric and deviatoric strains. a is set as 0.07 (Bessho et al. 2007).
Computer Methods in Biomechanics and Biomedical Engineering Publication details, including instructions for authors and subscription information: http://www.tandfonline.com/loi/gcmb20
Comparison between mechanical stress and bone mineral density in the femur after total hip arthroplasty by using subject-specific finite element analyses a
a
a
a
a
Hiroyuki Ike , Yutaka Inaba , Naomi Kobayashi , Yasuhide Hirata , Yohei Yukizawa , Chie a
a
a
Aoki , Hyonmin Choe & Tomoyuki Saito a
Click for updates
Department of Orthopaedic Surgery, Yokohama City University, 3-9, Fukuura, Kanazawaku, Yokohama, Kanagawa 236-0004, Japan Published online: 24 Mar 2014.
To cite this article: Hiroyuki Ike, Yutaka Inaba, Naomi Kobayashi, Yasuhide Hirata, Yohei Yukizawa, Chie Aoki, Hyonmin Choe & Tomoyuki Saito (2015) Comparison between mechanical stress and bone mineral density in the femur after total hip arthroplasty by using subject-specific finite element analyses, Computer Methods in Biomechanics and Biomedical Engineering, 18:10, 1056-1065, DOI: 10.1080/10255842.2013.869320 To link to this article: http://dx.doi.org/10.1080/10255842.2013.869320
PLEASE SCROLL DOWN FOR ARTICLE Taylor & Francis makes every effort to ensure the accuracy of all the information (the “Content”) contained in the publications on our platform. However, Taylor & Francis, our agents, and our licensors make no representations or warranties whatsoever as to the accuracy, completeness, or suitability for any purpose of the Content. Any opinions and views expressed in this publication are the opinions and views of the authors, and are not the views of or endorsed by Taylor & Francis. The accuracy of the Content should not be relied upon and should be independently verified with primary sources of information. Taylor and Francis shall not be liable for any losses, actions, claims, proceedings, demands, costs, expenses, damages, and other liabilities whatsoever or howsoever caused arising directly or indirectly in connection with, in relation to or arising out of the use of the Content. This article may be used for research, teaching, and private study purposes. Any substantial or systematic reproduction, redistribution, reselling, loan, sub-licensing, systematic supply, or distribution in any form to anyone is expressly forbidden. Terms & Conditions of access and use can be found at http:// www.tandfonline.com/page/terms-and-conditions
Computer Methods in Biomechanics and Biomedical Engineering, 2015 Vol. 18, No. 10, 1056– 1065, http://dx.doi.org/10.1080/10255842.2013.869320
Comparison between mechanical stress and bone mineral density in the femur after total hip arthroplasty by using subject-specific finite element analyses Hiroyuki Ike, Yutaka Inaba*, Naomi Kobayashi, Yasuhide Hirata, Yohei Yukizawa, Chie Aoki, Hyonmin Choe and Tomoyuki Saito Department of Orthopaedic Surgery, Yokohama City University, 3-9, Fukuura, Kanazawa-ku, Yokohama, Kanagawa 236-0004, Japan
Downloaded by [Selcuk Universitesi] at 10:48 17 January 2015
(Received 7 February 2013; accepted 21 November 2013) The mechanism underling bone mineral density (BMD) loss that occurs in the femur after total hip arthroplasty (THA) remains unknown. We compared the equivalent stress and strain energy density (SED) to BMD in the femur after THA using subject-specific finite element analyses. Twenty-four patients who had undergone primary cementless THA were analysed. BMD was measured using dual-energy X-ray absorptiometry (DEXA) at 1 week and 3, 6 and 12 months after THA. Seven regions of interest (ROIs) were defined in accordance with Gruen’s system (ROIs 1 – 7). Computed tomography images of the femurs were acquired pre- and postoperatively, and the images were converted into three-dimensional finite element (FE) models. Equivalent stress and SED were analysed and compared with DEXA data. BMD was maintained 1 year after THA in ROIs 3, 4, 5 and 6, whereas BMD decreased in ROIs 1, 2 and 7. FE analysis revealed that equivalent stress in ROIs 3, 4, 5 and 6 was much higher than that in ROIs 1, 2 and 7. A significant correlation was observed between the rate of changes in BMD and equivalent stress. Reduction of equivalent stress may contribute to decrease in BMD in the femur after THA. Keywords: finite element analysis; bone mineral density; total hip arthroplasty
1.
