Generic selectors
Exact matches only
Search in title
Search in content
Post Type Selectors
Search in posts
Search in pages
Filter by Categories
Case Report
Clinical research study
Current Issue
Editorial Board
Literature Review
Narrative review
Original Article
Research Article
Review Article
Short Report
Surgical techniques
Generic selectors
Exact matches only
Search in title
Search in content
Post Type Selectors
Search in posts
Search in pages
Filter by Categories
Case Report
Clinical research study
Current Issue
Editorial Board
Literature Review
Narrative review
Original Article
Research Article
Review Article
Short Report
Surgical techniques
View/Download PDF

Translate this page into:

55 (); 16-22
doi:
10.1016/j.jor.2024.04.002

Comparative finite element analysis of contact and stress distribution in tibiotalar articular cartilage: Healthy versus varus ankles

, ,
a School of Mechanical Engineering, University of Tehran, Tehran, Iran
b Department of Biomedical Engineering, University of Isfahan, Isfahan, Iran

⁎Corresponding author: Mohadese Rajaeirad. mohadeserajaeirad@gmail.com

Received: , Accepted: ,
Professor P K Surendran Memorial Education Foundation
Disclaimer:
This article was originally published by Reed Elsevier India Pvt. Ltd. and was migrated to Scientific Scholar after the change of Publisher.

Abstract

Abstract

The distribution of forces within the ankle joint plays a crucial role in joint health and longevity. Loading disorders affecting the ankle joint can have significant detrimental effects on daily life and activity levels. This study aimed to enhance our understanding of the mechanical behavior of tibiotalar joint articular cartilages in the presence of varus deformity using finite element analysis (FEA) applied to patient-specific models.

Two personalized ankle models, one healthy and another with varus deformity, were created based on CT scan images. Four static loading scenarios were simulated at the center of pressure (COP), coupled to the hindfoot complex. The contact area, contact pressure, and von Mises stress were computed for each cartilage.

It was found that the peak contact pressure increased by 54% in the ankle with varus deformity compared to the healthy ankle model. Furthermore, stress concentrations moving medially were observed, particularly beneath the medial malleolus, with an average peak contact pressure of 3.5 MPa and 4.7 MPa at the tibial and talar articular cartilages, respectively.

Varus deformities in the ankle region have been consistently linked to elevated contact pressure, increasing the risk of thinning, degeneration, and eventual onset of osteoarthritis (OA), emphasizing the need for prompt interventions aimed at mitigating complications.

Abstract

Graphical abstract

Image 1

Keywords

Ankle joint
Varus deformity
Patient-specific model
Articular cartilage
Finite element analysis
Osteoarthritis
1

1 Introduction

The ankle joint, with its uniaxial synovial hinge joint properties and range of motion in plantarflexion and dorsiflexion, plays a crucial role in fundamental activities such as walking.1 Mechanical stress contributes significantly to the development and progression of OA, therefore irregularities in joint function are a major concern for orthopedic specialists.2,3 The health and well-being of a synovial joint heavily rely on mechanical stress placed on the articular cartilage. Malalignment in the frontal plane of the lower tibia can create an imbalance in joint loading, resulting in damaged articular cartilage, decreased mobility, and discomfort in the ankle joint. Such degenerative changes may ultimately lead to pain and restricted movement. By allowing for inversion and eversion motions, the subtalar joint compensates for varus deformations up to 15° and valgus deformations up to 30°.1,4,5

Osteoarthritis (OA) is a prevalent condition that affects people all over the world. The most common cause of ankle OA is post-traumatic OA (PTOA), which affects up to 70% of patients. PTOA in the ankle is not typically caused by a fracture; rather, it is caused by various types of injury or instability.6–8 Cartilage degeneration in OA is often linked to mechanical stress on articular surfaces. Current approaches to preventing further degeneration focus on correcting underlying mechanical abnormalities, but a lack of patient-specific quantitative information makes this challenging.2

