Analysis of a femoral hip prosthesis designed to reduce stress shielding

Analysis of a femoral hip prosthesis designed to reduce stress shielding

Journal of Biomechanics 33 (2000) 1655}1662 Analysis of a femoral hip prosthesis designed to reduce stress shielding Makarand G. Joshi , Suresh G. Ad...

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Journal of Biomechanics 33 (2000) 1655}1662

Analysis of a femoral hip prosthesis designed to reduce stress shielding Makarand G. Joshi , Suresh G. Advani , Freeman Miller, Michael H. Santare * Department of Mechanical Engineering, University of Delaware, Newark, DE 19716, USA Department of Pediatric Orthopedics, Alfred I. duPont Institute, Wilmington, DE 19899, USA Accepted 5 May 2000

Abstract The natural stress distribution in the femur is signi"cantly altered after total hip arthroplasty (THA). When an implant is introduced, it will carry a portion of the load, causing a reduction of stress in some regions of the remaining bone. This phenomenon is commonly known as stress shielding. In response to the changed mechanical environment the shielded bone will remodel according to Wol!'s law, resulting in a loss of bone mass through the biological process called resorption. Resorption can, in turn, cause or contribute to loosening of the prosthesis. The problem is particularly common among younger THA recipients. This study explores the hypothesis that through redesign, a total hip prosthesis can be developed to substantially reduce stress shielding. First, we describe the development of a new femoral hip prosthesis designed to alleviate this problem through a new geometry and system of proximal "xation. A numerical comparison with a conventional intramedullary prosthesis as well as another proximally "xed prosthesis, recently developed by Munting and Verhelpen (1995. Journal of Biomechanics 28(8), 949}961) is presented. The results show that the new design produces a more physiological stress state in the proximal femur.  2000 Elsevier Science Ltd. All rights reserved. Keywords: Orthopedics; Prosthesis; Stress; Design

1. Introduction 1.1. Background The earliest practice of THA can be traced back to the 18th century (Scales, 1966). However, it was not until the late 1950s when Charnley (1960) demonstrated the use of an acrylic polymer for "xation, that long-term stability of metal implants was realized. This concept of initial rigid "xation was an essential step in the improved viability of the intramedullary hip prosthesis. The popularity of the Charnley technique is due to its very high rate of success in the older population (Lewallen and Cabanela, 1996; Madey et al., 1997). However, a much lower rate has been reported in younger patients (Sharp and Porter, 1985; Jacobsson et al., 1996; Callaghan et al., 1998). Other factors such as bone quality, weight, and activity level also a!ect the long-term success rate of arti"cial joints. Besides infection, aseptic loosening is the major postsurgery concern. Four principal causes of aseptic loosen-

ing are; mechanical failure of the implant or cement, introduction of wear debris into the interface region, relative motion across the interface, and stress shielding in the bone. Each of these phenomena can initiate a biological response in the bone leading to resorption and the eventual loosening of the implant (see, for example, Goldring et al., 1983; Gruen et al., 1979). An alternate surgical technique is cementless "xation employing direct bone-prosthesis contact. This method was developed in an attempt to overcome the problems associated with the cement. Quality of the initial "t is a critical issue in cementless implants since "xation requires intimate contact along the interface. Today, both "xation techniques are practiced; however, the bene"ts of one over the other is a debated issue (see for example, Engh et al., 1987; Van Rietbergen et al., 1993; Huiskes and Verdenschot, 1997). Although there are several, interacting factors that contribute to aseptic loosening, this paper focuses only on the analysis of the stresses in the bone. 1.2. Motivation

* Corresponding author. Tel.: #1-302-831-2246; fax: #1-302-8313619. E-mail address: [email protected] (M.H. Santare).

Fig. 1 shows schematic representation of the load transfer in the proximal femur before and after hip

0021-9290/00/$ - see front matter  2000 Elsevier Science Ltd. All rights reserved. PII: S 0 0 2 1 - 9 2 9 0 ( 0 0 ) 0 0 1 1 0 - X

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using proximal "xation was developed by Munting and Verhelpen (1995) and has shown promising initial results. This design is "xed on the lateral side of the proximal femur by means of a bolt and employs "ns along the medial border to provide resistance to torsional motion. Their in vitro experiments show minimal micromotion and the short-term clinical studies show low initial failure rates. The motivating hypothesis for the current study, is that an alternate femoral component design will reduce the level of stress shielding in the femur following total hip arthroplasty. We reiterate that other issues will generally be of concern, such as the quality of the bone}implant interface and the presence of wear debris, but for the purposes of this presentation, bone stress is the primary design criterion.

