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Journal of Orthopaedics logoLink to Journal of Orthopaedics
. 2023 Apr 21;40:7–16. doi: 10.1016/j.jor.2023.04.016

Finite element analysis of a healthy knee joint at deep squatting for the study of tibiofemoral and patellofemoral contact

Rohan Kothurkar a,∗, Ramesh Lekurwale a, Mayuri Gad b, Chasanal M Rathod b,c
PMCID: PMC10151221  PMID: 37143926

Abstract

Background

In non-western countries, deep squatting is a daily activity, and prolonged deep squatting is common among occupational squatters. Household tasks, taking a bath, socializing, using toilets, and performing religious acts are among the activities frequently carried out while squatting by the Asian population. High knee loading is responsible for a knee injury and osteoarthritis. Finite element analysis is an effective tool to determine stresses on the knee joint.

Methods

Magnetic Resonance Imaging (MRI) and Computed Tomographic (CT) images were acquired of one adult without knee injuries. The CT images were acquired at the fully extended knee and one more set of images was acquired with the knee at a deeply flexed knee position. The MRI was acquired with the fully extended knee. 3-Dimensional models of bones were created using CT and soft tissue using MRI with the help of 3D Slicer software. Kinematics and finite element analysis of the knee was performed for standing and deep squatting posture using Ansys Workbench 2022.

Results

High peak stresses were observed at deep squatting compared to standing along with the reduction in the contact area. Peak von Mises stresses on femoral cartilage, tibial cartilage, patellar cartilage, and meniscus were increased from 3.3 MPa to 19.9 MPa, 2.9 MPa to 12.4 MPa, 1.5 MPa to 16.7 MPa and 15.8 MPa to 32.8 MPa respectively during deep squatting. Posterior translation of 7.01 mm, and 12.58 mm was observed for medial and lateral femoral condyle respectively from full extension to 153° knee flexion.

Conclusions

Increased stresses in the knee joint at deep squat posture may cause cartilage damage. A sustained deep squat posture should be avoided for healthy knee joints. More posterior translations of the medial femoral condyle at higher knee flexion angle warrant further investigation.

Keywords: Osteoarthritis, Articular cartilage, Deep squat, Finite element analysis

1. Introduction

The need for knee joint analysis has become important nowadays because of changes in the lifestyles of the human being for every age group. Squats can be categorized into partial squats with around 40° knee flexion angle, half squats from 70° to 100° knee flexion angle, and deep squats greater than 100° knee flexion angle.1 Deep squatting is a common practice in countries like India, China, Japan, and the Middle East. The sustained deep squat can be widely seen amongst occupational squatters. Most of the world's population including India, Japan, China & middle east use eastern-style toilets where a person needs to squat over a hole.2 Due to the diverse culture and religion of India and the prevalence of floor-based everyday activities, sitting positions that necessitate deep joint flexion are extremely important to this population.3 Some occupational activities like mining, construction, and manufacturing require deep squatting.4 Squatting, however, increases the risk of developing knee osteoarthritis compared to other activities like walking, lifting, and climbing stairs.5

As the knee joint is a highly complex and heavily loaded joint in the human body, knowledge of knee joint contact forces is very much important for different treatment options and to optimize clinical outcomes.6 Knee osteoarthritis also referred to as a degenerative joint disease, is frequently caused by wear and tear and the gradual loss of articular cartilage. The elderly are the demographic where osteoarthritis occurs most frequently, but it can also be initiated by an unusual load distribution across the joint. Moderate mechanical loading which are forces acting on the knee joint is necessary for maintaining healthy cartilage and abnormal joint loading increases the risk of osteoarthritis.7 It is very important to determine internal knee joint loading as it will help to understand deep squatting posture and will affect to design of physiotherapy exercise protocol.

