Thickness effects on maximum von-mises stress of a cement mantle in total hip replacement - a finite element study

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1 Journal of Applied Biomaterials & Biomechanics 2009; Vol. 7 no. 2, pp Società Italiana Biomateriali Thickness effects on maximum von-mises stress of a cement mantle in total hip replacement - a finite element study Y.S. Arun Kumar, Bhaskar Pant, Konjengbam Darunkumar Singh Department of Civil Engineering, Indian Institute of Technology, Guwahati - India Abstract: Aim: The present study seeks to increase the life term of fully cemented total hip replacements by minimizing the stress values within the cement mantle. Methods: Three-dimensional (3D) finite element analyses have been carried out to investigate the effects of varying cement thickness on the von-mises stress of a cement mantle. The magnitude and location of maximum von-mises stress within the cement mantle have been studied for both straight and tapered prosthetic stems. Results: For prosthetic stems having lower radii sizes, the maximum stress zone is found in the upper region of the cement mantle whilst for stems with higher radii sizes the maximum stress zone is found in the lower region of the cement mantle. For the same cement thickness, straight stems are found to produce lower maximum stress values in the cement when compared to tapered stems. Finally, for the straight models with the same cement thickness, maximum stress values are found to decrease with increasing stem radius. Conclusions: It can be concluded that the maximum stress values in the cement mantle decrease with decreasing cement thickness. (Journal of Applied Biomaterials & Biomechanics 2009; 7: 111-5) Key words: Cement, Stem, Von-Mises stress, Finite element modeling Received 20/08/08; Revised 25/09/08; Accepted 09/10/08 Introduction Total hip arthroplasty has gained popularity with the increasing successful results of hip replacement surgery. Therefore, it becomes imperative to look into various ways of increasing the life of these replacements to limit cases of revision operations. Total hip arthroplasty can be achieved through cemented or uncemented prosthetic stems. In spite of the recent focus on uncemented hip replacement (the primary advantage being easier surgery), those are not without the usual problems of wear and aseptic loosening, extended recovery period, ie longer time taken for the natural bone to grow and attach to the prosthesis, and constraints in activities for up to approximately 3 months to protect the hip joint. In older patients, the anatomical considerations may not permit an uncemented femur, thereby limiting its wider applicability. Moreover, the natural process of bone growth in uncemented hip replacement surgeries can induce severe thigh discomfort/pain. Cemented prostheses have been reported to help in mobility and in reducing pain soon after surgery, and are popular with people having osteoporosis (or people with weak bones) and less active people (1-4). Therefore, in this study, the emphasis is on cemented total hip replacements. The most commonly used bone cement is polymethylmethacrylate (PMMA), which can provide long-term bonding and distribution of stresses for cemented hip replacements. The PMMA cement has a relatively high compressive strength, but weak tensile and shear strength; and therefore, can easily fail in a brittle manner at comparatively high tensile loadings (3, 5, 6). It has been reported that the predominant reason for the failure of fully cemented hip replacement surgeries is aseptic loosening of the femoral stem (7). Loosening is mainly caused by the fatigue failure of the cement mantle under cyclic loading. Fatigue failure can be influenced by stress intensity and frequency of the stress cycles. The number of cycles required to cause fatigue failure at a particular maximum stress is generally quite high, but it significantly decreases as the stress is increased. Therefore, the life span of the artificial hip after the replacement surgery is dependant on the stress values in the cement mantle and even a minor reduction in these values could greatly improve its performance over time. Hence it becomes important to minimize the stress values in the cement mantle during loading in order to increase its longevity. Amongst the various parameters that can influence cement failure, namely stem material, stem geometry and cement material, cement mantle thickness is considered important (8-12). Although Fisher et al (8) have reported experimental observations on the effects of cement mantle thickness on cement strains, to the best of our knowledge there are very limited numerical studies (e.g. Hsu (13)). Hsu made a recent attempt using a finite /111-05$25.00/0 JABB_ _Kumar.indd :11:46