2. Methods Fig. 1. Schematic representation of the load transfer before and after THA.

replacement (Oh and Harris, 1978; Huiskes, 1990, 1995). In the natural state, the stress is distributed over the entire cross section of the femur. Bending and axial compression are the major modes of loading. The postsurgery stress state is signi"cantly di!erent mainly due to the manner in which the load is transferred to the femur. In this case, the load is partially transferred through shear across the bone/cement/prostheses interfaces (Huiskes, 1990; Huiskes et al., 1992). This altered load transfer leads to increased stresses at the interface and unloading of the bone away from the prosthesis. The interface shear stresses are further increased due to the sti!ness ratio between the prosthesis and the bone, typically of the order of 10 : 1 and higher. In addition, the bending displacements in the bone surrounding the stem are reduced because of the relatively high #exural sti!ness of the prosthesis. This reduced bending unloads the outer "bers of femur leading to a state of stress shielding. The change in the load distribution increases stresses in some regions and reduces them in others. If these changes are large enough, they can lead to adaptive bone remodeling. Areas that see higher loads, may experience an increase in bone mass, while areas that see a reduction in load may experience a decrease. The other factors mentioned earlier might also play a role in this remodeling but stress shielding is often implicated. An apparent solution to the shielding problem would be a prosthesis which loads the proximal end of the femur in a manner similar to the natural state. Some of the early prosthesis designs re#ect this approach as seen from the survey by Scales (1966). Recently, a new prosthesis design

2.1. Design methodology The "rst stage in the current design was the development of a general geometry that restores, as much as possible, the natural load-transfer mechanism through the proximal femur. A detailed "nite element model of the femur (described in the next section) was used to calculate the stresses in the bone. The change in stress, caused by the introduction of the prosthesis, was used as the standard for comparison. Preliminary studies were conducted using a conventional intramedullary prosthesis with a variable-sti!ness stem. This initial study indicated there was a signi"cant bene"t from the use of a short stem verses a long stem in terms of the interfacial shear stresses in the bone. Kuiper and Huiskes (1997) reached a similar conclusion. Of course, reducing the stem length may have an adverse e!ect on bone}implant interface stability, but the focus of this study is reducing stress di!erences in the bone. Next, a proximal plate was added to distribute the contact load over the entire cross section of the femur and reduce stress shielding in the cortical bone. By designing the plate as a separate component, the prosthesis can be more easily customized to "t di!erent sized femurs. The combination of a shortened stem and a proximal plate results in a major reduction in both stress shielding and interfacial shear stress. These changes however, make it necessary to devise a proximal method of "xation. One recent example of a proximal "xation device is the design by Munting and Verhelpen (1995) described in the introduction. However, to avoid using a sti! metal bolt through the relatively brittle lateral cortex, a cabling system was developed. The cables not only anchor the prosthesis to the bone; they also help produce a more natural bending load over the cross section of the femur by "xing the trochanter to the

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Fig. 2. Schematic representation of the proposed hip prosthesis design.

implant. On the medial side, a short screw into the stem is used to hold the plate against the medial calcar. Extensive parametric studies were conducted to evaluate the e!ects of stem length, contact surface orientations and cable positions and diameters. A schematic representation of the resulting geometry is shown in Fig. 2. In the following sections, we present details of the stress analyses and comparisons with other designs. 2.2. Finite element model Comprehensive reviews of the "nite element method in hip prosthesis development, are found in Huiskes and Chao (1983) and Joshi et al. (2000). Computer tomography (CT) data of a typical adult male femur was used as the template for the "nite element model. The scans used were taken at 3 mm intervals proximally and 10 mm distally and a gray-scale map was generated at each cross section. The gray-scale-to-bone density relationship was calibrated by taking CT scans of several samples of known density, using the same magni"cation and settings used for the anatomical scans. The gray-scale values were then matched to the density values of the known samples to develop a calibrated scale. Density information for the cancellous bone was then used to estimate the sti!ness through an empirical relationship between density and Young's modulus given by Rho et al. (1993). This resulted in a nonhomogeneous distribution of sti!ness ranging from 1 to 5.6 GPa for the cancellous bone. We assigned orthotropic properties to the cortical bone using the sti!ness values given in the literature by Cheal et al. (1992). An average of the reported sti!ness values of the diaphysis and metaphysis were used for the entire cortical region resulting in sti!ness values of 19.7, 13.1 and 10.4 GPa in the axial, circumferential and thickness directions respectively. A negligible sti!ness (0.02 GPa) was

