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Hip joint degeneration due to cam impingement: A finite element analysis
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F.L. Hellwiga, J. Tonga*, J.G. Hussellb
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aMechanical
Behaviour of Materials Group, School of Engineering, University of Portsmouth, Portsmouth, UK
b
Orthopaedics and Trauma Centre, Queen Alexandra Hospital, Portsmouth, UK
* Corresponded Author Tel.: 0044(0)2392842326.
Email address: Jie.Tong@port.ac.uk
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Hip joint degeneration due to cam impingement: A finite element analysis
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The goal of this study was to investigate the impact of cam impingement, a
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biomechanical risk factor, on hip joint degeneration and ultimately coxathrosis.
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3D finite element solid models of a healthy and a pathologic hip were developed
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based on clinical reports. The biphasic characteristics of cartilaginous tissues
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were considered to identify localised solid matrix overloading during normal
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walking and sitting down. Localised femoral intrusion at the anterior-superior
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pelvic horn was revealed in the pathologic hip during sitting down, where the
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radial
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circumferential solid-stresses within the acetabular labrum increased by 3.7, 1.5
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and 2.7 times, respectively. The increased solid-on-solid stresses, reduction in
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fluid-load support and associated higher friction during articulation may result in
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joint wear and other degenerative changes in the hip.
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Keywords: Hip Joint, Cartilage Degeneration, Biphasic Model, Contact
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Pressure, Finite Element, Impingement
and
meridional
solid-stresses
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in
the
acetabular
cartilage
and
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Introduction
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Excessive contact stresses in the hip joint due to obesity (Rečnik et al. 2009) or decreased
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weight bearing area typical in a dysplastic hip (Mavčič et al. 2002; Russell et al. 2006) are
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thought to result in coxathrosis. Recent clinical studies hypnotised a link between abnormal
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anatomical conditions of femoral head-neck junction and early degenerative changes of the
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hip joint, such as osteochondral defects and labral tear leading ultimately to idiopathic
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osteoarthritis (Ito et al. 2001). The pathologic condition, named cam type femoroacetabular
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impingement, is caused by jamming of a non spherical extension of the femoral head into the
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acetabular cavity (Ganz et al. 2003, 2008). Nötzli et al. (2002) characterised this anatomic
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abnormality by introducing an alpha angle (Figure 1). This angle is measured between the
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femoral neck axis and a line extended from the point C, the femoral head centre, to point D,
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which is the point of deviation from femoral head sphericity. The abnormality might emerge
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as an anterior bump, spigot or thickened femoral neck, limiting the range of motion (ROM)
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(Ito et al. 2001; Ganz et al. 2003, 2008).
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Recently, a finite element study (Chegini et al. 2009) of normal and impinged
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articulation has been presented to examine the joint mechanics during daily activities of
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normal walking and sitting down, for which the maximum contact force was reported as
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233% and 156% bodyweight, respectively (Bergmann et al. 2001). Chegini et al. (2009)
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focused on the total stress responses of the cartilaginous tissues, which were represented as
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isotropic linear elastic materials. The cartilage and labrum, however, are fully fluid saturated
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porous mediums (Mow et al. 1980), hence the load is shared between the interstitial fluid and
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a solid extracellular matrix (ECM):
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𝜎𝑡𝑜𝑡 = 𝜎𝑠𝑜𝑙𝑖𝑑 + 𝛥𝑝𝐼
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where 𝜎𝑡𝑜𝑡 is the total stress of the tissue, 𝜎𝑠𝑜𝑙𝑖𝑑 is the stress acting on the ECM and 𝛥𝑝𝐼 is the
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pore pressure of the interstitial fluid (Mow et al. 1980). Early macroscopic changes in
(1)
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articular cartilage were reported to begin with fraying at the superficial zone of the ECM
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(Pritzker et al. 2006), a sign of joint wear accelerated with increased friction (Mow and
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Huiskes 2005) and associated with decreased fluid-load support (Krishnan et al. 2004).
