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The importance of femur/acetabulum cartilage in the biomechanics of the intact hip: experimental and numerical assessment a

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R.J. Duarte , A. Ramos , A. Completo , C. Relvas & J.A. Simões a

Department of Mechanical Engineering, TEMA, University of Aveiro, 3810-193 Aveiro, Portugal Published online: 21 Nov 2013.

Click for updates To cite this article: R.J. Duarte, A. Ramos, A. Completo, C. Relvas & J.A. Simões (2015) The importance of femur/ acetabulum cartilage in the biomechanics of the intact hip: experimental and numerical assessment, Computer Methods in Biomechanics and Biomedical Engineering, 18:8, 880-889, DOI: 10.1080/10255842.2013.854335 To link to this article: http://dx.doi.org/10.1080/10255842.2013.854335

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Computer Methods in Biomechanics and Biomedical Engineering, 2015 Vol. 18, No. 8, 880– 889, http://dx.doi.org/10.1080/10255842.2013.854335

The importance of femur/acetabulum cartilage in the biomechanics of the intact hip: experimental and numerical assessment R.J. Duarte, A. Ramos*, A. Completo, C. Relvas and J.A. Simo˜es Department of Mechanical Engineering, TEMA, University of Aveiro, 3810-193 Aveiro, Portugal

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(Received 22 February 2013; accepted 8 October 2013) Experimental studies have been made to study and validate the biomechanics of the pair femur/acetabulum considering both structures without the presence of cartilage. The main goal of this study was to validate a numerical model of the intact hip. Numerical and experimental models of the hip joint were developed with respect to the anatomical restrictions. Both iliac and femur bones were replicated based on composite replicas. Additionally, a thin layer of silicon rubber was used for the cartilage. A three-dimensional finite element model was developed and the boundary conditions of the models were applied according to the natural physiological constrains of the joint. The loads used in both models were used just for comparison purposes. The biomechanical behaviour of the models was assessed considering the maximum and minimum principal bone strains and von Mises stress. We analysed specific biomechanical parameters in the interior of the acetabular cavity and on femur’s surface head to determine the role of the cartilage of the hip joint within the load transfer mechanism. The results of the study show that the stress observed in acetabular cavity was 8.3 to 9.2 MPa. When the cartilage is considered in the joint model, the absolute values of the maximum and minimum peak strains on the femur’s head surface decrease simultaneously, and the strains are more uniformly distributed on both femur and iliac surfaces. With cartilage, the cortex strains increase in the medial side of the femur. We prove that finite element models of the intact hip joint can faithfully reproduce experimental models with a small difference of 7%. Keywords: numerical analysis; experimental; total hip replacement; strain; stress

1.

Introduction

The hip joint is highly requested through daily tasks and, although it is resistive, it leads to natural wear or to degenerative process symptoms, usually associated to osteoarthritis, showing higher rigidity and pain, causing discomfort and restriction of movements to the patients (Novak 2002; Relvas 2007). Since one of the main functions of the hip joint is to support and locomotion to the human body, it is compulsory that it is healthy. When the joint starts to become damaged, it is necessary to replace it with a partial or total hip arthroplasty (THA). Due to aging of the world population, THA is one of the most performed and successful surgical procedures (Etgen et al. 2004). Although in the beginning of the history of the arthroplasty the results were not so successful, this scenario started to change in 1958 when the English surgeon Sir John Charnley employed innovative techniques for the hip arthroplasty (Wroblewski 2002). The analysis of strains in the hip joint during physiological loading conditions is necessary to understand the mechanical behaviour of the bone structures (femur and acetabulum). According to this, and in order to study biomechanical characteristics with computational models, previous numerical-experimental validation is needed to theoretically define the quality of the numerical

