© 2016. Published by The Company of Biologists Ltd | Journal of Experimental Biology (2016) 219, 341-353 doi:10.1242/jeb.125799
RESEARCH ARTICLE
Comparative limb bone loading in the humerus and femur of the
tiger salamander: testing the ‘mixed-chain’ hypothesis for skeletal
safety factors
ABSTRACT
Locomotion imposes some of the highest loads upon the skeleton,
and diverse bone designs have evolved to withstand these demands.
Excessive loads can fatally injure organisms; however, bones
have a margin of extra protection, called a ‘safety factor’ (SF), to
accommodate loads that are higher than normal. The extent to which
SFs might vary amongst an animal’s limb bones is unclear. If the
limbs are likened to a chain composed of bones as ‘links’, then similar
SFs might be expected for all limb bones because failure of the
system would be determined by the weakest link, and extra protection
in other links could waste energetic resources. However, Alexander
proposed that a ‘mixed-chain’ of SFs might be found amongst bones
if: (1) their energetic costs differ, (2) some elements face variable
demands, or (3) SFs are generally high. To test whether such
conditions contribute to diversity in limb bone SFs, we compared the
biomechanical properties and locomotor loading of the humerus and
femur in the tiger salamander (Ambystoma tigrinum). Despite high
SFs in salamanders and similar sizes of the humerus and femur that
would suggest similar energetic costs, the humerus had lower bone
stresses, higher mechanical hardness and larger SFs. SFs were
greatest in the anatomical regions where yield stresses were highest
in the humerus and lowest in the femur. Such intraspecific variation
between and within bones may relate to their different biomechanical
functions, providing insight into the emergence of novel locomotor
capabilities during the invasion of land by tetrapods.
KEY WORDS: Biomechanics, Bone stress, Intraspecific variation,
Skeleton, Locomotion, Tetrapod
INTRODUCTION
Bones must regularly withstand applied forces, or loads, imposed
internally by the contraction of muscles and externally by interactions
with the environment. When bones are unable to withstand loads,
injury to the skeleton could lead to inferior predator evasion, inability
to acquire food, or other detriments including death (Biewener, 1993).
Terrestrial locomotion is particularly noteworthy in this context,
because limb bones must accommodate the forces imposed by body
support and propulsion, generating some of the highest demands
upon the skeleton (Biewener, 1993). Despite these demands, bones
can normally withstand loads greater than those they typically
1
National Institute for Mathematical and Biological Synthesis, University of
2
Tennessee, Knoxville, TN 37996, USA. Department of Materials Science and
3
Engineering, Clemson University, Clemson, SC 29634, USA. Department of
4
Bioengineering, Clemson University, Clemson, SC 29634, USA. Department of
Biological Sciences, Clemson University, Clemson, SC 29634, USA.
*Author for correspondence ([email protected])
Received 10 June 2015; Accepted 9 November 2015
experience. This ratio between the typical load sustained and the
maximum load the structure can withstand is called a ‘safety factor’
(SF), and provides a margin of protection to structures for performing
functions with variable demands (Alexander, 1981, 1997, 1998;
Diamond, 2002).
SFs for bones commonly allow protection against loads ranging
from 2 to 10 times greater than ordinary, with variation across taxa
and among the limb bones within a species (Alexander, 1981;
Biewener, 1993; Blob et al., 2014; Currey, 2002; Diamond, 2002;
Sheffield and Blob, 2011). Several factors contribute to interspecific
variation in SFs (Blob and Biewener, 1999; Blob et al., 2014), but
explanations for intraspecific variation are less intuitive. For a single
structure, the SF is expected to be sufficiently high to prevent it from
being compromised by applied loads, but low enough to minimize
the energetic costs to produce such a structure (Alexander, 1997).
Yet, the performance of one structure may influence the
performance of another within a skeleton. Structures are organized
into interconnected systems based on shared biological functions,
and the interdependency of structures within a system can limit the
performance of individual structures. Alexander (1997) described
the integrated nature of structures using a metaphor of chains in
which a biological system represents a ‘chain’ composed of interconnected ‘links’, such as the bones within the leg. Given that a
chain’s overall strength depends upon the strength of its weakest
link, it might be assumed that all components within a system should
have comparable biological performance, thus avoiding wasted
energy in the production of higher-quality components that would
be superseded by the inferior performance of weaker ones
(Alexander, 1997). However, Alexander (1997) proposed several
scenarios under which variation in SFs, or a ‘mixed-chain’, might be
expected within an organism. First, structures that are energetically
costly to move or maintain could have lower SFs. Second, structures
that experience more variable loading regimes than the rest of the
skeleton might have higher SFs, protecting against occasionally
higher loads. Third, for species in which all structures of the skeleton
exhibit high SFs, there might be greater opportunity for variation in
SFs across elements. Diamond (2002) further suggested higher SFs
in structures with higher penalties for failure. For instance, a broken
nasal bone might impair olfaction, but a broken cranium could be
fatal, so greater SFs would be expected for the cranium.
Limited empirical evidence has supported the presence of
‘mixed-chains’ of SFs in the locomotor skeleton. Currey (2002)
found a higher incidence of fracture (implying lower SFs) in the
distal limb bones of racehorses, compared with proximal bones.
Similarly, Blob and Biewener (1999) found lower SFs in the tibia
(distal bone) versus the femur ( proximal bone) in the hindlimbs of
iguanas and alligators. Comparisons between bones of the forelimb
and hindlimb are also appropriate to consider in the context of
‘mixed-chains’ because, although the girdles and vertebrae
341
Journal of Experimental Biology
Sandy M. Kawano1, *, D. Ross Economy2, Marian S. Kennedy2, Delphine Dean3 and Richard W. Blob4
List of symbols and abbreviations
AHLAHM
AP
ASMAC
BW
CBL
CDF
CPIT
CV
DCF
DV
Fm
FACR
FACU
FDC
FE
FPC
GRF
HV
ILFM
ISF
J
LD
LMM
P
PCSA
PIFE
PIT
PTB
RGRF
rc
rm
SC
SF
T
y
Θ
σb
σyieldstress
τ
Ω20
anconaeus humeralis lateralis and anconaeus
humeralis medialis
anteroposterior
anconaeus scapularis medialis and anconaeus
coracoideus
body weight
coracobrachialis longus
caudofemoralis
caudalipuboischiotibialis
coefficient of variation
deep complex of plantar flexors of the carpus
dorsoventral
muscular forces (N)
flexor antebrachii et carpi radialis
flexor antebrachii et carpi ulnaris
flexor digitorum communis
fixed effect
flexor primordialis communis
ground reaction force
Vickers hardness
iliofemoralis
ischioflexorius
polar moment of area (mm4)
latissimus dorsi
linear mixed-effects model
pectoralis
physiological cross-sectional area (mm2)
puboischiofemoralis externus
puboischiotibialis
pubotibialis
moment arm of the GRF relative to the joint (m)
moment arm due to curvature
moment arm of the muscle forces (mm)
supracoracoideus
safety factor
moment of the GRF vector relative to the
long axis of the bone
distance of the centroid from the bone cortex (mm)
angle between the muscle and the long axis of the bone
bending stress (MPa)
tensile yield stress (MPa)
torsional stress (MPa)
analog for coefficient of determination for LMMs
intervene between these limbs, both limbs function to support the
body in quadrupeds, and a break in any leg would impair
locomotion. However, data for such comparisons are more
limited, with a single study finding higher SFs in the humerus
versus the femur of alligators (Blob et al., 2014). With respect to
proposed factors contributing to ‘mixed-chains’ (Alexander, 1997;
Diamond, 2002), the higher humeral SFs of alligators were
attributed to the generally high SFs in the limbs of reptiles and
the smaller size of the humerus that might make high SFs less costly
than for the femur (Blob et al., 2014). However, with such patterns
evaluated for only a single species, their generality is unclear.
Understanding the prevalence of ‘mixed-chains’ of limb bone SFs
could inform how the different functions of forelimbs and hindlimbs
contributed to the invasion of land. Fossil evidence suggests that
terrestrial capabilities occurred in the forelimb before the hindlimb,
and while the forelimbs could have powered propulsion on land in
some of the earliest amphibious stem tetrapods (Nyakatura et al.,
2014; Pierce et al., 2012), hindlimbs were the primary propulsor on
land thereafter for many tetrapods, and may have contributed to
hindlimb-driven aquatic locomotion in sarcopterygian fishes (King
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Journal of Experimental Biology (2016) 219, 341-353 doi:10.1242/jeb.125799
et al., 2011) and some early stem tetrapods (Pierce et al., 2013).
