The influence of wire positioning upon the initial stability of scaphoid fractures fixed using Kirschner wires

Medical Engineering & Physics 29 (2007) 652–660

The influence of wire positioning upon the initial stability of scaphoid fractures fixed using Kirschner wires A finite element study F. Ezquerro a,∗ , S. Jim´enez a , A. P´erez a , M. Prado a , G. de Diego b , A. Sim´on a a

Department of Mechanical Engineering, Universidad de M´alaga, ETSII, Pza. El Ejido s/n, 29013 M´alaga, Spain b Servicio de Traumatolog´ıa, Hospital Virgen de la Vitoria, Colonia Sta. In´ es s/n, 29010 M´alaga, Spain Received 15 June 2006; received in revised form 4 August 2006; accepted 7 August 2006

Abstract A finite element model of the carpal scaphoid and its joints was developed to study how wire positioning affects the initial stability of the fixation of scaphoid waist fractures using Kirschner wires. A transverse fracture of the scaphoid waist was simulated along with its fixation using five different two-wire configurations. The resulting models were subjected to a load simulating a 200 N force passing through the wrist. Friction between bony fragments was taken into account; as the friction coefficient of cancellous bone is unknown, three different values were analysed. For each of these friction coefficient values, the smallest transverse interfragmentary displacements, and consequently maximum initial stability, were obtained for the model that simulated the maximum gap between wires in the plane of fracture. Results also show that for a similar gap in the plane of fracture, more stable fixation can be achieved when wires cross each other not only in the frontal plane of the hand, but also perpendicularly to it. © 2006 IPEM. Published by Elsevier Ltd. All rights reserved. Keywords: Biomechanics; Finite element analysis; Wrist; Internal fixation

1. Introduction The scaphoid is the carpal bone most prone to fracture. A large percentage of scaphoid fractures are successfully treated via immobilization in a cast. However, in some cases, such as unstable or displaced fractures, or those in which the fusion fails to heal, internal fixation is required to encourage the union of bone fragments and to reduce the immobilization period. The aim of the fixation system employed is to provide the initial stability that will facilitate the bone fusion required for fracture consolidation. Screws and Kirschner wires (K-wires) are the devices most commonly used for the internal fixation of scaphoid fractures. In an in vitro biomechanical study, Carter et al. [1], found that Herbert and cannulated screws have greater strength and provide better initial stability than K-wires, though only one ∗

Corresponding author. Tel.: +34 952 131314; fax: +34 952 132691. E-mail address: [email protected] (F. Ezquerro).

example involving two K-wires in a parallel position was considered by the authors, and other possible configurations were not taken into account. On the other hand, the use of Kwires is simpler and more flexible than the use of screws and, furthermore, provides stable fixation with minimal dissection and avoids unwanted shearing and longitudinal moment during application [2]. Merrel et al. [3] reviewed several clinical studies of the treatment of scaphoid nonunions, reporting a high variability in union rate for the fractures treated with K-wires. For example, in a study by Barton [4], union was achieved in 56% of cases, whereas in a similar undertaking by Chen et al. [2], it was attained in all patients. Some studies even reported similar clinical outcomes for screws and K-wire fixation techniques in the treatment of scaphoid nonunions [5] and acute displaced scaphoid waist fractures [6]. The inconsistencies in the clinical outcomes published can be attributed to differences in the position of the K-wires. While techniques for screw implantation are described in

