A biomechanical analysis of the anterolateral ligament of the knee - a finite element analysis

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A BIOMECHANICAL ANALYSIS OF THE ANTEROLATERAL

LIGAMENT OF THE KNEE: A FINITE ELEMENT ANALYSIS

David Delgadillo Arias. M.D. December 2015.

In Partial Fulfillment of the Requirements for the Degree Master of Biomedical Engineering

University of los Andes Engineering Faculty

Department of Biomedical Engineering Bogota, Colombia.

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ACKNOWLEDGMENTS

I want to thank to all the people who supported this research and also those who advised me to overcome the every difficult steps in the research.

The knee surgeons of the Department of Orthopedics of Fundación Santa Fe de Bogotá, Drs Gamal Zayed, Klaus Mieth, Germán Carrillo and Andrés Patiño. The professor of biomechanics Jaebum Son. The radiologists Oscar Rivero and Rafael Gómez from Fundación Santa Fe de Bogotá. The associate researcher of Utah University, USA, Steve Maas, and the undergraduate students of biomedical engineering of University of los Andes Laura Daza Barragán and Silvana Castillo Gómez.

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iii SUMMARY

Recently there has been an increased interest in a human anatomical structure called anterolateral ligament (ALL) located at the anterolateral region of knee.

Many researchers claim that ALL acts as a stabilizer during internal rotation and flexion of knee, supporting the functions of the anterior cruciate ligament. In this work, a finite element analysis (FEA) was conducted to verify its role claimed by those researchers.

For this purpose, geometrical data of a knee was acquired from an in-vivo magnetic resonance imaging. The structure including the intra- and extra-articular ligaments and ALL was reconstructed in 3D, and an FEA simulation of flexion and internal rotation of the joint was conducted to analyze the behavior of the ligament.

The result suggested that ALL contribute force during internal rotation and flexion of the knee joint. A ligament with this morphology may have an important role during rotational stabilization of the knee.

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TABLE OF CONTENTS

INTRODUCTION ... 1

Context ... 1

Previous research ... 3

Objectives ... 3

Literature review ... 3

METHODS ... 4

Finite element method ... 5

Mesh generation ... 8

Contacts definition ... 10

Materials definition ... 11

Simulation of the finite element model ... 11

Boundary conditions ... 11

Computer specifications ... 12

RESULTS ... 13

DISCUSSION... 15

Limitations ... 15

Future work ... 16

CONCLUSION ... 167

REFERENCES ... 18

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INTRODUCTION

Context

In 1879, Dr. Paul Segond (1) reported the existence of a "pearly, fibrous and resistant band which tightened during internal rotation of the knee” in the anterior and lateral corner of the joint, during his description of a fracture pattern in the anterolateral and proximal tibia. However, it is only after several decades that the structure was mentioned again in the medical literature.

Since 2007 there has been an increase of the interest of this structure located in the anterolateral and external region of the articular capsule of the knee joint, specially due to the paper of Vieira et al. (2) who conducted a detailed analysis of the iliotibial band and observed the anterolateral ligament as an anatomic and functional well defined structure with a location and morphology appropriate to be a ligament. The term “anterolateral ligament of the knee (ALL) was suggested firstly by Terry et al. in 1986 due to similar conclusions about the possible role of this band in the joint (3,4,5).

In later years, Vincent et al. (6), Helito et al. (7), Claes et al. (8), Dodds et al. (9), Stijak et al. (10) and Evan et al. (11) conducted cadaveric studies to find and describe this ligament in the anterolateral region of the knee. The researchers maintained the same name “anterolateral ligament”.

Also, in 2014 some authors (12-19) published the visualization of the ALL in diagnostic images as magnetic resonance imaging (MRI) and ultrasound technology.

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The estimated incidence in the cadaveric studies made since 2007 is of 92.7%. The incidence reported in the studies of MRI is of 91.35%.

Referring to the morphology of the ALL, many investigations has been conducted with several variations. Among them, Claes et al. (8) reported the result from cadaveric dissections of 41 knees. He could find the same anatomic characteristics in all specimens.