Salamanders are often used as modern locomotor analogs to early
stem tetrapods given their morphological and ecological similarities
(Gao and Shubin, 2001). Thus, salamanders are an intriguing system
to test the ‘mixed-chain’ hypothesis and explore how locomotor
function can leave biomechanical signatures in bones, providing a
foundation for inferring locomotor capabilities of fossil taxa. Femoral
stresses have been evaluated for the tiger salamander Ambystoma
tigrinum during terrestrial locomotion (Sheffield and Blob, 2011), but
corresponding analyses for the humerus have not been performed.
Combined with work on Alligator mississippiensis (Blob et al.,
2014), comparisons of locomotor loading between the humerus and
femur of A. tigrinum would help identify factors that drive structural
and functional diversity within the locomotor system. Additionally,
information regarding form–function relationships in the locomotor
system of a modern analog to early stem tetrapods can facilitate
modeling early stages in the invasion of land.
To more broadly test the prevalence of ‘mixed-chains’ of SFs
within the appendicular system, we compared biomechanical
properties and loading mechanics during terrestrial locomotion
between the humeri and femora of A. tigrinum. Given that its
humerus and femur are subequal in size and might require similar
energy to move, similar SFs might be expected for these bones
(Blob et al., 2014). Alternatively, a ‘mixed-chain’ of SFs might
emerge between the limbs in tiger salamanders for several reasons.
First, different muscle configurations between salamander limbs
(Walthall and Ashley-Ross, 2006) result in fewer muscles that are
active during stance spanning the mid-shaft (and contributing to
stress) in the humerus than in the femur (Fig. 1), potentially
resulting in different sustained loads (the denominator of the SF
calculation) between the limbs. Alexander’s second condition
predicted higher SFs with increased load variation. In another
sprawling quadruped, Tiliqua scincoides intermedia, long axis
rotation was greater in the humerus (78 deg) than in the femur
(53 deg) (Nyakatura et al., 2014), potentially increasing variation in
humeral loads. Increased load variation could also result from the
non-locomotor roles of the humerus, such as burrowing (Semlitsch,
1983). In addition, relatively high SFs for tiger salamander femora
(∼10: Sheffield and Blob, 2011) suggest the potential for variation
in SF across salamander limb bones (Alexander, 1997; Blob et al.,
2014).
We used a biomechanical model to estimate locomotor stresses
(as proxies for loads) and SFs (specifically, ratio of yield stress to
mean peak locomotor stress) for the humeri and femora of tiger
salamanders by integrating measurements of bone geometry,
Vickers hardness (HV), muscle moment arms and anatomy as well
as calculations of ground reaction forces (GRFs) and kinematics.
Through our tests of the ‘mixed-chain’ hypothesis of SFs between
salamander limb bones, we evaluated (1) whether the femur bore
greater stresses because of its greater contribution to acceleration
(Kawano and Blob, 2013) or muscular configuration (Walthall
and Ashley-Ross, 2006), and (2) whether variation in hardness
across a limb bone corresponded with regional differences in
locomotor stresses. Moreover, these data establish a foundation for
considering ‘mixed-chains’ of limb bone SFs in generalized
quadrupeds, in the context of transitions in limb function amongst
stem tetrapods.
MATERIALS AND METHODS
Animals
Bone-loading mechanics were analyzed for adult, male tiger
salamanders (Ambystoma tigrinum Green 1825) used in a
Journal of Experimental Biology
RESEARCH ARTICLE
RESEARCH ARTICLE
Journal of Experimental Biology (2016) 219, 341-353 doi:10.1242/jeb.125799
A
C
O
C
PCH
ILT
EDB
PTB
II
III
PIFI
DS
AbED1
EDB
AbED1
EACR
ECT
I
IMC
I
II
ETT
HAB
III
ILC
IV
IMT
LD
IV
ILFB
PIFE
ELD4
ASM
V
ECTF
PIT
CDF
EDC
ISF
AHL
EDC
EACU
B
D
PCH
FBS
AbED1
SC
II
III
I
EACR
PIT
FPC
IMC
PTB
FACR
ECT
IV
HAB
ETT
I
II
P
III
FBS
ELD4
ISF
CPIT
IV
IMT
ECTF
FMFB
FDC
ISC
AC
FACU
V
CBL
AHM
Adductor
Retractor
Retractor and elbow extensor
Elbow/knee extensor
Elbow/knee and wrist/ankle extensors
Retractor + ankle extensors
Fig. 1. Superficial musculature of the forelimbs and hindlimbs of salamanders that were incorporated into the biomechanical model of limb bone
stress production. Left, forelimb: A, dorsal; B, ventral. Right, hindlimb: C, dorsal; D, ventral. The illustration is based on myology figures of the California
newt, Taricha torosa (Walthall and Ashley-Ross, 2006; permission to re-use from John Wiley and Sons, Inc.). Details of these anatomical structures and their
associated acronyms can be found in Walthall and Ashley-Ross (2006). Muscles active during stance were assumed to contribute to joint moments to counter the
ground reaction force (GRF), but could only contribute to bone stress if they spanned the mid-shaft of either the humerus or the femur. Two deep muscles
[DCF (deep complex of plantar flexors of the carpus in the forelimb) and ILFM (iliofemoralis) in the hindlimb] were modeled as a wrist extensor and a hip retractor,
respectively, but are not illustrated. The top of each figure is oriented in the anterior direction of the animal. Scale bars represent 1 cm.
Table 1. Comparison of anatomical data for the humeri and femora of
Ambystoma tigrinum
Length (mm)
Cross-sectional area (mm2)
rc(AP) (mm)
rc(DV) (mm)
yAP (mm)
yDV (mm)
IAP (mm4)
IDV (mm4)
J* (mm4)
Humeri
Femora
15.244±0.463
1.007±0.201
0.099±0.056
−0.349±0.128
1.406±0.089
1.368±0.062
0.134±0.048
0.191±0.072
0.325±0.118
14.906±0.478
0.879±0.343
0.040±0.031
−0.138±0.103
0.613±0.029
1.000±0.077
0.201±0.107
0.131±0.048
0.333±0.154
Values are means±s.d. (N=5 individuals for each group). All of the listed
variables except ‘length’ were evaluated at the mid-shaft of the bone. Statistical
comparisons were not conducted because of the small sample size.
rc, moment arm due to curvature; y, distance from neutral axis to cortex;
I, second moment of area; J, polar moment of area; AP, anteroposterior
direction; DV, dorsoventral direction. For rc(AP): positive is concave posterior,
negative is concave anterior. For rc(DV): positive is concave ventral, negative is
concave dorsal. *J=IAP+IDV (Lieberman et al., 2004).
and frozen for subsequent anatomical measurements (Tables 1–3).
Experimental and animal care procedures were approved by the
Clemson University Institutional Animal Care and Use Committee
( protocols 2009-071, 2010-066).
Collection of synchronized 3D kinematics and kinetics
Methods for collecting synchronized 3D kinematic and kinetic data
for salamanders have been documented (Kawano and Blob, 2013;
Sheffield and Blob, 2011), but are summarized with additional
details herein. Dorsal and lateral views of animals walking across a
custom-built, multi-axis force platform (K&N Scientific, Guilford,
VT, USA) were recorded at 100 Hz with digitally synchronized
high-speed digital video cameras (Phantom v4.1, Vision Research
Inc., Wayne, NJ, USA). Data on the force production of individual
limbs were recorded at 5000 Hz with LabVIEW (v6.1, National
Instruments, Austin, TX, USA), and calibrated daily. A 4×9 cm
aluminium insert reduced the contact area of the platform,
facilitating data collection from isolated limbs (see fig. 1 of
Kawano and Blob, 2013). The platform was covered with shelf liner
to prevent damage to the salamander’s skin. Data from the force
platform and high-speed videos were synchronized with a 1.5 V
pulse on the force traces that matched the onset of a light pulse on
the lateral video of each trial.
Stance phase kinetics were processed in R (v3.1.2) to generate
mediolateral, anteroposterior and vertical components of the GRF,
and angles of orientation in the mediolateral and anteroposterior
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Journal of Experimental Biology
previous study on GRF production (Kawano and Blob, 2013). Two
trials from this earlier study were excluded herein because they
generated unrealistic estimates of bone stress (e.g. calculations
suggested that limb retractor muscles did not activate during stance).
