Axial stiffness and ring deformation of complete and incomplete single ring circular external skeletal fixator constructs

Caleb C. Hudson Comparative Orthopaedic and Biomechanics Laboratory, University of Florida, Gainesville, FL 32610.
Department of Small Animal Clinical Sciences, College of Veterinary Medicine, University of Florida, Gainesville, FL 32610.

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Daniel D. Lewis Comparative Orthopaedic and Biomechanics Laboratory, University of Florida, Gainesville, FL 32610.
Department of Small Animal Clinical Sciences, College of Veterinary Medicine, University of Florida, Gainesville, FL 32610.

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Alan R. Cross Georgia Veterinary Specialists, 455 Abernathy Rd NE, Atlanta, GA 30328.

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MaryBeth Horodyski Comparative Orthopaedic and Biomechanics Laboratory, University of Florida, Gainesville, FL 32610.
Department of Orthopaedics and Rehabilitation, College of Medicine, University of Florida, Gainesville, FL 32610.

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Scott A. Banks Comparative Orthopaedic and Biomechanics Laboratory, University of Florida, Gainesville, FL 32610.
Department of Mechanical and Aerospace Engineering, College of Engineering, University of Florida, Gainesville, FL 32610.

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Antonio Pozzi Comparative Orthopaedic and Biomechanics Laboratory, University of Florida, Gainesville, FL 32610.
Department of Small Animal Clinical Sciences, College of Veterinary Medicine, University of Florida, Gainesville, FL 32610.

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Abstract

Objective—To compare the axial stiffness, maximum axial displacement, and ring deformation during axial loading of single complete and incomplete circular (ring) external skeletal fixator constructs.

Sample—32 groups of single ring constructs (5 constructs/group).

Procedures—Single ring constructs assembled with 2 divergent 1.6-mm-diameter Kirschner wires were used to stabilize a 60-mm-long segment of 16-mm-diameter acetyl resin rod. Construct variables included ring type (complete or incomplete), ring diameter (50, 66, 84, or 118 mm), and fixation wire tension (0, 30, 60, or 90 kg). Axial loading was performed with a materials testing system. Construct secant stiffness and maximum displacement were calculated from the load-displacement curves generated for each construct. Ring deformation was calculated by comparing ring diameter during and after construct loading to ring diameter prior to testing.

Results—Complete ring constructs had greater axial stiffness than did the 66-, 84-, and 118-mm-diameter incomplete ring constructs. As fixation wire tension increased, construct stiffness increased in the 66-, 84-, and 118-mm-diameter incomplete ring constructs. Maximum axial displacement decreased with increasing fixation wire tension, and complete ring constructs allowed less displacement than did incomplete ring constructs. Incomplete rings were deformed by wire tensioning and construct loading.

Conclusions and Clinical Relevance—Mechanical performance of the 66-, 84-, and 118-mm-diameter incomplete ring constructs improved when wire tension was applied, but these constructs were not as stiff as and allowed greater displacement than did complete ring constructs of comparable diameter. For clinical practice, tensioning the wires placed on 84- and 118-mm-diameter incomplete rings to 60 kg is recommended.

Abstract

Objective—To compare the axial stiffness, maximum axial displacement, and ring deformation during axial loading of single complete and incomplete circular (ring) external skeletal fixator constructs.

Sample—32 groups of single ring constructs (5 constructs/group).

Procedures—Single ring constructs assembled with 2 divergent 1.6-mm-diameter Kirschner wires were used to stabilize a 60-mm-long segment of 16-mm-diameter acetyl resin rod. Construct variables included ring type (complete or incomplete), ring diameter (50, 66, 84, or 118 mm), and fixation wire tension (0, 30, 60, or 90 kg). Axial loading was performed with a materials testing system. Construct secant stiffness and maximum displacement were calculated from the load-displacement curves generated for each construct. Ring deformation was calculated by comparing ring diameter during and after construct loading to ring diameter prior to testing.

Results—Complete ring constructs had greater axial stiffness than did the 66-, 84-, and 118-mm-diameter incomplete ring constructs. As fixation wire tension increased, construct stiffness increased in the 66-, 84-, and 118-mm-diameter incomplete ring constructs. Maximum axial displacement decreased with increasing fixation wire tension, and complete ring constructs allowed less displacement than did incomplete ring constructs. Incomplete rings were deformed by wire tensioning and construct loading.

