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Fluid load support and contact mechanics of hemiarthroplasty in the natural hip joint
Medical Engineering & Physics 33 (2011) 96–105
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Fluid load support and contact mechanics of hemiarthroplasty in the natural hip joint Sainath Shrikant Pawaskar ∗ , Eileen Ingham, John Fisher, Zhongmin Jin Institute of Medical and Biological Engineering, University of Leeds, Leeds LS2 9JT, UK
a r t i c l e
i n f o
Article history: Received 16 March 2010 Received in revised form 12 August 2010 Accepted 16 September 2010 Keywords: Articular cartilage Biphasic Contact mechanics Finite element Hemiarthroplasty Fluid load support Activities of daily living
a b s t r a c t The articular cartilage covering the ends of the bones of diarthrodial synovial joints is thought to have evolved so that the loads are transferred under different and complex conditions, with a very high degree of efficiency and without compromising the structural integrity of the tissue for the life of an individual. These loading conditions stem from different activities such as walking, and standing. The integrity of cartilage may however become compromised due to congenital disease, arthritis or trauma. Hemiarthroplasty is a potentially conservative treatment when only the femoral cartilage is affected as in case of femoral neck fractures. In hemiarthroplasty, a metallic femoral prosthesis is used to articulate against the natural acetabular cartilage. It has also been hypothesized that biphasic lubrication is the predominant mechanism protecting the cartilage through a very high fluid load support which lowers friction. This may be altered due to hemiarthroplasty and have a direct effect on the frictional shear stresses and potentially cartilage degradation and wear. This study modelled nine activities of daily living and investigated the contact mechanics of a hip joint with a hemiarthroplasty, focussing particularly on the role of the fluid phase. It was shown that in most of the activities studied the peak contact stresses and peak fluid pressures were in the superior dome or lateral roof of the acetabulum. Total fluid load support was very high (∼90%) in most of the activities which would shield the solid phase from being subjected to very high contact stresses. This was dependent not only on the load magnitude but also the direction and hence on the location of the contact area with respect to the cartilage coverage. Lower fluid load support was found when the contact area was nearer the edges where the fluid drained easily. © 2010 IPEM. Published by Elsevier Ltd. All rights reserved.
1. Introduction A person undergoes a series of activities including walking, climbing stairs, rising from a chair in the course of a day. The joints of the lower extremities have to bear not only the weight of the body but also the forces that are generated due to muscles and their moments. The hip joint for example, is known to withstand very high loads of 7–9 times body weight [1,2] with the highest of those forces experienced during stumbling. The acetabulum and the femur of the hip joint also articulate with varying speed depending upon the activity and this may range between extremes of slow walking and fast running of an athlete. However, the opposing articular cartilages usually survive the lifetime of an individual despite the harsh operating conditions they are subjected to. Cartilage may
∗ Corresponding author at: Institute of Medical and Biological Engineering, School of Mechanical Engineering, The University of Leeds, Leeds LS2 9JT, UK. Tel.: +44 0113 343 5011; fax: +44 0113 242 4611. E-mail addresses: [email protected], [email protected] (S.S. Pawaskar).
however break down due to injury, congenital disease or the development of arthritis [3,71]. Mechanical factors may cause structural as well as biochemical changes in articular cartilage [4–6]. Loss of cartilage in the hip joint may lead to total hip joint replacement to alleviate pain and improve quality of life. When only the femoral head is affected, hemiarthroplasty is an option. In hemiarthroplasty only the femoral head is replaced by a rigid metallic prosthesis, which then articulates with natural acetabular cartilage. To understand the potential effect of hemiarthroplasty on the acetabular cartilage and improve prosthetic design, it is important to investigate the conditions under which the joint operates during different activities of daily living. Instrumented prostheses have been used to measure in vivo contact forces [2,7–10] and contact stresses [11–15] in both natural and artificial hip joints. Bergmann et al. have used instrumented prostheses to record the hip contact forces for nine activities [16]. They found the forces to be as low as 0.26 time body weight (BW) during rising from a chair and as high as 2.6 times BW during stair descent. Many numerical studies have concentrated on the contact stresses [17,18] since they play an important role in the tribology of the cartilage [12,19], cartilage degradation [20–22] and
1350-4533/$ – see front matter © 2010 IPEM. Published by Elsevier Ltd. All rights reserved. doi:10.1016/j.medengphy.2010.09.009
S.S. Pawaskar et al. / Medical Engineering & Physics 33 (2011) 96–105
“preoperative planning and postoperative rehabilitation” [18]. The prediction of contact area from contact mechanics analysis may also give an indication of the areas of acetabular cartilage which are most susceptible to breakdown. A finite element model of contact mechanics of the human hip joint has been experimentally validated using cadaveric tissue in which cartilage was modelled as a hyperelastic material [23]. However, none of the three-dimensional FE/numerical studies, to the best of authors’ knowledge, have considered the biphasic nature of the cartilage. Hence, those studies are not able to account for interstitial fluid pressurization and its influence on tribology and the contact mechanics of the articular cartilage within the joint. Biphasic lubrication, which is due to the load partitioning between fluid and solid phases with the fluid phase sustaining most of the load, aids in maintaining a very low friction [24–26]. This coefficient of friction of the articulating cartilages usually lies in the range of 0.001–0.02 [24,27,28]. The role of fluid pressurisation within cartilage in reducing the frictional coefficient has been hypothesized by many authors [25–27,29–36]. It has not only been directly measured [37–39] but has also been shown to be linearly correlated with the coefficient of friction in sliding experiments of cartilage against glass under constant load [39]. It has been shown that the fluid phase is capable of supporting more than 90% of the load thus resulting in low solid-to-solid contact and hence a lower effective coefficient of friction [27,32,37,38]. Thus, the biphasic properties of articular cartilage play an important role in the tribology of natural synovial joints. Hemiarthroplasty may alter the biphasic fluid load support. The aim of this study was to investigate the hip joint with a hemiarthroplasty during several activities of daily living in order to understand the tribology and contact mechanics of the biphasic cartilage under varying and complex conditions. 2. Material and models A solid model of male left pelvis created from CT scans [40] (Fig. 1) was used to create finite element (FE) model of the hip by using I-DEAS (ver. 11, Siemens PLM Software, Plano, TX, USA) and ABAQUS (ver. 6.7-1, Dassault Systemes, Suresnes Cedex, France). FE analyses considering different activities of daily living were carried out using ABAQUS.
