**3. Results**

### *3.1. About Model Validation*

Deformation found in the model is very approximated for a patient in a loading test. Found values can be included in the inter-subject variability under healthy conditions, represented as light loading (minimal contact with the ground) and a normal standing load (Table 2). These were compared with the average deformation of all the evaluated points measured in Rx-images in the sagittal view of 12 healthy patients.


**Table 2.** Results of the validation process. The values correspond to the difference between the measured distance from each point to the ground, under two different loading values: Light loading (minimal contact with the ground) and normal standing load [9].

#### *3.2. Flatfoot Simulation and MCO Structural Correction*

Quantification of structural changes generated by both the simulated pathological scenarios and the MCO cases was carried out by measuring the vertical displacement of the entire foot skeletal structure (in millimeters). The values show by how much each foot region falls or rises (see Figure 5). Blue represents falling while red represents elevation. As can be seen, in simulations performed before applying MCO, the medial foot region suffers higher displacements downwards. These changes are also related to arch lengthening and foot pronation. After applying MCO, the tendency towards supination of the foot structure can be seen clearly, also causing fewer vertical displacements and less arch lengthening because of this (please see the Hallux fingertip—the tip of the big toe).

**Figure 5.** Structural changes obtained after simulating the model in different pathological cases. Values measure vertical displacement. Blue represents negative displacement (downwards). The color scale was normalized to 2.70, which is the maximum displacement reported in the healthy case. The maximum displacement values when these are higher than the reference is shown at the top of the color scale.

The effectiveness of MCO in the correction of the forefoot pronation and hindfoot valgus can be seen. Additionally, it can be observed how well MCO can compensate for the failure of both the spring ligament and the tibialis posterior tendon, reducing the effects expected by these failures (mainly forefoot pronation) [3,9].

The medialization of the calcaneus, through an osteotomy, manages to reduce the typical pronator moment of the subtalar joint. In this situation, the functional demand of the native structures to preserve the plantar arch, spring ligament, and tibiabis posterioris is significantly lower. If the pronator moment is maintained, the mechanical

demands are very high and this may explain the known failure in isolated arthrodeses of the talocuneiform joint.

#### *3.3. Stress in Forefoot Bones Generated by MCO*

The first analyzed results were stresses on metatarsals. This magnitude was measured in Megapascals (MPa). The color scale was normalized to 60 MPa to better visualize the results (Figure 6). However, for each color scale, we also show the highest value obtained from each case and the stress measured in lateral metatarsals. Meaning of the scale: red means high stress, green represents medium stress, while blue represents low stress. It is observed that MCO increases the stress around the fourth metatarsal, and it increases even more when the PF or TPT fails. Additionally, the MCO reduces the forefoot maximum stress by approximately 35% (from 240,04 MPa to 155,06 MPa). These results are relevant because they show how the MCO by itself caused this stress reduction in metatarsals.

**Figure 6.** Stress in metatarsals (MPa). All simulations were performed after applying MCO, except for the first case which was included for comparison. The maximum stress values obtained are shown at the top of the color scale.

#### *3.4. Stress in Hindfoot Bones Generated by MCO*

In the second place, stresses in hindfoot bones were also evaluated for all the abovementioned pathological cases for MCO (Figure 7). Now, the color scale for stress values was normalized to 20 MPa to better visualize the results. It can be noted that there is an increase in the stress concentration around the osteotomized region, when one of the main stabilizers fails (PF, TPT or SL).

A summary of bones stress changes is shown in Table 3, including the relative changes obtained from each case against simulating an MCO with healthy soft tissues. The results in Table 3 come from the stress results shown in Figures 6 and 7.

**Figure 7.** Stress in hindfoot bones (MPa). All simulations were performed after applying MCO, except for the first case which was included for comparison. The maximum stress values obtained are shown at the top of the color scale.

**Table 3.** Relative differences obtained from simulations, considering the simulation of MCO with healthy soft tissues as reference. This table is related to Figures 6 and 7. Please see these figures to find the maximum stress locations. All stress values are in megapascals (MPa).