Conclusions and Clinical Relevance—Mechanical performance of the 66-, 84-, and 118-mm-diameter incomplete ring constructs improved when wire tension was applied, but these constructs were not as stiff as and allowed greater displacement than did complete ring constructs of comparable diameter. For clinical practice, tensioning the wires placed on 84- and 118-mm-diameter incomplete rings to 60 kg is recommended.

Circular external skeletal fixation and linear-circular hybrid external skeletal fixation have become well-established techniques for addressing a variety of orthopedic problems affecting dogs and cats.1–12 Circular fixators and the circular components of hybrid constructs typically use small-diameter transosseous wires as fixation elements.13 The incorporation of fixation wires, which are generally tensioned to improve construct stiffness, imparts unique biomechanical properties to circular fixators, compared with linear fixators.14,15,a The fixation wires are secured to ring components, which are the supporting elements unique to circular and hybrid fixators.9,11,14,16,17 The rings can be complete or incomplete (ie, containing an open section in the circumference of the ring).9,10,14,18

Several studies15,18–21 have evaluated the biomechanical properties of circular fixator systems designed specifically for use in dogs and cats. These studies15,18–21 have primarily evaluated the mechanical characteristics of constructs with complete rings. Complete rings confer biomechanical advantages,19 but incomplete rings are often incorporated in fixator constructs used in clinical situations because of anatomic constraints.1,19 Incomplete rings are often used when a ring is placed adjacent to a joint, with the open section of the ring positioned to allow a greater range of motion in that joint.4,9,11 Despite the routine incorporation of incomplete rings in circular and hybrid constructs in dogs and cats,9–12 little is known about the biomechanical effects associated with the use of incomplete rings. Cross et al19 evaluated 6 configurations of distal ring blocks, 3 of which included incomplete rings, and demonstrated that constructs incorporating incomplete rings were less stiff than comparable constructs with complete rings. However, that study19 did not evaluate the effect of different fixation wire tensions and only evaluated constructs made with 84-mm-diameter rings.

The purpose of the study reported here was to compare the biomechanical properties of complete and incomplete (five-eighths circumference) single circular (ring) external skeletal fixator constructs subjected to axial loading. Axial stiffness, axial displacement, and ring deformation resulting from wire tensioning and application of an axial load were evaluated. Constructs varied with regard to ring diameter (50, 66, 84, or 118 mm) and the fixation wire tension applied (0, 30, 60, or 90 kg). We hypothesized that complete ring constructs would be significantly stiffer than incomplete ring constructs and that axial stiffness would increase with increasing wire tension and decrease with increasing ring diameter. We also hypothesized that considerable ring deformation would occur in incomplete but not in complete rings as a result of wire tensioning and as a result of axial loading.

Materials and Methods

Construct preparation—Single ring constructsb were made with 50-, 66-, 84-, or 118-mm (inner diameter) complete and incomplete (five-eighths circumference) rings. A 60-mm length of 16-mm-diameter acetyl resin rodc was used as a bone model.15,19 Two pilot holes were made in the acetyl resin rod with a 1.58-mm twist drill bit mounted in a drill press. Pilot holes were oriented transversally to the longitudinal axis of the acetyl resin rod and had crossing angles analogous to the wire divergence angles used for each specific ring diameter. Wire divergence angles used were 67.5° (50- and 118-mm-diameter rings), 72° (66-mm-diameter rings), and 60° (84-mm-diameter rings). Wire crossing angles varied among ring diameters to allow the Kirschner wires to be secured in the holes adjacent to the open section of the incomplete rings and to cross at the center of each ring. Two 1.6-mm-diameter stainless steel (316L) Kirschner wires were inserted through the pilot holes with a variable-speed cordless drill.d Kirschner wires were secured to opposing surfaces of each ring with the cannulation in the fixation bolts.b The fixation bolts positioned farthest from the open section of the ring in incomplete rings and the analogous bolts in complete ring constructs were tightened to a torque of 10.5 N•m with a factory-calibrated torque wrench.22,e Kirschner wires were tensioned simultaneously with 2 calibrated dynamometric wire tensioners.f Wire tensions of 0, 30, 60, or 90 kg were used. After wire tensioning, the nuts on the fixation bolts adjacent to the tensioners were tightened to a torque of 10.5 N•m.