Fig. 1. FE model of hip hemiarthroplasty.
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A spherical horseshoe shaped acetabular cartilage of uniform thickness of 2 mm was used in all the simulations. The acetabular bone cavity was of radius 30 mm and the inner radius of the acetabular cartilage was 28 mm [41,42]. The acetabular cartilage was approximately divided into four regions; viz. lateral roof, medial roof, anterior and posterior horns [18]. The superior dome was assumed to be at the centre covering parts of lateral and medial roofs. The cortical bone layer of the pelvis was assumed to have thickness of 1.41 mm [43]. A femoral prosthetic head of radius 27.5 mm was used throughout to give a radial clearance of 0.5 mm. The centres of both the cartilage surface and prosthetic head were at the origin of the coordinate system. Biphasic poroelastic elements were used for the acetabular cartilage whereas bones were assumed linearly elastic. The elements used for each component of the hip joint along with their material properties are given in Table 1. There was a minimum of three elements through the cartilage thickness [23]. The permeability of the cartilage was k = 9.83 × 10−16 m4 /N s [44] and the water content was 80% [45]. The cartilage solid phase was modelled as neo-Hookean, with elastic strain energy potential given in Eq. (1) [46]. W (C) =
G K (I1 − 3) + (J − 1)2 2 2
(1)
where, C, right Cauchy–Green deformation tensor; G, Shear modulus; I¯1 , first deviatoric strain invariant; K, Bulk modulus; J, total volume ratio when linear thermal expansion strain is not considered. Bulk modulus, K and shear modulus, G are related to Young’s modulus, E and Poisson’s ratio, by Eqs. (2) and (3). The surfaces of the acetabular cartilage and metallic prosthetic head were slave and master respectively. The head was coarsely meshed due to strict master-slave algorithm which prevents slave node penetration into the master [46]. The mesh was finalized after sensitivity analysis to ensure that the error in predictions was less than 5% when the consecutive meshes of different densities were used. E = 3K(1 − 2)
(2)
E = 2G(1 + )
(3)
The pelvis was pinned by restricting all three translational degrees of freedom of the nodes of the sacro-iliac joint and those of the contralateral side of the pubic symphysis. The peripheral surfaces of the cartilage through its thickness were always exposed and hence free flow was prescribed on these surfaces. The back surface of the acetabular cartilage was tied to the impermeable lunate surface of the acetabular cavity. Fluid flow on the contacting cartilage surface was imposed depending upon developing contact [47]. Frictionless contact was assumed. One cycle each of the nine activities of daily living as shown in Table 2 was simulated with their respective load vectors [16]. A long-time duration of five cycles was analysed only for normal walking. Femoral rotation was already accounted for in these load vectors. The hip joint contact force data used in this study also accounted for muscle forces [16]. The pelvis rotates about both the transverse axes during activities [16]. The load vectors were rotated to take into account this pelvic orientation. The loads were applied at the centre of the head, as shown in Fig. 1. The entire analysis was quasi-static with different load vectors being applied one after the other in each step without changing any of the boundary conditions. Another set of models, representing all the activities were analysed using non-linear void ratio dependent permeability (VRDP). This was calculated using Eq. (4) [48,49]. Material parameters, M and used in this equation were 4.638 and 0.0848 respectively
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Table 1 Elements used for various components of hip joint along with their material properties. Component
Cancellous bone (pelvis) Cortical bone (pelvis) Subchondral bone (pelvis) Acetabular cartilage Prosthetic head
Element Type
Quantity
C3D4 C3D6 C3D4 C3D8RP C3D6 C3D8
12,165 3468 247 14,772 432 2304
Elastic modulus, E (MPa)
Poisson’s ratio,
Reference
70 17,000 2000 1.072 220,000
0.2 0.3 0.3 0.011 0.3
[72] [72] [72] [44] [73]
Table 2 List of activities with their start and end [16]. Activity
Starts at
Ends at
Cycle time (s)
Slow walk (0.98 m/s) Normal walk (1.09 m/s) Fast walk (1.46 m/s) Stand Up (chair height – 500 mm) Sit down (chair height – 500 mm) Down stairs (stair height – 170 mm) Up stairs (stair height – 170 mm) Knee bend Stand 2-1-2 leg
Heel strike Heel strike Heel strike Beginning of getting up Standing position Toe off Heel strike Standing position Two legged stance
Ipsilateral heel strike Ipsilateral heel strike Ipsilateral heel strike Standing position Sitting in a relaxed position Ipsilateral toe off Ipsilateral heel strike Standing position Two legged stance
1.248 1.103 0.953 2.489 3.719 1.439 1.593 4.665 6.703
Fig. 2. (a) Peak contact pressure, (b) peak fluid pressure, (c), (d) acetabular contact area and (e) total fluid load support during first cycle of slow, normal and fast walking.
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Table 3 Maximum peak contact pressure with corresponding peak fluid pressure, contact area and total fluid load support (TFLS) for different activities and where and when they occurred. Activity
Peak contact pressure (MPa)
Peak fluid pressure (MPa)
Where
Contact area (%)
TFLS (%)
Cycle time (%)
Slow walk Normal walk Fast walk Stand up Sit down Down stairs Up stairs Knee bend Stand 2-1-2 leg
2.97 2.78 2.99 2.98 2.57 4.63 3.00 2.42 4.40
2.77 2.59 2.77 2.53 2.19 3.85 2.77 2.10 3.71
Superior dome Superior dome Superior dome Posterior horn Posterior horn Lateral roof Superior dome Medial roof nearer posterior side Lateral roof
49.64 52.00 53.10 55.13 49.88 38.88 53.79 46.77 40.43
90.11 91.21 90.95 84.10 85.39 81.80 91.07 86.99 83.42
16.5 15.5 12.5 44.5 45.0 88.0 16.0 53.5 46.0
[50]. Initial permeability (k0 ) and initial void ratio (e0 ) representing water content, were constant permeability and void ratio values respectively, that were used in the models without void ratio dependent permeability.
k=k
e e0
exp
M 2
1+e 2 1 + e0
−1
(4)
3. Results The variation of peak contact pressure on the acetabular cartilage surface for one cycle of slow, normal and fast walking is depicted in Fig. 2a. In the case of normal walking, the maximum peak contact pressure of 2.78 MPa was found in the superior dome of the acetabulum at 15.5% of the cycle (Fig. 2a and Table 3). The pressure distribution was in the antero-posterior direction but slightly towards the posterior side similar to that observed at 15%
Fig. 3. Contours of contact stresses (MPa) in acetabular cup during different phases of first cycle of normal walking (A – anterior; P – posterior; M – medial; L – lateral).