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Ferguson et al. (2000a) utilised an isotropic poroelastic material model in ABAQUS (Wu et
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al. 1998) to simulate the sealing function of the acetabular labrum.
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alterations in solid-on-solid stress with the changes in fluid-load support for a static load up to
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75% bodyweight held constant for up to 10,000s. More recently, in order to study the
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cartilage response to elevated loading during unstable motion, Goreham-Voss et al. (2007)
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modelled the articulating cartilage layers in knee joints, considering the directional-dependent
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material properties of the extracellular matrix.
They correlated
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The aim of this work is to study the stresses in the cartilage in the principal directions
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of an orthotropic ECM and the fluid-load support during normal and 'cam'-type impinged
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articulations under selected physiological loading conditions. To do so the cartilaginous
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tissues were modelled as biphasic orthotropic materials and the results for normal and 'cam'-
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type impinged articulation were compared.
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Numerical Methods
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Geometry and Materials
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A normal hip joint model with alpha = 40° was developed based on morphologic
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simplifications and dimensions of Chegini et al. (2009) (Figure 2(a)), whilst a typical cam-
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impinged hip joint with alpha = 74° was also modelled based on Nötzli et al. (2002) (Figure
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2(b)), using ABQUS CAE. The finite element model, depicted in Figure 2(c), of the normal
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hip joint (c) consists of acetabular labrum (1), acetabular cartilage (2), femoral cartilage (3),
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impermeable membrane (4) and femoral head neck section (5), following (Chegini et al.
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2009). The pathologic case was identical except the anterior hump at the head-neck junction.
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Femoral and pelvic bones were considered rigid (Anderson et al. 2008) and the
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cartilaginous tissues were considered as fully fluid saturated porous mediums (Mow et al.
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1980), taking into account the orthotropic structure of the ECM following Goreham-Voss et
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al. (2007). A spherical coordinate system was used to allocate the directional-dependent
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material properties. The permeabilities of the femoral and acetabular cartilage and labrum are
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9.15, 8.98 and 4.98 x 10-4 mm4/Ns, respectively (Athanasiou et al. 1994; Ferguson et al.
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2001), and they were converted from the biphasic, k, to the poroelastic model, k', via:
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k' = 𝛾k
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where the volumetric weight of the interstitial water, 𝛾, was taken as 9.81 x 10-6 N mm-3 (Wu
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et al. 1998). The solid matrix compressive radial moduli '1'of femoral and acetabular cartilage
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and labrum were averaged to 1.23, 1.18 and 0.157 MPa (Athanasiou et al. 1994; Ferguson et
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al. 2001), respectively. For cartilage, the tangential moduli in circumferential '2' and
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meridional '3' directions were extracted from the toe region as 8.5 MPa (Roth and Mow,
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1980). To permit opening between the acetabular labrum and femoral cartilage under load, a
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tangential moduli of 26 MPa was chosen in direction '2', close to that of the toe region (20
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MPa) reported in Ferguson et al. (2001). According to the ratio of meridional to
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circumferential strength of the meniscus (Tissakht and Ahmed, 1995), the tangential modulus
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of the labrum in direction '3' was set to 3 MPa, since labrum and meniscus exhibit a similar
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ultra structure (Ferguson et al., 2001). As shear stresses peak at the cartilage-bone interface
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(Goreham-Voss et al. 2007), a shear modulus of 2.5 MPa (Wong et al. 2008) was chosen.
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Shear modulus and volumetric response (ν12, ν23) (Athanasiou et al. 1994; Federico et al.
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2005) are given for cartilage in Table 1, similar values were assigned to the labrum due to the
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lack of data. A Summary of all material properties used in the models is given in Table 1.
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As tissue properties were taken from different sources due to limited availability, a
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pre-study on the sensitivity to material property variation (± 50%) was performed. The peak
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contact force for normal walking, taken from Bergmann et al. (2001), was applied to the hip
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joint centre during a 1 second ramp phase for the normal articulation.
