Carpal hyperextension is a common injury in dogs and usually is a consequence of a second- or third-degree sprain of the palmar carpal ligaments and fibro-cartilage.1 During situations in which overloading occurs in a limb, compressive forces can cause fractures of the carpal and metacarpal bones, and tensile forces or hyperextension can cause damage in the ligamentous structures.2 Most of these injuries involve falls from a height, overuse injuries in working dogs, or road traffic accidents, all of which can cause carpal hyperextension with irreversible damage to the palmar ligaments and fibrocartilaginous support. Other injuries include carpal fractures, intra-articular fractures, traumatic or congenital luxations, nonunions, or severe arthritis.3
Repair of these injuries generally requires pancarpal arthrodesis, which is commonly performed with straight compression plates or HDCPs. These plates are secured to a metacarpal bone (usually the third metacarpal bone) distally and, as such, generally require the use of an additional cast or splint to mechanically support the bone in the early recovery period.4 In contrast, CLPs, which are a newer concept, distribute the load at the third and fourth metacarpal bones and are presumed to not require additional cast or splint support.5 This castless concept with the CLP has the potential to simplify early postoperative recovery and thus avoid potential bandage-related problems.
The purpose of the study reported here was to investigate how these 2 plate designs would affect the load transfer to the applied bones, in addition to the implant stresses sustained when the bone-plate constructs were loaded (via calculations of the load during trotting). To do so, the aim was to develop a computational model with directed input from mechanical tests of these 2 constructs. Our hypothesis was that an FE model could be developed to assess the peri-implant strain distribution around each pancarpal plate, which could then be used to compare their respective failure likelihoods (high strain areas) with commonly reported clinical failure modes of the respective implants.
Materials and Methods
Specimen preparation—Both forelimbs of a 35-kg 13-year-old castrated male Golden Retriever euthanized for reasons unrelated to the study were harvested and used for biomechanical and computational investigations. The forelimbs were positioned in a typical standing angle, the position verified with scout view, and then scanned with a clinical CT scannera (resolution, 0.4 mm; slice thickness, 1.0 mm). Bilateral pancarpal arthrodeses were then performed by a board-certified veterinary surgeon, who used 2 implants. An HDCPb was placed on the right forelimb (four 3.5-mm screws were placed into the distal aspect of the radius, 1 into the radiocarpal bone, and 4 into the third metacarpal bone); a 120-mm CLPc was placed on the left forelimb (four 3.5-mm screws were placed into the radius, one 3.5-mm screw was placed into the radiocarpal bone, and three 2.7-mm screws were placed into the third and fourth metacarpal bones). Craniocaudal and lateral radiographic projections of these constructs were obtained to verify appropriate implant positioning (Figure 1). All articular surfaces were left intact. The specimens were frozen at −20°C for further testing.
Craniocaudal and mediolateral radiographic views of the CLP (A and B) and HDCP (C and D) constructs evaluated in right and left forelimb specimens, respectively, from a 13-year-old Golden Retriever. In both constructs, the plates were secured to the distal aspect of the radius with four 3.5-mm screws, with one 3.5-mm screw in the radiocarpal bone. In the CLP construct, three 2.7-mm screws were angled into both the third and fourth metacarpal bones; in the HDCP construct, four 3.5-mm screws were placed into the third metacarpal bone. The level of the radiocarpal screw is indicated by the horizontal line. The plates were selected so as to cover a similar amount of the metacarpal bone length.
Citation: American Journal of Veterinary Research 73, 11; 10.2460/ajvr.73.11.1687
Mechanical testing—Prior to testing, the specimens were thawed overnight at room temperature (approx 20°C). During preparation and testing, the specimens were kept moist with saline (0.9% NaCl) solution. All soft tissues were removed from the humerus proximal to the elbow joint; the elbow joint capsule and all ligaments at this level were left intact. The proximal end of the humerus was removed, and the remaining diaphysis (15 cm) was embedded in a PMMA cylinder. For each specimen, 3 uniaxial strain gaugesd were glued in accordance with standard protocols6–8 on the dorsal plate surface at the level of the carpometacarpal joint and onto the dorsal aspect of the third and fourth metacarpal bones immediately adjacent to the distal plate edge (Figure 2). The strain gauges were aligned with the relative bone-plate major axis in full bridge configuration.
