3-D computer modelling of malunited posterior malleolar fractures: effect of fragment size and offset on ankle stability, contact pressure and pattern

The ankle joint is a synovial hinge joint permitting movement, plantarflexion and dorsiflexion of the foot, in a single plane [1]. It is composed of the distal articular surfaces of the tibia, the fibula and the talus guided by tendons and ligaments [2, 3]. The ankle joint is very stable due in the main to the congruency between the bony articulations of the joint supported by the ligaments of which the deltoid ligaments and the lateral collateral ligament and the syndesmotic ligament complexes play an important role in ankle dynamics [1]. The close fitting of the articular surfaces of the talar dome in the mortice formed by the tibial plafond, medial malleolus and lateral malleolus together with the supporting ligaments ensures the stability of the ankle complex [4, 5]. However, because the articulating surfaces of the talus are wider anteriorly compared to posteriorly, stability is greater during dorsiflexion than during plantarflexion. In a normal healthy joint at a neutral weight-bearing standing position, the calcaneus typically remains stationary while the talus moves freely on it [4].

The ankle joint is a major joint prone to injuries and conditions including fracture and arthritis. Recent studies have determined that the incidence of ankle fractures accounts for about 9% of all bone fractures [6, 7]. Although isolated fractures of the posterior malleolus, anatomically the bony protrusion that helps keep the talus in its position [8], are relatively rare [9], it has been determined that between 7 and 44% of all ankle fractures involve a posterior malleolus fracture component [9‐11]. These fractures are classified as 44A3 or 44B3 under the Arbeitsgemeinschaft für Osteosynthesefragen, AO classification [12, 13]. It has been reported that larger fractures of the posterior malleolus can result in posterior subluxation of the talus and articular incongruity of the tibial plafond which, if not corrected can lead to posterior instability of the ankle and secondary traumatic arthritis [8, 14, 15] and whilst smaller fractures may not result in posterior subluxation, it has been suggested that they can still potentially lead to tibiotalar instability [16] and degenerative changes. Posttraumatic osteoarthritis resulting from fractures of the posterior malleolus can occur due to malreduction of the fracture fragment, cartilage damage due to the trauma and ankle instability [17].

Historically, nonsurgical treatment has generally been employed for stable, isolated posterior malleolus fractures and the decision to undertake surgical intervention has been taken based on fragment size [9, 16] commonly measured as the percentage of involvement of the distal tibial articular surface [9]. However, there is a lack of consensus amongst the clinical studies reported in the literature as to the fragment sizes which require internal fixation and this has been attributed to the difficulty in determining fragment size accurately using lateral radiographs, which have traditionally been used, and the need for standardization in measuring the functional outcomes of interventions [18]. A number of studies have recommended anatomic reduction with internal fixation when the fragment size is larger than 25 to 33% of the tibial plafond [9, 11, 18‐25] although others have argued that the level of evidence as to whether internal fixation of posterior malleolar fractures leads to improved outcomes is not sufficiently high to support this recommendation [17, 19].

A number of experimental, biomechanical studies have been undertaken which have investigated the effect of posterior malleolar fracture on tibiotalar contact area, articular load distribution and contact stress [19, 23, 26]. Load characteristics of the ankle are complex [20]. When loaded, the ankle has a smaller contact surface area than both the knee and the hip [20] and it has been demonstrated that during normal walking the ankle joint is subjected to greater compressive forces than both these joints, with values up to and exceeding five times the body weight reported [11].

The review undertaken by van den Bekerom et al. [18] analysed and reported on several biomechanical studies investigating ankle instability amongst which were two cadaveric based studies that examined the change in contact area following posterior malleolar fracture [18, 23, 24]. In the biomechanical cadaver-based investigations performed by both Hartford et al. [23] and Macko et al. [24] tibiotalar contact area was found to decrease with increasing posterior malleolar fracture fragment size. In addition, load distribution patterns were found to alter, as fragment size increased confluence and load concentration also increased. Although stresses were not reported in these studies, it was suggested that the reduction in articular surface area could cause peak stresses and rates of post traumatic arthritis to increase [9]. In the unconstrained, dynamic cadaver model utilised by Fitzpatrick et al. [27] joint contact area was found to reduce slightly but significantly only following a 50% posterior malleolus osteotomy compared to the intact ankle. Although no increase in peak contact stress was observed following fracture, the contact stress pattern shifted anteromedially, particularly in dorsiflexion. The authors suggest that the shift causes stress on cartilage that usually sees little load and that this may contribute to posttraumatic arthrosis. Similarly, Vrahas et al [28] also reported seeing no elevation in peak tibiotalar peak stress in their cadaver based posterior malleolar fracture model but again a change in the articular stress distribution was found.