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F. Ezquerro et al. / Medical Engineering & Physics 29 (2007) 652–660

detail in scientific literature, the positioning of K-wires has not been clearly established. It is unusual to find a description of K-wire layout in the numerous clinical reports that analyze this technique [2,5–8]. To the authors’ knowledge, this present study is the first to examine the influence of K-wire positioning on the initial stability of scaphoid fractures. Interfragmentary displacement (IFD) is the magnitude most commonly used to evaluate stability at the fracture site. In the face of the difficulties encountered during experimental studies in accurately measuring IFD, mathematical modeling provides an effective alternative tool. Though not entirely devoid of problems, it does offer numerous advantages such as non-invasive load bearing simulation and the possibility of performing parametric analysis. Two modeling techniques are habitually employed in the mathematical study of carpal bones: finite element models [9–12] and multibody models, which include rigid bodies and springs [13–16]. The aim of the present study was to mathematically investigate which configuration of K-wires afforded stiffer fixation and, therefore, higher initial stability to fractures of the scaphoid waist. Specifically, a transverse fracture at the middle third of the scaphoid was analyzed, as this is one of the most frequent injuries of the carpus [17]. For this purpose, a fractured scaphoid treated via internal fixation using five different K-wire configurations and immobilized in a cast in its neutral position was modeled using the finite element method. The IFD values computed at the fracture site for each case were analyzed and compared to evaluate stability.

2. Materials and methods A 3D-finite element model (FEM) of the scaphoid with its corresponding joints and surrounding bones was built. The model simulated a fracture of the scaphoid waist, with the wrist in the neutral position and immobilized in a cast, as is the routine practice after internal fixation with K-wires. From this base model, five specific FEMs were generated via five different fixation techniques, all of which featured two K-wires but in different configurations. 2.1. Finite element models The geometry of the scaphoid was created with the aid of eleven contour curves. These curves were extracted from slices of an in vivo conventional computer tomography (CT) scan, at 2 mm intervals, of the right wrist of a healthy young male using the commercial software Mimics (Materialise, Belgium). The scaphoid bone was assigned linear elastic and heterogeneous material properties. The Poisson’s ratio, ν, was 0.3 for the whole scaphoid [18]. The Young’s moduli, E, were calculated from the CT density at each point using a modified version of the free access software Bonemat [19] in the following manner: first, apparent density, ρa , was associated to CT density via linear calibration obtained

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using a density phantom included in the scan images. E (MPa) was then calculated as a two-branch function of ρa (kg/m3 ). This function was established using two empirical correlations found in scientific literature: Hodgskinson and Currey’s correlation [20], E = 0.00372ρa1.96 , for a wide range of density associated with trabecular tissue, and Rho et al. correlation [21], E = −3842 + 13ρa , for cortical tissue. The articular surfaces of the scaphoid with the radius, lunate, capitate, trapezoid, and trapezium were then identified. These surfaces were extruded from the bone surface in order to model the cartilage layers corresponding both to the scaphoid and to the bone with which it articulates, each layer being assigned a thickness of 1 mm. The joint of the scaphoid with the trapezoid and trapezium was treated as a single surface in view of the relative lack of mobility between the two bones [22]. The cartilage layers were assigned linear elastic and homogenous mechanical properties. In the different carpal models published, the Young’s modulus of the cartilage ranges from 1 MPa to 10 MPa and the Poisson’s ratio between 0.45 and 0.49 [9,10,23]. For the purposes of the present study, intermediate values were selected, specifically E = 5 MPa and ν = 0.48. Finally, a frictionless contact problem between both cartilage layers of each articulation was established to simulate force transmission through each joint (Fig. 1). Ligamentous constraints were provided by the modeling of six ligaments, three palmar and three dorsal. Each ligament was simulated using two cable elements (Fig. 1b) with linear elastic material properties obtained from scientific literature (Table 1) [9]. The FEM also included a portion of the distal radius and the cartilage layer of the radio-scaphoid joint for the sole purpose of applying the external load transmitted to the scaphoid through said joint. For this reason, the radius was equipped with uniform linear elastic material properties of sufficient rigidity via the selection of E and ν values within the range typical for compact bone, specifically 15 GPa and 0.3. A transverse fracture at the middle third of the scaphoid was simulated by cutting the geometry at the scaphoid waist along a plane normal to its longitudinal axis: the plane of fracture (POF) (Fig. 1). The contact between bone fragments resulting from the fracture was dealt via the establishment of a friction contact problem between the two surfaces cut by the POF. To the authors’ knowledge, there are currently no Table 1 Stiffness and connections of the modeled ligaments Connection