Introduction
Periprosthetic bone loss, i.e. decrease in bone mineral density (BMD) around an implant, is a major concern following total hip arthroplasty (THA) (Malchau et al. 1993; Dorr et al. 1997). Severe periprosthetic bone loss may contribute to aseptic loosening of the prosthesis or the risk of periprosthetic fracture (Bougherara et al. 2007) and presents serious problems if revision surgery becomes necessary (Kerner et al. 1999). Several studies have reported that BMD decreases following THA, particularly in the proximal femur (Kroger et al. 1996; Kim et al. 2007). Most changes in BMD occur during the first postoperative year, after which BMD is maintained (Nishii et al. 1997; Kroger et al. 1998; Rosenthall et al. 1999). This phenomenon may be an adaptive remodelling response of the bone structure to significantly alter its stress environment due to the implantation. Therefore, mechanical stress may be associated with the patterns in BMD changes. In particular, in cementless THA, an optimal fit of the stem into the metaphyseal region of the femur reportedly leads to a reduction in periprosthetic bone loss (Ostbyhaug et al. 2009). A major cause of this phenomenon may be that the fit-and-fill type of prosthesis was designed to improve proximal fixation and physiological load transfer in the proximal femur. Wolff (1892) proposed that trabecular bone in the proximal femur adapts to external mechanical loads. This structural change is caused by bone remodelling, which
*Corresponding author. Email: [email protected] q 2014 Taylor & Francis
couples bone resorption by osteoclasts and bone formation by osteoblasts (Jaworski 1984). It is generally accepted that bone tissue can detect and respond to its mechanical environment, but there is no consensus regarding how bone cells detect mechanical loads (Turner et al. 1995). Various biomechanical parameters have been investigated as the remodelling stimulus. Huiskes et al. (1987) examined whether strain energy density (SED) controls bone remodelling. Carter et al. (1996) examined the stress and Stulpner et al. (1997) examined the equivalent strain as signals. Adachi et al. (1997) proposed that the driving force of the remodelling is the local nonuniformity of the scalar function of stress. The existence of various theories indicates that the mechanism of bone remodelling is not well understood. Several simulation models based on the micro-scale bone remodelling theory have reproduced some characteristics of the trabecular bone or BMD in the human femur (Adachi et al. 1997). Kwon et al. (2013) proposed a method to predict a change in bone structure, based on a trabecular bone remodelling model. They concluded that mechanical remodelling simulation could effectively estimate bone resorption and the occurrence of the stress shielding after THA. Jang and Kim (2010) developed a micro finite element (FE) model to represent the full trabecular architecture in the human proximal femur. They showed that the external shape of the cortical bone and internal morphology of the trabecular bone adapted to the surrounding mechanical environment.
Downloaded by [Selcuk Universitesi] at 10:48 17 January 2015
Computer Methods in Biomechanics and Biomedical Engineering
1057
Subject-specific FE models based on geometry and mechanical properties derived from computed tomography (CT) have been described in several studies (Keyak et al. 1998; Taddei et al. 2007; Pettersen et al. 2009). Furthermore, relationships between results of subjectspecific FE analyses and bone density have been investigated. Cody et al. (1999) carried out subjectspecific FE analyses and bone density measurements for predicting the fracture load of femurs. Tawara et al. (2010) evaluated the vertebral strength using the subject-specific FE models and BMD. However, few studies have focused on the validity of subject-specific FE analyses in assessing BMD changes in the femur after THA. In this study, we constructed subject-specific FE models of femurs and assessed changes in equivalent stress and SED using clinical samples before and after THA. Therefore, the purpose of this study was to investigate the equivalent stress and SED using subject-specific FE analyses and to compare the results of the FE analyses with changes in BMD in the femur after fit-and-fill type cementless THA. 2. Materials and methods This study was approved by our Institutional Review Board. Informed consent was obtained from all individuals before enrollment. Twenty-four patients (16 women and 8 men) who underwent primary cementless THA using the same fit-and-fill type of prosthesis (collarless Versys Fiber Metal MidCoat; Zimmer, Inc., Warsaw, IN) were enrolled in this prospective study. Collarless Versys Fiber Metal MidCoat is a fit-and-fill type femoral component composed of titanium alloy with a fibre metal porous coating on the proximal region of the implant (Figure 1). Patients treated with bisphosphonate, vitamin D or systemic oestrogen were excluded from the study. The mean age of the patients at the time of THA was 63 ^ 11 years (range 44– 82). After surgery, all patients were allowed to transfer from the bed to a wheelchair with full weight bearing on postoperative day 1 followed by gait exercise as soon as possible. 2.1
Figure 1. Collarless Versys Fiber Metal MidCoat.