The origin of the ALL is in the lateral femoral epicondyle, posterior to the origin groove of the external collateral ligament (ECL) and proximal and posterior to the insertion of the popliteal tendon. The course is oblique to the anterolateral part of the proximal tibia.

The insertion is in the proximal tibia, creating a thick capsular fold, always posterior to the Gerdy’s tubercle. The insertion point is in half-way between a line that connects the Gerdy’s tubercle with the head of the fibula.

During neutral rotation and flexion of 90º, the total longitude is 41.5 ± 6.7 and 38.5 ± 6.1 mm; the average width is 8.3 ± 2.1 mm, to the articular line it narrows to 6.7 ± 3.0 mm and after it wide to 11.2 ± 2.5 mm. The thickness is 1.3 ± 0.6 mm.

The average distance between proximal border of the cartilage of the lateral part of the tibia and the insertion site of the ALL is 6.5 ± 1.4 mm. The center of the tibial insertion point of the ALL is located about 21.6 ± 4.0 mm posterior to the center of the Gerdy’s tubercle and 23.2 ± 5.7 mm anterior to the tip of the head of the fibula.

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3 Previous research

Referring to the biomechanical functions, Parsons et al. (20) analyzed eleven cadaveric knees. They applied the anterior pulling force of 134 N at flexion angles between 0º and 90º and also internal rotation of 5 Nm at the same flexion angles.

The authors concluded that the ALL is an important stabilizer during internal rotation in flexion angles above 35º. Due to this the lesion to this ligament could generate instability in the knee in higher flexion angles; this is the reason why it could be observed a positive pivot shift sign in some patients with an intact anterior cruciate ligament (ACL).

Objectives

According to the recently published articles about ALL, its possible clinical relevance, and the advice of the Knee Section of the Orthopedics Department of Fundación Santa Fe de Bogotá, a project was begun to complement the knowledge about the possible biomechanical functions of this extracapsular ligament via the finite element methodology.

Literature review

The information consulted for this project is from a literature review about ALL. The bases reviewed were Medline, ScienceDirect and SpringerLink for articles in English and Spanish with some of the next search terms: anterolateral ligament of the knee. There were found a total of 27 articles in English, of which 24 were original articles, 2 editorials and 1 poster memory.

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With this information a Topic Review was written to summarize historic, anatomic, radiologic and biomechanical information about the ALL. After this step the development of the finite element analysis was conducted.

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5 METHODS

Finite element method

The finite element method (FEM) started in the 50’s at engineering as a tool to analyze stress in mechanical structures. In 1972 Brekelmans et al. (21) reported for first time this methodology in the orthopedic literature. Since then there are numerous investigations published about FEM applied to biomechanics for the solution of different situations. This quick evolution and application are due to three relevant events: 1) the development of the non-linear theory of mechanics during 50s and 60s 2) the development of FEM and consequently 3) the quick advance of computation science (22).

Three free, open-source software applications developed by images and biomedical engineering laboratories of the universities of Utah, Pennsylvania, Colombia, and Italy were used for this project. ITK-SNAP® (23) was used for the 3D reconstruction of bone tissues and the intra- and extra-capsular ligaments of the knee joint. MeshLab® (24) was used for the mesh preparation of the model reconstructed in the previous step. Finally, FEBio® was used for the non-linear finite element analysis (25).

The simulation was conducted by assigning appropriate materials for the relevant structures. The bones were considered as rigid bodies due to it significantly higher stiffness over soft tissues. Several researchers had done this same assumption (26-29). The ligaments were assumed to have the property of a Mooney-Rivlin model which is very appropriate for structures with one-directional fibers. This material

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model was developed for computer applications of soft biological tissues (30-32) such as tendons, ligaments, and muscles.

Development of the finite element model Creating the geometry

The development of the finite element model started with a knee MRI. The patient was one young female adult with no history of pathologies neither trauma in her knee. The MRI was reviewed by a knee-fellowship (A.F.P.B) to exclude the presence of articular pathologies.

The MRI had three projections; a coronal with slices of 1 mm of thickness, the axial with slices of 0.5 mm of thickness and the sagittal with slices of 0.4 mm of thickness.

