Mesh Creation¶
This section describes the procedures that are used to create the geometric mesh that is used in the finite element model.
Software
Program Name | Version | link |
---|---|---|
IA_FEMesh | https://www.ccad.uiowa.edu/MIMX/projects/IA-FEMesh | |
Meshlab | 2016.12 | https://www.ccad.uiowa.edu/MIMX/projects/IA-FEMesh |
3D Slicer | 4.8.1 | https://www.slicer.org/ |
Bone¶
Triangulated surface mesh is used to represent the geometry of bones in .stl format. If you have already followed all the steps in the Geometric Reconstruction section, the .stl file you have is appropriately meshed otherwise, look at the Tissue Specific Procedure section in Geometric Reconstruction section and follow all the required step for smoothing and re-meshing of your tissue of interest and after that perform Cleaning and Repairing process which is in Geometric Reconstruction section aswell.
Description | Mesh Type | Comments |
---|---|---|
Femur surface | triangle | The osseous surface of the femur. This surface is hollow however it should be a closed surface. |
Tibia surface | triangle | The osseous surface of the tibia. This surface is hollow however it should be a closed surface. |
Patella surface | triangle | The osseous surface of the patella. This surface is hollow however it should be a closed surface. |
Meniscus¶
Note
If in the future, a ligament and/or tendon is being modeled as a continuum, then the geometry should be segmented and reconstructed, the meshed following these procedures.
Mesh Generation¶
Hexahedral elements are used to represent the geometry of the menisci. The smoothed .stl surfaces (described in Geometric Reconstruction) are loaded into IA_FEMesh, and blocks are manually define and oriented around the surface (Fig. 43). The number of seed nodes along the axes of each block should be defined, and the specific number of seed points should be determined with a convergence analysis. Smoothing should not be used when generating the mesh (the mesh may be smoothed in later steps).
Cartilage¶
The cartilage is being modeled using an elastic foundation model [LKST15],:cite:halloran_comparison_2005. As such, only a surface mesh is needed. The triangular mesh that was created from the segmentation and reconstruction steps is converted into a quadrilateral dominated mesh. This is performed using MeshLab, where there is an option to convert a triangular mesh into a quadrilateral dominated mesh. Using MeshLab, the triangular mesh (imported from the .stl file) is converted into a quadrilateral dominated mesh. The option for Fewer Triangles should be selected. Note that this creates a mesh that may have still have triangular elements.
The surfaces that are converted into quadrilaterl dominated meshes are:
- Femoral cartilage
- Tibial cartilage - medial
- Tibial cartilage - lateral
- Patellar cartilage
Mesh Quality¶
If the resulting mesh does not approximate the smoothed surface (i.e. the hex mesh has sharp points along surfaces that are smooth in the input surface), the mesh can be smoothed for 1 or 2 iterations using the Elliptical
interpolation option. If the mesh still does not approximate the smoothed surface, then the number of seed nodes should be increased, and the surface should be remeshed.
After generating a mesh that matches the input geometry, the mesh should be imported into Abaqus to measure the mesh quality. Following the Abaqus documentation, the mesh should meet the criteria described in Table 3. If all of the elements in the mesh do not have the desired quality metrics, then the blocks should be adjusted as needed, and the geometry should be remeshed. If the desired quality metrics are still not achieved after several iterations, then the affected geometry should be documented, and the mesh with the best quality elements should be used. Thin areas in the geometry, such as the inner rim of the meniscus, may not have elements with the desired quality.
Metric | Value |
---|---|
Smaller face corner angle | 10 deg |
Larger face corner angle | 160 deg |
Aspect ratio | 10 |
Meniscal Attachments¶
Similar to other studies ([NBJvdG+17]), the meniscal attachments are modeled as bundles of nonlinear springs. The mensical attachments are defined in the same was as described in the Ligaments and Tendons section. In short, insertion points are manually defined from the MR images, and these points are used to create the attachment’s mesh (Fig. 44).
Ligaments and Tendons¶
Ligaments and tendons are represented as a bundle of nonlinear springs. Bundles are composed of a line of equally space fibers, where adjacent fibers are connected by tension only corss-springs Fig. 44.

Fig. 44 An example of the (a) points used to define a ligament, (b) the point to point mesh that is generated from the four points, and (c) the mesh wrapping around the femur and tibia osseous surfaces. The example shows six ligament fibers that are oriented in the proximal-distal direction, and the connecting springs that are oriented in the anterior-posterior direction that make up a total of 20 divisions in the mesh. This is a medial view of a right knee. Note that this is used as an example, and not used to describe the insertion locations or size of any specific ligament.
