Tissue material properties and computational modelling of the human tibiofemoral joint: a critical review

Articular cartilage

Articular cartilage is a type of fibrous connective tissue composed of cells forming between 2% and 15% of the total weight and an extracellular matrix (ECM) forming the remaining 85–98%, of which 65–80% is water (Martini, 1998). Its primary function is to maintain a smooth surface allowing lubricated, near-frictionless movement and to help transmit articular forces, thereby minimising stress concentrations across the joint. It is most commonly found within synovial and diarthrodial joints forming a 1–6 mm thickness and covering the epiphysis of bone. The knee joint is composed of both hyaline and fibrocartilage in the form of articular cartilage covering the end of bones articulating within the joint and fibrocartilage forming the menisci (Martini, 1998).

Material properties of articular cartilage have been widely reported giving compressive, tensile and shear forces at the macro- (Armstrong & Mow, 1982; Setton, Elliott & Mow, 1999; Kleemann et al., 2005), micro- (Stolz et al., 2009; Desrochers, Amrein & Matyas, 2010) and nano-scale (Stolz et al., 2009) within the ECM of multiple species. Various techniques have been utilised including confined and unconfined compression (Kleemann et al., 2005; Hori & Mockros, 1976; Franz et al., 2001) and more recently atomic force microscopy (AFM) (Wen et al., 2012; Wilusz, Zauscher & Guilak, 2013; Wang et al., 2013) and nanoindentation (Taffetani et al., 2014). Custom made indentation instruments have also previously been used to measure articular cartilage stiffness during compression (Hori & Mockros, 1976; Kempson, Freeman & Swanson, 1971; Lyyra et al., 1995; Kiviranta et al., 2008) as well as being used to calculate dynamic modulus (Kiviranta et al., 2008), creep modulus (Kempson, Freeman & Swanson, 1971), shear, bulk and elastic modulus and Poisson’s ratio (Hori & Mockros, 1976).

One of the first studies to explore human knee joint cartilage material properties utilised uniaxial confined compression on 20 proximal tibia samples. Age and gender of donors were not specified; however each sample was classified with a grade of OA using the Bollet system (Bollet, Handy & Sturgill, 1963 cited in Hori & Mockros (1976)). Progressive compression loads were manually applied giving an elastic modulus between 1.3 and 10.2 MPa. When categorising elastic modulus to grade of OA averages were 6.82, 6.74, 4.76 and 2.99 MPa for grades 0, 1, 2 and 3 respectively, although this correlation was not significant (Hori & Mockros, 1976). Testing specifications and resultant data can be seen in Table 1 alongside information from all reviewed human knee joint cartilage material property research.

In more recent decades there has been considerable focus on microscale unconfined compression testing. In consecutive studies by Shepherd & Seedhom (1997, 1999a), human femoral condyle and tibial plateau cartilage were tested. Earlier research utilised a total of five donors although no age or gender was specified. Results indicated an elastic modulus of between 2.6 and 18.6 MPa depending on physiological loading rate (Shepherd & Seedhom, 1997). In the latter study 11 humans cadavers (three males and eight females, aged 33–80 years old) were tested giving an elastic modulus of 6.0–11.8 MPa (Table 1) across all cadavers with no correlation to age (Shepherd & Seedhom, 1999a).

Thambyah, Nather & Goh (2006) tested cartilage from seven fresh frozen healthy human male tibias (62–70 years old) using uniaxial tensile testing at a rate of 300 kPa/s to compare articular cartilage from beneath the menisci to that independent from the menisci. Results showed an individual mean elastic modulus from all seven cadavers between 2.13 and 5.13 MPa (Table 1) across varying testing locations. Hydration maintenance was not specified within the methodology.

Kleemann et al. (2005) explored the macroscopic composition of articular cartilage within 15 females and 6 males OA tibial plateau samples (70 ± 13 years old). Research obtained architectural data from histology using haematoxylin and eosin staining and elastic modulus of cartilage was determined by unconfined uniaxial compression. An inverse correlation was observed between the elastic modulus of the articular cartilage against the International Cartilage Repair Society (ICRS) grade (Brittberg & Peterson, 1998) seen in Fig. 1 (Grade 1 0.50 MPa, Grade 2 0.37 MPa, and Grade 3 0.28 MPa (Table 1)). The research also suggested a relationship between changes in histology, structure and mechanics of the articular cartilage during all stages of OA degeneration although this was not compared with age of donor. Moreover Bae et al. (2003) found decreased indentation stiffness and an increased ICRS score was associated with degeneration of cartilage rather than with age or cartilage thickness. This suggests that it is possible to reliably distinguish degeneration of cartilage by microscopic histological analysis and macroscopic observations.

Franz et al. (2001) used a handheld indenter with a constant load of 300 μm to collate the shear modulus of 24 human cartilage samples (32–89 years old) obtained from the medial and lateral femoral condyles. Shear modulus was converted to elastic modulus (using the Poisson’s ratio expressed in the original research) for the purpose of this paper, which were 4.32 MPa and 4.88 MPa (Table 1) in the lateral and medial femoral condyles respectively; however this was not correlated to the age of cadaver. Cartilage samples were graded for OA using the Mankin system (Mankin et al., 1971) and results indicated a positive correlation between a slightly roughened cartilage surface and stiffness at the medial femoral condyle. However, it should be noted that no samples presented with gross fibrillation or surface irregularities. Sample shear modulus was, however, presented in age categories with corresponding proteoglycan and collagen content which are known to adapt during ageing and disease.

The development of increasingly sophisticated testing techniques has further advanced our understanding of cartilage material properties by allowing measurements to be made at the nanoscale. With the use of nanoscale indentation stiffening of cartilage due to age-related influences alongside stiffness differences in healthy and OA cartilage can be detected more accurately in comparison to microindentation (Stolz et al., 2009). It has been shown that microindentation is either unable to detect such changes or produces a lower stiffness measurement when compared to nanoindentation leading some to question its accuracy (Stolz et al., 2004, 2009). Additionally, stiffness is higher in articular cartilage collagen fibrils than in proteoglycans; however when measured at microscale, this differentiation may not be detected (Loparic et al., 2010). A change in the structure and content of proteoglycans often accompanies the process of OA along with reduced stiffness through loosening of the collagen network causing alteration to the material properties, further enhancing the need for testing at the nanoscale (Wang et al., 2013).

Incorporating nanotechnology, Wen et al. (2012) utilised AFM at a loading rate of 2.11 nm/s to test elastic modulus of tibial plateau articular cartilage fragments obtained from three female patients undergoing arthroplasty surgery. Samples from the surface, superficial middle, deep middle and bone–cartilage interface regions were graded for OA with the Outerbridge scoring system (Outerbridge, 1961). Collagen fibres were obtained from the overlap zone from each layer which can be mechanically stiffer than collagen fibres in the gap region (Minary-Jolandan & Yu, 2009). Results show there is a significant mechanical stiffening of individual human collagen fibrils between healthy (aged 35 years old) and mild OA (aged 52 and 59 years old), at the surface of articular cartilage (2,650–3,110 MPa respectively) through to the bone–cartilage interface (3,700–5,640 MPa respectively) (Table 1). It must be noted that tissue samples were dehydrated with ethanol prior to testing which will alter the true mechanical properties of cartilage; however the aim of this research was to identify the differences in elastic modulus of healthy and OA tissues where mechanical alterations would change simultaneously in both healthy and OA samples.