2 Thickness effects on maximum von-mises stress of a cement mantle in total hip replacement - a finite element study A B Fig. 1 - Schematic diagram of the model for a) straight and b) tapered stems. element method to account for the effect of cement mantle thickness on the maximum stress values in the cement mantle. Similar attempts have been made in this work by including the tapered prosthetic stems and by studying the effect of prosthetic stem radius on the position of maximum stresses in the cement mantle. Finite element modeling 3D finite element models were generated using commercial finite element software, ANSYS, (ANSYS Version 6, Canonsburg PA, USA) (14). The prosthetic stem, bone cement and bone were all modeled using SOLID92 elements. This element is a 3D 10-noded tetrahedral structural solid having three degrees of freedom at each node: translations in the nodal x, y, and z directions. All the finite element models were analyzed under the assumption that the prosthetic stem and cement, the cement and bone are perfectly bonded/glued to each other. Table I shows the material properties adopted for the stem, cement and bone (14). Figure 1 shows a schematic diagram of the idealized model geometry for both straight and tapered stems. The length, top outer diameter and bottom diameter of the bone are taken as 400, 60 and 40 mm, respectively (15). The TABLE I - MATERIAL PROPERTIES OF CEMENT, STEM AND BONE (LENNON AND PRENDERGAST (6)) Material Young s modulus, Poisson s e (GPa) ratio (n) Stem Cement Cancellous bone head diameter is taken as 20 mm and is connected to the stem with a cylindrical arc of radius mm such that the total neck length is mm. The stem length from the center of the head is taken to be mm (15). In Figure 1a, r 1 denote the radii of the stem and outer surface of the cement mantle, respectively. For tapered stem subscripts, b and t denote radii values corresponding to the bottom and top parts of the stem, respectively (Fig. 1b). The load that acts on the prosthetic stem head is reported to be the maximum at 45% of the gait cycle and is found to be around 4.6 times the body weight (13, 16). Therefore, for a person weighing 50 kg, the total load would be 2300 N. Resolving this load into components yields, Fx = -900 N, Fy = N, Fz = 370 N, with x, y, z orientations, as shown in Figure 2. Figure 2 also shows a typical finite element mesh with approximately 25,000 SOLID92 elements, for the linear elastic static analyses carried out. Results As mentioned above, one of the prime causes for the failure of total hip replacement operations is due to the failure of the cement mantle, so in this work emphasis was laid on the stress analysis of the cement mantle, particularly in estimating the maximum von-mises stress for different cement mantle thicknesses, by varying radii, r 1. In addition, results are presented for both straight and tapered stems, with constant cement thickness in the following sub sections. The results presented below are based on meshes considered fine enough, as further refinements did not alter the peak stresses significantly. 112 JABB_ _Kumar.indd :11:46