Constructs, once assembled, were mounted on a custom fixture for testing. The fixture consisted of a 200 × 200 × 76-mm aluminum block with a complete base ring (the same diameter as the ring to be tested), which was firmly bolted 1 cm off the surface of the aluminum block by means of five 6-mm-diameter threaded rods screwed into the aluminum block. Two blocks of milled acetyl resin were secured to the upper surface of the base ring with bolts inserted through the lower surface of the base ring and screwed into the acetyl resin blocks. One of the 6-mm threaded rods that attached the complete base ring to the aluminum block was longer than the other rods and protruded 3 cm above the top of the acetyl resin blocks (Figure 1). Test constructs were mounted to the fixture by passing the protruding section of the threaded rod through one of the holes on the side arm of an incomplete ring or through an analogous hole in a complete ring. The construct to be tested was aligned directly over the base ring so that the construct ring rested on the acetyl resin blocks attached to the base ring. Each construct was fixed in place by tightening nuts on the protruding threaded rod against opposing surfaces of the construct ring. Five replicates of each construct were evaluated (32 groups; total, 160 constructs). New Kirschner wires were used for each construct, and new rings were used for each construct with incomplete rings. After evaluation, complete rings without visible evidence of deformation were subsequently reused to make other constructs.

Figure 1—
Figure 1—

Photographs of a custom fixture for testing the axial stiffness, maximum axial displacement, and ring deformation during axial loading of complete and incomplete circular (ring) external skeletal fixator constructs. A—Testing jig consisting of an aluminum block with a complete base ring bolted to the surface of the block. Two acetyl resin spacers (solid white arrows) and a segment of threaded rod (white outline arrow) support the test construct. B—Testing jig with a 118-mm-diameter incomplete ring construct secured in place prior to axial loading.

Citation: American Journal of Veterinary Research 73, 12; 10.2460/ajvr.73.12.2021

Axial stiffness and displacement measurements—The fixture with an attached construct was positioned in a servohydraulic testing system.g Load was applied axially to the proximal end of the acetyl resin rod at a rate of 200 N/s to a maximum load of 400 N with a preload of 5 N. Each construct was axially loaded for 15 cycles at a rate of 0.25 Hz. Servohydraulic testing system software recorded axial force (N) and axial actuator displacement (mm) for all testing cycles. Data were collected at a rate of 100 points/s. Load-displacement curves were plotted from the axial force and displacement data for each construct. Data from the 15th cycle were used for analysis. The secant stiffness was calculated for each load-displacement curve by calculating the slope of a line connecting the preload value of 5 N and the chosen endpoint of 375 N.23 Maximum displacement was defined as the total axial displacement from displacement at an axial load of 0 N (prior to preload application) to that at an axial load of 375 N.

Ring deformation measurement—During construct preparation, 2 measurement points were scribed on each ring with a steel punch. Ring measurement points were scribed at the peripheral edge of the upper surface of each ring at the location bisected by a plane passing through the center of the ring, perpendicular to a plane bisecting both the center of the ring and the hole in the center of the closed end of the incomplete rings (and the analogous hole in the complete rings). A 3-D digitizing system with an articulating armh was used to record the position of the ring measurement points at specific times during the testing sequence. Measurements were obtained with the digitizing system before application of tension to fixation wires, after tensioning the fixation wires but prior to construct loading, during maximal axial load application for the 15th cycle, after unloading for the 15th cycle, and after releasing the tension on fixation wires. The ring measurements were digitally exported to a spreadsheet programi as X, Y, and Z coordinates, which described the location of the scribed points in space relative to the digitizing system. To calculate the distance between the 2 scribed points (peripheral ring diameter) obtained for each ring during the testing sequence, ring measurement data were analyzed via the Euclidean distance formula:

article image

Statistical analysis—Statistical analysis was performed with commercially available statistical software.j A Shapiro-Wilk test was performed to assess the normality of data distribution. The effect of ring type and wire tension on axial stiffness and on axial displacement was analyzed by ring diameter via a multivariate ANOVA. When significant interactions existed, a univariate ANOVA was used to identify significant differences between constructs on the basis of ring type and wire tension. A Sidak correction was performed to adjust the P value to account for multiple comparisons. This correction decreased the P value for determining significance from the initially selected value of P ≤ 0.05 to a value of P ≤ 0.013 for constructs with 50-, 66-, and 84-mm-diameter rings and to a value of P ≤ 0.01 for constructs with 118-mm-diameter rings.