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Table 4 Average total fluid load support (TFLS) for different activities. Activity
Average TFLS (%)
Slow walk Normal walk Fast walk Stand up Sit down Down stairs Up stairs Knee bend Stand 2-1-2 leg
89.28 90.96 90.08 87.74 87.18 88.45 89.82 88.97 88.23
the swing phase. It moved more medially in cases of slow and fast walking compared to normal walking (Fig. 5). The predictions of important parameters for all the activities that were analysed are listed in Tables 3 and 4. The predicted peak contact pressure, peak fluid pressure, contact area and total fluid load support for standing up and sitting down are shown in Fig. 6. The variation of parameters for going down the stairs and climbing up the stairs is shown in Fig. 7 as a function of percentage cycle whereas the results for knee bending and standing on one leg are shown in Fig. 8. The peak contact pressure, peak fluid pressure and acetabular contact area for different activities generally showed the same time-dependent trend as that of contact force. However, while going down the stairs and in one-legged stance, the contact area variation was found to be somewhat deviating from that of the contact force (Figs. 7c, d and 8c, d). The variation of total fluid load support was different to that of the contact force for almost all activities except for some similarity in slow and fast walking (Fig. 2e). When void ratio dependent permeability was used, the variations of all the parameters of interest remained similar to the predictions with constant permeability. The maximum difference with respect to constant permeability predictions was 3.87% in total fluid load support during standing up. In normal walking this difference was even less and was around 1.93%. The variation of total fluid load support during normal walking for void ratio dependent model and the one without is shown in Fig. 9 which shows a close similarity between the two curves.
Fig. 4. Total fluid load support for five normal walking cycles.
4. Discussion and 20% cycle time (Fig. 3). The corresponding contact area was 52.00% of the total potential contact area and total fluid load support was 91.21%. The maximum fluid pressure at this instant was 2.59 MPa. The variation of peak contact pressure, peak fluid pressure and the contact area with respect to time was similar to that of contact force for all three walking speeds (Fig. 2a–d). The variation of total fluid load support in general seemed to follow contact force variation for slow and fast walking whereas it deviated towards the last 35% of the cycle in the case of normal walking (Fig. 2e). However, it always remained high and on an average it was found to be 89.28%, 90.96% and 90.08% for slow, normal and fast walking respectively (Table 4). The total fluid load support decreased only slightly (0.17%) over five cycles of normal walking (Fig. 4). The contours of the contact pressure at different stages of one normal walking cycle for the first cycle are shown in Fig. 3. It can be seen that throughout the stance phase when the load was high, the contact was mostly maintained in the superior dome of the acetabulum. It then started moving towards the medial roof during
A limited number of FE/numerical studies of the contact mechanics of the hip joint exist. However, none of these studies have investigated the role played by interstitial fluid pressurization in the contact mechanics and tribology of the cartilage in a whole joint model. Therefore nine different activities of daily living were simulated to investigate the extent of effect that the fluid phase has in the tribological functioning of the hip joint after hemiarthroplasty. The methodology used in analyzing these models was validated using porcine acetabular cups loaded with a rigid metallic prosthesis [70]. The variation of acetabular cartilage peak contact pressure followed that of contact force in all the activities of daily living as observed previously [17]. A similar correlation was observed by Park et al. with respect to hip joint forces [15] and ground reaction forces for the stance phase [7,15]. The peak contact pressure was maximal when going down the stairs just before toe-off. This was the most strenuous of all the activities investigated. Standing on one leg was the next demanding activity. In both these activities the corresponding contact areas were smaller and were on the
Fig. 5. Contours of contact stresses at 84% of first walking cycle.
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Fig. 6. (a) Peak contact pressure, (b) peak fluid pressure, (c), (d) acetabular contact area and (e) total fluid load support during first cycle of standing up and sitting down.
lateral roof of the acetabulum. The contact stresses for descending stairs were found to be higher than those during stair ascent as has been also observed in clinical [14] and analytical studies [51]. The variation of peak fluid pressure also showed patterns similar to those of contact forces for all the activities of daily living. The total fluid load support in all the activities was found to be around 90%. This reduced the load supported by the solid phase of the cartilage which would reduce the effective coefficient of friction [26,27,29,31,34,39]. This would then reduce the frictional shear stresses thus protecting the cartilage from wear. This fluid load support was high over most of the cycle for all the activities. The drop in the fluid load support was very small even after five cycles of normal walking. The migration of contact probably helped in rehydration of the cartilage thus maintaining high interstitial fluid pressurization [52,19]. It has been also hypothesised that the contact migrating faster than the diffusive velocity of the interstitial fluid (∼10−4 –10−6 mm/s) does not allows enough time for the fluid to flow to the regions of low pressure and may help in maintaining higher fluid pressurisation over longer time duration [53,36]. It reduced only when the contact moved towards the edges of the acetabular cartilage. This was because, the acetabular labrum was
not modelled in the present study and free flow was prescribed on the edges of the cartilage. Thus more fluid exudation occurred when the contact moved towards any edge. In the presence of the labrum which has lower permeability than the cartilage [54], this edge effect will reduce. The anomaly seen in total fluid load support between 60% and 95% of the normal walking cycle in Fig. 2e was due to the contact being slightly away from the medial edge as seen in Fig. 5. The contact area was generally small in spite of the conforming contacting surfaces. The contact areas for all activities did not exceed 55.59% which happened at 47.5% of the standing up cycle. The contact moved medially but slightly towards the posterior horn during this time. This was lower than that observed by Yoshida and colleagues in their discrete element analysis study [18]. However, the clearance used by Yoshida et al. was not mentioned. Acetabular fit has been cited as an important parameter in the prevention of acetabular erosion [55,56]. The current study used a radial clearance of 0.5 mm between the acetabular cartilage and the metallic prosthetic head which might have reduced the contact areas. The smallest contact area was 23.77% at 7% of the standing up cycle when the contact moved to the posterior horn of the acetabular cup.
