Finite element analysis of mechanical behavior of human dysplastic hip joints: a systematic review

Osteoarthritis and Cartilage xxx (2016) 1e10

Review

Finite element analysis of mechanical behavior of human dysplastic hip joints: a systematic review B. Vafaeian y, D. Zonoobi z, M. Mabee z, A.R. Hareendranathan z, M. El-Rich y x, S. Adeeb y a, J.L. Jaremko z * y Department of Civil and Environmental Engineering, University of Alberta, 7-203 Donadeo Innovation Centre for Engineering, 9211-116 Street, Edmonton, Alberta, T6G 1H9, Canada z Department of Radiology and Diagnostic Imaging, University of Alberta, 2A2.41 WMC, 8440-112 Street, Edmonton, Alberta, T6G 2B7, Canada x Department of Mechanical Engineering at Khalifa University (UAE), United Arab Emirates

a r t i c l e i n f o

s u m m a r y

Article history: Received 8 April 2016 Accepted 28 October 2016

Developmental dysplasia of the hip (DDH) is a common condition predisposing to osteoarthritis (OA). Especially since DDH is best identified and treated in infancy before bones ossify, there is surprisingly a near-complete absence of literature examining mechanical behavior of infant dysplastic hips. We sought to identify current practice in finite element modeling (FEM) of DDH, to inform future modeling of infant dysplastic hips. We performed multi-database systematic review using PRISMA criteria. Abstracts (n ¼ 126) fulfilling inclusion criteria were screened for methodological quality, and results were analyzed and summarized for eligible articles (n ¼ 12). The majority of the studies modeled human adult dysplastic hips. Two studies focused on etiology of DDH through simulating mechanobiological growth of prenatal hips; we found no FEM-based studies in infants or children. Finite element models used either patient-specific geometry or idealized average geometry. Diversities in choice of material properties, boundary conditions, and loading scenarios were found in the finite-element models. FEM of adult dysplastic hips demonstrated generally smaller cartilage contact area in dysplastic hips than in normal joints. Contact pressure (CP) may be higher or lower in dysplastic hips depending on joint geometry and mechanical contribution of labrum (Lb). FEM of mechanobiological growth of prenatal hip joints revealed evidence for effects of the joint mechanical environment on formation of coxa valga, asymmetrically shallow acetabulum and malformed femoral head associated with DDH. Future modeling informed by the results of this review may yield valuable insights into optimal treatment of DDH, and into how and why OA develops early in DDH. © 2016 Osteoarthritis Research Society International. Published by Elsevier Ltd. All rights reserved.

Keywords: Human dysplastic hip Finite element modeling Infant hip dysplasia Systematic review

Introduction Developmental dysplasia of the hip (DDH) is a common anatomic deformity leading to hip dysfunction and osteoarthritis (OA). Present in 1e3/1000 live births1, DDH accounts for one-third of hip replacement surgeries in patients under 60 years old2. Untreated dysplastic hips are associated with mechanical instability, limited mobility, muscle imbalance, abnormal joint load, increased * Address correspondence and reprint requests to: J.L. Jaremko, Department of Radiology and Diagnostic Imaging, University of Alberta, 2A2.41 WMC, 8440-112 Street, Edmonton, Alberta, T6G 2B7, Canada. Fax: 1-780-4073853. E-mail addresses: [email protected] (B. Vafaeian), [email protected] (D. Zonoobi), [email protected] (M. Mabee), [email protected] (A.R. Hareendranathan), [email protected] (M. El-Rich), [email protected] (S. Adeeb), [email protected] (J.L. Jaremko). a Website: http://sameradeeb.srv.ualberta.ca.

cartilage contact pressure (CP), subluxation3e5, and OA3,5e7. In addition to age, trauma, activity, weight, and genetics, OA in DDH relates to anatomic hip abnormalities5e7. Since the mechanical environment strongly affects bone growth and development6,8e13, understanding hip mechanical behavior can provide insight into how premature OA occurs6,7,14, and help optimize treatment10,15e18. Hip mechanical behavior has been studied through experimental measurements, theoretical models, and computational methods including multibody dynamics (MBD), discrete element analysis (DEA), and finite element modeling (FEM)19e21. Experimental studies14,22e27 measure hip CP directly using sensors, but these are invasive and it is difficult to maintain physiological conditions during measurement20,21. Theoretical models6,14,28e33 estimate articular surface CP with fundamental methodological simplifications limiting their predictive validity20,34. MBD35,36 can

http://dx.doi.org/10.1016/j.joca.2016.10.023 1063-4584/© 2016 Osteoarthritis Research Society International. Published by Elsevier Ltd. All rights reserved.