Wilusz, Zauscher & Guilak (2013) also used AFM at a rate of 15 μm/s on eight human femoral condyles (six females and two males) aged 53–83 years old. Cadavers were graded for OA using the Collins System (Collins, 1939, 1949 cited in Wilusz, Zauscher & Guilak (2013)) giving four healthy and four OA samples grades 2–3. Results indicate that elastic modulus of the pericellular matrix (PCM) decreased in OA samples (0.096 ± 0.016 MPa) when compared to healthy controls (0.137 ± 0.022 MPa). Also the ECM elastic modulus was decreased in OA samples (0.270 ± 0.076 MPa) when compared to healthy controls (0.491 ± 0.112 MPa) (Table 1); although this was only significant on the medial femoral condyle. In agreement, Wang & Peng (2015) used AFM to quantify elastic modulus of 12 knee articular cartilage samples (age and gender not specified) in various grades of OA and found an increase in elastic modulus in the presence of mild and moderate OA but a decrease with severe OA, although actual values are not stated.

Atomic force microscopy has also been used to identify nanoscale adaptations at varying indentation depths in five human (age and gender not specified) femoral condyles obtained from healthy, mild and severe OA cartilage (Wang et al., 2013). Cartilage samples were graded using the Outerbridge scoring system (Outerbridge, 1961) and exposed to PBS during testing to maintain hydration. Stiffness was higher at a lower indentation depth for all cohorts; however, stiffness was highest with mild OA (0.61 MPa) and lowest with healthy controls (0.16 MPa) when comparing to severe OA (0.19 MPa) (Table 1) (Wang & Peng, 2015).

Bone

There are two different types of bone including cortical and trabecular material. The cortical material is found on the outside of bone and is highly dense in nature and the trabecular material is located inside of the bone and has a greater porosity. The low and high densities work in coordination to absorb stresses through the rigid outer surface and strains through the spongy inner material in order to resist breaking or deformation (Nigg & Herzog, 2006; Martini, 1998).

Recent research has started to direct focus onto the relationship between cartilage and bone in the progression of OA. Research has observed abnormal remodelling of subchondral bone in OA showing the trabecular structure alters in density, quantity and separation, with the greatest proliferation in volume evident at the bone–cartilage interface (Kamibayashi et al., 1995; Bobinac et al., 2003). This suggests a synergistic relationship between bone and cartilage during the progression of OA. The role of subchondral bone in OA appears to be an essential component in the initiation and advancement of the disease (Burr, 1998; Lajeunesse & Reboul, 2003; Madry, van Dijk & Mueller-Gerbl, 2010). However research is unclear as to whether disruption of subchondral bone remodelling occurs pre- or post-initiation of OA (Intema et al., 2010; Kuroki, Cook & Cook, 2011). Kuroki, Cook & Cook (2011) suggested that a more comprehensive understanding of the disease mechanisms of OA including material properties of all tissues involved could yield considerable progression in clinical practice and treatment methods.

In previous decades uniaxial compression testing of human femoral and tibial trabecular bone was carried out by several researchers in order to obtain macroscale material properties. Behrens, Walker & Shoji (1974) tested both femoral condyle and tibial plateau trabecular bone samples from six females and four males (40–92 years old) resulting in an elastic modulus of 158.9–277.5 MPa for femoral bone and 139.3–231.4 MPa for tibial samples (Table 2). Testing only femoral condyle trabecular bone, Ducheyne et al. (1977) found a slightly lower elastic modulus of 1.9–166.1 MPa (Table 2) based on donors aged 43–77 years old (four males, two females).

Carter & Hayes (1977) tested 100 human trabecular bone samples (age and gender unspecified) from tibial plateaus by uniaxial compression and found an elastic modulus between 56.6 and 83.7 MPa (Table 2). Also using uniaxial compression, Lindahl (1976) tested four females and four males human cadavers (14–89 years old) showing a higher elastic modulus in males (average 34.6 MPa) compared to females (average 23.1 MPa) (Table 2).

Interestingly, as well as differences between male and female cadavers, material properties also vary according to anatomical location. Goldstein et al. (1983) utilised uniaxial compression testing to determine the elastic modulus of trabecular bone from the tibial plateau from five cadavers (50–70 years old) across varying depths of the joint. Results showed high variation across cadavers and testing location (4.2–430 MPa (Table 2)) with the highest values at load bearing sites. Utilising an alternative method, Hvid & Hansen (1985), used an osteopenetrometer on the tibial plateau of 12 healthy human donors aged 26–83 years old (three females and nine males). Medial tibial plateau samples had an elastic modulus of 13.8–116.4 MPa and lateral tibial plateau samples had a lower elastic modulus of 9.1–47.5 MPa (Table 2) further evidencing high variability in material properties across the joint.

Burgers et al. (2008) obtained four male and four female human cadavers (totalling 10 femurs aged 45–92 years old). Cylindrical trabecular specimens (n = 28) were tested using unconfined compression. Results were separated into superior or inferior and medial or lateral samples giving a pooled elastic modulus of 376 ± 347 MPa (Table 2) with the greatest variation apparent between superior and inferior femoral condyle samples.

Previous studies researching human knee bone material properties, specifically in OA, are abundantly missing; however one study by Zysset, Sonny & Hayes (1994) explored human tibial material properties from six cadavers (61–91 years old) with grades 1–3 OA, scored using the Ahlback system (Ahlback, 1968). Compression tests were conducted on cuboidal specimens giving an axial elastic modulus of the subchondral trabecular bone between 31 and 1,116 MPa which decreased with increasing grades of OA. Although epiphyseal and metaphyseal trabecular bone samples showed that elastic modulus increased with OA grade in the axial (102–1,726 MPa) and coronal (8–287 MPa) planes (Table 2). Corresponding OA grade and elastic modulus values can be seen in Fig. 2.

In more recent years, testing bone at the tissue level has proven to be more accurate (Nigg & Herzog, 2006) particularly for the inclusion of FE models; however this has rarely been applied to femoral or tibial human bone. Using nanoindentation Rho, Tsui & Pharr (1997) explored the tissue level material properties of a single osteon and interstitial lamellae of two longitudinal human (57 and 61 years old) tibial cortical bone. Results presented an elastic modulus of 22,500 MPa and 25,800 MPa for osteon and interstitial lamellae samples respectively (Table 2).

Ligaments

Ligaments are soft tissues that are fibrous in nature and composed primarily of collagen. They have a hierarchal structure of fibres, fibrils, subfibrils, microfibrils and tropocollagen but also contain water, proteoglycans and several glycoproteins. They function to guide and resist motion at a joint by connecting bone to bone. It has also been suggested that they act as a strain sensor to restrict degrees of freedom in order to stabilise the joint and prevent excessive movement (Harner et al., 1995; Woo et al., 2006). Ligaments have direct and indirect insertions into the bone and periosteum respectively allowing variation in fibre bundles to respond to different movements and resist loading during ranges of rotation at the joint. The entheses portion of the ligament is stiffer compared to the medial portion allowing decreased concentrations of stress and therefore reducing the opportunity for damage or tears at the bone–ligament interface (Woo et al., 2006).

