a Universidade Federal Fluminense, Niterói, RJ, Brazil
b “Prof. Dr. Donato D’Ângelo” Orthopedics and Traumatology Service, Hospital Santa Teresa, Petrópolis, RJ, Brazil
c Universidade Federal de Minas Gerais, Belo Horizonte, MG, Brazil
d Department of Orthopedics and Traumatology, Escola Paulista de Medicina (EPM), Universidade Federal de São Paulo (UNIFESP), São Paulo, SP, Brazil
e Santa Casa de São Paulo, Pavilhão Fernandinho Simonsen, São Paulo, SP, Brazil
Introduction
Fractures of the calcaneus account for 60% of the fractures of the tarsus.1,2 Although calcaneal fractures account for only 1–2% of all fractures in all parts of the skeleton, they are still a major challenge for orthopedists.2–6 In young patients, they are frequently caused by high-energy trauma. Approximately 75% of these fractures are intra-articular.4,7,8 Calcaneal fractures present a high rate of unsatisfactory results, with great morbidity for the patients.
The ideal treatment for intra-articular fractures of the calcaneus remains a matter of controversy, despite the advances in imaging diagnostics and surgical techniques.9 Several surgical techniques for treating displaced intraarticular fractures exist, and these include: open reduction with internal fixation,5,9 minimally invasive techniques,10 percutaneous techniques,11 percutaneous calcaneoplasty4 and external fixation.12 Independent of the technique used, various anatomical structures in the medial region ofthe heel may be at risk of iatrogenic injuries caused by the tips of screws, drill bits, external fixator pins or Kirschner wires.13–15
The objective of this study was to investigate whether the number ofscrews or pins placed in the heel would increase the risk of injury, in using three different techniques for treating calcaneal fractures.]
Material
A retrospective analysis was conducted on 126 radiographs on patients who suffered displaced fractures of the heel in 2013 and 2014. Cases of fractures without displacement and fractures treated conservatively, and patients for whom no postoperative radiographic control was available, were excluded. Three surgical techniques were analyzed in interobserver form: 31 radiographs from patients who were treated using a plate that was not specific for the calcaneus, 48 with a specific plate and 47 with an external fixator. These patients were treated at four institutions.
to the end of the posterior tuberosity of the talus. Zones IIIA and IIIB were located in the region of the posterior tuberosity of the calcaneus.
According to Labronici et al.,15 the probability of injuries to the arteries, veins, nerves and tendons in the six zones studied was based on the classification of Licht et al.16 for high risk, as shown in Table 1. This study demonstrated that, for example, the likelihood of artery injury upon crossing the medial cortex in zone IA was 0.434 or 43.4%
Generalizing, the total likelihood of injury of an anatomical point, in placing n wires or screws, is the sum of all the individual probabilities (one by one) minus the probabilities of the two-by-two combinations, plus the probabilities of all the three-by-three combinations, minus the probabilities ofall the four-by-four combinations, plus the sum of all the five-by-five combinations, and so on, until the n-by-n combinations are reached.
Pr(Fi) − Pr(Fi ∩ Fj) + Pr(Fi ∩ Fj ∩ Fk)
− Pr(Fi ∩ Fj ∩ Fk ∩ Fl) + Pr(Fi ∩ Fj ∩ Fk ∩ Fl ∩ Fm)
− Pr(F1 ∩ F2 ∩ F3 ∩ F4 ∩ F5 ∩ F6)
This was the mathematical formula that was determined for calculating the risk. It was transformed into a computer program and then was analyzed by three researchers independently, in order to measure the three techniques used (Fig. 2).
Statistical methodology
The data gathered were analyzed through multiple linear regression in the SPSS software (Statistical Package for the Social Sciences), version 22.0. Multiple linear regression analysis is a technique for confirming dependence. Its aim is to examine the behavior of a dependent variable, measured as a function of other explanatory variables. The objective of this study was to evaluate the relationship between the risk of injury to an artery, vein or nerve and the number of screws or pins placed in each region of the calcaneus (A1, A2, A3, B1, B2 or B3). If Ai is the number of screws or pins placed in region A, index ‘i’, and Bi is the number ofscrews or pins placed in region B, index ‘i’, the general linear regression model that explains the relationship between the risk of injuring an artery, vein or
nerve and the number of screws placed in each region is given by:
Risk = a1A1 + a2A2 + a3A3 + b1B1 + b2B2 + b3B3 + u, (1) where risk is the dependent variable; ai and bi are the angular coefficients of each respective variable Ai and B; and u is the error term or residual difference between the real risk and the value predicted by the model. This error represents the variables that were not included in the model and may have some power for explaining the risk.
The theoretical model chosen does not have an intercept, since the risk should be null when no screw or pin is placed. All the parameters of model (1) were estimated through the ordinary least squares method. The significance ofthe parameters wa s evaluated using Student’s t test and the significance of the model was evaluated using the ANOVA F test. The assumptions of the model (i.e. normal distribution of the independent variable, absence of heteroscedasticity and absence of multicollinearity) were analyzed using the Kolmogorov–Smirnov test, Glejser test and VIF and tolerance statistics, respectively.
