Evaluation of the performance of three tenodesis techniques for the treatment of scapholunate instability: flexion-extension and radial-ulnar deviation

3-D finite element (FE) models of the right wrist from a 63-year-old female were created using 133 slices of computer tomography (CT) scan data. The slices were of 0.7 mm thickness and the transverse resolution was 512 × 512; the pixel size was 0.289 × 0.289 mm. 3-D image data processing software was used to create the surfaces of the geometry from the CT scan data. In addition, to optimise the element size of the mesh, data resampling using a pixel spacing of 0.4 × 0.4 × 0.4 mm was performed.

Reconstruction of each of the 15 cortical bone surfaces considered in the 3-D FE models was performed using a thresholding method. Masks created in the image data processing software to describe the cortical bone were exported as 3-D geometries and imported into Abaqus 6.14 (Dassault Systemes, RI, USA). The metacarpal bones were fixed and only a cortical shell was included as these geometries do not come into contact with the scaphoid and lunate bones, the main bones of interest in this study. For the remaining bones, once the cortical layer was defined, the internal volume was filled virtually and assigned trabecular bone material properties. The cortical layer thickness was determined from the CT scan and varied for each bone; the average thickness for all the bones was 2.35 mm. Metacarpal bones have an average thickness of 2.4 mm, radius and ulna 3.0 mm and the carpal bones 1.65 mm [12].

The Abaqus 6.14 software was used to create the solid mesh from the surfaces of the cortical bone geometry imported previously. Linear tetrahedral elements (C3D4) were used to mesh the bone geometry. Linear tetrahedral elements were considered adequate for the analysis in this case as the study was primarily concerned with predicting the relative position of the bones as a result of various movements rather than obtaining accurate stress estimates. The same software was used to assemble the meshed bone geometry in order to create the wrist model. Wedge elements (C3D6) were used to simulate the cartilage for the articulation between bones. The thickness of the cartilage was obtained by taking half of the distance between two articulating bones [12, 13]. Two-node spring elements defined in tension were used to simulate the 31 ligaments used in the models, 10 extrinsic ligaments, 16 intrinsic ligaments and 5 interosseous. Each of these ligaments was incorporated in the models using multiple elements allowing the distribution of the force over the area of attachment so as to avoid stress concentrations. Stiffness values of between 10 and 325 N/mm were identified from the existing literature [13‐15] and applied in the FE models to the two-node spring element representations employed for the ligaments. In addition, the dorsal radiocarpal ligament, dorsal intercarpal ligament and volar radioscaphocapitate ligament, ligaments that wrap around the bone structure of the wrist anatomy, were simulated using shell elements (Fig. 1). This was achieved by first creating virtual points in the assembly following the curvature of the ligaments. The points were connected with wires to form a closed loop from which an internal surface was created which was then defined as shell geometry. Anatomic literature was used to identify the insertion points of these ligaments in the models [16, 17]. The stress-strain relationships and corresponding cross-sectional areas [17] were obtained based on the stiffness. Table 1 shows the number of elements and nodes used in each model. The neutral position of the wrist was used to set the coordinate system. For cortical and trabecular bone, a Young’s modulus of 18,000 and 100 MPa, respectively [12, 13, 19], was employed. Furthermore, a Poisson’s ratio of 0.2 was used for the cortical bone and a corresponding value of 0.25 for the trabecular bone [12, 13, 19]. Homogeneous and isotropic material behaviour was considered for the bones. Mooney-Rivlin parameters C10 of 4.1 and C01 of 0.41 were used to define the hyper-elastic material behaviour of the cartilage [12, 13]. A low value for the coefficient of friction (0.02) was assigned to the articulating surfaces in order to approximate frictionless contact [20]. Surface-to-surface contacts were assigned in the FE models to the articulations involving proximal carpal bones in order to allow free movement of triquetrum, scaphoid and lunate. In terms of the distal carpal bones, as the motion between these can be considered to be negligible [21], the articulations were assigned using tie constraints. Table 2 lists the interactions between the articulations.

