The potential role of variations in juvenile hip geometry on the development of Legg-Calvé-Perthes disease: a biomechanical investigation

Abstract Legg-Calvé-Perthes disease (LCP) is one of the most poorly understood diseases in paediatric orthopaedics. One common trait of LCP is the marked morphological difference between healthy and pathological hips, early deviations of which (i.e. prior to disease onset) have been suggested to lead to the overload and collapse of the epiphysis. Here, the impact of common variations in geometry is investigated with a finite element model of a juvenile femur under single leg standing and landing. Here, the impact of typical variations in geometry is investigated with a finite element model of a juvenile femur under single leg standing and landing. The variations appear to have only a limited effect on the stress distribution in the femoral epiphysis even during high impact activities. This suggests that, for this individual at least, they would be unlikely to cause epiphyseal overload and collapse, even in the presence of a skeletally immature epiphysis.


Introduction
) is commonly referred to as avascular necrosis of the femoral epiphysis, and is characterized by collapse and flattening of the femoral head. The disease was described more than 100 years ago by four studies carried out by Calvé (1910); Legg (1910); Perthes (1910); Waldenström (1909). However, LCP remains one of the most poorly understood disorders in paediatric orthopaedics, and the underlying mechanisms that lead to the morphological changes in the pathological hip are yet unknown.
Clinical observations showed that LCP develops in four stages, namely: osteonecrosis, fragmentation, reossification and healing, and the inability to recover the spherical shape during the re-ossification phase can lead to a permanent flattening of the femoral head, which may ultimately result in early osteoarthritis (Kim and Herring 2013). Early detection of the disease is fundamental in preventing this irreversible change in hip geometry, and to allow normal development thereafter. There is a general consensus about the ischaemic nature of LCP (Kim and Herring 2013), however the nature of the vascular insult is still unknown (Berthaume et al. 2016).
One of the most plausible triggers of the disease is the altered biomechanics differences observed between the healthy and pathological hip. The morphological variations include lateral displacement of the femoral head, widening of the joint space, broadening and shortening of the femoral neck, widening and reduction of the acetabular depth, and flattening and subluxation of the femoral head. For instance, Pienkowski et al. (2009) observed a statistically significant difference between the femoral head size and acetabular radius in children (average age 8.2 years) with unilateral LCP, with the affected hips having greater femoral head size and acetabular radius, with the radius ratio between femoral head and acetabulum being smaller than in normal hips. The average centre-to-centre distance was also significantly higher in LCP (of 3.0 ± 1.3 (SD) mm) when compared with 1.2 ± 0.5 height of 30.0 cm the GRF is reported to be 2.94BW while the KJR can reach 8.13BW (Mokhtarzadeh et al. 2013). The muscle forces necessary to balance these external forces applied were computed using a non-linear static free-body diagram (FBD) optimization code developed in MATLAB R2014a (MathWorks, Massachusetts, USA). In the FBD protocol, all muscles were modelled as single lines of action connecting the centres of the origin and insertion areas of the muscles derived from the literature (Schünke et al. 2010). The physiological cross-section areas (PCSA) of each muscle were obtained from Handsfield et al. (2014), Pierrynowski (1982), and scaled taking into account a target body weight of 23.0 kg (Lappin et al. 2003). To compute the maximum achievable force for each muscle (F i max ) a specific tension of 133 N∕cm 2 was considered (Lieber and Burkholder 2007), with FBD optimization applied to minimize muscle activation according to (Modenese et al. 2011): subject to: SD) mm in the normal side. In addition, Huhnstock et al. (2014) analysed the changes in the acetabulum in children with unilateral LCP and observed that during the first year after the diagnosis. The acetabular depth-to-width ratio (ADR) decreased when compared with the normal hip, due to a decrease in depth of 10% and an increase in width of 10%. However, whether these differences are a cause or a consequence of the disease is still unclear. In addition, retardation of bone growth in the appendicular skeleton is also very common in LCP patients, typically of 1 to 2 years (Kim and Herring 2013). Berthaume et al. (2016) proposed five hypotheses describing how Perthes' disease might develop through either epiphyseal vessel obstruction or femoral head overload arising from altered biomechanics. In this current paper, the possibility of the onset of LCP due to epiphyseal overload as a direct consequence of the morphological changes in the hip is investigated. To achieve this, typical morphological variations observed in the pathological hip are incorporated in the finite element model of a heathy 7.9-year-old male. Their impact is then investigated by comparing the mechanical loading observed in the normal and modified hips, in particular whether these changes are sufficient to cause the collapse of the femoral epiphysis.