Stiffness (N/mm)

Dorsal ligaments Dorsal intercarpal Dorsal intercarpal Dorsal scapholunate

Capitate Trapezium Lunate

150 150 230

Palmar ligaments Radial arcuate Scaphotrapezial Palmar scapholunate

Capitate Trapezium Semilunar

40 150 230

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F. Ezquerro et al. / Medical Engineering & Physics 29 (2007) 652–660 Table 2 Positioning of the wires in the configurations studied KW1

KW2

KW3

KW4

KW5

α angle α1 α2 A = |α1 − α2 |

5.5◦ −13.5◦ 19◦

5.5◦ −135◦ 19◦

6◦ 6◦ 0◦

4◦ −4◦ 8◦

15◦ −15◦ 30◦

β angle β1 β2 B = |β1 − β2 | Ω

−16◦ −16◦ 0◦ 18.7◦

−15◦ −25◦ 10◦ 20.4◦

−21◦ −21◦ 0◦ 0◦

Intersecting point coordinates (mm) m1 0.221 0.098 0.564 0.749 m2 −3.450 −3.301 d1 −1.801 −1.747 d2 Gap (mm)

1.684

1.685

−20◦ −20◦ 0◦ 7.5◦

−30◦ 0◦ 30◦ 41.4◦

−1.101 2.475 −2.486 −1.906

−1.312 2.452 −2.712 −1.359

0.799 2.770 −0.394 −3.137

3.623

4.000

3.378

The parameters are depicted in the sketch in Fig. 2. Subscripts 1 and 2 refer to each K-wire. Ω is the total angle between both K-wires. Gap is the gap between the wires in POF.

Fig. 1. (a) Extruded image of the entities in the FEM, showing the contact problem at the scapho-lunate joint. (b) Perspective of the complete FEM.

published studies aimed at estimating the trabecular bone-totrabecular bone friction coefficient, μbb . Therefore, in order to investigate its influence on the results, each simulation was carried out for three values of μbb : a small value, 0.1, which has been used in different biomechanical studies to simulate a lower bound of the friction coefficient in both implant surfaces-to-trabecular bone contact [24,25] and subchondral bone-to-subchondral bone contact [26]; an upper value, 0.7, which is the upper limit in the figures reported by Shirazi-Adl et al. [27] for friction between cancellous bone and porouscoated metal and an intermediate value, 0.4. The K-wires were modeled as steel cylinders 1.4 mm in diameter, E = 2.1 MPa and ν = 0.3. Each wire went through the scaphoid from its distal insertion point to the inner surface of the cortical shell at the proximal end of the bone. The cylinder-scaphoid interfaces were established as frictionless contact problems, so that the wires were free both to move

along their longitudinal axes in the opposite direction to their points of insertion and to rotate upon their own axes. Five separate FEMs, referred to as KW1 to KW5, were built to simulate five different configurations clinically viable for internal fixation, with two K-wires adopting a volar approach. Furthermore, an intact, unfractured model of the scaphoid was also built in order to compare its response with experimental pressure measurements obtained from literature. The positioning of the K-wires in each model is depicted in Fig. 2 and described in Table 2, using as a reference the ‘ldm’ coordinate system, which is derived from the centroid of the area of the scaphoid marked out by the POF; the l axis is normal to the POF and points distally, while the d and m axes lie in the POF with d pointing dorsally and m normal to d, creating a right-handed system (Fig. 1b). The parameters used to establish the position of the K-wire identified by the subscript i in Table 2 were: the angle between the l axis and the projection of the K-wire in the lm plane, αi ; the angle between the K-wire and the lm plane, βi ; the coordinates of the point of intersection of the wire with the POF, mi and di . Also indicated for each model is the angle between the projection of the wires in the frontal plane of the hand, A = α1 − α2 , and the difference between the angles formed by the wires with the frontal plane of the hand, B = β1 − β2 . KW1 and KW2 represent positionings habitually used in surgical practice. In both cases, the wires are passed through the scaphoid tuberosity with the aim of inserting a considerable length of wire into both bone fragments and producing a significant angle between them in the frontal plane. The difference between the two models is the value of angle β, 0◦ for KW1 and the highest possible value for KW2. Model KW3 simulates the parallel positioning of the wires that provides maximum separation between them when inserted through the scaphoid tuberosity. KW4 seeks to maximize the gap between the wires in the POF, disregarding the value of the