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Finite element modelling
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The cartilaginous tissues were meshed with first order pore pressure brick elements, and the
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femoral-head neck section and the impermeable membrane were meshed with quadrilateral
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bilinear rigid and quadrilateral membrane elements, respectively. Reduced integration was
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used for deformable elements to reduce the calculation time. The selected grid sizes and
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element number are given in Table 2.
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Since the pelvis was assumed rigid the nodes of the acetabular cartilaginous tissue on
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the bone-cartilage interface were fully constrained. The hip joint forces for normal walking
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and sitting down were taken from Bergman et al. (2001) and applied incrementally as a point
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force to the centre of the femoral head. The hip joint force was synchronized with the
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locomotion data prescribed as rotational movements of the femur. The analysis was
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performed by first establishing contact between the femur and the acetabulum, then applying
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an initial load of 33.31% or 55.51% of the peak load for normal walking (NW) and sitting
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down (SD), respectively, ramped over 1 second, and finally simulating the locomotion cycle
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in 60 sequences. The bodyweight was assumed 86 kg.
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Contact was implemented using the penalty method assuming frictionless finite
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sliding, due to small coefficient of friction (Pawaskar et al. 2007). Throughout the analysis the
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femur was the master and the acetabulum the slave surface. Further, for poroelastic mediums
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the contact model should satisfy the biphasic jump condition, where in areas of contact fluid
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velocity should be continuous or otherwise interstitial fluid should be free-draining (Hou et al.
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1989). However, as contact pressure varies, local rehydration occurs (Pawaskar et al. 2007)
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and fluid efflux and cross-flow are minimal for loadings such as NW and SD (Pawaskar et al.
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2011), hence the biphasic jump condition was not considered.
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Since in a biphasic medium load is shared between the fluid and the solid phase (Mow
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et al. 1980), the total contact pressure is carried by both phases. However, in the ABAQUS
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model for porous mediums in contact, the fluid phase contribution to the total contact pressure
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is ignored to ensure point-wise continuity of the pore pressure at opposing sides (Hibbitt et al.
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2007). On the other hand, contact pressure between a porous and an impermeable material
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includes contributions from both solid and fluid phase (Hibbitt et al. 2007). In this work, the
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total contact pressure was obtained by inserting an impermeable membrane (E = 1 MPa; ν =
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0.49) between the cartilaginous tissues (Wilson et al. 2003; Manda et al. 2011). This
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membrane has only a minor effect on contact pressure results (Wilson et al. 2003).
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Results
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Normal articulation
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For both normal walking and sitting down, the weight bearing area, peak contact and peak
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pore pressure vary during the course of the simulated activity, and the variation is consistent
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with that of the applied contact force. The peak contact pressures of 2.86 MPa and 3.66 MPa
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are located in the superior region for normal walking and the posterior region for sitting
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down, respectively. However, weight bearing area changes from superior-anterior to superior-
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posterior for NW and from superior to posterior during SD, hence the contact and pore
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pressure are distributed asymmetrically about the applied load. The timing of the occurrence
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of peak contact and peak pore pressure coincided with the peak contact force. The peak
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contact pressure (P-CPRESS), the related contact area (CAREA), the timing and the location
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of their occurrence for NW and SD are summarised in Table 3. In addition, the peak pore
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pressure (P-POR), which corresponded to the location of the peak contact pressure, and the
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related compressive radial stress (S11) are also summarised in Table 3.
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For normal walking, a plot of the results, including the stress components of the solid
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matrix, is given in Figure 3. The locations of maximum P-CPRESS (2.87 MPa) and maximum
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P-POR (2.85 MPa) are shown in Figure 3(a) & (b), where the distribution patterns are
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identical. Stresses within the ECM in the three directions are highest on the articulating
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surface. The highest stress concentrations, radial stress - 0.05 MPa and meridional stress 0.50
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MPa, are found on the edges of the acetabular cartilage, where the pore pressure is minimal
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(Figure 3(c) & (e)). Circumferential stress is the highest in the acetabular labral ring (0.33
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MPa, Figure 3(e)). Shear stress, however, peaked at the cartilage-bone interface along the
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edge of the acetabular cartilage, rising up to 1.35 MPa (Figure 3(f)). The ratio of fluid load-
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support is 99.3% and 98.4% for NW and SD, respectively, indicating a similarity in fluid-
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solid interaction in both cases.