Following completion of experiments, animals were humanely
killed with buffered tricane methanesulfonate (MS-222; 2 g l−1),
RESEARCH ARTICLE
Journal of Experimental Biology (2016) 219, 341-353 doi:10.1242/jeb.125799
Table 2. Comparison of anatomical data for the forelimb muscles of A. tigrinum
rm (mm)
2
Θ (deg)
Shoulder
Elbow
Wrist
Bone stress
N/A
6±2.236
2.402±0.239
4.060±0.991
N/A
N/A
N/A
N/A
No
Yes
N/A
N/A
4.342±0.589
4.008±1.039
N/A
N/A
N/A
N/A
No
No
2.460±0.652
7.565±1.698
6±2.236
0±0
1.820±0.253
N/A
1.690±0.380
1.942±0.735
N/A
N/A
Yes
Yes
6.719±1.603
3.150±0.836
1.570±0.594
2.694±0.971
N/A
N/A
N/A
N/A
N/A
N/A
N/A
N/A
1.546±0.382
1.356±0.440
1.500±0.401
N/A
1.708±0.726
1.006±0.326
0.948±0.334
0.890±0.293
No
No
No
No
PCSA (mm )
Humeral retractors
LD
CBL
Humeral adductors
P
SC
Elbow extensors
ASMAC*
AHLAHM
Wrist extensors
FDC‡
FACR‡
FACU‡
DCF
4.010±0.632
3.092±0.550
10.105±2.902
11.165±2.781
Values are means±s.d. (N=5).
PCSA, physiological cross-sectional area; Θ, angle between the muscle and the long axis of the bone; rm, moment arm of the muscle forces about the joint. See
List of symbols and abbreviations for muscle names. Rightmost column indicates whether the muscle was assumed to contribute to bone stress.
Statistical comparisons were not conducted because of the small sample size.
*ASMAC also exerts a humeral retractor moment about the shoulder. ‡FDC, FACR and FACU also exert extensor moments at the elbow.
directions. Force magnitudes were normalized to units of body
weight (BW) for each animal to standardize for minor differences in
body size. Data on GRFs were padded at the beginning and end to
avoid edge effects (Smith, 1989), and then filtered with a secondorder, zero-phase, low-pass Butterworth filter using the ‘signal’
package in R. Filter parameters were determined using custom
specifications, with normalization to Nyquist frequency to prevent
aliasing of data (Smith, 1997). Filtered data were then interpolated
to 101 points with a cubic spline using signal::interp1
(method=‘spline’). Standardization to 101 points allowed data to
be analyzed throughout stance at 1% increments (0%=beginning of
stance, 100%=penultimate to swing), facilitating direct comparison
between kinematics and kinetics. Fifty and 48 trials were evaluated
for the forelimb and hindlimb, respectively, with about 10 trials
from each of five individuals for each limb. Comparisons were
performed throughout stance, when GRFs were greatest ( peak net
GRF; Table 4), and during peak tensile stresses (Table 5).
Kinematics were quantified by digitizing coordinate data from the
dorsal and lateral (right) views of each trial with DLTdv3 in
MATLAB (Hedrick, 2008). High-speed videos were cropped to
encompass stance. Joint and anatomical landmarks digitized in each
video included: (1) the tip of the longest digit of the manus/pes, (2)
the metacarpophalangeal/metatarsophalangeal joint, (3) the wrist/
ankle, (4) the elbow/knee, (5) the shoulder/hip and (6) the two
points along the midline of the body that were dorsal to the pectoral/
pelvic girdles (Fig. S1). Every other frame was digitized for videos
longer than 40 frames. Otherwise, every frame was digitized.
Digitized coordinates were then smoothed with a quintic spline
using pspline::smooth.Pspline. As generalized cross-validation is
unreliable for high-speed videos (Walker, 1998), custom smoothing
parameters were quantified as the variation of each variable
obtained from a single person (S.M.K.) digitizing the first 10
frames of a trial for each limb 3 times. The variance amongst the
three digitizing attempts was used as a separate smoothing
parameter for each anatomical landmark in each perspective
(dorsal and lateral).
Several criteria were used for quality control of data. Trials were
excluded if the animal: (1) turned, stopped, or fell on the platform;
(2) moved diagonally across the platform; (3) did not have its
manus/pes completely on the platform; or (4) had other parts of its
body (e.g. head, throat, belly) in contact with the platform during
stance. If the peak of the net GRF occurred within ∼5% of the
rm (mm)
Femoral retractors
CPIT
CDF
ILFM
Femoral adductors
PIFE
PIT
PTB
Ankle extensors
ISF*
FPC
PCSA (mm2)
Θ (deg)
Hip
Knee
Ankle
Bone stress
3.708±0.473
4.895±0.915
2.243±0.711
N/A
N/A
N/A
4.072±0.834
5.942±1.198
2.668±0.574
N/A
N/A
N/A
N/A
N/A
N/A
No
No
No
7.357±0.713
8.475±0.998
2.219±0.406
11±2.236
9±2.236
10±0
2.124±0.185
2.946±0.530
2.198±0.380
N/A
3.946±0.730
2.308±0.603
N/A
N/A
N/A
Yes
Yes
Yes
1.595±0.447
6.152±1.321
8±2.739
N/A
5.944±0.635
N/A
3.234±0.408
1.064±0.188
2.668±0.466
1.482±0.619
Yes
No
Values are means±s.d. (N=5).
PCSA, physiological cross-sectional area; Θ, angle between the muscle and the long axis of the bone; rm, moment arm of the muscle forces about the joint. See
List of symbols and abbreviations for the muscle names. Rightmost column indicates whether the muscle was assumed to contribute to bone stress.
Statistical comparisons were not conducted because of the small sample size.
*ISF also exerts a hip retractor moment.
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Journal of Experimental Biology
Table 3. Comparisons of anatomical data for the hindlimb muscles of A. tigrinum
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Journal of Experimental Biology (2016) 219, 341-353 doi:10.1242/jeb.125799
Table 4. Comparison of GRF parameters at the time of peak net GRF for A. tigrinum
Forelimb
Time of peak net GRF (%)
Net GRF (BW)
Vertical GRF (BW)
Mediolateral GRF (BW)
Anteroposterior GRF (BW)
Mediolateral angle (deg)
Anteroposterior angle (deg)
Hindlimb
Mean±s.e.m.
FE±s.e.m.
t-value
Mean±s.e.m.
FE±s.e.m.
t-value
Ω20
61.080±1.008
0.457±0.009
0.447±0.009
−0.068±0.004
−0.028±0.008
−8.671±0.531
−3.206±0.996
28.294±1.824
−0.022±0.012
0.007±0.014
0.002±0.007
−0.179±0.012
0.360±0.964
−23.225±1.782
15.511
−1.798
0.475
0.206
−15.394
0.374
−13.036
32.667±1.628
0.479±0.010
0.439±0.013
−0.071±0.007
0.151±0.009
−9.271±0.897
20.033±1.511
32.786±1.854
0.478±0.017
0.440±0.020
−0.069±0.009
0.151±0.008
−9.031±1.171
20.018±1.406
17.688
28.266
21.609
−7.377
18.145
−7.712
14.241
0.732
0.236
0.248
0.179
0.712
0.165
0.646
Values are means±s.e.m. (N=50 and N=48 trials averaged across five individuals for the forelimb and hindlimb, respectively). Timing of the peak net ground
reaction force (GRF) is represented as a percentage into the stance phase of the limb cycle. Peak net GRF values were determined for each individual trial, and
then averaged across all trials to produce the mean and s.e.m. Mean values assume all trials were independent.
Fixed effect (FE) estimates account for non-independence due to sub-sampling of individuals, and values for the humerus indicate differences from the femur
point estimates (e.g. net GRF was about 0.02 BW lower in the humerus than in the femur).
Statistical analyses were based on the model: lmer(y∼Limb+(1|Individual), REML=True). The hindlimb was treated as the intercept, by default.
Ω20 represents a coefficient of determination for linear mixed-effects models (LMMs), whereby values closer to 1.0 indicate stronger concordance between the
data and the LMM.
The t-value represents the test statistic based on a t-distribution, and can be used to estimate the likelihood that the differences between the forelimb and hindlimb
could have been derived by chance through a null hypothesis testing framework (note: t-values are not used in inference herein, but are presented for
convenience).