Please cite this article in press as: Vafaeian B, et al., Finite element analysis of mechanical behavior of human dysplastic hip joints: a systematic review, Osteoarthritis and Cartilage (2016), http://dx.doi.org/10.1016/j.joca.2016.10.023

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only estimate joint reaction force (JRF), not CP. DEA34,37e41 and FEM19,20 are both capable of simulating articular surface CP, contact area, and JRF. Although more computationally intensive, FEM can also model the sliding contact mechanism inside the hip joint, cartilage deformations in all directions, bone deformations, material anisotropy, and stresses inside tissue layers19,20. Mechanical behavior of adult normal hips has been well studied through FEM, with generally good agreement with experimental outcomes19e21,27. In contrast, FEM-based studies on dysplastic hips have not been specifically reviewed. A dedicated review on this complex topic can clarify the diverse methods in use to study DDH from prenatal initiation to adult morbidity. Notably we could find no published FEM of infant (post-birth) dysplastic hips. Since the most important time to diagnose and treat DDH to prevent OA is in infancy, this is an important gap in the literature. The objective of this systematic review was to determine the state-of-the-art in FEM of human dysplastic hips, with a view to making informed recommendations for future FEM of infant dysplastic hips. Materials and methods Search strategy We performed a systematic review, searching PubMed, Medline and Elsevier (ScienceDirect) for relevant peer-reviewed articles with English-language abstracts published from 1946 to June 25th, 2016 based on these keywords: (“dysplasia” OR “hip dysplasia” OR “dysplastic hip”) AND (“finite element” OR “computational” OR “computer simulation” OR “mechanics”). Reference lists of relevant publications were also reviewed to avoid missing relevant articles. Selection criteria Titles and abstracts of all potentially relevant articles were reviewed. Article selection was performed by an engineer/research associate (BV) and confirmed in consensus with a radiologist/ biomedical engineer (JJ). Full-text articles were included when they (1) demonstrated mechanical behavior of the human dysplastic hip through FEM of full or partial three-dimensional (3D) geometries of natural and/or post-acetabular-osteotomy dysplastic hip joints; and/or (2) employed FEM to study formation of human dysplastic hip morphology. We excluded articles related to total hip arthroplasty, and those in which hip mechanics were investigated by methods other than FEM, i.e., theoretical models, MBD, and DEA. However, noting that the closest alternative to FEM is DEA and to capture merits of DEA in this area, we included a brief review on applications of DEA for studying human dysplastic hips at the end of this paper. To better understand potential biases, we stratified studies by data source (patient-specific or virtual) and structures modeled. The summary measures reviewed were differences in model outputs between normal and dysplastic hips. Results We found 76 unique articles. 29 merited full-text review, and 12 met eligibility criteria (Fig. 1). The included studies, published between 2004 and 2016, fell into three groups. The first group42e46 compared mechanical behavior of dysplastic vs normal hips (Tables IeIII). The second group compared the behavior of dysplastic hips before and after physical16 or virtual15,17,46e48 acetabular osteotomy (Tables IeIII). The third group8,11 investigated DDH etiology by mechanobiological prediction of patterns of prenatal hip growth (Table IV). When an article also included FEM of joints with other pathology

Fig. 1. Study selection flow chart.

(protrusio, femoroacetabular impingement44,46), we focused on the results obtained in dysplastic hips. All studies contained FEM of either adult hips or simplified prenatal hips. We found no studies regarding post-birth pediatric hips. Discussion The following sections summarize methods and results from the reviewed studies modeling dysplastic hips. Geometry Hip FEM requires computational geometries for the pelvis and proximal femur (PF), from either (1) patient-specific volumetric data, usually from computed tomography (CT) scan, or (2) idealized computer-aided design (CAD) models (Table I). Patient-specific CT data for both normal and dysplastic hips were employed in several studies42,43,45. Others had only access to either normal17 or dysplastic15,47,48 patient-specific CT data and generated models of dysplastic or close-to-normal hips by deforming the acetabular rim or changing morphological parameters of the acetabulum through virtual osteotomy. One study employed patient-specific CT data of dysplastic hips pre- and post-osteotomy16. CT-based models demonstrate bony anatomy well, but generating accurate geometries of soft tissues (cartilage and ligaments) is difficult since these structures are poorly seen on CT images. Some studies42,43,45,48 used CT arthrography (CTA), which is invasive but clearly demonstrates articular cartilage (AC) boundaries, to directly model cartilage thickness (0.5e2.8 mm45, 0.8e2.0 mm42,43). Non-

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Table I Subjects and FEM specifications of adult hip joints Study

Simulated hips

FEM

Normal Dysplastic Other

Geometry

Parts

Bone material

PB PF AC Lb CL Cortical (ILE)

Soft tissue material Cancellous (ILE) AC

11

N

Patient-specific (CTA) Y

Y Y

1

3*

3 VPPAO

Patient-specific (CT)

Y

Y Y

Henak (2011)43

1

1

N

Patient-specific (CTA) Y

Y Y

N N E ¼ 2 GPa, n ¼ 0.3 E ¼ 120 MPa, (Subchondral bone) n ¼ 0.3 Y N E ¼ 17 GPa, n ¼ 0.3 E ¼ 70 MPa, n ¼ 0.2 Y N E ¼ 17 GPa, n ¼ 0.29 NA

Zou (2013)15

N

5

24 VPPAO Patient-specific (CT)

Y

Y Y

N Y

10

10

N

Patient-specific (CTA) Y

Y Y

Y

Ike (2015)16

N

13

13 PRAO

Patient-specific (CT)

Y

Y Y

Liu (2015)

47

N

4

4 VPPAO

Patient-specific (CT)

Y

Y Y

N N E: CT density-based values, n ¼ 0.4 N N E ¼ 17 GPa, n ¼ 0.3 NA

Liu (2016)

48

N

10z

40z VPPAO Patient-specific (CTA) Y

Y Y

N N E ¼ 17 GPa, n ¼ 0.3

Chegini (2009)44 4

4

NA

CAD-based

Yx Y Y

Y

N Rigid

Liechti (2015)46 1

1

NA

CAD-based

Yx Y Y

Y

N Rigid

Russell (2006)45 1 Zhao (2010)