assigned to the tissue in the medullary space since this tissue is not structural regardless of its density. The modulus of cobalt chromium alloy (200 Gpa, isotropic) was used for all the prostheses. The prosthesis solid models were digitally positioned relative to the femur model using standard surgical practices. Special care was taken to simulate a good "t with relatively little removal of bone tissue. Although a more precise positioning technique could have been used, this method was chosen for its simplicity and its similarity to common surgical practice. The models for the prostheses themselves were generated by partitioning the femur into several distinct regions, ones which would be removed in THA surgery and ones which would not. For example, in the stress analysis of the natural femur, appropriate bone properties were assigned to the various tissues in the head and neck. Since these regions are removed in surgery, for the post-THA simulations these same regions were assigned the material properties of the prosthesis and/or void as appropriate. This approach was adopted to ensure that we used an identical "nite element mesh to model the bone before and after THA and therefore reduce the e!ect of mesh sensitivity on the comparative results. The resulting 3-D model volume was discretized using 4-node, linear, tetrahedral elements as shown in Fig. 3. A perfect interface boundary condition (full bone ingrowth) was used to simulate the entire interface between the prosthesis and the bone. Although a more realistic model would include some areas without complete ingrowth, it is not known a priori which areas will achieve ingrowth and which will not. Therefore, we imposed perfect interfaces to reduce the number of unknown variables for the purposes of comparison between models. Quadratic truss elements were used to simulate the cables when present. The model was loaded using an

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M.G. Joshi et al. / Journal of Biomechanics 33 (2000) 1655}1662 Table 1 Muscle and joint contact loads used in models (data from Cheal et al., 1992) Load case and muscle

Magnitude (BW)

Unit vector X

Fig. 3. 3-D meshes used in the "nite element analysis of the natural and conventional prosthesis models.

average of all the loading cases given by Cheal et al. (1992) including the joint contact and muscle loads (see Table 1). In the model of the intact femur, these loads were distributed over the nodes at the appropriate locations on the surface of the model. In the cases where a prosthesis was present, the joint loads were applied to the trunion (actually a simpli"ed model of a trunion). Generally, this loading causes an o!set relative to the natural loading on the femoral head; therefore, we included an additional couple load on the end of the trunion. This additional couple was calculated to correspond to loading on an arti"cial femoral head of the same size and in the same position as the natural femoral head. In order to compare the stresses between models, a zero o!set was used in each case to eliminate o!set as a variable. The boundary condition at the distal end had no e!ect on the stresses in the proximal region. This was chosen as "xed to avoid rigid-body motion. The "nite element models were used to compare the stresses in the bone arising from a conventional intramedullary prosthesis without a collar, the proximally "xed design by Munting and Verhelpen (1995), and the proposed design depicted in Fig. 2. Cobalt chromium steel was used for all the three prostheses designs, and in the designs including cables, a cable cross-sectional area of 5 mm was used. In preliminary studies, several levels of mesh re"nement were tested to ensure that the model achieved