Photographs of the CLP (A and B) and HDCP (C) applied to forelimb specimens from a 13-year-old Golden Retriever. A—Right forelimb instrumented with the CLP in a typical vertical standing position; the construct is shown fixed in a servohydraulic material testing machine. Distally, the specimen is restrained by the sandpaper-covered aluminum plate. Proximally, the PMMA-embedded humerus is connected to the material testing device at an elbow joint angle of 135°. Notice that the limb is slightly angled in the frontal plane to place the paw flat on the distal surface. B—The CLP secured to the third and fourth metacarpal bones of the right forelimb. The scale measure at the bottom of the image is in cm. C—The HDCP secured to the third metacarpal bone of the left forelimb. Strain gauges can be seen in panels B and C overlying the third and fourth metacarpal bones adjacent to the plates (black arrows) and also on the plate surface overlying the level of the carpometacarpal joint (green arrows).
Citation: American Journal of Veterinary Research 73, 11; 10.2460/ajvr.73.11.1687
Both specimen constructs were fixed in a servohydraulic material testing machinee featuring a 6 degrees of freedom load cellf (4 kN; 250 N·m). The PMMA-embedded cylinder was secured in a custom clamp so as to secure the limb in a restrained position with the elbow joint at 135° of flexion and the forelimb in a typical standing position (approximately perpendicular to the ground). Distally, the paw of each specimen was placed in contact with an aluminum plate covered by sandpaper to prevent paw slippage during testing. To place the paw in a typical standing position, the paw was centered slightly forward relative to the elbow joint (Figure 2). Each strain gauge was connected to an acquisition system.g An axial compression load was applied to each limb under load control as described. A preload axial force of 15 N was applied, followed by a 50-N axial force increased stepwise to 300 N, which was repeated 10 times. Each load step was reached with a 10 N/s ramp and maintained for 5 seconds. The actuator axial displacement and the axial load were recorded at 64 Hz. After completion of this phase of testing, each specimen was loaded with a 1-Hz increasing sinusoidal axial load (constant valley load, 50 N; peak increase rate, 0.1 N/cycle) until construct failure.9,10 Failure was defined as a sudden increase in the recorded displacement due to implant (plate or screw) or bone failure.
FE modeling—The original CT data (Digital Imaging and Communications in Medicine files) from both noninstrumented limbs were semiautomatically reconstructed through single-threshold and manual labeling.h,i The bone marrow and the medullary cavity as well as the cancellous and cortical bone were separated on the basis of thresholds of 100 and 500 Hounsfield units, respectively.j The 3-D reconstructions of the radius, ulna, and radiocarpal and metacarpal bones of the right forelimb were imported into a computational software program.k Intermetacarpal and intraosseous ligaments were simulated with linear axial spring elements with a stiffness of 100 N/mm.11 Distally, the radius and ulna were also coupled with linear spring elements simulating the radioulnar ligament. To reproduce the contact between the distal portion of the metacarpal bones and the ground, the paw was included in the model and the contact properties between these structures simulated via rigid coupling. Proximally, the elbow joint was simulated via 2 rigidly coupled reference points, which transmitted the load to the radius and ulna. These reference points gave the ulna rotational freedom around the elbow joint axis (Figure 3). The contact between the radiocarpal bone, distal aspect of the radius, and proximal aspect of the metacarpal bones was simulated via linear spring elements for which stiffness was optimized during the model validation process. Distally, the paw was restrained in all degrees of freedom.
Diagrams showing a craniocaudal view (left) and mediolateral view (right) of a 3-D model of a forelimb of a Golden Retriever instrumented with an HDCP. On the mediolateral view, the loading and boundary conditions of the model are shown. The entire axial load is carried by the metacarpal pad, which connects rigidly to the ground surface. Notice that the limb is slightly angled in the sagittal plane to place the paw flat on the distal surface, as also shown in panel A of Figure 2.