17

Henak (2014)

42

E ¼ 17 GPa, n ¼ 0.3

E ¼ 70 MPa, n ¼ 0.2 N E ¼ 17 GPa, n ¼ 0.29 NA

NA

Lb

ILE (E ¼ 12 MPa, n ¼ 0.42) ILE (E ¼ 15 MPa, n ¼ 0.45) Neo-Hookean IHE (K ¼ 1359 MPa, G ¼ 13.6 MPa) ILE (E ¼ 15 MPa, n ¼ 0.45) Neo-Hookean IHE (K ¼ 1359 MPa, G ¼ 13.6 MPa) ILE (E ¼ 10.35 MPa, n ¼ 0.4) ILE (E ¼ 15 MPa, n ¼ 0.45) ILE (E ¼ 15 MPa, n ¼ 0.45) ILE (E ¼ 12 MPa, n ¼ 0.45) ILE (E ¼ 12 MPa, n ¼ 0.45)

NA ILE (E ¼ 15 MPa, n ¼ 0.45) Transversely IHEy

NA Transversely IHEy

NA NA NA ILE (E ¼ 20 MPa, n ¼ 0.4) ILE (E ¼ 20 MPa, n ¼ 0.4)

Y: Yes, N: No, NA: not applicable, VPPAO: virtual post-periacetabular osteotomy, PRAO: post-rotational acetabular osteotomy, K: bulk modulus, G: shear modulus. * Dysplastic hip models were generated by deforming the acetabular rim of the normal hip model. y See ref. 43 for details. z The models (10 dysplastic and 40 VPPAO) were replicated but with constant cartilage thicknesses instead of the patient-specific cartilage thicknesses. x Includes only the acetabular cup.

Table II Analysis conditions and finite element analysis specifications of adult hip joints Study

Analysis conditions (subjects' body weight)

Finite element analysis Loading method

Fixed boundary conditions

Joint contact

Direct output

Software

Russell (2006)45

Gait (51e90 kgf) One leg stance (74 kgf)

JRF at femoral head centroid

Medial pelvic wall

Y

CP and areay,z

ABAQUS

Vertical load on superior aspect of sacrum Abductor force JRF by displacement control technique

Distal end of PF

Y

JRF Von-Mises stressy,z,x

MSC.Marc

Pubis and the Sacro-iliac joints Distal end of PF*

Y

CP and areay,x Lb load support Deflection of the Lb

NIKE3D

JRF on pelvic bone

Distal end of PF

Y

ABAQUS

JRF by displacement control technique

Pubis and the Sacro-iliac joints Distal end of PF*

Y

CP and areay Von-Mises stressy CP and areay,x Lb load support

Vertical load on superior aspect of sacrum JRF at femoral head centroid

Distal end of PF

N

Von-Mises stressy

ANSYS

Y

CP and areay

ABAQUS

Y

CP and areay

ABAQUS

JRF at femoral head centroid

Pubis and top surface of pelvis Distal end of PF* Pubis and top surface of pelvis Distal end of PF* Acetabulum

Y

CPy,x Von-Mises stressy

ABAQUS

JRF at femoral head centroid

Acetabulum

Y

CPy Von-Mises stressy

ABAQUS

Zhao (2010)17

Henak (2011)43

Zou (2013)15 Henak (2014)

42

Ike (2015)16 Liu (2015)

47

Liu (2016)48 Chegini (2009)44

Liechti (2015)46

* y z x

Gait (heel strike and midstance) Stair descent and ascent (heel strike) (Female: 66 kgf; Male: 87 kgf) One leg stance (70 kgf) Gait (heel strike and midstance) Stair descent and ascent (heel strike) (70 ± 13.9 kgf) Nonphysiological load (Load: 183.5 kgf) One leg stance (66.3 kgf) One leg stance (66.3 kgf) Gait Stance to sit (85 kgf) Gait Stance to sit (71.5 kgf)

JRF at femoral head centroid

NIKE3D

Fixed or limited displacement only in lateral-medial and anterior-posterior directions. Acetabular cartilage. Femoral cartilage. Lb.

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Table III Simulation results of adult hip joints Study

Significant findings

Significant model outputs Circumstances

Output

Normal

Dysplastic

Ratio*

Russell (2006)45

Gait

Peak CP (MPa) Contact area (mm2)

1.8 2265

3.6e9.9 215

2.0e5.7 0.1

Zhao (2010)17

One-leg stance

Peak svon (MPa)

15.2

22.7e30.7

1.5e2.0

Henak (2011)43

Gait Stair descent Stair ascent

Peak CP (MPa) Average CP (MPa) Contact area (mm2) Lb load support

6e14 1.1e1.3 680e800 1e2%

6e14 0.5e1.2 350e440 4e11%

NR 0.4e1.2 0.4e0.7 2e11

Zou (2013)15

One-leg stance

Average CP (MPa) Contact Area (mm2) Average svon (MPa)

3.59e6.07y 319e531y 1.4e2.2y

3.9e6.2 304e492 1.5e2.4

1.0e1.1 0.9e1.0 1.0e1.1

Henak (2014)42

Gait Stair descent Stair ascent

Peak CP (MPa) Average CP (MPa) Lb load support

5.0e15.0 0.5e1.9 2.6e3.3%

2.5e16.2 0.1e2.1 8.2e10.3%

0.5e1.1 0.2e1.3 2.8e4.0

Ike (2015)16

Non-physiological

Peak svon (MPa)