Materials and methods
A 3D FE model of a healthy male subject 7.9-years-old was created from computed tomography (CT) image data, with image segmentation carried out according to the protocol in (Pinheiro and Alves 2015). The hip is characterized by an acetabular radius of 21.5 mm femoral head radius 15.2 mm, angle of Wiberg of 23.5°, and a centre-to-centre distance of approximately 0.5 mm, (which shows that it falls within the normal range of geometry for a child of that age (Szuper et al. 2015;Than et al. 2004). The pelvis and femurs were initially positioned in an upright position by computing the geometrical centres of the hip, knee and ankle along the same vertical line, both in the coronal and sagittal plane. The mechanical axis of the leg was then rotated to a single-leg stance position. Since the ankle data was not available, anthropometric relations between femur and tibia (Irving 2016) were used to estimate and positon the joint in the midline of the body (Figure 1(a)).

Free-body diagram optimization
Two loading conditions were considered, namely standing on one-leg and single-leg landing (for example from jumping). For the single-leg stance position considered here, the knee reaction force (KJR) and ground reaction force (GRF) were both assumed to be equal to the body weight (BW), whereas for single-leg drop landing from a where m is the number of muscles considered, F i max is the maximum force that muscle i can generate, ⃗ r ij is the moment arm of ith muscle and M j is the moment acting around the jth axis (Modenese et al. 2011), and n = 2 to minimize the overall muscle activation (Kaufman et al. 1991). The 24 main muscles acting around the hip were represented individually, with the exception of the iliotibial band and the adductor minimus, which were combined with other muscle groups because of their parallel action with them (Figure 1(a)).

Finite element model
The key anatomical structures of the normal, healthy juvenile hip considered in the FE models are shown in the cutaway view in Figure 1(b). Since the different cartilage layers weren't visible on the CT scan, the cartilage of the femoral head was defined by offsetting the epiphyseal surface by 2.0 mm, thereby matching the cartilage thickness reported in (Castriota-Scanderbeg and De 1995) for a child of that age. The remainder of the cartilage volume was defined as acetabular cartilage. The basic model was then modified to simulate some of the reported morphological variations observed in LCP hips. In particular, hip joint incongruity was considered through medial and lateral displacement of the femoral head by ± 3.0 mm (Pienkowski et al. 2009), and a decrease in acetabular depth of 10% (1.7 mm) and an increase in acetabular opening of 10% (2.0 mm) were examined (Huhnstock et al. 2014). Skeletal immaturity was simulated by uniformly offsetting the boundary of the epiphysis by approximately 2.30 mm throughout, which corresponds to skeletal immaturity of approximately 2.0 years (Kitoh et al. 2003). The outlines of the different geometries are shown schematically in Figure 1(c).
Muscle forces were applied to the centroid of the muscle insertion areas, whereas KJR was applied to the geometrical centre of the knee. Symmetry was assumed along the sagittal plane, and therefore only half the pelvis and one femur were modelled in the FE analyses. The models were meshed with quadratic tetrahedral elements for solution in ANSYS v 15.0.7 (ANSYS, Inc., Canonsburg, USA). The mesh was generated with a specified minimum edge length of 0.5 mm using the FE mesher vcat2tets (Labelle and Shewchuk 2007), and model convergence was checked and confirmed with approximately 3.0 million elements (not reported here). All materials were modelled as linear elastic, isotropic and homogeneous, with mechanical properties summarized in Table 1. Fixed boundary conditions were applied to the surface of the sacroiliac joint with symmetry boundary conditions applied to the pubic joint ensuring the pelvis was not over-constrained. Additional constraints were added to the medial and lateral condyles of the knee to avoid medio-lateral displacements arising from rounding errors and inconsistencies in force mapping from the FBD to the FE model (Figure 1(a)). To quantify the amount of epiphyseal volume at risk of collapse the work of Hambli (2013) is considered, where, for the trabecular bone elastic modulus of 1500 MPa considered in this work (Table 1, BV ∕TV = 28.2% (Yang et al. 1999), the ultimate compressive stress is estimated to be approximately 20.8 MPa (Hambli 2013). Table 2 compares the forces predicted in the 8 muscles with the largest muscle activation values for the different model variations. The main muscle activations were observed in the gluteus medius and minumus, tensor fascia, rectus femoris and psoas. Moving the femoral head from a medial position to a more lateral position increases all muscle activities with the exception of the rectus femoris which decreases slightly. The changes in muscle activation due to the change in the geometry of the acetabular roof are minimal compared to the reference model (hence are not included). In single-leg landing, there is a significant increase in muscle recruitment, especially in the gluteus medius, tensor fascia and psoas muscle ( Table 2). The hip joint reaction (HJR) force is generally insensitive to model variation, and changes only slightly with femoral head whereas lateral displacement increases it throughout the femoral epiphysis (Figure 2(c)). Little change is observed when the depth and width of the acetabulum were changed (Figure 2(d)-(e)). For the skeletally immature epiphysis, a maximum von Mises stress of approximately 9.0 MPa was observed at the lower edge of the epiphysis (Figure 2(f)).

