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RESEARCH ARTICLE
Comparative limb bone loading in the humerus and femur of
thetiger salamander: testing the ‘mixed-chain’ hypothesis for
skeletalsafety factorsSandy M. Kawano1,*, D. Ross Economy2, Marian
S. Kennedy2, Delphine Dean3 and Richard W. Blob4
ABSTRACTLocomotion 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,
boneshave a margin of extra protection, called a ‘safety factor’
(SF), toaccommodate loads that are higher than normal. The extent
to whichSFs might vary amongst an animal’s limb bones is unclear.
If thelimbs are likened to a chain composed of bones as ‘links’,
then similarSFs might be expected for all limb bones because
failure of thesystemwould be determined by the weakest link, and
extra protectionin other links could waste energetic resources.
However, Alexanderproposed that a ‘mixed-chain’ of SFs might be
found amongst bonesif: (1) their energetic costs differ, (2) some
elements face variabledemands, or (3) SFs are generally high. To
test whether suchconditions contribute to diversity in limb bone
SFs, we compared thebiomechanical properties and locomotor loading
of the humerus andfemur in the tiger salamander (Ambystoma
tigrinum). Despite highSFs in salamanders and similar sizes of the
humerus and femur thatwould suggest similar energetic costs, the
humerus had lower bonestresses, higher mechanical hardness and
larger SFs. SFs weregreatest in the anatomical regions where yield
stresses were highestin the humerus and lowest in the femur. Such
intraspecific variationbetween and within bones may relate to their
different biomechanicalfunctions, providing insight into the
emergence of novel locomotorcapabilities during the invasion of
land by tetrapods.
KEY WORDS: Biomechanics, Bone stress, Intraspecific
variation,Skeleton, Locomotion, Tetrapod
INTRODUCTIONBones must regularly withstand applied forces, or
loads, imposedinternally by the contraction ofmuscles and
externally by interactionswith the environment. When bones are
unable to withstand loads,injury to the skeleton could lead to
inferior predator evasion, inabilityto 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 bodysupport and propulsion,
generating some of the highest demandsupon the skeleton (Biewener,
1993). Despite these demands, bonescan normally withstand loads
greater than those they typically
experience. This ratio between the typical load sustained and
themaximum load the structure can withstand is called a ‘safety
factor’(SF), and provides a margin of protection to structures for
performingfunctions with variable demands (Alexander, 1981, 1997,
1998;Diamond, 2002).
SFs for bones commonly allow protection against loads
rangingfrom 2 to 10 times greater than ordinary, with variation
across taxaand 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
interspecificvariation in SFs (Blob and Biewener, 1999; Blob et
al., 2014), butexplanations for intraspecific variation are less
intuitive. For a singlestructure, the SF is expected to be
sufficiently high to prevent it frombeing compromised by applied
loads, but low enough to minimizethe 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
organizedinto interconnected systems based on shared biological
functions,and the interdependency of structures within a system can
limit theperformance of individual structures. Alexander (1997)
describedthe integrated nature of structures using a metaphor of
chains inwhich a biological system represents a ‘chain’ composed of
inter-connected ‘links’, such as the bones within the leg. Given
that achain’s overall strength depends upon the strength of its
weakestlink, it might be assumed that all components within a
system shouldhave comparable biological performance, thus avoiding
wastedenergy in the production of higher-quality components that
wouldbe superseded by the inferior performance of weaker
ones(Alexander, 1997). However, Alexander (1997) proposed
severalscenarios under which variation in SFs, or a ‘mixed-chain’,
might beexpected within an organism. First, structures that are
energeticallycostly to move or maintain could have lower SFs.
Second, structuresthat experience more variable loading regimes
than the rest of theskeleton might have higher SFs, protecting
against occasionallyhigher loads. Third, for species in which all
structures of the skeletonexhibit high SFs, there might be greater
opportunity for variation inSFs across elements. Diamond (2002)
further suggested higher SFsin structures with higher penalties for
failure. For instance, a brokennasal bone might impair olfaction,
but a broken cranium could befatal, 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
thedistal 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 ofiguanas and alligators. Comparisons between bones of
the forelimband hindlimb are also appropriate to consider in the
context of‘mixed-chains’ because, although the girdles and
vertebraeReceived 10 June 2015; Accepted 9 November 2015
1National Institute for Mathematical and Biological Synthesis,
University ofTennessee, Knoxville, TN 37996, USA. 2Department of
Materials Science andEngineering, Clemson University, Clemson, SC
29634, USA. 3Department ofBioengineering, Clemson University,
Clemson, SC 29634, USA. 4Department ofBiological Sciences, Clemson
University, Clemson, SC 29634, USA.
*Author for correspondence ([email protected])
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intervene between these limbs, both limbs function to support
thebody in quadrupeds, and a break in any leg would
impairlocomotion. However, data for such comparisons are
morelimited, with a single study finding higher SFs in the
humerusversus the femur of alligators (Blob et al., 2014). With
respect toproposed factors contributing to ‘mixed-chains’
(Alexander, 1997;Diamond, 2002), the higher humeral SFs of
alligators wereattributed to the generally high SFs in the limbs of
reptiles andthe smaller size of the humerus that might make high
SFs less costlythan for the femur (Blob et al., 2014). However,
with such patternsevaluated 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
hindlimbscontributed to the invasion of land. Fossil evidence
suggests thatterrestrial capabilities occurred in the forelimb
before the hindlimb,and while the forelimbs could have powered
propulsion on land insome of the earliest amphibious stem tetrapods
(Nyakatura et al.,2014; Pierce et al., 2012), hindlimbs were the
primary propulsor onland thereafter for many tetrapods, and may
have contributed tohindlimb-driven aquatic locomotion in
sarcopterygian fishes (King
et al., 2011) and some early stem tetrapods (Pierce et al.,
2013).Salamanders are often used as modern locomotor analogs to
earlystem tetrapods given their morphological and ecological
similarities(Gao and Shubin, 2001). Thus, salamanders are an
intriguing systemto test the ‘mixed-chain’ hypothesis and explore
how locomotorfunction can leave biomechanical signatures in bones,
providing afoundation for inferring locomotor capabilities of
fossil taxa. Femoralstresses have been evaluated for the tiger
salamander Ambystomatigrinum during terrestrial locomotion
(Sheffield andBlob, 2011), butcorresponding 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 andfemur of A. tigrinum would help
identify factors that drive structuraland functional diversity
within the locomotor system. Additionally,information regarding
form–function relationships in the locomotorsystem of a modern
analog to early stem tetrapods can facilitatemodeling early stages
in the invasion of land.
