Asymptomatic geometry preparation
This study was approved by our university’s Institutional Animal Care and Use Committee (IACUC). The CT images from a purpose-bred, adult, healthy, male Beagle dog weighing 10.7 kg were used to create a femoral varus model and were selected as the baseline for the present study. No abnormalities were found via physical or orthopedic examinations or radiography in the Beagle dog. A computed tomographic (AlexionTM, Toshiba Medical Systems, Tochigi, Japan) scan of the Beagle dog was performed in the normal-standing position with the hip joint positioned according to that in the procedure previously reported [31]. The CT images were obtained using bone and soft tissue filters at 120 kV and 120 mA, respectively, and a slice thickness of 1 mm. The aLDFA and anteversion angle (AA) of each femur of the Beagle dog were measured (both left and right aLDFAs were 95° with an AA of 16°) (Figure 4). The three-dimensional (3D) geometries of the left femur, patella, and tibia were extracted and segmented using 3D modeling software (Mimics innovation suite 20, Materialise NV, Leuven, Belgium). Fluoroscopic (BV Pulsera, Philips, Netherlands) images of the Beagle dog were taken while walking on the treadmill at 53 kVp and 3.86 mAs with a pulse rate of 30 frames/s and a pulse width of 11.1 ms. The beam center of the fluoroscope was focused on the stifle mediolaterally. The geometries of these bones were manually aligned to the fluoroscopic images in the stance phase of gait cycle using previously described 3D-to-2D image registration software (JointTrack, University of Florida, http://sourceforge.net/projects/jointtrack/) [32].
Femoral varus model creation
The asymptomatic normal stifle geometry of the Beagle and the center of rotation of angulation (CORA) were used to create the femoral varus geometry (Figure 4). The position of CORA, located at the distal one-third of the femur, was based on the computed tomographic (CT) images of a client-owned Maltese dog’s femur, which had an aLDFA of 110°. It was consistent with a previous report of CORA in MPL [8, 9].
The normal femur geometry was then bent at the CORA using meshing software (3dsMax, Autodesk, San Rafael, CA, USA) to create deformed geometries. First, the geometry was scaled to fit the height of the client-owned Maltese dog’s femur and bent at the same CORA level as that of the affected femur until it reached an aLDFA of 110° [33]. After confirming that there was no translocation in the CORA position in the bent model, the remaining angle models were reproduced using a ratio of aLDFA of 95° to 110°.
A total of thirteen different aLDFAs were simulated; normal aLDFA values from 95° (baseline) to 98° and affected angles from 100° to 110° were evaluated in one-degree increments.
The vertical position of the patellar segment was aligned to the stance phase of the stifle during the gait cycle based on the fluoroscopic images using the 3D-to-2D image registration technique. The angle between the normal femur and tibia segments in the sagittal plane was 127° and remained static during the experiment. The ratio of the length of the patellar ligament to the length of the patella (L:P) was 1.55, which was within the range of values reported in clinically normal large-breed dogs [34]. During this process, the patella and the femoral trochlea remained anatomically undeformed so that every varus deformation had the same patella and trochlear groove geometries (Figure 5).
FE model development
Thirteen stifle meshes were created using meshing software. To maintain an equivalent joint plane between the femur and tibia in all models, the tibia and distal epiphysis of the femur were fixed in the model before the femur was bent to create the deformity. Each stifle mesh model had specific tetrahedral solids because the solids were reconstructed by using a 3D stereolithography model before the mesh models were created (Figure 5B). The mechanical behavior of the patellofemoral joint models was analyzed using Explicit FEM Multi Flexible Body dynamic analysis (LS-DYNA, Livermore Software Technology Corporation, Livermore, CA, USA). The cortical bone was modeled as a solid elastic material with a Young’s modulus of 15.0 GPa and a Poisson’s ratio of 0.3, which were chosen on the basis of the reported values [20, 24]. Cancellous bone was excluded due to its insignificant mechanical role in contact stress predictions, and bones were treated as complete solids in the model [35, 36].
The extensor or quadriceps mechanism includes the quadriceps (rectus femoris, vastus lateralis, vastus medialis, and vastus intermedius muscle), quadriceps tendon, patella, patellar ligament, and tibial tuberosity [2]. In the present study, only the rectus femoris muscle was modeled with a beam element with Hill’s muscle model-based material (Material 156-MUSCLE), provided by LS-DYNA, to represent the quadriceps [37, 38]. The Hill-based model was designed according to Hill’s equation describing the mechanical response of skeletal muscle [39]. In brief, Hill muscle models consist of a contractile element (CE) and parallel element (PE). The contractile element represents the force created by the activation of a muscle, while the parallel element represents the energy stored due to muscle elasticity.
The origin of the rectus femoris muscle model was located based on the CT scan images with a sagittal plane hip angle of 125.2° and constrained for all six degrees of freedom at a virtual point matching the actual anatomical location of the ilium (Figure 5B).
To transfer more physiological load to the patella, the quadriceps tendon and ligament were separated into three beam elements and configured as linear spring materials with an elastic stiffness of 0.19 kN/mm [22, 40, 41]. The properties of the materials used for the muscle were adapted from previous reports (Table 2) [42, 43].
Table 2. The properties of the parameters used to calculate the force generated by the rectus femoris.
Parameter
|
Density
|
Initial relative length
|
Maximum strain rate
|
Peak isometric stress
|
Parallel constant k
|
PCSA
|
Value
|
1e-5 kg/mm3
|
1.0
|
2.0
|
5e-4 GPa
|
6.0
|
1850 mm2
|
*Note that parameters are normalized. For example, the peak isometric stress is normalized by dividing the peak isometric force by PCSA (physiological cross-sectional area).
Boundary conditions
Both the femur and tibia bone models were fully constrained to prevent unnecessary bony rotation or displacement during quadriceps loading, while the patella was unconstrained with three translational and three rotational degrees of freedom. The interaction between the patella and the femoral trochlea groove was defined as a surface-to-surface contact with a friction coefficient of 0.02 [18, 44].
Because a sudden increase in muscle-developed force can cause a large contact force between the patella and femur, which disarticulates the patella unnaturally, thirteen stifle models were simulated with a constant muscle activation level that linearly increased for 0 to 5 sec from 0% to 20% and remained at 20% from time points 5 to 50 sec, without any changes in the stifle angle.
Data Analysis
Patellar positions and the reaction force between the patella and the femoral trochlear groove in all FE models were calculated under constant activation of the rectus femoris muscle. When muscle activation was initiated and the first contact point of the patella and the groove was zero, the patellar displacement was expressed as a negative value for the medial direction and a positive value for the lateral direction, according to the global coordinate value.
Then, the critical aLDFA causing medial luxation of the patella was determined. The reaction force (rcforce) (kN) between the patella and the medial trochlear ridge was calculated for each aLDFA during the simulation. The total simulation time was set to 50 seconds to stabilize the motion of the patella in all of the aLDFA models.