2.2 Finite element analysis CT scans (Sensation16; SiemensAG, Erlangen, Germany) of the femurs of all patients were acquired pre- and postoperatively (1 week after surgery). Scanner settings were approximately 140 kV and 300 mA, with a slice thickness of 2 mm, 512 £ 512 pixel resolution and a 0.70 mm £ 0.70 mm £ 2 mm voxel size. We calibrated the Hounsfield unit values in the CT using a water phantom once a day.
BMD measurement
BMD was measured 1 week after THA as reference baseline, with subsequent measurements taken at 3, 6 and 12 months postoperatively. BMD measurement was carried out with dual-energy X-ray absorptiometry (DEXA) on the Hologic Discovery system (Hologic, Inc., Waltham, MA). Patients were placed in the supine position with the affected leg in 208 internal rotation for limiting measurement errors. The BMD was measured using the ‘Array prosthetic mode’ in which metal was excluded from analysis of regions of interest (ROIs). ROIs were defined in accordance with the system established by Gruen et al. (1979) (Figure 2). Pixel size was 1.1 mm £ 0.56 mm.
Figure 2. ROIs for BMD measurements in accordance with the system established by Gruen.
Downloaded by [Selcuk Universitesi] at 10:48 17 January 2015
1058
H. Ike et al.
FE models of the femur and stem were obtained from pre- and postoperative CT data using Mechanical Finder ver. 6.0 (Research Center of Computational Mechanics, Inc., Tokyo, Japan), which is a software that creates FE models showing individual bone shape and density distribution (Bessho et al. 2007). A global threshold algorithm was used to extract the bone area with a threshold of 200 mg/cm3 with manual correction if necessary. For extracting the bone area when the density was extremely low, we used a closing algorithm in addition to the global threshold algorithm (Bessho et al. 2007). A global threshold algorithm was used to extract the stem area with a threshold of 2000 Hounsfield Units. Three-dimensional FE models, using 1 – 4 mm tetrahedral elements for the trabecular and inner cortical bone and 3-nodal-point shell elements with a thickness of 0.3 mm for the outer surface of the cortical bone, were constructed for each patient (Figure 3). FE models of the femur consisted of approximately 600,000 elements in addition to 200,000 elements for the stem. The bone density was determined on the basis of CT density values, using the calibration equation (Table 1). The elastic modulus of the bone was determined on the basis of bone density values, using the equations proposed by Keyak et al. (1994, 1998) and Keller (1994) (Table 1). The Poisson’s ratio of the bone was 0.40. The stem was an isotropic titanium alloy with an elastic modulus of 109.0 GPa and a Poisson’s ratio of 0.28. The models assumed a completely bonded interface between the stem and the bone. The onelegged standing condition was simulated. The femoral shaft was fully restrained, and force was applied to the femoral head and greater trochanter. A load of 2400 N was applied to the femoral head at an angle of 158 relative to the femoral axis, and a load of 1200 N was applied to the greater trochanter at an angle of 208 (Bergmann et al. 2001; Herrera et al. 2009) (Figure 4). Linear FE analysis was carried out. Equivalent stress and SED were analysed in ROIs 1– 7 and compared with the DEXA data. Average equivalent stress and SED in a sphere with a radius of 3 mm, the centre of
which was on the surface of the femur, were measured for each ROI. We adopted the Drucker – Prager equivalent stress (Appendix A). Stem alignment was measured on postoperative anteroposterior radiographs by measuring the angle formed between the long axis of the stem and the long axis of the femur. Stem alignment of less than 28 was considered neutral (Gonzalez Della Valle et al. 2005). The Wilcoxon signed-rank test was used to analyse changes in BMD. Correlations between BMD and other values were analysed using Pearson’s product-moment correlation coefficient. p-Values , 0.05 were considered significant. All data are expressed as the mean ^ standard deviation.
3.
Results
The relative BMD values in the femur at 1 week and 3, 6 and 12 months after THA are shown in Figure 5. Relative BMD values are expressed as percentage of the baseline measurement. Similarly, equivalent stress and SED are expressed as percentage of the preoperative values. BMD was maintained 12 months after THA in ROIs 3, 4, 5 and 6, whereas it decreased significantly by 19%, 11% and 27% in ROIs 1, 2 and 7, respectively, 12 months after THA. Stem alignment was neutral in 20 subjects (83%), 28 of the varus in 2 subjects (8%), 38 of the varus in 1 subject (4%) and 28 of the valgus in 1 subject (4%). No valgus or varus stem alignment greater than 38 was observed. The elastic modulus, equivalent stress and SED in preand postoperative models are shown in Figure 6. FE analyses revealed that equivalent stress and SED were maintained in ROIs 3, 4 and 5 after THA, whereas both decreased in ROIs 1, 2, 6 and 7 (Figure 7). In particular, in ROI 7, equivalent stress, SED and relative BMD values exhibited the lowest values of all regions examined ( p , 0.05). A significant correlation was observed between the rate of changes in BMD and equivalent stress
Figure 3. Diagram of mesh model. Trabecular bone and the inner portion of cortical bone were modelled using 1 –4 mm tetrahedral elements, while the outer cortex was modelled using 3-nodal-point shell elements with a thickness of 0.3 mm.