(Fig. S2). These models incorporated only muscles that are likely to
be active during stance and capable of countering the GRF. Joints
were considered to be in static rotational equilibrium (Biewener,
1983), allowing contributions of muscle forces (Fm) to bone stresses
to be calculated as:
Fm ¼
Calculation of bone stresses
Bone stresses were evaluated using conventions for the anatomical
planes of the limbs for sprawling animals, accounting for their
rotation during stance (Blob and Biewener, 2001; Butcher and Blob,
2008; Sheffield and Blob, 2011). Bone stresses were analyzed at the
mid-shaft, where the most complete records of the biomechanical
loading regime are stored (Sanchez et al., 2010) and loads are
predicted to be greatest (Biewener and Taylor, 1986). A
biomechanical model for calculating locomotor stresses in
A. tigrinum femora was applied to the femur data and modified for
the humerus. Although data on the loading of A. tigrinum femora
during terrestrial locomotion are available (Sheffield and Blob,
2011), new data were collected to directly compare forelimb and
hindlimb function within individuals.
In addition to accounting for bone stresses imposed by the GRF,
mathematical models were used to evaluate the contributions of
limb muscles to bone stress due to moments imposed by the GRF
RGRF GRF
;
rm
ð1Þ
where RGRF is the moment arm of the GRF relative to the joint
(obtained from force platform analyses) and rm is the moment
arm of the muscle needed to counter the GRF moment about the
joint. Muscles that did not span the mid-shaft could contribute to
joint moments countering the GRF, but not to mid-shaft bending
stresses (Blob and Biewener, 2001; Sheffield and Blob, 2011). If
more than one muscle counteracted the GRF to maintain
equilibrium at a joint, a mean moment arm was calculated for
the group weighted by the physiological cross-sectional areas
(PCSAs) of the contributing muscles (Alexander, 1974;
Biewener, 1983; Sheffield and Blob, 2011). Muscular moment
arms were measured during post-mortem dissections, while
stabilizing the limb in a mid-stance orientation. Detailed
descriptions of salamander myology, including origins and
insertions of muscles, are given in Walthall and Ashley-Ross
(2006).
Table 5. GRF parameters at the timing of peak tensile stress for A. tigrinum forelimbs and hindlimbs
Forelimb
Net GRF (BW)
Vertical GRF (BW)
Mediolateral GRF (BW)
Anteroposterior GRF (BW)
Mediolateral angle (deg)
Anteroposterior angle (deg)
Hindlimb
Mean±s.e.m.
FE±s.e.m.
t-value
Mean±s.e.m.
FE±s.e.m.
t-value
Ω20
0.376±0.011
0.369±0.011
−0.052±0.004
0.001±0.007
−8.337±0.628
0.355±1.029
−0.061±0.016
−0.039±0.015
0.028±0.010
−0.115±0.010
2.940±1.349
−16.21±1.495
−3.927
−2.508
2.854
−12.083
2.180
−10.98
0.429±0.013
0.399±0.014
−0.081±0.011
0.116±0.006
−11.667±1.522
16.820±1.065
0.434±0.022
0.404±0.024
−0.081±0.010
0.116±0.008
−11.561±1.714
16.860±1.392
19.919
16.991
−8.019
15.002
−6.744
12.109
0.350
0.339
0.231
0.687
0.280
0.660
Analyses were based on N=42 and N=29 trials averaged across five individuals for the forelimb and hindlimb, respectively, due to data that were removed during
times of overlap with other body structures. FE, fixed effect.
GRF parameters were evaluated at the timing of peak tensile stress, and then averaged across all trials to produce the mean and s.e.m. for each limb.
Statistical analyses were based on the model: lmer(y∼Limb+(1|Individual), REML=True). The hindlimb was treated as the intercept, by default.
The format of statistical analyses follows that described for Table 4. Timings of the peak tensile stress are reported in Table 6.
345
Journal of Experimental Biology
beginning or end of stance, that trial was excluded because the
animal’s body likely contacted the platform while shifting between
its limbs. Acceptable trials had negligible differences in speed
between the limbs (Table 6). For trials selected for analysis, data
were excluded when the limb overlapped with another body part
(e.g. hindlimb during a forelimb trial) to ensure that calculations of
GRFs, moments and bone stresses resulted from isolated limbs.
RESEARCH ARTICLE
Journal of Experimental Biology (2016) 219, 341-353 doi:10.1242/jeb.125799
Table 6. Timings and magnitudes of peak bone stresses for A. tigrinum, with average speed during stance
Humerus
Peak tensile stress (MPa)
Peak compressive stress (MPa)
Peak axial stress (MPa)
Peak shear stress (MPa)
Time of peak tensile stress (%)
Time of peak axial stress (%)
Time of peak compressive stress (%)
Time of peak shear stress (%)
Average speed during stance (cm s−1)
Femur
Mean±s.e.m.
CV
FE±s.e.m.
t-value
Mean±s.e.m.
CV
FE±s.e.m.
t-value
Ω20
7.006±0.282
−7.376±0.292
−0.930±0.063
−3.261±0.171
66.540±1.508
36.540±1.589
65.640±1.446
24.560±1.484
10.347±0.311
0.285
−0.280
−0.476
−0.371
0.160
0.308
0.156
0.427
0.213
−5.531±0.740
10.014±0.911
1.625±0.098
0.412±0.272
44.335±2.716
16.959±1.673
47.586±1.525
−5.433±2.328
−0.177±0.564
−7.471
10.993
16.569
1.510
16.330
10.130
31.210
−2.334
−0.315
12.505±1.051
−17.294±1.305
−2.495±0.161
−3.704±0.360
22.188±2.299
19.458±0.589
17.875±0.689
29.938±1.841
10.613±0.493
0.582
−0.523
−0.448
−0.673
0.718
0.210
0.267
0.426
0.322
12.537±1.939
−17.410±2.370
−2.555±0.349
−3.672±0.720
22.205±2.057
19.581±1.581
18.054±1.753
29.993±1.909
10.524±0.549
6.464
−7.346
−7.322
−5.101
10.790
12.390
10.300
15.710
19.156
0.641
0.712
0.832
0.549
0.739
0.547
0.915
0.091
0.097
Muscles assumed to contribute to humeral joint moments and
stresses included retractors and adductors, and elbow and wrist
extensors (Fig. 1A,B, Table 2). Forelimb muscle activity patterns
were inferred from electromyography (Delvolvé et al., 1997;
Székely et al., 1969), anatomical descriptions of Taricha torosa
(Walthall and Ashley-Ross, 2006) and direct observations of
A. tigrinum. Latissimus dorsi (LD) and coracobrachialis longus
(CBL) were considered to retract the humerus (Fig. 1A,B: red).
The four bundles of the anconaeus complex were inferred to act
as elbow extensors, and subdivided into two functional units
according to their anatomical positions: anconaeus scapularis
medialis and anconaeus coracoideus (ASMAC; Fig. 1A,B:
purple), and anconaeus humeralis lateralis and anconaeus
humeralis medialis (AHLAHM; Fig. 1A,B: blue). ASMAC was
inferred to exert an additional retractor moment due to its moment
arm at the shoulder. Wrist extensors included the flexor digitorum
communis (FDC), flexor antebrachii et carpi radialis (FACR),
flexor antebrachii et carpi ulnaris (FACU) and a deep complex of
carpal plantiflexors (DCF). These muscles were assumed to be
active to oppose the moment of the GRF tending to dorsiflex/
extend the wrist, with FDC, FACU and FACR also spanning the
extensor aspect of the elbow joint (Fig. 1A,B: yellow). Pectoralis
(P) and supracoracoideus (SC) insert on the crista ventralis of the
humerus ( proximal end), and adduct the humerus (Fig. 1A,B:
orange). Of these muscles that exert moments about the joints,
only three (ASMAC, AHLAHM and CBL) spanned the mid-shaft
of the humerus and contributed directly to bone stresses.
The bone loading model for the femur incorporated ankle
extensors, and femoral retractors and adductors (Fig. 1C,D,
Table 3), with these actions inferred from electromyographic
(Ashley-Ross, 1995) and anatomical (Ashley-Ross, 1992) data.