When measuring material properties of knee ligaments (ACL, PCL, MCL and LCL) typical analyses includes tensile stress and strain at ultimate failure, tangent modulus and strain energy density, primarily obtained using a tensile testing machine. These parameters are tested in vitro by taking either a cross-section of the involved ligament (Quapp & Weiss, 1998) or more commonly a bone–ligament–bone sample (e.g. Fig. 3). During this process bone blocks are ordinarily embedded within polymethyl-methacrylate (PMMA) and the ligaments are wrapped in saline soaked gauze for protection (Harner et al., 1995; Butler et al., 1992; Momersteeg et al., 1995; Hewitt et al., 2001; Robinson, Bull & Amis, 2005; Bonner et al., 2015). Additionally samples may be tested as a whole structure or divided into anatomical fibre bundles. Woo et al. (2006) suggests that the ACL has an anteromedial and posterolateral bundle and the PCL has an anterolateral and posteromedial bundle which are loaded differently. Ligaments therefore may need to be separated during tensile testing, in order to gain a true understanding of their unique material properties. A summary of the reviewed ligament material property research papers is provided in Table 3.

Harvesting a cross-sectional area of a ligament, Quapp & Weiss (1998) explored the longitudinal and transverse mechanical behaviour of the MCL from 10 human cadavers (62 ± 18 years old). Specimens were preconditioned and loaded to failure. Results included average tensile strength (38.6 and 1.7 MPa), average ultimate strain (17.1% and 1.7%) and average tangent modulus (332.2 and 11.0 MPa) for longitudinal and transverse specimens respectively (Table 3).

Further research on the tensile properties of ligaments utilised the bone–ligament–bone method. One of the first studies to explore ligament material properties harvested the ACL, PCL, MCL and LCL from seven healthy human cadavers aged 29–55 years old (gender not specified). Ligaments were preconditioned over five cycles and loaded to failure at 100% strain rate, which is a change in strain equivalent to the initial length of the ligament. Stiffness was measured at 138.3, 179.5, 70.3 and 59.8 N/mm for the ACL, PCL, MCL and LCL respectively, whilst failure load resided at 620.8, 658.0, 515.8 and 376.6 N (Table 3) (Trent, Walker & Wolf, 1976).

Noyes & Grood (1976) tested young (16–26 years old) and old (48–86 years old) anterior cruciate bone–ligament–bone material properties, also at a 100% strain rate, although excluded any preconditioning. The research found a reduction in stiffness (129 and 182 N/mm), failure load (734.0 and 1730.0 N), elastic modulus (65.3 and 111.0 MPa), maximum stress (13.3 and 37.8 MPa) and strain (30.0% and 44.3%) when comparing older samples to younger samples respectively (Table 3).

Butler, Kay & Stouffer (1986) also tested young (21–30 years old) ACL, PCL and LCL elastic modulus (278–447 MPa), maximum stress (30–44 MPa) and maximum strain (11–19%) where ranges were inclusive of all ligaments. Approximate values are given in Table 3 estimated from presented graphs (Butler, Kay & Stouffer, 1986). The ligaments were divided into their fibre bundles and tested to failure at a 100%/s strain rate (Table 3). Further research by Butler et al. (1992) looked at the differences in seven human ACL (26 ± 4 years old) divided into anteromedial, anterolateral and posterior fibre bundles. Specimens were not exposed to preconditioning but were loaded to failure at a 100%/s strain rate. This resulted in anterior fibres having a higher maximum modulus (284 MPa), stress (38 MPa) and strain rate (17.6%) when compared to posterior fibres (155 MPa, 15 MPa, 15.2%) at failure (Table 3).

Race & Amis (1994) and Harner et al. (1995) loaded to failure the anterolateral and posteromedial fibres bundles of the human PCL. Race & Amis (1994) obtained 10 samples from donors aged 53–98 years old which resulted in higher stiffness (347.0 and 770 N/mm), failure load (1620.0 and 258.0 N), elastic modulus (248.0 and 145.0 MPa) and maximum stress (35.9 and 24.4 MPa) for the anterolateral fibres in comparison to the posteromedial fibres respectively (Table 3). Interestingly maximum strain was lower for the anterolateral fibres (18.0%) when compared to the posteromedial fibres (19.0%). Harner et al. (1995) tested five samples (48–77 years old) and also found a higher failure load in the anterolateral fibres (1120.0 N) in comparison to the posteromedial fibres (419.0 N) (Table 3) showing in both studies wide variation depending on the location of the tissue.

A more recent study by Robinson, Bull & Amis (2005) harvested three sections of the femur–MCL–tibia complex from eight humans (77 ± 5.3 years old), namely the superficial MCL (SMCL), deep MCL (DMCL) and posteromedial capsule (PMC) based on fibre orientation and tested samples using the bone–ligament–bone approach. The SMCL is often used to define the overall MCL length; however, it is thought that each section tenses and fully elongates under different loading axis or directions and functions to stabilise the knee joint in various ways. Samples were preconditioned and loaded to failure resulting in failure loads of 534, 194 and 425 N for the SMCL, DMCL and PMC respectively (Table 3). The results indicated a bony avulsion in 75% of tested samples after which the bone was removed and the end of the ligament was attached directly in the clamps and re-loaded to failure. Additionally mid-substance failure of the ligament as opposed to bony avulsion equated to 74% higher maximum load.

Further variations in tensile properties can exist due to the angle of the femur in correlation to the tibia and the loading axis in correlation to ligament fibre loading direction. Woo et al. (1991) preconditioned and tested the ACL to failure along both the tibial and ligament axis and found higher stiffness values on the ligament axis with increasing extension angle when testing young and old cadavers. Significant variations in anatomical orientation failure load were apparent between age groups: 2,160 N for 22–35 years old (N = 9), 1,503 N for 40–50 years old (N = 9) and 658 N for 60–97 years old (N = 9) (Table 3) as seen in Fig. 4. However, there was no correlation between age and orientation.

Interestingly, Chandrashekar et al. (2006) found gender-based differences in tensile properties showing human female ACL (N = 9) (17–50 years old) had 22.49% lower elastic modulus and 8.3% and 14.3% lower maximum strain and stress respectively when compared to human male ACL (N = 8) (26–50 years old) (Table 3). These differences can be partially accounted for due to the physically smaller size of the female ACL (Anderson et al., 2001; Chandrashekar, Slauterbeck & Hashemi, 2005); however, when adjusted for covariates the tensile properties of the ACL are still lower. This may in turn explain the higher rates of ACL injuries in female athletes (Chandrashekar et al., 2006).

