### Abstract

Objective - Evaluate the effects of varying ring diameter, wire tension, and wire-divergence angle on the axial stiffness characteristics of circular external skeletal fixator single-ring constructs. Study Design - Biomechanical evaluation using circular fixator components and a Delrin cylinder bone model. Methods - Single ring constructs using two 1.6 mm diameter Kirschner wires to secure a 19 mm Delrin cylinder centered within the ring were examined. Component variables evaluated were ring diameter (50 mm, 66 mm, 84 mm, and 118 mm), wire-divergence angle (30°, 60°, and 90°), and wire tension (0 kg, 30 kg, 60 kg, and 90 kg). A total of 48 constructs were examined. Rings were rigidly mounted on a universal testing system and the cylinder loaded in axial compression (7.4 N/s) to 220 N. Load/displacement curves were analyzed to determine the following: the displacement (mm) that occurred before the slope of each load/displacement curve became linear, the stiffness (N/mm) of the linear portion of each load/deformation curve, and the total displacement (mm) produced at maximal load. Least-squares linear regression was used to model response variables as linear functions of ring diameter, wire divergence angle, and wire tension. Three-way interactions and 2-way interactions among independent component variables were evaluated first in the modeling process and included in a best model if response variables were found to have statistically significant regression coefficients. The regression coefficients and corresponding standard errors and covariances were used to estimate the maximal effect and standard error attributable to wire divergency angle (change from 30° to 90°) and wire tension (change from 0 to 90 kg) for each ring diameter. Results - All load/deformation curves had an initial exponential increase in stiffness, with the slope becoming linear at higher loads. The exponential phase was more pronounced in larger-diameter ring constructs and was mitigated by tensioning the wires. Ring diameter had the greatest influence on displacement that occurred before the curve became linear (semipartial r^{2} [sp-r^{2}] = .89), stiffness (sp-r^{2} = .94), and total displacement (sp-r^{2} = .93). Wire tension exerted a smaller influence on displacement that occurred before the curve became linear (sp-r^{2} = .06), stiffness (sp-r^{2} = .03), and total displacement (sp-r^{2} = .05). Wire divergence angle had a nominal effect on displacement that occurred before the curve became linear (sp-r^{2} = .0001), on stiffness (sp-r^{2} = .004), and on total displacement (sp-r^{2} = .003). Conclusions - Ring diameter had a profound effect on the axial stiffness characteristic of single ring constructs. Tensioning of the fixation wires can improve the axial stiffness characteristics of these constructs, particularly in larger diameter ring constructs, by mitigating the initial exponential phase of the load/deformation curve. Wire divergence angle had only a nominal differential effect on axial stability. Clinical Relevance - Understanding how individual component variables and their interactions influence bone segment stability should help surgeons to optimize interfragmentary strain. Tensioning fixation wires is probably unnecessary in 50 mm diameter ring constructs, but assumes greater importance as ring diameter increases.

Original language | English (US) |
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Pages (from-to) | 386-394 |

Number of pages | 9 |

Journal | Veterinary Surgery |

Volume | 30 |

Issue number | 4 |

DOIs | |

State | Published - Jul 2001 |

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### ASJC Scopus subject areas

- veterinary(all)

### Cite this

*Veterinary Surgery*,

*30*(4), 386-394. https://doi.org/10.1053/jvet.2001.24397

**Axial characteristics of circular external skeletal fixator single ring constructs.** / Lewis, Daniel D.; Bronson, Dwight G.; Cross, Alan R.; Welch, Robert D.; Kubilis, Paul S.

Research output: Contribution to journal › Article

*Veterinary Surgery*, vol. 30, no. 4, pp. 386-394. https://doi.org/10.1053/jvet.2001.24397

}

TY - JOUR

T1 - Axial characteristics of circular external skeletal fixator single ring constructs

AU - Lewis, Daniel D.

AU - Bronson, Dwight G.

AU - Cross, Alan R.

AU - Welch, Robert D.

AU - Kubilis, Paul S.