Computer Methods in Biomechanics and Biomedical Engineering Table 1. bone.
Equations used to calculate the elastic modulus of the
Bone density
r¼0 0 , r # 0.27 0.27 , r , 0.6 0.6 # r
Elastic modulus (MPa) 0.001 33,900r 2.20 5307r þ 469 10,200r 2.01
Notes: r(g/cm3) ¼ (HU þ 1.4246) £ 0.001/1.058 (HU . 2 1) ¼ 0.0 (HU # 2 1), where HU represents CT density values in Hounsfield Units. The elastic modulus of the bone is determined on the basis of CT density values, using the equations proposed by Keyak et al. and Keller.
Downloaded by [Selcuk Universitesi] at 10:48 17 January 2015
(R ¼ 0.426, p , 0.01). However, no significant correlation was observed between the rate of changes in BMD and SED (R ¼ 0.183, p ¼ 0.053) (Figure 8). 4. Discussion Postoperative BMD loss, which can occur around implants after THA, may be related to changes in mechanical stress conditions. This loss is an important issue, which requires a multifactorial approach. The goal of this study was to reveal the relationship between BMD loss and changes in mechanical stress conditions after cementless THA involving fit-and-fill type stems using subject-specific FE analyses. The present subject-specific analyses of the femurs of 24 subjects before and after THA revealed a significant correlation between changes in BMD and equivalent stress.
Figure 4. Diagram of loading and restriction conditions. The femoral shaft is fully restrained, and force is applied to the femoral head and the greater trochanter. A load of 2400 N is applied to the femoral head at an angle of 158 relative to the femoral axis, and a load of 1200 N is applied to the greater trochanter at an angle of 208.
1059
Previous investigations have predominantly used changes in SED for bone adaptation remodelling. However, the results obtained from our preliminary analysis indicated that the SED variation in the femur was relatively large, and there was a very weak correlation between the rate of changes in BMD and SED. In contrast, the equivalent stress decreased in the proximal femur and was maintained in the distal femur, in most cases, after THA. The changes in equivalent stress showed similar patterns compared with the changes in BMD. From a previous report, a good correlation was reported between the results of equivalent stress and DEXA (Herrera et al. 2007). Therefore, we focused on SED and equivalent stress in this study. After THA, the stress load is transferred to the distal femur through the stem rather than to the periprosthetic bone due to the high elastic modulus of the stem (Maistrelli et al. 1991; Decking et al. 2006). Therefore, equivalent stress in the proximal femur may decrease after stem implantation. These results were consistent with those of previous studies (Herrera et al. 2009; Pettersen et al. 2009). We assessed the effect on bone remodelling of the collarless Versys Fiber Metal MidCoat, a porouscoated titanium-alloy fit-and-fill type stem. Although this implant is meant to provide proximal fixation, BMD and equivalent stress in the proximal femur decreased postoperatively. These results indicate that stress transfer to the proximal femur may be insufficient for maintaining BMD. Our results showed that BMD decreased by 19%, 11% and 27% in ROIs 1, 2 and 7, respectively, 12 months after THA. The changes in BMD noted in this study were similar to those reported by others (Aldinger et al. 2003; Boden and Adolphson 2004).
Figure 5. Bar graph of changes in BMD 1 week and 3, 6 and 12 months after THA in each ROI. Changes in BMD are calculated as percent decreases of the status at 1 week. BMD significantly decreased by 19%, 11% and 27% in ROIs 1, 2 and 7, respectively, 12 months after THA (*p , 0.05, which was significantly different from the 1-week value with a Wilcoxon signed-rank test). BMD was maintained 12 months after THA in ROIs 3, 4, 5 and 6.