Finally an analysis by Momersteeg et al. (1995) chose not to separate the fibre bundles but instead tilted the orientation of the loading axis at 5° increments (up to 25°) to recruit different fibres at varying angles to explore the changes in tensile properties during sub-ultimate testing. Bone–ligament–bone samples were harvested for the ACL, PCL, MCL and LCL of five human cadavers (63–81 years old) and subjected to preconditioning before applying up to 7% and 10% strain rates for the collateral and cruciate ligaments respectively. Results indicate that strain levels were higher for cruciate ligaments than collateral ligaments and for every 5° of tilt there was a decrease in tensile stiffness (averages: −11.6 Nmm⁻¹ ACL, −20.96 Nmm⁻¹ PCL, −2.66 Nmm⁻¹ MCL, −3.76 Nmm⁻¹ LCL) (Table 3). The research suggests there is a greater decrease in stiffness for the cruciate ligaments as they have a shorter and wider morphology when compared to the long thin nature of collateral ligaments. These authors go on to conclude that ligaments are highly sensitive to a small change in orientation and therefore unidirectional tensile testing is not effective at defining ligament stiffness properties (Momersteeg et al., 1995).

3D FE models of healthy human knee joints

This review reveals that FE models most commonly use previously published data for material properties; however, there is usually a lengthy referencing chain when tracing these material properties to their original and primary data research article. Material properties are likely to vary with age, gender and disease status (Kleemann et al., 2005; Lindahl, 1976; Woo et al., 1991; Chandrashekar et al., 2006) and therefore donor demographics in previously published material property studies will undoubtedly impact upon the quantitative results obtained in FE analyses. Our review highlights a wide spectrum of matches in this respect to the extent that the absence of appropriate data has in some cases led to the use of non-human material properties in FE models of the knee. Material property sources from reviewed FE models are summarised in Table 4.

Wang, Fan & Zhang (2014) attempted to estimate cartilage stress under forces incurred during kneeling in a young healthy male (26-year-old), using primary MRI data to create their FE model, which it should be noted included the patella (Fig. 5). The referencing chain starting from Wang, Fan & Zhang (2014) follows up to five secondary references until the original research article is cited. Original demographics include human tibial plateau and femoral neck samples for bone (Rho, Ashman & Turner, 1993; Zysset et al., 1999), human femoral condyle and tibial plateau samples for cartilage (Shepherd & Seedhom, 1999a), human (Tissakht & Ahmed, 1995) and bovine menisci (Skaggs, Warden & Mow, 1994) and human ACL, PCL, LCL, quadriceps tendon and patella ligament samples for ligament material properties (Race & Amis, 1994; Woo et al., 1991; Staubli et al., 1999; Blankevoort, Huiskes & De Lange, 1988; Brantigan & Voshell, 1941). Where human samples were used for bone material properties the original research articles either do not state donor age (Rho, Ashman & Turner, 1993) or donor age was 53–93 years old (Zysset et al., 1999). Human cartilage ranged from 33 to 80 years old (Shepherd & Seedhom, 1999a) whilst menisci was either 29–45 years old (Skaggs, Warden & Mow, 1994) or information was not available. Human ligament samples had an average age of 24.9 years old (Staubli et al., 1999), an age range of 53–98 years old (Race & Amis, 1994), 43–74 years old (Blankevoort, Huiskes & De Lange, 1988), or it stated that donors were ‘young’ (Butler, Kay & Stouffer, 1986) or it was unspecified (Brantigan & Voshell, 1941) (Table 4). The specific material properties used within Wang, Fan & Zhang (2014), can be found in the Table 5 alongside the material properties from other FE modelling studies reviewed.

Consecutive studies by Peña et al. (2005, 2006) carried out FE modelling of a healthy knee joint using CT and MRI data of a healthy male volunteer (age not specified) to generate a model that included bone, ligaments, tendons and articular and meniscal cartilages using previously published material property data. The aims of these studies were to compare stress and strain in a healthy human knee to those experienced after meniscal tears and meniscectomies (Peña et al., 2005) and to analyse the non-uniform stress–strain fields that the menisci and ligaments encounter during the loading of the human knee joint (Peña et al., 2006). The referencing chain starting from Peña et al. (2006) also follows up to four secondary references until the original research article is cited. As bones were modelled as rigid this requires no material property input; cartilage material properties could not be traced; menisci material properties were based on canine meniscal material properties (LeRoux & Setton, 2002) and ligaments on human ACL, PCL, MCL and LCL material properties with ages specified as 38 years old (Butler et al., 1990), 37–61 years old (91), 43–74 years old (Blankevoort, Huiskes & De Lange, 1988) or simply denoted as ‘young’ (Butler, Kay & Stouffer, 1986) or unspecified (Brantigan & Voshell, 1941). Peña et al. (2005) used the same original sources for cartilage and menisci material properties and adopted ligament material property data from a review article (Weiss & Gardiner, 2001) for the representation of a healthy knee joint, summarised in Table 4.

Guo, Zhang & Chen (2009) created a 3D human knee joint model from a CT scan on a 45-year-old healthy female to understand the contact pressures on the femoral and tibial cartilages during different phases of the gait cycle. Material properties were referenced from previous FE modelling papers; however, the referencing chain provides information that menisci data was originally presented by LeRoux & Setton (2002) based on canine meniscal properties. Unfortunately, bone, cartilage and ligament material property sources cannot be traced back to a primary data collection reference (Table 4).

A recent FE study explored misalignment differentiation of the knee joint to understand how this influences contact pressure (Mootanah et al., 2014). An MRI of a 50-year-old cadaveric male was used for geometry and validation of the model through mounting the knee joint and matching loading and boundary conditions. Mootanah et al. (2014) obtained material properties from the literature with a referencing chain going back through three other research papers to the original primary research article. Bone material properties were based on human femoral condyle and tibial plateau samples aged 45–68 years old (Hobatho et al., 1991) whilst cartilage was based on ages stated as 33–80 years old (Shepherd & Seedhom, 1997, 1999b). It is unclear how the meniscal material properties were obtained. Ligament material property data was obtained through primary data collection of the ACL, PCL, MCL and LCL giving validated values for the geometry of the FE model (Table 4).

Kazemi et al. (2011) used a MRI scan of a healthy 26-year-old male to construct an FE model to understand the differences in creep behaviour of intact knee joints that have undergone meniscectomies. Subsequent research by Kazemi & Li (2014) similarly used an MRI of a healthy 27-year-old male, and modelled structures with the same modelling theories as Kazemi et al. (2011), although marginally adapted these material property inputs in order to understand the poroelastic response of soft tissues in the knee joint under large compression forces. Original data collection for material properties used within both studies was derived from bovine humeral head cartilage (Langelier & Buschmann, 1999; Woo, Akeson & Jemmott, 1976) and human tibial plateau (29–45 years old) along with human menisci (Tissakht & Ahmed, 1995). However ligament material properties, specifically toe region fibril data, were based on previous studies of the human patella tendon aged 29–93 years old (Hansen et al., 2006; Johnson et al., 1994) and human calcaneal (Achilles) tendon aged 57–93 years old (Louis-Ugbo, Leeson & Hutton, 2004). The non-fibril ligament material properties can be traced back to a theoretical modelling paper (Ault & Hoffman, 1992a), whose results are represented in a companion paper with experimental work carried out on a rat tail tendon (Ault & Hoffman, 1992b). Ligament initial strains used within Kazemi & Li (2014) can be traced back to Peña et al. (2006) which as discussed previously are originally sourced from human specimens aged 43–74 years old (Blankevoort, Huiskes & De Lange, 1988), 53–98 years old (Race & Amis, 1994), or ages are described as ‘young’ (Butler, Kay & Stouffer, 1986) or unspecified (Brantigan & Voshell, 1941) (Table 4).