To more broadly test the prevalence of ‘mixed-chains’ of
SFswithin the appendicular system, we compared
biomechanicalproperties and loading mechanics during terrestrial
locomotionbetween the humeri and femora of A. tigrinum. Given that
itshumerus and femur are subequal in size and might require
similarenergy to move, similar SFs might be expected for these
bones(Blob et al., 2014). Alternatively, a ‘mixed-chain’ of SFs
mightemerge 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
areactive during stance spanning the mid-shaft (and contributing
tostress) in the humerus than in the femur (Fig. 1),
potentiallyresulting in different sustained loads (the denominator
of the SFcalculation) between the limbs. Alexander’s second
conditionpredicted higher SFs with increased load variation. In
anothersprawling quadruped, Tiliqua scincoides intermedia, long
axisrotation was greater in the humerus (78 deg) than in the
femur(53 deg) (Nyakatura et al., 2014), potentially increasing
variation inhumeral loads. Increased load variation could also
result from thenon-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 variationin 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
tomean peak locomotor stress) for the humeri and femora of
tigersalamanders by integrating measurements of bone
geometry,Vickers hardness (HV), muscle moment arms and anatomy as
wellas calculations of ground reaction forces (GRFs) and
kinematics.Through our tests of the ‘mixed-chain’ hypothesis of SFs
betweensalamander limb bones, we evaluated (1) whether the femur
boregreater stresses because of its greater contribution to
acceleration(Kawano and Blob, 2013) or muscular configuration
(Walthalland Ashley-Ross, 2006), and (2) whether variation in
hardnessacross a limb bone corresponded with regional differences
inlocomotor stresses. Moreover, these data establish a foundation
forconsidering ‘mixed-chains’ of limb bone SFs in
generalizedquadrupeds, in the context of transitions in limb
function amongststem tetrapods.
MATERIALS AND METHODSAnimalsBone-loading mechanics were analyzed
for adult, male tigersalamanders (Ambystoma tigrinum Green 1825)
used in a
List of symbols and abbreviationsAHLAHM anconaeus humeralis
lateralis and anconaeus
humeralis medialisAP anteroposteriorASMAC anconaeus scapularis
medialis and anconaeus
coracoideusBW body weightCBL coracobrachialis longusCDF
caudofemoralisCPIT caudalipuboischiotibialisCV coefficient of
variationDCF deep complex of plantar flexors of the carpusDV
dorsoventralFm muscular forces (N)FACR flexor antebrachii et carpi
radialisFACU flexor antebrachii et carpi ulnarisFDC flexor
digitorum communisFE fixed effectFPC flexor primordialis
communisGRF ground reaction forceHV Vickers hardnessILFM
iliofemoralisISF ischioflexoriusJ polar moment of area (mm4)LD
latissimus dorsiLMM linear mixed-effects modelP pectoralisPCSA
physiological cross-sectional area (mm2)PIFE puboischiofemoralis
externusPIT puboischiotibialisPTB pubotibialisRGRF moment arm of
the GRF relative to the joint (m)rc moment arm due to curvaturerm
moment arm of the muscle forces (mm)SC supracoracoideusSF safety
factorT moment of the GRF vector relative to the
long axis of the boney distance of the centroid from the bone
cortex (mm)Θ angle between the muscle and the long axis of the
boneσb bending stress (MPa)σyieldstress tensile yield stress (MPa)τ
torsional stress (MPa)Ω0
2 analog for coefficient of determination for LMMs
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previous study on GRF production (Kawano and Blob, 2013).
Twotrials from this earlier study were excluded herein because
theygenerated unrealistic estimates of bone stress (e.g.
calculationssuggested that limb retractor muscles did not activate
during stance).Following completion of experiments, animals were
humanelykilled with buffered tricane methanesulfonate (MS-222; 2 g
l−1),
and frozen for subsequent anatomical measurements (Tables
1–3).Experimental and animal care procedures were approved by
theClemson University Institutional Animal Care and Use
Committee(protocols 2009-071, 2010-066).
Collection of synchronized 3D kinematics and kineticsMethods for
collecting synchronized 3D kinematic and kinetic datafor
salamanders have been documented (Kawano and Blob, 2013;Sheffield
and Blob, 2011), but are summarized with additionaldetails herein.
Dorsal and lateral views of animals walking across acustom-built,
multi-axis force platform (K&N Scientific, Guilford,VT, USA)
were recorded at 100 Hz with digitally synchronizedhigh-speed
digital video cameras (Phantom v4.1, Vision ResearchInc., Wayne,
NJ, USA). Data on the force production of individuallimbs were
recorded at 5000 Hz with LabVIEW (v6.1, NationalInstruments,
Austin, TX, USA), and calibrated daily. A 4×9 cmaluminium insert
reduced the contact area of the platform,facilitating data
collection from isolated limbs (see fig. 1 ofKawano and Blob,
2013). The platform was covered with shelf linerto prevent damage
to the salamander’s skin. Data from the forceplatform and
high-speed videos were synchronized with a 1.5 Vpulse on the force
traces that matched the onset of a light pulse onthe lateral video
of each trial.
Stance phase kinetics were processed in R (v3.1.2) to
generatemediolateral, anteroposterior and vertical components of
the GRF,and angles of orientation in the mediolateral and
anteroposterior
I
IIIII
IV
EACR
C
O
PCH
HAB
EDC
EACU
ELD4
AbED1EDB
IMC
AHL
ASM
LD
DS
I
II
III
IV
EACR
P
SC
PCH
HAB
CBLAHM
FDC
FACU
FACR
ELD4
AbED1FBS
IMC
AC
I II
III
IV
VILFB
PTB
PIFIILT
CDF
ECTF
ECT
PIT
PIFE
ISF EDC
EDB
ILCIMT
ETT
AbED1
I II
III
IV
V
PIT
ISC
CPIT
PTB
FPC
ISF
FMFB
ECT
ECTF
ETT
FBS
IMT
Retractor Elbow/knee extensorAdductor Elbow/knee and wrist/ankle
extensors Retractor + ankle extensors
A
B
C
D
Retractor and elbow extensor
Fig. 1. Superficial musculature of the forelimbs and hindlimbs
of salamanders that were incorporated into the biomechanical model
of limb bonestress production. Left, forelimb: A, dorsal; B,
ventral. Right, hindlimb: C, dorsal; D, ventral. The illustration
is based on myology figures of the Californianewt, Taricha torosa
(Walthall and Ashley-Ross, 2006; permission to re-use from John
Wiley and Sons, Inc.). Details of these anatomical structures and
theirassociated acronyms can be found inWalthall and Ashley-Ross
(2006). Muscles active during stancewere assumed to contribute to
joint moments to counter theground 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
ofAmbystoma tigrinum
Humeri Femora
Length (mm) 15.244±0.463 14.906±0.478Cross-sectional area (mm2)
1.007±0.201 0.879±0.343rc(AP) (mm) 0.099±0.056 0.040±0.031rc(DV)
(mm) −0.349±0.128 −0.138±0.103yAP (mm) 1.406±0.089 0.613±0.029yDV
(mm) 1.368±0.062 1.000±0.077IAP (mm
4) 0.134±0.048 0.201±0.107IDV (mm
4) 0.191±0.072 0.131±0.048J* (mm4) 0.325±0.118 0.333±0.154
Values are means±s.d. (N=5 individuals for each group). All of
the listedvariables except ‘length’were evaluated at themid-shaft
of the bone. Statisticalcomparisons 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, anteroposteriordirection; DV, dorsoventral
direction. For rc(AP): positive is concave posterior,negative is
concave anterior. For rc(DV): positive is concave ventral, negative
isconcave dorsal. *J=IAP+IDV (Lieberman et al., 2004).
