Methods
Finite element model design
The present study is based on the model proposed by Morales Orcajo et al [11, 24]. The model reconstructs a normal human unloaded foot, based on tomography images (radiographs to 0.6 mm/slide) acquired from the right foot of a healthy male aged 35 years, with a height of 176 cm and a weight of 72 kg. This study was conducted in accordance with ethical principles of research and was approved by the Medical Ethics Committee of XXX. The volunteer signed an informed consent form for the experimental protocol and purpose. The segmentation and tissue reconstruction were performed using MIMICS 20 software (Materialise, Leuven, Belgium). The Geometry processing was performed using Geomagic Studio 2014 software (3D Systems, South Carolina, United States). The model refinement for further cutting and assembling was performed using Unigraphics NX 1911 software (Siemens, Munich, Germany). The model includes the bones and the cartilage morphology. The PF, SL, tendons, ligaments and fat pad were included based on anatomical images taken from atlases and cadaver dissection, under the advice of specialist foot and ankle surgeons. These tissues are fundamental for an adequate analysis of adult acquired flatfoot deformity (AAFD) development. In order to simulate the situation of standing on the ground, we designed a rectangular parallelepiped model larger than the sole surface of the foot with Unigraphics NX 1911 software. The sole plate size is about 300*120*12mm. The sole plate and the ground are relatively fixed, and there is no sliding (See Fig. 1).
Meshing
The model’s meshing was performed using Ansys Workbench 2019 software (Canonsburg, Pennsylvania, United States), generating 28 bone pieces, 26 cartilage segments, 6 tendons, 7 ligaments, the plantar fascia and fat pad (See Fig. 2A-B). The tetrahedral mesh of soft tissue that was generated is shown in Fig. 2C as an example. A trialerror approach was employed to optimize the mesh size of each segment, following the recommendations of Burkhart et al [25] who suggest that in all the parameters measured. The equilibrium was found with 1,401,813 linear tetrahedral elements (C3D4) with element sizes as follows: 1 mm for the smallest cartilages between phalanges, 2 mm for the phalanges, the thinnest ligaments and the rest of the cartilages, 3 mm for the metatarsals and the rest of the tendons, and 5 mm for the large bones in the hindfoot. The solution time for the model was CPU time 3.5h (CPU- Intel Xeon Gold 6230 40 cores Memory 192G).
Boundary condition
The model reconstructs a non-weight-bearing foot (unloaded), thus an initial simulation to obtain a loading position was performed. The model was simulated including all the tissues using a 720N load that represents the full-weight-bearing of an adult person about 72Kg, leaning on one foot. This condition emulates a traditional AAFD diagnostic assessment scenario.
The load was introduced in a descending vertical direction, with 10 degrees of inclination (distributed in the zone of contact Tibia-Astragalus (90%) and Fibula-Astragalus (10%)[11]. The simulations were performed by maintaining fixed nodes at the lower part of the calcaneus and blocking the Z-axis displacement (vertical) of the lower nodes of the metatarsals. This was done in order to simulate the ground effect when an adult person is leaning on one foot. Meanwhile, applying traction force to peroneus longus tendon, peroneus brevis tendon, flexor longus tendon, Achilles tendon, posterior tibial tendon, flexor digitorum longus tendon as reported in the Arangio and Salathe study (set peroneal longus tendon 69N, peroneal brevis tendon 34N, flexor longus tendon 24N, Achilles tendon 300N, posterior tibial tendon 49N, flexor digitorum longus tendon 12N) for simulating dynamic stabilizer of the plantar arch (See Fig. 3A) [26].
Tissue biomechanical properties
The model includes the plantar fascia, spring ligament, the anterior talofibular ligament, the calcaneofibular ligament, the posterior talofibular ligament, the deltoid ligament, and the anterior and posterior tibiofibular syndesmosis as well as major tendons including Achilles tendon, peroneal brevis tendon, posterior tibial tendon, flexor digitorum longus tendon, and flexor digitorum longus tendon in appropriate anatomical positions, and fat pad. These tissue models were considered such as an elastic-linear material, using biomechanical properties reported in the literature: bone (E = 17,000 MPa, v = 0.3), ligaments (E = 260 MPa, v = 0.4) and plantar fascia (E = 350 MPa, v = 0.4), fat pad (E = 1.0MPa, v = 0.45), E being Young’s modulus and v Poisson’s ratio [27, 28]. The tendons and cartilage were modeled as hyper-elastic materials (Ogden model), using the parameters (tendons: E = 1200MPa, v = 0.4; cartilage: E = 10MPa, v = 0.49) used in specialized articles [29, 30]. The Ogden model describes the hyperelastic behavior of rubber-like materials. Its strain energy density function U is:
where the initial shear modulus µ = 4.4, the strain hardening exponent α = 2 and the compressibility parameter D = 0.45.
