Flying with Membrane Wings:
How Bats Shape Their Wings with Their
Hindlimbs, Skin Mechanics, and Wing Membrane Muscles
By Jorn Andre Cheney
B.A., Lewis & Clark College, Portland OR, 2007
A Dissertation Submitted in Partial Fulfillment of the
Requirements for the Degree of Doctor of Philosophy
in the Department of Ecology and Evolutionary Biology
at Brown University
Providence, Rhode Island
May 2015
© Copyright 2015 by Jorn Andre Cheney
This dissertation by Jorn Andre Cheney is accepted in its present form by the
Department of Ecology and Evolutionary Biology as satisfying the dissertation
requirement for the degree of Doctor of Philosophy.
Date____________
_____________________________________
Sharon M. Swartz, Advisor
Recommended to the Graduate Council
Date____________
_____________________________________
Elizabeth L. Brainerd, Reader
Date____________
_____________________________________
Kenneth S. Breuer, Reader
Date____________
_____________________________________
Christian Franck, Reader
Date____________
_____________________________________
Thomas J. Roberts, Reader
Approved by the Graduate Council
Date____________
_____________________________________
Peter M. Weber, Dean of the Graduate School
iii
Curriculum Vitae
Jorn A Cheney was born on December 24, 1984 in Evanston, Illinois to
Alice Cheney. He spent the majority of his youth in Chicago, Illinois. Upon
graduation from University High in 2003, he moved to Portland, Oregon to attend
Lewis & Clark College. At Lewis & Clark College, he worked in Kellar Autumn’s
laboratory on gecko adhesion biomechanics. He received a Bachelor of Arts
degree in Biology in 2007. And in 2008, Jorn began pursuing his graduate
studies at Brown University in Providence, Rhode Island, where he worked
toward a Doctor of Philosophy in the Ecology and Evolutionary Biology
department. His thesis investigated bat wing structure and its capability to deform
passively and actively.
Publications
 Cheney J A, Konow N, Middleton K M, Breuer K S, Roberts T J, Giblin E L,
and Swartz S M 2014 Membrane muscle function in the compliant wings of
bats. Bioinspiration & Biomimetics, 9 025007. DOI:10.1088/17483182/9/2/025007

Cheney J A, Ton D, Konow N, Riskin D K, Breuer K S, and Swartz S M 2014
Hindlimb motion during steady flight of the lesser dog-faced fruit bat,
Cynopterus brachyotis. PloS One, 9 e98093.
DOI:10.1371/journal.pone.0098093
Teaching Experience
Teaching Assistant, Brown University Alpert Medical School
 Human Gross Anatomy, 2010 & 2011
Teaching Assistant, Brown University
 Comparative Biology of the Vertebrates, 2009
Guest Lecturer, Brown University
 Biological Design: Structural Architecture of Organisms, 2012
iv
Preface and acknowledgements
This thesis is the culmination of many years of effort that would not have
been possible without the help and support of a great many people. I was
fortunate enough to work with many inspiring and generous colleagues.
I would like to express my gratitude for the guidance and support provided
by my advisor Sharon Swartz. She encouraged me to explore a broad array of
topics and provided me with the necessary resources to do so. This thesis would
not have been possible without her support. I am particularly grateful for all of her
help training me to become more than just a researcher, but a communicator.
I am also incredibly thankful for my supportive thesis committee, Beth
Brainerd, Kenny Breuer, Christian Franck, and Thomas Roberts. I would also like
to give special thanks to Steve Gatesy who carefully considered every one of my
arsenal of questions. All of the insightful suggestions by these wonderful scholars
have made this work significantly better. I am also extremely grateful for them
entertaining long discussions with me in their offices.
My graduate experience would not have been the same without the
amazing faculty in the department, my kind fellow graduate students, brilliant
postdoctoral fellows, and tireless lab managers and technicians. I have learned
so much from them, and working with them has transformed me into the scientist
and person that I am today. I hope that the following people understand how truly
grateful I am to them: Cosima Schunk, Rye Waldman, Erika Giblin, Arnold Song,
Attila Bergou, Nicolai Konow, Kimberley Abbott, Shannon Silva, Tatjana Hubel,
v
Rhea von Busse, Robert Kambic, Joseph Bahlman, Daniel Riskin, and Andrew
Bearnot.