1.7e4.0y

1.2e6.5

0.7e1.8

Liu (2015)47

One-leg stance

Peak CP (MPa) Contact Area (mm2)

3.8e6.3y 834e1497y

5.5e18.9 503e1005

1.5e3.6 0.5e0.7

Liu (2016)48

One-leg stance

Peak CP (MPa) Contact Area (mm2)

4.5e10y 480e1198y

5.5e15 425e1166

1.1e2.9 0.6e1.0

Chegini (2009)44

Gait Stance to sit

Peak CP (MPa) Peak CP (MPa)

2.4e3.4 3.3e3.7

6.1e9.9 3.5e3.6

1.8e4.1 0.9e1.1

Liechti (2015)46

Gait

Peak Peak Peak Peak

1.4 0.7 1.3 0.8

2.0 1.4 1.5 1.0

1.4 2.0 1.2 1.3

Stance to sit

CP (MPa) svon (MPa) CP (MPa) svon (MPa)

Bone irregularities in dysplastic hip models led to localized elevated cartilage CP. In dysplastic hip models, peak CP was not coincident with maximum JRF during gait cycles as a consequence of incongruous surfaces of dysplastic hips. Decrease in CE and vertical centre anterior (VCA) angles (from 25 to 10 ) of the simulated hips led to increase in the cartilage stress and altered the uniform stress distribution of the normal joint to stress concentration in the acetabular edge in the dysplastic joint models.. Due to shallow acetabulum in the dysplastic hip model, the Lb significantly contributed to the joint stability (lateral stability in particular) and load transfer in the dysplastic hip model in comparison with the normal hip model. Consequently, cartilage CP did not substantially increase in the dysplastic hip model. Average cartilage stresses (pressure and von-Mises) and contact area were not linearly and monotonically correlated with CE angle (10 e45 ). However, patient-specific optimal CE angles minimizing the cartilage stresses and maximizing the contact areas were found for the dysplastic hip models. The load supported by the Lb (especially on the lateral side) was significantly higher in the dysplastic hip models than in normal hip models. CPs in the dysplastic hip models were not elevated compared with the normal hip models because the Lb provided additional contact surface in the dysplastic hip models. Moderate correlations between von Mises stress in the joint and morphological parameters, CE angle (R ¼ 0.65), acetabular head index (R ¼ 0.60), acetabular angle (R ¼ 0.48), and acetabular roof angle (R ¼ 0.57), were observed. Acetabular inclination and version, femoral head coverage ratio and CE angle were morphological parameters engaged in the status of CP and area of normal and dysplastic hips. Peak CP and contact area predicted by models using constant thickness cartilage respectively had moderate (R ¼ 0.63) and strong (R ¼ 0.87) correlations with their corresponding values resulted from models employing varying-thickness cartilage obtained from patient-specific data. An optimal range of CE angle minimizing the peak CP and maximizing the contact area was found to be 23.5 e38.9 . Activities with high load (gait) rather than with large range of motion (stance to sit) led to higher pressure and von Mises stress in the dysplastic hip models. An optimal range of CE angle to minimize the CP and von Mises stress was found to be 20 e30 . During gait, the area of peak CP in the normal hip model was centered in the acetabular roof whereas this area shifted towards the lateral face of the acetabular cartilage in the dysplastic hip model. During stance to sit, the area of peak CP in both the normal and the dysplastic hip models was located on the posterior aspect of the lunate surface.

svon: Von-Mises stress in cartilage or the underneath cortical shell, NR: not reported, VCA: vertical center-anterior margin. *

y

Ratio of the simulated values corresponding with dysplastic hips to those of normal hips. The models of VPPAO and PRAO leading to minimized CP and maximized contact area are listed as normal hips.

arthrographic studies15e17,47,48 assumed constant AC thickness (1.8e2 mm), simplifying FEM. However, Anderson et al.49 demonstrated that use of constant-thickness cartilage in normal hip FEM overestimated cartilage CP and underestimated contact areas. In dysplastic hips, Liu et al.48 found 21 ± 19% and 17 ± 14% error in simulated CP and area respectively when replacing patient-specific cartilage thickness with a constant-thickness cartilage layer. Therefore, utilizing patient-specific cartilage thickness likely enhances simulation accuracy49; especially in dysplastic hips in which cartilage thickness is greater and more variable than in normal hips50. The cartilage-labrum (Lb) boundary is usually not visible even in arthrograms. Studies either determine this based on morphology and reader judgment17,42,43, or simply disregard the Lb15,16,45,47,48. Several studies that included the Lb found its mechanical contribution in hip stabilization and load transfer from cartilage was

greater (by 2e11 times) in dysplastic than normal hips. Not including the Lb in FEM of dysplastic hips therefore notably affects its simulated mechanical behavior42e44. Defining capsular ligaments (CLs) on CT images is as difficult as defining the Lb. Only one study (15) incorporated these ligaments in FEM, however, in simple fashion with ligaments modeled as discrete spring elements, with no report of the functionality and effects of modeling these ligaments. The stabilizing contribution of the hip capsule depends on the joint angular position and congruency51e53, and is greater in dysplastic hips51. The circumstances in which including the capsule may affect FEM results were not discussed in the reviewed studies, and require further investigation and experimental validation. To investigate the effect of wide variations in hip geometry on mechanical behavior, some studies used CAD-based rather than patient-specific models44,46. Averaged anatomic measurements led

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Table IV FEM methodology and simulation results of prenatal hip joint growth Study

Significant findings

FEM specifications Model components (CAD-based)

Material (ILE)

Boundary conditions and load

Contact

Stress output

Shefelbine (2004)8

PF (3D)*

Boundary conditions: fixed distal end of PF Load: varying angle JRF with arbitrary magnitude

N

Hydrostatic pressure Octahedral shear

Normal hip JRF loading history led to a convex shape of the growth front, whereas dysplastic hip loading history resulted in formation of coxa valga.