The ankle joint is particularly interesting for studying OA secondary to contact stress aberrations due to its infrequent development of primary OA but frequent development of secondary OA following even modest mechanical abnormalities.9 Joint incongruities following fractures can lead to post-traumatic arthritis by reducing contact area and increasing contact stresses.10 Ramsey and Hamilton found that a lateral talar shift of 1 mm resulted in a 40% decrease in the tibiotalar contact area.11 However, Vrahas et al. observed no increase in peak stresses in a cadaver model of ankle malunion.12 Residual incongruities or irregularities in articular surfaces may result in stress distribution abnormalities and OA.12 Researchers developed an FE model using CT scans from patients with intra-articular fractures, validating the results against physical measurements from corresponding cadaveric loading tests to provide strong support for FE model biofidelity.12,13

Although several studies have investigated ankle joint biomechanics, significant limitations and gaps remain. These include a failure to account for ligamentous laxity,13,14 ignoring COP,15,16 modeling bony tissue with an oversimplified representation that neglects the multi-layered nature of bone, and inaccurately modeling the static loading of the Achilles tendon.16 This paper investigates the effects of varus deformity on tibiotalar joint articular cartilage using finite element analysis. The distribution of forces within the ankle joint is known to significantly impact joint health and longevity, resulting in detrimental effects on daily life and activity levels. Therefore, two personalized FE models of the ankle were created, one healthy and the other one varus, to explore the impact of varus deformity and joint alignment on the mechanical behavior of the tibiotalar joint.

2

2 Methods

2.1

2.1 Three-dimensional model generation

In adherence to ethical guidelines, the computed tomography (CT) scan images used in this study were obtained from routine clinical practice and anonymized for patient confidentiality. As this study is retrospective and doesn't involve direct patient interaction, formal ethical permission for image use may not apply. The DICOM format CT scan images were utilized to create 3D models of a 30-year-old male (BMI of 24.2) patient's right and left ankles, with a varus deformity in the right ankle. The images had a resolution of 512 × 512 pixels, pixel size of 0.703 mm, and slice thickness of 1.25 mm. Material assignment was based on Hounsfield Unit (HU) values obtained from the CT scans. For comparative purposes, the left ankle of the same individual was chosen for analysis to ensure comparable bone quality.

The Lateral Distal Tibia Angle (LDTA) was measured to assess frontal plane deformities in the distal tibial region, yielding 97.38° for the right ankle, indicating an 8.38° varus deformity. The left ankle showed a measurement of 90.32°, within the normal range for LDTA: 89° ± 3° (Fig. 1) according to orthopedic guidelines.5,17

3D personalized models of right and left ankle joint and lateral distal tibial angle (LDTA) measurement.
Fig. 1 3D personalized models of right and left ankle joint and lateral distal tibial angle (LDTA) measurement.

Articular cartilages with a uniformly distributed thickness of 1 mm were generated on the articular surfaces of both the tibia and talus for both healthy and varus models.18,19 Furthermore, the tibia and fibula were cut to a length of 70 mm superior to the joint to optimize computational cost in the FE study.

2.2

2.2 Finite element model development

The present study utilized two FE models, comprising linear tetrahedral elements (C3D4), with 120,908 and 96,135 total elements in the right and left ankles, respectively, to examine the biomechanical behavior of the ankle joint. The material assignment was performed based on HU derived from CT scan images for the bony components of the model. Homogeneous, and linear isotropic material properties were assigned to the articular cartilage, which are presented in Table 1.