The effect of fixation wire tensioning and construct loading on the measured peripheral ring diameter within each construct type was analyzed via repeated-measures ANOVA. A post hoc Bonferroni correction was used when significant differences in ring diameter during a testing cycle were identified. Values of P ≤ 0.05 were considered significant.

Results

The 50-, 66-, and 84-mm-diameter incomplete ring constructs failed by catastrophic plastic deformation when tension on the fixation wires was increased to 90 kg. The ring deformation started as in-plane deformation, resulting in a decrease in the width of the open section of the ring, and rapidly progressed to catastrophic out-of-plane plastic deformation with folding of the ring and loss of wire tension (Figure 2). Thus, none of the 50-, 66-, or 84-mm-diameter complete or incomplete ring constructs were tested with the fixation wires tensioned to 90 kg; 90-kg tension could only be applied to the fixation wires in 118-mm-diameter complete or incomplete ring constructs.

Figure 2—
Figure 2—

Representative photograph of ring failure in a 66-mm-diameter incomplete ring external skeletal fixator construct. Ring failure occurred during an attempt to apply tension of 90 kg to the fixation wires of the construct. Notice the out-of-plane deformation (folding), which was characteristic of the failure pattern noted in all failed 50-, 66-, and 84-mm-diameter incomplete ring constructs.

Citation: American Journal of Veterinary Research 73, 12; 10.2460/ajvr.73.12.2021

Peripheral ring diameter of complete ring constructs was nominally and not consistently affected by wire tensioning or construct loading; a permanent change in ring diameter was not induced in any complete ring construct as a result of wire tensioning or construct loading. There was a consistent decrease in the diameter of the incomplete ring constructs associated with wire tensioning and axial loading. Deformation was greater at higher wire tensions and in larger diameter constructs. Application of tension of 60 kg to fixation wires in the 66-mm-diameter incomplete ring constructs and tension of 90 kg to fixation wires in the 118-mm incomplete ring constructs resulted in a significant residual decrease in ring diameter of 1% and 5%, respectively, after fixation wire tension was released at the end of testing (Table 1).

Table 1—

Mean ± SD peripheral ring diameter (mm) in complete and incomplete ring external skeletal fixator constructs measured after performance of a testing sequence to evaluate construct characteristics during axial loading.