Simplified FE models of the healthy human knee joint

For computational simplicity FE models of a human knee joint often make adjustments to their model including representing ligaments as non-linear one dimensional springs (Li, Lopez & Rubash, 2001; Blankevoort & Huiskes, 1991; Blankevoort et al., 1991; Li et al., 1999; Donlagic et al., 2008), bones as rigid bodies lacking material properties (Li, Lopez & Rubash, 2001; Li et al., 1999; Bendjaballah, Shirazi-Adl & Zukor, 1995; Jilani, Shirazi-Adl & Bendjaballah, 1997; Shirazi, Shirazi-Adl & Hurtig, 2008) or exclusion of particular structures such as the menisci (Blankevoort & Huiskes, 1991; Blankevoort et al., 1991) or ligaments (Guess et al., 2010; Donahue et al., 2002, 2003).

Models that have been highly simplified but still integrate all the main structures of the knee joint include studies by Blankevoort et al. (1991) and Blankevoort & Huiskes (1991) who created mathematical models of the knee joint, developed originally by Wismans et al. (1980), specifically focusing on the articular contact and interaction between ligaments and bones. Utilising the previously developed modelling theories (Blankevoort & Huiskes, 1991; Blankevoort et al., 1991). Li et al. (1999) and Li, Lopez & Rubash (2001) used a MRI of a 65-year-old male cadaver to create a 3D model of the knee joint and conducted a sensitivity analysis varying input parameters to assess the effect on joint contact stresses. In continuation, Yang et al. (2010) also utilised the work proposed by Blankevoort et al. (1991) and Blankevoort & Huiskes (1991) to define MRI scans from three young volunteers (21–23 years old) to determine cartilage contact stress during gait; however, noticeable differences between studies include the representation of the menisci within Yang et al. (2010).

Within these corresponding studies ligaments were modelled as ‘bars,’ which are one-dimension (1D) non-linear tension-only elements with just two nodes, although material properties are still assigned. It should also be noted that Li, Lopez & Rubash (2001) stated that ligament stiffness was optimised for the model to ensure numerical stability and model convergence rather than utilising a value measured experimentally. Blankevoort et al. (1991), Blankevoort & Huiskes (1991), Yang et al. (2010), Li et al. (1999) and Li, Lopez & Rubash (2001) sourced ligament material properties from human ACL, PCL and LCL samples aged ‘young’ (Butler, Kay & Stouffer, 1986) or aged 43–74 years old (Blankevoort, Huiskes & De Lange, 1988). Unfortunately, cartilage material properties were ambiguous due to multiple references available in the cited sources (Kempson, 1980; Mow, Lai & Holmes, 1982) making the origin of the input data unclear. Additionally, the menisci were modelled within Yang et al. (2010); however, the original data collection reference could not be traced. Referencing information from these FE studies are summarised in Table 4.

In addition to simplifying anatomical geometry it is also common for investigators to reuse medical image data sets to create different models. In sequential studies CT data of a 27-year-old female was used to construct a FE model of the human knee joint to explore contact pressures (Bendjaballah, Shirazi-Adl & Zukor, 1995), varus and valgus alignment (Bendjaballah, Shirazi-Adl & Zukor, 1997), axial rotation (Jilani, Shirazi-Adl & Bendjaballah, 1997), anterior–posterior forces (Bendjaballah, Shirazi-Adl & Zukor, 1998), ACL and PCL coupling (Moglo & Shirazi-Adl, 2003) and cartilage collagen fibril response to compression (Shirazi, Shirazi-Adl & Hurtig, 2008). Figure 6 illustrates the model created within these studies and highlights the differences in comparison to Fig. 5 in mesh generation and inclusion of all structures in 3D form. When tracing the material properties assigned to structures within these corresponding FE models cartilage primary data was ascertained from human tibial plateau samples aged 48–70 years old (Hayes & Mockros, 1971), ligaments from human ACL, PCL and LCL samples, referenced with ages of 53–98 years old (Race & Amis, 1994), or from samples described as ‘young’ (Butler, Kay & Stouffer, 1986). Menisci material properties were based on human meniscal samples aged 29–45 years old (Tissakht & Ahmed, 1995) alongside additional data which could not be traced (Table 4).

Another simplified FE model was developed by Beillas et al. (2004) who modelled the whole lower limb of a 30-year-old male and coordinated this with in vivo kinematics of a one-leg hop. However, this model was simplified with a 1D representation of the ligaments. Bone material properties were originally obtained from proximal femur and mid femur human samples aged either 28–91 years old (Lotz, Gerhart & Hayes, 1991), or age was unspecified (Reilly & Burstein, 1975), or bovine samples were used (Mente & Lewis, 1994). Cartilage material properties can be traced to human tibial plateau samples although age was not specified (Repo & Finlay, 1977) and some further cartilage information was untraceable. Menisci data also came from human samples although again age was not specified (Fithian, Kelly & Mow, 1990). Finally, ligament material properties were based on human ACL, PCL, MCL and LCL data obtained from donors aged 16–86 years old (Noyes & Grood, 1976), 29–55 years old (Trent, Walker & Wolf, 1976), and 22–97 years old (Woo et al., 1991) (Table 4).

Incorporating some of the material properties presented by Beillas et al. (2004), Donlagic et al. (2008) utilised a patient specific approach to derive geometry and loads for their FE model using an MRI of a 22- and 52-year-old male alongside primary kinematic data of flexion and extension locomotion. However, additional material property sources were also used for the representation of the cartilage including bovine and porcine femoral condyle and tibial plateau samples (Laasanen, 2003) (Table 4).

FE models of OA human knee joints

It was discussed previously (Section A—Material Properties, above) that changes in tissues structure during OA progression can result in changes in material properties. This in turn would correlate with a change in the response to loads and biomechanics of the whole knee joint. With this in mind, FE modelling has the potential to analyse such alterations in the presence of OA, assuming that tissue material properties representative of diseased tissues are incorporated into models. Although some FE studies have attempted to investigate contact stresses to understand how OA can initiate and progress (Peña et al., 2007b; Dong et al., 2011; Mononen et al., 2011, 2012, 2016; Venäläinen et al., 2016) or how arthroplasty procedures can affect the knee joint (Baldwin et al., 2012; Tuncer et al., 2013) there is only a handful of research papers that utilise a whole knee joint FE model based specifically on healthy versus OA material properties.

One of the first studies to attempt this examined how osteochondral defects influence the ongoing degeneration and stress concentrations of cartilage in the knee joint during compression based on the geometry and anatomical location of the defect (Peña et al., 2007b). Healthy material properties were identical to Peña et al. (2006) described in detail above and therefore included human and canine tissue. However, when modelling cartilage with defects the elastic modulus of the cartilage was adjusted to 1.5 MPa with data originally sourced from Athanasiou et al. (1995) who explored the elastic modulus of rabbit cartilage with artificially induced OA. A similar study by Dong et al. (2011) also explored the cartilage defects but kept the elastic modulus consistent for both healthy and OA simulations.