Table 1 Material properties of FE components in SI (mm) system18,20.
Components Layers Layers' name Density ρ (kg/m3) Young's modulus E (MPa) Poisson's ratio v
Tibia 3 Medullary canal 980 1 0.3
Cancellous 1100 445 0.3
Cortical 2000 17,500 0.3
Fibula 1 Cortical 2000 17,500 0.3
Talus 2 Cancellous 1100 445 0.3
Cortical 2000 17,500 0.3
Calcaneus 2 Cancellous 1100 445 0.3
Cortical 2000 17,500 0.3
Articular cartilages 1 – 1100 10 0.4

A Dynamic/implicit (quasi-static) solver in ABAQUS/Standard (Dassault Systemes, 2021) was utilized to conduct the simulations. As per previous studies,16,21 the proximal sides of the tibia and fibula were assumed fully fixed. To incorporate the stabilizing effect of the gastrocnemius muscle, the Achilles tendon insertion line on the posterior side of the cancellous bone (Fig. 2) was constrained from rotation (UR = 0). Frictionless contact between cartilages was assumed due to their lubricating nature,18 with cartilages fully bonded to respective bones.

Detailed FE model of the right ankle. The stiffness of ligaments is given in Table 3.
Fig. 2 Detailed FE model of the right ankle. The stiffness of ligaments is given in Table 3.

To address the absence of the forefoot, the foot's COP was determined based on prior research.22,23 Specifically, normal COP was adjusted according to varus ankle COP changes reported by Paley.5 Additionally, a kinematic coupling between COP and the inferior elements of the calcaneus was applied. Four loading scenarios, including bipedal standing, neutral position, dorsiflexion, and plantar flexion during normal gait, were considered. Associated forces and moments are detailed in Table 2.21,24

Table 2 Applied forces (N) and moments (N.m) to the model simulation of four loading scenarios.21,24
FX FY FZ Moment (Y)
Bipedal standing 0 0 350 –
Neutral (0°) −280 150 600 −2.85
Dorsiflexion (−10°) −185 −185 1600 −6.2
Plantarflexion (+15°) −245 100 400 0.1

To enhance simulation accuracy, we integrated 16 ligaments into both models (Fig. 2),21 crucial for facilitating proper joint movement. Ligament anatomies followed the Netter Atlas of Anatomy.25 Each ligament was represented by four springs in the FE model (64 springs in total) to prevent stress concentration at origin and insertion points. Ligament stiffness and coefficients, drawn from previous studies, are detailed in Table 3.

Table 3 Ligament stiffness considered in the present study.26–29
Ligaments Stiffness (N/mm)
Interosseous membrane I-IV 400
Anterior tibiofibular ligament (ATiFL) 90
Anterior tibiotalar ligament (ATiTL) 70
Posterior tibiofibular ligament (PTiFL) 90
Anterior talofibular ligament (ATaFL) 90
Posterior talofibular ligament (PTaFL) 70
Calcaneofibular ligament (CaFL) 70
Posterior tibiotalar ligament (PTiTL) 80
Tibiocalcaneal ligament (TiCa) 122
Interosseous talocalcaneal ligament (ITaCL) 70
Lateral talocalcaneal ligament (LTaCL) 70
Medial talocalcaneal ligament (MTaCL) 70
Posterior talocalcaneal ligament (PTaCL) 70
2.3

2.3 Model validation and comparison

The validation of the healthy ankle was conducted by comparing various parameters, such as contact area, contact pressure, and stress, with those reported in previous clinical and numerical studies. The D parameter was calculated using Eq. (1) for all comparisons. Furthermore, the increase percentage (IP) was calculated using Eq. (2) to assess the deterioration of varus deformity and compare it with the healthy ankle.(1)D=|A1−A2|(A1+A2)2×100(2)IP=σVarus−σHealthyσHealthy×100

3

3 Results

3.1

3.1 Healthy model validation

To validate the healthy model employed in this study, a comparison with previous research was conducted. As Muralidharan et al.30 in a recent study reported a peak contact pressure of 4.34 MPa on talar cartilage, while our study found 4.63 MPa on the same cartilage, indicating a difference of 6.5%. Suckel et al.31 in an in-vitro study observed an anterolateral contact pattern with a pressure of 4.8 MPa under 350 N vertical (bipedal) loading, which was also consistent with our findings with a 3.5% difference. The intra-articular peak contact pressure during the stance phase was found to be between 4.63 MPa and 5.84 MPa (Table 4), which agrees with previous research.11–13,23,27,30,32–34