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directions. Force magnitudes were normalized to units of
bodyweight (BW) for each animal to standardize for minor
differences inbody size. Data on GRFs were padded at the beginning
and end toavoid edge effects (Smith, 1989), and then filtered with
a second-order, zero-phase, low-pass Butterworth filter using the
‘signal’package in R. Filter parameters were determined using
customspecifications, with normalization to Nyquist frequency to
preventaliasing of data (Smith, 1997). Filtered data were then
interpolatedto 101 points with a cubic spline using
signal::interp1(method=‘spline’). Standardization to 101 points
allowed data tobe analyzed throughout stance at 1% increments
(0%=beginning ofstance, 100%=penultimate to swing), facilitating
direct comparisonbetween kinematics and kinetics. Fifty and 48
trials were evaluatedfor the forelimb and hindlimb, respectively,
with about 10 trialsfrom each of five individuals for each limb.
Comparisons wereperformed throughout stance, when GRFs were
greatest (peak netGRF; 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
inMATLAB (Hedrick, 2008). High-speed videos were cropped
toencompass 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 twopoints along the midline of the body that were dorsal to
the pectoral/pelvic girdles (Fig. S1). Every other frame was
digitized for videoslonger than 40 frames. Otherwise, every frame
was digitized.Digitized coordinates were then smoothed with a
quintic splineusing pspline::smooth.Pspline. As generalized
cross-validation isunreliable for high-speed videos (Walker, 1998),
custom smoothingparameters were quantified as the variation of each
variableobtained from a single person (S.M.K.) digitizing the first
10frames of a trial for each limb 3 times. The variance amongst
thethree digitizing attempts was used as a separate
smoothingparameter for each anatomical landmark in each
perspective(dorsal and lateral).
Several criteria were used for quality control of data. Trials
wereexcluded if the animal: (1) turned, stopped, or fell on the
platform;(2) moved diagonally across the platform; (3) did not have
itsmanus/pes completely on the platform; or (4) had other parts of
itsbody (e.g. head, throat, belly) in contact with the platform
duringstance. If the peak of the net GRF occurred within ∼5% of
the
Table 2. Comparison of anatomical data for the forelimb muscles
of A. tigrinum
rm (mm)
PCSA (mm2) Θ (deg) Shoulder Elbow Wrist Bone stress
Humeral retractorsLD 4.010±0.632 N/A 2.402±0.239 N/A N/A NoCBL
3.092±0.550 6±2.236 4.060±0.991 N/A N/A Yes
Humeral adductorsP 10.105±2.902 N/A 4.342±0.589 N/A N/A NoSC
11.165±2.781 N/A 4.008±1.039 N/A N/A No
Elbow extensorsASMAC* 2.460±0.652 6±2.236 1.820±0.253
1.690±0.380 N/A YesAHLAHM 7.565±1.698 0±0 N/A 1.942±0.735 N/A
Yes
Wrist extensorsFDC‡ 6.719±1.603 N/A N/A 1.546±0.382 1.708±0.726
NoFACR‡ 3.150±0.836 N/A N/A 1.356±0.440 1.006±0.326 NoFACU‡
1.570±0.594 N/A N/A 1.500±0.401 0.948±0.334 NoDCF 2.694±0.971 N/A
N/A N/A 0.890±0.293 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. SeeList 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.
Table 3. Comparisons of anatomical data for the hindlimb muscles
of A. tigrinum
rm (mm)
PCSA (mm2) Θ (deg) Hip Knee Ankle Bone stress
Femoral retractorsCPIT 3.708±0.473 N/A 4.072±0.834 N/A N/A NoCDF
4.895±0.915 N/A 5.942±1.198 N/A N/A NoILFM 2.243±0.711 N/A
2.668±0.574 N/A N/A No
Femoral adductorsPIFE 7.357±0.713 11±2.236 2.124±0.185 N/A N/A
YesPIT 8.475±0.998 9±2.236 2.946±0.530 3.946±0.730 N/A YesPTB
2.219±0.406 10±0 2.198±0.380 2.308±0.603 N/A Yes
Ankle extensorsISF* 1.595±0.447 8±2.739 5.944±0.635 3.234±0.408
2.668±0.466 YesFPC 6.152±1.321 N/A N/A 1.064±0.188 1.482±0.619
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. SeeList 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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beginning or end of stance, that trial was excluded because
theanimal’s body likely contacted the platform while shifting
betweenits limbs. Acceptable trials had negligible differences in
speedbetween the limbs (Table 6). For trials selected for analysis,
datawere excluded when the limb overlapped with another body
part(e.g. hindlimb during a forelimb trial) to ensure that
calculations ofGRFs, moments and bone stresses resulted from
isolated limbs.
Calculation of bone stressesBone stresses were evaluated using
conventions for the anatomicalplanes of the limbs for sprawling
animals, accounting for theirrotation during stance (Blob and
Biewener, 2001; Butcher and Blob,2008; Sheffield and Blob, 2011).
Bone stresses were analyzed at themid-shaft, where the most
complete records of the biomechanicalloading regime are stored
(Sanchez et al., 2010) and loads arepredicted to be greatest
(Biewener and Taylor, 1986). Abiomechanical model for calculating
locomotor stresses inA. tigrinum femora was applied to the femur
data and modified forthe humerus. Although data on the loading of
A. tigrinum femoraduring terrestrial locomotion are available
(Sheffield and Blob,2011), new data were collected to directly
compare forelimb andhindlimb function within individuals.In
addition to accounting for bone stresses imposed by the GRF,
mathematical models were used to evaluate the contributions
oflimb muscles to bone stress due to moments imposed by the GRF
(Fig. S2). These models incorporated only muscles that are
likely tobe active during stance and capable of countering the GRF.
Jointswere considered to be in static rotational equilibrium
(Biewener,1983), allowing contributions of muscle forces (Fm) to
bone stressesto be calculated as:
Fm ¼ RGRF � GRFrm ; ð1Þ
where RGRF is the moment arm of the GRF relative to the
joint(obtained from force platform analyses) and rm is the
momentarm of the muscle needed to counter the GRF moment about
thejoint. Muscles that did not span the mid-shaft could contribute
tojoint moments countering the GRF, but not to mid-shaft
bendingstresses (Blob and Biewener, 2001; Sheffield and Blob,
2011). Ifmore than one muscle counteracted the GRF to
maintainequilibrium at a joint, a mean moment arm was calculated
forthe group weighted by the physiological cross-sectional
areas(PCSAs) of the contributing muscles (Alexander, 1974;Biewener,
1983; Sheffield and Blob, 2011). Muscular momentarms were measured
during post-mortem dissections, whilestabilizing the limb in a
mid-stance orientation. Detaileddescriptions of salamander myology,
including origins andinsertions of muscles, are given in Walthall
and Ashley-Ross(2006).