H. Ike et al.
Downloaded by [Selcuk Universitesi] at 10:48 17 January 2015
1060
Several previous studies have described the application of FE analysis in investigating bone remodelling patterns around implants. However, most of these models were not subject specific. For example, mechanical properties of the bone were homogeneous (Herrera et al. 2009) or parts of the bone model were based on the geometry of a typical femur (Kerner et al. 1999). Weinans et al. (2000) reported that subject-specific FE models may be useful for explaining variations in bone adaptation responsiveness between different subjects. In our study, CT scans were obtained from all patients pre- and postoperatively, and subject-specific FE models were constructed to investigate bone heterogeneity by using the
equations proposed by Keyak et al. (1994, 1998) and Keller (1994). Variations in equivalent stress and SED between patients resulted from the subject-specific geometry and mechanical properties of the femur. DEXA is a precise method for quantifying bone mass and density changes during follow-up after THA. Kroger et al. (1996) reported that the average precision error of DEXA is 2.3% for the uncemented stem and concluded that small changes in the bone can be measured. Changes in BMD are influenced by the size, coating, design and stiffness of the stem, initial bone density, focal osteolysis and timing of weight bearing (Engh et al. 1987; Nishii et al. 1997; Boden and Adolphson 2004). Varus or valgus
1061
Downloaded by [Selcuk Universitesi] at 10:48 17 January 2015
Computer Methods in Biomechanics and Biomedical Engineering
stem alignment leads to changes in the stress distribution of the femur, which may affect the BMD changes. In this study, no valgus or varus stem alignment greater than 38 was observed. Therefore, the effects of stem alignment on stress distribution and BMD changes are considered negligible. This study demonstrated that equivalent stress correlates to changes in BMD in the femur in the 12 months following THA. Our results suggest that the rate of changes in equivalent stress could be an important factor for changes in BMD; however, the determination coefficient was only 18%. Therefore, equivalent stress alone was insufficient for predicting changes in BMD. The
strain-adaptive bone remodelling theory was used to simulate changes in BMD after THA; Huiskes et al. (1987) reported that the SED distribution represents the regions where resorption and apposition is expected. However, other studies have shown that stress parameters, rather than strain parameters, are better predictors of bone remodelling. The clinical data and simulation results showed a correlation between average equivalent stress and BMD (Herrera et al. 2007; Kwon et al. 2013). As these examples suggest, controversy still exists with regard to whether equivalent stress or SED is an appropriate parameter for evaluating bone remodelling. Our results suggest that the decrease in equivalent stress caused the
H. Ike et al.
Downloaded by [Selcuk Universitesi] at 10:48 17 January 2015
1062
Figure 6. Distributions of (a) elastic modulus, (b) equivalent stress and (c) SED in the femur. Pre- and postoperative elastic modulus showed similar patterns, suggesting that changes of bone density after implantation of the femoral stems were small. Equivalent stress and SED were maintained in the distal femur after THA, whereas both decreased in the proximal femur.
decrease in BMD in the proximal femur after THA. Furthermore, no significant correlation was observed between the rate of changes in BMD and SED. This result might be explained by the considerable dispersion in SED. Figure 7 shows relatively large values of standard deviation in SED. Another possible explanation is that the equivalent stress more strongly influences the bone tissue in sensing the surrounding mechanical environment than does the SED. In this study, equivalent stress and SED were measured in the cortex of the femur around the
stem, because the stem was inserted into the femur using the press-fit technique in which the femoral canal was filled with the stem. Equivalent stress rather than SED may be an appropriate parameter for analysing bone remodelling in the cortex bone. There are several limitations to this study. First, all analyses were carried out using only one static-loading condition, and the patients’ age, gender and activity levels, which might affect the changes in BMD, were not taken into account. Second, in the FE analysis, we did not
Computer Methods in Biomechanics and Biomedical Engineering
1063
Downloaded by [Selcuk Universitesi] at 10:48 17 January 2015
Figure 7. Bar graph of the results of SED, equivalent stress and BMD 12 months after THA. In ROI 7, equivalent stress, SED and relative BMD values showed the lowest values.
consider the surface properties of the implant (e.g. hydroxyapatite coatings), which affect fixation of the implant in the femur and may influence bone remodelling around the implant (Boe et al. 2011). The surface texture, localisation and magnitude of the surface material can facilitate bone ingrowth (Baad-Hansen et al. 2011). The fibre metal porous coating, which was applied to the proximal portion of the collarless Versys Fiber Metal MidCoat, exhibited high levels of osseointegration (Rahbek et al. 2005). Our models assumed a completely bonded interface, which did not allow micromotion between the stem and bone. Consideration of the surface properties of the implant and degree of stem fixation would be useful to construct more realistic models. Third, CT scans were acquired without the calibration phantom. Quantitative CT-based FE models can improve the prediction of the bone mechanical properties. A reference phantom is typically used to standardise measurements to a mineral reference and correct for potential analytical errors arising from beam hardening and radiation scattering (Habashy et al. 2011). The calibration of Hounsfield unit values, using a reference phantom, improves the model accuracy and may affect the SED and equivalent stress results. In addition, the effect of metal artefacts caused by implants is a major concern in CT-based FE analysis. During CT scanning, metallic objects absorb and scatter radiant energy at various sites, causing metal artefacts. Titanium is recognised as having fewer artefacts on CT (Lawton et al. 1996). In this study, the stems were composed of titanium alloy and small artefacts were observed in the vicinity of the stems in CT images. We used a moderately high peak voltage to acquire images with fewer artefacts. Barrett and Keat (2004) reported that increasing the peak voltage increases the likelihood that radiation energy will penetrate the metallic hardware; thus, artefacts are expected to be diminished with higher peak voltages (Lee et al. 2007).