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Fig. 7. (a) Peak contact pressure, (b) peak fluid pressure, (c), (d) acetabular contact area and (e) total fluid load support during first cycle of going down stairs and climbing stairs.
It should be noted that the commercial femoral head prostheses are available in increments between 1 and 2 mm [57]. Thus a radial clearance of 0.5 mm represented the smallest realistic clearance for hemiarthroplasty for spherical acetabular cup assumption. The acetabular cavity was assumed to be spherical in this study which is not the case in an anatomical joint. The non-spherical articular surface would, in turn, introduce variable clearance in the joint and adversely affect both the contact pressures and fluid load support. The total fluid load support in this case might be reduced if there was a greater area available for fluid exudation (as in higher clearances) or the permeability was increased (when water content increases as in case of OA) [45,58]. This would then increase the coefficient of friction and hence frictional shear stresses. The increased contact stresses along with the increased shear stresses have the potential to induce cartilage fibrillation thus compromising the integrity of the hip joint in general and cartilage in particular. In OA joints in which the cartilage structure has already been compromised and diminished, higher local contact stresses might enhance this effect. However, it should be noted, that the long term survivorship has been shown in both unipolar [59] and
bipolar [60] hemiarthroplasties which may be due to higher fluid load support and lower contact stresses. Contact area and peak contact pressure depended not only on the magnitude of the load but also on the location of the contact. For example, in standing on one leg, contact stresses were 3.65 MPa and 2.88 MPa for similar loads of 1937 N and 1935 N respectively during two different stages of the activity. However, in the first case the contact was near the lateral roof (contact area – 42.45%) whereas in the second case it was in the superior dome (contact area – 48.43%) where larger area was available for contact. The contact areas and their location also varied depending upon the activity. In most of the activities the contact was found in the superior dome of the acetabular cartilage as can be seen from Table 3. McGibbon et al. observed this frequent loading of the superior dome in their clinical hemiarthroplasty study which may explain cartilage degradation in this area [14]. Although the present study focused on hemiarthroplasty, these findings may also be related to the natural joint. The thickness of the cartilage has been hypothesized to vary with contact stresses [14], the thickest cartilage is found anterosuperiorly near lateral roof [61,62]. The concentration of stresses
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Fig. 8. (a) Peak contact pressure, (b) peak fluid pressure, (c), (d) acetabular contact area and (e) total fluid load support during first cycle of knee bending and standing on one leg.
in the superior dome and near lateral roof seemed to support this hypothesis. The values of contact pressure in general were however lower than those measured using endoprosthesis in hemiarthroplasty studies [12,14,15,63]. For example, in normal walking, peak contact pressure in the present study was 2.78 MPa during the stance phase as compared to clinical values of 5.5 MPa [13] and 3.69 MPa [63]. Hodge et al. also reported a reduced peak pressure of 4.0 MPa after 36 months of surgery [13] during walking. Bachtar et al. have reported 5.5 MPa in their finite element study [17]. However, predictions in the current study were more in line with the mathematical/numerical models in which a spherical geometry was assumed for the acetabulum and femoral head [64–66]. Ipavec et al. found a peak stress of 3 MPa during the stance phase of normal walking. In a discrete element model with spherical acetabular cartilage of uniform thickness, peak contact pressure of 3.26 MPa has been reported for normal walking [18]. It has been shown recently that both conchoid and spherical shapes underestimate peak contact stresses by nearly 50% and overestimate contact areas by around 25% when compared to subject-specific models [67]. It
should be noted that the study of failure is associated with material properties as well as level of stresses. The use of void ratio dependent permeability did not change the predictions substantially in spite of large cartilage deformation (around 44% when maximum load of 2.6 times BW was applied during walking down the stairs). This may be due to a very low permeability of cartilage and a small variation in it due to corresponding small change in void ratio (∼0.06% of initial value). One of the limitations of the current study was that the predictions were totally dependent on only one set of kinematic and force data [16]. Thus some of the inferences may be purely due to the data being used and might not be a general trend, for example, the contact moving away from the medial edge in normal walking visà-vis slow and fast walking (Fig. 5). Moreover, as mentioned above, a more realistic geometry of the acetabular cartilage needs to be considered to take into account the effect of variable clearance. The contact stresses and fluid load support have been predicted for the hemiarthroplasty in the hip. Although the stresses were lower than in total joint replacement [68], currently it is not known how natural cartilage will respond to this level of cyclic stress over
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References
Fig. 9. Comparison of total fluid load support during first cycle of normal walking between model using void ratio dependent permeability and the one without.
prolonged periods. Further experimental work is needed to understand the response of articular cartilage in the hip to this type of tribological and biomechanical demand. We have recently shown in the knee that at higher levels of contact stress and shear stress, failure of cartilage can occur [69]. Further experimental studies are needed in the hemiarthroplasty in the hip. In conclusion, the present study showed that mean contact areas were generally only around 40% of the total potential contact area despite the surfaces being conforming. Certain activities could result in an increase in contact stresses and decrease in fluid load support consistent with the load. However, the fluid load support was high in most of the activities aiding in stress shielding of the cartilage matrix. This may explain the remarkable survival of articular cartilage in the hemiarthroplasty. Acknowledgements Sainath Shrikant Pawaskar was supported by Overseas Research Students Awards Scheme. This work was supported by the NIHR (National Institute for Health Research) as a part of collaboration with the LMBRU (Leeds Musculoskeletal Biomedical Research Unit), by EPSRC, by the Leeds Centre of Excellence in Medical Engineering funded by the Wellcome Trust and EPSRC, WT088908/z/09/z. John Fisher is an NIHR senior investigator. Appendix A List of notations C3D4 four-node linear tetrahedral elements C3D6 six-node linear triangular prism C3D8 eight-node linear brick C3D8RP eight-node trilinear displacement and pore pressure, reduced integration E Young’s modulus G Shear modulus K Bulk modulus Poisson’s ratio VRDP void ratio dependent permeability Conflict of interest The authors do not have any conflict of interests pertaining to the study submitted for publication in the Medical Engineering and Physics.