Table 4. Comparison of GRF parameters at the time of peak net
GRF for A. tigrinum
Forelimb Hindlimb
Ω02Mean±s.e.m. FE±s.e.m. t-value Mean±s.e.m. FE±s.e.m.
t-value
Time of peak net GRF (%) 61.080±1.008 28.294±1.824 15.511
32.667±1.628 32.786±1.854 17.688 0.732Net GRF (BW) 0.457±0.009
−0.022±0.012 −1.798 0.479±0.010 0.478±0.017 28.266 0.236Vertical
GRF (BW) 0.447±0.009 0.007±0.014 0.475 0.439±0.013 0.440±0.020
21.609 0.248Mediolateral GRF (BW) −0.068±0.004 0.002±0.007 0.206
−0.071±0.007 −0.069±0.009 −7.377 0.179Anteroposterior GRF (BW)
−0.028±0.008 −0.179±0.012 −15.394 0.151±0.009 0.151±0.008 18.145
0.712Mediolateral angle (deg) −8.671±0.531 0.360±0.964 0.374
−9.271±0.897 −9.031±1.171 −7.712 0.165Anteroposterior angle (deg)
−3.206±0.996 −23.225±1.782 −13.036 20.033±1.511 20.018±1.406 14.241
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 groundreaction 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, andthen 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 femurpoint 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.Ω02 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 hindlimbcould have
been derived by chance through a null hypothesis testing framework
(note: t-values are not used in inference herein, but are presented
forconvenience).
Table 5. GRF parameters at the timing of peak tensile stress for
A. tigrinum forelimbs and hindlimbs
Forelimb Hindlimb
Ω02Mean±s.e.m. FE±s.e.m. t-value Mean±s.e.m. FE±s.e.m.
t-value
Net GRF (BW) 0.376±0.011 −0.061±0.016 −3.927 0.429±0.013
0.434±0.022 19.919 0.350Vertical GRF (BW) 0.369±0.011 −0.039±0.015
−2.508 0.399±0.014 0.404±0.024 16.991 0.339Mediolateral GRF (BW)
−0.052±0.004 0.028±0.010 2.854 −0.081±0.011 −0.081±0.010 −8.019
0.231Anteroposterior GRF (BW) 0.001±0.007 −0.115±0.010 −12.083
0.116±0.006 0.116±0.008 15.002 0.687Mediolateral angle (deg)
−8.337±0.628 2.940±1.349 2.180 −11.667±1.522 −11.561±1.714 −6.744
0.280Anteroposterior angle (deg) 0.355±1.029 −16.21±1.495 −10.98
16.820±1.065 16.860±1.392 12.109 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 duringtimes 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.
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Muscles assumed to contribute to humeral joint moments
andstresses included retractors and adductors, and elbow and
wristextensors (Fig. 1A,B, Table 2). Forelimb muscle activity
patternswere inferred from electromyography (Delvolvé et al.,
1997;Székely et al., 1969), anatomical descriptions of Taricha
torosa(Walthall and Ashley-Ross, 2006) and direct observations ofA.
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 actas elbow
extensors, and subdivided into two functional unitsaccording to
their anatomical positions: anconaeus scapularismedialis and
anconaeus coracoideus (ASMAC; Fig. 1A,B:purple), and anconaeus
humeralis lateralis and anconaeushumeralis medialis (AHLAHM; Fig.
1A,B: blue). ASMAC wasinferred to exert an additional retractor
moment due to its momentarm at the shoulder. Wrist extensors
included the flexor digitorumcommunis (FDC), flexor antebrachii et
carpi radialis (FACR),flexor antebrachii et carpi ulnaris (FACU)
and a deep complex ofcarpal plantiflexors (DCF). These muscles were
assumed to beactive to oppose the moment of the GRF tending to
dorsiflex/extend the wrist, with FDC, FACU and FACR also spanning
theextensor aspect of the elbow joint (Fig. 1A,B: yellow).
Pectoralis(P) and supracoracoideus (SC) insert on the crista
ventralis of thehumerus (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-shaftof
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 abrief summary follows.
Caudalipuboischiotibalis (CPIT),caudofemoralis (CDF) and
iliofemoralis (ILFM) retract the femur(Fig. 1C,D: red).
Ischioflexorius (ISF) is a multi-articular musclethat contributes
to femoral retraction, and spans distally to extendthe 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)
andpuboischiofemoralis externus (PIFE)] contribute to
femoraladduction 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
PIFE. Knee extensors were not incorporated into the
biomechanicalmodel because the muscles acting to extend the knee in
salamanders(i.e. iliotibialis anterior and posterior) do not have a
consistent phaseof activity during stance (Ashley-Ross, 1995).
Thus, differences in muscle configuration and PCSA betweenthe
limbs could contribute to differences in loading between thehumerus
and femur. Consequently, these wrist extensors reducethe force that
primary elbow extensor muscles (e.g. anconaeuscomplex) must
generate to counter the elbow flexor momentstypically imposed by
the GRF, without increasing humeral stresses.In contrast, ankle
extensors spanning the knee add to its flexormoment, rather than
its extensor moment, often requiring elevated(rather than reduced)
forces from knee extensors (Sheffield andBlob, 2011). Also, a lower
proportion of forelimb musclescontribute to bone stresses. Only 30%
of the forelimb musclesconsidered in the biomechanical model were
likely to contribute tohumeral stresses (Table 2), with a
cumulative PCSA of about13 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 hindlimbPCSA.
Forces acting on the bones were resolved into axial and
transversecomponents. These were combined with bone length,
cross-sectional area, second and polar moments of area, and
thebending moment arms imposed by shaft curvature (rc:
Biewener,1983) (Table 1) to calculate axial compressive stress and
bendingstresses in the anteroposterior plane (σb,AP, influenced by
humeralretractors) and dorsoventral plane (σb,DV, influenced by
elbowextensors) (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)
weremeasured with BoneJ (Doube et al., 2010) in ImageJ64
(v1.47t,Bethesda, MD, USA). The magnitude of the net bending stress
atthe mid-shaft was calculated as the vector sum of stresses in
twoplanes, allowing the orientation of peak bending stress
(relative tothe AP axis) to be calculated as:
ab;net ¼ tan�1 sb;DVsb;AP
� �: ð2Þ
The net neutral axis of bending was determined as
perpendicularto this axis of peak stress (Sheffield et al.,
2011).