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‘Cam’-type impinged articulation
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The pathologic hip joint revealed localised impingement at the anterior-superior pelvic horn
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during deep flexion. Hence, pore pressure increased significantly by 8 times from 0.42 MPa
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to 3.76 MPa at the anterior-superior horn due to the intrusion of the femoral hump (Figure 4).
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Compressive radial stresses, within the acetabular cartilage, increased at the impinged
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location by 3.7 times from 0.07 MPa to 0.33 MPa. Tensile circumferential and meridional
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stresses are at peaks within the acetabular labrum and at the cartilage-labral interface,
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respectively (Figure 4(a) & (b)), and increased by a factor of 2.7 and 1.5, respectively. S22
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and S33 rose from 0.84 MPa to 2.26 MPa and 0.92 MPa to 1.37 MPa (Figure 4(a) & (b)).
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Fluid-load support in the impinged zone dropped to 91.9%, as opposed to 98.4 % in the
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posterior region. Shear stress also doubled to 2.61 MPa on the acetabular surface and
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surpassed the maximum at the acetabular cartilage-bone interface in the normal articulation.
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Effect of material property variation
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The influence of material property variation on some of the key parameters such as femoral
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head displacement, contact pressure and pore pressure is summarized in Figure 5. The highest
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model sensitivity was recorded for a reduction of 50% in shear modulus, with an increase of
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46.18 % of femoral head displacement, although the contact pressure and the pore pressure
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dropped only marginally by 2.89% and 3.68%. Reducing the tangential modulus by 50%
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resulted in only marginal influence on femoral head displacement (-4.28%), contact (2.7%)
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and pore pressure (1.97%), respectively. For all other variations the changes in the key
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parameters are insignificant < 1%. This gives us confidence that the observed enhanced
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responses in impinged case are indeed due to the abnormal articulation, and the influence of
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model parameters are insignificant except the shear modulus.
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Discussion
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The goal of this study was to explore how 'cam'-type impinged articulation can affect cartilage
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stresses compared with those under normal articulation; and whether or not cartilage
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structural integrity may be assessed based on a comparison of the total contact pressure, fluid-
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load support (FLS) and generated stress components within the solid extracellular matrix
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(ECM) in these two conditions. Special emphasis was placed on the consideration of
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orthotropic properties of the cartilaginous tissue structures.
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Comparisons with previous work seem to suggest that the locations identified for peak
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contact pressure during normal walking and sitting down are consistent with those published
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(Yoshida et al., 2006; Chegini et al., 2009). The maximum contact pressures in a normal joint
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are found to be 2.87 MPa and 3.66 MPa during NW and SD, compared well with those (2.35
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MPa and 3.34 MPa, respectively) reported by Chegini et al. (2009). Other subject-specific
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models, however, predicted higher peak contact pressures, such as 6.6 MPa in Jorge et al.
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(2014) and 10.78 MPa in Anderson et al. (2008). According to Anderson et al. (2010),
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cartilage thickness variation accounted for more than doubled peak contact pressure compared
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with a constant cartilage thickness. Harris et al. (2012) reported a peak contact pressure rage
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of 7.51 ± 2.11 MPa for walking, and suggested that the peak contact pressure varies with
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subjects. Hence, it seems reasonable that our results are within the range of reported data,
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given the variation of the joint geometries.
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Experimentally measured peak contact pressures seem to be higher than predicted by
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the simplified FE models. According to Afroke et al. (1987), peak contact pressure varied
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strongly with subjects (4.9 to 10.2 MPa). Anderson et al. (2008) reported a rather in-
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homogeneous contact pressure distribution with a peak of 10 MPa for normal walking. In
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contrast to that Brown and Shaw (1982) reported a peak contact pressure of 3.45 MPa, close
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to our findings. To the best of the authors’ knowledge, the stresses within the solid phase have
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not been measured in a cadaveric hip joint.