The FE models were created based on the intact (ligament) wrist model. The models simulate three reconstruction techniques; the scapholunate axis method (SLAM), Corella and MBT, with the hand in the neutral position, in the ulnar-deviated clenched fist position, at 20° flexion, 20° extension, 15° radial deviation and 15° ulnar deviation. In addition, for each wrist position, models were created to simulate the wrist joint following SLIL sectioning, where the connection between the scaphoid and lunate bone is severed (Fig. 2c).

Virtual surgery was undertaken based on the description of the three tendon graft reconstruction techniques. In the case of the Corella reconstruction method [5], two holes are drilled one in the scaphoid and another in the lunate. The hole in the lunate bone is drilled from dorsal to volar at the medial area (Fig. 2e). The two bones (scaphoid and lunate) are then connected by tendon grafts one in the dorsal and the other in the volar region [5]. In order to perform the virtual surgery simulating the SLAM [3], the wrist is viewed in the coronal plane (Fig. 2f) and holes drilled, in the scaphoid and lunate, with tendon grafts at the dorsal and central areas used to connect the two bones. In the MBT technique [8], the tendon graft connects the lunate and scaphoid bone at the dorsal area only (Fig. 2d). This technique involves the drilling of a hole through the scaphoid bone from palmar tuberosity to a dorsal point of insertion of the dorsal SLIL. The tendon graft is then passed through the hole from volar to dorsal side.

In the FE models of the surgery, solid elements were used to mesh the 3-mm diameter cylinders shapes used to represent the tendon grafts for the three reconstruction techniques.

The tendon graft representations were assumed to be in perfect contact (tie) with the internal surfaces of the scaphoid/lunate. The cylindrical hole drilled through the bone was included in the model in order to give a more accurate representation of the surgical procedures. For the intact model, in all positions, the scaphoid and lunate were joined with SLIL Fig. 2b. The SLIL stiffness was used to represent the stiffness of the tendons grafts in the FE numerical models. An explicit algorithm was employed for FE model solution.

The finite element wrist models were validated by comparing model predictions with data from a cadaveric study. Six scenarios were considered for the validation:

Fifteen cadaveric hands and wrists from specimens with a mean age of 75 years, range 54 to 94, were used for this study. The specimens were sectioned at the mid-forearm. To measure SL (dorsal) gap and angle of the specimens [22, 23], the hands were positioned in the neutral position and posteroanterior (SL) and lateral (angle) plain radiographs taken. A Steinman pin of known dimension was included in all lateral (angle) plain radiographs enabling distance to be measured accurately using calibrated software. SL gap measurement was undertaken using the methodology described by Lee et al. [23].

To be able to reproduce the motion considered in this study, six tendons of the cadaver wrists were exposed: flexor carpi ulnaris (FCU), flexor digitorum superficialis (FDS), flexor digitorum profundus (FDP), flexor pollicis longus tendon (FPL), extensor carpi ulnaris (ECU) and extensor digitorum communis (EDC). Five tendon groups (FCU, ECU, FDS, FDP/FPL and EDC) were created using FiberWire locking stitches. The ulnar-deviated clenched fist position was created by first cementing the cadaveric hands in a cylindrical plastic container which was then fixed on the edge of a table utilising a clamp. Loads of 15 and 20 N were hung separately from FDP/FPL, FCU, FDS, ECU and EDS tendons (Fig. 3).

The SLIL of all the cadaveric hands was sectioned using a scalpel blade in order to reproduce the scapholunate instability. For the position of the ulnar-deviated clenched fist, the angle and SL (dorsal) gap were determined before and after sectioning through the PA and lateral plain radiograph stress views [22, 23]. Specimens were then allocated to either the MBT, SLAM or Corella tendon graft reconstruction techniques randomly. Following the procedure, the wrists were loaded as described previously to produce the ulnar-deviated clenched fist position. Prior to and following loading, plain radiographs were taken enabling SL angle and (dorsal) gap to be ascertained.