In the current study an investigation was undertaken into the effect of fragment size and offset of a malunited posterior malleolus on tibiotalar joint contact area, pressure and stability. A 3-dimensional finite element (FE) model of ankle was developed enabling virtual osteotomies to be undertaken in order to simulate fragment sizes ranging from 6 to 15 mm at offsets of between 1 to 4 mm. Three static positions of the ankle were considered: the neutral position, at 20° dorsiflexion and at 30° plantarflexion. The loads corresponding to those experienced during a two legged stand of a 70 kg subject were applied and tibiotalar contact area and pressure calculated for each fragment size, offset and ankle position combination.

The purpose of the study was threefold:

Finite element analysis was chosen for the current study for a number of reasons. The Finite Element Method has become widely accepted as a valuable numerical tool for studying the biomechanics and the influence of mechanical forces on biological systems [29]. It is ideal for undertaking stress and strain analysis of bone and joints and load bearing implants [30]. It has been successfully used for the biomechanical analysis of major joints of human body including the shoulder [31], hip [32], spine [33] and knee [34]. Finite element analysis has a number of advantages compared with experimental and cadaveric studies, such as, amongst others, analyses are repeatable, there are no ethical considerations and the study parameters can be modified quickly and easily at low cost [29, 30]. They can be employed to help interpret clinical and experimental results and in cases when experiments are difficult [30, 35]. With cadaveric studies, obtaining significant numbers of specimens may be challenging from both availability and financial standpoints. In addition, cadaveric specimens are more likely to have undergone degenerative bone and ligament changes which can influence results [18]. A further advantage with a finite element based model is that due to its deterministic nature, complex statistical analyses of model generated data (predictions) is not required.

We found a lack of consensus among previous cadaveric ankle studies of ankle instability [23, 24, 27, 28]. A finding which had also has been reported with ankle and foot ankle impact injury studies [35]. Utilising our finite element model we investigated the effect of fragment size and offset of a malunited posterior malleolus on tibiotalar joint contact area, pressure and stability in an attempt to help clarify the cadaveric data available to-date. Model validation against experimental data is essential to ensure confidence in simulation predictions [36]. We validated our ankle model by comparing predicted contact area values and peak contact pressure magnitudes for the intact ankle with the results from a number of cadaveric studies. Once validated, a finite element model such as ours can be utilised to investigate scenarios where cadaveric or in-vivo experimentation and measurement is difficult, expensive or where a consensus has failed to be established from previous studies. In our case, we utilised our validated finite element ankle model to investigate a range of fracture scenarios as findings from previous cadaveric studies of ankle instability had failed to establish a consensus.

This study investigates the effect on tibiotalar joint stability of malunion following a posterior malleolus fracture, in particular, the influence of fracture fragment size and offset on joint contact area and stress is examined. First, a 3D model of a healthy ankle joint was created. Virtual osteotomy procedures were then performed to simulate malunited posterior malleolar fractures with different fragment sizes and offsets. Fracture fragment sizes ranging from 6 to 15 mm at increments of 3 mm were simulated in combination with offsets of between 1 to 4 mm using a 1 mm increment. The loading condition corresponding to that of a 70 kg subject in a two leg stand position was applied. The ankle was considered in the neutral position, at 20° dorsiflexion and at 30° of plantarflexion and tibiotalar joint contact area and stress calculated in each position for all fracture fragment size—offset combinations.

The 3D finite element model was created from CT scan data of the healthy, left foot, and included the distal tibia, fibula, talus, calcaneus, cuboid and navicular bones, and the sixteen ligaments associated with the ankle joint. The procedure employed to obtain the 3-dimensional bone geometries of the ankle complex for use in the current analysis was based on that used previously by Alonso-Rasgado et al. [37] to generate bone geometries from CT scan data for inclusion in a 3-D numerical model of a hip joint.