Table 4 The maximum values of von Mises stress (MPa), contact pressure (MPa), and pressure stress (MPa) in tibial (Tib) and talar (Tal) articular cartilages of healthy (left) and varus (right) ankles.
Loading scenarios Healthy Ankle Varus Ankle
Max von Mises stress (MPa) Max contact pressure (MPa) Max pressure stress (MPa) Max von Mises stress (MPa) Max contact pressure (MPa) Max pressure stress (MPa)
Bipedal Tib 1.61 4.44 3.27 2.40 6.85 4.76
Tal 1.65 4.63 3.93 2.88 6.94 4.89
Neutral Tib 2.43 5.76 4.32 3.15 8.88 5.86
Tal 2.03 5.84 3.79 3.79 9.39 6.73
Dorsiflexion Tib 4.47 9.32 6.61 4.52 12.49 8.81
Tal 3.98 9.23 6.63 7.84 12.94 9.57
Plantarflexion Tib 2.73 4.64 3.44 2.73 7.76 5.06
Tal 1.72 4.80 3.99 3.36 8.13 5.80
3.2

3.2 Comparison of stress and contact distribution in healthy and varus models

The von Mises stress distribution patterns for the tibial and talar cartilages were obtained via FEA under four loading conditions, as shown in Fig. 3, with similar patterns observed for contact pressure and pressure stress distribution. In a healthy ankle joint, stress concentration is greater on the lateral side of both cartilages, while in a varus ankle, it's more concentrated on the medial side. Table 4 presents the maximum values of von Mises stress, contact pressure, and pressure stress for each cartilage in both healthy and varus ankle models.

Von Mises stress distribution in talar and tibial articular cartilages under four loading scenarios in the healthy and varus model (MPa). Maximum values are given in Table 4.
Fig. 3 Von Mises stress distribution in talar and tibial articular cartilages under four loading scenarios in the healthy and varus model (MPa). Maximum values are given in Table 4.

To study the alterations in contact area caused by varus deformity, contact area patterns for each cartilage in both models are depicted in Fig. 4, with a comparative representation of the total contact area presented in Fig. 5. In both models, contact area was predominantly anterolateral in healthy ankles and posteromedial in varus ankles. The mean and maximum (during dorsiflexion) values of total contact area exhibited a difference (D) of 26.3% and 15.8%, respectively.

Contact nodal area (mm2) patterns in healthy and varus ankles in four loading scenarios.
Fig. 4 Contact nodal area (mm2) patterns in healthy and varus ankles in four loading scenarios.
Total contact area (mm2) in articular surfaces in healthy and varus models.
Fig. 5 Total contact area (mm2) in articular surfaces in healthy and varus models.

The IP (Eq. (2)) in von Mises stress, contact pressure, and pressure stress were calculated for the tibial and talar articular cartilages. The values obtained were 35.3%, 52.4%, and 40.3% for von Mises stress, contact pressure, and pressure stress of the tibial cartilage, respectively. Similarly, for the talar cartilage, the IPs were determined to be 88.5%, 55.1%, and 47.9% for von Mises stress, contact pressure, and pressure stress, respectively.

3.3

3.3 Medial malleolus

Significant contact and stress were observed in the medial malleolus region of the varus ankle (Fig. 4). The talar cartilage experienced higher von Mises stress compared to the tibial cartilage, with maximum values of 1.77 MPa during neutral loading and 1.76 MPa during dorsiflexion loading. In healthy ankles, the mean maximum von Mises stress was 0.13 MPa on the tibial cartilage and 0.05 MPa on the talar cartilage, whereas in varus ankles, it increased to 1.22 MPa and 1.58 MPa, respectively (Table 5).