Giorgi (2015)11

PF Acetabular cup (2D)y

Bonez: E ¼ 500 MPa, n ¼ 0.2 Cartilagex: G ¼ 2 MPa, n ¼ 0.49 Cartilage: E ¼ 1.1 MPa, n ¼ 0.49

Boundary conditions: Fixed acetabulum, arbitrary distalproximal displacement of distal end of the PF, planar rotation of the femoral head

Y

Hydrostatic pressure

Symmetric prenatal hip rotation within normal ranges promoted normal formation of acetabulum, whereas reducedrange rotations led to prediction of shallow acetabulum. Asymmetric rotations simulated formation of asymmetrically shallow acetabulum and malformed femoral head associated with DDH.

* y z x

A 7-month fetal PF with a non-ossified head located above a thin cartilaginous growth region supported by a bony diaphysis. Idealized 2D geometries of a non-ossified PF, and an acetabular cup associated with a fetus at 11th gestational week. E ¼ 500 MPa distally, linearly decreasing toward the cartilaginous femoral head. Young's modulus can be calculated as 5.96 MPa.

to idealized ball-and-socket geometries of adult hips: hemispherical femoral head and acetabulum. Articular surfaces were modeled as portions of smooth spherical surfaces, including horseshoeshaped acetabular cartilage. Reducing the lateral center-edge (CE) angle introduced dysplasia into these models. Although convenient, this likely does not lead to reliable quantitative prediction of hip mechanical behavior. In comparison with patient-specific models of normal hips, CPs were underestimated by 25e50%49 from CAD-based FEM, due at least partly to contact area overestimation44,46,49. This error is likely greater in dysplastic hips, where shape irregularities cause incongruent articulation and locally increased CP45, not accounted for by CAD-based models using simplified/smoothed geometry44,46. These stress concentrations at the lateral acetabular roof may be important in OA development. Use of patient-specific geometry is therefore preferred, as it limits the risk of bias from anatomic assumptions. The studies modeling prenatal hips (Table IV) utilized CADbased modeling of either a non-ossified fetal PF8, or an idealized hip joint including non-ossified femoral and acetabular components11. Mechanical properties of materials Deformations and stresses inside the hip depend on material properties of its components including bone, cartilage and ligaments. Adult patient-specific FEM15e17,42,43,45,47,48 all assumed homogeneous isotropic linear-elastic (ILE) materials for cortical and cancellous bone. This simplifying assumption has been shown to be appropriate for analyzing hip mechanical behavior54,55, and requires only two mechanical constants, Young's modulus E and Poisson's ratio n. For cortical bone most studies used E ¼ 17 GPa, while those that modeled cancellous bone separately used E ¼ 70e120 MPa (Table I). One study16 used location-dependent values of E based on CT data. Because cortical bone is much stiffer than cancellous bone and forms a sandwich shell over it55, some consider cancellous bone to have only a minor effect on CP27,49. Therefore, some FEM studies disregarded cancellous bone42,43,47,48. Some CAD-based models use rigid material for bone44,46, further simplifying FEM. One of these groups showed this assumption to have no effect on predicted cartilage stresses, since bone is much stiffer than AC44. However, the assumption that bone is rigid may not be appropriate in patient-specific models, where use of rigid bones led to a significant increase in predicted CP49.

In a CAD-based prenatal femur model8, the bony part was modeled as an elastic deformable material since simulation of mechanical stress in the growth front within the diaphysis was required (Table IV). Unlike bone, cartilage exhibits time- and rate-dependent behavior under physiological loads. Nevertheless, these complex effects can be disregarded if external load on the cartilage is instantaneous19,56e58, such as with loading time less than 150 ms56 or loading cycles less than 1 s (gait, stair descent/ascent, stance-tosit, onset of one-leg stance)57,58. Since cartilage is reportedly incompressible under instantaneous load59, this simplified FEM of adult hips allowing use of either nearly incompressible ILE15e17,44e48 or incompressible isotropic hyperelastic (IHE) models42,43 for cartilage (Table I), with parameters determined based on fastloading experimental conditions. Cartilage in the prenatal hip models8,11 was modeled as a nearly incompressible ILE material (Table IV). Disregarding time and rate properties of the cartilage may not be associated with physiological loading conditions inside the uterus, however, it satisfies the minimum FEM requirements for cross-comparison purposes between the simulation results. The acetabular Lb consists primarily of type 1 collagen fiber bundles extending around the acetabular rim60, and is therefore highly anisotropic, having different mechanical response to loads parallel vs perpendicular to the fibers. Assuming any direction except circumferential has similar properties, the Lb can still be considered transversely isotropic. Moreover, time- and ratedependent properties can be neglected under fast loading rates. Thus, the Lb has been modeled as incompressible transversely IHE material42,43, or as a nearly incompressible isotropic material with linear elastic properties measured along the fibers17,44,46. Isotropic labral material assumption reportedly overestimates the load supported by the Lb by 2e11%43, since an isotropic Lb is unrealistically stiff perpendicular to the fibers compared with the circumferential direction. Another simplification of material properties in adult hips was employing the soft tissue material properties of the normal hips for dysplastic hips. As noted by Henak et al.42, cartilage may be stiffer and softer, respectively, in dysplastic than normal hips. Contact mechanism In a hip joint, the convex femoral articular surface slides against the concave acetabulum. Articular friction is demonstrated to be negligible (frictional coefficient of 0.002e0.02) when synovial fluid

