Keywords biomechanics - working length - plate–bone distance - stiffness - strain
Introduction
Adequate understanding of the biomechanical requirements for repair of a particular
fracture is necessary to ensure that the chosen repair will remain biomechanically
effective for the time required for fracture healing. Construct stiffness has been
shown to be a determinant of the type and rate of fracture healing, with inadequate
stiffness contributing to delayed healing or nonunion,[1 ] or implant-fatigue failure.[1 ]
[2 ]
[3 ]
[4 ] Implants with lower stiffness will undergo higher stress, which has been shown to
increase the risk of fatigue failure.[5 ]
[6 ]
Plate working length significantly affects the stiffness of a construct; however,
conflicting interpretations of investigations are cited.[1 ]
[2 ]
[3 ]
[4 ]
[7 ] Stoffel and colleagues[4 ] reported that a longer plate working length resulted in less construct stiffness
in a 4.5-mm locking compression plate (LCP) fracture gap model with a 6-mm fracture
gap. However, in a 1-mm gap model, longer working lengths had higher construct stiffness
due to deformation of the construct resulting in transcortical contact and load sharing.
Whether the in vivo increase in stiffness in the 1-mm gap model would be sustainable in a clinical case
due to the resultant high interfragmentary strain produced on transcortical contact
is questionable. Similar discrepancies have been cited regarding the effects of working
length on plate strain; however, recent biomechanical studies[2 ]
[3 ]
[8 ] showed that a short working length had lower plate strain than a long working length.
Plate–bone distance, or standoff , can also affect construct stiffness. Ahmad and colleagues[9 ] reported plastic deformation and failure at lower loads in 4.5-mm LCP constructs
with a 5-mm plate–bone distance compared with a 2-mm plate–bone distance. Other studies
in human orthopaedics have shown that greater plate–bone distance results in less
construct stiffness in both axial compression and torsion.[4 ]
[10 ] No published studies have evaluated the effect of plate–bone distance in small locking
constructs such as those used in small animal orthopaedics. Furthermore, no studies
have examined the interaction between working length and plate–bone distance in locking
constructs, nor plate strain associated with varying plate–bone distance.
The objectives of this study were to determine the effect of three working lengths
in combination with three plate–bone distances on 2.0-mm locking construct stiffness
and strain in a diaphyseal fracture gap model. It was hypothesized that a long working
length or greater plate–bone distance would result in low construct stiffness in compression
bending and torsion, and high plate strain in compression bending. We also hypothesized
that there would be an interaction between plate–bone distance and working length
for both stiffness and strain.
Materials and Methods
A mid-diaphyseal fracture gap model was created with polyacetal tubing (Delrin, McMaster-Carr,
Elmhurst, IL, United States) with an outer diameter of 12.7 mm and an inner diameter
of 6.35 mm. Each Delrin fragment was drilled with a computer-controlled mill using
a 1.5-mm drill bit as per AO guidelines for 2.0-mm locking screws.[11 ] Each fragment had all five potential screw holes drilled at a distance of 7 mm between
the center of adjacent holes, with the center of the innermost screw hole positioned
2.5 mm from the fragment-fracture end. Each tube was also predrilled with a 4.0-mm
screw hole, 35 mm from the distal end of the tube. This hole was used for screw fixation
to the loading jig to prevent relative motion during testing. The Delrin tubes were
stabilized with a 12-hole 2.0-mm LCP (DePuy Synthes, Paolo, PA, United States), with
three bicortical locking screws in each fragment in a symmetrical configuration with
a 6-mm fracture gap centered over the sixth combination screw hole ([Fig. 1 ]). To enable a change in plate working length with no change in screw number and
symmetrical screw placement on either side of the fracture gap with a single central
vacant hole spanning the fracture gap, a 12-hole 2-mm LCP was used leaving a single
unused plate hole at one end of the plate.
Fig. 1 Schematic showing working length configurations. A 12-hole 2.0-mm LCP with locking
holes numbered from 1 through 11, with “F” indicating the fracture gap spanning hole
6 and “S” the stacked hole, which was not used in any of the tested constructs.
Construct Configuration
Three different working lengths were generated by applying three different screw configurations.