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Prior to this study, ECM of articular cartilage was assumed to deform linear elastic
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isotropically (Ferguson et al., 2000a; 2000b; Macirowski et al. 1994) or hyper elastic
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isotropically (Haemer et al., 2012), as the material properties of the cartilage were taken from
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uni-axial compression tests (Mow et al., 1980; Macirowski et al., 1994; Wu and Herzog,
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2000) where shear cannot be measured. To accommodate the multi-directional cartilage
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deformation whilst using linear or hyper elastic isotropic properties, either lateral extension
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was permitted (Macriowski et al., 1994) and applied load reduced (Ferguson et al., 2000a), or
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the stress-bearing area increased, neglecting the lunate shape of the acetabular cartilage
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(Haemer et al., 2012). None of these modelling techniques seem to be sufficient to answer the
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current research questions.
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Taking the different modelling techniques into account, the high FLS of 99.3% during
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normal walking, compares reasonable well with 98.0% and 96.0% obtained by Haemer et al.
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(2012) and Macirowski et al. (1994) for a ramp load of 1 second, but less favourably with
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91.7% (following 1,000 static load) reported by Ferguson et al. (2000a).
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In the pathologic case, alpha = 74°, the anterior protrusion produced an intrusion into
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the anterior-superior acetabular cavity during sitting down, which is consistent with earlier
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observations (Chegini et al. 2009; Jorge et al. 2014). Whilst the intrusion of the abnormal
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protrusion did not yield significant elevated peak contact pressure, the FLS was affected and
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the stress components of the ECM elevated. Although the FLS was still above 90%, the radial
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compressive stress (or solid-on-solid) increased significantly (3.7 times) and the ECM was
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not shielded from elevated solid-on-solid stress (Athesian and Mow, 2005). This may explain
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some of the early macroscopic changes in the cartilage found in clinical observation (Ganz et
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al. 2003, 2008; Beck et al. 2005), leading to severe osteoarthritis (Pritzker et al. 2006).
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Circumferential stress in the labrum was doubled, although this might not be as
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significant due to the labral design to withstand high exposure in this direction (Ferguson et
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al. 2001), The elevated stresses are mainly found in the cartilage-ECM, as opposed to those
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reported by Chegini et al. (2009) in cartilage and labrum simultaneously. The increased
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meridional stresses within the cartilage at the cartilage-labral interface seems to support the
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hypothesis that cam impingement results in cartilage defects and subsequent separation of the
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acetabular cartilage from the labrum (Ganz et al. 2003; 2008; Beck et al. 2005), and not
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otherwise as discussed (McCarthy et al. 2001).
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The emphasis of earlier numerical work (Chegini et al., 2009; Jorge et al., 2014) was
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on severe abnormal femoral protrusions at high loads. Chegini et al. (2009) predicted,
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dependent on the morphology of the femoral neck, peak contact pressures are in the range of
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3.68 MPa to 12.84 MPa for 'cam'-type impingement. Jorge et al., (2014) also reported high
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peak contact pressures up to 16.4 MPa. Due to the varied abnormal conditions presented, the
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results cannot be readily compared with the current ones. Nonetheless, Ganz et al. (2003),
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suggested that mild to unrecognisable, in the eye of an observer, abnormal femora are the
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genesis of impingement. To the best of the authors knowledge, tissue stresses during 'cam'-
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type impinged articulation have not been measured.