*Corresponding author. Email: [email protected] q 2013 Taylor & Francis

predictions. Validation is normally performed with experimental models that replicate natural ones (Cristofolini et al. 1996). The combination and validation of finite element and experimental models gives the possibility to determine stresses and strains of bone structures (Ramos et al. 2011). Finite element analysis with the strain gauge technique is used to study the biomechanics of the joint, particularly the femur and pelvic bone structures (Cristofolini and Viceconti 1997; Heiner and Brown 2001; DiasRodrigues et al. 2004; Philips et al. 2007; Ghosh et al. 2011; Ramos et al. 2011). This procedure has also been used for other bone structures such as the tibia (Majumder et al. 2004) and mandible (Ramos et al. 2011) and so on (Heiner and Brown 2001; Ramos et al. 2011). Validation has been made to validate synthetic commercial femur bones to evaluate the performance of hip prostheses (Cristofolini and Viceconti 1997; DiasRodrigues et al. 2004). The iliac bone structure usually requires higher degree of simplification, especially with regard to the ligaments. Philips et al. (2007), in order to complete the information concerning this problem, reproduced the muscular and ligaments boundary conditions using spring elements distributed over realistic attachment sites. A few studies were previously conducted to study the biomechanics of

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Computer Methods in Biomechanics and Biomedical Engineering

Figure 1.

Composite femur and iliac with strain gauges and cartilage replica.

the pelvic bone. In these studies, the boundary conditions considered are not consensual and change case to case (Majumder et al. 2004; Ghosh et al. 2011). A different approach was followed by Ghosh, Gupta, Pal, et al. (2011), which assumed that the application of the hip joint reaction force on the acetabulum would have a predominant effect on the quantitative values of stresses and strains, particularly those on the acetabular region. According to this, similar boundary conditions were assumed in our study, except for the load case that was applied in a different region, which is a more realistic one. Despite the few experimental and numerical studies that have been performed, there is a significant lack of information relative to the hip joint considering the role of the cartilage structure. In the present work, we validated a numerical model based on the results of experimental models of the hip joint biomechanics including the cartilage element. 2.

Materials and methods

2.1 Experiments models For the experimental part of the study, we used a composite model of a left iliac (ref. 3405) and a composite

Figure 2.

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CAD model, mould and silicon cartilage.

left femur (ref. 3406), commercially available by Sawbonesw (Pacific Research Labs, Vashon Island, WA, USA) (Figure 1). Composite bones are frequently used for experimental studies because of their similarity to real bones (Heiney et al. 2008; Ramos and Simoes 2009; Goswami et al. 2011). According to Cristofolini et al. (1996), some acknowledged advantages of these composite bones over natural human bones are less interspecimen variability, immediate availability, easy to handle and they do not degrade easily. We also placed a thin layer of silicone rubber between the femur’s head and the acetabular cavity to simulate the behaviour of natural cartilage of the hip joint (Figures 1 and 2). Some studies (Fergunson et al. 2000) have considered that cartilage is composed by two components, and others (Wei et al. 2005; Bachtar et al. 2006; Gu et al. 2011) have considered it as three components to evaluate the influence of the acetabular labrum on the consolidation of cartilage layers of the hip joint and to determine the maximum contact pressure between the two cartilage elements. Other studies (Anderson et al. 2005, 2010) consider cartilage as a single component of 2 mm constant thickness.

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We analysed the influence of cartilage thickness element from 1 to 3 mm (Ateshian et al. 1991; Adam et al. 1998; Ateshian and Hung 2006). The cartilage model was created from computerized tomography scans of an intact hip, and the outside surfaces of the acetabulum cavity and femoral head were adjusted to allow total surface fit. With the three-dimensional digital model, we designed a moulding tool to manufacture the cartilage replica structure using polyurethane (Renshape BM 5460, density of 0.7 g/cm3, Huntsman, Salt Lake City, UT, USA) (Figure 2(b)). A room temperature vacuum (RTV) rubber mould (Figure 2(a)) was manufactured (Ramos and Simoes 2009; Zhou et al. 2010) and the cartilage structure replica was casted with a vacuum casting equipment (Model 001 LC). VT750 rubber and CAT 750 catalyst (10:1 mixing ratio) of MCP HEK Tooling GmbH (Kaninchenborn, Lu¨beck, Germany) were used to build the cartilage structure (Figure 2(b)). 2.2 Experimental measurements According to many published papers, the use of strain gauges is a very simple procedure, although some cautions must be considered (Little and Finlay 1992; Ramos et al. 2011). To evaluate the mechanical behaviour of the experimental model, two tri-axial strain gauges were placed near the femur’s head and four around the acetabular cavity as depicted in Figure 1. The tri-axial strain gauges used are commercially available by Kyowa Electronic Instruments Co. (Tokyo, Japan), with reference numbers KFG-3-120-D17-11 L3M2S (3 mm size) (applied on the femur’s neck) and KFG-1-120-D17-11 L3M2S (1 mm size) (applied on the acetabular cavity). To place