PY - 2001/7

Y1 - 2001/7

N2 - Objective - Evaluate the effects of varying ring diameter, wire tension, and wire-divergence angle on the axial stiffness characteristics of circular external skeletal fixator single-ring constructs. Study Design - Biomechanical evaluation using circular fixator components and a Delrin cylinder bone model. Methods - Single ring constructs using two 1.6 mm diameter Kirschner wires to secure a 19 mm Delrin cylinder centered within the ring were examined. Component variables evaluated were ring diameter (50 mm, 66 mm, 84 mm, and 118 mm), wire-divergence angle (30°, 60°, and 90°), and wire tension (0 kg, 30 kg, 60 kg, and 90 kg). A total of 48 constructs were examined. Rings were rigidly mounted on a universal testing system and the cylinder loaded in axial compression (7.4 N/s) to 220 N. Load/displacement curves were analyzed to determine the following: the displacement (mm) that occurred before the slope of each load/displacement curve became linear, the stiffness (N/mm) of the linear portion of each load/deformation curve, and the total displacement (mm) produced at maximal load. Least-squares linear regression was used to model response variables as linear functions of ring diameter, wire divergence angle, and wire tension. Three-way interactions and 2-way interactions among independent component variables were evaluated first in the modeling process and included in a best model if response variables were found to have statistically significant regression coefficients. The regression coefficients and corresponding standard errors and covariances were used to estimate the maximal effect and standard error attributable to wire divergency angle (change from 30° to 90°) and wire tension (change from 0 to 90 kg) for each ring diameter. Results - All load/deformation curves had an initial exponential increase in stiffness, with the slope becoming linear at higher loads. The exponential phase was more pronounced in larger-diameter ring constructs and was mitigated by tensioning the wires. Ring diameter had the greatest influence on displacement that occurred before the curve became linear (semipartial r2 [sp-r2] = .89), stiffness (sp-r2 = .94), and total displacement (sp-r2 = .93). Wire tension exerted a smaller influence on displacement that occurred before the curve became linear (sp-r2 = .06), stiffness (sp-r2 = .03), and total displacement (sp-r2 = .05). Wire divergence angle had a nominal effect on displacement that occurred before the curve became linear (sp-r2 = .0001), on stiffness (sp-r2 = .004), and on total displacement (sp-r2 = .003). Conclusions - Ring diameter had a profound effect on the axial stiffness characteristic of single ring constructs. Tensioning of the fixation wires can improve the axial stiffness characteristics of these constructs, particularly in larger diameter ring constructs, by mitigating the initial exponential phase of the load/deformation curve. Wire divergence angle had only a nominal differential effect on axial stability. Clinical Relevance - Understanding how individual component variables and their interactions influence bone segment stability should help surgeons to optimize interfragmentary strain. Tensioning fixation wires is probably unnecessary in 50 mm diameter ring constructs, but assumes greater importance as ring diameter increases.

AB - Objective - Evaluate the effects of varying ring diameter, wire tension, and wire-divergence angle on the axial stiffness characteristics of circular external skeletal fixator single-ring constructs. Study Design - Biomechanical evaluation using circular fixator components and a Delrin cylinder bone model. Methods - Single ring constructs using two 1.6 mm diameter Kirschner wires to secure a 19 mm Delrin cylinder centered within the ring were examined. Component variables evaluated were ring diameter (50 mm, 66 mm, 84 mm, and 118 mm), wire-divergence angle (30°, 60°, and 90°), and wire tension (0 kg, 30 kg, 60 kg, and 90 kg). A total of 48 constructs were examined. Rings were rigidly mounted on a universal testing system and the cylinder loaded in axial compression (7.4 N/s) to 220 N. Load/displacement curves were analyzed to determine the following: the displacement (mm) that occurred before the slope of each load/displacement curve became linear, the stiffness (N/mm) of the linear portion of each load/deformation curve, and the total displacement (mm) produced at maximal load. Least-squares linear regression was used to model response variables as linear functions of ring diameter, wire divergence angle, and wire tension. Three-way interactions and 2-way interactions among independent component variables were evaluated first in the modeling process and included in a best model if response variables were found to have statistically significant regression coefficients. The regression coefficients and corresponding standard errors and covariances were used to estimate the maximal effect and standard error attributable to wire divergency angle (change from 30° to 90°) and wire tension (change from 0 to 90 kg) for each ring diameter. Results - All load/deformation curves had an initial exponential increase in stiffness, with the slope becoming linear at higher loads. The exponential phase was more pronounced in larger-diameter ring constructs and was mitigated by tensioning the wires. Ring diameter had the greatest influence on displacement that occurred before the curve became linear (semipartial r2 [sp-r2] = .89), stiffness (sp-r2 = .94), and total displacement (sp-r2 = .93). Wire tension exerted a smaller influence on displacement that occurred before the curve became linear (sp-r2 = .06), stiffness (sp-r2 = .03), and total displacement (sp-r2 = .05). Wire divergence angle had a nominal effect on displacement that occurred before the curve became linear (sp-r2 = .0001), on stiffness (sp-r2 = .004), and on total displacement (sp-r2 = .003). Conclusions - Ring diameter had a profound effect on the axial stiffness characteristic of single ring constructs. Tensioning of the fixation wires can improve the axial stiffness characteristics of these constructs, particularly in larger diameter ring constructs, by mitigating the initial exponential phase of the load/deformation curve. Wire divergence angle had only a nominal differential effect on axial stability. Clinical Relevance - Understanding how individual component variables and their interactions influence bone segment stability should help surgeons to optimize interfragmentary strain. Tensioning fixation wires is probably unnecessary in 50 mm diameter ring constructs, but assumes greater importance as ring diameter increases.

UR - http://www.scopus.com/inward/record.url?scp=0035403263&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0035403263&partnerID=8YFLogxK

U2 - 10.1053/jvet.2001.24397

DO - 10.1053/jvet.2001.24397

M3 - Article

C2 - 11443601

AN - SCOPUS:0035403263

VL - 30

SP - 386

EP - 394

JO - Veterinary Surgery

JF - Veterinary Surgery

SN - 0161-3499

IS - 4

ER -