ETD

Archivio digitale delle tesi discusse presso l'Università di Pisa

Tesi etd-04022019-192350


Tipo di tesi
Tesi di laurea magistrale
Autore
DEIDDA, MICHELA
URN
etd-04022019-192350
Titolo
Modelling knee contact mechanics in OpenSim
Dipartimento
INGEGNERIA DELL'INFORMAZIONE
Corso di studi
INGEGNERIA BIOMEDICA
Relatori
relatore Prof.ssa Di Puccio, Francesca
correlatore Dott.ssa Curreli, Cristina
Parole chiave
  • Elastic Foundation Model
  • OpenSim
  • Hunt and Crossley Model
  • knee contact
Data inizio appello
24/04/2019
Consultabilità
Non consultabile
Data di rilascio
24/04/2089
Riassunto
Introduction

One of the most important topics in orthopaedics is determining how the net force and moment at a joint are transmitted by the muscles and ligaments and by contact between the articular surfaces. The study of the knee is of particular interest because of the high incidence of ligament injury and osteoarthritis which is one of the main causes of total knee arthroplasty. The forces transmitted across the tibiofemoral joint of the knee cannot be measured directly. It is therefore necessary to develop musculoskeletal models in order to estimate the mechanical quantities. An important consideration in creating a musculoskeletal model to simulate and study human motion, is determining a suitable trade-off between model complexity and simulation speed. For example torque-driven models are computationally fast but they are limited in their biological accuracy. At the other extreme, finite-element simulations well represent complex muscle geometry, but are computationally expensive. Between these extremes are muscle-driven models with Hill-type muscle actuators and 3D skeletal geometry, such as the OpenSim musculoskeletal models. The aim of this thesis is to study the knee contact forces in OpenSim with different contact force models and different force estimation procedures for a linear knee flexion.

Materials and Methods

OpenSim is an open-source software that enables to build, exchange, and analyse musculoskeletal models and dynamic simulations of movement in several applications, i.e. biomechanics research, orthopaedics and rehabilitation science, robotics research. With this software it is possible to compute the joint reactions with models which simplify the knee joint as a hinge (1 degree of freedom (dof)), or with more detailed knee models (6 dof) which involve compliant contact models. Specifically, in OpenSim two compliant contact models are available: Hunt and Crossley Model (HCM) and Elastic Foundation Model (EFM). The constitutive law’s choice is not arbitrary, but depends on the contact surfaces geometry. In OpenSim three types of surface models are available: planes, spheres and triangular meshes. Particularly, HCM is used when simple geometries, such as spheres and planes are involved in the contact phenomenon. In this model the contact force is based on an hertzian term and a dissipation force. However, when complex geometries are involved in the contact event, the triangular meshes are utilized and the EFM is applied. It implements a "bed of springs" contact model and the contact force includes two components: a conservative elastic force and a dissipation force.
In order to study the contact phenomenon the first simulations were carried out with simple geometries such as a sphere and a plane. Firstly, the elastic contact of a bouncing sphere on a plane was studied in four different cases where the geometries were realized with the OpenSim functions or imported as triangular meshes. Secondly, a quasi-static case of a sphere on a plane was carried out and the contact phenomenon was studied when an external force was applied and also when a vertical translation of the sphere was set from the user. For all these studies a comparison between the HCM and EFM was performed. Specifically for the EFM, several geometries with different mesh density were realized in order to investigate how this parameter affects the estimation of contact forces.
In the second part of the thesis, the contact knee analysis was carried out by studying the linear flexion task of the knee with two different methods: a serial approach, based on two steps, and a cosimulation approach. In the first step of the serial approach a whole body model with a hinge knee joint was used to estimate the muscle forces with the Static Optimization (SO) and the Computed Muscle Control (CMC) tools. Secondly, the hinge joint was replaced with a detailed knee model with 7 dof (6 dof for the tibiofemoral joint and 1 dof for the patellofemoral joint), which includes 18 ligament bundles and the contact geometries: two spheres in the femur condyles and a plane in the tibial plateau. With this model and the muscle force data obtained in the first step, the contact forces between the spheres and the plane were computed using the different contact models and changing the mesh density and the stiffness parameter for the EFM.
In the cosimulation the muscle forces estimation with the CMC and the contact force analysis were both computed directly in the whole body with the detailed knee model.

Results and discussion

Sphere on a plane simulations
In the quasi-static case of a sphere on a plane, the results showed that, when an external force is applied, the maximum value of the contact force is greater for the EFM than the HCM and the body indentation is greater for the HCM. In the EFM case it is possible to see how the maximum contact force value and the indentation of the body decrease with the mesh density.
When a vertical translation is set to the sphere, the contact force reacts with a greater value for the EFM with respect to the HCM and is higher in the denser mesh. For the HCM some simulations with different values of the stiffness parameter were performed, showing how it plays a crucial role for the contact between the two bodies in terms of response forces and indentation.

Knee simulations
In the serial approach the muscle forces estimation computed in the knee hinge joint with the SO and CMC tools returned different but close results. The contact forces obtained with the EFM in the detailed knee model showed an oscillatory trend with respect to the HCM results. Thus, different parameters were changed in order to obtain a smoother trend. The stiffness parameter was changed to the same value of the HCM stiffness. The results obtained showed a better behaviour.
The kinematics coordinates obtained with the 7 dof model showed that the knee flexion angle did not achieve 90 degrees, meanwhile the other rotations and translation are greater than the hinge coordinates. Therefore, a cosimulation was performed in order to compute the muscle and contact forces directly in the 7 dof model. This approach had some critical issues, such as the computational cost of the simulations (higher for the denser mesh), the choice of the CMC look-ahead window and the need to add a reserve actuator in order to achieve the force necessary to execute the required task. The kinematical coordinates showed a better behaviour with respect to the serial approach coordinates: the FE angle achieved the 90° and the other coordinates showed more reasonable results. The three components of the contact forces between the two spheres and the plane, defined the magnitude of the medial and lateral forces acting in the knee.

Conclusion

The knee contact force estimation is strongly dependent on the stiffness and damping parameters defined in the contact model (EFM, HCM). The serial approach based on the SO tool produces closer results to those estimated with the hinge joint than the cosimulation. As for the CMC tool, when applied in the serial approach it is faster than the cosimulation but may alter the desired kinematics. Meanwhile the cosimulation analyses can have convergence problems and higher computational cost but produce more meaningful results.
These results obtained in the detailed knee model could depend on the different parameters and structures adopted in the model, such as the ligaments. In fact, in a knee model with several dof, the passive action of the ligaments is of particular interest in terms of knee stability. Thus, a future development could involve the ligament properties and the study of the contact force estimation with respect to different ligament parameters. Finally, more elaborate tasks such as gait could be analysed.
File