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becomes pressurized at the onset of loading and remains pressurized for a prolonged duration61e63. Accordingly, the reviewed studies accounting for the sliding mechanism of the joint assumed a frictionless contact mechanism11,15,17,42e48. This allows the small tangential (shear) component of the JRF to be neglected. One study, however, modeled AC as one entity without considering the sliding mechanism16. Ignoring the joint sliding contact mechanism overestimates cartilage stresses and does not permit evaluation of joint CP. The studies that included the Lb also assumed frictionless cartilage-Lb contact17,42e44,46. Boundary conditions and loading To analyze hip behavior, each bone should be in a state of force equilibrium. Commonly the adult hip is analyzed assuming static loads and immobilized bones. Generally42e48, the pelvic bone (PB) was immobilized by applying fixed-displacement boundary conditions (i.e., no motion), and a load exerted on the PF already oriented within the hip according to the analysis conditions (Table II). Boundary conditions may also be applied to the femur to fix or limit its medial-lateral or antero-posterior displacements42,43,47,48. Typically, the femur is initially mobile in distal-proximal direction, and becomes immobilized and statically stable in the acetabular socket once femoral-acetabular articular contact is completely established. Other studies15e17 applied fixed-displacement boundary conditions for the distal femur and applied load to the PB to analyze natural anatomic posture, e.g., one-leg stance. The reviewed studies investigated adult hip mechanical behavior under different physiological (gait, stair descent/ascent, stance-to-sit, one-leg stance) and non-physiological loading scenarios (Table II). Most studies consider the JRF vector obtained experimentally23,64 to be the loading input for the FEM. JRF is the balancing force transmitted at articular surfaces due to ligament and muscle forces, and body weight. JRF can be used to avoid difficulties in locating, distributing and orienting individual muscle forces in FEM, as long as analysis results near the joint (i.e., acetabulum and femoral head including soft tissues) are the focus of FEM. JRF can be applied either under load control or displacement control. Under load control, JRF was applied at the femoral head centroid44e48 or at the upper pelvis15. Applying JRF at the femoral head centroid requires kinematic coupling of femoral head finiteelement nodes to the centroid, i.e., assumption of a rigid femoral head, which induces a potentially undesirable approximation in the results49. Applying JRF to the upper hemi-pelvis involves kinematic coupling of upper pelvis finite-element nodes to a single point such that the line of action of the force, applied at the reference point, passes through the femoral head centroid, allowing the femoral head model to remain deformable. Two reviewed studies employed displacement-control loading42,43, in which the PF was pushed against the acetabulum along the line of action of JRF until the desired force was achieved. Since the displacement vector (as boundary condition) was applied to the femoral shaft, the deformable property of the femoral head was preserved. A methodological limitation of employing JRF in the hip models is that the JRF vectors in the reviewed studies were based on in vivo measurement data from instrumented implants within hips after total hip arthroplasty, scaled by patient weight. These estimates are not necessarily equivalent to the JRF one might actually observe in patient-specific models, especially in dysplastic hips. Rather than loading along the line of action of JRF, some studies instead applied a vertical load to the upper sacrum16,17, to assess one-leg stance and non-physiological loading65. For one-leg stance17, gluteus medius abductor muscle force was also applied to the PB and the greater trochanter to maintain static force equilibrium. Unlike the direct utilization of JRF in FEM, applying the

loading conditions to the upper sacrum preserved patient-specific effects of the joint geometry on the predicted JRF. The prenatal studies employed both direct and displacement control loading (Table IV). Applying fixed displacement boundary conditions at the distal femur, Shefelbine et al.8 used a dynamically varying-angle JRF vector distributed symmetrically on the cartilaginous femoral head. The force angles assumed JRF angles in normal (25 , 40 , 50 ) and dysplastic (60 , 85 , 105 ) joints. The two-dimensional (2D) model by Giorgi et al.11 had an immobilized acetabular cup and a freely rotating femur. The femur was proximally displaced towards the acetabulum for contact force initiation, and dynamically rotated in-plane according to reported ranges of motion from early to late gestation (±40 to ±5 respectively). Symmetric and asymmetric rotations were tested. Contact forces in both studies had an arbitrary magnitude, adequate for crosscomparison but not necessarily physiologic.