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Admittedly, we only considered a typical case of impingement and limited loading
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scenarios. The geometries considered are simplified versions based on CT images and
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reported anatomic characteristics, although we believe they contain the essence of a typical
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case of ‘cam’-type impingement. The finite element mesh was optimised to obtain
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convergence during ‘cam’-type impinged articulation; the chosen grid size was the optimum
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from a sensitivity study. Although the normal and the abnormal joints were meshed slight
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differently, it should not affect the results. The grid-ratios on both acetabular and femoral side
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were chosen carefully to obtain contact convergence. The slope of the contact-pressure
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overclosure relationship was also adjusted to minimise nodal penetration and contact pressure
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errors. Further, loading scenarios considered here are limited to normal walking and sitting
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down. In certain sporting activities, such as martial arts, a higher range of motions is required
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hence higher stresses due to impingement may be expected.
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As in all numerical work, experimental verification would be highly desirable, but it is
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not yet possible to quantify the load sharing between the fluid and solid phase or measure the
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strains within the ECM directly. Nonetheless, the key parameters were found to be generally
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insensitive to the variation of material properties even by variation of ± 50% (Figure 5).
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Because linear behaviour was considered for the fluid (permeability) and the solid phase
273
(elastic orthotropic), the error during a cam-impinged articulation should be similar to that
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determined during static loading. The shear modulus, however, does seem to affect the
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femoral head displacement, thus cartilage consolidation. Mansours (2009) argued that, during
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cartilage compaction, elevated shear stresses will occur at the cartilage-bone interface, see
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Figure 3 (f), as the cartilage layers are next to the much stiffer underlying subchondral bone
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layer, and high lateral contraction is a result of compression of the opposing cartilage layers.
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Hence, it is important to consider the orthotropic properties of the cartilage extracellular
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matrix when simulating multi-directional deformation of cartilage.
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Conclusions
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Results from a biphasic analysis of a healthy and a cam-impinged joint show that 'cam'-type
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impingement can elevate stresses significantly in the extracellular matrix of cartilaginous
284
tissues. During sitting down, the peak radial and the peak meridional stresses within the
285
cartilage and the circumferential stress within the acetabular labrum increased by 3.7, 2.7 and
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1.5 times, respectively, compared with those in the normal joint. Peak pore pressure also
287
increased at the anterior-superior 'cam'-type impinged zone. The increased solid-on-solid
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stresses and associated decrease in fluid-load support would result in higher friction during
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articulation and hence joint wear. In summary, 'cam'-type impingement is a risk factor that
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could increase cartilaginous tissue strains leading to joint wear and other degenerative
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changes in the hip, consistent with clinical findings.
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Acknowledgement
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The authors gratefully acknowledge access to the Sciama High Performance Computer (HPC)
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Cluster, which was supported by the ICG, SEPNet and the University of Portsmouth and
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support by Sciama technician Gary Burton.
Page 14
List of Figures
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297
298
299
300
Anterior
D
Anterior Hump
C
Medial
Lateral
α
Posterior
301
302
Figure 1. Illustration of a pathologic femur (anterior hump): The deviation of femoral head
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sphericity is measured by the α angle between the femoral neck axis, passing though the
304
femoral neck and head centre C, and a line extended from the point C to D, the point of
305
deviation from femoral head sphericity (edge of hump).
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(1)
(1)
(2)
(3)
(4)
(5)
(a)
(b)
(c)
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308
Figure 2. The solid models for a normal (a) and a pathologic femur with hump (b). The finite
309
element model of the normal hip joint (c) consists of acetabular labrum (1), acetabular
310
cartilage (2), femoral cartilage (3), an impermeable membrane (4) and femoral head neck
311
section (5), following (Chegini et al., 2009).
312
Page 15
contact pressure
(CPRESS)
(a)
radial stress
(S11)
(d)
A
max = 2.87 MPa
max = 2.84 MPa
pore pressure
(POR)
fluid velocity
(FLVEL)
(c)
(b)
A
A-A
circumferential stress
(S22)
A-A
meridional stress
(S11)
A-A
(e)
A-A
(f)
Tresca stress
(S, Tresca)
A-A
(g)
Figure 3. The peak contact pressure (MPa) (a) during normal walking; the related pore pressure (MPa) (b) and the stress components (MPa) in the
solid matrix: Radial (c), circumferential (d), meridional (e) and Tresca stress (f), section A-A as indicated in (a).