The model was detailed in Sheffield and Blob (2011), but a
brief summary follows. Caudalipuboischiotibalis (CPIT),
caudofemoralis (CDF) and iliofemoralis (ILFM) retract the femur
(Fig. 1C,D: red). Ischioflexorius (ISF) is a multi-articular muscle
that contributes to femoral retraction, and spans distally to extend
the ankle (Fig. 1C,D: magenta). Flexor primordialis communis
(FPC) is situated to extend the ankle and knee (Fig. 1C,D: yellow).
Three muscles [ puboischiotibialis (PIT), pubotibialis (PTB) and
puboischiofemoralis externus (PIFE)] contribute to femoral
adduction and countering the abductor moment of the GRF
(Fig. 1C,D: orange). Muscles that span the mid-shaft and, thus,
could contribute to femoral stress include the ISF, PIT, PTB and
346
PIFE. Knee extensors were not incorporated into the biomechanical
model because the muscles acting to extend the knee in salamanders
(i.e. iliotibialis anterior and posterior) do not have a consistent phase
of activity during stance (Ashley-Ross, 1995).
Thus, differences in muscle configuration and PCSA between
the limbs could contribute to differences in loading between the
humerus and femur. Consequently, these wrist extensors reduce
the force that primary elbow extensor muscles (e.g. anconaeus
complex) must generate to counter the elbow flexor moments
typically imposed by the GRF, without increasing humeral stresses.
In contrast, ankle extensors spanning the knee add to its flexor
moment, rather than its extensor moment, often requiring elevated
(rather than reduced) forces from knee extensors (Sheffield and
Blob, 2011). Also, a lower proportion of forelimb muscles
contribute to bone stresses. Only 30% of the forelimb muscles
considered in the biomechanical model were likely to contribute to
humeral stresses (Table 2), with a cumulative PCSA of about
13 mm2 (25% of the total PCSA for the forelimb). In contrast, 50%
of the hindlimb muscles contributed to femoral stresses (Table 1),
with almost 20 mm2 constituting about 54% of the total hindlimb
PCSA.
Forces acting on the bones were resolved into axial and transverse
components. These were combined with bone length, crosssectional area, second and polar moments of area, and the
bending moment arms imposed by shaft curvature (rc: Biewener,
1983) (Table 1) to calculate axial compressive stress and bending
stresses in the anteroposterior plane (σb,AP, influenced by humeral
retractors) and dorsoventral plane (σb,DV, influenced by elbow
extensors) (Blob and Biewener, 2001). The second moment of area
(reflecting resistance to bending) and polar moment of area
(reflecting resistance to torsion) (Lieberman et al., 2004) were
measured with BoneJ (Doube et al., 2010) in ImageJ64 (v1.47t,
Bethesda, MD, USA). The magnitude of the net bending stress at
the mid-shaft was calculated as the vector sum of stresses in two
planes, allowing the orientation of peak bending stress (relative to
the AP axis) to be calculated as:
ab;net
sb;DV
:
¼ tan
sb;AP
1
ð2Þ
The net neutral axis of bending was determined as perpendicular
to this axis of peak stress (Sheffield et al., 2011).
Journal of Experimental Biology
Values are means±s.e.m. (N=50 and N=48 trials averaged across five individuals for the humerus and femur, respectively). FE, fixed effect; CV, coefficient of
variation (=s.d./mean).
Timings of peak stresses are represented as a percentage into the stance phase of the limb cycle. Peak stress values were determined for each individual trial,
and then averaged across all trials to produce the mean and s.e.m.
Statistical analyses were based on the model: lmer(y∼Bone+(1|Individual), REML=True). The femur was treated as the intercept, by default.
The format of statistical analyses follows that described for Table 4.
Journal of Experimental Biology (2016) 219, 341-353 doi:10.1242/jeb.125799
Torsional stresses (τ) produced by the GRF were calculated as:
y
t ¼ T ð Þ;
J
ð3Þ
where T is calculated as the moment of the GRF vector relative to the
long axis of the bone, y is the distance from the centroid of the bone
to its cortex and J is the polar moment of area (Table 1), calculated
as the sum of the second moments of area in the DV and AP
directions (Lieberman et al., 2004).
Mechanical testing of salamander humeri and femora
Microindentation was used to compare hardness between and
within bones. Right humeri and femora were air-dried, mounted in
Caroplastic (Carolina Biological, Burlington, NC, USA), a noninfiltrating resin, and sectioned transversely at the mid-shaft. Cut
surfaces from the distal half were polished to visualize crosssectional geometries and prepare for microindentation. Mounted
specimens were affixed to a 100×61×2 mm Plexiglas slide with
cyanoacrylate glue, and loaded onto an automated polisher
(EXAKT Technologies, D-4000, Oklahoma City, OK, USA).
Samples were ground with moistened silicon carbide paper of
decreasing grit sizes (P800, P1200, P2500, P4000), for 5 min each.
Agglomerate-free alumina suspensions were used to polish the
specimens to 3.0 μm (Baikalox Type 3.0 CR Alpha), 0.3 μm
(Baikalox Type 0.3 CR Alpha) and finally to 0.05 μm (Buehler
Micropolish II) using a polishing pad (Buehler, Lake Bluff, IL,
USA) for 3 min each. Grinding and oscillation speeds were set at
30 rpm, with a 99.3 g weight applied. Samples were rinsed with
deionized water after each step to remove abrasive particulates, air
dried and then stored at −20°C for less than 72 h. Prior to
indentation, samples were equilibrated to room temperature and
cleaned with methanol. These procedures allowed mechanical
testing of hydrated bones. HV was measured with a Digital Display
Microhardness Tester (Model HVS-1000B, Beijing, China)
configured with a Vickers indenter tip, 0.49 N load and 15 s
dwell time, following procedures for microindentation of
salamander femora (Sheffield and Blob, 2011). About five
indents were performed in the dorsal, ventral, anterior and
posterior regions to test for regional heterogeneity in hardness.
Data were collected away from cavities and edges of the bone to
avoid potential edge effects. No cracks or pile-up were observed.
Sample preparation and testing conditions can influence hardness
measurements, but were likely minimal in this study. HV (1) is
consistent for dwell times up to 30 s (Johnson and Rapoff, 2007),
(2) does not differ between bones that were fresh versus frozen at
−20°C for 3 months and (3) is only 4% lower in bones that are
embedded in infiltrating media rather than non-embedded (Evans
et al., 1990). We used a non-infiltrating plastic to stabilize the bones
and, therefore, expect the difference between mounted and
unmounted bones to be minimal. Hardness values have been up
to ∼50% higher for bones tested dry rather than wet with a
nanoindenter (Hoffler et al., 2005), but only about 9% greater for
bones that were dried for 2 days or longer and tested with a
microindenter (Johnson and Rapoff, 2007). Our use of a noninfiltrating resin kept the bones hydrated. Although the humerus of
individual 1 underwent slightly different testing conditions
(0.981 N load, and no data from the posterior region), available
data still followed general patterns observed between the humeri and
femora (Fig. S3). Also, hardness is consistent for applied loads
between 15 and 300 g (Zysset, 2009), encompassing the 0.49 and
0.981 N used in this study. Thus, our protocol likely had minimal
effect on hardness comparisons.
HV data were entered into a linear regression equation (Wilson
et al., 2009), derived using empirical data from various tetrapod
bones (Hodgskinson et al., 1989), to estimate tensile yield stress
(σyieldstress; MPa):
syieldstress ¼ 32:571 þ 2:702 HV :
ð4Þ
Tensile yield stress has important consequences for organisms
because bone failure tends to occur on the tensile side during
bending (Currey, 2002). Compressive yield stress was also
estimated from HV to evaluate regional heterogeneity of bone
biomechanics. Data on compressive yield stress are not available for
salamanders, so estimates were based on the assumption that tensile
yield stresses are 25% lower than compressive yield stresses
(Currey, 1984). SFs were then calculated as:
SF ¼
syieldstress
mean peak stress
ð5Þ
and ‘worst-case’ scenario estimates (SFWC) as:
SFWC ¼ syieldstress 2 s:d:syieldstress
mean peak stress þ 2 s:d:smean peak stress :
ð6Þ
HV, yield stress and SF were reported separately for each of the
anatomical regions (Table 7, Table S1). Calculations of yield stresses
and SFs were based on dorsal and posterior regions being loaded in
tension, and anterior and ventral regions loaded in compression.