Figure 3.

the strain gauges correctly, the surface sites were previously prepared (Gautier and Cordey 1999), and after the adequate conditions of the tri-axial strain gauges were verified, they were linked to a measuring equipment (National Instruments PXI 1050; National Instruments, Austin, TX, USA) with signal acquisition software (LabView Signal Express). The experimental model was placed in the anatomical position of the joint; this is 78 on the sagittal plane and 98 on the front plane (Figure 3). The model was placed in the loading machine and its fixation was made through the iliac on both wings of the illium and ischial tuberosity. The femur was fixed at the distal cortex as shown in Figure 3. Three incremental vertical loads were applied: 600, 1200 and 1700 N (Figure 4). The loading device was designed to apply the load on four points of the iliac (Figure 3). The femur was supported through a spherical element placed on the base of the loading device, allowing rotation of the femur to promote physiological load transfer. The position of the iliac relative to the femur was maintained by a guiding support on the base of the device (Figures 3 and 4). 2.3

Finite element analysis

Geometrical modelling of the hip joint structures was made based on the experiments. The solid models of the hip joint structures were created with a shape editor after digitalisation using CATIA V5R19 (Dassault Systems, Ve´lizyVillacoublay, France). The model’s material properties assigned were the same as the ones indicated by the manufacturer of the synthetic bones and are presented in Table 1. We assumed that all the hip joint materials were

Position of the femur and iliac in the experimental loading device.

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element methods analysis (FEM). A glue connection between cortical and cancellous bones of the iliac and femur was considered and therefore sharing all the efforts. A bonded connection between the iliac and cartilage was created. Between the cartilage and the femur’s head, we considered sliding contact with a friction coefficient of 0.001 (Linn 1967; Mow and Lai 1979; Unsworth et al. 1974, 1975). The FEM analysis was performed with HyperWorks 11 (Altair Engineering, Inc., Troy, MI, USA). The selection of the number of nodes and element dimension was made based on the results of convergence tests previously performed. The hip joint mesh was composed by 472,203 elements, 115,182 nodes and 345,546 degrees of freedom and is presented in Figure 5. The maximum and minimum principal strains of the bone structures of the hip joint were obtained and matched with the experimental strain values measured on the same locations.

Figure 4.

Load system and articulation assembly.

homogeneous, isotropic and with linear elastic behaviour (Athanasiou et al. 1991; Heiney et al. 2008). The femur was clamped on its diaphysis and both sagittal and frontal angles were maintained in the finite Table 1.

Material properties.

Designation

Material

Cortical bone Cancellous bone Cartilage

Short fiber glass composite Polyurethane foam Silicon rubber

Figure 5.

3. Results The experimental strains were on an averaged of five measurements made for each load. Table 2 presents the strains and standard deviations for each tri-axial strain gauge of the femur and iliac. A linear regression analysis was performed to determine the correspondence between the strains obtained numerically and those obtained through experimental measurements (Figure 6). A close match between results was obtained. In fact, the correlation value R2 and slope of the regression line were 0.939 and 0.912,

Finite element model of the hip joint.