Given that the risks of injuring an artery, vein or nerve are independent, a linear regression model was proposed for each of the risks, for each type of procedure analyzed: placement of nonspecific plates, plates specific for the calcaneus and external fixators. In this manner, nine regression models were obtained. In addition to the analysis on the multiple linear regression model, a simple regression model between the risk and the total number of pins (T) placed was analyzed, given by:
Risk = aT + e, (2) where a is the angular coefficient of the variable to be estimated and e is the error term.
Despite the recommendation to use beta regression for the risk variable, since this is a variable of limited interval [0,1], simple linear regression was chosen because this had the advantages that the results could be easily interpreted, the sample size ensured non-violation of normality for the variables and none of the models proposed violated the assumptions of the multiple linear regression model (absence of heteroscedasticity and absence of multicollinearity). In addition, the models were evaluated by means of beta regression, which confirmed the significance of all the variables proposed, in all the models.
Results Table 2 demonstrates the p-values ofthe Kolmogorov–Smirnov test. This test was used to assess whether each of the
dependent risk variables presented normal distribution, for each type of procedure analyzed: placement of nonspecific plates, plates specific for the calcaneus and external fixators. It was observed that none of the p-values greater than 5% led to rejection of the null hypothesis of normality, which was the desired situation.
In addition to the test for normal distribution, the Glejser test and the VIF and tolerance statistics also provided the assurance that heteroscedasticity and multicollinearity were absent from all the models proposed.
Table 3 demonstrates the estimates for the coefficients of each proposed model, described as defined in Eq. (1). For the nine models proposed, the overall statistical significance of the model was confirmed (p-value of the ANOVA F test < 0.001), along with the significance of all of the variables (numbers of pins and screws in each area), separately (p-value ofStudent’s t test < 0.001). All the models presented high explanatory power for the risk evaluated, given that the values of the coefficient of determination R2 were greater than 98.6 for all the models. Therefore, the variables studied explained more than 98.6% of the variation of the risks of injury to the arteries, veins or nerves, and can be classified as excellent models for injury prevention. In comparing the adjusted values for the coefficient
of determination R2, it was observed that the models for predicting the risk ofnerve injury were best, since they explained approximately 100% of the risk
On the last two lines of Table 3, the correlation and coefficients of determination R2 of the model proposed by Eq. (2) are also analyzed. In this, the risk is only considered as a function of the total number of pins and screws. It was observed that the models thus proposed presented low explanatory power for the risk. Thus, these models have not been displayed. The risk of injury to arteries, veins or nerves was not defined by the total number of pins or screws. The region and the number of pins or screws in each region explained and determined the distribution of risk better.
Discussion
For each procedure (nonspecific plates, plates specific for the calcaneus and external fixators), this study used statistical multiple linear regression models that efficiently estimated the risk of injury to arteries, veins and nerves from the number ofpins or screws that each procedure in each region would use. To judge which procedure is least invasive, the number of pins or screws to be placed in each procedure in each region needs to be planned and the expected value for the respective risk should be calculated from the equations obtained. The coefficients thus estimated showed that the pins and screws in the region A1 were the ones that contributed most toward increasing the risk of injury to the arteries, veins or nerves. Pins orscrews in the regions A2 and B1 also contributed toward the risks of injury.
Meticulous knowledge of the anatomy of the hindfoot is an important prerequisite for planning for placement of pins or for open reduction and internal fixation of heel fractures. Structures contained within the tarsal tunnel, which are close to the medial region of the calcaneus, are vulnerable to injury caused by pins, drill bits or screws that penetrate the medial cortex ofthe calcaneus.15 Albert et al.17 divided the calcaneus into three zones. Zone I starts at the calcaneocuboid joint and extends posteriorly as far as Gisane’s critical angle; zone II starts at Gisane’s angle and extends posteriorly to include all of the posterior facet; and zone III encompasses the posterior tuberosity. The risk of injury to the structures of the medial region was calculated for each location into which pins were inserted in the lateral region. They concluded that pins placed in the subchondral bone of the posterior facet or anterior to Gisane’s critical angle might increase the risk of injury to the medial structures of the calcaneus. Labronici et al.15 demonstrated that division into six zones was more reproducible, with their respective risks of injury to the anatomical structures. The risk of injury can be quantified through the law of addition of probabilities, and this allows better planning with regard to the sites of lower risk for pin placement. However, it is important to emphasize the difficulty involved in predicting the likelihood of neurovascular injury caused by anatomical variations that are encountered in the tarsal canal, with subdivision of the tibial nerve into its medial plantar, lateral and medial calcaneal branches.
Some authors18–21 observed that the injuries most frequently affecting cutaneous nerves were to the sural nerve laterally and the tibial nerve posteromedially. These injuries usually result in hypoesthesia and are treated conservatively, except if a neuroma develops, which should then be treated surgically.
Conclusion
Through comparing the risk estimates obtained, surgeons can evaluate which procedure would be safest, so as to avoid the risk of injury to arteries, veins or nerves.
The coefficients estimated through this study showed that pins and screws in the region A1 were the ones that contributed most toward increasing the risk of injury to the arteries, veins or nerves. Pins or screws in the regions A2 and B1 also contributed toward the risk of injury.
The risk of injury to the arteries, veins and nerves is not defined by the total number of pins and screws. The region and the number ofpins and screws in each region explain and determine the distribution of the risk.
Conflicts of interest
The authors declare no conflicts of interest.
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