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Fluid load support and contact mechanics of hemiarthroplasty in the natural hip joint Sainath Shrikant Pawaskar ∗ , Eileen Ingham, John Fisher, Zhongmin Jin Institute of Medical and Biological Engineering, University of Leeds, Leeds LS2 9JT, UK
a r t i c l e
i n f o
Article history: Received 16 March 2010 Received in revised form 12 August 2010 Accepted 16 September 2010 Keywords: Articular cartilage Biphasic Contact mechanics Finite element Hemiarthroplasty Fluid load support Activities of daily living
a b s t r a c t The articular cartilage covering the ends of the bones of diarthrodial synovial joints is thought to have evolved so that the loads are transferred under different and complex conditions, with a very high degree of efficiency and without compromising the structural integrity of the tissue for the life of an individual. These loading conditions stem from different activities such as walking, and standing. The integrity of cartilage may however become compromised due to congenital disease, arthritis or trauma. Hemiarthroplasty is a potentially conservative treatment when only the femoral cartilage is affected as in case of femoral neck fractures. In hemiarthroplasty, a metallic femoral prosthesis is used to articulate against the natural acetabular cartilage. It has also been hypothesized that biphasic lubrication is the predominant mechanism protecting the cartilage through a very high fluid load support which lowers friction. This may be altered due to hemiarthroplasty and have a direct effect on the frictional shear stresses and potentially cartilage degradation and wear. This study modelled nine activities of daily living and investigated the contact mechanics of a hip joint with a hemiarthroplasty, focussing particularly on the role of the fluid phase. It was shown that in most of the activities studied the peak contact stresses and peak fluid pressures were in the superior dome or lateral roof of the acetabulum. Total fluid load support was very high (∼90%) in most of the activities which would shield the solid phase from being subjected to very high contact stresses. This was dependent not only on the load magnitude but also the direction and hence on the location of the contact area with respect to the cartilage coverage. Lower fluid load support was found when the contact area was nearer the edges where the fluid drained easily. © 2010 IPEM. Published by Elsevier Ltd. All rights reserved.
1. Introduction A person undergoes a series of activities including walking, climbing stairs, rising from a chair in the course of a day. The joints of the lower extremities have to bear not only the weight of the body but also the forces that are generated due to muscles and their moments. The hip joint for example, is known to withstand very high loads of 7–9 times body weight [1,2] with the highest of those forces experienced during stumbling. The acetabulum and the femur of the hip joint also articulate with varying speed depending upon the activity and this may range between extremes of slow walking and fast running of an athlete. However, the opposing articular cartilages usually survive the lifetime of an individual despite the harsh operating conditions they are subjected to. Cartilage may
∗ Corresponding author at: Institute of Medical and Biological Engineering, School of Mechanical Engineering, The University of Leeds, Leeds LS2 9JT, UK. Tel.: +44 0113 343 5011; fax: +44 0113 242 4611. E-mail addresses: [email protected], [email protected] (S.S. Pawaskar).
however break down due to injury, congenital disease or the development of arthritis [3,71]. Mechanical factors may cause structural as well as biochemical changes in articular cartilage [4–6]. Loss of cartilage in the hip joint may lead to total hip joint replacement to alleviate pain and improve quality of life. When only the femoral head is affected, hemiarthroplasty is an option. In hemiarthroplasty only the femoral head is replaced by a rigid metallic prosthesis, which then articulates with natural acetabular cartilage. To understand the potential effect of hemiarthroplasty on the acetabular cartilage and improve prosthetic design, it is important to investigate the conditions under which the joint operates during different activities of daily living. Instrumented prostheses have been used to measure in vivo contact forces [2,7–10] and contact stresses [11–15] in both natural and artificial hip joints. Bergmann et al. have used instrumented prostheses to record the hip contact forces for nine activities [16]. They found the forces to be as low as 0.26 time body weight (BW) during rising from a chair and as high as 2.6 times BW during stair descent. Many numerical studies have concentrated on the contact stresses [17,18] since they play an important role in the tribology of the cartilage [12,19], cartilage degradation [20–22] and
1350-4533/$ – see front matter © 2010 IPEM. Published by Elsevier Ltd. All rights reserved. doi:10.1016/j.medengphy.2010.09.009
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“preoperative planning and postoperative rehabilitation” [18]. The prediction of contact area from contact mechanics analysis may also give an indication of the areas of acetabular cartilage which are most susceptible to breakdown. A finite element model of contact mechanics of the human hip joint has been experimentally validated using cadaveric tissue in which cartilage was modelled as a hyperelastic material [23]. However, none of the three-dimensional FE/numerical studies, to the best of authors’ knowledge, have considered the biphasic nature of the cartilage. Hence, those studies are not able to account for interstitial fluid pressurization and its influence on tribology and the contact mechanics of the articular cartilage within the joint. Biphasic lubrication, which is due to the load partitioning between fluid and solid phases with the fluid phase sustaining most of the load, aids in maintaining a very low friction [24–26]. This coefficient of friction of the articulating cartilages usually lies in the range of 0.001–0.02 [24,27,28]. The role of fluid pressurisation within cartilage in reducing the frictional coefficient has been hypothesized by many authors [25–27,29–36]. It has not only been directly measured [37–39] but has also been shown to be linearly correlated with the coefficient of friction in sliding experiments of cartilage against glass under constant load [39]. It has been shown that the fluid phase is capable of supporting more than 90% of the load thus resulting in low solid-to-solid contact and hence a lower effective coefficient of friction [27,32,37,38]. Thus, the biphasic properties of articular cartilage play an important role in the tribology of natural synovial joints. Hemiarthroplasty may alter the biphasic fluid load support. The aim of this study was to investigate the hip joint with a hemiarthroplasty during several activities of daily living in order to understand the tribology and contact mechanics of the biphasic cartilage under varying and complex conditions. 2. Material and models A solid model of male left pelvis created from CT scans [40] (Fig. 1) was used to create finite element (FE) model of the hip by using I-DEAS (ver. 11, Siemens PLM Software, Plano, TX, USA) and ABAQUS (ver. 6.7-1, Dassault Systemes, Suresnes Cedex, France). FE analyses considering different activities of daily living were carried out using ABAQUS.