Finite element analysis, outputs and results Hip FEM can be categorized as a contact problem since loads are transferred by the contact mechanism of the joint. In the reviewed studies, FEM offered a choice of model outputs for adult hips. Cartilage CP (distributed form of the JRF on the surfaces in contact) and von Mises stress (indicator of internal distortion energy inside the tissues) are parameters that reflect the status of the load transfer mechanism and mechanical stresses inside the joint respectively. High cartilage CP may lead to OA when accumulated over years6,14 and elevated von Mises stress may be associated with cartilage damage44. The reviewed studies on adult hip joints show widely varying ranges of CP and area, and von Mises stress in normal and dysplastic hips under a variety of loading scenarios (Table III). Each study performed mesh sensitivity analysis to minimize FEM error and produce accurate results. Most of the studies (except Refs. 16 and 48) validated their FEM by showing that simulated CP and contact area were comparable with or in range of available measured experimental data. The numeric ranges of simulated values are not directly comparable with each other because the models are associated with different joint geometry, material properties, and loading vectors, methods and scenarios. Fortunately, the diversity of model design reduces the risk of bias in results across studies. Qualitative comparisons between the FEM results of dysplastic vs normal hips were performed. Simulating gait cycles, some researchers44e46 found peak CP to be 1.4e5.7 times higher in dysplastic hips than normal joints. In contrast, Henak et al.42,43 found peak CP were actually larger in normal hip models than dysplastic hips, because dysplastic hip geometry shifted part of the JRF towards the Lb, engaging part of the labral surface to contact femoral head cartilage. The extra labral contact area helped redistribute JRF, sparing cartilage by increasing load on the Lb. According to Henak et al.42, other studies predict elevated CP during gait in dysplastic hips because they disregard either the Lb45 or patient-specific joint geometry44,46. The fact that the superior Lb was most affected by shift of JRF in the dysplastic hip models may explain the high clinical prevalence of superior or anterosuperior labral tears and adjacent cartilage damage. Cartilage contact area during gait was reportedly smaller in dysplastic than normal hips, whether or not the Lb was included in FEM43,45. Groups investigating mechanical behavior of dysplastic hips under one-leg stance conditions15,17,47,48 simulated acetabular osteotomies to create close-to-normal hip models out of dysplastic hips. They reported that maximizing contact area in dysplastic hips via acetabular reorientation generally decreased CP and von Mises stress. However, minimized peak CP may not be always concurrent

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with the maximized contact area48, due to stress concentrations at patient-specific bone irregularities45. Two studies investigating stance-to-sit conditions44,46 both reported higher CP and von Mises stress in dysplastic hips, accentuated by activities with high load (gait) rather than with large range of motion (stance-to-sit). The reviewed prenatal studies recruited other FEM-simulated stress components (Table IV). Shefelbine et al.8 evaluated the mechanobiological theory that growth is accelerated by intermittent octahedral shear stress and inhibited by intermittent hydrostatic pressure66. Giorgi et al.11 assessed the theory that growth is accelerated by dynamic hydrostatic pressure and inhibited by static pressure67. Growth in both studies was simulated through computational expansion of finite elements with rates calculated based on the growth theories. These simulations provided insights on the effect of the mechanical environment on cartilage growth within limited and idealized assumptions. Shefelbine et al.8 found that in normal hips, hydrostatic pressure was higher peripherally and octahedral shear stress was highest centrally, promoting a convex shape of the growth front. In dysplastic hips, octahedral shear stress was increased on the medial side of the growth region, imbalancing the growth front toward coxa valga. Giorgi et al.11 showed that asymmetric rotations of the femoral head inside the acetabulum prenatally led to asymmetric joint loading which eventually opened the acetabulum toward the direction of the generated JRF, giving the asymmetrically shallow acetabulum and malformed femoral head of DDH. Such asymmetric rotations of a prenatal hip joint might result from fetal breech position or increased joint laxity.

Limitations of, and alternatives to, FEM The reviewed studies show that FEM provides a versatile tool to assess etiology and effects of DDH. Nevertheless, FEM is timeintensive and computationally expensive, especially with detailed finite-element meshes, nonlinear material properties and nonlinear contact mechanism formulation20. This can paralyze the method if analysis time is a critical factor, such as in large population studies37e39,68e70, osteotomy surgical planning71,72 or realtime intraoperative feedback73e75. Trading strict accuracy for faster modeling in these settings, DEA can be regarded as the closest alternative to FEM76. DEA (or rigid body-spring modeling) considers bones as rigid bodies, and AC as one-dimensional springs

connecting the acetabulum and femoral head34,40. Ligaments are represented by springs. Neglecting mechanical stresses inside bones, DEA estimates joint CP from forces in compressive springs distributed on the joint surfaces. This does not accurately model the joint sliding contact mechanism, but can still demonstrate patterns of contact area and CP distribution regardless of absolute magnitudes. This makes DEA appropriate for studies comparing mechanical behavior of normal vs dysplastic hips, and pre- vs postoperative joints34,40 (Table V).

Recommendations for FEM of infant hips We found no FEM-based studies in infants or children. Prenatal FEM-based studies focus on DDH etiology. Pathological consequences of the dysplastic mechanical environment in infant hips, and optimal methods of DDH correction in children, have not, to our knowledge, been modeled yet. Adult studies are likely not directly applicable to infant hips, since unlike in adults most of the infant/prenatal hip is composed of cartilage, including the femoral head and the pubic rami. Given the extent to which small changes in cartilage thickness affect results in patient-specific adult hip models48, the proportionately thicker infant hip AC likely alters infant hip mechanical behaviour compared to adults. It is also unclear to what extent infant cartilage mechanical properties differ from adult cartilage77. Patient-specific computational geometries of infant hips are challenging to produce via CT which poorly depicts cartilage, and CT is not practical for this indication due to radiation dose concerns in infants. Magnetic resonance imaging (MRI) shows clearer boundaries of soft tissue structures78,79, without ionizing radiation, but infants may require sedation, and spatial resolution is lower than on CT. 3D ultrasound is an emerging modality offering high spatial resolution with no ionizing radiation. Since early results show promising geometric accuracy80, this may be useful in future patient-specific modeling. Loading scenarios in adult hip FEM such as walking, climbing stairs or one-leg standing are obviously not relevant in infants, where more important loading scenarios include positioning within a swaddle, sling, car seat or Pavlik harness. In-utero loading scenarios are also uniquely challenging. Verbruggen81 evaluated fetal movements, and reaction force of fetal kicking against the uterine wall. Unlike in adults, infant load scenarios may involve prolonged slow loading, as with corrective harnesses worn 24 h/ day. According to Hjelmstedt et al.12,13, long-duration moderate