Page 16
(a) 'cam'-type impinged articulation
pore pressure
(POR)
radial stress
(S11)
circumferential stress
(S22)
meridional stress
(S33)
Tresca stress
(S, Tresca)
radial stress
(S11)
circumferential stress
(S22)
meridional stress
(S33)
Tresca stress
(S, Tresca)
(b) normal articulation
pore pressure
(POR)
Figure 4. Pore pressure for normal (a) and CAM-Impinged (b) acetabular labral and cartilage exposure during sitting down: Radial, circumferential,
meridional and Tresca stresses (MPa) within the ECM.
Page 17
(A)
Femoral Head Displacement
G
Ec
v12/13
v23
k
-0.11%
-0.09%
High
Low
-0.77%
-3.58%
-0.67%
-17.99%
2.5%
0.07%
0.19%
4.23%
0.86%
-2.5%
0.08%
0.0%
0%
46.18%
Deviation
25%
-25%
Et
5.0%
50%
-5.0%
-50%
Low
High
Low
High
(B)
Low
High
Low
High
Low
High
Contact Pressure
G
Ec
Et
v12/13
v23
k
0.00%
-0.02%
-0.19%
-1.79%
-0.13%
2.5%
-2.89%
High
Low
0.02%
0.14%
Low
0.11%
High
2.70%
-2.5%
0.33%
0.0%
1.95%
Deviation
5.0%
-5.0%
Low
High
Low
(C)
High
Low
High
Low
High
Pore Pressure
G
Ec
Et
v12/13
v23
k
-0.05%
-0.02%
High
Low
High
-0.01%
-1.64%
-0.75%
2.5%
-3.68%
Low
High
0.01%
0.03%
Low
0.14%
High
1.90%
-2.5%
0.97%
0.0%
2.18%
Deviation
5.0%
-5.0%
Low
High
Low
Low
High
Figure 5. The variation in the femoral head displacement, contact pressure and pore pressure
due to the variation in the material parameters (Low: - 50%; High: + 50 %).
Page 18
List of Tables
Table 1. The numbers of elements and grid sizes used in the FE models of the normal and the
abnormal hip joint.
Element Type
Healthy Joint
Abnormal Joint
Number
Grid Size
Number
Grid Size
Acetabular cartilage and labrum
C3D8RP
21,460
0.70
21,460
0.70
Femoral cartilage
C3D8RP
13,666
0.90
12,420
1.00
R3D4
9,956
0.90
8,767
1.00
M3D4R
4,004
1.15
4,166
0.95
Femoral head-neck section
Impermeable membrane
Table 2. Material properties used in this study.
Biphasic Formulation
E1
E2
E3
ν 12
ν 13
ν 23
G
k’
[MPa]
[MPa]
[MPa]
-
-
-
[MPa]
[mm/s]
Tissue
Acetabular
Labrum
Φ
-
b
0.157 a
26 a
3e
0.04
0.04
0.1
4.89
x 10-09
1.5
4
d
Acetabular
Cartilage
1.23 b
8.5 c
8.5 c
0.044 b
0.044 b
0.146 d
2.5 f
8.52
x 10-09
4
Femoral
Cartilage
1.18 b
8.5 c
8.5c
0.046 b
0.046 b
0.146 d
2.5 f
8.98 d
x 10-09
4
a
(Ferguson et al. 2001)
b
(Athanasiou et al. 1994)
f
(Tisskaht & Ahmed 1995)
g
(Wong et al. 2008)
c
d
(Roth et al. 1980)
(Frederico et al. 2003)
Table 3. Peak biphasic response for normal walking and siting down for normal articulation.
Activity
Location
Biphasic Response
-
-
P-CPRES
CAREA
P-POR
S11
Time of Cycle
-
-
[MPa]
[mm2]
[MPa]
[MPa]
[%]
Normal Walking
Superior
2.87
1798
2.84
-0.03
54
Sitting Down
Posterior - Medial
3.58
1574
3.54
-0.04
46.23
Page 19