Note
If in the future, a ligament and/or tendon is being modeled as a continuum, then the geometry should be segmented and reconstructed, then meshed following the same proceedure as described for meshing the menisci.
Manually Defined Data¶
- For each ligament/tendon mesh, there are two types of data that are manually defined by the user
- Points that define both insertion areas Fig. 44 (a)
- The correspondence of the points between insertion areas
The MR images are used to manually define the insertions of the ligaments/tendons. Using 3D Slicer, two points are manually placed in the MR image at the margins of the ligament/tendon’s insertion area. These two points should form a line that bisects the insertion area. The literature should be used to confirm the relative locations of the insertions (Table 4), and when literature based measurements are available, the ruler
tool in 3D Slicer should be used to verify the ligament/tendon insertion’s size and location. The links in Table 4 contain the literature sources used to define the insertions, and measurements that were referenced to verify the insertion area size and location.
After the points that represent the ligament/tendon’s insertion area have been defined (4 points total, 2 for each end of the ligament/tendon’s insertion) the user should manually define the corresponding points between insertion sites. The corresponding points are used to define the fibers at the margins of the ligament/tendon’s insertion area. For example, in Table 4, the anterior point on the tibia’s insertion corresponds with the anterior point of the femur’s insertion. Due to possible ambiguity, notes for corresponding points in the ACL and PCL bundles are provided on their anatomy description page Table 4.
Mesh Generation¶
- Using the manually defined data, two inputs are needed to define the coarseness of the mesh. Appropriate values should be determined through a convergence analysis.
The fibers at the margins of the insertion sites are defined using the manually defined points, and additional fibers are mapped between these fibers. The insertion points of the additional fibers are equally spaced between each manually defined point. Adjacent fibers are connected with tension only springs, and the locations of these springs are defined by evenly distributing the same number of points along the length of each fiber.
Due to the use of explicit analysis in Abaqus, there are mass elements defined at every node, and dashpot elements are defined to be in parallel with every spring element. The material properties of all the elements in the ligament mesh can be found here: Initial Material Properties.
Description | File Type | Anatomy description |
---|---|---|
Anteromedial ACL (amACL) | Spring | ACL Anatomy |
Posteriolateral ACL (plACL) | Spring | ACL Anatomy |
Anterolateral PCL (alPCL) | Spring | PCL Anatomy |
Posteromedial PCL (pmPCL) | Spring | PCL Anatomy |
Superficial MCL | Spring | MCL Anatomy |
Deep MCL | Spring | MCL Anatomy |
LCL | Spring | LCL Anatomy |
ALL | Spring | ALL Anatomy |
PFL | Spring | PFL Anatomy |
OPL | Spring | OPL Anatomy |
MPFL | Spring | MPFL Anatomy |
Quadriceps Tendon | Spring | Quadriceps Tendon Anatomy |
Patellar Tendon | Spring | PatellarTendonAnatomy |
Reference State¶
The ligament spring meshes do not account for wrapping when they are defined. This could lead to unusual recruitment when defining ligament prestrain. Additionally, nodes that may be tied to the meniscus cannot be identified from the initial ligament spring mesh.
To account for ligament wrapping when setting up the FE model, an initial FE simulation will be used to define ligament node positions when wrapping is enforced (Fig. 45). The ligament meshing procedures will be used to define the mesh for the initial simulation, and the results of this simulation will be used to define the node positions in subsequent simulations (such as passive flexion).

Fig. 45 An example of (a) the initial mesh that is defined from insertion point to insertion point data, and (b) the reference state where the ligament’s mesh wrapped around the femur and tibia surfaces. Note that this is used as an example, and not used to describe the insertion locations or size of any specific ligament.
Note
The joint in the reference state is in the same position/orientation as the image state. Ligament prestrain is defined with respect to the reference state, therefore prestrains are defined with respect to the position/orientation that the knee was in during imaging.
Method - Reference State¶
In the initial reference simulation, the femur, tibia, patella, menisci, and cartilage are rigid and fixed. This keeps those bodies in the same position as in the MR images. To prevent the ligaments from being slack, they will be assigned a uniform prestrain of -5%. The stiffness of the ligaments will not be changed from their normally assigned values (Initial Material Properties).
The simulation enforces contact between the ligaments and the femur, tibia, patella, menisci, and cartilage. The results of this simulation are used to define the initial ligament node positions for all subsequent simulations. These node positions are used when calculating fiber lengths which is used then assigning prestrain. Additionally, the node positions of the dMCL are used to define which nodes are tied to the medial meniscus (dMCL and Meniscus Ties).
Note
The reference simulation should be performed after mesh convergence has been established.
Additionally, if there is a change in ligament or medial meniscus geometry, then the reference simulation should be re-run.