Fig. 1. FE model of hip hemiarthroplasty.
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A spherical horseshoe shaped acetabular cartilage of uniform thickness of 2 mm was used in all the simulations. The acetabular bone cavity was of radius 30 mm and the inner radius of the acetabular cartilage was 28 mm [41,42]. The acetabular cartilage was approximately divided into four regions; viz. lateral roof, medial roof, anterior and posterior horns [18]. The superior dome was assumed to be at the centre covering parts of lateral and medial roofs. The cortical bone layer of the pelvis was assumed to have thickness of 1.41 mm [43]. A femoral prosthetic head of radius 27.5 mm was used throughout to give a radial clearance of 0.5 mm. The centres of both the cartilage surface and prosthetic head were at the origin of the coordinate system. Biphasic poroelastic elements were used for the acetabular cartilage whereas bones were assumed linearly elastic. The elements used for each component of the hip joint along with their material properties are given in Table 1. There was a minimum of three elements through the cartilage thickness [23]. The permeability of the cartilage was k = 9.83 × 10−16 m4 /N s [44] and the water content was 80% [45]. The cartilage solid phase was modelled as neo-Hookean, with elastic strain energy potential given in Eq. (1) [46]. W (C) =
G K (I1 − 3) + (J − 1)2 2 2
(1)
where, C, right Cauchy–Green deformation tensor; G, Shear modulus; I¯1 , first deviatoric strain invariant; K, Bulk modulus; J, total volume ratio when linear thermal expansion strain is not considered. Bulk modulus, K and shear modulus, G are related to Young’s modulus, E and Poisson’s ratio, by Eqs. (2) and (3). The surfaces of the acetabular cartilage and metallic prosthetic head were slave and master respectively. The head was coarsely meshed due to strict master-slave algorithm which prevents slave node penetration into the master [46]. The mesh was finalized after sensitivity analysis to ensure that the error in predictions was less than 5% when the consecutive meshes of different densities were used. E = 3K(1 − 2)
(2)
E = 2G(1 + )
(3)
The pelvis was pinned by restricting all three translational degrees of freedom of the nodes of the sacro-iliac joint and those of the contralateral side of the pubic symphysis. The peripheral surfaces of the cartilage through its thickness were always exposed and hence free flow was prescribed on these surfaces. The back surface of the acetabular cartilage was tied to the impermeable lunate surface of the acetabular cavity. Fluid flow on the contacting cartilage surface was imposed depending upon developing contact [47]. Frictionless contact was assumed. One cycle each of the nine activities of daily living as shown in Table 2 was simulated with their respective load vectors [16]. A long-time duration of five cycles was analysed only for normal walking. Femoral rotation was already accounted for in these load vectors. The hip joint contact force data used in this study also accounted for muscle forces [16]. The pelvis rotates about both the transverse axes during activities [16]. The load vectors were rotated to take into account this pelvic orientation. The loads were applied at the centre of the head, as shown in Fig. 1. The entire analysis was quasi-static with different load vectors being applied one after the other in each step without changing any of the boundary conditions. Another set of models, representing all the activities were analysed using non-linear void ratio dependent permeability (VRDP). This was calculated using Eq. (4) [48,49]. Material parameters, M and used in this equation were 4.638 and 0.0848 respectively
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Table 1 Elements used for various components of hip joint along with their material properties. Component
Cancellous bone (pelvis) Cortical bone (pelvis) Subchondral bone (pelvis) Acetabular cartilage Prosthetic head
Element Type
Quantity
C3D4 C3D6 C3D4 C3D8RP C3D6 C3D8
12,165 3468 247 14,772 432 2304
Elastic modulus, E (MPa)
Poisson’s ratio,
Reference
70 17,000 2000 1.072 220,000
0.2 0.3 0.3 0.011 0.3
[72] [72] [72] [44] [73]
Table 2 List of activities with their start and end [16]. Activity
Starts at
Ends at
Cycle time (s)
Slow walk (0.98 m/s) Normal walk (1.09 m/s) Fast walk (1.46 m/s) Stand Up (chair height – 500 mm) Sit down (chair height – 500 mm) Down stairs (stair height – 170 mm) Up stairs (stair height – 170 mm) Knee bend Stand 2-1-2 leg
Heel strike Heel strike Heel strike Beginning of getting up Standing position Toe off Heel strike Standing position Two legged stance
Ipsilateral heel strike Ipsilateral heel strike Ipsilateral heel strike Standing position Sitting in a relaxed position Ipsilateral toe off Ipsilateral heel strike Standing position Two legged stance
1.248 1.103 0.953 2.489 3.719 1.439 1.593 4.665 6.703
Fig. 2. (a) Peak contact pressure, (b) peak fluid pressure, (c), (d) acetabular contact area and (e) total fluid load support during first cycle of slow, normal and fast walking.
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Table 3 Maximum peak contact pressure with corresponding peak fluid pressure, contact area and total fluid load support (TFLS) for different activities and where and when they occurred. Activity
Peak contact pressure (MPa)
Peak fluid pressure (MPa)
Where
Contact area (%)
TFLS (%)
Cycle time (%)
Slow walk Normal walk Fast walk Stand up Sit down Down stairs Up stairs Knee bend Stand 2-1-2 leg
2.97 2.78 2.99 2.98 2.57 4.63 3.00 2.42 4.40
2.77 2.59 2.77 2.53 2.19 3.85 2.77 2.10 3.71
Superior dome Superior dome Superior dome Posterior horn Posterior horn Lateral roof Superior dome Medial roof nearer posterior side Lateral roof
49.64 52.00 53.10 55.13 49.88 38.88 53.79 46.77 40.43
90.11 91.21 90.95 84.10 85.39 81.80 91.07 86.99 83.42
16.5 15.5 12.5 44.5 45.0 88.0 16.0 53.5 46.0
[50]. Initial permeability (k0 ) and initial void ratio (e0 ) representing water content, were constant permeability and void ratio values respectively, that were used in the models without void ratio dependent permeability.
k=k
e e0
exp
M 2
1+e 2 1 + e0
−1
(4)
3. Results The variation of peak contact pressure on the acetabular cartilage surface for one cycle of slow, normal and fast walking is depicted in Fig. 2a. In the case of normal walking, the maximum peak contact pressure of 2.78 MPa was found in the superior dome of the acetabulum at 15.5% of the cycle (Fig. 2a and Table 3). The pressure distribution was in the antero-posterior direction but slightly towards the posterior side similar to that observed at 15%
Fig. 3. Contours of contact stresses (MPa) in acetabular cup during different phases of first cycle of normal walking (A – anterior; P – posterior; M – medial; L – lateral).