Citation: American Journal of Veterinary Research 73, 11; 10.2460/ajvr.73.11.1687
The bone model was meshed with 4-node linear tetrahedral elements (C3D4) up to a global mesh size of 2 mm for the radius and ulna and 1 mm for the metacarpal bones. Linear elastic material behavior was assigned to the cortical (E-modulus, 19 GPa) and cancellous bone (E-modulus, 1.9 GPa).10 The elements representing the bone marrow and the medullary cavity were modeled with a negligible Young modulus of 5 MPa. A Poisson ratio of 0.3 was used in all instances.12,13
Three-dimensional models of HDCP and CLP designs as well as unthreaded 2.7- and 3.5-mm cortical screws were built from computer-aided design files and imported into a computational software program.k Plate and screw models were meshed with 4-node linear tetrahedral elements (C3D4) up to a global mesh size between 0.5 and 0.8 mm with linear elastic behavior, with a Young modulus of 186 GPa and a Poisson ratio of 0.3.12,13
Each implant model was positioned on an identical copy of the 3-D reconstruction of the right forelimb according to the position determined from the radiographic projections.l Instrumentation with either implant system was realized with Boolean operations.
The bone-to-screw and plate-to-screw contact was modeled tying the relative knots. The plate to bone contact was modeled as frictional surface contact with Coulomb friction (μ, 0.2).14 A frictional surface-to-surface contact interface with normal behavior (force perpendicular to the plate surface) was used for this purpose.
Simulations and validation iterations—The same load steps used to mechanically test both constructs on the servohydraulic material testing machinee were applied to the reference points controlling the proximal radial and ulnar surfaces, axial to the forelimb's major axis. Iterative calculations were performed to validate the FE model instrumented with the CLP. Characteristics that varied between iterations included paw position, carpal spring stiffness, locked and unlocked screws, and bone material properties. For each iteration and load step, the experimentally recorded and computationally calculated strains were compared and the process repeated until the results retrieved in this FE model showed the closest behavior to the results retrieved in the same location of the ex vivo model. The model instrumented with the HDCP design was then updated with this optimized parameter set of boundary conditions. Finally, the 2 FE models were used to estimate the bone and implant von Mises stresses when loaded with an axial load of 500 N, simulating trotting loads.15–17
Data evaluation—For all tests, the construct axial displacements, axial loads, and strains were recorded. All raw data recorded during the ex vivo tests were evaluated with statistical software.j Computational data were retrieved as output of the computational software program.k Variables of interest were the strain of the various elements in the direction measured by the strain gauges and the calculated von Mises stress of the elements. Additionally, the mean and maximum von Mises stress around the distal screw holes in the metacarpal bones was evaluated in a cylindrical volume (radius, 3.0 mm). To gauge the amount of bone and implant potentially at failure risk, the 2 plate systems were loaded to 500 N,12 simulating loading during trotting.
Results
Mechanical testing—The strains recorded during the 5 load steps of the CLP and HDCP constructs in forelimb specimens were summarized (Table 1). The dorsal strain gauges of both plates were strained in tension. Strain magnitudes ranged between 0 to 120 microstrain in the CLP construct and between 0 to 80 microstrain in the HDCP construct. In the CLP construct, the strain magnitude was similar between the third and fourth metacarpal bones at each load step; in the HDCP construct, the strain magnitude recorded on the third metacarpal bone surface was higher than that recorded on the fourth metacarpal bone starting at all load ranges (Figure 4). The HDCP construct failed at 10,890 cycles loaded at 1,017 N; the CLP construct failed at 8,107 cycles loaded at 963 N. In each forelimb specimen, the metacarpal bones fractured either adjacent to the most distal screw holes or end of the plate (Figure 5).
Mean ± SD recorded degrees of strain (microstrain) on the third and fourth metacarpal (MC) bones and on a CLP or HDCP construct applied to forelimb specimens from a 13-year-old Golden Retriever during 10 independent measurements.