Table 6. Timings and magnitudes of peak bone stresses for A.
tigrinum, with average speed during stance
Humerus Femur
Ω02Mean±s.e.m. CV FE±s.e.m. t-value Mean±s.e.m. CV FE±s.e.m.
t-value
Peak tensile stress (MPa) 7.006±0.282 0.285 −5.531±0.740 −7.471
12.505±1.051 0.582 12.537±1.939 6.464 0.641Peak compressive stress
(MPa) −7.376±0.292 −0.280 10.014±0.911 10.993 −17.294±1.305 −0.523
−17.410±2.370 −7.346 0.712Peak axial stress (MPa) −0.930±0.063
−0.476 1.625±0.098 16.569 −2.495±0.161 −0.448 −2.555±0.349 −7.322
0.832Peak shear stress (MPa) −3.261±0.171 −0.371 0.412±0.272 1.510
−3.704±0.360 −0.673 −3.672±0.720 −5.101 0.549Time of peak tensile
stress (%) 66.540±1.508 0.160 44.335±2.716 16.330 22.188±2.299
0.718 22.205±2.057 10.790 0.739Time of peak axial stress (%)
36.540±1.589 0.308 16.959±1.673 10.130 19.458±0.589 0.210
19.581±1.581 12.390 0.547Time of peak compressive stress (%)
65.640±1.446 0.156 47.586±1.525 31.210 17.875±0.689 0.267
18.054±1.753 10.300 0.915Time of peak shear stress (%) 24.560±1.484
0.427 −5.433±2.328 −2.334 29.938±1.841 0.426 29.993±1.909 15.710
0.091Average speed during stance (cm s−1) 10.347±0.311 0.213
−0.177±0.564 −0.315 10.613±0.493 0.322 10.524±0.549 19.156
0.097
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 ofvariation (=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.
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Torsional stresses (τ) produced by the GRF were calculated
as:
t ¼ TðyJÞ; ð3Þ
where T is calculated as the moment of the GRF vector relative
to thelong axis of the bone, y is the distance from the centroid of
the boneto its cortex and J is the polar moment of area (Table 1),
calculatedas the sum of the second moments of area in the DV and
APdirections (Lieberman et al., 2004).
Mechanical testing of salamander humeri and
femoraMicroindentation was used to compare hardness between
andwithin bones. Right humeri and femora were air-dried, mounted
inCaroplastic (Carolina Biological, Burlington, NC, USA), a
non-infiltrating resin, and sectioned transversely at the
mid-shaft. Cutsurfaces from the distal half were polished to
visualize cross-sectional geometries and prepare for
microindentation. Mountedspecimens were affixed to a 100×61×2 mm
Plexiglas slide withcyanoacrylate glue, and loaded onto an
automated polisher(EXAKT Technologies, D-4000, Oklahoma City, OK,
USA).Samples were ground with moistened silicon carbide paper
ofdecreasing grit sizes (P800, P1200, P2500, P4000), for 5 min
each.Agglomerate-free alumina suspensions were used to polish
thespecimens 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
(BuehlerMicropolish II) using a polishing pad (Buehler, Lake Bluff,
IL,USA) for 3 min each. Grinding and oscillation speeds were set
at30 rpm, with a 99.3 g weight applied. Samples were rinsed
withdeionized water after each step to remove abrasive
particulates, airdried and then stored at −20°C for less than 72 h.
Prior toindentation, samples were equilibrated to room temperature
andcleaned with methanol. These procedures allowed
mechanicaltesting of hydrated bones. HV was measured with a Digital
DisplayMicrohardness Tester (Model HVS-1000B, Beijing,
China)configured with a Vickers indenter tip, 0.49 N load and 15
sdwell time, following procedures for microindentation ofsalamander
femora (Sheffield and Blob, 2011). About fiveindents were performed
in the dorsal, ventral, anterior andposterior regions to test for
regional heterogeneity in hardness.Data were collected away from
cavities and edges of the bone toavoid 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)
isconsistent 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
areembedded in infiltrating media rather than non-embedded (Evanset
al., 1990). We used a non-infiltrating plastic to stabilize the
bonesand, therefore, expect the difference between mounted
andunmounted bones to be minimal. Hardness values have been upto
∼50% higher for bones tested dry rather than wet with ananoindenter
(Hoffler et al., 2005), but only about 9% greater forbones that
were dried for 2 days or longer and tested with amicroindenter
(Johnson and Rapoff, 2007). Our use of a non-infiltrating resin
kept the bones hydrated. Although the humerus ofindividual 1
underwent slightly different testing conditions(0.981 N load, and
no data from the posterior region), availabledata still followed
general patterns observed between the humeri andfemora (Fig. S3).
Also, hardness is consistent for applied loadsbetween 15 and 300 g
(Zysset, 2009), encompassing the 0.49 and0.981 N used in this
study. Thus, our protocol likely had minimaleffect on hardness
comparisons.
HV data were entered into a linear regression equation (Wilsonet
al., 2009), derived using empirical data from various tetrapodbones
(Hodgskinson et al., 1989), to estimate tensile yield
stress(σyieldstress; MPa):
syieldstress ¼ 32:571þ 2:702� HV: ð4Þ
Tensile yield stress has important consequences for
organismsbecause bone failure tends to occur on the tensile side
duringbending (Currey, 2002). Compressive yield stress was
alsoestimated from HV to evaluate regional heterogeneity of
bonebiomechanics. Data on compressive yield stress are not
available forsalamanders, so estimates were based on the assumption
that tensileyield stresses are 25% lower than compressive yield
stresses(Currey, 1984). SFs were then calculated as:
SF ¼ syieldstressmean peak stress
ð5Þ
and ‘worst-case’ scenario estimates (SFWC) as:
SFWC ¼ syieldstress � 2� s:d:syieldstressmean peak stressþ 2�
s:d:smean peak stress :
ð6Þ
HV, yield stress and SF were reported separately for each of
theanatomical regions (Table 7, Table S1). Calculations of yield
stressesand SFs were based on dorsal and posterior regions being
loaded intension, 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 Femur
Anterior Dorsal Posterior Ventral Anterior Dorsal Posterior
Ventral
HV 36.3±0.9 41.7±1.5 44.4±1.2 36.6±0.9 33.7±1.2 36.0±1.1
34.6±0.9 31.5±1.1HV sample sizes 23 24 20 22 25 25 25 24Mean yield
stress (MPa)* 174.1±3.3 145.2±4.0 152.6±3.2 175.4±3.2 164.8±4.2
129.8±3.0 126.1±2.4 156.7±4.1Standard SF 23.6±0.5 20.7±0.6 21.8±0.5
23.8±0.4 9.5±0.2 10.4±0.2 10.1±0.2 9.1±0.2CV of SF 0.092 0.136
0.095 0.085 0.128 0.117 0.095 0.128SFWC 12.3±0.3 8.1±0.3 9.5±0.2
12.6±0.3 5.7±0.2 3.7±0.1 3.8±0.1 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 andventral 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.
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Data accessibilityKinetic, kinematic, bone microhardness, safety
factor and stress dataare available from the Dryad Digital
Repository: http://dx.doi.org/10.5061/dryad.7f1j1.
Statistical analysesLinear mixed-effects models (LMMs), fitted
by restrictedmaximumlikelihood via lme4::lmer, were used to
evaluate differences withinresponse variables, with individual as a
random effect for a randomintercepts model (Bates et al., 2014).
Random effects representedsubsamples of a population and an
additional source of variation(e.g. individuals within species)
whereas fixed effects were factorsto compare (e.g. forelimb versus
hindlimb) (Bolker et al., 2009).Regional heterogeneity of HV within
a bone was assessed withanatomical region as a fixed effect.