The most important factor in the success of this thesis was my wife Lana
Linscott. I am eternally grateful for her support and kindness. This dissertation
was a joy, but also challenged me in ways that I had never encountered. I could
not have done this without her.
vi
Table of Contents
Curriculum Vitae
iv
Preface and Acknowledgements
v
List of Tables
viii
List of Figures
ix
Introduction
1
Chapter 1
8
Hindlimb motion during steady flight of the lesser dog-faced
fruit bat, Cynopterus brachyotis
Chapter 2
36
Membrane muscle function in the compliant wings of bats
Chapter 3
69
A wrinkle in flight: the role of elastin fibers in the mechanical
behavior of bat wing membrane
Chapter 4
106
Bat wing membrane architecture: the elastin network and
muscles of the plagiopatagium
vii
List of Tables
Chapter 2
Table 1
63
Summary of successful EMG recordings from plagiopatagiales.
Chapter 4
Table 1
130
Summary of imaged bats sorted by family.
Table 2
134
Summary of muscles observed in bats.
viii
List of Figures
Chapter 1
Figure 1
Modifications to the bat hindlimb skeleton.
29
Figure 2
The hindlimb serves as a boundary condition for the wing membrane.
30
Figure 3
Illustration of the eight anatomical markers used in this study and the
parameters measured.
31
Figure 4
Ankle position was variable among wingbeats.
32
Figure 5
Direction of ankle motion was consistent among wingbeats.
33
Figure 6
Wing membrane tension varied in a consistent pattern among
wingbeats.
34
Figure 7
Ankle motion consistently resisted wing membrane tension.
35
Chapter 2
Figure 1
Method of electrode implantation into the plagiopatagiales.
64
Figure 2
Representative electromyographic data and kinematics.
65
ix
Figure 3
66
Plagiopatagiales activate during downstroke at low- and high-speed flight.
Figure 4
Plagiopatagiales activate in synchrony.
67
Figure 5
Schematic of hypothesized plagiopatagiales function.
68
Chapter 3
Figure 1
95
Bat wing membranes support and deform in response to aerodynamic load.
Figure 2
Elastin fibers form a parallel array, allowing uniaxial testing parallel and
perpendicular to the fibers.
96
Figure 3
Elastin fibers are necessary for wing wrinkling.
97
Figure 4
Wing membrane mechanical behavior was nonlinear and anisotropic,
when referenced to relaxed configuration.
98
Figure 5
Wing membrane tested both parallel and perpendicular to elastin fibers
behaves isotropically at higher stretch and stress, when referenced to
sample length at 1 MPa; whereas its behavior is anisotropic at very low
stretch and stress.
99
Figure 6
100
Bat wing membrane is an anisotropic composite of pre-stressed compliant
elastic fibers embedded in an isotropic matrix with excess length parallel
to the fibers.
x
Supplemental Figure 1
Measurements from representative mechanical testing trial.
101
Supplemental Figure 2
Effects of preconditioning are minor after cycle 1.
102
Supplemental Figure 3
The elastin network was similar across wings, both within and
among individuals.
103
Supplemental Figure 4
Wing membrane mechanical behavior was nonlinear, anisotropic, and
highly variable when referenced to relaxed configuration.
104
Supplemental Figure 5
Bat wings can collapse their large surface area into a tightly packed
volume.
105
Chapter 4
Figure 1
Tissues illuminate under cross-polarized light in a manner consistent
with anatomical description.
128
Figure 2
Validation of cross-polarized light imaging using histology.
129
Figure 3
Schematic of the muscles of the plagiopatagium.
131
Figure 4
Schematic of elastin network.
132
Figure 5
Elastin fibers run along the wing spreading axis, but some regions
contain a second population of elastin fibers.
133
xi
Figure 6
Elastin fibers are analogous to muscle tendons.
135
Figure 7
136
Collagenous periphery of elastin fibers anchors to the surrounding matrix.
Figure 8
137
Convergent sheet-like muscle morphology in the plagiopatagiales proprii.
xii
Introduction
Over fifty million years ago, the limbs of ancestral bats were exapted for
use as wings (Gunnell and Simmons 2005). During development, a cellular cue
triggering apoptosis was lost: the cells that were normally carved away to provide
unrestricted motion of the digits and limbs remained, forming a membrane
composed of a thin bilayer of skin (Cretekos et al 2005). This membrane
provided bats with an aerodynamic surface, allowing them to invade the skies
and exploit an ecological niche previously denied to mammals.