Figure 8. Scatter plot of the relationship (a) between BMD and equivalent stress and (b) between BMD and SED. BMD values 1 year after THA were expressed as percentage of the baseline measurements (1 week after THA). Postoperative equivalent stress and SED, which were analysed using the CT data 1 week after THA, were expressed as percentage of the preoperative values. (a) A significant correlation was observed between the rate of changes in BMD and equivalent stress (R ¼ 0.426, p , 0.01). (b) No significant correlation was observed between the rate of changes in BMD and SED (R ¼ 0.183, p ¼ 0.053).
Finally, the maximum length of the tetrahedral elements (4 mm) was relatively large and might straddle the boundary between the cortical and cancellous area in the FE models. Therefore, the elastic modulus of the element straddling the boundary would contain some errors. Chen et al. (2010) reported that the distribution of bone density becomes smoother as the element size decreases. A smaller element size provides more accurate results in the FE analysis. To overcome this limitation, we adopted triangular shell elements on the outer surface of the cortical area to represent the thin cortical shell for reproducing the cortical area (Bessho et al. 2007). Furthermore, the number of elements in our FE models is larger than that of other recent reports (Perez and SeralGarcia 2013; van der Ploeg et al. 2012). Further studies involving these factors are necessary to more accurately simulate postoperative conditions.
1064
H. Ike et al.
5. Conclusion We confirmed a correlation between changes in BMD and equivalent stress through subject-specific FE analysis before and after THA. BMD and equivalent stress decreased in the proximal femur after THA. The rate of changes in equivalent stress could be an important factor for changes in BMD after THA.
Downloaded by [Selcuk Universitesi] at 10:48 17 January 2015
References Adachi T, Tomita Y, Sakaue H, Tanaka M. 1997. Simulation of trabecular surface remodeling based on local stress uniformity. Jpn Soc Mech Eng. 40:782 – 792. Aldinger PR, Sabo D, Pritsch M, Thomsen M, Mau H, Ewerbeck V, Breusch SJ. 2003. Pattern of periprosthetic bone remodeling around stable uncemented tapered hip stems: a prospective 84-month follow-up study and a median 156month cross-sectional study with DXA. Calcif Tissue Int. 73:115 – 121. Baad-Hansen T, Kold S, Olsen N, Christensen F, Soballe K. 2011. Excessive distal migration of fiber-mesh coated femoral stems. Acta Orthop. 82:308– 314. Barrett JF, Keat N. 2004. Artifacts in CT: recognition and avoidance. Radiographics. 24:1679 – 1691. Bergmann G, Deuretzbacher G, Heller M, Graichen F, Rohlmann A, Strauss J, Duda GN. 2001. Hip contact forces and gait patterns from routine activities. J Biomech. 34:859 – 871. Bessho M, Ohnishi I, Matsuyama J, Matsumoto T, Imai K, Nakamura K. 2007. Prediction of strength and strain of the proximal femur by a CT-based finite element method. J Biomech. 40:1745– 1753. Boden H, Adolphson P. 2004. No adverse effects of early weight bearing after uncemented total hip arthroplasty: a randomized study of 20 patients. Acta Orthop Scand. 75:21– 29. Boe BG, Rohrl SM, Heier T, Snorrason F, Nordsletten L. 2011. A prospective randomized study comparing electrochemically deposited hydroxyapatite and plasma-sprayed hydroxyapatite on titanium stems. Acta Orthop. 82:13 – 19. Bougherara H, Bureau M, Campbell M, Vadean A, Yahia L. 2007. Design of a biomimetic polymer-composite hip prosthesis. J Biomed Mater Res. 82:27 – 40. Carter DR, Van Der Meulen MC, Beaupre GS. 1996. Mechanical factors in bone growth and development. Bone. 18:5S – 10S. Chen G, Schmutz B, Epari D, Rathnayaka K, Ibrahim S, Schuetz MA, Pearcy MJ. 2010. A new approach for assigning bone material properties from CT images into finite element models. J Biomech. 43:1011– 1015. Cody DD, Gross GJ, Hou FJ, Spencer HJ, Goldstein SA, Fyhrie DP. 1999. Femoral strength is better predicted by finite element models than QCT and DXA. J Biomech. 32:1013 – 1020. Decking R, Puhl W, Simon U, Claes LE. 2006. Changes in strain distribution of loaded proximal femora caused by different types of cementless femoral stems. Clin Biomech (Bristol, Avon). 21:495– 501. Dorr LD, Lewonowski K, Lucero M, Harris M, Wan Z. 1997. Failure mechanisms of anatomic porous replacement I cementless total hip replacement. Clin Orthop Relat Res. 334:157 – 167. Engh CA, Bobyn JD, Glassman AH. 1987. Porous-coated hip replacement. The factors governing bone ingrowth, stress shielding, and clinical results. J Bone Joint Surg Br. 69:45 – 55.