Although not modelling a whole knee, consecutive studies by Mononen et al. (2011, 2012) segmented the femoral and tibial cartilage from 29- and 61-year-old healthy males for FE analysis modelling the cartilage with fibril-reinforced poroviscoelastic properties. Mononen et al. (2011) compared normal, OA and repaired cartilage giving a strain dependent fibril network modulus of 673, 168 and 7–505 MPa respectively; an initial fibril network modulus of 0.47, 0.47 and 0.005–0.35 MPa respectively; an elastic modulus of 0.31, 0.08 and 0.31 MPa respectively; and finally a Poisson’s ratio of 0.42 for all samples. Mononen et al. (2012) compared only normal and OA samples with the same material properties. When following the referencing chain and tracing cartilage material properties back to their original research they used input data from bovine articular cartilage (DiSilvestro & Suh, 2001; Korhonen et al., 2003) where OA was artificially induced (Korhonen et al., 2003).

Material properties

There is considerable variation in the elastic modulus of articular cartilage obtained from the human knee joint within the literature. This can be at least attributed to differences in testing parameters and structure and quality of the tissue sample, in addition to known and ambiguous variation in donor characteristics. To summarise, samples within the literature include hydrated (Wilusz, Zauscher & Guilak, 2013; Kleemann et al., 2005; Hori & Mockros, 1976; Franz et al., 2001; Wang et al., 2013; Shepherd & Seedhom, 1997, 1999a) and dehydrated (Wen et al., 2012) femoral and tibial localities and ages between 32 and 89 years old. Furthermore OA samples have been graded using the Collins (Collins, 1939, 1949 cited in Wilusz, Zauscher & Guilak (2013)), Bollet (Bollet, Handy & Sturgill, 1963 cited in Hori & Mockros (1976)) and Outerbridge (Outerbridge, 1961) scoring systems, creating inconsistencies in categorisation. Both confined and unconfined compression testing has been employed (Kleemann et al., 2005; Hori & Mockros, 1976; Thambyah, Nather & Goh, 2006) alongside indentation techniques (Franz et al., 2001; Shepherd & Seedhom, 1997, 1999a) and AFM (Wen et al., 2012; Wilusz, Zauscher & Guilak, 2013; Wang et al., 2013). Research also incorporates extensive ranges in testing specifications including indentation tip radius (10–30.4 mm) (Hori & Mockros, 1976; Wen et al., 2012; Franz et al., 2001; Shepherd & Seedhom, 1997, 1999a; Thambyah, Nather & Goh, 2006; Wilusz, Zauscher & Guilak, 2013; Wang et al., 2013), loading force (0.019–11.8 N) (Kleemann et al., 2005; Hori & Mockros, 1976) and recovery phases if included (5 min) (Thambyah, Nather & Goh, 2006).

As discussed in ‘Section A—Material Properties,’ length scale dependency can affect the values derived from testing. For example, heterogeneity can be more easily identified in cartilage using nanoindentation when compared to microindentation (Stolz et al., 2009, 2004), which is particularly important when changes due to OA can be subtle. When reviewing current efforts at measuring elastic modulus of human knee joint cartilage, variation will indeed exist due to differing length scales between 10 nm (Wen et al., 2012) and 30.4 mm (Hori & Mockros, 1976) which may have an effect on obtained modulus. Moreover, studies also present varying elastic modulus, namely instantaneous (Franz et al., 2001; Hori & Mockros, 1976; Shepherd & Seedhom, 1997; Shepherd & Seedhom, 1999a; Thambyah, Nather & Goh, 2006; Wilusz, Zauscher & Guilak, 2013) and equilibrium modulus with some citing a 30 s (Wen et al., 2012) to 10 min (Kleemann et al., 2005) hold period. The circumstances under which tissues are measured will influence the results, and therefore the ability to compare across studies and accurately apply such data in FE models. It has previously been shown that there are considerable differences in instantaneous and equilibrium modulus, where instantaneous produces a much higher value (Julkunen et al., 2009), highlighting the need for a more standardised method of testing to determine any subtle change in material properties during healthy ageing and OA that may not be comparable across multiple data sources.

With these variations in mind elastic modulus for hydrated healthy cartilage samples varies between 0.1and 18.6 MPa (Wilusz, Zauscher & Guilak, 2013; Thambyah, Nather & Goh, 2006; Brittberg & Peterson, 1998; Bae et al., 2003; Shepherd & Seedhom, 1997, 1999a), hydrated OA grade 1 samples range between 0.5 and 10.2 MPa (Kleemann et al., 2005; Hori & Mockros, 1976; Franz et al., 2001; Wang et al., 2013) and hydrated OA grade 2 and 3 between 0.1 and 0.5 MPa (Wilusz, Zauscher & Guilak, 2013; Kleemann et al., 2005; Wang et al., 2013), noting that different OA grading systems are used across these studies. Furthermore, age ranges stated within the literature have a wide variation, the broadest being 33–80 years old within one study (Shepherd & Seedhom, 1999a). Some values cannot be explicitly linked to age ranges. Future work is required to more definitely define changes in cartilage material properties associated to explicitly with age and therefore help understand how alterations through disease can be separated from alterations during healthy ageing.

In comparison to the available data on human knee joint cartilage, there is significantly less data for femoral or tibial bone samples. Indeed, this research found only one study that quantitatively measured material properties of cortical bone from the human knee joint (Rho, Tsui & Pharr, 1997). Data on trabecular properties is present but it is difficult compare data from different anatomical locations collected with different techniques, specifically traditional compression approaches (Lindahl, 1976; Goldstein et al., 1983; Burgers et al., 2008) and more recent nanoindentation methods (Rho, Tsui & Pharr, 1997), which is yet to be applied to the human femoral condyle. Similar ambiguity in the relationship between age and material properties also exists. Age ranges vary between 14 and 92 years old across studies with the smallest age cohort (with the exception of individual donors) spanning 20 years in one study (Goldstein et al., 1983). Some studies also used donors under the age of 30 where donors may not have reached skeletal maturity and material properties may not reflect peak bone mass (Matkovic et al., 1994). Overall, trabecular bone elastic modulus ranges from 1.9 MPa to 664.0 MPa across reviewed studies (Behrens, Walker & Shoji, 1974; Ducheyne et al., 1977; Carter & Hayes, 1977; Lindahl, 1976; Goldstein et al., 1983; Hvid & Hansen, 1985; Burgers et al., 2008; Zysset, Sonny & Hayes, 1994) and cortical bone from 22,500 MPa to 25,800 MPa (Rho, Tsui & Pharr, 1997).

Studies reviewed in ‘Section A—Material Properties’ mostly involve experimental work on trabecular bone which is less commonly used within FE models. Compression techniques utilised to obtain macroscale measurements of trabecular bone as a whole structure as opposed to measuring individual trabeculae, will inevitably produce lower elastic modulus values due to the nature of testing; however, more sophisticated techniques incorporating tissue level material properties can more accurately represent a structure such as trabecular bone at the level in which it is typically modelled in FE research (Nigg & Herzog, 2006). This variability in techniques inevitably makes a comparison between studies challenging as well as the lack of distinct age cohorts to ultimately define young and old parameters in order to definitively link this to a change in properties due to injury or disease, such as OA. Despite some research incorporating material properties of varying OA grades there are no healthy controls included to explicitly link significant findings to OA status (Zysset, Sonny & Hayes, 1994). Evidently there is also no material property data for human trabecular bone obtained from the distal femur or proximal tibia at the tissue level, comparing healthy and OA samples.