Otherwise, limb bone was thefixed effect. Given that HV within an
anatomical region may varyamongst individuals, anatomical region
was also added as a randomeffect to create a random intercepts and
slopes LMM. Pair-wisecomparisons between anatomical regions and
bones were fitted witha contrast matrix in multcomp::glht. P-values
provide limitedinformation regarding the strength of evidence to
supportconclusions (Anderson et al., 2001), so LMMs were reported
interms of effect sizes and an estimate of precision (e.g. Ω0
2; Xu,2003), emphasizing the magnitude of the differences and
the levelof uncertainty in supporting those differences,
respectively.
RESULTSKinematic comparison of forelimbs and hindlimbsAlthough
the limbs have similar kinematic profiles, numerousdifferences were
identified. At the beginning of stance, the shoulderand hip are
adducted by ∼10–15 deg (Fig. 2A), with the wrist andankle showing
similar degrees of extension (Fig. 2B). The femur ismore protracted
than the humerus until about 80% of stance
(Fig. 2C), and the elbow is more flexed than the knee until
about90% of stance (Fig. 2D). Flexion and extension of the elbow
andknee follow similar profiles; however, the ankle becomes
flexedalmost twice as much as the wrist towards mid-stance.
Anothermajor difference between the limbs is that the femur
remainsadducted (e.g. knee closer to the ground than the hip)
throughoutstance (Fig. 2A), but the humerus becomes abducted (elbow
higherthan shoulder) after about 30% of stance. Additionally,
althoughboth bones begin in a protracted orientation (i.e. distal
joint cranialto the girdle for almost all of stance), the humerus
is initially nearlyperpendicular to the long axis of the body (∼0
deg in Fig. 2C) andretracts at about 10% of stance, whereas
retraction of the femur ismore evenly split between protracted and
retracted orientations(Fig. 2C).
Moments produced by the GRF about limb jointsGRF production was
generally similar between the forelimbs andhindlimbs (Table 4, Fig.
3), contributing to similarities in the jointmoments imposed by the
GRF (Fig. 4). The GRF imposes adorsiflexion (positive) moment about
the wrist and ankle (Fig. 4A)due to the anterior position of the
GRF relative to these joints. Tomaintain equilibrium at these
joints, wrist and ankle extensors needto 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 andhip, though for the latter this
shifts to an adductor momentapproximately 75% into stance (Fig.
4B). The GRF also imposes aprotractor moment about the shoulder and
hip, though protraction atthe shoulder is lower in magnitude and
occurs later in stance (40%)than at the hip (10% stance) (Fig. 4C).
Finally, torsional momentsimposed by the GRF are similar between
the humerus and femur(Fig. 4D), changing from a tendency to impose
anterior axialrotation to posterior rotation at about 60% of
stance.
Pro
tract
ion/
retra
ctio
n an
gle
(deg
)A
bduc
tion/
addu
ctio
n an
gle
(deg
)
Elb
ow/k
nee
angl
e (d
eg)
Wris
t/ank
le a
ngle
(deg
)
−50 Retraction
−25
0
25
50
−20
0
20
60
80
100
0
Forelimb
120
140
160
60
80
100
120
140
160A B
C DProtraction
Adduction
Abduction
Flexion
Extension
Flexion
Extension
Stance (%)25 50 75 100 0 25 50 75 100
0 25 50 75 100 0 25 50 75 100
Hindlimb
Fig. 2. Comparison of stance phasekinematic profiles between
theforelimbs and hindlimbs of tigersalamanders, Ambystoma
tigrinum.Lines and adjacent shading representmeans±s.e.m. pooled
across all trials forthe forelimbs (N=50) and hindlimbs(N=48), with
all trials normalized as apercentage of stance. Negative values
arehighlighted in gray, and indicate adductionin A and retraction
in C. Kinematiccomparisons include: (A) abduction/adduction angle
of the limbs,(B) extension/flexion of the wrists andankles, (C)
protraction/retraction angle ofthe limbs and (D) extension/flexion
of theelbows and knees. See Fig. S1 forillustration of these
kinematic angles.
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Despite these similarities, different configurations of the
forelimband hindlimb influence how the GRF imposes moments on
theselimbs (Fig. S2). In salamanders (and most quadrupeds), the
elbowpoints posteriorly whereas the knee points anteriorly.
However, theGRF is directed essentially vertically for most of
stance for bothlimbs (Fig. 3). Consequently, the flexor/extensor
moment of theGRF tends to change in different directions for these
joints, shiftingfrom 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
theforelimb [e.g. ankle versus wrist in dorsiflexion (Fig. 4A), hip
versusshoulder in anteroposterior and dorsoventral rotations (Fig.
4B,C),and knee versus elbow in flexion and extension (Fig.
4E)].
Comparison of bone stressesLower stresses were estimated for
locomotor loads upon thehumerus, though the difference between the
bones was lesspronounced for shear (Table 6). Peak tensile and
compressivestresses occurred later in stance for the humerus (∼67%)
than thefemur (∼22%) (Table 6, Fig. 5A,B). This pattern corresponds
withthe peak net GRF, which also occurred later in stance (∼61%)
for the
forelimb than the hindlimb (∼33%) (Table 4, Fig. 3).
Afteraccounting for variation amongst individuals, total external
forces(‘net GRF’) at the time of peak tensile stresses for each
bone were0.061±0.016 BW lower in the humerus, with vertical
andanteroposterior components lower by 0.04 and 0.115
BW,respectively (Table 5).
The neutral axis of bending for the humerus was directed
suchthat the posterodorsal region was loaded in tension and
theanteroventral region in compression through the time
ofmid-stance to peak loading (Fig. 5C,D). The neutral axis
ofbending was aligned closer to the anatomical anteroposterior axis
atpeak tensile stress for the femur, placing the dorsal portion
intension and the ventral portion in compression. Nonetheless,
theanterodorsal cortex of the femur was loaded in tension and
theposteroventral cortex in compression at 50% of stance (Fig.
5C,D).
Biomechanical properties and SFs of the salamander humeriand
femoraComparisons indicated higher HV for the humerus and
regionalheterogeneity within each bone (Table 7, Table S1). The
LMMexplained about 68% of the variation inHV based onΩ0
2 (Xu, 2003),
Forelimb
Stance (%)
Hindlimb
0 25 50 75 100 0 25 50 75 100
0 25 50 75 100 0 25 50 75 100
0 25 50 75 100 0 25 50 75 100
Ant
erop
oste
rior a
ngle
(deg
)
−40
−20
0
20
40
Ant
erop
oste
rior (
BW
)
−0.1
0
0.1
0.2
Net
GR
F (B
W)
0.1
0.2
0.3
0.4
0.5
Verti
cal (
BW
)
0.1
0.2
0.3
0.4
0.5
0
Med
iola
tera
l (B
W)
−0.075
−0.050
−0.025
0.000
−0.100
Med
iola
tera
l ang
le (d
eg)
−20
−10
0
−30
Posterior
Anterior
Medial
Lateral
Posterior
Anterior
Medial
Lateral
Vertical Vertical Fig. 3. GRF production by the forelimband
hindlimb of A. tigrinum throughoutstance. Lines and adjacent
shadingrepresent means±s.e.m. pooled across alltrials for the
forelimbs (N=50) andhindlimbs (N=48), with all trials normalizedas
a percentage of stance.Anteroposterior angles were set relative
tovertical (0 deg), so that negative valuesindicate a GRF directed
posteriorly.Mediolateral angles were also relative tovertical (0
deg), so that negative valuesindicate a GRF directly medially.