Methods to determine knee loading includes experimental and theoretical studies. Experimental methods can be further classified into in vivo and in vitro experiments. In vivo studies use instrumented knee implants to measure knee joint contact forces and moments. A lot of in vivo studies8 have assessed the forces at the tibiofemoral joint during squatting, however, the greatest knee flexion angle was only about 100°. The drawback of this method is, it measured forces on knee implants and not on the physiological joint surfaces. Moreover, this method does not estimate contact areas, contact pressure, and stress distribution on soft tissues like cartilage and meniscus. A cadaver can be used for in vitro experimental studies to quantify joint contact forces and pressure, but this has the drawback that neither agonist nor antagonist muscle control is available. Previous in vitro cadaver studies9, 10, 11, 12, 13, 14, 15 measured knee joint contact forces requiring a knee joint simulator. Mathematical modeling can be further classified into mathematical modeling and Finite Element Analysis (FEA) studies. A lot of work has been done to estimate knee joint contact forces using two-dimensional and three-dimensional mathematical modeling during squatting but the major drawback of this method is that it estimates only contact forces and moments.8 Recently, musculoskeletal modeling and simulation give better prediction of knee joint contact forces compared to traditional 2D or 3D modeling. A systematic review8 reported that the knee joint contact forces peaked at an angle of knee flexion of around 90° rather than at the maximum angle but forces at maximum knee flexion angle are also considerably high. Finite element study on the other hand is capable to determine contact forces, contact areas, and stresses in the knee joint's soft tissues. In biomechanics, FEA has been widely used, and more studies of the knee using FEA techniques are being published. The knee joint FEA is a computer simulation that represents three-dimensional geometry, material properties, loads, and movements and produces useful results. This study used FEA with knee joint contact forces as input loading conditions.

A lot of research has been done to understand the tibiofemoral contact of the natural knee (knee without injury) using FEA to simulate various activities like static standing16, 17, 18, 19, 20 and walking,21, 22, 23, 24 but very few for deep squatting.25 The greatest angle of knee flexion analyzed using FEA during squatting is around 130° but the greatest angle of knee flexion achieved by the non-western population is around 165°.2 Moreover, the Indian knee is smaller compared to the western,26 Chinese, and Hispanic knees.27 FEA can also be used to understand cartilage degeneration.28

Most of the static standing studies use body weight as input contact force.17,29 Some studies use kinematics and joint contact forces22,23 as input for FEA while some use muscle forces.30 On the articular cartilage, it can be presumed that stress that is more than normal may contribute to knee osteoarthritis. Potential reasons for higher stress are obesity, physical activities, and joint trauma. Contact area reduction at higher flexion activity is a possible reason for higher stresses.25 When squatting, the medial and lateral femoral condyles can be seen moving from full extension to deep knee flexion. Understanding healthy deep flexion kinematics would help develop a conservative clinical rehabilitation regimen for knee osteoarthritis and in improving knee prosthesis design.

The goal of our study was to create a subject-specific knee joint 3D model to comprehend deep squatting kinematics and conduct FEA which provides the tissue-level mechanical response. Additionally, this mechanical reaction may shed light on the cause of osteoarthritis as a result of deep squatting. The 3D model includes bones, articular cartilages, and menisci to examine the contact stress distributions on the menisci and articular cartilages at full extension and deep flexion. For this purpose, knee joint contact forces from the literature were used as input conditions to perform FEA of the subject-specific 3D knee model.

2. Materials and methods

2.1. MRI and CT acquisition

One adult (33 years, 55 kg, and 1.7 m, male, right knee) without knee injury underwent MRI (1.5T, 1.5 mm slice thickness) and CT (0.6 mm slice thickness) scans. Under the Institutional Ethical Committee's approval, the subject gave informed consent. The CT images were acquired with the fully extended knee and one more set of images was acquired with the knee in a deep flexion posture (Fig. 1). The MRI was acquired with the fully extended knee.

Fig. 1.

Fig. 1

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Workflow of the study.

2.2. Three-dimensional model creation

A 3D model of the bones and soft tissue was produced using CT and MRI, respectively. All the Digital Imaging and Communications in Medicine (DICOM) formatted images were used to create a 3D solid of the femur, tibia, femoral articular cartilage, tibial articular cartilages, and menisci using 3D Slicer software (Fig. 2). Under the supervision of an experienced orthopaedist, the manual segmentation procedure of bony and non-bony structures of the knees was carried out to reduce variation in the models. The surface geometry was then transformed into a solid geometry by using the AutoSkin feature of ANSYS SpaceClaim.

Fig. 2.

Fig. 2

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The procedure for segmenting contours in 3D Slicer software: (a) cartilages and menisci using MRI (b) bone at full extension using CT (c) bones at deep flexion using CT.