First, DICOM data from the CT scans of the foot (Fig. 1a) were imported into an image processing software application enabling 3D surfaces of each of the bones included in the model to be produced through a segmentation process (Fig. 1b) [37]. The surface data were then exported from the image processing software and imported into SolidWorks® (Dassault Systèmes, SolidWorks Corp, Waltham, MA, USA), where solid models were generated from the surface data and the cartilage geometry and the insertion points for the ligaments (Fig. 1c) were added. The components were then imported and assembled in the Abaqus 6.13-3® FE analysis software (Abaqus, Inc., Dassault Systemes Simulia Corp, Providence, RI) where solid geometry pre-processing tools were employed to undertake the virtual osteotomies. Mesh generation and model analysis was then performed using the Abaqus software (Fig. 1d).

In order to perform the virtual osteotomies, a typical posterior malleolus fracture location was identified from the literature and confirmed by a surgeon. Virtual osteotomies were performed on the healthy ankle model (intact) creating additional models representing sixteen malunited posterior malleolus fracture scenarios. Four different section lengths (fracture fragment sizes) were simulated, 6, 9, 12 and 15 mm representing 18, 26, 35 and 44% of the total distal tibial articular surface, respectively. Each section length was modelled in combination with section offsets of 1, 2, 3 and 4 mm.

This study has described a 3-D finite element model of the ankle that can predict the contact area and contact pressure in the tibiotalar joint region for different ankle positions. Using this model, we have investigated the contact area and contact pressure of the joint when malunion occurs in a posterior malleolar fracture for a finite combination of section length and section offsets for the ankle in the neutral position, 20° dorsiflexion and 30° plantarflexion. The contact area defined is the articulation area of the distal tibial plafond against the surface of the talus.

The effect of section length and section offset of a posterior malleolar fracture on joint contact area was investigated in this study. Our model predicted that, compared to the intact joint, contact area was greater in all malunion scenarios considered. Some earlier cadaveric studies (1991–1993) [23, 24] reported that tibiotalar contact area decreased with increasing fracture fragment. Macko et al. [24] reported reductions in tibiotalar contact area of between 4 and 35% for fracture fragments of 25, 33 and 50% in their cadaveric model whilst Hartford et al. [23] found contact area reduced by 4–22% for fracture fragments of 25–50%. However, in a more recent study (2004), Fitzpatrick et al. [27] reported no significant change of contact area following the creation of a 50% posterior malleolar fracture. In the earlier cadaver studies [23, 24], pressure sensitive film was employed to measure ankle joint contact pressure under static loading conditions, whereas the more recent study by Fitzpatrick et al.[27], with which our model predictions closely agree, employed a dynamic unconstrained model which provided for a more realistic loading pattern. In the cadaveric studies, ankle joint arthroplasty was required for insertion of the pressure sensitive film and this, combined with the presence of the film during the tests could potentially have altered ankle kinematics and joint stress, accounting for additional differences with cadaver study results and our model predictions [27]. In addition, soft tissue constraints were removed from some of the cadaveric ankles and the cadaveric specimens are more likely to have undergone degenerative bone and ligament changes than the patients presenting with posterior malleolar fractures in the clinical setting [18].

From our study we also found that, in the neutral position, joint contact area increased with fracture section length, and whilst total joint contact area remained relatively constant regardless of section length and offset in plantarflexion, in dorsiflexion, joint contact area reduced as fragment size increased beyond 6 mm (8% fracture). Overall, section length had a greater effect on joint contact area than section offset. The model predicted joint instability in only one of the scenarios considered, for a section length of 15 mm, section offset 4 mm in dorsiflexion.