Table 7. Regional heterogeneity of hardness values and safety factors across the limb bone mid-shafts of A. tigrinum
Humerus
HV
HV sample sizes
Mean yield stress (MPa)*
Standard SF
CV of SF
SFWC
Femur
Anterior
Dorsal
Posterior
Ventral
Anterior
Dorsal
Posterior
Ventral
36.3±0.9
23
174.1±3.3
23.6±0.5
0.092
12.3±0.3
41.7±1.5
24
145.2±4.0
20.7±0.6
0.136
8.1±0.3
44.4±1.2
20
152.6±3.2
21.8±0.5
0.095
9.5±0.2
36.6±0.9
22
175.4±3.2
23.8±0.4
0.085
12.6±0.3
33.7±1.2
25
164.8±4.2
9.5±0.2
0.128
5.7±0.2
36.0±1.1
25
129.8±3.0
10.4±0.2
0.117
3.7±0.1
34.6±0.9
25
126.1±2.4
10.1±0.2
0.095
3.8±0.1
31.5±1.1
24
156.7±4.1
9.1±0.2
0.128
5.4±0.2
Values represent means±s.e.m.
HV, Vickers hardness; SFWC, worst case SF.
*Mean yield stress for dorsal and posterior regions (under tension) was calculated using the equation: 32.571+2.702×HV (Wilson et al., 2009). For anterior and
ventral regions (under compression), it was calculated as (tensile yield stress)/0.75.
Statistical analyses were based on the model: lmer(y∼Bone/AnatomicalLocation+(1+AnatomicalLocation|Individual), REML=True).
Statistical comparisons can be found in Table S1.
347
Journal of Experimental Biology
RESEARCH ARTICLE
Journal of Experimental Biology (2016) 219, 341-353 doi:10.1242/jeb.125799
Wrist/ankle angle (deg)
Abduction
20
0
−20
160
50
25
50
75
C
120
100
80
0
160
Protraction
0
−25
−50
25
50
75
50
75
D
100
Extension
120
100
80
60
100
Stance (%)
Forelimb
Flexion
0
25
50
75
100
Hindlimb
Data accessibility
Kinetic, kinematic, bone microhardness, safety factor and stress data
are available from the Dryad Digital Repository: http://dx.doi.org/
10.5061/dryad.7f1j1.
Statistical analyses
Linear mixed-effects models (LMMs), fitted by restricted maximum
likelihood via lme4::lmer, were used to evaluate differences within
response variables, with individual as a random effect for a random
intercepts model (Bates et al., 2014). Random effects represented
subsamples of a population and an additional source of variation
(e.g. individuals within species) whereas fixed effects were factors
to compare (e.g. forelimb versus hindlimb) (Bolker et al., 2009).
Regional heterogeneity of HV within a bone was assessed with
anatomical region as a fixed effect. Otherwise, limb bone was the
fixed effect. Given that HV within an anatomical region may vary
amongst individuals, anatomical region was also added as a random
effect to create a random intercepts and slopes LMM. Pair-wise
comparisons between anatomical regions and bones were fitted with
a contrast matrix in multcomp::glht. P-values provide limited
information regarding the strength of evidence to support
conclusions (Anderson et al., 2001), so LMMs were reported in
terms of effect sizes and an estimate of precision (e.g. Ω20; Xu,
2003), emphasizing the magnitude of the differences and the level
of uncertainty in supporting those differences, respectively.
RESULTS
Kinematic comparison of forelimbs and hindlimbs
Although the limbs have similar kinematic profiles, numerous
differences were identified. At the beginning of stance, the shoulder
and hip are adducted by ∼10–15 deg (Fig. 2A), with the wrist and
ankle showing similar degrees of extension (Fig. 2B). The femur is
more protracted than the humerus until about 80% of stance
348
25
Fig. 2. Comparison of stance phase
kinematic profiles between the
forelimbs and hindlimbs of tiger
salamanders, Ambystoma tigrinum.
Lines and adjacent shading represent
means±s.e.m. pooled across all trials for
the forelimbs (N=50) and hindlimbs
(N=48), with all trials normalized as a
percentage of stance. Negative values are
highlighted in gray, and indicate adduction
in A and retraction in C. Kinematic
comparisons include: (A) abduction/
adduction angle of the limbs,
(B) extension/flexion of the wrists and
ankles, (C) protraction/retraction angle of
the limbs and (D) extension/flexion of the
elbows and knees. See Fig. S1 for
illustration of these kinematic angles.
140
Retraction
0
Flexion
60
100
25
Extension
140
Adduction
0
B
(Fig. 2C), and the elbow is more flexed than the knee until about
90% of stance (Fig. 2D). Flexion and extension of the elbow and
knee follow similar profiles; however, the ankle becomes flexed
almost twice as much as the wrist towards mid-stance. Another
major difference between the limbs is that the femur remains
adducted (e.g. knee closer to the ground than the hip) throughout
stance (Fig. 2A), but the humerus becomes abducted (elbow higher
than shoulder) after about 30% of stance. Additionally, although
both bones begin in a protracted orientation (i.e. distal joint cranial
to the girdle for almost all of stance), the humerus is initially nearly
perpendicular to the long axis of the body (∼0 deg in Fig. 2C) and
retracts at about 10% of stance, whereas retraction of the femur is
more evenly split between protracted and retracted orientations
(Fig. 2C).
Moments produced by the GRF about limb joints
GRF production was generally similar between the forelimbs and
hindlimbs (Table 4, Fig. 3), contributing to similarities in the joint
moments imposed by the GRF (Fig. 4). The GRF imposes a
dorsiflexion ( positive) moment about the wrist and ankle (Fig. 4A)
due to the anterior position of the GRF relative to these joints. To
maintain equilibrium at these joints, wrist and ankle extensors need
to be active to counter the flexor moments imposed by the GRF.
The primarily vertical orientation of the GRF throughout stance
(Fig. 3) tends to impose an abductor moment on the shoulder and
hip, though for the latter this shifts to an adductor moment
approximately 75% into stance (Fig. 4B). The GRF also imposes a
protractor moment about the shoulder and hip, though protraction at
the shoulder is lower in magnitude and occurs later in stance (40%)
than at the hip (10% stance) (Fig. 4C). Finally, torsional moments
imposed by the GRF are similar between the humerus and femur
(Fig. 4D), changing from a tendency to impose anterior axial
rotation to posterior rotation at about 60% of stance.
Journal of Experimental Biology
A
Elbow/knee angle (deg)
Protraction/retraction angle (deg)
Abduction/adduction angle (deg)
RESEARCH ARTICLE
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Journal of Experimental Biology (2016) 219, 341-353 doi:10.1242/jeb.125799
Vertical
Vertical
0.5
0.4
0.4
Vertical (BW)
Net GRF (BW)
0.5
0.3
0.2
0.3
0.2
0.1
0.1
0
0
25
50
75
Mediolateral (BW)
0.1
0
25
50
75
40
−20
−40
Posterior
0
25
50
75
100
−0.025
−0.050
−0.075
Medial
0
25
50
75
0
Anterior
0
75
Lateral
100
20
50
−0.100
Posterior
0
25
0.000
Anterior
−0.1
Anteroposterior angle (deg)
0
Mediolateral angle (deg)
Anteroposterior (BW)
0.2
100
Fig. 3. GRF production by the forelimb
and hindlimb of A. tigrinum throughout
stance. Lines and adjacent shading
represent means±s.e.m. pooled across all
trials for the forelimbs (N=50) and
hindlimbs (N=48), with all trials normalized
as a percentage of stance.
Anteroposterior angles were set relative to
vertical (0 deg), so that negative values
indicate a GRF directed posteriorly.
Mediolateral angles were also relative to
vertical (0 deg), so that negative values
indicate a GRF directly medially. Gray
rectangles distinguish negative values
within each plot. Although the peak values
for the net GRF and the vertical
component were similar (∼0.45 body
weight, BW) and the GRF remained
medial, positive anterior values
throughout stance indicate that the
hindlimbs had a greater acceleratory role
than the forelimbs.