It should be noted that the studies cited herein utilised varying indenter sizes ranging from 20 nm (Rho, Tsui & Pharr, 1997) to 2.5 mm (Hvid & Hansen, 1985). A length scale under 200 nm is able to determine more heterogeneity in bone structure than those applied above 200 nm (Yao et al., 2011). When comparing studies discussed herein it should be considered that comparisons are challenging, and indeed reiterates the importance of site and subject-specific material properties, preferably obtained at the nanoscale to accurately present the human knee joint using FE modelling (Yao et al., 2011).

Likewise, there is also significant variation in ligament tensile properties reported in the literature and this could be attributed to a number of factors including the variation in cadaver cohorts, equipment and testing protocol and technique. Experimental procedures for ligament material properties vary between cross-sectional samples (Momersteeg et al., 1995) or bone–ligament–bone samples spanning a variety of age ranges with current data in the literature ranging from 16 to 97 years old (Harner et al., 1995; Quapp & Weiss, 1998; Butler et al., 1992; Robinson, Bull & Amis, 2005; Trent, Walker & Wolf, 1976; Noyes & Grood, 1976; Butler, Kay & Stouffer, 1986; Race & Amis, 1994; Woo et al., 1991; Chandrashekar et al., 2006). Preconditioning, which is often included as a ‘warm up’ for the ligament to achieve load-displacement parameters that are repeatable (Momersteeg et al., 1995) is absent from some research studies (Momersteeg et al., 1995; Noyes & Grood, 1976). Furthermore data varies across individual studies where elastic modulus of the knee ligaments ranges between 1.7 and 447.0 MPa (Quapp & Weiss, 1998; Butler et al., 1992; Noyes & Grood, 1976; Butler, Kay & Stouffer, 1986; Race & Amis, 1994; Chandrashekar et al., 2006) and failure load between 194.0 and 2160.0 N (Harner et al., 1995; Robinson, Bull & Amis, 2005; Trent, Walker & Wolf, 1976; Noyes & Grood, 1976; Race & Amis, 1994; Woo et al., 1991; Chandrashekar et al., 2006). Comparisons between young and old have been correlated for the ACL in two studies (Noyes & Grood, 1976; Woo et al., 1991) both concluding that young donors have a higher stiffness and failure load. However, this is yet to be explored in the PCL, MCL and LCL along with research into how ligament tensile properties are correlated to pathological existence in the form of OA.

FE modelling

Finite elements models have been used for various applications involving the whole knee joint including healthy representation (Peña et al., 2006; Wang, Fan & Zhang, 2014), joint replacement mechanics (Baldwin et al., 2012; Tuncer et al., 2013), meniscectomy research (Tanska, Mononen & Korhonen, 2015), cartilage contact stresses (Li, Lopez & Rubash, 2001; Guo, Zhang & Chen, 2009) and ligament–bone interaction (Blankevoort et al., 1991) to name a few. Material properties used within the reviewed FE models are often sourced from the literature including previous modelling studies or primary experimental research. This typically results in highly variable data sets based on multiple structures and species. The material properties of human tissue vary according to its mineral and protein composition and the orientation of its micro-architecture (Wilusz, Zauscher & Guilak, 2013; Marticke et al., 2010; Temple-Wong et al., 2009). These factors in turn vary with anatomical location (e.g. femur vs humerus; knee vs ankle), age and health of the tissue. Therefore, donor characteristics will significantly impact results. It is clear that current whole joint FE models use material properties with highly variable, or non-specific material properties, with variation in the age, species, location and disease state of the tissue from which material properties were obtained.

When the values used for material properties within published FE models are traced to their original research citation it becomes clear that there is considerable variation in terms of age range. FE models produced by Beillas et al. (2004) and Donlagic et al. (2008) have a total age range across all structures of 16–97 years old. The smallest age range used for material properties within a single study is 43–74 years old (Li, Lopez & Rubash, 2001; Blankevoort & Huiskes, 1991; Blankevoort et al., 1991; Li et al., 1999; Yang et al., 2010), with other ages ranging between 37 and 74 years old (Peña et al., 2005), 33–80 years old (Mootanah et al., 2014), 29–93 years old (Kazemi & Li, 2014), 29–98 years old (Kazemi & Li, 2014; Bendjaballah, Shirazi-Adl & Zukor, 1995; Jilani, Shirazi-Adl & Bendjaballah, 1997; Shirazi, Shirazi-Adl & Hurtig, 2008; Bendjaballah, Shirazi-Adl & Zukor, 1997, 1998; Moglo & Shirazi-Adl, 2003) and 25–98 years old (Wang, Fan & Zhang, 2014). In many FE modelling studies, some information including age of donors from the original sources of material properties could not be traced (Peña et al., 2005, 2006; Wang, Fan & Zhang, 2014; Li, Lopez & Rubash, 2001; Guo, Zhang & Chen, 2009; Mootanah et al., 2014; Kazemi & Li, 2014; Blankevoort & Huiskes, 1991; Blankevoort et al., 1991; Li et al., 1999; Donlagic et al., 2008; Bendjaballah, Shirazi-Adl & Zukor, 1995, 1997, 1998; Jilani, Shirazi-Adl & Bendjaballah, 1997; Shirazi, Shirazi-Adl & Hurtig, 2008; Yang et al., 2010; Moglo & Shirazi-Adl, 2003; Beillas et al., 2004). Where material properties are categorised by age there are considerable differences between cohorts, most noticeably in ligament data (Noyes & Grood, 1976; Woo et al., 1991). In particular Woo et al. (1991) recorded the site of failure in ligaments when loaded in the anatomical location and concluded that in younger donors the ACL will predominantly fail by avulsion and in older donors the ACL will predominantly fail at the mid-substance, due to a change in material properties. This is especially important to factor into FE models if safety factors in the joint are being researched. The effect of using material properties from broad, and in some cases unknown age ranges, impacts on the conclusions of FE modelling is currently unclear because at present no study has compared these models to one constructed using anatomical geometry and material properties for all tissues from the same individual, or a homogeneous age and gender cohort of individuals. Such a model would clearly represent the ‘gold-standard’ with respect to geometry and material property definition in a FE knee model.