Muscle activation and hip reaction force
In Figure 3 the von Mises stress through the femoral epiphysis during landing are shown. Again, skeletal immaturity and the lateral displacement lead to an increase of position (Table 3). For example, there is a 3.57% decrease for 3.0 mm medial displacement of the femoral head and a 2.68% increase for an equivalent lateral displacement. Conversely, jumping and landing on one-leg increases the HJR force by a factor of 5.6, when compared with the reference single-leg stance model. Figure 2 shows the distribution of von Mises stress through the femoral head for all the morphological changes considered. In the reference model (Figure 2(a)), the peak von Mises stress is found to be 4.0 MPa at the lower edge of the epiphysis. Medial displacement of the femoral head decreases the stress in the trabecular bone (Figure 2(b)),

Discussion
A 3D FE model was developed to investigate the biomechanical implications of the main morphological changes observed in LCP disease. The biomechanical changes across the femoral epiphysis were assessed by comparing the stresses predicted in the healthy juvenile hip model with the morphologically altered models (Figure 1(c)). A 3D musculoskeletal model of a 7.9-years-old male was developed, considering 24 muscles of the thigh. FBD optimization was employed to determine the muscle activations and HJR forces for standing and drop landing in one-leg.
There are several simplifications in the model which need further comment. Firstly, all materials were modelled as homogeneous and linear elastic, but both bone and cartilage are known to exhibit non-isotropic behaviour (Cohen et al. 1998). For the bone, subtle site-specific variations in material properties based on CT grey scale values could have been included in the reference model, but then an assumption would have had to be made regarding the distribution of property values in the skeletally immature version. Rather than detecting those differences and generally confounding the effects of the geometry variations, it was therefore decided that it would be better to use uniform property values derived from juvenile subjects (Ohman et al. 2011). Similarly, individual-specific cartilage properties were unknown, and again to avoid the confounding effect of using arbitrary values, the use of a constant value was again considered to be most appropriate in this study, especially when differences rather than absolute values are of primary interest.
Information regarding HJR forces acting in the juvenile hip is extremely scarce. Heimkes et al. (1993) developed a 2D model of the hip and simulated a single-leg stance, whereas Carriero et al. (2012) performed 3D gait study of healthy children with ages between 6 and 12 years old. Similar HJR forces were obtained in both studies (3.10BW and 3.05BW, respectively), while in the current study a HJR of 3.34 ± 0.02BW was predicted for a one-legged stance. These values compare well with the juvenile values, but interestingly are all higher than the data recorded for adults for both walking and standing on one leg (of typically 2.38BW (Bergmann et al. 1993)).
In single-leg landing the HJR force in this juvenile model was predicted to be 19.07 ± 0.70BW. Under extreme conditions joint reaction forces in adults may also reach high values. For example, peak GRF and KJR forces up to 10BW have been measured during jumping exercises (McNair and Prapavessis 1999) and plyometric training (Jensen 2005), whereas HJR forces of 10BW were recorded during stumbling (Bergmann et al. 2004) and values up to 15BW during vigorous exercise are documented in the the stress in the ossified epiphysis, when compared to the reference (Figure 3(b)-(c)). For the skeletally immature epiphysis the percentage of volume above the failure limit of 20.8 MPa is approximately 10.0% of the ossified volume, whereas for the laterally displaced version, only 2.0% of the ossified volume is above the critical value.
