An FE model of subtalar instability was developed based on one of our previous studies[15]. The subtalar instability was simulated by removing the CFL, ITCL and CL, as suggested by a previous cadaveric study[13]. Due to the fact that subtalar instability rarely occurs alone, the ATFL was also removed before performing the analysis of Schon triligamentous reconstruction and Mann triligamentous reconstruction.
Model development
First, computerized tomography(CT) scans of the foot and ankle at 0.5 mm intervals of a healthy male adult volunteer(30 years old with a height of 170cm and a weight of 68 kg)were used to develop bony structures. The DICOM formation data of the CT images was imported to MIMICS 17.0(Materialise, Belgium) for processing. These images were then segmented in order to identify the boundaries of the bones. Then, the STL data of each bone was imported to Geomagic studio 12.0(Geomagic Inc., Research Triangle Park, NC), and the point clouds data was transferred to a non-uniform rational B-spline(NURBS) curve model with a smooth bone surface in Geomagic studio. Finally, all the geometric models of the bony structures were imported to Hypermesh 13.0 to generate the FE model. The bony structures were meshed with rigid surface elements in view of their small strain compared to soft structures.
Subsequently, the magnetic resonance imaging (MRI) scans were used to develop the soft tissue geometry, including ligaments and cartilage. Ligaments were added manually into the 3D models. The insertion and the original site were identified by MRI presentations while referencing to previous journal papers and textbooks[16, 17]. Then, the ligaments of hindfoot and midfoot(24 ligaments) were added into the model, but the forefoot ligaments were simplified for they might not contribute to hindfoot stability. The cartilages of tibiotalar, subtalar, talonavicular and calcaneocuboid joints were identified on T1-weight MRI images. Then, their geometries were generated in MIMICS and modified in Geomagic studio. Finally, these cartilages were incorporated to the joints and meshed in Hypermesh. The final FE model consisted of 178370 elements and 69517 nodes(Figure.1). The simulation was performed in ABAQUS 6.13(SIMULIA Inc., US).
The ligaments of the tibia and fibula were assigned with non-linear force-displacement equations[18]. The material properties were expressed as curve fit data (a and b) for an elastic force-strain response function(T(ε)=a(ebε-1)). The tibionavicular ligament was assigned with a linear stiffness k, which was provided[19](Table 1).The mechanical properties of the hindfoot and midfoot ligaments were assumed to be equal to the ATFL and scaled by their relative cross-sectional areas. The ATFL had a cross-sectional area of 62.85mm2[19], and the areas for other ligaments were provided by Mkandawire[20] and Shin[21] (Table 2). The linear elastic stiffness values of the long/short plantar ligaments and plantar fascia were given by literature[22, 23](Table 3).
Table 1.Properties of tibia, fibula and hindfoot ligaments[18, 19].
Ligament
|
a(N)
|
b
|
Anterior talofibular
|
7.18
|
12.50
|
Anterior tibiofibular
|
5.52
|
22.63
|
Anterior tibiotalar
|
2.06
|
20.11
|
Calcaneofibular
|
0.20
|
49.63
|
Posterior talofibular
|
0.14
|
44.35
|
Posterior tibiofibular
|
6.87
|
20.07
|
Posterior tibiotalar
|
1.34
|
28.65
|
Tibiocalcaneal
|
0.51
|
45.99
|
Tibionavicular
|
k=39.1 N/mm
|
|
Table 2.Properties of hindfoot and midfoot bone ligaments[20, 21].
Ligament
|
Area (mm2)
|
Area ratio
|
Anterior talocalcaneal
|
14.4
|
0.229
|
Posterior talocalcaneal
|
14.96
|
0.238
|
Lateral talocalcaneal
|
6.84
|
0.109
|
Medial talocalcaneal
|
14.91
|
0.237
|
Interosseous talocalcaneal
|
72.80
|
1.158
|
Dorsal talonavicular
|
35.15
|
0.559
|
Interosseous calcaneocuboid
|
72.80
|
1.158
|
Plantar calcaneocuboid
|
98.70
|
1.570
|
Inferior calcaneonavicular
|
9.23
|
0.147
|
Superomedial calcaneonavicular
|
161.00
|
2.560
|
Dorsal cuboideonavicular
|
13.10
|
0.208
|
Plantar cuboideonavicular
|
27.80
|
0.442
|
Interosseous cuboideonavicular
|
14.01
|
0.223
|
Table 3.Properties of plantar fascia and long/short plantar ligaments[22, 23].