As well as wide variation in age, some FE models use material property data based just on tibial plateau cartilage (Kazemi & Li, 2014; Donlagic et al., 2008; Bendjaballah, Shirazi-Adl & Zukor, 1995, 1997, 1998; Jilani, Shirazi-Adl & Bendjaballah, 1997; Shirazi, Shirazi-Adl & Hurtig, 2008; Moglo & Shirazi-Adl, 2003; Beillas et al., 2004) or bone samples lacking any femoral condyle measurements (Wang, Fan & Zhang, 2014). Furthermore, they may be based on non-knee joint anatomical locations including femoral neck and mid femur bone material properties (Donlagic et al., 2008; Beillas et al., 2004) and humeral head for cartilage material properties (Kazemi et al., 2011; Kazemi & Li, 2014). As an example of the magnitude of disparity in material properties between different anatomical locations, Shepherd & Seedhom (1999a) tested the elastic modulus of ankle, knee and hip joint cartilage finding differences of up to 6.8 MPa (36.6%) between ankle and knee cartilage samples from the same donor and 3.6 MPa (30.54%) between knee and hip cartilage samples from the same donor. Indeed, it has been shown that variations in material properties from the same tissue exists within and across the knee joint suggesting that a location dependent modulus for various tissues would be most appropriate for FE models (Behrens, Walker & Shoji, 1974; Deneweth, Arruda & McLean, 2015; Akizuki et al., 1986). Thus, while better than using values from outside the knee joint itself, representing structures with homogeneous (i.e. only one value) properties, or for example, assuming tibial and femoral material properties are identical, may be sub-optimal and functionally important. Ligament material properties are also often replicated where original data is only based on selective ligaments of the knee joint (Wang, Fan & Zhang, 2014; Li, Lopez & Rubash, 2001; Kazemi & Li, 2014; Blankevoort & Huiskes, 1991; Blankevoort et al., 1991; Li et al., 1999; Bendjaballah, Shirazi-Adl & Zukor, 1995, 1997, 1998; Jilani, Shirazi-Adl & Bendjaballah, 1997; Shirazi, Shirazi-Adl & Hurtig, 2008; Yang et al., 2010; Moglo & Shirazi-Adl, 2003). In some instances tendon data is used for the representation of ligament material properties including the quadriceps tendon (Wang, Fan & Zhang, 2014), patella tendon (Wang, Fan & Zhang, 2014; Kazemi et al., 2011; Kazemi & Li, 2014), Achilles tendon (Kazemi et al., 2011; Kazemi & Li, 2014) and rodent tail tendon (Kazemi et al., 2011; Kazemi & Li, 2014).

Animal material property data is also commonly used in the representation of human knee FE models including bovine (Wang, Fan & Zhang, 2014; Mootanah et al., 2014; Shepherd & Seedhom, 1999b; Kazemi & Li, 2014; Donlagic et al., 2008; Beillas et al., 2004; Mononen et al., 2011, 2012), canine (Peña et al., 2005, 2006; Guo, Zhang & Chen, 2009), porcine (Donlagic et al., 2008), rat (Kazemi et al., 2011; Kazemi & Li, 2014) and rabbit (Peña et al., 2007b) data. A number of recent studies have highlighted the structural, mechanical and physiological differences between bovine and human soft tissue and questioned the suitability of bovine material property data for functional studies of humans (Demarteau et al., 2006; Jeffrey & Aspden, 2006; Nissi et al., 2007; Pedersen et al., 2013; Plumb & Aspden, 2005). Athanasiou et al. (1991) explored the differences between material properties of cartilage from the femoral condyle of different species and found variation between the Poisson’s ratio of human (0.074–0.098), canine (0.3–0.372), bovine (0.383–0.396) and rabbit (0.197–0.337) along with aggregate modulus of human (0.588–0.701 MPa), canine (0.603–0.904 MPa), bovine (0.894–0.899 MPa) and rabbit (0.537–0.741 MPa). Although differences were not statistically significant, potentially due to low samples numbers (n = 4–10) there was evidently a difference between species all of which have been used in some of the reviewed FE models. Further, it has also been shown that not only do material properties vary by species but they vary spatially within the same joint. For example, Peters et al. (2017) found differences of up to 10.5 MPa in elastic modulus of cartilage samples taken from different locations within a single canine knee joint. This can indeed have an effect on subsequent FE model behaviour predictions and should be taken into consideration where possible in future studies.

As discussed earlier, it is very common for FE modelling studies to source and reference their material property data from previous modelling studies rather than the original experimental studies in which practical measurements were obtained. However, when the referencing chain is followed through sequentially cited modelling papers it is often the case that the primary experimental source of material property data is untraceable (Yang et al., 2010; Peña et al., 2006). In other instances it eventually becomes clear that material property values are not source for direct experimental measures, but have been derived directly or indirectly from theoretical research in which mathematical solutions for modelling a specific structure have been derived (Mak, Lai & Mow, 1987 cited in Peña et al. (2005, 2006), Li, Lopez & Rubash (2001), Guo, Zhang & Chen (2009)).

Use of varying ages, species and anatomical locations for material property information undoubtedly represent important limitations in current FE models, but the magnitude of error is presently difficult to quantify and probably varies widely across studies due to the highly ‘mixed’ nature of input data used. At present, the best indication of error comes from studies that have conducted sensitivity analyses on material properties. Li, Lopez & Rubash (2001) conducted a sensitivity analysis varying cartilage elastic modulus from 3.5 MPa to 10 MPa and showed that peak contact stresses linearly increased by up to 10%, whilst an increase in Poisson’s ratio significantly varied peak von Mises stress by 100% in the knee joint cartilage. Additionally, a more sophisticated sensitivity analysis was carried out by Dhaher, Kwon & Barry (2010) who adjusted the intrinsic material properties of knee joint ligaments to aid understanding of the functional consequences of different activity levels, age, gender and even species. The research measured simulation outcomes by incorporating a multi-factorial global assessment, which indicated a change in tibial–femoral internal and external rotation, patella tilt and patella peak contact stresses, associated with modified ligament material properties (Dhaher, Kwon & Barry, 2010).

This review of published material property (Section A—Material Properties) and FE modelling (Section B: FE Modelling, above) studies of the human knee raises the question of how well specific cohorts or even human demographics can currently be accurately represented in a FE model. For example, does sufficient material property data exist to construct a whole-knee joint FE model representative of a young, healthy human or to represent a knee of any age with a specific category of OA? Attempting to build an FE model of a healthy knee joint from the literature data tabulated in ‘Section A—Material Properties’ (Tables 1–3) yields data for healthy femoral and tibial cartilage, although without the breakdown of age specific material properties; healthy tibial cortical bone from older donors; healthy ACL, PCL, MCL and LCL from young donors, and ACL, PCL and MCL from healthy older donors. Thus, ‘healthy’ material properties can be pieced together from different studies for most tissues but mixing gender and a considerable age range (16–97 years old) is necessary. In terms of a model for studying OA, data exists for cartilage material properties based on OA grades 1–3 although this is not broken down into age categories, whilst trabecular bone material properties do exist for OA grades 1–3 for older donors although challenges occur as no healthy control was used within this particular study as a baseline measurement. Further no study has yet explored the effect of OA on cortical bone material properties in the human knee. There is currently no data incorporating the effect of OA on ligament material properties despite it being well known that there is a relationship between OA and ligament injury (Mullaji et al., 2008; Cushner et al., 2003). However, there are currently no research papers to the authors’ knowledge that have collected primary data on bone and cartilage material properties and used these measurements to build a subject specific FE model. Hence, material properties are still collated from various sources within the literature. A key goal for future research should be adoption of a more subject specific approach in which material properties from all tissues are derived from homogenous donor cohorts to improve accuracy and precision of knee FE models.