The wing membrane is very different from mammalian skin as a whole. A
network of elastin fibers and a number of muscle arrays are contained within the
bilayer of skin (Morra 1899, Quay 1970, Holbrook and Odland 1978, Crowley and
Hall 1996). One of the muscle arrays, the plagiopatagiales proprii, is particularly
unusual because it both originates and inserts into the membrane (Gupta 1967).
Perhaps the most important difference between the skin of other mammals and
that of the wing membrane is that thickness is substantially reduced and is
almost an order of magnitude less than body skin in bats (~15 vs 100–200 µm for
a ca. 6 g bat; Madej et al 2013).
Wing skin thickness reduction in combination with its natural compliance
makes bat wing membranes extremely soft and flexible, in contrast to insect
wings and bird feathers. The tangent modulus of wing skin is two orders of
magnitude less than that of either cuticle or keratin, which form the wings of
insects and feathers of birds respectively (3-30 MPa vs 0.3–10.9 GPa or 1.78–
2.76 GPa; Bonser and Purslow 1995, Swartz et al 1996, Smith et al 2000).
1
Because of the compliance of skin and the slenderness of the membrane, the
wing membrane has negligible bending stiffness. Thus, membrane wings can
bear aerodynamic load in tension only.
When wing membranes with negligible bending stiffness are placed under
aerodynamic load, they deflect and stretch until sufficient tension in the
membrane resists the aerodynamic load (Song et al 2008, Waldman and Breuer
2013). In this way, an important aeroelastic coupling is formed, whereby
aerodynamic force reconfigures and partially determines the three-dimensional
form of the wing, and the form of the wing determines aerodynamic force. An
improper match between membrane elasticity and aerodynamic force can
increase drag significantly and decrease performance (Hu et al 2008). Because
bats fly capably over a large range of aerodynamic conditions, they likely
manipulate this aeroelastic interaction to avoid detrimental combinations.
Studies of human-engineered membrane wings have identified a handful
of mechanisms for tuning membrane aeroelastic interactions, many of which may
also be employed by bats. The general goal of aeroelastic control is to adjust the
magnitude of deflections and the resulting curvature of the membrane (Hu et al
2008, Abudaram 2009), although other effects such as membrane vibrations may
also be important (Timpe et al 2013, Waldman and Breuer 2013). Membrane
wing form can be adjusted by modifying the orientation or shape of the
supporting frame (wing skeleton). Membrane deflection can be decreased by
increasing membrane stiffness (Hays et al 2012). Finally, a membrane with
excess length, that is, a membrane where the length exceeds that of the
2
supporting frame, will undergo greater deflection (Rojratsirikul et al 2010). Over
the next few chapters, I will relate the function of the hindlimb, wing membrane
muscles, and elastin fibers to these engineering mechanisms. Specifically, I will
address how wing configuration is influenced by the hindlimb interacting with the
wing membrane, how active plagiopatagiales proprii should reduce deflections in
the wing membrane, and how passive properties of the membrane-elastin
architecture are well suited for large deflections. To conclude, I census the
architecture of the distinctive elastin fibers of bat wings, and describe the
diversity of the arrays of wing membrane muscles across the bat phylogeny,
which helps elucidate how function of these morphological features do and do
not vary.
Chapter One is a kinematic study of the hindlimb, the skeletal anchor of
the wing’s trailing edge, and addresses hindlimb movement in flight and how this
limb interacts with the wing membrane; it has been published in PLOS ONE
(Cheney et al 2014a). The wing membrane spans numerous joints in the hand,
arm, hindlimb, and trunk. But of these skeletal structures, the hindlimb may be of
particular interest, because it moves largely independently from the rest of the
wing in at least some species (Riskin et al 2008). In this work, my colleagues and
I find that the hindlimb generally moves in phase with the wingbeat, but that
hindlimb position at any time in the wingbeat cycle is highly variable. Hindlimb
movement consistently resisted wing membrane tension, demonstrating that the
hindlimb was not moved passively by the wing membrane. The large
dorsoventral motions that we observed in flight suggest that the hindlimb may
3
play an important role in shaping the wing and adjusting the chordwise pressure
distribution on the wing membrane.