The screw configurations were symmetrical in each fragment. The screw holes were numbered,
with “1” being the screw hole adjacent to the slipper toe end of the plate and “11”
being the screw hole adjacent to the stacked hole. The stacked hole was not filled
in any construct and the fracture gap spanned the sixth hole in all constructs. All
screws were 2.0-mm locking screws (20-mm length, self-tapping locking screws, DePuy
Synthes) inserted bicortically with a standardized insertion torque of 0.4 Nm (Torque
limiter, 0.4 nM with AO quick coupling, DePuy Synthes), as per AO recommendations
for 2.0-mm locking screws.[11 ] The short working length constructs had screws in plate holes 1, 4, 5 and 7, 8,
11; the medium working length constructs had screws in plate holes 1, 3, 4, and 8,
9, 11; and the long working length constructs had screws in plate holes 1, 2, 3, and
9, 10, 11 ([Fig. 1 ]).
Plate–bone distance was maintained with rigid plastic spacers (tiling spacers, Rubi,
Spain, and Qep Australia) during screw insertion, with 1-, 1.5-, and 3-mm spacers.
Prior to construct assembly, a sample of 20 spacers from each size were selected and
measured with vernier callipers, confirming their reported thickness (1-mm spacers:
mean 1.00 mm [SD ± 0 mm]; 1.5-mm spacers: mean 1.48 mm [SD ± 0.06 mm]; 3-mm spacers:
mean 2.94 mm [SD ± 0.07 mm]). Each construct was assembled by a European College of
Veterinary Surgeons board-certified surgeon (MG).
A sample size of six replicates per construct configuration was used, for a total
of 54 constructs. A sample size of six would detect a minimum effect size of 1.75
(power = 0.8; α = 0.05; error variance = 10%), which was sufficient based on previously reported
data.[8 ]
Biomechanical Testing
Nondestructive Four-Point Bending
The assembled constructs were fixed in a custom loading jig with a 4.0-mm screw in
the predrilled jig-positioning hole to prevent rotation during testing. Each end of
the fully assembled construct was seated 35 mm within the custom loading jig ([Fig. 2 ]). Each construct underwent a four-point compression bending by a materials testing
machine (Instron 5566, Instron, Norwood, MA, United States) with a 100-N load cell
applied parallel to the screw axis and the plate positioned on the compression surface.
A support roller with 290-mm spacing supported the constructs within the loading jig,
and a load roller with 230-mm spacing allowed a uniform load and bending moment to
be applied to the construct. Each construct was preloaded to 0.4 N, then ramp loaded
for three cycles under displacement control at 10 mm/min to a force of 40 N, as per
a previously published protocol.[2 ] This load protocol produced a peak bending moment of 0.6 Nm in compression bending
which is within the elastic limits of the constructs based on previous testing. Eighteen
complete sets of implants were used in this study and reconfigured twice to allow
evaluation of 54 different constructs (6 replicates of 9 different configurations).
Randomization of construct testing order was determined by assigning each construct
replicate a number between 1 and 54 and determining the order of testing using a random
number generator.
Fig. 2 Biomechanical testing setup for four-point compression bending (left) and torsion
(right).
Nondestructive Torsion
The constructs were secured in a custom jig, clamped at one end, while the opposite
end of the construct was supported while still allowing free rotation around the construct's
longitudinal axis. The constructs were placed in the jig horizontally and load was
applied to the distal jig screw resulting in a lever arm of 25 mm. Torque was applied
to the construct with each construct loaded to 0.4 N before undergoing three consecutive
cycles of load under displacement control at 10 mm/min, resulting in a torsional displacement
of approximately 11 degrees. All constructs were loaded to a minimum peak load of
20 N.
Stiffness and Strain
All data from the material testing were measured at a rate of 10 Hz. All constructs
underwent three loading cycles in each direction of testing (compression bending and
torsion). As per previously published protocols,[2 ]
[3 ]
[8 ] the load displacement measurements were recorded from the third cycle of testing.
The bending and torsional stiffness for each construct was determined from the slope
of the linear elastic portion of the load displacement curve.
Strain data were collected with three-dimensional digital image correlation (DIC),
which allowed precise measurement of plate strain within a specified field of view.[2 ]
[12 ] Plate strain was measured during compression bending only. A speckle pattern on
the surface of the plates enabled correlation-based displacement measurements to calculate
strain.
The speckle pattern for strain analysis was applied using a hand speckled technique.