Table 5 Maximum von Mises stress under medial malleolus in each loading condition (MPa).
Articular Cartilage Bipedal Standing Neutral Dorsiflexion Plantarflexion
Healthy Varus Healthy Varus Healthy Varus Healthy Varus
Tibial Cartilage 0.05 0.83 0.08 1.41 0.32 1.35 0.06 1.28
Talar Cartilage ≈0 1.10 ≈0 1.77 0.20 1.76 ≈0 1.69

Furthermore, the maximum contact pressure in the varus ankle (Fig. 6) was observed during dorsiflexion loading: 4.07 MPa on the tibial cartilage and 5.44 MPa on the talar cartilage. On average, the medial malleolus region in the varus ankle experienced contact pressures of 3.51 MPa and 4.69 MPa on the tibial and talar articular cartilages, respectively.

Maximum contact pressure (MPa) on tibial and talar cartilages in the medial malleolus region under different loading conditions in the varus ankle.
Fig. 6 Maximum contact pressure (MPa) on tibial and talar cartilages in the medial malleolus region under different loading conditions in the varus ankle.
4

4 Discussion

The study revealed that varus deformity is associated with increased stress on the cartilage, which can lead to thinning and degeneration over time, contributing to the development of osteoarthritis. The stress distribution in a varus ankle is more concentrated on the medial side, whereas a healthy ankle distributes stress laterally.12,35 Subsequently, the medial side of cartilages in varus ankles could experience increased wear and tear, which supports previous studies that reported a higher prevalence of osteoarthritis in patients with varus deformity.23,36–39

The initial observation when comparing a healthy ankle to a varus ankle is the noticeable alteration in the stress distribution pattern. Previous studies have consistently reported that the contact distribution and loading within the tibiotalar joint during weight-bearing exhibit a non-uniform nature,12,40 similar to what has been observed in the knee and hip joints.41,42 In a healthy ankle, it has been noted that the peak contact stress is predominantly distributed antero-laterally.12–14,30,33,35 Conversely, in a varus ankle, stress concentrations are displaced medially, which can lead to degeneration and thinning of the articular cartilage on the medial side.5,23,37,43 It is important to acknowledge that anatomical differences between individuals may contribute to variations in loading and contact distribution, resulting in differences in magnitude and patterns.12,44 For instance, Vrahas et al. conducted a study involving 10 cadaveric specimens and found intra-articular pressure in the tibiotalar joint ranging from 1.9 to 12.4 MPa.12

In a recent study conducted by Zhu et al.,23 the biomechanical changes in varus ankles were investigated using Teckscan sensors on 8 cadavers exposed to a compressive load of 600 N. The results showed that an 8-degree varus deformity led to a peak pressure stress of 4.7 MPa, with a slight deviation of 1.6% from our research findings. Table 4 demonstrated considerable alterations in stress and contact pressure when comparing varus ankles to healthy models.23,36,37,40,43,45 Specifically, there was an average increase of approximately 54% in peak contact pressure values for varus ankles compared to healthy ankles.

The maximum contact area was measured during dorsiflexion at 327.3 mm2, while in the neutral position, it was found to be 179 mm2 (Fig. 5). A difference of approximately 1.8% was found compared to Muralidharan et al.,30 around 28% when compared to Kimizuka et al.,33 and a high level of agreement was observed with the results of Driscoll et al.32 and Ramsey and Hamilton.11 Wan et al. 46 in an in-vivo study reported a difference of approximately 5.1% during walking (272–417 mm2), and Alonso-Rasgado et al.34 reported a contact area of 240 mm2. Vrahas et al.12 observed a wide range of variation (160–590 mm2) due to anatomical differences among individuals.