| Force (N) | CLP | HDCP | ||||
|---|---|---|---|---|---|---|
| MC III | MC IV | Plate | MC III | MC IV | Plate | |
| 50 | −557.92 ± 7.33 | −401.80 ± 2.18 | 31.07 ± 2.36 | −327.78 ± 72.08 | −234.06 ± 5.18 | 35.16 ± 3.25 |
| 100 | −906.00 ± 5.56 | −711.50 ± 5.75 | 42.49 ± 1.93 | −516.37 ± 45.32 | −399.66 ± 5.56 | 43.91 ± 4.03 |
| 150 | −1,083.12 ± 10.86 | −987.70 ± 4.66 | 54.11 ± 2.61 | −747.02 ± 62.38 | −503.84 ± 12.76 | 48.76 ± 7.31 |
| 200 | −1,197.26 ± 14.82 | −1,243.54 ± 23.81 | 71.13 ± 4.16 | −903.67 ± 44.80 | −561.21 ± 12.94 | 56.64 ± 7.64 |
| 250 | −1,302.96 ± 25.51 | −1,481.09 ± 7.39 | 94.58 ± 5.36 | −1,018.71 ± 44.48 | −590.91 ± 8.48 | 66.59 ± 7.79 |
| 300 | −1,402.84 ± 33.00 | −1,700.31 ± 38.09 | 119.91 ± 5.65 | −1,128.53 ± 54.83 | −625.78 ± 13.60 | 80.21 ± 8.65 |
Values for experimentally recorded microstrain during a step load axial force test (0 to 300 N) of a CLP (A) or HDCP (B) construct applied to forelimb specimens from a 13-year-old Golden Retriever. Negative sign indicates compression strain. MC = Metacarpal bone. SG = Strain gauge.
Citation: American Journal of Veterinary Research 73, 11; 10.2460/ajvr.73.11.1687
Craniocaudal radiographic views of the CLP (A) and HDCP (B) constructs in the forelimb specimens from Figure 1 after cyclic loading to failure. In the CLP, the failure occurred in the metacarpal bones directly at the distal screw holes, whereas in the HDCP, the failure occurred just below the plate edge. Arrows indicate fracture location.
Citation: American Journal of Veterinary Research 73, 11; 10.2460/ajvr.73.11.1687
FE modeling—The CLP model was considered validated when the maximum error recorded between the experimental and computational values for plate strain in all load steps was < 15%. This configuration featured a reduction in the Young modulus of cortical and cancellous bone to 15 and 1.5 GPa, respectively. Similarly, for the model to fit the experimental data, the most proximal radial screw and the middle metacarpal screws were simulated as locked through rigid coupling. In addition, modeling of the springs connecting the radiocarpal bone to the radius and to the metacarpal bones was set at 10 kN/mm. With this optimal parameter set at an axial load of 300 N, the mean error between computational and numeric results was < 13% when the mean of all strain measurements was calculated (Table 2).
Mean ± SD strain recorded and calculated on the surface of a CLP applied to a forelimb specimen from a 13-year-old Golden Retriever during mechanical testing and with FE analyses under an axial load of 300 N.
| Variable | MC III | MC IV | Plate |
|---|---|---|---|
| Experimental value (microstrain) | −1,402.84 ± 33.00 | −1,700.31 ± 38.10 | 119.91 ± 5.65 |
| Computational value (microstrain) | −1,229.91 ± 259.72 | −1,256.21 ± 294.52 | 120.57 ± 25.76 |
| Error (%) | 12.33 | 26.12 | 0.55 |
The discrepancy between the experimental and computational data is reported as percentage error.
MC = Metacarpal bone.
The FE simulations revealed the highest stress to the bone elements to be those located in the metacarpal bones at the level of the distal screw holes. The comparison between both models at an axial load of 500 N revealed a slightly higher amount of elements at risk in the third metacarpal bone (7.2%) of the HDCP model, compared with in the CLP model (third metacarpal bone, 4.9%; fourth metacarpal bone, 5.8%; Figure 6). However, in both constructs, no elements reached a degree of stress higher than the cortical failure threshold under a simulated trotting load. The mean von Mises stress recorded around the distal screw holes in the third metacarpal bone was 12.9 MPa (maximum, 80.7 MPa) for the HDCP model and 9.7 MPa (maximum, 46.1 MPa) in the third metacarpal bone and 14.0 MPa (maximum, 88.6 MPa) in the fourth metacarpal bone for the CLP model.
Distribution of von Mises stress (MPa) at 500-N axial load in the third and fourth metacarpal bones with the CLP (A) and the HDCP (B) plate constructs in the forelimb specimens in Figure 1. The peak stress was consistently located at the level of the most distal screw holes.
Citation: American Journal of Veterinary Research 73, 11; 10.2460/ajvr.73.11.1687
The FE simulations indicated that the highest stress to both plates was at the level of the radiocarpal bone. The CLP model revealed a higher degree of higher stress (495 MPa) than did the HDCP model (247 MPa; Figure 7). The FE model also revealed that the highest stresses to the screws were present at the most proximal position in the plate (in the radius) and the most distal position in the plate (in the metacarpal bones; mean, 10 to 20 MPa; maximum, 110 to 190 MPa) in both models. The junction of the screw head to the shaft revealed the highest stresses; however, these stress magnitudes were well below the yield stress of the screws.