In our model, for the ankle joint, the automated surface-to-surface contact option in Ansys Workbench was used to simulate the frictionless contact relationship between articular surfaces. Intertarsal joints, tarsometatarsal joints, metatarsophalangeal joints and intermetatarsal joints were assumed to exhibit only small movements in the standing condition and were therefore simplified by connecting the articular surfaces with solid elements comprising cartilage stiffness. The tissue to bone contact property was bonded contact relationship and the tissue to ligament contact property was no separation contact relationship which means separation of surfaces in contact is not allowed but small amounts of frictionless sliding can occur along contact surfaces. The tissue failures or attenuation applied to simulate AAFD development were performed applying the Isotropic Hardening theory that generates a progressive tissue attenuation [31].
Applying optimal plantar support force for finite element model
We applied supporting load on the sole of the foot, respectively 10% (72N), 15% (108N), 20% (144N) of the body-weight-bearing as simulating the support effect of the insole on the arch of the foot, and evaluated the appropriate arch support force. The supporting load is uniformly distributed in the foot plantar support area (see Fig. 3B-C).
Evaluation criteria and simulation conditions
To determine the plantar arch height and the relative contribution of each tissue, we calculated the difference between each performed simulation and the results of the model in normal load conditions. To quantify the quasi-clinical deformation values of the model and obtain a relative comparison of each analyzed tissue, we performed a simulation maintaining the bones, cartilage, ligaments and tendons, following the methodology proposed by Tao et al [28] for a tissue experimental test using cadaver models. In this way, the quasi-clinical possible deformation of our model was obtained. The height fall of the medial longitudinal arch was evaluated following the displacement of the lower part of the head of the talus, navicular, midpoint of medial cuneiform and the first metatarsal. In order to determine the biomechanical contribution of each tissue, the simulations were carried out maintaining and weakening each one of the evaluated tissues. Although damaged tissues continue working after an injury, herein we wanted to identify how important each tissue is to maintain the foot arch in a normal position. The normal standing load was considered as a reference standard. Subsequently, the flexible flatfoot was simulated with the PF attenuation under full weight-bearing condition followed by applying force to the sole to simulate the plantar support for the medial longitudinal arch. The variation of the height fall of the medial longitudinal arch, equivalent stress on the articular surface of each joint in the medial longitudinal arch and maximum principal stress of the ligaments around the ankle were evaluated.
Validation of the foot finite element model
The model constructed in this study was validated following the recommendations of Tao et al[32], measuring some anatomical parameters from the sagittal view under different loading conditions (non-weight bearing and normal standing weight bearing). The changes of these anatomical points allow us to compare the vertical displacements visible in radiographic images of a normal foot with respect to the finite element model predictions. We measured the vertical distance of the highest point of the Talus (TAL), the Navicular (NAV), the middle of the Cuneiform (CUN), and the highest point of the first metatarsal head (MTH1), as can be seen in Fig. 4. By measuring the vertical displacement change of these points in twelve radiographic images (under non-weight-bearing and normal standing weight-bearing condition ) of six patients’ right foot, the average value and standard deviation were obtained, and the model prediction results were objectively compared. All the six patients signed an informed consent form for the experimental protocol and purpose. The demographic details of the six patients is shown in Table 1. The acceptable data difference between the predicted model and patient measurement according to the study reported was within ± 0.25 mm for all cases [32].
|
No |
Male/Female |
Age(y) |
Weight(kg) |
Height(cm) |
|---|---|---|---|---|
|
1 |
Male |
35 |
71.5 |
170.2 |
|
2 |
Female |
46 |
73.2 |
175.4 |
|
3 |
Female |
38 |
68.4 |
165.5 |
|
4 |
Male |
27 |
70.2 |
168.7 |
|
5 |
Male |
26 |
72.0 |
172.6 |
|
6 |
Male |
40 |
75.1 |
178.1 |