The observed contact area patterns (Fig. 5) largely align with previous discussions,23,43,45 but our results show a slight increase in the varus model, contrary to prior findings. This difference can be attributed to our inclusion of the malleolar region of the articular cartilage, which exhibited substantial contact area and stress in the varus model compared to the healthy model. Notably, our study highlights the importance of considering contact area and relative stress on the medial malleolus region,12 often overlooked in prior research.13,14,30,35 Our findings reveal a mean von Mises stress of 1.22 MPa and 1.58 MPa in the tibial and talar cartilages, respectively, with mean contact pressure values of 3.51 MPa and 4.69 MPa beneath the medial malleolus. Considering these outcomes, future investigations should explore the combined impact of distal tibial deformities on ankle joint biomechanics.

The study underscores the importance of early diagnosis and intervention for ankle deformities, particularly varus deformity, to prevent osteoarthritis progression and enhance patient outcomes. By confirming varus deformity's role in cartilage degeneration and associated symptoms, clinicians can prioritize timely diagnosis and treatment strategies. The findings also offer insights into stress distribution and changes in contact area within the tibiotalar joint cartilage, aiding surgical interventions and pre-operative planning. Patient-specific modeling and FEA hold promise for personalized treatment based on anatomical variations, potentially improving long-term outcomes.

While this study provides valuable insights, it is important to acknowledge its limitations. MRI images of the patient were unavailable, so anatomical atlases and prior studies were used to model soft tissues around the ankle. Additionally, while the study focused on varus deformity's effects on the tibiotalar joint, factors like obesity, trauma, and aging can also contribute to cartilage degeneration and pain. Future research could investigate these combined effects using patient-specific modeling. Moreover, the study made simplifications, such as assuming linear elastic and isotropic modeling of articular cartilage. Although more advanced models exist, linear elastic behavior is widely accepted for whole-joint contact simulations under physiological loading rates. Previous studies have similarly employed this approach.13,14,30

5

5 Conclusion

In conclusion, this study utilized patient-specific modeling and finite element analysis to examine varus deformity's impact on tibiotalar joint cartilage mechanics. The findings reveal increased stress and pressure, particularly on the medial side, leading to progressive thinning and degeneration. A critical region under the medial malleolus was identified in the varus model. These insights emphasize the importance of early detection and treatment of ankle deformities to prevent further deterioration. Patient-specific modeling offers valuable insights for optimizing treatment strategies and improving patient outcomes.

Funding

This research did not receive any specific grant from funding agencies in the public, commercial or not-for-profit sectors.

Ethical statement

In adherence to ethical guidelines, the computed tomography (CT) scan images used in this study were obtained from routine clinical practice and anonymized for patient confidentiality. As this study is retrospective and doesn't involve direct patient interaction, formal ethical permission for image use may not apply. No human subjects were directly involved in this Finite Element Analysis (FEA) study, and no identifiable patient information was utilized. Therefore, ethical considerations primarily focused on ensuring patient confidentiality and data integrity. The research adhered to all relevant laws, regulations, and guidelines governing data protection and research integrity.

Guardian/patient's consent

The study was conducted using CT scan images obtained as part of routine clinical practice, thus no IRB approval or patient consent was required.

CRediT authorship contribution statement

Mohadese Rajaeirad: Conceptualization, Methodology, Software, Data curation, Writing – original draft, Visualization, Investigation, Validation, Writing – review & editing. Morad Karimpour: Conceptualization, Project administration, Supervision, Writing – review & editing. Mohammad Reza Hairi Yazdi: Supervision, Writing – review & editing.