2.3. Material properties and meshing

The femur was modeled as an isotropic elastic material with an elastic modulus of E = 17,000 MPa and Poisson's ratio of v = 0.3.31 The tibia was modeled as an isotropic elastic material with an elastic modulus of E = 13,000 MPa and Poisson's ratio of v = 0.3.31 The inner structures of bone were ignored as we aim to study cartilage behavior during squatting. The patella was modeled as a homogenous isotropic linear elastic material of E = 15,000 MPa, Poisson ratio v = 0.30.32 The articular cartilages were modeled as an isotropic elastic material with an elastic modulus of E = 20 MPa and Poisson's ratio of v = 0.49.33 The menisci were modeled as transversely isotopic elastic using a cylindrical coordinate system (Fig. 3) with material properties out-of-plane Young's modulus 20 MPa, in-plane Young's modulus 159.60 MPa, in-plane Poisson's ratio = 0.3, out-of-plane Poisson's ratio 0.01, the out-of-plane shear modulus 50 MPa.33 To find the appropriate mesh size, the mesh density was gradually increased until the maximum errors in the calculated stresses were less than 5%. The convergence results showed that when the mesh size was reduced for cartilages and menisci from 3 mm to 2.5 mm, 2.5 to 2 mm, 2 mm–1.5 mm, and 1.5 mm–1 mm, the highest contact stresses change to 9.8%, 8.4%, 6.1%, and 4.1%, respectively. Therefore, it was decided that an average element size of 1.5 was acceptable. Quadratic tetrahedral elements were used to perform thses simulations. Menisci and cartilages were represented by 98,261 elements, and bone surfaces were represented by 44,135 elements. For bone, a size of 1.5 mm was used only at the contact between cartilages using the contact sizing feature of ANSYS Workbench 2022 to reduce computational cost (Fig. 4).

Fig. 3.

Fig. 3

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3D solid knee model with cylindrical coordinate system and spring elements for meniscus.

Fig. 4.

Fig. 4

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3D solid knee model with the mesh type, bones, and soft tissues for the knee a) tibiofemoral during standing b) patellofemoral during standing c) tibiofemoral during deep squatting d) patellofemoral during deep squatting.

2.4. Boundary condition and loading

Analysis was done using ANSYS Workbench 2022. Knee joint contact forces and kinematics were used as boundary conditions to simulate standing and deep squatting. The tibia was considered fixed (constrain all degrees of freedom) and tibiofemoral contact force was applied to the femur to mimic a fully extended as well as deep squat position. A separate simulation was performed for a patellofemoral joint where the femur is considered fixed and a load was applied to the patella at deep flexion. Static analysis was carried out in the deep flexion and complete knee extension positions. A force of 700 N was applied to the mechanical axis while standing from the middle of the femoral head (CPU time = 733.45 s, memory used = 2125 MB). In the deep squatting position, a resultant load of 1100 N was applied to the femur through a remote point at the joint center (CPU time = 1578.46 s, memory used = 6472 MB). To estimate patellofemoral stresses a load of 50 N was applied to the patella and the femur was kept fixed simulating standing (CPU time = 361.37 s, memory used = 1488 MB). To simulate a deep squatting posture, a resultant load of 2000 N was applied to the patella keeping femur fixed (CPU time = 1620.1 s, memory used = 2602 MB). All load values were taken from the previous study34 that estimated knee joint contact forces during stand to deep squat using OpenSim software. Fig. 4 illustrates all loading conditions where input forces were represented by a red arrow. For connections between cartilage and bones, a ‘Bonded’ (then no sliding or separation between faces or edges is allowed) contact type was defined. Between menisci to cartilage, femoral cartilage to tibial cartilage, and patella cartilage to femur cartilage the ‘frictionless’ contact type was used. A penalty-based approach was employed to define contacts. Linear springs with a rigidity of 2000 N/mm were attached to the tibia plateau at each horn connection (Fig. 3).35,36

2.5. Translation measurement

To measure tibiofemoral kinematics, femoral reference points that were unaffected by knee flexion were defined. The posterior femoral condyles appear circular in the sagittal plane and the centers of these circles are called the ‘Flexion Facet Center’ (FFC).37 These centers were used as reference points to measure the relative movement of the tibia. We placed circles over the mid-medial and mid-lateral sagittal plane of the 3D model created in ANSYS SpaceClaim to identify the centers of the circles. For both the deep flexion and full extension positions, the distance between this center and the ipsilateral posterior tibial cortex was evaluated following the procedure used by H. Iwaki et al.38 The method to calculate this distance is shown in Fig. 9, and the translation was determined by comparing the distances at maximum extension and deep flexion.

Fig. 9.

Fig. 9

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Distance between FFC and ipsilateral posterior tibial cortex a) medial component at extension b) medial component at deep flexion c) lateral component at extension d) lateral component at deep flexion.

3. Results

For tissue FEA, the von Mises stress is frequently used to quantify stress. The von Mises failure prediction methods give information about biological tissues that are susceptible to failure. In considering the current static upright and deep squatting stance, peak stress was evaluated according to the Von Misses criteria. The peak von Mises stresses and their distribution may suggest the initiation of osteoarthritis.