Distribution of von Mises stress (MPa) in the CLP (A) and HDCP (B) under 500-N axial load in the forelimb specimens in Figure 1. For both plates, the yield point of 690 MPa was not reached at this load level (maximum von Mises stress: CLP, 495 MPa; HDCP, 247 MPa).
Citation: American Journal of Veterinary Research 73, 11; 10.2460/ajvr.73.11.1687
Discussion
The present study demonstrated that an FE model could be successfully developed of a dog's forelimb through use of information derived from biomechanical testing, whereby the FE model mimicked the mechanical tests within a reasonable limit. Similarly, this model could reasonably assess the stresses to the bone in response to pancarpal plate application and the stresses applied to the respective implants. The model also could be used to show the differences and similarities between the 2 plate designs investigated. The model could be further inferred to be valid because the individual failure risks (high-strain areas) were in identical areas commonly reported for experimental and clinical failure modes of the respective implants.4,18,19 We propose that this FE model could be used to predict the behavior of an implant applied for a pancarpal arthrodesis in the mechanical conditions tested.
The HDCP was designed to transmit the entire limb load to the third metacarpal bone. Clinically, pancarpal arthrodeses performed with this plate are supported by an additional cast or splint so as to share the applied loads and to decrease failure risk in the third metacarpal bone.4 In contrast, the CLP was designed to distribute the load to both third and fourth metacarpal bones, thereby proposing to reduce the stresses to the metacarpal bones, avoiding the need for additional cast or splint.5 Despite the lack of any statistical comparison between these 2 constructs, there were no substantial differences observed at each region of increased stress in the bones or plates with mechanical evaluation of the constructs or with the FE modeling.
The strain and stress results of the implants and the bones were used to evaluate construct differences. A paired ex vivo strain comparison ideally would have allowed a statistical comparison; however, because only 2 instrumented forelimb specimens were used, such a comparison was not possible. With a greater number of specimens, such comparisons also would require identical setups in which, for example, the strain gauges would need to be placed in identical locations; this would be difficult at best, notwithstanding the greater error in recording from strain gauges attached to bone (vs the implant). All these factors would require many more specimens for testing.
Alternatively, we approached this problem by creating computational models of the implants and bones under investigation. This approach provided considerable information that would not be obtained from a purely mechanical evaluation. However, the intrinsic limitations of the approach are directly related to model complexity. In any such evaluation that crosses a joint or multiple joints and involves many bones, there is an inherent complexity that may result in several possible errors. Because of the complexity of the forelimb construct, some simplifications in model design and development were necessary to minimize possible areas of inherent error and simultaneously decrease the computational scale. Reasonable results were obtained despite the complexity, and an acceptable match was deemed to have been achieved between the ex vivo specimen and the FE model.
Limitations related to the complexity of the model described in this report must be addressed. For the biomechanical testing, the articular cartilage was not removed so as to avoid adding a procedural bias due to low intersample reproducibility. Additionally, a limited number of strain gauges was placed on the implants and bone, close to regions with the expected highest strains as determined on the basis of clinically relevant presumptions. In building the FE model, it was recognized that the mechanical testing needed to be performed with several constraints. The CLP and HDCP constructs were loaded in a standing position, and staircase quasistatic loading was repeated 10 times to account for any potential implant or bone settling. Additionally, each load step was maintained for 5 seconds to allow for adequate time to collect several strain data points. Finally, cyclic sinusoidal loading to failure was used to identify whether the applied loading mode was able to reproduce the typical fracture patterns observed clinically.20,21 The strains recorded when testing the specimen instrumented with the CLP had a comparable magnitude in both metacarpal bones at all load ranges. In contrast, testing of the specimen instrumented with the HDCP showed an increasing deviation between metacarpal strain with increasing load. As expected clinically, loading both constructs elicited a failure in the metacarpal bones at the distal metacarpal screw holes. Given that a sole pair of limbs was tested, no true difference in cycles to failure or failure load could be determined between the CLP and HDCP constructs.