The experimental setup described in the above section was simulated in the model by setting a boundary condition that constrained motion in all directions at the proximal end of the ulna and radius bones (Fig. 4). The Z-axis at the proximal area of pisiform and dorsal base of the fifth metacarpal was used to apply vertical loads of 15 N in each area; hence, simulation of the loading of FCU and ECU tendons was achieved (Fig. 4). The simulation of the clenched fist position was achieved by applying a 20 N load on the EDC tendon and a 15N load on the FDS tendon, distributed equally on the medial four metacarpal bones, and a 15N load on the FDP/FPL tendon group was distributed on all the five metacarpal bones (Fig. 4). Figure 4 shows the magnitudes of the forces applied in the model. The three virtual reconstruction methods MBT, SLAM and Corella were performed with the hand in neutral position before boundary and loading conditions were applied to produce the ulna-deviated clenched fist posture, ulnar and radial deviation, and flexion and extension positions. Free motion was allowed at the lunotriquetral, scaphoid-lunate, scaphoid-capitate, scaphoid-radius, scaphoid-trapezoid, scaphoid-trapezium, lunate-capitate, lunate-radius, triquetrum-hamate and radius-ulna joints. The volar and dorsal sides SL gaps were calculated by determining the distance between the midpoints of the scaphoid and lunate articulation surface margins (Fig. 5). The method described by Larsen et al. [22] was used to calculate the SL angle (α) (Fig. 5). These values, SL dorsal gap and angle of each model, were used to validate the models by comparing them against the results obtained from the cadaveric study described in Section 3.1.

Initial model validation consisted of comparing joint contact area and contact pressure predictions from our intact (ligament) wrist model with those determined experimentally in the cadaveric study undertaken by Tencer et al. [24]. The specimen mounting and loading conditions employed in the cadaveric study were simulated in our intact (ligament) model.

Our model predicted a contact area/total area ratio of 0.182 compared to 0.206 ± 0.0495 in the cadaveric study and a scaphoid/lunate contact area ratio of 3.02 compared to 3.72. The peak joint contact pressure predicted by the model, 4.52 MPa, was in the range determined in the cadaveric study, 2–5.6 MPa.

A mesh sensitivity analysis was undertaken to investigate model convergence. Mesh density was increased in the loaded intact ligament model until SL gap and angle changed by less than 1%. This density was then employed for subsequent analyses.

The results of the extended model validation exercise are shown in Fig. 6 where SL gap (dorsal) and SL angle predicted by the FE model for the six validation scenarios are compared against the corresponding mean values obtained from the cadaveric study. Upon inspection of the SL gap comparison shown in Fig. 6a, it can be seen that model predictions are in good agreement with the experimentally determined values; for all scenarios, the predicted SL gap is within 0.2 mm or 11% of the corresponding mean cadaveric study value except for the intact ligament in the ulna-deviated clench fist posture, where the model prediction is 0.4 mm or 16% lower than the experimental value.

A comparison of experimentally determined and FE model-predicted SL angle is presented in Fig. 6b. Generally, there is good agreement between mean SL angle obtained from the cadaver study and that predicted by our numerical model. Model predictions are within 5° and 11% of the experimental data for all scenarios except the Corella tendon reconstruction case, where the FE model predicts an SL angle which is 7.7° greater than the experimental value; however, the FE-predicted SL angle is still within the range of the cadaveric study data values, 36–53° for this scenario.

It is interesting to note that following SLIL sectioning, the SL gap increased significantly under loading compared to the intact loaded ligament case, by 1.2 mm (50%) in the experimental study and by 1.8 mm (90%) in our numerical model. In contrast, SLIL sectioning had less effect on SL angle, resulting in a mean reduction of just 3.2° (6%) in the cadaveric case and an increase of 1.4° (2.8%) in the FE model compared to the intact loaded ligament case. Tendon reconstruction reduced (dorsal) SL gap back to the original intact loaded ligament values or below in the cadaver experiments and to within 10% for our FE model cases. In addition, tendon reconstruction resulted in an SL angle less than the corresponding intact loaded ligament value in both the cadaver and FE model studies.