3.1. von Mises stress in the tibiofemoral joint

A higher value of tibiofemoral stress was observed during squatting (Fig. 6) as compared to sanding (Fig. 5). Additionally, it was found that the contact stress location on the tibia cartilage is more posterior in the squatting posture than it is when upright, where it is uniformly dispersed. Moreover, The contact area on the tibial cartilage was 519.7 mm2 for standing and 349.8 mm2 for squatting posture.

Fig. 6.

Fig. 6

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Simulated outcomes of a knee at squatting a) femoral cartilage, b) tibia medial cartilage, c) tibia lateral cartilage d) medial menisci e) lateral menisci.

Fig. 5.

Fig. 5

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Simulated outcomes of a knee at standing a) femoral cartilage, b) tibia medial cartilage, c) tibia lateral cartilage d) medial menisci e) lateral menisci.

3.2. von Mises stress in the patellofemoral joint

Similar results were obtained in the case of patellofemoral stress. A higher value of patellofemoral stress was observed during squatting (Fig. 8) as compared to sanding (Fig. 7). Additionally, it was found that the contact stress location on the patella cartilage is more at corners in the squatting posture than it is when upright, where it is at the center. The contact area on the patella 97.06 mm2 cartilage was for standing and 268.7 mm2 for squatting posture.

Fig. 8.

Fig. 8

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Simulated outcomes of patellofemoral stresses of a knee at squatting a) femoral cartilage, b) patella cartilage.

Fig. 7.

Fig. 7

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Simulated outcomes of patellofemoral stresses of a knee at standing a) femoral cartilage, b) patella cartilage.

3.3. Translation measurement

The medial femoral condyle demonstrated a posterior translation of 7.01 mm, while the lateral femoral condyle demonstrated a posterior translation of 12.58 mm from 153° of knee flexion to maximum extension (Fig. 9).

The tibia cartilage and femoral were discovered to be the most affected structures, even though von Mises stress increases in all components at deep squatting posture. This may make it easier to comprehend how and where osteoarthritis initiates as a result of repeated deep squatting.

4. Discussion

In this study, a 3D FEA model of the knee joint was developed to simulate deep squatting activity and to understand the stress distribution pattern. The primary goal of the study was to compare the contact stress distributions in the patellofemoral and tibiofemoral joints at full extension and deep flexion. Furthermore, kinematics analysis was carried out to comprehend deep squatting kinematics. FEA can mimic biomechanical situations in real life that would be difficult or unethical to perform using experimental study. The FEA study was carried out for deep squatting because it may be a daily habit that contributes to osteoarthritis in non-Western populations. The 3D model geometry created was compared with the open-source OpenKnee project39 available. This study showed that stresses were more at the deepest flexion compared to standing. Peak von Mises stresses on femoral cartilage, tibial cartilage, patellar cartilage, and meniscus were increased from 3.3 MPa to 19.9 MPa, 2.9 MPa–12.4 MPa, 1.5 MPa–16.7 MPa and 15.8 MPa–32.8 MPa respectively during deep squatting. Peak tibiofemoral stresses obtained during standing and deep squatting are consistent with the literature (Table 1 and Table 2). Patellofemoral stresses for standing were also consistent with a previous study where peak stress was 1.87 MPa for a 300 N load. The increase in von Mises stress was because, as the flexion angle increases, the contact area of the tibiofemoral joint was reduced, moreover applied contact forces are much more at squatting than standing. Similar results were obtained in previous studies.25,40 The 19.19 MPa was the maximum contact stress analysis result of the current study near 25 MPa cartilage rupture limitation.41 The contact area at the tibial plateau measured by in vitro cadaver studies was around 599 mm2 at 98°9 and 150 mm2 at 120°.42 The lateral femoral condyle translated up to the meniscus posterior horn. In our study, no contact was observed between lateral femoral cartilage and meniscus. This is because the spring element was used for the horns of the meniscus that attach with bone. In comparison to the literature, there were differences in stresses and contact area, and these differences vary from individual to individual depending on the loading direction, force applied, soft tissue thickness, and knee measurements. Higher stresses indicate more chances of tibiofemoral and patellofemoral knee osteoarthritis due to deep squatting which is consistent with clinical studies.43

Table 1.

Comparison of the peak tibiofemoral Von Mises stresses (MPa) recorded at static standing in this investigation with previous research.

Author Femoral cartridge (MPa) Lateral Tibial cartridge (MPa) Medial Tibial cartridge (MPa) Lateral meniscus (MPa) Medial meniscus (MPa) Applied load (N)
Kemal Gokkus12 1.75 1.68 5.14 10.94 1000
Wang et al.18 – 13 – – 400 to quadriceps and 300 to knee
Trad et al.37 1.75 1.93 2.65 – – 740
Jiang et al.38 11.81 760
Thienkarochanakul et al.39 2.34 1.582 4.781 800
The present work 3.3 2.3 2.9 14.3 15.8 700
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Table 2.