Grayrectangles distinguish negative valueswithin each plot.
Although the peak valuesfor the net GRF and the verticalcomponent
were similar (∼0.45 bodyweight, BW) and the GRF remainedmedial,
positive anterior valuesthroughout stance indicate that
thehindlimbs had a greater acceleratory rolethan the forelimbs.
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an analog of R2 for LMMs. The greatest magnitude of HV, and
thusestimated yield stresses, at these mid-shafts was generally in
theposterodorsal region (Table 7), corresponding with the
typicallocation of tensile loads about the neutral axis of bending
(Fig. 5B).
Femoral SFs ranged from ∼9 to 10 (Table 7), corresponding
withthe 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
dorsalcortex, where HV was greatest, yet SFs at humeral mid-shafts
weregreater in the anteroventral region, where HV was lower (Table
7).This differencewas largely due to peak bone stresses that were
abouttwo times lower in the humerus (Table 6), although higher
yieldstresses in the humerus also contributed to SF differences
from thefemur (Table 7). The worst-case scenario SF (SFwc) was
about twotimes lower than standard SF calculations for both bones,
but stillindicated ample margins of safety (∼8–13 for the humerus,
∼3–6for the femur; Table 7). Biomechanical differences along
thedorsoventral and anteroposterior planes of the bones were
alsoreflected in their structural response to bending, as evidenced
bysecond moments of area that were greater in the dorsoventral
planefor the humerus and the anteroposterior plane for the
femur(Table 1).
DISCUSSIONMechanisms underlying elevated SFs in salamander
humeriHumeri have higher SFs (∼22) than femora (∼10) in
salamanders, adisparity greater than that reported in alligators
(8.4 for the humerusversus 6.3 for the femur; Blob et al., 2014).
The difference betweenhumeral and femoral SFs relates primarily to
differences in yieldstrain for alligators (Blob et al., 2014), but
from both lower stressesand structural reinforcement in salamander
humeri (Tables 6, 7).
Critical factors that are likely contributing to the relatively
lowerstresses 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 ofthe elbow in A. tigrinum, the GRF only exerts a
flexor moment at theelbow late in stance (Fig. 4E). This reduces
the need for elbowextensors (e.g. anconaeus complex) to counter GRF
moments at theelbow, reducing the stress they place on the humerus
(Table 2,Fig. 1). Humeral stresses are additionally reduced by
contributionsof wrist extensors (FDC, FACR, FACU) to the elbow
extensormoment, further reducing the force that elbow extensors
spanningthe humeral mid-shaft must exert. Moreover, adductor
musclescontributing to forelimb movement (P and SC) insert
proximally onthe humerus, and do not contribute to stresses
experienced at mid-shaft.
Beyond these stress-reducing characteristics of
forelimbmusculature in salamanders, HV of the humerus is generally
greaterthan that of the femur, with different patterns of
regionalheterogeneity (Table 7, Table S1) between the bones. The
highestSFs 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 theanteroposterior direction (IAP), but the humerus has a
greater secondmoment of area in the dorsoventral direction (IDV;
Table 1). Theseresults suggest that these limb bones show
differences in structure andmechanical response that reduce bending
stress in different directions.Given the extent to which humeral
SFs (>20) of salamanders aregreater than those of the femur
(∼10), it is difficult to envisage howthe entire magnitude of
differences in humeral and femoral SFs ofsalamanders could be
adaptive. Nonetheless, elevated SFs supportedby greaterHVand
structuralmodifications suggest the possibility that,
0.00075
0.00050
0.00025
0
−0.000250 25 50 75 100
0.006
0.004
0.002
0
−0.0020 25 50 75 100
0.0015
0.0010
0.0005
−0.0005
−0.00100 25 50 75 100
0
0.0010
0.0005
−0.0010
−0.00150 25 50 75 100
0
−0.0005
0.002
0.001
−0.002
−0.0030 25 50 75 100
0
−0.001
Forelimb
Stance (%)
Hindlimb
Flexion
Extension
Rotate anteriorly
Rotate posteriorly
Retraction
Protraction
Adduction
Abduction
Plantarflexion
DorsiflexionA
B
C
D
E
Elb
ow/k
nee
(N m
)B
one
tors
ion
(N m
)G
irdle−A
P ax
is (N
m)
Gird
le−D
V a
xis
(N m
)W
rist/a
nkle
(N m
)
Fig. 4. Comparison of moments exerted by the GRF for the
forelimb andhindlimbofA. tigrinum. Lines representmean values
obtained fromdata pooledacross all trials for the forelimbs (N=50)
and hindlimbs (N=48), with the shadingdepicting the standard error.
Negative values are highlighted in gray, and thedirections of
rotation indicated by positive and negative values are labeled in
thepanels. Girdle refers to the shoulder and hip. AP,
anteroposterior; DV,dorsoventral.SeeFig.S2 for
illustrationofGRFmomentarmsrelative to limb joints.
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to some extent, the high load-bearing capacity of salamander
humerimay facilitate the multi-functional role of the forelimbs for
locomotorand non-locomotor behaviors (e.g. burrowing).
Relevance of ‘mixed chains’ to tetrapod evolutionComparisons of
SFs for the humerus and femur of salamandersprovide an additional
empirical example of a ‘mixed-chain’(Alexander, 1997, 1998) within
the locomotor skeleton oftetrapods. ‘Mixed-chains’ of SFs were
identified betweenproximal and distal limb bones in horses (Currey,
2002), andiguanas and alligators (Blob and Biewener, 1999).
However, dataherein reinforce additional patterns observed in
alligators (Blobet al., 2014), which demonstrated different SFs
between theproximal bones of the forelimb and the hindlimb. As in
alligators(Blob et al., 2014), the humerus has a higher SF than the
femur insalamanders (Table 7).Some of the factors proposed by
Alexander (1997) that might
contribute to differences in SFs between these bones in
alligators donot apply to salamanders. For example, alligator
humeri are smallerthan the femora, which might allow for more
economicalmaintenance of a high SF (Blob et al., 2014). However,
thehumerus and femur are roughly equal in length in
salamanders(Table 1), so Alexander’s first condition for
‘mixed-chains’ likelydoes 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 inloads (i.e. femur) did not have higher SFs (Table 6),
suggesting thatelevation of humeral SFs in salamanders likely was
not an adaptiveresponse for protection against unpredictable high
loads.