Large fractures of the posterior malleolus have been implicated in posttraumatic osteoarthritis [8, 14, 15] whilst smaller fractures, it has been suggested, may lead to tibiotalar instability [16] and degenerative changes. It was initially thought that posttraumatic osteoarthritis occurred as a result of a reduction in joint contact area and a corresponding increase in contact pressure [18]. However, this has been questioned more recently following a number of biomechanical studies of posterior malleolar fractures [18, 27]. In addition, several studies have reported no elevation of peak contact pressure following fracture in biomechanical models [27, 28]. The results from our study concur with these two experimentally determined observations; our model predicted no decrease in tibiotalar joint contact area and no overall elevation of peak contact pressure as a result of malunion following posterior malleolar fractures of 6–15 mm. However, as has been reported in a number of cadaveric studies [27, 28], our model predicted a definite modification to contact pattern following fracture. In the neutral position, following fracture, additional areas of contact were established anteriorly and medially on the tibia and also on the fibula. In plantarflexion, tibia contact area grew medially and fibula contact area also increased. In dorsiflexion, tibia contact area grew anterior and medial in the fracture scenarios, a finding also reported by Fitzpartick et al. [27]. These results support the view that in cases of posterior malleolar fracture, posttraumatic osteoarthritis occurs as a result of a change in joint contact pattern which causes load on areas of cartilage not used to loading and not, as previously thought, due to an increase in contact pressure.

Current consensus suggests internal fixation for posterior malleolus fractures of greater than 25% of the tibial plafond [17]. We found no evidence to support this from our study. Our model predicted instability only with the highest level of fracture in a loaded limb at an extreme position of dorsiflexion. This concurs with a number of previous studies that determined that following fracture, posterior stability is likely to be maintained so long as lateral ligaments remain intact [27, 51, 52]. The lack of instability (except in one extreme case), combined with the fact no increase in peak ankle joint contact pressure was found for the fracture scenarios points to posterior malleolus fractures being relatively benign in nature. This supports the findings of an earlier review of the literature on the biomechanical and clinical evaluation of posterior malleolar fractures [18] and a recent study of the long-term outcome of 886 combined cases of posterior malleolar fractures from 1978 to 2014 undertaken by Veltman et al [17]. Veltman et al found that conservative treatment of posterior malleolar fractures showed comparable results on long-term outcome to surgical treatment, with no evidence to support the current consensus of fixing posterior malleolus fractures of greater than 25% of the tibial plafond.

When analysing ankle repositioning in the fracture scenarios considered, the model determined that force increased significantly in two ankle ligaments, anterior talofibular and anterior tibiofibular, in dorsiflexion. It is not known if the increased forces in these ligaments would result in clinical symptoms for patients.

Our finite element model is subject to some limitations and simplifications typically associated with complex numerical analyses in orthopaedic-related biomechanics. However, we validated our intact ankle model by comparing predicted contact area values and peak contact pressure magnitudes with the results from a number of cadaveric studies, which suggests that the simplifications and assumptions adopted in our model did not introduce significant error. Ligament and cartilage (soft tissue) behaviour was assumed to be linear elastic. Ligaments typically exhibit non-linear viscoelastic behaviour. To model this behaviour requires the specification of a significant number of parameters, for which accurate data are not readily available [53]. In addition, ligaments are known to operate close to the linear region [54], therefore a purely linear representation would enable good accuracy to be achieved. A neo-Hookean hyperelastic model is generally considered to provide a more accurate representation of cartilage behaviour. However, in finite element studies concerned primarily with joint contact stress and area analyses, little difference has been reported between predictions obtained assuming linear cartilage behaviour compared to neo-Hookean hyperelastic behaviour [55]. We analysed a single ankle specimen. The purpose of the study was to compare, for a given anatomy, ankle joint contact pressure and area for different malleolar fracture fragment sizes and offsets, not to quantify ankle joint pressure and contact area for a range of ankle specimens, therefore the use of a single ankle specimen was appropriate for this purpose.

For future research, we suggest applying our model to clinical case data. For example, by utilising our ankle model in conjunction with a randomized controlled trial it may be possible to establish a pathomechanical foundation for applying fixation for particular levels of fracture backed by clinical results.

The model predicted joint instability only with the highest level of fracture in a loaded limb at an extreme position of dorsiflexion. No increase of peak contact pressure as a result of malunion was predicted but contact pattern was modified.

These results suggest that posterior malleolus fractures are relatively benign in nature. We found no evidence to support the current consensus of fixing posterior malleolus fractures of greater than 25% of the tibial plafond. In addition, the results of our study support the view that in cases of posterior malleolar fracture, posttraumatic osteoarthritis occurs as a result of a change in joint contact pattern which causes load on areas of cartilage not used to loading and not, as previously thought, due to an increase in contact pressure.

Ankle repositioning resulted in increased force in two ankle ligaments. Our finding could explain commonly reported clinical observations.