Heel strike Adductor longus 0.20 !0.47 Adductor magnus 0.20 !0.75 Gleuteus maximus 1.28 !0.53 Gleuteus medius 0.72 !0.66 Gleuteus minimus 0.54 !0.77 Vastus intermedius 0.40 !0.01 Vastus lateralis 0.40 !0.05 Vastus medialis 0.33 0.02 Joint contact 4.64 0.36 Midstance Gleuteus medius 0.80 !0.67 Gleuteus minimus 0.30 !0.78 Iliopsoas 1.30 !0.10 Joint contact 3.51 0.35 Toe o! Adductor longus 0.30 !0.43 Adductor magnus 0.30 !0.77 Gleuteus medius 1.18 !0.71 Gleuteus minimus 0.61 !0.80 Iliopsoas 2.60 !0.10 Piriformis 0.20 !0.98 Joint contact 4.33 0.31 Extension of the #exed hip (stair ascent) Biceps femoris 1.21 !0.25 Gleuteus maximus (a) 0.97 !0.52 Gleuteus maximus (p) 0.97 !0.51 Semimembranosus 2.24 0.06 Semitendinosus 0.36 0.05 Joint contact 7.70 0.48 Flexion of the extended hip Adductor brevis 0.10 !0.70 Iliopsoas 2.62 !0.10 Pectineus 0.13 !0.65 Rectus femoris 1.56 !0.07 Sartorius 0.13 0.08 Joint contact 7.70 0.44 Adduction of the abducted hip Adductor brevis 0.20 !0.72 Adductor longus 0.66 !0.43 Adductor magnus 1.70 !0.76 Gracilis 0.06 !0.11 Pectineus 0.26 !0.49 Joint contact 7.70 !0.01 External rotation of the neutral hip Gemelli 0.13 !0.98 Obturator externus 0.35 !0.98 Obturator internus 0.33 !0.98 Piriformis 0.41 !0.98 Quadratus femoris 0.48 !0.96 Joint contact 7.70 0.41

Y

Z

0.16 !0.07 0.18 0.45 0.42 0.02 0.07 0.09 !0.10

0.87 0.66 0.83 0.61 0.48 !1.00 !1.00 !1.00 !0.93

0.18 0.21 0.73 0.05

0.72 0.59 0.68 !0.93

0.26 0.23 0.00 0.07 0.73 !0.17 !0.10

0.87 0.59 0.70 0.59 0.68 0.05 !0.95

0.09 0.25 !0.01 0.05 0.06 !0.46

0.96 0.81 0.86 1.00 1.00 !0.75

0.35 0.73 !0.06 0.00 0.15 0.35

0.62 0.68 0.76 1.00 0.99 !0.83

0.21 0.22 0.10 0.15 0.02 !0.04

0.67 0.87 0.65 0.98 0.87 !1.00

!0.17 !0.10 !0.17 !0.11 0.28 0.02

!0.05 !0.14 !0.05 0.15 !0.02 !0.91

convergence. Although this is not a validation of the results, we reiterate that identical "nite element meshes were used to simulate the bone in all models. In addition the same, loadings, material properties and interface

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conditions were used to analyze all the three prostheses and the models had an average of approximately 25000 degrees of freedom.

3. Results To estimate the e!ect of the prosthesis on the stress distribution in the bone, the von Mises stress, calculated at the centroid of each "nite element, was chosen as the base line. Strictly speaking, von Mises stress may not be the most relevant measure of mechanical stimulus in anisotropic, nonhomogeneous materials such as cancellous bone. However, this is a relatively convenient, scalar measure of stress at a point. In addition, a recent study by Terrier et al. (1997), con"rms that bone adaptation models using strain energy density and von Mises criteria give very similar results. The di!erence in the stress for each element before and after THA was calculated and divided by the stress occurring in the element pre-THA. This ratio was then volume-averaged over a speci"c region and called the `stress di!erencea for that region. Since the von Mises stress is strictly non-negative, positive stress di!erence values indicate an increase in overall stress level and negative values indicate a decrease. The proximal femur below the neck and above the shaft was divided into "ve medial regions (numbered 3}7) and "ve lateral regions (numbered 8}12) as shown in Fig. 4. Each of these regions is the lateral or medial half of a threedimensional, 9 mm (approximately) thick slice of the proximal femur. Region 1 represents the proximal diaphysis and region 2 the greater trochanter. The size of the regions was chosen to represent several di!erent levels within the critical volume without producing an overwhelming quantity of data. Fig. 5 compares the stress di!erences for the three designs analyzed. In this example, perfect bonding was used for all contact surfaces between the prosthesis and the femur. Fig. 6 shows the same data rescaled to compare the two proximally "xed designs, Munting and Verhelpen (1995) and the current design. Fig. 5 shows that in all the regions, except region 2 (greater trochanter), the conventional prosthesis produces signi"cant stress shielding. In region 2, the conventional prosthesis causes a 100% overstress. This is because a portion of the trochanter is removed to accommodate the conventional prosthesis yet the trochanter muscle loads remain. The proposed design and the Munting and Verhelpen (1995) design both show far less stress shielding everywhere except in region 12. In addition, both proximally "xed designs cause no signi"cant change in the stresses in the diaphysis as expected. The closer comparison between the proximally "xed designs in Fig. 6 clearly shows that the current design produces lower magnitude stress di!erences in all regions. Region 7 is the medial calcar, which is a site of major concern due