Ring diameter (mm)Wire tension (kg)Ring typePhase of test cycle
PretensioningPreloadingUnder loadPostloadingWire tension released
500Complete76.1 ± 0.376.3 ± 0.576.0 ± 0.576.1 ± 0.676.2 ± 0.5
Incomplete76.4 ± 0.476.3 ± 0.476.2 ± 0.376.4 ± 0.376.4 ± 0.3
30Complete76.0 ± 0.576.1 ± 0.575.9 ± 0.576.2 ± 0.476.2 ± 0.5
Incomplete76.3 ± 0.4a75.8 ± 0.5b75.7 ± 0.3b75.9 ± 0.4b76.4 ± 0.3a
60Complete76.1 ± 0.276.0 ± 0.476.0 ± 0.276.0 ± 0.375.9 ± 0.4
Incomplete76.3 ± 0.5a75.1 ± 0.5b75.0 ± 0.5b75.1 ± 0.5b76.1 ± 0.5a
660Complete91.9 ± 0.391.9 ± 0.491.8 ± 0.491.9 ± 0.391.8 ± 0.3
Incomplete92.5 ± 0.4a92.4 ± 0.3a91.7 ± 0.3b92.4 ± 0.3a92.2 ± 0.3a
30Complete92.2 ± 0.492.2 ± 0.492.3 ± 0.592.2 ± 0.492.0 ± 0.6
Incomplete92.3 ± 0.5a91.3 ± 0.5b91.1 ± 0.2b91.5 ± 0.3b92.2 ± 0.4a
60Complete91.9 ± 0.291.9 ± 0.491.9 ± 0.391.9 ± 0.291.8 ± 0.3
Incomplete92.4 ± 0.6a90.0 ± 0.4b89.6 ± 0.6b90.0 ± 0.6b91.5 ± 0.6c
840Complete110.4 ± 0.4110.5 ± 0.4110.2 ± 0.4110.4 ± 0.3110.3 ± 0.5
Incomplete110.8 ± 0.4a110.8 ± 0.4a109.6 ± 0.5b110.7 ± 0.4a110.8 ± 0.4a
30Complete110.3 ± 0.3110.0 ± 0.2109.8 ± 0.3110.1 ± 0.3110.1 ± 0.3
Incomplete110.8 ± 0.3a109.5 ± 0.3b108.8 ± 0.2c109.5 ± 0.2b110.8 ± 0.2a
60Complete109.9 ± 0.4109.8 ± 0.4109.7 ± 0.3109.8 ± 0.4109.7 ± 0.4
Incomplete111.0 ± 0.2a108.3 ± 0.3b107.9 ± 0.4c108.4 ± 0.4b110.5 ± 0.5a
1180Complete144.3 ± 0.3144.3 ± 0.3144.0 ± 0.2144.2 ± 0.2144.1 ± 0.4
Incomplete144.6 ± 0.5a144.4 ± 0.4a142.0 ± 0.4b144.3 ± 0.4a144.5 ± 0.4a
30Complete144.3 ± 0.4a144.0 ± 0.5b144.0 ± 0.4b144.2 ± 0.4a,b144.2 ± 0.4a,b
Incomplete144.3 ± 0.7a141.8 ± 0.5b140.6 ± 0.6c141.8 ± 0.6b144.4 ± 0.5a
60Complete144.4 ± 0.5144.2 ± 0.5144.2 ± 0.4144.3 ± 0.4144.2 ± 0.6
Incomplete144.8 ± 0.5a140.2 ± 0.4b139.3 ± 0.5c140.2 ± 0.4b144.2 ± 0.6a
 90Complete144.3 ± 0.4a144.1 ± 0.2b143.9 ± 0.4b144.2 ± 0.2a,b144.1 ± 0.3a,b
 Incomplete147.4 ± 2.4a135.6 ± 0.6b134.8 ± 0.8c135.4 ± 0.6b,c140.9 ± 0.6d

Each construct was mounted on a custom fixture for testing; for each construct type, 5 replicates were evaluated (32 groups; total, 160 constructs). Measurements were obtained with the digitizing system before application of tension to fixation wires (pretensioning), after tensioning the fixation wires but prior to construct loading (preloading), during maximal axial load application in the 15th cycle (under load), after unloading for the 15th cycle (postloading), and after releasing the tension on fixation wires. No data were obtained for the 50-, 66-, and 84-mm-diameter incomplete ring constructs when tension on the fixation wires was increased to 90 kg because of ring failure (catastrophic plastic deformation).

Within a construct type (along rows), ring diameters at different cycle phases with different superscript letters are significantly (P ≤ 0.05) different as a result of wire tensioning and construct loading. Absence of superscript letters (along rows) indicates that no significant differences in peripheral ring diameter were detected for that particular construct during the testing sequence.

All load-displacement curves had a characteristic initial exponential increase in stiffness, with the slope of the curves becoming more linear as the applied load increased. This initial phase of exponentially increasing stiffness was more prolonged in the load-displacement curves for incomplete ring constructs than in the curves for complete ring constructs that were of comparable diameter and similarly tensioned. Decreasing ring diameter as well as increasing wire tension resulted in load-displacement curves with a more linear appearance (Figure 3). Significant differences in construct stiffness were noted between similar constructs with incomplete versus complete rings. Axial stiffness increased with sequential tensioning of the fixation wires; the increase was significant in most incomplete ring constructs and some complete ring constructs (Table 2).

Table 2—

Mean ± SD axial secant stiffness (N/mm) in complete and incomplete ring external skeletal fixator constructs measured during the 15th cycle of a testing sequence to evaluate construct characteristics during axial loading.