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Fig. 2. Perspective of the five K-wire configurations simulated and diagram showing the parameters used to define the positioning of each K-wire.

angle between the wires. Finally, KW5, like KW2, aims to produce the highest possible angle between the wires, but without the need for insertion via the scaphoid tuberosity. The commercial software Cosmos/M was used to discretize the FEM and to compute the results. Node to Surface contact elements (N–S) were used to model contact problems and first order tetrahedrons to mesh volumes, since the software displayed compatibility problems between N–S elements and second order tetrahedrons. The selection of the size of the elements in each zone of the model was carried out by means of a convergence study, resulting in finer meshes for the zones near a contact area than for the rest of the bone volume. The number of tetrahedron elements (70,873–80,380) and N–S elements (2121–2224) depended on the wire configurations. Fig. 1b shows an image of the resulting model.

was modeled by applying a load to the radius in a longitudinal direction so that it was transmitted by compression through the radio-scaphoid joint. A compression force of 200 N is a reasonable value to represent the force that can be expected to pass through the wrist under normal physiological loading conditions [28,29]. The force-transmission ratio through the radio-scaphoid contact surface has been estimated to be between 44% and 55% of the total force transmitted through the radio-ulno-carpal joint [14–16]. If an intermediate ratio of 50% is accepted, the total force transmitted at the radioscaphoid articulation can be estimated at close to 100 N. This was the magnitude selected for the force applied to the model in the present study, which was introduced as a uniform load acting in the direction of the axis of the radius (Fig. 3a).

2.2. Load and boundary conditions

3. Results

The immobilization of the wrist in a cast in its neutral position is common practice following K-wire fixation of a scaphoid fracture. This situation was simulated by restricting the displacement of the nodes on the external surfaces of the cartilage layers corresponding to the bones that articulate with the scaphoid, except for the radius, which was limited to moving along its longitudinal axis in order to facilitate load transmission, as explained in the following paragraph, and granting unconstrained 3D motion to all other nodes on the scaphoid (Fig. 3b). The scaphoid must bear the load transmitted between the radius and the distal row of the carpus generated by potential muscle actions, even under immobilization. This situation

All of the models dealt with in this study remained stable under the load and boundary conditions described above, so that response could be computed and no luxation of the scaphoid occurred. Table 3 summarizes the most significant results computed for all models at each μbb value. The global motion of the scaphoid with respect to the surrounding bones resulted in a displacement in the volar and radial directions along with a slight rotation in extension, which was approximately the same for all models and for all μbb values studied. The most significant variations among the different K-wire configurations were found in maximum wire stress and IFD values. The maximum wire stress value, 34.5 MPa, which was found

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Fig. 4. Transversal IFD distribution on the POF for KW1 with μbb = 0.4. D, R, P and U refer to the dorsal, radial, palmar and ulnar zones of the POF (Fig. 5).

to the differences between configurations, it can be seen that the maximum transversal IFD was always lower for KW4 (between 3.9 ␮m for μbb = 0.7 and 4.7 ␮m for μbb = 0.1) and that the highest maximum transversal IFD was always obtained for KW1 (between 7.20 ␮m and 10.68 ␮m, respectively). Pressure distribution at the radio-scaphoid joint, the forces on the articulations and the ligamentous forces computed with the different models were found to be practically unaffected either by the positioning of the wires or by μbb . These results were also virtually identical for the intact model. The pressure distribution at the radio-scaphoid joint for the intact model is shown in Fig. 6. Fig. 3. Load and boundary conditions. (a) An axial load of 100 N was applied to the distal radius. (b) The motion of the radius (R) was constrained to displacements in its axial direction, displacements of the external surfaces of the cartilage layers corresponding to the lunate (L), capitate (C) and trapeziumtrapezoid (T) bones were prescribed.