Gonzalez Della Valle A, Slullitel G, Piccaluga F, Salvati EA. 2005. The precision and usefulness of preoperative planning for cemented and hybrid primary total hip arthroplasty. J Arthroplasty. 20:51– 58. Gruen TA, McNeice GM, Amstutz HC. 1979. “Modes of failure” of cemented stem-type femoral components: a radiographic analysis of loosening. Clin Orthop Relat Res. 334:157– 167. Habashy AH, Yan X, Brown JK, Xiong X, Kaste SC. 2011. Estimation of bone mineral density in children from diagnostic CT images: a comparison of methods with and without an internal calibration standard. Bone. 48:1087– 1094. Herrera A, Panisello JJ, Ibarz E, Cegonino J, Puertolas JA, Gracia L. 2007. Long-term study of bone remodelling after femoral stem: a comparison between DEXA and finite element simulation. J Biomech. 40:3615 – 3625. Herrera A, Panisello JJ, Ibarz E, Cegonino J, Puertolas JA, Gracia L. 2009. Comparison between DEXA and finite element studies in the long-term bone remodeling of an anatomical femoral stem. J Biomech Eng. 131:041013. doi: 10.1115/1. 3072888. Huiskes R, Weinans H, Grootenboer HJ, Dalstra M, Fudala B, Slooff TJ. 1987. Adaptive bone-remodeling theory applied to prosthetic-design analysis. J Biomech. 20:1135 – 1150. Jang IG, Kim IY. 2010. Computational simulation of simultaneous cortical and trabecular bone change in human proximal femur during bone remodeling. J Biomech. 43:294– 301. Jaworski ZF. 1984. Coupling of bone formation to bone resorption: a broader view. Calcif Tissue Int. 36:531– 535. Keller TS. 1994. Predicting the compressive mechanical behavior of bone. J Biomech. 27:1159 – 1168. Kerner J, Huiskes R, van Lenthe GH, Weinans H, van Rietbergen B, Engh CA, Amis AA. 1999. Correlation between preoperative periprosthetic bone density and post-operative bone loss in THA can be explained by strain-adaptive remodelling. J Biomech. 32:695 – 703. Keyak JH, Lee IY, Skinner HB. 1994. Correlations between orthogonal mechanical properties and density of trabecular bone: use of different densitometric measures. J Biomed Mater Res. 28:1329 – 1336. Keyak JH, Rossi SA, Jones KA, Skinner HB. 1998. Prediction of femoral fracture load using automated finite element modeling. J Biomech. 31:125 – 133. Kim YH, Yoon SH, Kim JS. 2007. Changes in the bone mineral density in the acetabulum and proximal femur after cementless total hip replacement: alumina-on-alumina versus alumina-on-polyethylene articulation. J Bone Joint Surg Br. 89:174– 179. Kroger H, Miettinen H, Arnala I, Koski E, Rushton N, Suomalainen O. 1996. Evaluation of periprosthetic bone using dual-energy X-ray absorptiometry: precision of the method and effect of operation on bone mineral density. J Bone Miner Res. 11:1526 –1530. Kroger H, Venesmaa P, Jurvelin J, Miettinen H, Suomalainen O, Alhava E. 1998. Bone density at the proximal femur after total hip arthroplasty. Clin Orthop Relat Res. 352:66 – 74. Kwon JY, Naito H, Matsumoto T, Tanaka M. 2013. Estimation of change of bone structures after total hip replacement using bone remodeling simulation. Clin Biomech (Bristol, Avon). 28:514 – 518. Lawton MT, Ho JC, Bichard WD, Coons SW, Zabramski JM, Spetzler RF. 1996. Titanium aneurysm clips. Part I. Mechanical, radiological, and biocompatibility testing. Neurosurgery. 38:1158– 1164. Lee MJ, Kim S, Lee SA, Song HT, Huh YM, Kim DH, Han SH, Suh JS. 2007. Overcoming artifacts from metallic
Downloaded by [Selcuk Universitesi] at 10:48 17 January 2015