References

  1. , , . Biomechanics of the ankle. Orthop Trauma. 2016;30(3):232-238.
    [Google Scholar]
  2. , , . Joint injury, repair, and remodeling: roles in post-traumatic osteoarthritis. Clin Orthop Relat Res. 2004;423:7-16.
    [Google Scholar]
  3. , , , et al . Osteoarthritis: new insights. Part 1: the disease and its risk factors. Ann Intern Med. 2000;133(8):635-646.
    [Google Scholar]
  4. , , , , , . Basic Techniques for Extremity Reconstruction: External Fixator Applications According to Ilizarov Principles. 2018
    [Google Scholar]
  5. , . Principles of Deformity Correction. 2002
    [Google Scholar]
  6. , , , , , . Post-traumatic ankle arthritis. Bull NYU Hosp Jt Dis. 2013;71(1):104.
    [Google Scholar]
  7. , , , , , . Posttraumatic osteoarthritis: a first estimate of incidence, prevalence, and burden of disease. J Orthop Trauma. 2006;20(10):739-744.
    [Google Scholar]
  8. , , , , , . Etiology of ankle osteoarthritis. Clin Orthop Relat Res. 2009;467(7):1800-1806.
    [Google Scholar]
  9. , , . Ankle arthritis. J Bone Jt Surg. 2003;85(5):923-936.
    [Google Scholar]
  10. , , , , , , . Contact stress aberrations following imprecise reduction of simple tibial plateau fractures. J Orthop Res. 1988;6(6):851-862.
    [Google Scholar]
  11. , , . Changes in tibiotalar area of contact caused by lateral talar shift. J Bone Jt Surg. 1976;58(3):356-357.
    [Google Scholar]
  12. , , , . Intraarticular contact stresses with simulated ankle malunions. J Orthop Trauma. 1994;8(2):159-166.
    [Google Scholar]
  13. , , , et al . Intra-articular contact stress distributions at the ankle throughout stance phase–patient-specific finite element analysis as a metric of degeneration propensity. Biomech Model Mechanobiol. 2006;5:82-89.
    [Google Scholar]
  14. , , , , , , . Physical validation of a patient-specific contact finite element model of the ankle. J Biomech. 2007;40(8):1662-1669.
    [Google Scholar]
  15. , , , , , . Assessment of stress distribution in ankle joint: simultaneous application of experimental and finite element methods. Int J Exp Comput BioMech. 2015;3(1):45-61.
    [Google Scholar]
  16. , , . The effects of implant orientations and implant–bone interfacial conditions on potential causes of failure of tibial component due to total ankle replacement. J Med Biol Eng. 2019;39:541-551.
    [Google Scholar]
  17. , , , . Mann's Surgery of the Foot and Ankle E-Book: Expert Consult-Online. 2013
    [Google Scholar]
  18. , , . Finite element analysis of large deformation of articular cartilage in upper ankle joint of occupant in military vehicles during explosion. Arch Metall Mater. 2015;60(3):2115-2121.
    [Google Scholar]
  19. , , , , , , . Quantification of ankle articular cartilage topography and thickness using a high resolution stereophotography system. Osteoarthritis Cartilage. 2007;15(2):205-211.
    [Google Scholar]
  20. , , , . A finite element model of the foot and ankle for automotive impact applications. Ann Biomed Eng. 2012;40:2519-2531.
    [Google Scholar]
  21. , , . A numerical study on stress distribution across the ankle joint: effects of material distribution of bone, muscle force and ligaments. J Orthop. 2017;14(3):329-335.
    [Google Scholar]
  22. , , . Study of center of pressure (COP) in gait analysis of elderly women in Romania. 2018:361-366.
    [Google Scholar]
  23. , , , . Ankle joint pressure change in varus malalignment of the tibia. BMC Muscoskel Disord. 2020;21(1):148.
    [Google Scholar]
  24. , , , , . Finite element analysis of a total ankle replacement during the stance phase of gait. J Biomech. 2006;39(8):1435-1443.
    [Google Scholar]
  25. , . Atlas of Human Anatomy, Professional Edition E-Book: Including NetterReference. Com Access with Full Downloadable Image Bank. 2014