Chapter Two identifies a muscular mechanism that may allow bats to
increase membrane tension/stiffness without bone motion; it has been published
in Bioinspiration and Biomimetics (Cheney et al 2014b). My colleagues and I
found that the plagiopatagiales proprii muscles activate during downstroke.
Further, we correctly predicted that if the muscles were active in flight, multiple
muscles would activate synchronously to maximize force production; theory
predicts the force generated by individual muscles is low, and would likely have
been insufficient to substantially alter membrane tension. Consistent with the
hypothesis that these muscles modulate membrane tension/stiffness, muscle
activation timing varied with flight speed. From these results, we constructed a
simple mechanical model of muscle function, which identified the importance of
muscle length to active membrane stiffness. This model provides the first
explanation for the great length of the plagiopatagiales proprii, and discusses
how the distinctive morphology of these muscles is well-suited to increase
membrane stiffness and reduce wing deflections.
Chapter Three addresses the passive mechanical behavior of the wing
membrane, and seeks to understand how macroscopic elastin fibers and the
matrix tissue in which the fibers are embedded contribute to the mechanical
behavior. My colleagues and I find that wing membrane mechanical behavior can
be well-modeled as an isotropic, stiff matrix embedded with spanwise,
prestressed, compliant elastin fibers. In this arrangement, the prestressed elastin
4
fibers compressively buckle the wing matrix and dominate mechanical behavior
until the matrix unfurls. However, once the matrix unfurls, it bears the majority of
load, and elastin fiber contribution quickly becomes negligible. Therefore, when
wing skin is loaded parallel to the direction of elastin fibers, the mechanical
behavior of the buckled wing membrane is biphasic: in the first phase it is
compliant and extensible (traits of elastin), and in the second phase it is stiff and
its mechanical properties are similar to those observed when skin is loaded in the
chordwise direction, where matrix always dominates. This biphasic behavior
makes bat wing membranes analogous to human-engineered wing membranes
with excess length, and suggests that this architecture will tend to increase wing
deflections.
Chapter Four details variation among bats in a number of key architectural
features of elastin fibers and wing membrane muscles that were identified as
critical to their function in the previous two chapters (Chapters Two and Three).
Specifically, we address elastin fiber orientation along with presence, number,
orientation, and length of wing membrane muscles. The few published
observations of these morphological traits have identified great variation in these
structures among bats (Morra 1899, Gupta 1967, Holbrook and Odland 1978,
Crowley and Hall 1994). We used cross-polarized light to image the wing
membrane and assess these traits in 130 species, representing all bat families
except the monospecific Craseonycteridae. We found that elastin fibers run
predominantly spanwise in all species studied. Thus, the mechanical
contributions of elastin fibers, as discussed in Chapter Three, can be considered
5
broadly applicable, given the similarity in elastin architecture in all bats. We also
found the plagiopatagiales proprii present in every species, unlike other wing
membrane muscles. This is consistent with the hypothesis that they are critical
for flight, as discussed in Chapter Two. Finally, all of the wing membrane
muscles varied in morphology, but closely-related species were more similar, and
variation was not clearly correlated with ecology.
References
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aCheney
J A, Ton D, Konow N, Riskin D K, Breuer K S and Swartz S M 2014
Hindlimb motion during steady flight of the lesser dog-faced fruit bat,
Cynopterus brachyotis. PLOS ONE 9 e98093.
(DOI:10.1371/journal.pone.0098093)
bCheney
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7
Chapter 1
Hindlimb motion during steady flight of the lesser dog-faced
fruit bat, Cynopterus brachyotis
Jorn A Cheney1, Daniel Ton1, Nicolai Konow1, Daniel K
Riskin1, Kenneth S Breuer2,1, Sharon M Swartz1,2
1. Department of Ecology and Evolutionary Biology, Brown University, Providence, RI 02912
2. School of Engineering, Brown University, Providence, RI 02912
Abstract
In bats, the wing membrane is anchored not only to the body and forelimb,
but also to the hindlimb. This attachment configuration gives bats the potential to
modulate wing shape by moving the hindlimb, such as by joint movement at the
hip or knee. Such movements could modulate lift, drag, or the pitching moment.