Ring diameter (mm)Ring typeWire tension (kg)
0306090
50Incomplete190.5 ± 11.7218.8 ± 16.4223.7 ± 32.8NA
Complete205.9 ± 21.2230.5 ± 58.3232.1 ± 26.4NA
66Incomplete108.7 ± 2.2a118.8 ± 15.4a142.4 ± 13.9bNA
Complete153.7 ± 9.5a*153.7 ± 11.8a*176.1 ± 15.9b*NA
84Incomplete78.8 ± 2.5a89.1 ± 1.6b101.0 ± 6.8cNA
Complete123.9 ± 5.1a*124.0 ± 1.1a*135.0 ± 11.9a*NA
118Incomplete45.0 ± 2.1a51.2 ± 1.3a61.3 ± 3.1b68.4 ± 7.7b
Complete88.2 ± 3.0a*85.3 ± 2.0a*87.8 ± 3.9a*89.4 ± 9.0a*

For a given ring diameter at a given tension, the value for complete ring constructs differs significantly from that for the incomplete ring constructs (P ≤ 0.013 for 50-, 66-, and 84-mm-diameter constructs; P ≤ 0.01 for 118-mm-diameter constructs).

Within a construct type of a given ring diameter (along a row), axial secant stiffness values with different superscript letters differ significantly among wire tensions. Absence of superscript letters (along rows) indicates that no significant differences in axial secant stiffness values were detected at the different wire tensions for that particular construct.

NA = Not assessed.

See Table 1 for remainder of key.

Figure 3—
Figure 3—

Construct load-displacement curves from 4 representative complete (A) and 4 representative incomplete (B) 118-mm-diameter ring external skeletal fixator constructs at wire tensions of 0, 30, 60, or 90 kg (applied by use of dynamometric wire tensioners). The gray bar at the bottom of each graph represents the 5 N preload applied to all constructs. Notice that the slope of each load-displacement curve increases more rapidly and obtains a linear configuration at lower axial loads in the complete ring constructs, compared with findings for the incomplete ring constructs. In both complete and incomplete ring constructs, increasing fixation wire tension shifts the load-displacement curve to the left, resulting in less displacement for any given axial force value.

Citation: American Journal of Veterinary Research 73, 12; 10.2460/ajvr.73.12.2021

In both complete and incomplete ring constructs, maximum displacement at an axial load of 375 N decreased as a result of sequential wire tensioning. The decreases in displacement as a result of wire tensioning were significant in 66-mm-diameter complete ring constructs and in 50-, 84-, and 118-mm-diameter incomplete ring constructs. At equivalent fixation wire tensions, complete ring constructs allowed less maximum displacement than did incomplete ring constructs of comparable diameter, although the differences were not always significant (Table 3).

Table 3—

Mean ± SD axial displacement (mm) at an axial load of 375 N in complete and incomplete ring external skeletal fixator constructs measured during the 15th cycle of a testing sequence to evaluate construct characteristics during axial loading.

Ring diameter (mm)Ring typeWire tension (kg)
0306090
50Incomplete2.9 ± 0.3a2.2 ± 0.2a,b2.1 ± 0.4bNA
Complete2.1 ± 0.3a*2.0 ± 0.6a2.0 ± 0.3aNA
66Incomplete4.3 ± 1.0a3.9 ± 0.7a3.0 ± 0.2aNA
Complete3.1 ± 0.2a2.9 ± 0.2a,b2.6 ± 0.2bNA
84Incomplete6.1 ± 1.1a4.8 ± 0.7a,b4.2 ± 0.5bNA
Complete3.9 ± 0.6a*3.4 ± 0.4a*3.1 ± 0.5a*NA
118Incomplete9.9 ± 1.3a7.8 ± 0.6b6.7 ± 0.8b,c5.7 ± 0.6c
Complete5.8 ± 1.3a*5.2 ± 0.1a*5.0 ± 0.6a*4.7 ± 0.6a

Within a construct type of a given ring diameter (along a row), axial displacement values with different superscript letters differ significantly among wire tensions. Absence of superscript letters (along a row) indicates that no significant differences in axial displacement values were detected at the different wire tensions for that particular construct.

NA = Not assessed.

See Tables 1 and 2 for remainder of key.

Discussion

The nonlinear load-displacement behavior observed in both the complete and incomplete ring constructs in the present study was consistent with the results of other studies15,18,19,24,25 that evaluated the axial stiffness characteristics of circular fixators. Axial elasticity is a property inherent to circular fixators with small-diameter wires as fixation elements.15,18,24 This axial elasticity allows for controlled axial micromotion of the secured bone segments, which is purported to provide an environment conducive to bone healing.15,25–28 The precise amount of axial micromotion that optimizes bone healing is not known, although several studies29–31 in sheep and humans have revealed that axial micromotion in the range of 0.5 to 1 mm has beneficial effects on bone healing. The optimal amount of micromotion to promote osseous healing likely varies among individuals and is probably dependent on a number of variables, including the configuration and location of the fracture or osteotomy as well as the patient's species, body weight, and age.30,31

Fixation wire tensioning is performed in circular and hybrid fixator constructs to increase construct stiffness and prevent excessive motion of the secured bone segments during weight bearing.14,15,18 As expected, axial stiffness increased and axial displacement decreased as wire tension was sequentially increased in the complete or incomplete ring constructs in the study reported here. The tension-induced changes in axial stiffness or displacement were not always significant, but incomplete ring constructs consistently had a lower stiffness and allowed greater displacement than did complete ring constructs that were of comparable diameter and under similar fixation wire tension. The lower stiffness and increased displacement of the incomplete ring constructs, compared with analogous complete ring constructs, are the result of deformation of the incomplete rings that occurs during both wire tensioning and subsequent loading.25,32 The decrease in maximum axial displacement associated with increasing wire tension validates the benefit of fixation wire tensioning, even in constructs in which fixation wire tensioning does not increase construct stiffness.

In the present study, a preload of 5 N was used for all constructs. Axial displacement of the acetyl resin rod occurred when this preload was applied and was greater in constructs with larger-diameter rings and lower fixation wire tensions. The preload resulted in a self-tensioning effect on the fixation wires, which mitigated differences in the initial toe region of the load-displacement curves for complete ring constructs of similar diameter under different fixation wire tensions. Similar findings of studies24,25,27,33 evaluating the effects of fixation wire tension on construct stiffness have been reported.

The objective measurements of peripheral ring diameter in the present study revealed that all incomplete rings and 118-mm-diameter complete rings temporarily deformed when the fixation wires were tensioned or the construct was loaded. Ring diameter returned to a value statistically similar to the initial diameter once fixation wire tension was released in all constructs, with the exception of 66-mm-diameter incomplete ring constructs under 60-kg tension and 118-mm-diameter incomplete ring constructs under 90-kg tension. The clinical relevance of the elastic ring deformation in the constructs associated with application of tension to fixation wires and construct loading is unknown.32 We would suggest that permanent ring deformation may be detrimental to construct performance25 and should probably be avoided if possible. Deformation that resulted in catastrophic ring failure, as observed in the 50-, 66-, and 84-mm-diameter incomplete rings when attempts were made to apply 90 kg of tension to fixation wires, is of academic interest but is not clinically relevant, considering that wires are typically only tensioned to 90 kg when 118-mm-diameter rings are used.18

On the basis of the data obtained in the present study, some basic guidelines can be developed regarding appropriate tensioning of wires on incomplete rings. Application of tension to the fixation wires in 50-mm-diameter incomplete ring constructs did not increase construct stiffness. Fifty-millimeter-diameter incomplete ring constructs had greater stiffness and less axial displacement than did any of the constructs with larger diameter rings, irrespective of what tension was applied to the fixation wires. Thus, application of tension to wires attached to 50-mm-diameter incomplete rings is seemingly unnecessary, which is consistent with the recommendation based on findings of biomechanical studies15,18 to apply no tension to fixation wires attached to 50-mm-diameter complete rings. In constructs that used 66-mm-diameter incomplete rings, application of 60 kg of tension increased stiffness but caused permanent deformation of the rings. Based on biomechanical data18,34,35 and clinical experience, wires on 66-mm-diameter complete rings are usually not tensioned or are tensioned to 30 kg. Based on the results of this study and similar to the previous recommendations for 66-mm-diameter complete rings, we advocate that no tension or 30 kg of tension should be applied to wires attached to 66-mm-diameter incomplete rings. Stiffness of 84-mm-diameter incomplete ring constructs was significantly increased by increasing wire tension to 60 kg, and this wire tension did not result in substantial residual ring deformation. It has been recommended that a tension of 60 to 90 kg should be applied to wires attached to 84-mm-diameter complete rings.18,19,21,35 However, catastrophic ring failure occurred when we attempted to apply a tension of 90 kg to the fixation wires in the 84-mm-diameter incomplete ring constructs; thus, we recommend wire tensioning to 60 kg for 84-mm-diameter incomplete rings. Constructs that use 118-mm-diameter incomplete rings could be made considerably stiffer by applying tension of 60 kg to fixation wires. Application of 90 kg of wire tension resulted in permanent deformation of the 118-mm-diameter incomplete rings, and there was no significant increase in axial stiffness when wire tension was increased from 60 to 90 kg. The current recommendation for 118-mm-diameter complete rings is to apply 90-kg tension to fixation wires,18,35 but we would recommend that wire tension on 118-mm-diameter incomplete rings not exceed 60 kg.