All plates were sprayed with a base coat of matt white spray paint and allowed to
dry before being speckled with a 0.05-mm black pigment marker. As per recommendations
for DIC analysis, the speckles were placed in a random distribution, with a density
of approximately 50%.[13 ] All speckles were applied by the same investigator (AAE) using magnifying loupes.
High-definition recordings were collected with stereoscopic video cameras, with image
capture performed using VIC-Snap software (VIC-Snap software, Correlated Solutions
Inc., Irmo, SC, United States). Given the symmetrical configuration of the constructs,
the field of view for image correlation was focused on the plate spanning holes 1
to 6 including the fracture gap. The region of interest for strain evaluation was
defined as the region of the plate over the fracture gap. The von Mises strain for
each construct was plotted against load (N), and a line of best fit was used to calculate
the strain at a load of 40 N.
Statistical Analysis
Data were evaluated for normality with a Shapiro–Wilk test and non-normal data transformed.
Data were summarized as mean, SD, and 95% confidence interval of the mean. Stiffness
and strain data were analyzed using a two-way ANOVA, including the fixed effects of
working length and plate–bone distance, and the interaction. Post hoc pairwise comparisons were made when there were significant model effects, tested
against a Tukey adjusted p ≤ 0.05.
Results
Stiffness
In four-point compression bending, there was a significant interaction between working
length and plate–bone distance (p = 0.04). All short working length constructs, regardless of plate–bone distance,
were stiffer than all medium working length constructs, which in turn were stiffer
than all long working length constructs. The plate–bone distance did not affect construct
stiffness in bending within any working length ([Table 1 ]).
Table 1
Mean stiffness (N/mm) across working lengths and plate–bone distance in compression
bending
Short working length
Medium working length
Long working length
Plate–bone distance of 1 mm
33.751a
(95% CI: 31.48–36.02)
25.170b
(95% CI: 23.66–26.68)
19.651c
(95% CI: 18.7–20.61)
Plate–bone distance of 1.5 mm
36.323a
(95% CI: 33.27–39.38)
24.793b
(95% CI: 23.6–25.98)
18.626c
(95% CI: 17.8–19.45)
Plate–bone distance of 3 mm
33.726a
(95% CI: 31.19–36.27)
25.532b
(95% CI: 24.33–26.74)
18.209c
(95% CI: 17.34–19.08)
Abbreviation: CI, confidence interval.
Note: Means with the same superscript are not significantly different (p ≤ 0.05).
In torsion, there was no significant interaction between working length and plate–bone
distance (p = 0.216) but significant main effects of working length (p < 0.0001) and plate–bone distance (p < 0.0001; [Table 2 ]). All short working length constructs, regardless of plate–bone distance, were stiffer
than all medium working length constructs, which in turn were stiffer than all long
working length construct, except for the medium working length with the 3-mm plate–bone
distance, which was not different from the long working length with the 1 mm plate–bone
distance. The effect of plate–bone distance was evident within the short and long
working lengths, with stiffness significantly lower for the 3-mm plate–bone distance
than the 1.5- and 1.0-mm plate–bone distance (p < 0.0001 and 0.047 for short and long working length, respectively). There was no
discernible effect of plate–bone distance on stiffness for the medium working length.
A post hoc sample size calculation for the medium working length group determined a sample size
of nine replicates would be required to detect significance, suggestive of type II
error.
Table 2
Mean stiffness (N/degree) across working lengths and plate–bone distance in torsion
Short working length
Medium working length
Long working length
Plate–bone distance of 1 mm
1.487a
(95% CI: 1.41–1.566)
1.15c
(95% CI: 1.072–1.228)
0.966de
(95% CI: 0.881–1.053)
Plate–bone distance of 1.5 mm
1.445a
(95% CI: 1.39–1.492)
1.128c
(95% CI: 1.067–1.189)
0.913ef
(95% C.I 0.845–0.979)
Plate–bone distance of 3 mm
1.287b
(95% CI: 1.214–1.361)
1.062cd
(95% CI: 1.028–1.096)
0.844f
(95% CI: 0.774–0.914)
Abbreviation: CI, confidence interval.
Note: Means with the same superscript are not significantly different (p ≤ 0.05).