    [Google Scholar]
  26. , , . The distal fascicle of the anterior inferior tibiofibular ligament as a cause of tibiotalar impingement syndrome: a current concepts review. Knee Surg Sports Traumatol Arthrosc. 2007;15:465-471.
    [Google Scholar]
  27. , , , , . Ligament fibre recruitment and forces for the anterior drawer test at the human ankle joint. J Biomech. 2003;36(3):363-372.
    [Google Scholar]
  28. , , . Computational modeling to predict mechanical function of joints: application to the lower leg with simulation of two cadaver studies. J Biomech Eng. 2007;129(6):811-817.
    [Google Scholar]
  29. , , , , , . A biomechanical evaluation of the tibiofibular and tibiotalar ligaments of the ankle. Foot Ankle Int. 2003;24(5):426-429.
    [Google Scholar]
  30. , , , , , . A patient-specific numerical model of the ankle joint for the analysis of contact pressure distribution. Proc Inst Mech Eng [H]. 2020;234(9):909-920.
    [Google Scholar]
  31. , , , , . In vitro measurement of intraarticular pressure in the ankle joint. Knee Surg Sports Traumatol Arthrosc. 2010;18:664-668.
    [Google Scholar]
  32. , , , . Contact characteristics of the ankle joint. Part 1. The normal joint. J Am Podiatr Med Assoc. 1994;84(10):491-498.
    [Google Scholar]
  33. , , , . Load-bearing pattern of the ankle joint: contact area and pressure distribution. Arch Orthop Trauma Surg. 1980;96:45-49.
    [Google Scholar]
  34. , , , . 3-D computer modelling of malunited posterior malleolar fractures: effect of fragment size and offset on ankle stability, contact pressure and pattern. J Foot Ankle Res. 2017;10:1-12.
    [Google Scholar]
  35. , , , . A comparison of the in vivo contact pressure at the tibiotalar joint during walking and running. Foot Ankle Orthop. 2018;3(3)
    [Google Scholar]
  36. , , , et al . Joint-preserving surgery in varus ankle osteoarthritis. J Clin Med. 2022;11(8):2194.
    [Google Scholar]
  37. , , , , , . Indications for supramalleolar osteotomy in patients with ankle osteoarthritis and varus deformity. J Bone Jt Surg. 2011;93(13):1243-1248.
    [Google Scholar]
  38. , , , , . Low tibial osteotomy for osteoarthritis of the ankle. Results of a new operation in 18 patients. J Bone Joint Surg Br. 1995;77(1):50-54.
    [Google Scholar]
  39. , , , . Supramalleolar osteotomies for the treatment of ankle arthritis. J Am Acad Orthop Surg. 2016;24(7):424-432.
    [Google Scholar]
  40. , , , , , . Intra-articular pressure distributions in simulated ankle malunion. Foot Ankle Surg. 2002;8(1):53-57.
    [Google Scholar]
  41. , , . In vitro contact stress distribution on the femoral condyles. J Orthop Res. 1984;2(2):190-199.
    [Google Scholar]
  42. , , , . Contact pressures in the loaded human cadaver hip. J Bone Joint Surg Br. 1975;57(3):302-313.
    [Google Scholar]
  43. , , , , , , . Visualization and quantification of the degenerative pattern of the talus in unilateral varus ankle osteoarthritis. Sci Rep. 2019;9
    [Google Scholar]
  44. , , . The influence of articular surface incongruity on lubrication and contact pressure distribution of loaded synovial joints. Proc Inst Mech Eng [H]. 1998;212(1):11-22.
    [Google Scholar]
  45. , , , . Supramalleolar distal tibiofibular osteotomy for medial ankle osteoarthritis: current concepts. Clin Orthop Surg. 2020;12(3):271.
    [Google Scholar]
  46. , , , , . Determination of in-vivo articular cartilage contact areas of human talocrural joint under weightbearing conditions. Osteoarthritis Cartilage. 2006;14(12):1294-1301.
    [Google Scholar]

Fulltext Views
62

PDF downloads
35
View/Download PDF
Download Citations
BibTeX
RIS
Show Sections

Suggested read for related articles: