Healthy model

The healthy model presented was developed by the University of Zaragoza (Spain). 93 computed tomography scans were necessary for the foot scan. The creation of volumes was done considering cortical and trabecular bone. The maximum and minimum size element was of 3 mm and 0.31 mm respectively with an average of 1.78 mm solving in that way the model convergence problem. The foot is modelled during toe-off since at this phase the maximum stresses occur in the FRotF ^[7]. For bones and cartilage, we use tetrahedral elements due is a good type of element to mesh complicated geometries, for muscles and tendons we use beam elements because they experiment directly a pretension force due to the position of toe-off and for thin ligaments, plantar ligaments, and plantar fascia we use bar elements due they only suffer small displacements in their extreme nodes when the model is loaded ^{[4] [7] [9] [15] [16] [17] [18] [24]}. Fig. 1 shows the elements that this model contains. All bones, cartilage, and soft tissues were considered as homogeneous, isotropic, and linearly deformable bodies. This model (without an implant) contains 150,594 nodes and 802,294 elements. More details about this model can be found in ^{[4] [9]}.

Figure 1 Elements of the model without an implant. 

Hemiarthroplasty model

The second model presented in this article contains the insertion of the hemi-implant AnaToemics^® Phalangeal Prosthesis by Arthrex in the proximal phalanx of the great toe. To obtain the volume of the implant, we used a 3D scanner provided by the University of Zaragoza. According to the surgical procedure, the first proximal phalanx is resected to later introduce the implant. To make this cut in the proximal phalanx, Mimics 10.0 was used after the prosthesis was placed with the help of Softimage 2015 and exporting the entire model in the .STL format. The mesh for hemiarthroplasty model was creating with ICEM CFD 17.2 of ANSYS having in the entire model a maximum and minimum element size of 3.8 mm and 0.18 mm respectively with an average of 1.13 mm, in the implant the maximum and minimum size of element was 3 mm and 0.42 mm respectively with an average of 1 mm preserving in that way the geometry of the first ray after having developed the surgical procedure, in addition to solving the model convergence problem. When the maximum element size in the implant is 5 mm, the minimum size is 0.7 mm and the average size is 1.7 mm, there are no significant changes in the calculations of stresses and deformations in the implant. Hemiarthroplasty model has a more refined mesh than healthy model due to the surgical procedure. To maintain the geometry of the soft tissues MATLAB R2013b programming was used to insert muscles, tendons, and ligaments calculating the minimum distance of the nodes of healthy model with the nodes of hemiarthroplasty model.

For this model with implant, some muscles and tendons have been removed as well as some ligaments of the first metatarsophalangeal joint as part of the hemiarthroplasty process ^[10]. Fig. 2 shows the elements of the model with the implant and Fig. 3 shows the hemi implant and its mesh, it is worth to note that in the part of the implant (spikes) inserted in the trabecular bone of the first proximal phalanx, the stresses and deformations are small values, so the mesh size adequately solves the model convergence problem. Hemiarthroplasty model contains 1,836,607 elements and 329,159 nodes.

Figure 2 Elements of the model with the implant. 

Figure 3 The implant and mesh from the implant. 

Mechanical properties and boundary conditions

The mechanical properties, as well as boundary and load conditions that are used in the two models presented in this paper, are the same, so they will only be defined once ^{[4] [7]}. All elements were considered as homogeneous, isotropic, and linearly deformable elastic because there are only small displacements and small deformations. For cortical bone, trabecular bone, muscles, thin ligaments and plantar ligaments, a modulus of elasticity of 17000, 700, 450, 260 and 350 MPa respectively has been used, all the elements mentioned above have a Poisson coefficient of 0.3. For cartilage a Young’s modulus of 10 MPa and a Poisson’s ratio of 0.4 were used and for the cobalt-chrome hemi implant a Poisson's ratio of 0.29 and an elastic modulus of 210 GPa have been used ^{[11] [12] [13] [14]}.

Some authors divide the human gait cycle into three stages, while others define six or eight stages ^[15]. Regardless of the classification of the human gait that is taken, it is well-documented that the maximum efforts at the FRotF occur in the position of the toe-off ^[7].

The models presented are in the toe-off stage and correspond to a person weighing 60 kg. The analysis was performed in the Abaqus 6.13-5 software. For the analysis, two steps were used. In the first step, a pretension force of 2 % is added to the muscles as consequence of the toe-off phase. This pretension force has been obtained by measuring the elongation of the muscles during toe-off with cadavers ^{[16] [17] [18]}. All displacements of some nodes on the attachment surface of the Achilles tendon are restricted. All degrees of freedom were constrained at the base of the first two proximal phalanges. Vertical translations and rotations in the distal phalanges of the lesser toes are restricted. In the second step, the pretension force is maintained, and the weight of the person is added, considering a force of 1805 N ^[15]. A contact pair frictionless was used between the outer surface of the tetrahedral elements with the muscles and tendons. The master surface is made up of triangular elements while the slave surface is made up of the nodes of the muscles and tendons. Fig. 4 shows how the body weight acts on the model; this load was applied in the area where the fibula and the tibia meet the talus. With the aim to understand how the implant functions when it is overloaded, we simulate the foot during toeoff loading 2 and 2.5 times the weight of the person.

Figure 4 Loads due to the person’s own weight. 

Results for model without an implant

In the healthy model the first distal phalanx acquires a movement in the sagittal plane. This movement is due to the force reaction that the ground exerts on the person and produces a forward impulse, giving directionality to the gait ^[19]. In Fig. 5, we can see this movement, which is commonly known as the passive windlass mechanism, and we can see too the principal stresses for the model. For the first distal phalanx, the maximum concentration of principal stresses occurs in the dorsal area, where the tendons of extensor hallucis longus muscle act. Concentrations of principal stresses at the support points appear for the second and third ray of the foot. The maximum displacement occurs in the phalanges of the fifth ray of the foot.

Figure 5 Principal stresses in the model without an implant. 

Results for model with the implant

For the second model presented in this article, concentrations of principal stresses appear in the second ray of the foot and calcaneus. For the FRotF, the greatest concentration of principal stresses appears in the support points. For the second and third rays, the highest stress concentration occurs in the proximal phalanges. For the second and third rays of the foot, the greatest concentration of major stress occurs in the proximal plantar area of the proximal phalanges. The greatest displacement occurs in the third and fifth rays of the foot in the phalangeal area. The function of the passive windlass mechanism is lost. The stresses and displacements mentioned previously can be contemplated in Fig. 6. In upper part of Fig. 7 the displacements for the healthy model in the three loading conditions are shown. In the lower part, appear the displacements for the three loading conditions in the model with the implant. The units of the displacements are millimeters.

Figure 6 Principal stresses in the model with implant. 

Figure 7 Displacements values for healthy model (upper part) and hemiarthroplasty model (lower part) for all load conditions. 

The maximum von Mises stress on the implant is 27 MPa (Fig. 8). The maximum principal stress registered in the implant is 29 MPa, and this occurs in the join of the oval part with the pilot pin. The highest absolute value of the minimum principal stress in the implant is 27 MPa (compression stress), and it appears in the oval part. Table 1 presents a comparison of the maximum Von Mises stresses developed in the implant when loading condition is 1.0, 2.0 and 2.5 the body weight.

Figure 8 Von Mises stresses and absolute maximum principal stresses. 

Discussion

Arthroplasty using the AnaToemics^®Phalangeal Prosthesis by Arthrex is a recommended procedure for patients with HR grade 3 and 4 who have failed conservative treatment for at least 6 months. This procedure requires that the patient has a well-aligned and stable FMJ ^[5]. Despite the fact that the use of implants is becoming more and more common, no studies have been carried out using Finite Element Analysis to know the consequences that these types of implants produce in the foot ^[20].

Eric Eric Giza et al. ^[21] report 22 Hemiarthroplasties in the First Proximal Phalanx (HitFPP) in 20 patients. Preoperative radiographs revealed 14 cases of grade 3 and 8 cases of grade 4 HR, according to the classification of Coughlin and Shurnas. The average dorsiflexion of the FMJ improved from 41 with a Standard Deviation (SD) of 11 degrees to 49 with a SD of 10 degrees in 1 year. The average score of the AOFAS scale improved from 61 points (range: 35-80) to 86 points (range: 75-95). The VAS pain scale improved from 4.7 with a SD of 2.6 points to 2.5 with a SD of 1.9 points. One patient developed metatarsalgia in the second metatarsophalangeal joint and only required conservative treatment. Konkel et al. followed up 23 patients for 72 months (17 had HR grade 3, and 6 had HR grade 4). The average age was 62 years. There were two patients with mild clawing of the great toe and two of mild transfer metatarsalgia. The average plantar flexion increased from 1 degree with a range of (-15 to 15) to 13 degrees with a range of (-20 to 30). For dorsiflexion, there was an average improvement from 16 (5 to 50) to 60 (20 to 85) degrees. In the score of the AOFAS scale the change was from 19 (17 to 50) to 89 (40 to 100) points.

At the end of the follow-up there was a 68% of recurrent dorsal osteophytes, the recurrence was mild in 10 patients, moderate in 4, and severe in 6, while 8 patients had no recurrence. There were three unsatisfied patients; a hard- working man in the construction industry, a woman who worked in a marketing industry and had to wear designer shoes, and another man who worked as a machinist in a factory and had to stand all day ^[22].

In this paper two finite element models of the foot have been presented. The first model analyses a healthy foot and the second model analyses the same foot having released a HitFPP. We found that when the hemiarthroplasty is performed the rays 2 and 3 become overloaded. In the first model, it was also observed that thin ligaments between first metatarsal and proximal phalanx, the pedio muscle, capsularis, flexor hallucis brevis, hallux adductor, and hallux abductor muscles transmit the most loads to the first proximal phalanx in the toe-off stage; these muscles and ligaments are disconnected in the surgical procedure. When performing the arthroplasty, it was also observed that passive windlass mechanism is lost despite not having disconnected the extensor hallucis longus muscle in the surgical procedure. The FRotF gives the ability to walk on uneven terrain ^[23]. This capacity could be affected after having developed an HitFPP. We recommend further work to evaluate the mechanism of active windlass in patients during postsurgical follow-up. The tensile strength yield for CrCo alloy is 410 MPa and this value is higher than the von Mises stresses reported in this paper (27.47 MPa). This indicates that failure for this implant may be due to fatigue problem ^[25].