in configuration KW1 at the lowest friction value, μbb = 0.1, was extremely far from the yield strain of the material used to build the wires. IFD was computed by measuring the relative displacement between each pair of nodes in contact along the POF. Two IFD components were analyzed: axial IFD, the component normal to the POF and transversal IFD, the component in the POF itself. The distribution of both components varied among the different configurations and μbb values, but their maximum values were always found at the external edge of the POF, as shown in Fig. 4 for KW1 with μbb = 0.4. The distribution of the transversal IFD along the perimeter of the fracture as estimated for each model is plotted in Fig. 5. The axial IFD computed showed little variation in relation to μbb value, while transversal IFD was considerably lower for the two higher μbb values than for μbb = 0.1. With regard

4. Discussion In the present study, 3D-FEMs were built to comparatively assess the initial mechanical response of five different K-wire configurations used in the internal fixation of transverse fractures of the waist of the scaphoid. Planar FEMs have often been used to study the mechanical response of the carpus [10–12]. However, such models are not able to compute the displacements outside of the frontal plane of the hand known to occur in carpal kinematics. Carrigan et al. [9] presented a 3D model of the carpus to analyze load transmission pathways; however, in order to avoid the collapse of the model under the applied axial load, all of the carpal bones were restricted to moving parallel to the direction of load application. Furthermore, said study also analyzed the influence of several parameters on model response, revealing substantial variations in results when unconstrained motion of the scaphoid was permitted. In our study, 3D-FEMs were built to simulate the mechanical response of the fractured scaphoid under internal fixation. All of the models used permitted unconstrained motion of the scaphoid, limited only by

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Table 3 Results obtained for all models at each μbb KW1

KW2

KW3

KW4

KW5

μbb = 0.1 Global centroid displacements (␮m) x (radial/ulnar) y (dorsal/palmar) z (distal/proximal) Maximum transversal IFD (␮m) Maximum axial IFD (␮m) Maximum Von Mises K-wire stress (MPa)

35 −131 112 10.7 9.4 34.5

36 −120 104 8 9.8 29.9

35 −126 113 4.9 9.2 29.8

37 −123 105 4.7 8.9 26.7

38 −121 112 8.5 8.2 26.8

μbb = 0.4 Global centroid displacements (␮m) x (radial/ulnar) y (dorsal/palmar) z (distal/proximal) Maximum transversal IFD (␮m) Maximum axial IFD (␮m) Maximum Von Mises K-wire stress (MPa)

35 −131 112 7.3 9.6 25.6

35 −120 103 6.2 10.1 25.0

35 −126 113 4.2 9.3 23.7

37 −123 105 4 9.3 22.5

37 −121 112 4.3 8.6 23.7

μbb = 0.7 Global centroid displacements (␮m) x (radial/ulnar) y (dorsal/palmar) z (distal/proximal) Maximum transversal IFD (␮m) Maximum axial IFD (␮m) Maximum Von Mises K-wire stress (MPa)

35 −131 112 7.2 9.6 25.3

35 −119 103 5.3 10.1 23.4

35 −126 113 4.1 9.2 22.8

37 −123 105 3.9 9.2 21.9

37 −121 112 4.2 8.6 23.5

Global displacements of the centroid of the scaphoid are reflected in axes x, y and z in relation to the radius, as shown in Fig. 1a.