In this study we address: 1) how the ankle translates through space during the
wingbeat cycle; 2) whether amplitude of ankle motion is dependent upon flight
speed; 3) how tension in the wing membrane pulls the ankle; and 4) whether
wing membrane tension is responsible for driving ankle motion. We flew five
individuals of the lesser dog-faced fruit bat, Cynopterus brachyotis (Family:
Pteropodidae), in a wind tunnel and documented kinematics of the forelimb, hip,
ankle, and trailing edge of the wing membrane. Based on kinematic analysis of
hindlimb and forelimb movements, we found that: 1) during downstroke, the
ankle moved ventrally and during upstroke the ankle moved dorsally; 2) there
was considerable variation in amplitude of ankle motion, but amplitude did not
correlate significantly with flight speed; 3) during downstroke, tension generated
by the wing membrane acted to pull the ankle dorsally, and during upstroke, the
wing membrane pulled laterally when taut and dorsally when relatively slack; and
4) wing membrane tension generally opposed dorsoventral ankle motion. We
conclude that during forward flight in C. brachyotis, wing membrane tension does
not power hindlimb motion; instead, we propose that hindlimb movements arise
from muscle activity and/or inertial effects.
8
1. Introduction
Bats are well known for their forelimbs, which are significantly modified
into wings, but their hindlimbs are modified as well. The femur and tibia are more
slender than those of comparably-sized non-bat mammals (Howell and Pylka
1977, Riskin et al 2005, Swartz and Middleton 2008), and, in addition, the wing
membrane is anchored to the ankle. As a consequence, hindlimb movements
contribute to three-dimensional wing shape. Potential aerodynamic
consequences of wing shape alteration by these movements may include
modulation of lift, drag, and pitching moment. However, the extent of such motion
during bat flight is rarely documented, and it is not known whether hindlimb
movements during flight are actively controlled or result from external forces
acting on the limb.
Evolutionary reorganization of bat hip anatomy may provide clues to the
importance of hindlimb movement during bat flight. The bat hindlimb is rotated
90º or more relative to the ancestral mammal condition (figure 1). The ischium is
tilted dorsally, orienting the face of the acetabulum dorsally and laterally, and the
femoral head and shaft lie along approximately the same axis (Simmons 1994).
Consequently, the knee is oriented dorsolaterally and its flexion moves the ankle
and foot ventrally, rather than dorsally, the basal condition for mammals (figure
2). Thus, knee flexion pulls the trailing edge of the wing ventrally rather than
dorsally.
Because the wing is attached to the hindlimb, dorsoventral movement of
the hindlimb affects aerodynamics by modifying wing shape and angle of attack
9
(figure 2). This enables bats to control the trailing edge of the wing in a manner
similar to modern aircraft. Mechanical models of bats with fixed wings have
demonstrated that flexion of the hindlimb can considerably increase both lift and
the lift-to-drag ratio (Gardiner et al 2011). However, neither the forelimbs nor the
hindlimbs remain stationary during bat flight (Norberg 1970, Lindhe Norberg and
Winter 2006, Riskin et al 2009, Wolf et al 2010, Adams et al 2012, von Busse et
al 2012), so understanding the dynamics of limb motion is integral to interpreting
the aerodynamic effects of hindlimb position.
Bat hindlimbs are known to move both dorsoventrally and mediolaterally
during flight (Lindhe Norberg and Winter 2006, Wolf et al 2010, Adams et al
2012). During downstroke, dorsoventral hindlimb motion that is in phase with the
wingbeat cycle increases angle of attack of the proximal wing, while hindlimb
motion that is out of phase with the wingbeat cycle reduces this effect. During
take-off, vespertilionid bats oscillate their hindlimbs, tail, and uropatagium
through a large dorsoventral arc, and the motion of the hindlimb and forelimb
begin in phase, and then move out of phase by as much as 180 degrees (Adams
et al 2012). During steady flight, the hindlimbs of Glossophaga soricina (Family:
Phyllostomidae) move up and down in phase with the wings, and it has been
suggested that the amplitude of the motion may be more pronounced at low flight
speeds (Lindhe Norberg and Winter 2006).
