The Effect of Specimen Dimensions on Stress, Strain and Elastic Modulus in Tendon Fascicles
strain [%]
+1Legerlotz, K; 2Riley, G P; 1Screen, H R C
+1 Queen Mary University of London, UK, School of Engineering and Materials Science, 2University of East Anglia, Norwich, UK
K.Legerlotz@qmul.ac.uk
INTRODUCTION:
Force, deformation and stiffness, derived from an ultimate tensile
The high failure strains in shorter specimen length appeared to be a
strength test, provide sample specific information about the mechanical
result of significantly higher strains in the grip section, while the midbehaviour of tendon fascicles. From these values, stress, strain and
section strain was the same in both 20 and 40 mm long samples (Fig. 2).
elastic modulus can be derived in order to provide quantitative data
grip section
25
concerning the material properties, thus characterizing the material
*
mid section
irrespective of differences in sample dimensions. However, two brief
20
mid
grip
articles already published in the 1980s suggest this assumption should be
15
section
section
challenged1,2. The aim of our study was to investigate the applicability of
10
stress and strain to provide material characteristics in tendon and also to
5
characterise the influence of specimen dimensions on stress, strain and
0
elastic modulus in rat tail and bovine extensor tendon fascicles.
20
RESULTS:
Strain to failure was significantly influenced by specimen length. In rat
tail fascicles, failure strain was significantly (p≤0.05) higher at 5,10 and
20 mm lengths compared to 60, 80 and 100 mm lengths (Fig. 1). In
bovine extensors, failure strain also increased with decreasing specimen
length, in this instance being significantly different at all points.
Strain [%]
50
rat tail
bovine extensor
40
30
20
10
0
Stress [MPa]
100
Elastic Modulus [MPa]
120
1600
80
60
40
20
0
1200
800
400
0
0
20
40
60
80
Specimen Length [mm]
Figure 1: Strain, Stress and Elastic Modulus at different specimen lengths
100
40
specimen length [mm]
Figure 2: Mid and grip section strain. * significant difference in grip section
Specimen length did not influence failure stress in rat tail fascicles,
although in bovine fascicles, it was significantly lower in the long 40
mm compared to the 5 & 10 mm specimens. The elastic modulus was
also lower in short samples (statistical differences: bovine- 5 mm
compared to 10, 20 & 40 mm; rat- 5 mm compared to 20-100 mm).
5 mm
60
10 mm
20 mm
50
Strain [%]
METHODS:
Tendon fascicles were dissected from five rat tails and five bovine
foot extensors. Fascicle diameters were determined by a laser
micrometer, and the cross sectional area calculated assuming a circular
shape. Fascicles were then clamped with serrated grips in a material
testing machine and loaded to failure at a strain rate of 1 %/sec. Grip-togrip length was varied and 3-4 fascicles per animal per length were
tested: rat tail fascicles were tested at a length of 5, 10, 20, 40, 60, 80
and 100 mm (103 fascicles in total), bovine extensor fascicles were
tested at 5, 10, 20 and 40 mm (67 fascicles in total). Force and
deformation were continuously recorded at 50Hz and stress, strain and
elastic modulus (in the linear region of the stress strain curve) calculated
from the resulting data. To determine the strain distribution along the
length of the fascicles, markers were placed every 5 mm along the
bovine extensor fascicles (20 & 40 mm length samples). The quasi-static
tests to failure were filmed (Olympus C-740, 15 Hz) and the strain
distribution determined at both the beginning of the test and in the last
few frames prior to failure. The grip section was defined as the distance
of the second highest marker to the upper grip plus the second lowest
marker to the lower grip, and the mid section between the remaining
markers (Fig. 2). A One-Way-ANOVA was used to determine the effect
of specimen length on mechanical parameters. To describe the
relationship between mechanical parameters and cross sectional area,
Pearsons Correlation Coefficient was used. Mid section and grip section
strain were compared by an unpaired T-Test.
40 mm
40
Linear (40 mm)
Linear (20 mm)
30
Linear (10 mm)
Linear (5 mm)
20
10
0
0
0.05
0.1
0.15
0.2
0.25
0.3
2
Cross sectional Area [mm ]
Figure 3: Correlation between strain and cross sectional area in bovine fascicles
The cross sectional area of the fascicles was significantly correlated to
failure strain (Fig. 3), highlighting larger failure strains with increasing
sample area, but only in shorter samples of both rat tail and bovine
extensor. Failure stress and maximum modulus decreased as the sample
cross section increased, but whilst true for all rat fascicle lengths, this
was only the case in the shorter (5 & 10 mm) bovine specimens.
DISCUSSION:
We demonstrated with our study, that specimen length has a major
influence on the failure strain recorded, mainly due to increased local
strain near the gripping point, which has a disproportionately large effect
on short specimens. This confirms the results of Butler et al., who found
larger grip-to-grip strains than mid-region strains by testing whole
tendons3. Stress is less affected by sample length, however as a result of
the increased failure strain, the elastic modulus is significantly reduced
in short specimens. Although the effect of specimen length can be
explained by changes in the tissue structure at the gripping points, how
cross sectional area influences the measurement of mechanical
properties is less obvious. It could be assumed, that collagen fibers in the
centre of a larger fascicle experience less gripping pressure and are
therefore more likely to slip, thereby increasing strain. However, this
effect should be the same for short and long specimens, while our data
show an increased effect on short specimens.
Our findings have implications for the mechanical testing of tendon
tissue: while it is not always possible to control for fascicle length and/or
cross sectional area, these parameters have to be taken into account
when comparing samples of different dimensions. It seems advisable to
use longer specimens whenever possible to reduce the variability within
a given subgroup of a defined fascicle length
REFERENCES:
1. Haut (1986) J Biomech 19(11):951-5; 2. Sanjeevi et al. (1982) J
Biomech 15(3):181-3; 3. Butler et al. (1984) J Biomech 17(8):579-96
Poster No. 1187 • 56th Annual Meeting of the Orthopaedic Research Society