100
Lateral
−10
−20
−30
100
Medial
0
25
50
75
100
Stance (%)
Hindlimb
Despite these similarities, different configurations of the forelimb
and hindlimb influence how the GRF imposes moments on these
limbs (Fig. S2). In salamanders (and most quadrupeds), the elbow
points posteriorly whereas the knee points anteriorly. However, the
GRF is directed essentially vertically for most of stance for both
limbs (Fig. 3). Consequently, the flexor/extensor moment of the
GRF tends to change in different directions for these joints, shifting
from a flexor to an extensor moment for the knee at ∼50% stance,
but vice versa for the elbow at ∼75% stance (Fig. 4E). Also,
analogous moments were greater in the hindlimb than in the
forelimb [e.g. ankle versus wrist in dorsiflexion (Fig. 4A), hip versus
shoulder in anteroposterior and dorsoventral rotations (Fig. 4B,C),
and knee versus elbow in flexion and extension (Fig. 4E)].
Comparison of bone stresses
Lower stresses were estimated for locomotor loads upon the
humerus, though the difference between the bones was less
pronounced for shear (Table 6). Peak tensile and compressive
stresses occurred later in stance for the humerus (∼67%) than the
femur (∼22%) (Table 6, Fig. 5A,B). This pattern corresponds with
the peak net GRF, which also occurred later in stance (∼61%) for the
forelimb than the hindlimb (∼33%) (Table 4, Fig. 3). After
accounting for variation amongst individuals, total external forces
(‘net GRF’) at the time of peak tensile stresses for each bone were
0.061±0.016 BW lower in the humerus, with vertical and
anteroposterior components lower by 0.04 and 0.115 BW,
respectively (Table 5).
The neutral axis of bending for the humerus was directed such
that the posterodorsal region was loaded in tension and the
anteroventral region in compression through the time of
mid-stance to peak loading (Fig. 5C,D). The neutral axis of
bending was aligned closer to the anatomical anteroposterior axis at
peak tensile stress for the femur, placing the dorsal portion in
tension and the ventral portion in compression. Nonetheless, the
anterodorsal cortex of the femur was loaded in tension and the
posteroventral cortex in compression at 50% of stance (Fig. 5C,D).
Biomechanical properties and SFs of the salamander humeri
and femora
Comparisons indicated higher HV for the humerus and regional
heterogeneity within each bone (Table 7, Table S1). The LMM
explained about 68% of the variation in HV based on Ω20 (Xu, 2003),
349
Journal of Experimental Biology
Forelimb
RESEARCH ARTICLE
A
Dorsiflexion
0.00050
0.00025
0
−0.00025
Plantarflexion
Girdle−DV axis (N m)
0
0.006
Girdle−AP axis (N m)
50
100
Abduction
0.004
0.002
0
−0.002
Adduction
0.0015
25
50
75
C
100
Protraction
0.0010
DISCUSSION
Mechanisms underlying elevated SFs in salamander humeri
0.0005
0
−0.0005
−0.0010
Retraction
0
0.0010
25
50
D
75
100
Rotate posteriorly
0.0005
0
−0.0005
−0.0010
−0.0015
Rotate anteriorly
0
0.002
Elbow/knee (N m)
75
B
0
Bone torsion (N m)
25
25
50
75
100
Extension
E
0.001
0
−0.001
−0.002
−0.003
Flexion
0
25
50
75
100
Stance (%)
Forelimb
Hindlimb
Fig. 4. Comparison of moments exerted by the GRF for the forelimb and
hindlimb of A. tigrinum. Lines represent mean values obtained from data pooled
across all trials for the forelimbs (N=50) and hindlimbs (N=48), with the shading
depicting the standard error. Negative values are highlighted in gray, and the
directions of rotation indicated by positive and negative values are labeled in the
panels. Girdle refers to the shoulder and hip. AP, anteroposterior; DV,
dorsoventral. See Fig. S2 for illustration of GRF moment arms relative to limb joints.
350
an analog of R2 for LMMs. The greatest magnitude of HV, and thus
estimated yield stresses, at these mid-shafts was generally in the
posterodorsal region (Table 7), corresponding with the typical
location of tensile loads about the neutral axis of bending (Fig. 5B).
Femoral SFs ranged from ∼9 to 10 (Table 7), corresponding with
the published estimate of 10.5 (Sheffield and Blob, 2011). However,
humeral SFs were almost twice those of the femur, ranging from
∼20 to 24. The greatest SFs at femoral mid-shafts were in the dorsal
cortex, where HV was greatest, yet SFs at humeral mid-shafts were
greater in the anteroventral region, where HV was lower (Table 7).
This difference was largely due to peak bone stresses that were about
two times lower in the humerus (Table 6), although higher yield
stresses in the humerus also contributed to SF differences from the
femur (Table 7). The worst-case scenario SF (SFwc) was about two
times lower than standard SF calculations for both bones, but still
indicated ample margins of safety (∼8–13 for the humerus, ∼3–6
for the femur; Table 7). Biomechanical differences along the
dorsoventral and anteroposterior planes of the bones were also
reflected in their structural response to bending, as evidenced by
second moments of area that were greater in the dorsoventral plane
for the humerus and the anteroposterior plane for the femur
(Table 1).
Humeri have higher SFs (∼22) than femora (∼10) in salamanders, a
disparity greater than that reported in alligators (8.4 for the humerus
versus 6.3 for the femur; Blob et al., 2014). The difference between
humeral and femoral SFs relates primarily to differences in yield
strain for alligators (Blob et al., 2014), but from both lower stresses
and structural reinforcement in salamander humeri (Tables 6, 7).
Critical factors that are likely contributing to the relatively lower
stresses in the salamander humerus, compared with the femur,
include the configuration of joints and disposition of muscles.
Because of the range of motion of the arm (Fig. 2) and orientation of
the elbow in A. tigrinum, the GRF only exerts a flexor moment at the
elbow late in stance (Fig. 4E). This reduces the need for elbow
extensors (e.g. anconaeus complex) to counter GRF moments at the
elbow, reducing the stress they place on the humerus (Table 2,
Fig. 1). Humeral stresses are additionally reduced by contributions
of wrist extensors (FDC, FACR, FACU) to the elbow extensor
moment, further reducing the force that elbow extensors spanning
the humeral mid-shaft must exert. Moreover, adductor muscles
contributing to forelimb movement (P and SC) insert proximally on
the humerus, and do not contribute to stresses experienced at midshaft.
Beyond these stress-reducing characteristics of forelimb
musculature in salamanders, HV of the humerus is generally greater
than that of the femur, with different patterns of regional
heterogeneity (Table 7, Table S1) between the bones. The highest
SFs corresponded with areas loaded in tension (dorsal and posterior)
for the femur, but compression (anterior and ventral) for the humerus.
Moreover, the femur has a larger second moment of area in the
anteroposterior direction (IAP), but the humerus has a greater second
moment of area in the dorsoventral direction (IDV; Table 1). These
results suggest that these limb bones show differences in structure and
mechanical response that reduce bending stress in different directions.
Given the extent to which humeral SFs (>20) of salamanders are
greater than those of the femur (∼10), it is difficult to envisage how
the entire magnitude of differences in humeral and femoral SFs of
salamanders could be adaptive. Nonetheless, elevated SFs supported
by greater HV and structural modifications suggest the possibility that,
Journal of Experimental Biology
Wrist/ankle (N m)
0.00075
Journal of Experimental Biology (2016) 219, 341-353 doi:10.1242/jeb.125799
Tensile stresses (MPa)
RESEARCH ARTICLE
15
A
10
Dorsal
5
0
25
50
75
Ventral
100
B
D
−5
−10
Right humerus: peak stress
Right femur: peak stress
Neutral axis
–53 deg
−15
–3 deg
−20
0
50
25
50
75
100
C
Right humerus: 50% through stance
g stance
Right femur: 50% through
25
Axial rotation
Compressive stresses (MPa)
Posterior
Anterior
0
0
Neutral axis angle (deg)
Journal of Experimental Biology (2016) 219, 341-353 doi:10.1242/jeb.125799
0
−25
−50
0
25
50
Stance (%)
Humerus
75
–32 deg
18 deg
100
1 mm
1 mm
Femur
to some extent, the high load-bearing capacity of salamander humeri
may facilitate the multi-functional role of the forelimbs for locomotor
and non-locomotor behaviors (e.g. burrowing).
Relevance of ‘mixed chains’ to tetrapod evolution
Comparisons of SFs for the humerus and femur of salamanders
provide an additional empirical example of a ‘mixed-chain’
(Alexander, 1997, 1998) within the locomotor skeleton of
tetrapods. ‘Mixed-chains’ of SFs were identified between
proximal and distal limb bones in horses (Currey, 2002), and
iguanas and alligators (Blob and Biewener, 1999). However, data
herein reinforce additional patterns observed in alligators (Blob
et al., 2014), which demonstrated different SFs between the
proximal bones of the forelimb and the hindlimb. As in alligators
(Blob et al., 2014), the humerus has a higher SF than the femur in
salamanders (Table 7).