Comparison of the peak tibiofemoral Von Mises stresses (MPa) recorded at deep squatting in this investigation with previous research.

Author Femoral cartridge (MPa) Lateral Tibial cartridge (MPa) Medial Tibial cartridge (MPa) Lateral meniscus (MPa) Medial meniscus (MPa) Applied load (N) at knee flexion angle
Wang et al.18 21 – – 400 to quadriceps and 300 to knee at 140°
The present work 19.19 12.4 8.5 – 32 1100 at 153°
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The medial posterior translation was more in this study than in earlier ones, although the quantity of lateral compartment femoral posterior translation was marginally different. (Table 3). This variation might result from 1) different measurement techniques used, 2) differences in the size of the knee 3) weight-carrying and non-weight-carrying conditions, and 4) maximum knee flexion angle. The higher knee flexion angle of the current research in comparison to other research may be the reason for more medial component translation. Non-Western participants can achieve around 160° knee flexion angle44 and further study with more participants is demanded to understand deep squat kinematics. Understanding deep knee flexion kinematics may help high-flexion knee implant designers as kinematic patterns have been linked to overall survivability, outcome scores, and patient satisfaction with an implanted knee.45

Table 3.

Comparison of femur translation to previous studies.

Study Femur lateral component translation (mm) Femur medial component translation (mm) The femur external rotation or tibial internal (degree) Comment
Iwaki et al.32 19 2 20 6 male, cadaver knees, MRI, 140° knee angle
Tanifuji et al.42 15.6 3.9 26.1 10 male, 10 female, CT, 140° knee angle 140°
Asano et al.43 17.8 5.0 (anterior)
1.2 (posterior)		 29.1 6 in vivo knees, Japanese, CT, 120° knee angle
P. Johal31 30.9 8.4 – 10 males, Caucasian, MRI, 140° knee angle
The present work 12.58 7.01 15 1 male, Indian, CT, 153° knee angle
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Squatting cause higher values of stress with less contact area in the patellofemoral and tibiofemoral joints, which can impact knee health. Prolonged deep squatting should be avoided. The findings of this translation measurement study indicate that a more thorough investigation is necessary to fully comprehend the kinematics of deep flexion because the medial tibial component is more mobile at deeper flexion angles. This kinematic investigation will be helpful for high-flexion knee implant designers.

This study has some limitations. Tibiofemoral kinematics were determined in non-weight-carrying conditions which may produce a greater magnitude of tibia internal rotation.37 To understand deep flexion kinematics CT images were used only for full extension and deep flexion. Fluoroscopy46 or Mobile Biplane X-ray Imaging System47 can be used to understand the entire squat cycle. However, A lot of research has been done up to 140° knee flexion angle. Knee kinematics for maximum deep flexion should be taken into account in future research. All ligaments were neglected for FEA in this study. This is because we performed static simulations and the bones were constrained by boundary conditions. Moreover, the objective of this FEA study was only to understand cartilage. To analyze contact stresses, the cartilage was thought to behave as an isotropic, linearly elastic, and homogenous material. This is because, standing and deep squatting simulations were performed for a short period, and at knee flexion angles of 0° and 153°, it was considered that the time-dependent impact was minimal.

5. Conclusion

Finite Element Analysis is capable to provide detailed loading of the knee. This study found a significant increase in peak von Mises stresses on femoral cartilage, tibial cartilage, patellar cartilage, and meniscus during deep squatting, and the posterior portions of the medial and lateral tibial cartilage are the most vulnerable to the development of osteoarthritis as a result of deep squatting. The medial region showed more stress than the lateral region during standing as well as squatting. Both medial and lateral femoral condyle undergoes posterior translation but more posterior translations of the medial femoral condyle at higher knee angle compared to other studies warrant further investigation that may help knee implant designers. This study sheds light on stress and contact location that is most vulnerable to cartilage damage.

Funding/sponsorship

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

Informed consent

Informed consent was provided to the participant.

Institutional Ethical Committee approval

The study was approved by the Institutional Ethical Committee.

Author statement

Rohan Kothurkar (ME Mechanical) – Conceptualization, Software, Formal analysis.

Dr. Ramesh Lekurwale (Ph.D. Mechanical) – Methodology, Validation.

Dr. Mayuri Gad (MS Sports Science) - Data collection, Resources.

Dr. Chasnal Rathod (MS Orthopedics) – Validation, Supervision.

Declaration of competing interest

None.

Acknowledgment

None.

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