Here, we examine the movement of the hindlimbs and trailing edge of the
wing membrane during flight in the lesser dog-faced fruit bat, Cynopterus
brachyotis (Family: Pteropodidae), and discuss potential aerodynamic
10
consequences of these movements. In many species, hindlimb movements will
influence both the wing membrane and the tail membrane. We are able to isolate
hindlimb influence on the wing in C. brachyotis because it has a significantly
reduced tail membrane and lacks a tail. We propose that hindlimb motion could
arise from at least three sources: 1) passive tension exerted by the wing
membrane may cause hindlimb motion; 2) hip and knee muscles may directly
power hindlimb movement; and/or 3) vertical body oscillations could impose
oscillations on the hindlimb via inertial effects. We provide a body-referenced
kinematic description of ankle translation, which occurs in response to rotations
at the hip and/or knee, and using this data we address the first of these
possibilities. Accordingly, our aims are to: i) describe ankle motion over the
course of a wingbeat cycle, and ii) describe the orientation and length of the wing
membrane trailing edge over the course of a wingbeat cycle. From these data,
we test the hypotheses that 1) ankle motion amplitude is dependent upon flight
speed as previously proposed (Lindhe Norberg and Winter 2006), and 2) that
passive wing membrane tension is sufficient to explain the ankle motion we
observe.
2. Materials and Methods
2.1 Bats
Study subjects were adult, not aged, captive-bred female lesser dog-faced
fruit bats, Cynopterus brachyotis (N = 5; mean ± S.D. body mass = 33.6 ± 4.5 g.)
11
on loan from the Lubee Bat Conservancy (Gainesville, FL, USA). Animals were
housed in the animal care facilities of the Harvard University Concord Field
Station (Bedford, MA, USA), and provided with food and water ad libitum. All
experiments complied with ethical treatment policies and protocols, and were
authorized by the Institutional Animal Care and Use Committees of Brown
University (#67-07), Harvard University (#27-10), the Lubee Bat Conservancy
(#CP07-2), and the Division of Biomedical Research and Regulatory Compliance
of the Office of the Surgeon General of the United States Air Force (#6F050).
2.2 Kinematic recordings
We recorded the flight kinematics of each individual at a range of speeds.
To vary flight speed and to restrict filming volume, we flew each bat in a wind
tunnel with test section dimensions of 1.4 x 1.2 x 1.2 m (Harvard University
Concord Field Station Wind Tunnel). Wind tunnel performance and design
parameters have been detailed elsewhere (Hedrick et al 2002). The flights were
recorded at 1000 frames per second using three phase-locked high-speed
cameras with resolution of 1024 x 1024 pixels (Fastcam 1024 PCI; Photron USA,
Inc., San Diego, CA, USA). Further details about data collection were reported
previously (Riskin et al 2008).
Before experiments, each bat was anesthetized with isoflurane gas,
induced at 2.5% and maintained at 2% concentration. The duration of anesthesia
was brief, just long enough to place a series of eight markers on the body and
the skin of the left wing and hindlimb using a non-toxic acrylic paint marker
(figure 3A). We recorded flights at nine different speeds for each individual. The
12
flights were brief, lasting a few seconds. As the bat flew through our filming
volume, we filmed two to four complete wingbeats. Following each successful
trial, the bat rested for at least five minutes. Of the hundreds of wingbeats filmed,
we carefully selected twenty-five wingbeats for digitization that best represented
straight, steady, symmetrical, uninterrupted flight and captured a broad range of
flight speeds for each individual. Based on the three camera views, we selected
wingbeats that best exemplified station-holding, in which the body was aligned
with the wind tunnel and in which wingbeat kinematics were consistent with those
of previous wingbeats and exhibited left-right symmetry in amplitude. For
additional details concerning wingbeat cycle selection and summary statistics,
see Riskin and colleagues (2010). We used the upper reversal point of the wrist
marker to denote the beginning and end of the wingbeat cycle. The wingbeats
used in our study were performed at flight speeds ranging from 3.2 to 7.8 m/s.
To accurately reconstruct marker motion in the filmed wingbeats, the
filmed volume of the wind tunnel was calibrated using the direct linear
transformation (DLT) method (Abdel-aziz and Karara 1971). The calibration was
performed using a 35 x 35 x 28 cm calibration frame. In cases where a marker
was obscured in two or more camera views, the gap in kinematic data was filled
using a custom curve-fitting algorithm (Riskin et al 2008).