Fig. 4. Approximate partitioning of the femur into various regions for stress di!erence comparison.

to the common occurrence of bone resorption (Engh and Culpepper, 1997). Here, the new design produces less stress shielding than the Munting and Verhelpen (1995) design. Another region of concern is the brittle lateral cortex region (regions 9}11) where the Munting and Verhelpen (1995) design uses a sti! bolt. This bolt passes diagonally through regions 11 and 12 and contacts the lateral surface near the junction of regions 10 and 11. The net e!ect is a complex redistribution of the stresses in these and nearby regions. This redistribution causes the Munting and Verhelpen (1995) design to show a stress increase in region 12 and decreases in regions 9}11. Here too, the new design produces signi"cantly smaller stress di!erences than the other designs. In each of the models, the greater trochanter is subject to an assumed loading from the abductor muscles. In the post THA femur, the natural attachment of the femoral head to the trochanter is lost since the proximal bone mass is removed. Hence there is a signi"cant di!erence between the pre and post-THA stress states in the greater trochanter. In terms of this analysis, the conventional

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Fig. 5. Stress comparison, by region, for the conventional, Munting and Verhelpen (1995), and the proposed design.

Fig. 6. Stress comparision, by region, for the Munting and Verhelpen (1995) and the proposed design.

prosthesis shows by far, the highest stress di!erences, the Munting and Verhelpen (1995) design has greatly reduced stress di!erences due to the lateral-proximal "xation. The new design has the least stress di!erence in the greater trochanter, largely due to cable attachments around the trochanter and the assumed perfect bonding

interface condition. The cables employed in the proposed design produce a compressive stress in the trochanter by wrapping around this area tightly. But the addition of the cables also draws the trochanter back into the overall bending of the femur. The net e!ect is a small degree of shielding in region 2. Parametric studies show that

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without the cables, there is a large tensile stress at the interface between the proposed design and the underlying bone. For this analysis, no attempt was made to test for failure of the cables or the underlying bone.

4. Discussion The total hip arthroplasty procedure employing intramedullary "xation has a lower long-term success rate in younger patients than older patients. This study presents a design methodology and new design aimed at longterm "xation in the younger, more active population. The basis for this new design is an anchoring method providing proximal transfer of load. This prosthesis provides contact with the entire cross section of the proximal femur resulting in much lower stress shielding when compared with a conventional intramedullary design. In the numerical studies presented, the proposed design consistently produces less stress shielding than the traditional intramedullary design or the Munting and Verhelpen (1995) design. A large number of numerical parametric studies and a preliminary in vitro test were conducted to validate the "nite element models developed. Space does not permit us to elaborate here. In addition, as pointed out in Joshi et al. (2000), it is impossible to compare numerical results between di!erent "nite element studies due to di!erences in anatomy, meshing, loading conditions and material parameters. Within this study however, all these sources of variability are controlled by using identical bone models from case to case. Therefore, any inaccuracies introduced will be present in all cases and therefore have little or no e!ect on the comparative results as presented in Figs. 5 and 6. Stress shielding is certainly not the only mechanism that can lead to aseptic loosening. Other factors such as wear debris particles and the quality of the bone-implant interface are important mechanisms that have not been addressed in this study. In fact, with the proposed design, interface quality may become a key issue due to the smaller area of bone-prosthesis contact. These issues are best addressed through series of in vitro and in vivo tests, both of which are underway and will be reported in subsequent papers.

Acknowledgements This research was supported through the Whitaker Foundation Grant C RG-95-0250. The computation was supported by the National Center for Supercomputing Applications, at the University of Illinois, UrbannaChampaign, Grant C BCS970002N. We also thank Shawn Riley for his help with the "gures.

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