SFs for salamander limb bones, like those of alligators,
aregenerally high (>7) compared with those of many taxa,
includingmammals and birds (Blob et al., 2014). Thus, differences
betweenhumeral and femoral SFs for salamanders might simply reflect
anincreased opportunity for variation in SF across the
skeleton(Alexander’s third condition). Though this reason has been
invokedas a factor contributing to ‘mixed-chains’ in alligators
(Blob et al.,2014), data on the limb configuration, muscle
disposition andregional heterogeneity of HV in tiger salamanders
also suggestmechanistic reasons for high SFs in limb design.
Collectively, theelevated structural and material reinforcement to
withstand loads inthe humerus, and anatomical features of the
forelimb promoting lowloads, suggest that stochastic variation
associated with large SFsmay not completely account for differences
in humeral and femoralSFs observed in salamanders.
In addition to the three conditions promoting ‘mixed-chains’
ofSFs proposed by Alexander (1997), higher SFs may be found
instructures with higher penalties for failure (Diamond,
2002).Forelimbs and hindlimbs play different roles in legged
D Right humerus: peak stress
Neutral axis
Posterior
Ventral
Anterior
Dorsal
Axi
al ro
tatio
n
Right femur: peak stress
Right femur: 50% through stance
–3 deg
Right humerus: 50% through stance
–32 deg
–53 deg
18 deg
g
A
1 mm 1 mm
B
C
Humerus
Stance (%)Femur
0 25 50 75 100
0 25 50 75 100
0 25 50 75 100
50
25
−25
−50
0
0
−5
−15
−20
−10
0
5
10
15N
eutra
l axi
s an
gle
(deg
)C
ompr
essi
ve s
tress
es (M
Pa)
Tens
ile s
tress
es (M
Pa)
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) tensilestress 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 (solidred 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
andfemoral 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.
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locomotion (McElroy et al., 2014), which may provide insight
intoSF variation in salamander limb bones. Although hindlimbs
providethe primary propulsion in many non-mammalian
quadrupeds,forelimbs still make important contributions to
locomotion(Kawano and Blob, 2013; Nyakatura et al., 2014), and loss
oflocomotor function may be more detrimental for the forelimb.
Earlywork on salamander locomotion (Evans, 1946) demonstrated
thatforward propulsion could be achieved solely by the forelimbs
butnot the hindlimbs, suggesting that the forelimbs play a
moreimportant locomotor role than passive body support (at least
interrestrial salamanders such as Taricha and Ambystoma).
Moreover,there do not appear to be ready examples (among
non-bipedalvertebrates) in which the complete loss of the pectoral
appendagesoccurred while the pelvic appendages remained fully
intact: whenvertebrates lose an entire appendage, it is typically
the pelvicappendage (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
limbloss is associated with the evolution of fossorial or aquatic
life styles(e.g. amphisbaenians and cetaceans), the forelimbs are
typicallyretained rather than the hindlimbs (Caldwell, 2003).
Limbreduction, including the loss of digits, can be found in
theforelimb rather than the hindlimb in some taxa (Lerista
lizards:Skinner et al., 2008), but the loss of proximal limb
elements or theentire limb is generally less common for forelimbs.
Additionalstudies are required to verify whether there are strong
mechanical orselective advantages for forelimb retention in
non-bipedalvertebrates, or whether the conservatism of forelimb
retention isdue to developmental constraint. For instance,
hindlimbs developafter forelimbs (Tanaka and Tickle, 2007), and
structural reductiontypically occurs in the reverse order from
which structures develop(Lande, 1978), potentially making hindlimbs
more susceptible toloss via developmental truncation.Further
investigations of how loads vary across limb bones could
yield insights into the morphological evolution of limb bones
asvertebrates became terrestrial. The vertebrate
musculoskeletalsystem shifted from being essentially weightless as
a result ofbuoyancy underwater to counteracting the effects of
gravity on land,drastically shifting the loading regime imposed
upon the locomotorstructures. This shift may have made the
evolution of long, tubularlimb bone shafts advantageous compared
with their blockyprecursors (Currey, 2002). Microanatomical
analyses of a widerange of tetrapods have differentiated aquatic
and terrestriallifestyles from limb bone histology (Laurin et al.,
2011),facilitating the inference of the locomotor biomechanics of
fossiltaxa such as the Devonian fish Eusthenopteron (Laurin et al.,
2007)and stem stegocephalians (Laurin et al., 2004). Identifying
strongerform–function relationships between limb morphology
andlocomotor movements would facilitate efforts to reconstruct
thetransition from water to land by tetrapods (Nyakatura et al.,
2014;Standen et al., 2014). For instance, the mechanical properties
ofbones from extant taxa were combined with palaeopathology
totheorize the loading conditions that could have fractured the
radiusin the early stem tetrapod Ossinodus pueri in the context of
walkingon land (Bishop et al., 2015), suggesting the utility of
bone loadingdata during terrestrial locomotion to address the
mechanisms thatinfluenced how vertebrates became terrestrial.
Further application ofdata on locomotor stresses from extant taxa
could help answerquestions regarding the functional consequences of
morphologicalchanges observed in extinct tetrapodomorphs spanning
thetransition from water to land (Hohn-Schulte et al., 2013;
Kawanoand Blob, 2013).
AcknowledgementsWe are grateful to Marguerite Butler and Brad
Chadwell for advice about smoothingdata, and to Chad McMahan and
Linda Jenkins for assistance with samplepreparation. Earlier drafts
were improved by suggestions from Margaret Ptacek,Miriam
Ashley-Ross, Andrew Biewener, and two anonymous reviewers. Fig. 1
wasproduced using figures generously provided by Miriam
Ashley-Ross. We also thankRebecca Nelson, William Mitchell, Patrick
McGarity, Lauren Pruitt, Megan Gregoryand David Boerma for
assistance with video analysis. All experiments werecompleted at
Clemson University. An earlier draft was submitted by S.M.K. as
adissertation chapter in partial fulfillment of a doctoral degree
at Clemson University.
Competing interestsThe authors declare no competing or financial
interests.
Author contributionsS.M.K. collected and analyzed the data,
D.R.E., M.S.K. and D.D. provided themechanical testing equipment,
and trained/supervised S.M.K. inmechanical testing.R.W.B. developed
the biomechanical model, provided equipment for
quantifyingkinematics and kinetics, and supervised analyses. S.M.K.
and R.W.B. led theconception and design of the research. All
authors contributed to writing themanuscript.
FundingFunding was provided by the American Society of
Ichthyologists and HerpetologistsGaige 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 andIOS
0817794, to R.W.B.). Data analysis andmanuscript preparation were
completedwhile S.M.K. was a Postdoctoral Fellowat the National
Institute for Mathematical andBiological Synthesis (sponsored by
National Science Foundation Award DBI-1300426 and the University of
Tennessee, Knoxville).
Supplementary informationSupplementary information available
online
athttp://jeb.biologists.org/lookup/suppl/doi:10.1242/jeb.125799/-/DC1
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