The segmentation process started with the software ITK-SNAP® (23). The purpose was to do the segmentation of the biological tissues that act in flexion and internal rotation of the knee. The femur, tibia, fibula, anterior cruciate ligament (ACL), posterior cruciate ligament (PCL), internal collateral ligament (ICL) and external collateral ligament (UCL) were constructed in an individual way.

It was not possible to visualize the ALL in the MRI. This ligament was reconstructed in the same segmentation software taking into account the anatomic characteristics published by Claes et al. (8,14) because they have reported more number of cadaveric dissections and visualizations of the ALL in near 100% of the specimens. Table 1 summarizes the anatomic dimensions that were taking into account for this simulation.

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7 DIMENSIONS OF THE ALL (mm)

Total length 45

Tibial width 12

Femoral width 9

Articular line width 6

Tibial thickness 2

Articular line thickness

1.6

Femoral thickness 1.6

Table 1. Dimensions applied to the anterolateral ligament of the knee according to publications of Claes et al (8,14).

The segmentation process was supervised mainly by A.F.P.B. and by the knee surgeons of Fundación Santa Fe de Bogotá. The outcome obtained in this step consisted in eight different models of every of the previously mentioned tissues (Figure 1).

So, it was possible to obtain a 3D geometry of the knee joint with hard tissues and ligaments to continue with the creation of a finite element model of the knee and the simulation of the ALL functions.

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Figure 1. Geometry reconstructed from a magnetic resonance image of a knee. The model consists in femur, tibia, fibula, intra- and extracapsular ligaments of the knee. The segmentation of each structure was conducted individually. Mesh generation

After obtaining the knee geometry, the surface mesh of the reconstructed joint was generated in MeshLab® software (24), so to convert it again to volumetric mesh which allows finite element analysis. The results were eight different models with a variable quantity of internal elements. (Fig. 2) (Table 2).

The surface mesh of every structure was converted to volumetric mesh in the software FEBio Preview® (25). Also, in this software were set up the boundary conditions for the simulation.

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Figure 2. Surface meshes of the different models of bones and ligaments of the knee.

Table 2. Number of finite elements of each knee structure reconstructed. NUMBER OF FINITE ELEMENTS OF THE KNEE

STRUCTURES Structure N. of elements of the

surface mesh

N. of elements of the volumetric mesh

Femur 14207 6676

Tibia 11129 4938

Fibula 1580 806

ACL 592 414

PCL 1205 814

ECL 332 250

ICL 1362 876

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10 Contacts definition

Then the contacts and interaction between every knee structure was established in FEBio Preview®. The kind of contacts was rigid. In this type of interaction, it is defined a sort of deformable elements which contact to a rigid body. The elements with this kind of contact moves according to the planes of movement of the rigid body during the simulation (33).

This type of contact was the most appropriate because it allows an anatomic situation in the developed model; the bones are considered as rigid bodies and the ligaments are considered as deformable hyperelastic structures.

The contacts defined were:

1. External collateral ligament – Femur 2. External collateral ligament – Fibula 3. Internal collateral ligament– Femur 4. Internal collateral ligament – Tibia 5. Anterior cruciate ligament – Femur 6. Anterior cruciate ligament – Tibia 7. Posterior cruciate ligament – Femur 8. Posterior cruciate ligament – Tibia 9. Anterolateral ligament – Femur 10. Anterolateral ligament – Tibia

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11 Materials definition

The types of materials were assigned in FEBio Preview ®. The bones were configured as rigid bodies because it stiffness is very high in comparison to the ligaments. This assumption is well established in the literature (26-29) for this type of simulations.

The ligaments were considered as Mooney-Rivlin type. This type of material was developed for biological soft tissues as tendons, ligaments and muscles (30-32). In this kind of hyperelastic material it is necessary to apply coefficients to every structure. The constants used in this study come from a previous research published in 1996, where researchers determined the constants from cadaveric tests (34). In the appendix are presented the coefficients applied for this simulation.