Ligament
|
Stiffness k (N/mm)
|
Plantar fascia
|
203.3
|
Long/Short plantar ligament
|
75.9
|
The cartilage was defined as being neo-Hookean hyperelastic with E=10Mpa and v = 0.45[24]. The contact of joints was simulated by adding a surface-to-surface contact element between the cartilage of joints, with a coefficient of friction(μ) of 0. The peroneus brevis tendon used as graft was also considered as a linear elastic material with an elastic modulus value of E = 149.7 MPa and a cross sectional area of 19.5mm2[25]. The hamstring tendon used as graft was assumed as isotropic hyperelastic; its strain energy density function was obtained from a previous paper[26].
Simulation of subtalar instability and validation
In previous cadaveric studies, the subtalar instability was usually simulated by sectioning the CFL, CL and ITCL[4, 13]. This method was also adopted in our numerical analysis. The model was validated by comparing the results of our numerical analysis with previous experimental data[4, 13].It was found that the inversion and external rotation of the subtalar joint in the intact/instability model under a torsional moment of 4 Nm were consistent between our simulation and Pellegrini's experiment(Table 4). The inversion under 1.5Nm and the internal rotation under 3Nm of the subtalar joint in our simulation were close to Choisne's results(Table 5).
Table 4.Comparison of inversion(4Nm) and external rotation(4Nm) between our simulation and Pellegrini's experiment[4].
|
|
Cadaveric model
|
FE model
|
Intact
|
Inversion
|
7.2
|
7.0
|
External rotation
|
4.8
|
4.8
|
Subtalar instability
|
Inversion
|
12.8
|
12.7
|
External rotation
|
8.0
|
7.5
|
Table 5.Comparison of inversion(1.5Nm) and internal rotation(3Nm) between our simulation and Choisne's experiment[13].
|
|
Cadaveric model
|
FE model
|
Intact
|
Inversion
|
7.0
|
6.2
|
Internal rotation
|
7.2
|
6.7
|
Subtalar instability
|
Inversion
|
12.2
|
11.3
|
Internal rotation
|
9.8
|
8.9
|
Simulation of tenodesis reconstructions
5 different types of tenodesis reconstruction were simulated in our FE model. The procedures of Pisani ITCL reconstruction[11], Schon CL reconstruction[12] and Choisne CFL reconstruction[13],which recreated a single ligament in the subtalar joint, were simulated in group 1 on a FE model with CFL, CL and ITCL removed. The procedures of Schon triligamentous reconstruction[12] and Mann triligamentous reconstruction[14], which recreated the ATFL, CFL and CL simultaneously, were simulated in group 2 on a FE model with ATFL, CFL, CL and ITCL removed. In clinical approaches, some parts of the graft tendon pass through the bone tunnels in talus, calcaneus and fibula, but this was not simulated in our analysis.
(a)Pisani ITCL reconstruction: The attachment point of the graft on the bone was determined by clinical approaches[11]. One half-peroneus brevis graft was used in this procedure. A double stranded ITCL was recreated between two calcaneal and two talar tunnels. The part of half-peroneus brevis tendon connecting the fifth metacarpal base with calcaneus was also simulated. (Figure.2a)
(b)Schon CL reconstruction: This procedure was simulated based on clinical approaches[12],by using one half-peroneus brevis graft. The CL was recreated between the calcaneus and the talar neck. The part of half-peroneus brevis tendon connecting the fifth metacarpal base with calcaneus was also simulated.(Figure.2b)
(c)Choisne CFL reconstruction: This procedure was simulated based on clinical approaches[13],by using the entire peroneus brevis tendon. The graft passed from the anatomic insertion of CFL on fibula to the attachment on calcaneus.(Figure.2c)
(d)Schon triligamentous reconstruction: This procedure was simulated based on clinical approaches[12], by using the entire peroneus brevis tendon. The ATFL, CFL and CL were recreated simultaneously. The attachment of the graft on the calcaneus, talus and fibula was set on the native insertion of these ligaments. The part of entire peroneus brevis tendon connecting the fifth metacarpal base and calcaneus was also simulated. (Figure.3a)
(e)Mann triligamentous reconstruction: This procedure was simulated based on clinical approaches[14], by using the hamstring tendon. The ATFL, CFL and CL were also recreated simultaneously. The attachment of the graft on the bone was the corresponding anatomic insertion of these three ligaments.(Figure.3b)
Boundary conditions
To simulate different ankle positions in numerical analysis, the loading condition was applied in two steps. First, the fibula and tibia were flexed at 10°dorsiflexion/plantarflexion or in the neutral position, while the 6 degrees of freedom of the foot were fixed. Then, the 6 degrees of freedom of the tibia and fibula were fixed too, and a rotational moment of 4Nm was applied on the calcaneus. The rotational moment was set to 4Nm,which was the same as a previous cadaveric study of subtalar instability[4]. The internal stress in the ligament was considered to be free in the neutral position of the hindfoot. The inversion/eversion and internal/external rotation of the subtalar joint were measured at different ankle positions.