The present study had several limitations. We designed our testing fixture so that constructs were constrained at a single fixation hole only; the remainder of the construct was supported by 2 acetyl resin blocks. The acetyl polymer used has a low coefficient of friction and allowed the construct to deform during axial loading. By constraining the ring at a single hole, we replicated connecting elements typical of a type IA hybrid construct (ie, a construct consisting of a uniplanar linear component connected to a circular ring). Ring deformation would likely be restricted to a greater extent if an incomplete ring was used in a traditional circular fixator construct, which would typically have multiple connecting rods positioned around the circumference of the ring. The testing fixture in the present study used base rings that were analogous in diameter to the ring of the construct being tested, which potentially could have influenced the stiffness results. However, we secured threaded rods, which supported the testing fixture ring in close proximity to the acetyl resin blocks, to minimize any variation among constructs. The digitizing system used to measure ring diameter in the present study found an accuracy of 0.2 mm.36 The accuracy of the digitizing system limited our ability to detect very small changes in ring diameter, which might have been apparent had a measuring system with a greater accuracy been used.

Traditional circular fixator constructs typically consist of 3 or 4 rings, preferably with ≥ 2 rings stabilizing each major bone segment. In the present study, we tested only single ring constructs but did so to isolate differences between complete and incomplete rings.15,24,37 The constructs were tested in axial compression only. Further studies evaluating the biomechanical differences between constructs with complete and incomplete rings subjected to bending, and torsional loading should be performed to more fully elucidate the forces affecting fractures and osteotomies stabilized with circular and hybrid fixator constructs. Only 5 replicates of each construct were tested in the present study; this low number of constructs per group may have limited our ability to detect additional significant differences among constructs.

In the present study, a single diameter of acetyl resin rod was used as the bone model, irrespective of ring diameter, to allow us to make discreet comparisons among constructs of different diameters, a precedent established in other studies.15,18,24 Altering the diameter of acetyl resin rod for each ring diameter to approximate the diameter of the bone segment to which each ring diameter would be applied in a clinical setting would likely yield different results.18

The results of the present study indicated that incomplete ring constructs subjected to axial loading have nonlinear load-displacement behavior similar to that of complete ring constructs.15,18 In support of our initial hypotheses, the study revealed that complete ring constructs had greater axial stiffness than did analogous incomplete ring constructs, with this difference being significant for rings ≥ 66 mm in diameter. For both complete and incomplete ring constructs, axial stiffness increased with increasing fixation wire tension and decreased with increasing ring diameter. Compared with complete rings, incomplete rings deformed more readily as a result of fixation wire tensioning and axial loading, although the clinical importance of this ring deformation is unknown. Based on the study findings, we recommend that no wire tension is needed for 50-mm-diameter incomplete ring constructs and that wire tension should not exceed 30 kg in 66-mm-diameter incomplete rings and 60 kg in 84- and 118-mm-diameter incomplete rings. Future studies designed to evaluate the biomechanical properties of incomplete rings when loaded during bending and torsion are warranted.

a.

Stephan J, Bronson DG, Welch RD. Mechanical evaluation of hybrid circular ring fixators for fracture fixation in dogs (abstr), in Proceedings. 25th Annu Conf Vet Orthop Soc 1998;61.

b.

6061 T6 Aluminum, IMEX Veterinary Inc, Longview, Tex.

c.

Delrin acetal polymer, MSC Industrial Supply, Melville, NY.

d.

Bosch 14.4-V drill, Robert Bosch LLC, Farmington Hills, Mich.

e.

Craftsman, KCD IP LLC, Hoffman Estates, Ill.

f.

Smith and Nephew Inc, Memphis, Tenn.

g.

858 Mini Bionix II, MTS Systems Corp, Eden Prairie, Minn.

h.

MicroScribe-3DX, Immersion Corp, San Jose, Calif.

i.

Microsoft Office Excel 2003, Microsoft Corp, Redmond, Wash.

j.

SPSS, version 18, IBM Corp, Somers, NY.

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