Young’s modulus (MPa)

Poisson’s ratio

1700 400 0.625

0.29 0.29 0.4

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R.J. Duarte et al. Experimental measured strains. Load (N)

Designation

Bone

Rosete I Rosete II Iliac Rosete III Rosete IV Rosete V Femur Rosete VI

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a

Deformation (m1)a

600

1200

1700

11 12 11 12 11 12 11 12 11 12 11 12

24.1 (2.94) 2138.1 (1.38) 189.9 (0.71) 2297.2 (2.56) 301.0 (5.20) 2225.2 (3.65) 84.1 (9.34) 229.9 (10.49) 80.4 (3.85) 289.9 (2.70) 12.2 (3.57) 2759.2 (1.77)

129.7 (2.47) 2 427.5 (1.26) 509.3 (1.27) 2 765.3 (3.77) 571.0 (5.59) 2 548.4 (23.35) 221.3 (2.67) 2 51.6 (1.45) 137.2 (1.86) 2 157.0 (1.58) 25.0 (1.61) 21348.3 (4.78)

176.1 (2.47) 2 584.1 (4.81) 742.1 (2.03) 2 1146.0 (3.85) 794.9 (8.94) 2 795.1 (8.89) 321.3 (10.80) 2 81.4 (12.05) 209.8 (8.13) 2 238.4 (5.51) 39.1 (1.82) 2 2031.1 (8.91)

Average (STD).

respectively. These values are close to 1 which indicates a very satisfactory agreement between numerical and measured principal strains in the sites of the strain gauges. With the FE models, we determined the strain distribution in other important regions of the joint structures. The principal strain distribution on the cortical surface of the pelvic bone, around the acetabular cavity, was assessed and is presented in Figure 7 (maximum

Figure 6.

Correlation between experimental and numerical strains.

principal strains). For better definition of the localisation of the strains on the surface around the acetabular cavity, we divided it in four regions: inferior (I), posterior (P), superior (S) and anterior (A). The results were independent of the load intensity. The results show that the minimum principal strains are the highest and more critical in the posterior and anterior positions (Figure 8).

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Load Case Comparision 2000 ε1 - 600N ε1 - 1200N ε1 - 1700N

Maximum principal strain (µ strain)

1800 1600 1400 1200 1000 800 600 400

0

Figure 7.

I

P

S

A

I

Maximum principal bone strains around the iliac cavity.

Load Case Comparision 0 I

Maximum principal strain (µ strain)

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200

P

S

A

I

–1000

–2000

–3000

–4000

ε1 - 600N ε1 - 1200N ε1 - 1700N

–5000

–6000

Figure 8.

Maximum principal bone strains around the iliac cavity.

To evaluate the role of the cartilage, we also analysed the principal strains inside the acetabular cavity and on the femur’s head according to distinguished directions, anterior –posterior and medial –lateral to assess the degree of load transfer between these two structures. According to the minimum principal strain distribution on the anterior – posterior alignment (Figure 9), we can observe differences between the minimum principal iliac bone strains. The differences are more evident when the cartilage structure is

included in the system of the load transfer mechanism. In fact, the strain distribution is more homogeneous as a result of the absorption effect performed by the cartilage element of the joint. The minimum principal strain distribution on the cortex head surface of femur (Figure 10) with the use and non-use of the cartilage evidences significant differences. In fact, we observed an increase of 120% due to the absence of the cartilage which can provoke pain in the contact region.

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Figure 9.

Figure 10.

R.J. Duarte et al.

Minimum principal iliac bone strain distribution in the sagittal side.

Minimum principal femur head strain distribution.

It is interesting to note how cartilage can change the cortex strains on the surface of the femur, such as on the medial side of the femur’s neck (Figure 11). In the anterior aspect, we observed similar result mainly in the proximal region of the femoral head due to the increase of distance of loading relatively to the head centre (Ramos et al. 2006). The von Mises stress distribution was observed in surface cortex bone, presented in Figure 12 with maximum observed values between 8.3 and 9.2 MPa on the iliac and 9.3 and 11.8 MPa on the femur. These results are very

similar with other published works (Majumder et al. 2004; Wei et al. 2005; Philips et al. 2007; Gu et al. 2011). The critical region was near the contact area of femur’s superior section.

