1. Reference Simulation

This section describes the specific steps and boundary conditions that are being used during an Abaqus FE simulation that is used to define the reference ligament meshes (described here: Reference State).

Note

The femur, tibia, patella, cartilage, and menisci do not move or deform in this simulation. They remain in the same position as in the MR image throughout. The purpose of this simulation is to define the position of ligament and tendon mesh nodes so they do not overclose any other bodies.

In this simulation:

  • The femur, tibia, patella, cartilage, and menisci are fixed in all DOF
  • The femur, tibia, patella, cartilage, and menisci are rigid
  • Ligaments and tendons are defined with a prestrain of -5%

There are three steps for this simulation:

  1. Initial settle
  2. Wrap bones
  3. Wrap soft tissue

1.1. Initial settle

Ligaments may be overclosing other bodies by a large amount at the beginning of a simulation (due to the way that the ligament meshes are defined). Additionally, the ligaments may be assigned a prestrain where they will be carrying load at the start of the simulation. During pilot testing it was noticed that ligaments are more stable if there is an initial step where there are no active interactions between the ligaments and other surfaces.

The total time for this step is 0.01 seconds.

1.1.1. Interactions

There are no ligament interactions, and the other geometry is rigid and fixed, so there are no need to define interactions in this step.

1.1.2. Kinematic Boundary Conditions

Femur

The femur is fixed in all degrees of freedom throughout this step.

Tibia

The tibia is fixed in all degrees of freedom throughout this step.

Patella

The proximal nodes in the quadriceps tendon will be fixed in all degrees freedom in this step.

The patella is fixed in all degrees of freedom throughout this step.

1.1.3. Kinetic Boundary Conditions

Femur

No external loads are applied to the femur in this step.

Tibia

No external loads are applied to the tibia in this step.

Patella

No external loads are applied to the patella or the quadriceps tendon in this step.


1.2. Wrap bones

The ligament and tendon meshes are defined based on their insertion sites, and they may be overclosing other bodies in the simulation. This step activates the ligament and tendon interactions with the femur, tibia, and patella. These bodies are the first to have ligament interactions because their kinematics will remain fixed.

The total time for this step is 0.1 seconds.

1.2.1. Interactions

The ligament/tendon interactions with the osseous femur, tibia, and patella are activated. Interactions of the ligaments with the menisci and cartilage are still inactive in this step because the amount of overclosure may lead to instability.

Table 1.1 Active interactions between different bodies and structures during the Wrap bones step.
Name Femur Tibia Patella Femoral Cartilage Tibial Cartilage Patellar Cartilage Medial Meniscus Lateral Meniscus
amACL x x            
plACL x x            
alPCL x x            
pmPCL x x            
sMCLProx x x            
sMCLDist x x            
dMCL x x            
LCL x              
ALL x x            
PFL x x            
OPL x x            
MPFL x   x     x    
LPFL x   x     x    
Patellar Tendon x x            
Quadriceps Tendon x              

1.2.2. Kinematic Boundary Conditions

Femur

The femur is fixed in all degrees of freedom throughout this step.

Tibia

The tibia is fixed in all degrees of freedom throughout this step.

Patella

The proximal nodes in the quadriceps tendon will be fixed in all degrees freedom in this step.

The tibia is fixed in all degrees of freedom throughout this step.

1.2.3. Kinetic Boundary Conditions

Femur

No external loads are applied to the femur in this step.

Tibia

No external loads are applied to the tibia in this step.

Patella

No external loads are applied to the patella or the quadriceps tendon in this step.


1.3. Wrap soft tissue

The previous step activated ligament interactions with the bones, and this step activates ligament interaction with the cartilage and menisci.

The total time for this step is 0.1 seconds.

1.3.1. Interactions

The interactions from the previous step are still active, and the ligament/tendon interactions with the cartilage and menisci are activated. This step activates the remaining interactions that are being defined for the simulation.

Table 1.2 Active interactions between different bodies and structures during the Wrap soft tissue step.
Name Femur Tibia Patella Femoral Cartilage Tibial Cartilage Patellar Cartilage Medial Meniscus Lateral Meniscus
amACL x x   x x   x x
plACL x x   x x   x x
alPCL x x   x x   x x
pmPCL x x   x x   x x
sMCLProx x x   x x   x  
sMCLDist x x   x x   x  
dMCL x x   x x   x  
LCL x     x        
ALL x x   x x     x
PFL x x   x x     x
OPL x x   x x     x
MPFL x   x     x    
LPFL x   x     x    
Patellar Tendon x x   x        
Quadriceps Tendon x     x        

1.3.2. Kinematic Boundary Conditions

Femur

The femur is fixed in all degrees of freedom throughout this step.

Tibia

The tibia is fixed in all degrees of freedom throughout this step.

Patella

The proximal nodes in the quadriceps tendon will be fixed in all degrees freedom in this step.

The patella is fixed in all degrees of freedom throughout this step.

1.3.3. Kinetic Boundary Conditions

Femur

No external loads are applied to the femur in this step.

Tibia

No external loads are applied to the tibia in this step.

Patella

No external loads are applied to the patella or the quadriceps tendon in this step.