The relative effects of the geometry variants are summarized in the difference plots between the reference (normal) and customised models (Figure 4(a)-(e)). Positive values indicate higher stresses in the reference model (i.e. a model variation model leads to lower stresses), whereas negative values correspond to higher stresses in a model variation. Only subtle differences were observed between the normal hip and the pathological hips. The highest differences are clearly observed in the superior aspect of the epiphyseal cartilage. The stress values in the lateral surface of the epiphysis remained mostly unchanged in all cases ( Figure 4). Only slight variations (smaller than ± 1.0 MPa) in the equivalent stress were observed in the femoral head for standing in one-leg (Figure 4  . difference plots for the equivalent von mises stresses (mpa) for standing on one leg between the reference and (a) the 3.0 mm medial displacement model, (b) the 3.0 mm lateral displacement, and for landing on one leg between the reference and (c) the 3.0 mm medial displacement, (d) the 3.0 mm lateral displacement (positive differences correspond to higher stresses in the reference model, while negative differences correspond to higher stresses in the altered model).

Manuel da Silva Pinheiro
http://orcid.org/0000-0001-8234-6790 literature (Loudon et al. 2013). The differences are again interesting, but there is no reason to expect similar HJR values in juveniles and adults when differences in the relative dimensions of juvenile and adult hips and BWs are considered.
For the individual considered in this current study, the results show that the morphological changes considered in this analysis have a limited impact on the stress distribution in the femoral epiphysis (Figure 2). Although individual components are affected differently (the horizontal component increases by approximately 30% through just 3.0 mm of lateral displacement (Table 3)), the overall HJR increases by less than 3%. The loading of the femoral head is therefore clearly modified, but he overall effect appears to be insufficient to cause failure directly. With the rather extreme case of single-leg landing, the stress levels do show an increase due to the significant increase in load, and when combined with a skeletally immature epiphysis, approximately 10% of the epiphysis may experience a stress above the estimated ultimate stress (Figure 3). However, Nishii et al. (2002) and Lieberman et al. (2012) observed that tissue necrosis should account for approximately 30% of the adult femoral head volume to cause epiphyseal collapse. Although not directly comparable, this value provides an indication of the extent of epiphyseal compromise necessary for the failure of the femoral head.
The results suggest that morphological changes have a limited impact in the stress across the epiphysis ( Figure  4), and that even a skeletally immature epiphysis does not seem to be overload even in drop-landing. Similarly, because such a small proportion of the epiphysis is overloaded, the results do not provide significant evidence to support the alternative sequence of events that lead to Perthes' proposed by Berthaume et al. (2016), (hypothesis H3), where the overload of the immature epiphysis leads to failure, vascular occlusion and the development of LCP. Additional investigations need to be conducted to further confirm these results, especially with younger patients, since the initial trigger for the disease may occur at a younger age. A more advanced FE model incorporating the main epiphyseal arteries may also be an invaluable tool to evaluate the likelihood of vessel damage or obstruction as they travel up to and through the articular cartilage.

Disclosure statement
No potential conflict of interest was reported by the author.

Funding
This work was supported by The Henry Smith Charity and Action Medical Research [grant number GN2076].