the physiological restrictions derived from its articulations with the surrounding bones and from ligamentous forces. Under these conditions, all models remained stable, so that response could be computed without the need of any additional boundary condition. In order to validate the model with respect to results published in scientific literature, the response of an intact, unfractured scaphoid bone model subjected to the same load and boundary conditions as the fractured models was also evaluated. The pressure distribution computed at the radioscaphoid joint was almost the same for the model of the healthy scaphoid as for all five models with fracture described in previous sections. Ledoux et al. [11], also found similar values for pressure at the radio-scaphoid interface when computed with an FEM of the intact wrist and an FEM simulating a scaphoid waist fracture. The pressure distribution found at the radio-scaphoid joint for the intact model showed a highpressure area on the palmar side of the joint (Fig. 6). This result is in accordance with the findings of other authors for a healthy wrist in neutral position [9,10,30]. With regard to maximum normal pressure values at the radio-scaphoid joint, there is a considerable discrepancy among the works published, both of the experimental or mathematical model variety. These disparities are mainly due to the different load levels considered in each case and the different measurement or modeling techniques used. Nevertheless, the maximum pressure found in our study for the intact model, 1.54 MPa, fell within the range of maximum values published by several authors: 0.44–4.5 MPa [11,14,15,30–32].

Comparison of FEM results with published experimental pressure measurements denotes the ability of the model of the scaphoid and its joints to satisfactorily simulate the load transmitted to the scaphoid. Furthermore, it has to be taken into account firstly that the anatomy of the model was directly obtained from CT scan images of a healthy human bone, its mechanical properties being estimated using the information contained in said images by means of relationships experimentally validated in scientific literature, and secondly that the elastic properties of the wires themselves are easy to predict. Additionally, the aim of this study was to compare the initial mechanical response of a fractured scaphoid when treated via fixation with five different K-wire configurations, not to provide an accurate assessment of the response of the bone fragments in each case. Therefore, the authors consider that the results may be accurate enough for this comparative study. The initial stability provided by each K-wire configuration can be evaluated by analyzing the IFD values computed by its model. A certain amount of axial IFD has been shown to be acceptable, and even beneficial, in encouraging bone healing in long bone fractures [33], while transversal IFD has been clinically associated with non-unions [34]. Therefore, assuming that transverse IFD should be kept to a minimum, we shall consider a fixation configuration to be more stable where smaller transverse IFD values are computed. For all values of μbb , KW4 obtained the lowest transverse IFD results of all the models studied, so this configuration can be considered the most stable solution. KW4 sought to

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Fig. 5. Transversal IFD along the edge of the fracture for each model. D, R, P and U refer to the dorsal, radial, palmar and ulnar zones of the POF.

maximize the gap between the K-wires in the POF, though the angle between the two wires was not especially high. On the other hand, KW1 and KW2 always exhibited the highest transverse IFD. These configurations produced a considerably higher angle between the K-wires than did KW4, especially in the frontal plane of the hand, but the gap between them in the POF was minimal. As for KW3 and KW5, similar transverse IFD values were computed by both models, and these were found to be lower than those obtained for KW1 and KW2, though slightly higher than the results for KW4. Both configurations provided a significant gap between the wires in the POF, though this was smaller than the gap in configuration KW4 and with different angulations: parallel for KW3 and the maximum possible angulation in the case of KW5.

The only exception to these results was found when the minimum μbb value, 0.1, was used. In this case, the maximum transversal IFD computed by KW5 was considerably higher than the maximum values computed by KW3 and KW4. As explained earlier, since the magnitude of the trabecular-boneto-trabecular-bone friction coefficient is not known, three different values were dealt with for every FEM model—an upper value, μbb = 0.7, a lower value, μbb = 0.1 and an intermediate value, μbb = 0.4. The two higher coefficients yielded similar transversal IFD distributions in the POF for all five K-wire configurations. As illustrated in Fig. 4, such distributions displayed the maximum transversal IFD between the most ulnar area and the most dorsal area of the POF, while displacements in the radial zone were very small. However, when the lower μbb value was adopted, transversal IFD dis-

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Fig. 6. Contact pressure distribution at the radio-scaphoid articulation for the intact, unfractured model.