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Table 4 Average total fluid load support (TFLS) for different activities. Activity
Average TFLS (%)
Slow walk Normal walk Fast walk Stand up Sit down Down stairs Up stairs Knee bend Stand 2-1-2 leg
89.28 90.96 90.08 87.74 87.18 88.45 89.82 88.97 88.23
the swing phase. It moved more medially in cases of slow and fast walking compared to normal walking (Fig. 5). The predictions of important parameters for all the activities that were analysed are listed in Tables 3 and 4. The predicted peak contact pressure, peak fluid pressure, contact area and total fluid load support for standing up and sitting down are shown in Fig. 6. The variation of parameters for going down the stairs and climbing up the stairs is shown in Fig. 7 as a function of percentage cycle whereas the results for knee bending and standing on one leg are shown in Fig. 8. The peak contact pressure, peak fluid pressure and acetabular contact area for different activities generally showed the same time-dependent trend as that of contact force. However, while going down the stairs and in one-legged stance, the contact area variation was found to be somewhat deviating from that of the contact force (Figs. 7c, d and 8c, d). The variation of total fluid load support was different to that of the contact force for almost all activities except for some similarity in slow and fast walking (Fig. 2e). When void ratio dependent permeability was used, the variations of all the parameters of interest remained similar to the predictions with constant permeability. The maximum difference with respect to constant permeability predictions was 3.87% in total fluid load support during standing up. In normal walking this difference was even less and was around 1.93%. The variation of total fluid load support during normal walking for void ratio dependent model and the one without is shown in Fig. 9 which shows a close similarity between the two curves.
Fig. 4. Total fluid load support for five normal walking cycles.
4. Discussion and 20% cycle time (Fig. 3). The corresponding contact area was 52.00% of the total potential contact area and total fluid load support was 91.21%. The maximum fluid pressure at this instant was 2.59 MPa. The variation of peak contact pressure, peak fluid pressure and the contact area with respect to time was similar to that of contact force for all three walking speeds (Fig. 2a–d). The variation of total fluid load support in general seemed to follow contact force variation for slow and fast walking whereas it deviated towards the last 35% of the cycle in the case of normal walking (Fig. 2e). However, it always remained high and on an average it was found to be 89.28%, 90.96% and 90.08% for slow, normal and fast walking respectively (Table 4). The total fluid load support decreased only slightly (0.17%) over five cycles of normal walking (Fig. 4). The contours of the contact pressure at different stages of one normal walking cycle for the first cycle are shown in Fig. 3. It can be seen that throughout the stance phase when the load was high, the contact was mostly maintained in the superior dome of the acetabulum. It then started moving towards the medial roof during
A limited number of FE/numerical studies of the contact mechanics of the hip joint exist. However, none of these studies have investigated the role played by interstitial fluid pressurization in the contact mechanics and tribology of the cartilage in a whole joint model. Therefore nine different activities of daily living were simulated to investigate the extent of effect that the fluid phase has in the tribological functioning of the hip joint after hemiarthroplasty. The methodology used in analyzing these models was validated using porcine acetabular cups loaded with a rigid metallic prosthesis [70]. The variation of acetabular cartilage peak contact pressure followed that of contact force in all the activities of daily living as observed previously [17]. A similar correlation was observed by Park et al. with respect to hip joint forces [15] and ground reaction forces for the stance phase [7,15]. The peak contact pressure was maximal when going down the stairs just before toe-off. This was the most strenuous of all the activities investigated. Standing on one leg was the next demanding activity. In both these activities the corresponding contact areas were smaller and were on the
Fig. 5. Contours of contact stresses at 84% of first walking cycle.
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Fig. 6. (a) Peak contact pressure, (b) peak fluid pressure, (c), (d) acetabular contact area and (e) total fluid load support during first cycle of standing up and sitting down.
lateral roof of the acetabulum. The contact stresses for descending stairs were found to be higher than those during stair ascent as has been also observed in clinical [14] and analytical studies [51]. The variation of peak fluid pressure also showed patterns similar to those of contact forces for all the activities of daily living. The total fluid load support in all the activities was found to be around 90%. This reduced the load supported by the solid phase of the cartilage which would reduce the effective coefficient of friction [26,27,29,31,34,39]. This would then reduce the frictional shear stresses thus protecting the cartilage from wear. This fluid load support was high over most of the cycle for all the activities. The drop in the fluid load support was very small even after five cycles of normal walking. The migration of contact probably helped in rehydration of the cartilage thus maintaining high interstitial fluid pressurization [52,19]. It has been also hypothesised that the contact migrating faster than the diffusive velocity of the interstitial fluid (∼10−4 –10−6 mm/s) does not allows enough time for the fluid to flow to the regions of low pressure and may help in maintaining higher fluid pressurisation over longer time duration [53,36]. It reduced only when the contact moved towards the edges of the acetabular cartilage. This was because, the acetabular labrum was
not modelled in the present study and free flow was prescribed on the edges of the cartilage. Thus more fluid exudation occurred when the contact moved towards any edge. In the presence of the labrum which has lower permeability than the cartilage [54], this edge effect will reduce. The anomaly seen in total fluid load support between 60% and 95% of the normal walking cycle in Fig. 2e was due to the contact being slightly away from the medial edge as seen in Fig. 5. The contact area was generally small in spite of the conforming contacting surfaces. The contact areas for all activities did not exceed 55.59% which happened at 47.5% of the standing up cycle. The contact moved medially but slightly towards the posterior horn during this time. This was lower than that observed by Yoshida and colleagues in their discrete element analysis study [18]. However, the clearance used by Yoshida et al. was not mentioned. Acetabular fit has been cited as an important parameter in the prevention of acetabular erosion [55,56]. The current study used a radial clearance of 0.5 mm between the acetabular cartilage and the metallic prosthetic head which might have reduced the contact areas. The smallest contact area was 23.77% at 7% of the standing up cycle when the contact moved to the posterior horn of the acetabular cup.