3 Kumar et al Fig. 2 - A typical FE mesh (~25,000 Solid92 elements). Fig. 3 - Effect of r 2 on maximum von-mises stress for fixed r 1. Effect of varying r 2 Figure 3 shows the effect of varying the r 2 values for constant r 1 for two values of r 1 = 6 mm and 11 mm. It has been found that for low r 1 value (for eg r 1 = 6 mm) maximum stress is found in the upper region of the cement mantle, while for higher r 1 value (for eg r 1 = 11 mm) maximum stress is found in the bottom region of the cement. For r 1 = 6 mm, a reduction in the maximum stress can be seen by about 7.4% for a decrease in thickness from 5 mm to 2 mm, however, the maximum stress remains relatively stabilized at about 12.3 MPa for a higher r 1 value of 11 mm when the cement mantle thickness is varied from 6 mm to 3 mm. In either case, increasing r 1 value shows a lowering of the maximum von-mises stress, suggesting that a bigger stem diameter helps to reduce maximum stress in the cement mantle. Effect of varying r 1 Figure 4 shows the variation of maximum von-mises stress with r 1 for two r 2 values of 15 mm and 17 mm. It can be observed that for both the r 2 values the maximum stress decreases with increasing r 1 (or decreasing cement mantle thickness). It can be seen that there is a 13% reduction in maximum stress when the thickness is reduced from 8 mm to 2 mm. Again, as in Figure 3, reduction in maximum stress can be achieved by reducing the cement mantle thickness; of course a very low thickness may pose a practical difficulty in placing the stem. Comparison between tapered and cylindrical stems To compare the effect of the vertical cross-sectional shape of the cement mantle, a comparison was made Fig. 4 - Effect of r 1 on maximum von-mises stress for fixed r 2. between a tapered and straight cement mantle (Fig. 5). In the case of tapered models, both r 1 values varied along the stem length as shown above (Fig. 1b). Tapered models were compared with straight ones having the same cement thickness and having r 1 values equal to the corresponding values at the top of the tapered stem. It can be seen from Figure 5 that straight models gave lower values of maximum stress by about 9% from those of tapered models. Models with constant cement thickness In the above discussion, we have seen the effect of cement thickness variation on the value of maximum stresses in the cement mantle. For the models with constant cement thickness, it was observed that the maximum 113 JABB_ _Kumar.indd :11:47

4 Thickness effects on maximum von-mises stress of a cement mantle in total hip replacement - a finite element study Fig. 5 - Effect of cement mantle shape on maximum von-mises stress for fixed r 1 (t) = 12 mm. Fig. 6 - Effect of stem diameter on maximum von-mises stress for constant cement thickness (= 4 mm). stress values decrease with increasing r 1 values as shown in Figure 6 (thickness = 4 mm). Discussion The beneficial effect of increasing stem diameter in reducing peak stresses has been reported in this work and it is in agreement with the findings of Hsu (13). Shifting the position of the maximum stress from the bottom part of the cement mantle to the top part, when the stem diameter is reduced was observed in this study. This observation will be helpful for providing reinforcements in the cement to increase its durability. Although tapered stems are reported to provide better mechanical integrity due to a wedging action (16, 17), this study shows that tapered stems yield relatively higher peak stresses than straight ones. There are two major implications of this study, it has been noted that peak stress values in the cement mantle reduce with the increase of the stem radius (even when the cement mantle thickness is kept constant), so in the case of patients having a stronger bone structure, wherever possible, a prosthetic stem with a larger radius (>10 mm) could be suggested to minimize peak stresses, so that the necessity of revision surgery is alleviated. However, if a thinner prosthetic stem is suggested, for various reasons, namely weaker bone structures, and the inability to sustain larger cavities, peak stresses are likely to be found in the upper region of the cement mantle as reported above. For such cases, extra reinforcements could be provided at the top of the cement mantle by using metal meshes, carbon fibers, etc. Further improvements to this study could include frictional behavior modeling due to imperfect bonding between the prosthetic stem and the cement. In addition, in this study, only one load combination was considered (45% of the gait cycle during normal walking), but the stress values may rise significantly during stumbling, running or climbing stairs. A consideration of these effects will provide more insight for situations closer to real life scenarios. As comparable experimental reports are not available, to the best of our knowledge, further experimental investigations are necessary to validate the present findings. Conclusions The effect of cement mantle thickness and stem radii on the magnitude and position of maximum von-mises stresses have been reported in this work, using finite element analyses, and the results are summarized below. The maximum stress values in the cement mantle decrease with decreasing cement thickness. For prosthetic stems having low radii values, the maximum von-mises stress zone is found in the upper region of the cement mantle, while for stems with higher radii values the maximum stress zone is found in the lower region of the cement. Straight stems are found to produce lower stress values in the cement mantle when compared to tapered stems, the comparison being made between corresponding models with same cement mantle thickness. Finally, for the straight models with the same cement mantle thickness, maximum von-mises stress values are found to decrease with increasing r 1 values. Conflict of interest statement: None. 114 JABB_ _Kumar.indd :11:47

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