*3.5. Stress in Soft Tissues after MCO*

We compared the soft tissue stress before and after applying MCO, simulating a failure of one or two of the main stabilizers of the plantar arch (TPT, PF and SL) (Figure 8). The results were normalized using values that allow the differences to be easily identified: 100 MPa for the tibialis posterior tendon, 33 MPa for the plantar fascia and 29 MPa for the spring ligament. The color scale is organized in the same way as described above for the bone stress evaluation.

**Figure 8.** Comparison between stresses generated before and after applying MCO in the main soft tissues that support the plantar arch, in some pathological scenarios. The maximum stress values (MPa) obtained are shown at the top of the color scale.

The maximum stresses in the rest of the soft tissues included in the model were also quantified. The results are summarized in Figure 9.

**Figure 9.** Comparison of the maximum stress obtained in the rest of the tendons included in the model.

### **4. Discussion**

There are many treatment options for AAFD used by surgeons depending on the disease stage. For cases with a flexible deformity (IIa–IIb), tendon reinforcements are insufficient, requiring intervention in the bone structure. One of the most widely used options is medializing calcaneal osteotomy (MCO). Recently, Zanolli et al. and Patrick et al. [15,29] published experimental studies focused on comparing the foot's structural correction achieved with MCO with some other strategies such as Z-osteotomy or lateral column lengthening. Other authors have evaluated the outcomes of MCO and both its effect on the Achilles tendon and its contribution to correcting signs of AAFD [11]. Although the structural correction of the foot that can be achieved with MCO is widely known, some clinical studies have shown that MCO generates some long-term consequences such as stress distribution changes in the forefoot and probable risk of stress fractures, as has been reported with Evans' osteotomy [11,12,14]. These findings may be very relevant for the surgeon's decision-making process [30]. However, the biomechanical side-effects generated by MCO in both foot bones and the main soft tissues that support the plantar arch have not been analyzed sufficiently, mainly because of the difficulty of measuring tissue stress in cadaveric models [5,9].

Traditionally, the performance of an isolated arthrodesis of the cuneometatarsal joint for the treatment of flat feet in adults has been associated with a high rate of malunion. This fact has displaced the technique towards more aggressive ones, such as triple arthrodesis. However, associating an OCM reduces the pronator moment during gait and thus potentially allows it to act only on the cuneometatarsal joint. Selective arthrodesis of this joint would result in a clear clinical benefit.

In view of the above, a computational foot model was used to evaluate the changes on the biomechanics in foot tissue stresses when performing an MCO. This research alternative is used nowadays in clinical biomechanics studies. Thus, some examples such as these can be found in the literature. Smith et al. [31] designed a computational model to evaluate the structural effect of the Evans osteotomy. Wang et al. [13] proposed an FE study to evaluate different variables in MCO application, such as the angle and the medializing displacement distance. Normally, all these studies simplify the anatomy of the soft tissues and the biomechanical properties of bones. These simplifications penalize their use for analyzing the stress changes generated by MCO.

The proposed model can be reproduced, on the one hand, for loaded foot deformities and, on the other hand, for the main signs of AAFD such as foot pronation and the "too many toes" sign [4] (please see Figure 4 (bottom)). It is important to remark on two items: this model differentiates trabecular bone and cortical bone and this model contains the main soft tissues related to AAFD development. These make it possible to localize stress concentrations and evaluate stresses on both hard and soft tissues [3].

The results show that MCO effectively reduces the pronation of the hindfoot typically observed in patients with AAFD (see intense blue color around both astragalus and navicular bones). As can be seen in Figure 5, in most of the cases simulated with MCO, foot pronation was not generated. Moreover, these results indicate a good compensation of the MCO when the spring ligament fails. This is due to the supination momentum caused by the MCO over the foot structure. Nevertheless, if all the main soft tissues support the plantar arch failure, the MCO by itself cannot stop foot pronation. This means that, when performing an MCO, surgeons should add another strategy, such as artrodeses or tendon reinforcement, for example.