Strain
There was a significant interaction effect for working length and plate–bone distance
(p < 0.0001) on plate strain in compression bending ([Table 3 ]). Within the short and medium working lengths, there was no significant difference
in plate strain over the fracture gap for different plate–bone distances (p = 0.71–0.91 and 0.30–0.75, respectively). Within the long working length group, there
was significantly lower plate strain for the 1-mm plate–bone distance than both the
1.5-mm (p < 0.0001) and 3-mm (p < 0.0001) plate–bone distances, which were not different from each other (p = 0.73).
Table 3
Mean surface strain on the plate at the level of the fracture gap (mm/mm, reported
×10−
5 ) across working lengths and plate–bone distance in compression bending
Short working length
Medium working length
Long working length
Plate–bone distance of 1 mm
358ad
(95% CI: 324–392)
636bcd
(95% CI: 582–690)
476e
(95% CI: 387–565)
Plate–bone distance of 1.5 mm
344ad
(95% CI: 297–390)
648bcd
(95% CI: 579–716)
711b
(95% CI: 628–794)
Plate–bone distance of 3 mm
354ad
(95% CI: 279–429)
608c
(95% CI: 518–697)
698b
(95% CI: 627–768)
Abbreviation: CI, confidence interval.
Note: Means with the same superscript are not significantly different (p ≤ 0.05).
Across working length groups, the plate strain was significantly lower for the short
working length when compared with the medium working length (p < 0.0001) and the long working length (p < 0.0001–0.0038) constructs, regardless of the plate–bone distance.
Discussion
Based on the findings of our study, we accepted our hypothesis that a long working
length would result in low construct stiffness in compression bending and torsion,
and high plate strain in compression bending. We partially rejected our second hypothesis,
however, with a greater plate–bone distance resulting in lower construct stiffness
in torsion only, but a higher plate strain was observed for greater plate–bone distance
under compression bending. The results of our study support the previously published
literature on plate working length, showing that a long working length has lower construct
stiffness in a fracture gap model compared with a short working length under both
bending and torsional loads.[2 ]
[3 ]
[4 ]
[12 ] Furthermore, our study has demonstrated that plate strain over the fracture gap
was significantly lower in constructs with a short working length. This finding is
consistent with previous published studies.[2 ]
[3 ]
[4 ]
[12 ]
[14 ]
Working length was the major determinant of construct stiffness and strain, with plate–bone
distance only having a detectable effect in torsional loading, where overall stiffness
of the constructs was much less than in bending loads. With each incremental increase
in working length, construct stiffness was lower in both bending and torsion, and
plate strain was higher in bending. Historic controversy around the effect of working
length stems from the results of a 1-mm fracture gap model in a finite element analysis
study,[4 ] where transcortical contact during construct loading produced load sharing. In this
1-mm fracture gap model, a longer working length paradoxically resulted in high stiffness
subsequent to transcortical contact and consequently lower plate strain. Somewhat
surprisingly, this led to the recommendation to increase working length in narrow
fracture gap scenarios to facilitate early transcortical contact. In an in vivo situation, however, repetitive transcortical contact would, in the absence of plastic
deformation of the plate, result in unsustainably high interfragmentary strain of
100%. This would necessitate bone resorption and widening of the fracture gap to attempt
to reduce interfragmentary strain to a level compatible with the production of fibrous
tissue.[6 ]
[15 ]
[16 ] Whether fatigue implant failure would then occur in this situation in vivo would depend on the biologic capacity of the fracture site, the fatigue life of the
implant, and the frequency and magnitude of cyclic loading. Given the results of our
study, and other recently published evidence, it is reasonable to conclude that a
construct with a longer working length would be at greater risk of implant failure
than a construct with a shorter working length.[2 ]
[3 ]
[4 ]
[12 ]
[14 ]
Our study shows no effect of increasing plate–bone distance in bending. Under torsional
loading, however, incremental increases in plate–bone distance in short and long working
length constructs resulted in significantly lower stiffness. For medium working length
constructs, however, increments in plate–bone distance did not significantly affect
stiffness. We consider the absence of difference for medium working length constructs
is most likely the result of type II error.