The FE model included a number of simplified representations, including bones directly in contact with the implants and unthreaded screws only. The connection between bones was limited to reconstructing the basic forearm anatomic features thought to be important to allow proper kinematics; for example, the ulna was included in the model only on the basis of ligament reconstruction to pair its function with radial function. Furthermore, only the radial carpal bone was included, with the contribution of the remaining carpal bones simulated with linear spring elements. The 2 right limb models featuring either implant were then continuously updated to obtain the best fit parameter set and loaded with a force magnitude in a range consistent with a dog that is trotting; these loads were then used for the subsequent numeric comparisons.
The von Mises stress was calculated for each element of the model, and the results confirmed that the region of bone adjacent to the distal metacarpal screws underwent the greatest stress. The model featuring the CLP showed a 20% lower risk of failure of the metacarpal bones, compared with the HDCP. However, on the basis of our calculation for the loading conditions, the absolute peak stresses in these regions (approx 80 vs 90 MPa for the HDCP and CLP constructs, respectively) were clearly below the generally reported failure threshold of cortical bone (186 MPa), leaving a presumed consistent safety margin for clinical applications with either plate. At the same time, the comparable stress magnitude demonstrated in both models at the most distal screw holes in the metacarpal bones illustrated a potential problem attributable to the continued presence of these stress risers. Several factors may have been responsible for these stress risers: different screw diameters used to fix the plates to the metacarpal bones (plate size), number of screws chosen to fix each metacarpal bone (plate length), and position of the most distal screw with respect to the overall metacarpal bone length (plate length). Furthermore, any screw angulation might create off-axis stresses when not aligned parallel to the sagittal plane, the main bending plane of the limb.
Building an FE model is a process made of many interactive steps in which a limited set of parameters are iteratively changed, analysis performed, and computational and experimental results compared. At the beginning of the simulation, the set of parameters, including paw position, carpal spring stiffness, and ligament and bone mechanical properties, was constructed on the basis of reported values.22 As would be expected, these parameters did not necessarily mirror the condition of the constructs tested on the servohydraulic material testing machine.e Therefore, their values were tuned simulation after simulation, until gaining the best fit possible between experimental and computational strain data at each simulated load. Once the computational model can be shown to behave similarly to the experimental model, similar data can be retrieved for alternate load conditions. In our model, the agreement between experimental and computational data increased with increasing load and was best for loads in the range of 200 to 300 N. This can be readily explained by systematically larger experimental measuring errors with smaller absolute values and, perhaps more likely, the likely nonlinear behavior of the mechanical testing under small loads.
Despite all of its limitations, the CLP model was validated with an overall mean error < 15 ± 13%. The best agreement between data was achieved for the strain gauge on the plate surface, which was most likely attributable to the flat and clean attachment surface and the plate's strictly linear behavior under the applied loading conditions. In contrast, larger deviations were found in the strain gauges placed on the metacarpal bones. These greater deviations were expected because the gauges were applied on the anatomically complex surface shape of these bones and the variable contact properties of strain gauge-to-bone. Only the model featuring the CLP was truly validated under the described limitations. Furthermore, the computational results must be interpreted in view of the highlighted boundary conditions even when supported by the experimental data.
ABBREVIATIONS
| CLP | Castless pancarpal arthrodesis plate |
| FE | Finite element |
| HDCP | Hybrid dynamic compression plate |
| PMMA | Polymethylmethacrylate |
Aquilion 19, Toshiba America Medical Systems Inc, Tustin, Calif.
Jorgensen Laboratories Inc, Loveland, Colo.
Orthomed, Halifax, West Yorkshire, England.
N2A-06-T001N350, Vishay Micro-Measurements, Raleigh, NC.
MTS Bionix 858, MTS Systems Corp, Eden Prairie, Minn.
Huppert 6, Huppert GmbH, Herrenberg, Germany.
MGCplus AB22A/AB32, Hottinger Baldwin Messtechnik, Darmstadt, Germany.
AMIRA Visage Imaging GmbH, Berlin, Germany.
Geomagic, Geomagic Inc, Merrimack, NH.
Matlab, version 6.5.1, The MathWorks Inc, Natick, Mass.
ABAQUS, Dassault Systemes Simulia Corp, Providence, RI.
Image Tool, version 3.0, University of Texas, San Antonio, Tex.
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