Computer Methods in Biomechanics and Biomedical Engineering orthopedic implants at high-field-strength MR imaging and multi-detector CT. Radiographics. 27:791 – 803. Maistrelli GL, Fornasier V, Binnington A, McKenzie K, Sessa V, Harrington I. 1991. Effect of stem modulus in a total hip arthroplasty model. J Bone Joint Surg Br. 73:43– 46. Malchau H, Herberts P, Ahnfelt L. 1993. Prognosis of total hip replacement in Sweden. Follow-up of 92,675 operations performed 1978– 1990. Acta Orthop Scand. 64:497 – 506. Nishii T, Sugano N, Masuhara K, Shibuya T, Ochi T, Tamura S. 1997. Longitudinal evaluation of time related bone remodeling after cementless total hip arthroplasty. Clin Orthop Relat Res. 339:121 – 131. Ostbyhaug PO, Klaksvik J, Romundstad P, Aamodt A. 2009. An in vitro study of the strain distribution in human femora with anatomical and customised femoral stems. J Bone Joint Surg Br. 91:676 –682. Perez MA, Seral-Garcia B. 2013. A finite element analysis of the vibration behaviour of a cementless hip system. Comput Methods Biomech Biomed Engin. 9:1022 – 1031. Pettersen SH, Wik TS, Skallerud B. 2009. Subject specific finite element analysis of stress shielding around a cementless femoral stem. Clin Biomech (Bristol, Avon). 24:196– 202. Rahbek O, Kold S, Zippor B, Overgaard S, Soballe K. 2005. The influence of surface porosity on gap-healing around intraarticular implants in the presence of migrating particles. Biomaterials. 26:4728 – 4736. Rosenthall L, Bobyn JD, Brooks CE. 1999. Temporal changes of periprosthetic bone density in patients with a modular noncemented femoral prosthesis. J Arthroplasty. 14:71 – 76. Stulpner MA, Reddy BD, Starke GR, Spirakis A. 1997. A threedimensional finite analysis of adaptive remodelling in the proximal femur. J Biomech. 30:1063 – 1066. Taddei F, Schileo E, Helgason B, Cristofolini L, Viceconti M. 2007. The material mapping strategy influences the accuracy of CT-based finite element models of bones:
1065
an evaluation against experimental measurements. Med Eng Phys. 29:973 – 979. Tawara D, Sakamoto J, Murakami H, Kawahara N, Oda J, Tomita K. 2010. Mechanical evaluation by patient-specific finite element analyses demonstrates therapeutic effects for osteoporotic vertebrae. J Mech Behav Biomed Mater. 3:31 –40. Turner CH, Owan I, Takano Y. 1995. Mechanotransduction in bone: role of strain rate. Am J Physiol. 269:E438 – E442. van der Ploeg B, Tarala M, Homminga J, Janssen D, Buma P, Verdonschot N. 2012. Toward a more realistic prediction of peri-prosthetic micromotions. J Orthop Res. 30:1147 –1154. Weinans H, Sumner DR, Igloria R, Natarajan RN. 2000. Sensitivity of periprosthetic stress-shielding to load and the bone density– modulus relationship in subject-specific finite element models. J Biomech. 33:809 –817. Wolff J. 1892. Das Gesettz Der Transformation Der Knochen. Berlin: Hirschwald.
Appendix A. Drucker –Prager equivalent stress
pffiffiffiffiffi aJ 1 þ J 2 Drucker – Prager equivalent stress ¼ pffiffiffiffiffiffiffiffiffiffiffi ; ð1=3Þ 2 a J 1 ¼ sx þ sy þ sz ;
1 J 2 ¼ ðs2x þ s2y þ s2z 2 sx sy 2 sy sz 2 sz sx Þ þ t2xy þ t2yz þ t2zx ; 3 where s is the normal stress, t is the shear stress, J1 is the first invariant of stress, J2 is the second invariant of deviatoric stress and a is the constant value. a is a parameter that reflects the dilative potential of the material and it is related to the proportions of the volumetric and deviatoric strains. a is set as 0.07 (Bessho et al. 2007).