Some of the factors proposed by Alexander (1997) that might
contribute to differences in SFs between these bones in alligators do
not apply to salamanders. For example, alligator humeri are smaller
than the femora, which might allow for more economical
maintenance of a high SF (Blob et al., 2014). However, the
humerus and femur are roughly equal in length in salamanders
(Table 1), so Alexander’s first condition for ‘mixed-chains’ likely
does not apply. Alexander’s second condition for ‘mixed-chains’ of
SFs also likely does not apply to salamanders. Similar to alligators,
the salamander limb bone that was exposed to greater variation in
loads (i.e. femur) did not have higher SFs (Table 6), suggesting that
elevation of humeral SFs in salamanders likely was not an adaptive
response for protection against unpredictable high loads.
SFs for salamander limb bones, like those of alligators, are
generally high (>7) compared with those of many taxa, including
mammals and birds (Blob et al., 2014). Thus, differences between
humeral and femoral SFs for salamanders might simply reflect an
increased opportunity for variation in SF across the skeleton
(Alexander’s third condition). Though this reason has been invoked
as a factor contributing to ‘mixed-chains’ in alligators (Blob et al.,
2014), data on the limb configuration, muscle disposition and
regional heterogeneity of HV in tiger salamanders also suggest
mechanistic reasons for high SFs in limb design. Collectively, the
elevated structural and material reinforcement to withstand loads in
the humerus, and anatomical features of the forelimb promoting low
loads, suggest that stochastic variation associated with large SFs
may not completely account for differences in humeral and femoral
SFs observed in salamanders.
In addition to the three conditions promoting ‘mixed-chains’ of
SFs proposed by Alexander (1997), higher SFs may be found in
structures with higher penalties for failure (Diamond, 2002).
Forelimbs and hindlimbs play different roles in legged
351
Journal of Experimental Biology
Fig. 5. Bone stresses are lower in the humerus than in the femur for A. tigrinum, and vary in magnitude across these bones. Maximum (A) tensile
stress and (B) compressive stress, and (C) the angle of the neutral axis of bending from the anatomical AP axis. (D) Orientation of the neutral axis of bending (solid
red line) relative to the AP axis (dashed black line) at peak tensile stress (top) and 50% of stance (bottom), mapped onto cross-sections of the humeral and
femoral mid-shafts. Dark regions of the bone are in compression and light regions are in tension. Compared with the humerus, magnitudes of the peak tensile
(A) and compressive (B) stresses are about 1.7 and 2.3 times greater, respectively, in the femur. At both 50% of stance and the timing of the peak tensile stress
(C,D), the absolute angle of the neutral axis is greater than 30 deg for the humerus but less than 20 deg for the femur.
locomotion (McElroy et al., 2014), which may provide insight into
SF variation in salamander limb bones. Although hindlimbs provide
the primary propulsion in many non-mammalian quadrupeds,
forelimbs still make important contributions to locomotion
(Kawano and Blob, 2013; Nyakatura et al., 2014), and loss of
locomotor function may be more detrimental for the forelimb. Early
work on salamander locomotion (Evans, 1946) demonstrated that
forward propulsion could be achieved solely by the forelimbs but
not the hindlimbs, suggesting that the forelimbs play a more
important locomotor role than passive body support (at least in
terrestrial salamanders such as Taricha and Ambystoma). Moreover,
there do not appear to be ready examples (among non-bipedal
vertebrates) in which the complete loss of the pectoral appendages
occurred while the pelvic appendages remained fully intact: when
vertebrates lose an entire appendage, it is typically the pelvic
appendage (e.g. siren salamanders, amphisbaenids, cetaceans,
sirenian mammals, scincid lizards, and fishes from 100 families;
Gans, 1975; Lande, 1978; Yamanoue et al., 2010). Even when limb
loss is associated with the evolution of fossorial or aquatic life styles
(e.g. amphisbaenians and cetaceans), the forelimbs are typically
retained rather than the hindlimbs (Caldwell, 2003). Limb
reduction, including the loss of digits, can be found in the
forelimb rather than the hindlimb in some taxa (Lerista lizards:
Skinner et al., 2008), but the loss of proximal limb elements or the
entire limb is generally less common for forelimbs. Additional
studies are required to verify whether there are strong mechanical or
selective advantages for forelimb retention in non-bipedal
vertebrates, or whether the conservatism of forelimb retention is
due to developmental constraint. For instance, hindlimbs develop
after forelimbs (Tanaka and Tickle, 2007), and structural reduction
typically occurs in the reverse order from which structures develop
(Lande, 1978), potentially making hindlimbs more susceptible to
loss via developmental truncation.
Further investigations of how loads vary across limb bones could
yield insights into the morphological evolution of limb bones as
vertebrates became terrestrial. The vertebrate musculoskeletal
system shifted from being essentially weightless as a result of
buoyancy underwater to counteracting the effects of gravity on land,
drastically shifting the loading regime imposed upon the locomotor
structures. This shift may have made the evolution of long, tubular
limb bone shafts advantageous compared with their blocky
precursors (Currey, 2002). Microanatomical analyses of a wide
range of tetrapods have differentiated aquatic and terrestrial
lifestyles from limb bone histology (Laurin et al., 2011),
facilitating the inference of the locomotor biomechanics of fossil
taxa such as the Devonian fish Eusthenopteron (Laurin et al., 2007)
and stem stegocephalians (Laurin et al., 2004). Identifying stronger
form–function relationships between limb morphology and
locomotor movements would facilitate efforts to reconstruct the
transition from water to land by tetrapods (Nyakatura et al., 2014;
Standen et al., 2014). For instance, the mechanical properties of
bones from extant taxa were combined with palaeopathology to
theorize the loading conditions that could have fractured the radius
in the early stem tetrapod Ossinodus pueri in the context of walking
on land (Bishop et al., 2015), suggesting the utility of bone loading
data during terrestrial locomotion to address the mechanisms that
influenced how vertebrates became terrestrial. Further application of
data on locomotor stresses from extant taxa could help answer
questions regarding the functional consequences of morphological
changes observed in extinct tetrapodomorphs spanning the
transition from water to land (Hohn-Schulte et al., 2013; Kawano
and Blob, 2013).
352
Journal of Experimental Biology (2016) 219, 341-353 doi:10.1242/jeb.125799
Acknowledgements
We are grateful to Marguerite Butler and Brad Chadwell for advice about smoothing
data, and to Chad McMahan and Linda Jenkins for assistance with sample
preparation. Earlier drafts were improved by suggestions from Margaret Ptacek,
Miriam Ashley-Ross, Andrew Biewener, and two anonymous reviewers. Fig. 1 was
produced using figures generously provided by Miriam Ashley-Ross. We also thank
Rebecca Nelson, William Mitchell, Patrick McGarity, Lauren Pruitt, Megan Gregory
and David Boerma for assistance with video analysis. All experiments were
completed at Clemson University. An earlier draft was submitted by S.M.K. as a
dissertation chapter in partial fulfillment of a doctoral degree at Clemson University.
Competing interests
The authors declare no competing or financial interests.
Author contributions
S.M.K. collected and analyzed the data, D.R.E., M.S.K. and D.D. provided the
mechanical testing equipment, and trained/supervised S.M.K. in mechanical testing.
R.W.B. developed the biomechanical model, provided equipment for quantifying
kinematics and kinetics, and supervised analyses. S.M.K. and R.W.B. led the
conception and design of the research. All authors contributed to writing the
manuscript.
Funding
Funding was provided by the American Society of Ichthyologists and Herpetologists
Gaige and Raney Awards (S.M.K.), Sigma Xi Grants-in-Aid of Research (S.M.K.),
Clemson University (S.M.K.), and National Science Foundation (IOS 0517240 and
IOS 0817794, to R.W.B.). Data analysis and manuscript preparation were completed
while S.M.K. was a Postdoctoral Fellow at the National Institute for Mathematical and
Biological Synthesis (sponsored by National Science Foundation Award DBI1300426 and the University of Tennessee, Knoxville).
Supplementary information
Supplementary information available online at
http://jeb.biologists.org/lookup/suppl/doi:10.1242/jeb.125799/-/DC1
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