4.

Discussion

Good relation between the experimental and numerical results was achieved. An additional indicator for the overall absolute difference between numerical and experimental models, the root-mean-square-error

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Figure 11.

Minimum principal cortex strain distribution in medial aspect of the femur.

Figure 12.

Cortical von Mises stress distribution in the frontal plane.

(RMSE), was calculated. This statistic indicator is frequently used to measure the differences between predicted and real values. These differences, also called residuals, are aggregated into a single measure of predictive results (Collopy and Armstrong 1992). This indicator was expressed as a percentage (RMSE %) of the absolute measured peak strain and maximum amplitude strain. The correlation percentage achieved in this study was 5% relatively to the maximum amplitude of the strain values, and 7% relatively to the measured peak

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strain, which indicates excellent correlation between numerical and experimental results. A small value of the intercept indicates good agreement and in our study it was less than 1% relatively to the maximum value. The development of a numerical model as a tool to predict data was made based on in vitro strain measurements. Due to good agreement between the experimental and FE results, the numerical model gives enough confidence to speculate on the role of the cartilage in the biomechanics of the hip joint. The results show that

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there exists a proportionality between load and principal strains. Although this proportionality is not constant on the entire surface, the average of the principal strains can be considered as proportional to the load case. The strains are more pronounced on the iliac, especially on the superior and anterior regions, which is consistent with the study published by Dastra and Huiskes (1995). These authors observed the similar stress distribution in cortical bone, with a peak of 9.3 MPa, which is in agreement with our study presented in Figure 12. The contribution of non-spherical incongruent hip joint cartilage surface to the hip joint contact stress represented by von Mises stresses shows a peak stress inside the acetabular cavity between 10.7 and 14.8 MPa which is consistent with results Gu et al. (2011). The maximum observed was in the superior part of femur according previous works (Dastra and Huiskes 1995) and other previous studies conducted by Ghosh, Gupta, Dickinson, et al. (2011). In the study conducted by Ghosh, Gupta, Dickinson, et al. (2011), the correlation coefficient achieved was 0.91– 0.95, which is very similar to the one we obtained. The regression slope obtained is also similar to the one we obtained. As an improvement of our study, Majumder et al. (2004), despite the slight change of the boundary conditions, proved that adding several muscle forces, in order to approximate the experiments to a more realistic case, induces similar distribution of the strains and von Mises stress in the pelvic bone. The inclusion of the cartilage structure in experimental and numerical models is important because it provokes changes of the strain distribution around the proximal region of femur and on the iliac cavity. It is therefore mandatory that this structure must be included in the biomechanics of the hip joint for more realistic scientific output data. The results point out the influence of cartilage in the strain distribution, mainly in the proximal region of femur. The results present some importance specially when compare the strain distribution after a hip prosthesis with intact one. Normally this type of study does no include the cartilage, but is important in femur and iliac strain distributions. 5.

Conclusions

Relatively to the strain distribution, we observed that the critical region of the intact hip joint is the anterior – superior region of the iliac cavity where the cartilage plays an important role to attenuate the stresses and strains provoked by the loading, since there is a decrease of the principal strains between the femur and acetabulum surfaces. According to the proportionality of the loads of the models, we conclude that there is a linear relationship between the load and the principal strains around the acetabular cavity.

Based on our study’s results, the FE model developed replicates the experimental data with a difference of 7%. In this study, we prove that this model can be used to study the biomechanics of the hip joint that, according to the type of results and location for data assessment, is impossible to obtain with physical models.

Acknowledgements The authors gratefully acknowledge Fundac a˜o para a Cieˆncia e a Tecnologia through projects PTDC/EME-PME/112910/2009 and PTDC/EME-PME/112977/2009.

Conflict of interest I hereby declare that there are no conflicts of interest in relation to the work presented.

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acetabulum cartilage in the biomechanics of the intact hip: experimental and numerical assessment.

Experimental studies have been made to study and validate the biomechanics of the pair femur/acetabulum considering both structures without the presen...
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