Interactions and Ties¶
Ineraction - Ligaments and Tendons¶
These interactions are defined for both spring and continuum representation of ligaments and tendons.
Contact¶
A pressure-overclosure relationship is defined between the connective tissue and bodies that the tissue may contact. Contact damping is also specified so collisions between the tissues and contact surfaces is not perfectly elastic. This reduces the oscillation of the connective tissues in the simulation. To save on computational cost, interactions are only defined between connective tissues and nearby bodies Table 9.
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 |
A linear pressure-overclosure relationship is specified, where the interaction between the bone surface and a ligament node begins when the node has a clearance of 0.01 mm (i.e the node is not yet touching or overclosing the surface). Specifically, the relationship is a contact force-overclosure relationship. This is a force-overclosure relationship, and not a pressure-overclosure relationship because the ligament surface is defined as a node-surface. As the node overclosure increases, the contact force increases at a rate of 990 N/mm.
The Abaqus input for this interaction is defined as:
*Surface Behavior, pressure-overclosure=TABULAR
0.0e3, -0.01
1.0e3, 1.0
*Contact Damping, definition=DAMPING COEFFICIENT
0.25,
Ties/Connections¶
Insertion sites¶
The nodes that define each ligament/tendon fiber’s insertion are rigidly tied to the corresponding bone’s fixed coordinate system.
If in the future, a ligament and/or tendon is being modeled as a continuum, then the nodes at the ligament/tendon’s insertion will be defined with a nearest neighbor search between the body that the tissue inserts into and the surface nodes of the ligament/tendon.
dMCL and Meniscus Ties¶
The deep MCL (MCL Anatomy) inserts into the medial meniscus. To simulate this anatomy, one node from each fiber in the sMCL mesh are rigidly tied to the surface of the medial meniscus. These nodes are identified from the reference simulation results (Reference State). It is assumed that the dMCL is in contact with the medial meniscus in the reference simulation results. The dMCL mesh will be refined until a every fiber has at least one node in contact with the medial meniscus. The nodes that are tied to the medial meniscus are defined with a nearest neighbor search.
If in the future, the dMCL is being modeled as a continuum, then the dMCL geometry should have ties to the medial meniscus. The surface nodes that are closest to the medial meniscus (defined with a nearest neighbor search) will be rigidly tied to the medial meniscus’ surface.
Interaction - Bone, Cartilage, Meniscus¶
- Contact between the articulating surfaces and menisci is defined with a frictionless pressure-overclosure relationship. There are a total of six contact pairs between the articulating surfaces and the menisci.
- Femoral cartilage - tibial cartilage
- Femoral cartilage - lateral meniscus
- Femoral cartilage - medial meniscus
- Femoral cartilage - patellar cartilage
- Tibial cartilage - lateral meniscus
- Tibial cartilage - medial meniscus
Cartilage Contact¶
The cartilage is modeled as a rigid body, and contact pressures are calculated using pressure-overclosure relationship [LKST15][halloran_comparison_2005]. It is assumed that the cartilage has a constant thickness of 3 mm [LKST15].
Where \(\nu=0.45\), \(t=3\) mm [LKST15], and \(E=12\) MPa [DKB10].
Menisci Contact¶
A pressure-overclosure relationship is used to model the contact interaction between the articulating surfaces and the menisci. A “softened” nonlinear pressure-overclosure relationship Fig. 49 is used to promote the stability of the model.
*SURFACE BEHAVIOR, PRESSURE-OVERCLOSURE=EXPONENTIAL
0.01, 0.1, 75
The above specifies a pressure-overclosure relationship. The first value (\(c_0\) in Fig. 49) specifies that two surfaces begin to interact when the surfaces are 0.01 mm apart (out of contact), and reach a contact pressure of 0.1 MPa (\(p_0\) in Fig. 49) when the surfaces are in contact with zero overclosure. The maximum pressure is set to 225 MPa (\(K_{max}\) in Fig. 49). This maximum pressure is derived from an elastic foundation equation
where \(\nu=0.45\), \(t=3\), and \(E=60\) MPa. Note that \(t=3\) assumes a uniform thickness of 3 mm, which approximates cartilage thickness [LKST15]. Also note that \(E\) is five times larger than a normal value for cartilage (12 MPa [DKB10]). This is increased to limit potential overclosure between surfaces while limiting the maximum pressure-overclosure stiffness.
Ties/Connections¶
The cartilage and meniscal attachemnts are defined as being perfectly bonded to the bone.
The medial meniscus has ties with the dMCL. This is described elsewhere (dMCL and Meniscus Ties).