Additionally, the results sugges<sup>t</sup> that MCO compensates very well for the spring ligament failure. The supination momentum that MCO causes in the foot structure can explain these results. However, it is noticeable that, when all the main soft tissues that support the plantar arch fail, MCO cannot prevent foot pronation on its own. This means that MCO should be applied in combination with other strategies, such as tendon reinforcement or arthrodeses.

The results of the stress analysis on forefoot bones show that MCO reduces the bone stresses by approximately 35%, considering the healthy case as a reference and comparing the maximum stress values obtained from both healthy cases (without tissue weakness) before and after MCO (see Table 3 and Figure 6). However, when the foot arch stabilizers fail, our simulations found a stress increase in all the metatarsals, mainly in the first, second, and fourth. This increase is much more important if the plantar fascia or the tibialis posterior tendon fail, increasing the stress by approximately 34% and 28% respectively, compared to the maximum stress values obtained from MCO with healthy soft tissues (see Table 3). When the main arch stabilizers fail, the stress increases by 74%. This increase in the stress values and in its redistribution could explain the pain in the toes reported in patients treated with MCO [30] and the findings of Iaquinto [12], who concluded that corrective osteotomies shifted loads from the medial forefoot to the lateral forefoot, with greater impact for combination lateral column lengthening and MCO procedures. The stress on the third and fifth metatarsals increases less than the others, probably because of some differences in the tissue insertion on the phalanges. Despite these differences, it is important to note how the metatarsal stresses change in different scenarios.

The results of the soft tissue analysis show that MCO noticeably reduces the stress in the main foot arch stabilizers, especially when the plantar fascia (mainly) or tibialis posterior tendons fail (Figure 8). Additionally, the stress reduction generated in the peroneus longus tendon is considerable, except in the case simulated with failure of all the main foot arch stabilizers (Figure 9). This result is consistent with the structural analysis, which shows that MCO cannot correct foot pronation when these tissues fail. As expected, no significant stress changes were found in the Achilles' tendon. These results are close to those obtained by Hadfield et al. [11] and Kongsgaard et al. [32] in their study performed using cadaver models.

Finally, if some of the stabilizers of the main arch fail, such as the plantar fascia or tibialis posterior tendon, an important stress concentration around the osteotomy region appears (Table 3 and Figure 7). As is shown in Table 3, the maximum stress in these cases increased by 32% and 40%, respectively. When the foot arch stabilizers fail, the maximum stress concentration increases by about 95% (from 507 to 990 MPa). In this work, fixation methods were not evaluated since complete bone healing is assumed after calcaneal translation.

A limitation of this study is that the analysis was based on a static simulation. Thus, patients' variability in tissues and loading was not considered, because one case study was simulated. However, the relations and differences (in percentages) obtained could be useful for evaluating the MCO effects in all the scenarios simulated. Our results cannot be generalized because only one anatomy was investigated, but the relative differences obtained could help with the study of MCO effects on the foot structure. Additionally, our model does not include the plantar pad, the flexor hallux longus, or flexor digitorum longus tendons. However, clinical studies have shown that these tissues have a minor role in AAFD development and in the foot arch support, compared to the tissues included in the model used [27,33]. Additionally, our model does not include any artificial restriction for the tibialis posterior tendon motion, so the pathway generated after traction forces may not be anatomically correct. Additionally, we used an isotropic characterization for plantar fascia and ligament tissues, which could lead to non-real calculations of stress in the tissues. It is necessary to perform a parametric study to show how sensitive the model predictions are to the material properties chosen. Moreover, our study was based on small displacements and deformations, so a linear elastic behavior for these tissues does not greatly falsify the results. This model also does not allow for error predictions, since statistics or deviations on the model characteristics are not included. One way to be able to make error predictions could be using probabilistic finite elements. Finally, it is important to remark that the values of biomechanical stress found cannot be assumed to be true stress values for all people (because of inter-subject variability). Nevertheless, we can analyze

the relative differences generated in each case. The smaller increase in the third and fifth metatarsal stresses could be caused by differences in tissue insertion in the phalanges.