Table V DEA-based studies regarding human dysplastic hips Study

Modeling focus

Significant findings

Genda (1995)37

Evaluating CP in normal and acetabular dysplastic hip joints (loading scenarios: heel strike and toe-off phases of gait) Simulating 3D CP distribution in normal and dysplastic hips (loading scenario: one-leg stance phase of gait) Investigating effects of different acetabular rotations on hip subluxation (loading scenario: one-leg stance) Calculating pre- and post-operative CP in hip joints of PAO patients (loading scenarios: standing, gait, and sitting) Evaluating the effects of cartilage thickness distribution and compressive spring models of cartilage on optimal alignment of acetabulum in PAO patients (loading scenarios: standing, gait, and sitting)

Even distribution of CP over the joint surface and low peak CP (averaged 2.6 MPa) in normal joints (CE > 20 ). Concentration of CP on anterolateral edge of acetabulum and increasing peak CP (2.5 e17 MPa) with reduction of CE angle in dysplastic joints (1.75 < CE < 19.8 ). The peak CP in dysplastic hips (15 < CE < 7 ) was located at the edge of the acetabulum. The peak CP values in dysplastic hips (2.83e5.31 MPa) were higher in normal hips (1.83e2.51 MPa) with 24 < CE < 38 . Progressive anterolateral subluxation associated with hip dysplasia occurred in the hip models with CE < 20 . The subluxation was followed by dislocation in the models with CE < 0 . Models with CE  30 did not lead to lateral subluxation. Calculated peak CP values in preoperative dysplastic hips (1.9e7.7 MPa) were reduced (1.4e3.2 MPa) by an average factor of 1.7 after PAO. Reduction of the peak CP was not proportional with increase of CE angle. Choice of cartilage thickness distribution (patient-specific vs constant), or linear/non-linear spring models of cartilage did not affect the predicted optimal alignment of acetabulum.

Tsumura (1998)41

Rab (2007)70

Armiger (2009)69

Niknafs (2013)72

7

PAO: periacetabular osteotomy.

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loads can provoke DDH due to time-dependent deformations of cartilaginous femoral head and acetabulum. The rate- and timedependency of cartilage material properties may play a role in FEM of infant hips. Summary FEM of adult dysplastic hips is most commonly performed using patient-specific CT-based geometry, ILE models of bone, cartilage and Lb, omission of most muscles and ligaments, and assumptions of rapid loading to simplify cartilage mechanical properties. Load conditions modeled simulate situations such as walking or stairclimbing. Joint CPs and stresses are simulated. Most models demonstrate increased stress on cartilage and/or increased reliance on the Lb to bear load in dysplastic hips, correlating well to clinical findings of premature OA and early labral tearing in dysplastic hips. DEA offers a rapid alternative to FEM when computational time is an issue. FEM of prenatal hips demonstrates ways in which in-utero loading might produce DDH. FEM of infant dysplastic hips offers an opportunity to understand the stress environment and factors affecting it at a time when the dysplasia can still be corrected conservatively. Models in infants do not yet exist, and have special challenges, including the need to obtain accurate cartilage geometry, consideration of rate-dependent cartilage material properties, and infant-relevant loading scenarios. Hip mechanical modeling through the human life cycle may improve our understanding of the causes of DDH and of premature hip OA, and ultimately help us optimize DDH treatment to reduce its lifelong disability. Author contributions Author list: BV: B. Vafaeian DZ: D. Zonoobi MM: M. Mabee ARH: A. R. Hareendranathan ME: M. El-Rich SA: S. Adeeb JJ: J. L. Jaremko Contributions of authors (All authors should have made substantial contributions to all three of sections (1), (2) and (3))           

(1) Conception and design: BV, DZ, MM, ARH, ME, SA, JJ (1) Analysis and interpretation of the data: BV, DZ, MM, ARH (2) Drafting of the article: BV, JJ (2) Critical revision of the article for important intellectual content: BV, DZ, MM, ARH, ME, SA, JJ (3) Final approval of the article: BV, DZ, MM, ARH, ME, SA, JJ (.) Provision of study materials or patients: ME, SA, JJ (.) Statistical expertise: JJ (.) Obtaining of funding: JJ (.) Administrative, technical, or logistic support: DZ, ME, SA, JJ (1) Collection and assembly of data: BV, JJ Guarantor of overall integrity of the work: JJ

Conflict of interest None of the co-authors has any competing interests to disclose that could potentially and inappropriately influence the study. Acknowledgements Unrestricted funding support for this work was provided by the Capital Health Endowed Chair in Diagnostic Imaging and the CIHRHSC Young Investigator Award (NI15-004).

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Please cite this article in press as: Vafaeian B, et al., Finite element analysis of mechanical behavior of human dysplastic hip joints: a systematic review, Osteoarthritis and Cartilage (2016), http://dx.doi.org/10.1016/j.joca.2016.10.023