tribution was altered, revealing an increase in displacements in the radial zone of the POF. This change was due to the fact that the highest compression forces between bone fragments were transmitted through this area, hence, when high μbb values were used, friction was able to bear the shear forces which cause transversal displacements, but at μbb = 0.1, the lower friction provided less resistance to relative motion and consequently higher transversal IFD was generated in this zone. Comparatively speaking, the only configuration that was influenced by this effect was KW5. For this configuration, in order to achieve the maximum angulation between the wires, it was necessary to insert them across the POF through a more ulnar zone (positive value of mi in Table 2) than that used in any other configuration. Consequently, motion in the radial area of the POF was less constrained and the aforementioned effect amplified, thus increasing the transversal IFD in said area to a greater degree for KW5 than for the other configurations. As a result, the maximum transversal IFD value for KW5 was found to be higher than that computed for the other models, with the exception of KW1, when μbb = 0.1 was used. Nevertheless, the effect described above brought only a slight influence to bear on this comparative study, since the lowest transversal IFD values were obtained by the KW4 configuration at each μbb , while the highest transversal IFD was always found with KW1. The results of the present study, discussed in the preceding paragraphs, showed that when the K-wires are inserted, aiming for the maximum gap (rather than maximum angulation) between them in the POF is the most successful strategy in minimizing transversal IFD. However, it is always recommendable to insert the K-wires at a certain angulation, since parallel positioning will not be able to support loads in the direction of their axes. The load condition considered in this study simulated a compression of the proximal carpal bones, which is the habitual load borne by the scaphoid. Parallel positioning of the K-wires is able to stabilize such a compression force, but if the bone fragments were pulled in the direction of the wires at any moment, they would not be able to support the load and this could result in their loosening,

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which is one of the problems commonly associated with the use of K-wires as fixation devices [5]. In configurations KW1 and KW2, the K-wires cross each other forming the same angle in the plane of the hand—A = 19◦ , but with a different B angle: 0◦ for KW1 and 10◦ for KW2 (Table 2). It can be seen that by simply increasing the B angle in KW2 positioning while keeping the gap between the wires in the POF at similar values, the values of the transversal IFD were considerably reduced (Table 3). This result reveals that when the intersection points of the wires with the POF are similar, i.e. a similar gap prevails between the wires, more stable fixation is achieved by crossing the wires not only in the frontal plane of the hand, but also perpendicularly to it. The transversal IFD values computed were very low, under 10.7 ␮m for all models; it is therefore unlikely they would pose a problem to fracture consolidation. However, the minimum value of IFD that can jeopardize fracture consolidation is currently unknown. Moreover, the force transmitted by each subject through the wrist is also very difficult to estimate, so a situation in which a patient whose wrist is immobilized in a cast produces a load on the scaphoid in excess of the one considered for the purposes of this study, and which consequently exhibits higher IFD values, cannot be ruled out. For both of these reasons, the absolute values of IFD computed for each model have not been discussed but rather a comparative study has been carried out in order to evaluate which K-wire configuration provides the fracture with higher initial stability.

5. Conclusions The present study showed that the minimum transversal IFD for fractures of the waist of the scaphoid treated via fixation with K-wires were computed by the models that simulated configurations with maximum gap between wires in the plane of fracture. Since, lower transversal IFD values indicate higher initial stability of the fracture, and given that this is the goal of the fixation system, it can be concluded that, in order to better promote fracture consolidation, it is recommendable to insert the wires in such a way that the separation between them in the plane of fracture is as great as possible, a more advantageous option than seeking maximum angulation. In addition, the study showed that more stable initial fixation can be achieved by crossing the K-wires not only in the frontal plane of the hand, but also in any other plane.

References [1] Carter II FM, Zimmerman MC, DiPaola M, Mackessy RP, Parsons R. Biomechanical comparison of fixation devices in experimental scaphoid osteotomies. J Hand Surg [Am] 1991;16(5):907–12. [2] Chen CY, Chao EK, Lee SS, Ueng SW. Osteosynthesis of carpal scaphoid nonunion with interpositional bone graft and Kirschner wires: a 3 to 6-year follow-up. J Trauma 1999;47(3):558–63.

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