In our model, any effect of increasing plate–bone distance was not detected in four-point
compression bending. This differs from previous studies[4 ]
[9 ] where a significant reduction in stiffness in axial compression was noted when plate–bone
distance was greater than 2 mm. Both of the cited studies utilized axial compression
for bending, which creates a tensile load on the plate, which differs from the compression
bending induced in our study. Many previous biomechanical studies evaluate tension
bending and/or axial compression, as these are considered to mimic physiologic forces
on a fracture repair due to the eccentric position of bone plates relative to the
mechanical axis of long bones.[4 ]
[6 ]
[7 ]
[9 ]
[10 ]
[17 ]
[18 ] Loading of fracture gap models in this mode causes the fracture gap to close at
the trans-cortex. In constructs with low stiffness, this can result in contact between
the bone model fragments, causing load sharing between the bone column and implants.[4 ]
[19 ] Furthermore, tension bending can also result in plate–bone contact at the level
of the fracture gap, which reduces the working length defined by screw position to
a working length equivalent to the fracture gap.[19 ]
[20 ] Given that our study aimed to evaluate a true load-bearing construct with working
length as a primary explanatory variable, we elected to test compression bending to
prevent any bone–bone or bone–plate contact during testing, which could confound results.
Both compression and tension bending induce both bending and shear loads on the exposed
shaft of the screw, with a greater plate–bone distance increasing the length of screw
shaft exposed to these loads. Axial compression results in a nonuniform bending moment,
with greater bending moments experienced at the center of the construct. This increases
the shear and bending loads on the screws, which will magnify the effect of increasing
plate–bone distance in axial compression. In the locking plate study by Ahmad and
colleagues,[9 ] implant failure through screw head loosening was identified in three samples, which
for locking constructs is critical for maintaining the strength of the implant. As
a result, this may have resulted in the reduction in construct stiffness noted with
increasing plate–bone distance in axial compression in that study.
A previous study[10 ] evaluated both bending and axial compression using dynamic compression plates, and
identified a greater magnitude of stiffness reduction with increasing plate–bone distance
in axial compression compared with four-point bending. Since dynamic compression plates
were used, these findings cannot be directly applied to the model used in the present
study; however, they highlight the importance of experimental design and load conditions
on construct stiffness. Axial compression and four-point compression bending differ
in the bending moment produced, with a uniform bending moment in four-point compression
bending compared with three-point tension bending produced through axial compression.
The nonuniformity of the bending moment, and the subsequent increase in bending and
shear loads experienced by the screws may explain why construct stiffness has differed
for the same constructs under axial compression versus four-point bending in previous
studies.
While no effect of plate–bone distance on stiffness was detected in compression bending,
a significant effect on stiffness was noted in torsion, with a plate–bone distance
of 3 mm resulting in significantly reduced torsional stiffness. Reduced torsional
stiffness with greater plate–bone distance has previously been demonstrated in larger
locking plates (4.5- and 5.0-mm LCP), with plate–bone distances greater than 2 mm
shown to have significantly decreased torsional stiffness and lower overall loads
to failure.[4 ]
[9 ]
[17 ] The decreased torsional stiffness of implants with a greater plate–bone distance
can be attributed to the increasing length of exposed screw shaft being less resistant
to torsional forces compared with axial forces.[9 ]
[10 ]
Our results demonstrated a significant interaction between working length and plate–bone
distance, with a compounded reduction in stiffness noted for the longest working length
and the greatest plate–bone distance. The same construct configuration was also identified
to have the highest plate strain in compression bending. This interaction was more
evident under torsion testing, where the effect of a long working length could be
modulated by a low plate–bone distance. While not evaluated in the current study,
we would hypothesize that minimizing the plate–bone distance in a long working construct
would also reduce plate strain in torsion. While this is a biomechanical model rather
than a clinical study, these results suggest that when the fracture configuration
forces the use of a longer working length, efforts should be made to minimize the
plate–bone distance to optimize construct stiffness. Knowledge of the interaction
between a long working length and a higher plate–bone distance may necessitate consideration
of augmenting the repair to ensure adequate stiffness.
In our model, working length was the overwhelming determinant of construct stiffness
and plate strain, with plate–bone distance only a significant factor in torsional
loading. A long working length results in lower construct stiffness in compression
bending and in torsion, and results in higher plate strain in compression bending.
A significant interaction between working length and plate–bone distance in torsion
shows that using a small plate–bone distance could modulate the loss of stiffness
and increase in strain produced by a long working length.