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Fig. 7. (a) Peak contact pressure, (b) peak fluid pressure, (c), (d) acetabular contact area and (e) total fluid load support during first cycle of going down stairs and climbing stairs.
It should be noted that the commercial femoral head prostheses are available in increments between 1 and 2 mm [57]. Thus a radial clearance of 0.5 mm represented the smallest realistic clearance for hemiarthroplasty for spherical acetabular cup assumption. The acetabular cavity was assumed to be spherical in this study which is not the case in an anatomical joint. The non-spherical articular surface would, in turn, introduce variable clearance in the joint and adversely affect both the contact pressures and fluid load support. The total fluid load support in this case might be reduced if there was a greater area available for fluid exudation (as in higher clearances) or the permeability was increased (when water content increases as in case of OA) [45,58]. This would then increase the coefficient of friction and hence frictional shear stresses. The increased contact stresses along with the increased shear stresses have the potential to induce cartilage fibrillation thus compromising the integrity of the hip joint in general and cartilage in particular. In OA joints in which the cartilage structure has already been compromised and diminished, higher local contact stresses might enhance this effect. However, it should be noted, that the long term survivorship has been shown in both unipolar [59] and
bipolar [60] hemiarthroplasties which may be due to higher fluid load support and lower contact stresses. Contact area and peak contact pressure depended not only on the magnitude of the load but also on the location of the contact. For example, in standing on one leg, contact stresses were 3.65 MPa and 2.88 MPa for similar loads of 1937 N and 1935 N respectively during two different stages of the activity. However, in the first case the contact was near the lateral roof (contact area – 42.45%) whereas in the second case it was in the superior dome (contact area – 48.43%) where larger area was available for contact. The contact areas and their location also varied depending upon the activity. In most of the activities the contact was found in the superior dome of the acetabular cartilage as can be seen from Table 3. McGibbon et al. observed this frequent loading of the superior dome in their clinical hemiarthroplasty study which may explain cartilage degradation in this area [14]. Although the present study focused on hemiarthroplasty, these findings may also be related to the natural joint. The thickness of the cartilage has been hypothesized to vary with contact stresses [14], the thickest cartilage is found anterosuperiorly near lateral roof [61,62]. The concentration of stresses
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Fig. 8. (a) Peak contact pressure, (b) peak fluid pressure, (c), (d) acetabular contact area and (e) total fluid load support during first cycle of knee bending and standing on one leg.
in the superior dome and near lateral roof seemed to support this hypothesis. The values of contact pressure in general were however lower than those measured using endoprosthesis in hemiarthroplasty studies [12,14,15,63]. For example, in normal walking, peak contact pressure in the present study was 2.78 MPa during the stance phase as compared to clinical values of 5.5 MPa [13] and 3.69 MPa [63]. Hodge et al. also reported a reduced peak pressure of 4.0 MPa after 36 months of surgery [13] during walking. Bachtar et al. have reported 5.5 MPa in their finite element study [17]. However, predictions in the current study were more in line with the mathematical/numerical models in which a spherical geometry was assumed for the acetabulum and femoral head [64–66]. Ipavec et al. found a peak stress of 3 MPa during the stance phase of normal walking. In a discrete element model with spherical acetabular cartilage of uniform thickness, peak contact pressure of 3.26 MPa has been reported for normal walking [18]. It has been shown recently that both conchoid and spherical shapes underestimate peak contact stresses by nearly 50% and overestimate contact areas by around 25% when compared to subject-specific models [67]. It
should be noted that the study of failure is associated with material properties as well as level of stresses. The use of void ratio dependent permeability did not change the predictions substantially in spite of large cartilage deformation (around 44% when maximum load of 2.6 times BW was applied during walking down the stairs). This may be due to a very low permeability of cartilage and a small variation in it due to corresponding small change in void ratio (∼0.06% of initial value). One of the limitations of the current study was that the predictions were totally dependent on only one set of kinematic and force data [16]. Thus some of the inferences may be purely due to the data being used and might not be a general trend, for example, the contact moving away from the medial edge in normal walking visà-vis slow and fast walking (Fig. 5). Moreover, as mentioned above, a more realistic geometry of the acetabular cartilage needs to be considered to take into account the effect of variable clearance. The contact stresses and fluid load support have been predicted for the hemiarthroplasty in the hip. Although the stresses were lower than in total joint replacement [68], currently it is not known how natural cartilage will respond to this level of cyclic stress over
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References
Fig. 9. Comparison of total fluid load support during first cycle of normal walking between model using void ratio dependent permeability and the one without.
prolonged periods. Further experimental work is needed to understand the response of articular cartilage in the hip to this type of tribological and biomechanical demand. We have recently shown in the knee that at higher levels of contact stress and shear stress, failure of cartilage can occur [69]. Further experimental studies are needed in the hemiarthroplasty in the hip. In conclusion, the present study showed that mean contact areas were generally only around 40% of the total potential contact area despite the surfaces being conforming. Certain activities could result in an increase in contact stresses and decrease in fluid load support consistent with the load. However, the fluid load support was high in most of the activities aiding in stress shielding of the cartilage matrix. This may explain the remarkable survival of articular cartilage in the hemiarthroplasty. Acknowledgements Sainath Shrikant Pawaskar was supported by Overseas Research Students Awards Scheme. This work was supported by the NIHR (National Institute for Health Research) as a part of collaboration with the LMBRU (Leeds Musculoskeletal Biomedical Research Unit), by EPSRC, by the Leeds Centre of Excellence in Medical Engineering funded by the Wellcome Trust and EPSRC, WT088908/z/09/z. John Fisher is an NIHR senior investigator. Appendix A List of notations C3D4 four-node linear tetrahedral elements C3D6 six-node linear triangular prism C3D8 eight-node linear brick C3D8RP eight-node trilinear displacement and pore pressure, reduced integration E Young’s modulus G Shear modulus K Bulk modulus Poisson’s ratio VRDP void ratio dependent permeability Conflict of interest The authors do not have any conflict of interests pertaining to the study submitted for publication in the Medical Engineering and Physics.
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