Simulation of the finite element model

Boundary conditions

Based on previous research about biomechanics of the ALL and based on the experience of knee surgeons, it was proposed to simulate the flexion and internal rotation of the knee joint to analyze the possible functions of this ligament. There were applied boundary conditions to the femur, tibia and fibula that allow a more anatomical representation of this physiological situation.

In the femur it was restricted the movement in all axes except in the sagittal axe to simulate the flexion. In the tibia and fibula the restrictions were in all axes also except in the axial axe for the internal rotation of the leg.

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12 Computer specifications

The simulation and the analysis were conducted in a computer with a processor Intel Core i7-5500U 2.40GHz with RAM of 8 GB, running Windows 8.1 64 bits operating system

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13 RESULTS

The boundary conditions mentioned previously allowed obtaining information about the possible functions of the ALL. The simulation was done in the software FEBio® and was non-linear type. The total of steps was 10. The number of solid elements that correspond to all the evaluated structures was 30561; the total of nodes was 8691. The simulation consisted in a total of 2766 mathematical equations.

With the information obtained it was possible to observe the effective stress of the ligaments that suffered a deformation during flexion and internal rotation of the knee.

In the simulation it was observed effective stress especially in the ACL, but also in less magnitude in the ALL and in the ECL (Fig. 3).

Figure 3. Effective stress of the anterior cruciate ligament, (A), external collateral

ligament (B) and anterolateral ligament (C).

A B

C

A

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The variations observed in this simulation are agreed with the concept that the ACL is the main stabilizer during flexion and internal rotation of the joint (Figure 4). But the ALL also suffers stress during these movements (Figure 5). The other ligaments suffered a less effective stress during this simulation.

Figura 4. Graph of effective stress vs. time for the ACL.

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15 DISCUSSION

With this research a finite element model of ALL based on MRI was developed and its role during the knee movement was simulated.

The simulation consisted in simple articular movements (flexion and internal rotation) to observe the answer of the ligaments to that physiological situation, especially the behavior of the ALL.

It was possible to demonstrate the ALL acts during flexion and internal rotation of the knee as the ACL but in less magnitude (around a third part), which is a similar concept to the published by Parsons et al. in 2015 about the biomechanics of the ALL.

The software used in this Project were developed by relevant universities in the field of bioinformatics and also free access, which allows to extend the knowledge about the finite element models and its application to biomechanics.

Limitations

There were several limitations in the development of this study.

First, it was not possible to observe ALL in the MRI, probably due to the lack of a specific diagnostic protocol to visualize this structure in the Radiology Department consulted. Another possible reason that ALL was not identified that ALL has very small dimensions in comparison to other ligaments. Nevertheless, it was possible to reconstruct ALL according to the morphology published in the medical literature. Second, though it was possible to obtain a volumetric mesh for the simulation it could be better to develop a more complex mesh with more quantity of finite elements to obtain more precise outcomes.

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Third, the material model applied to the ligaments was developed in the past for biological structures; but nowadays there are other advanced material models that could allow a more accurate anatomic simulation.

Last, the methodology of finite elements is broadly used in biomechanical investigations. However, the results are usually validated with cadaveric models to improve the clinical relevance of the obtained information. In this research no cadaveric model was used to validate the result from the simulation.

Future work

It is necessary to develop a better finite element model with more complexity to complement the information obtained in this research. The development of more anatomical models with different clinical studies from several healthy patients would allowing obtaining more accurate information about the quantity of effective stress that suffer the ligaments, including the ALL.

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CONCLUSION

ALL of the knee is a real structure located outside the articular capsule. It has been studied since 2007 because of its possible roles in the rotation stabilization of the lower limbs. Nowadays the theory about its biomechanical functions is based in the secondary stabilization of the internal rotation of the lower leg due to its little size and the oblique course from the femur to the tibia.

It was possible to demonstrate in a finite element model that the ALL suffers effective stress during the flexion and internal rotation of the knee, which suggest a role during the stabilization of those movements.

It is necessary to conduct more biomechanical studies in cadaveric specimens and more finite element analysis with more complex models to validate the role of the ALL as a knee stabilizer.

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APPENDIX

<lam_max>1.03</lam_max>