2.3 Coordinate system
Reconstructed kinematic data were transformed to a right-handed
orthogonal body-referenced linear coordinate system, with the origin at the hip
marker. The orientation of the x-axis was aligned with the shoulder and hip, the
13
y-axis was made orthogonal to the x-axis and gravity (positive = bat’s left), and
the z-axis was made orthogonal to the x-axis and y-axis (positive = dorsal) (figure
3). The anatomical planes that can be approximated by pairs of axes are
parasagittal (xz-), frontal (xy-), and transverse (yz-) planes. We marked and
digitized only the left wing because cameras were focused on a single side of the
body. By focusing on the left wing and body, we increased spatial resolution by
reducing filming volume, and increased temporal resolution by minimizing marker
occlusion with careful camera placement. We then carefully selected straight,
unperturbed flight trials for analysis because we did not measure roll of the bat,
and because adding roll as an additional degree of freedom of motion would
have added greater complexity to the analysis.
2.4 Ankle marker kinematics and statistics
We describe ankle motion relative to the hip in the body-referenced
coordinate system. We project the vector from hip to ankle onto the frontal (xy-)
and parasagittal (xz-) planes. The projected rotations about the hip, relative to
the x-axis, are described as abduction/adduction and flexion/extension
respectively. These terms are typically reserved for rotations about a single joint,
but our usage describes the combined rotations of the hip and knee joints. The
difference between the maximum and minimum values observed within a
wingbeat was designated as the amplitude of motion (figure 3). We then tested
for speed-dependent change in abduction/adduction and flexion/extension
amplitude. Prior to statistical tests, we performed outlier analysis, and then
conducted mixed-model regression, testing for speed-dependent change in each
14
amplitude. To account for variation among individuals, we included individual as
a random effect (Systat 12, Systat Software, Inc.).
2.5 Trailing edge length and orientation
To approximate the force exerted on the ankle by the wing membrane in
the transverse (yz-) plane, we calculated trailing edge length as a proxy for the
magnitude of tension in the wing membrane, and the tangent of trailing edge
shape at the ankle, as a proxy for the direction of that tensile force. As the wing
membrane elongates elastically, tension is generated internally throughout the
membrane, which is ultimately transmitted to supporting skeletal elements. For
elastic deformations, the wing membrane behaves in a spring-like manner,
requiring greater force to produce greater elongation. To calculate the trailing
edge length and shape, we fit a parabola to the locations of the ankle, the tip of
digit V, and three markers spaced evenly between these skeletal landmarks
along the trailing edge. We selected a parabola because we found that it
provided a good fit to our five markers. Seven wingbeats in which it was not
possible to digitize all trailing edge markers were excluded from this portion of
the analysis.
We calculated trailing edge length by integrating the arc length of the
parabola. To compare across individuals, we normalized length by the maximum
observed within a wingbeat. We found that maximum length was consistent
within an individual, and the timing of maximum length with respect to the
wingbeat cycle was consistent among individuals. Ideally, wing membrane length
in an unloaded configuration would be our reference length, however, this
15
measurement was less consistent both within and among individuals. We
suspect this may be in part due to the J-shaped stress-strain behavior of the wing
membrane (Swartz et al 1996), where perturbations in aerodynamic load will
produce very different changes in membrane length depending on whether the
membrane is loaded versus unloaded when the perturbation is applied. When
loaded, the wing is relatively stiff and perturbations cause small changes in
length, but when the wing is relatively unloaded, and therefore quite compliant,
the same magnitude of force perturbation will cause a much greater change in
length. Thus, under stochastic forcing, wing membrane length would vary less at
high strains.
The orientation of the wing membrane trailing edge, where it attaches to
the ankle, was used to estimate the orientation of tension acting on the ankle in
two dimensions. We could not resolve the rostrocaudal (x) component of force,
so this component was omitted from our analysis. We described the direction of
tension on the ankle in the transverse (yz-) plane by calculating the angle, θ,
formed by the trailing edge relative to the mediolateral (y-) axis (figure 3B).
2.6 Normalization of the wingbeat time-course
To compare multiple wingbeats, the time course of all trials was
normalized to percent wingbeat cycle. Transitions from upstroke to downstroke
were defined by the minimum and maximum dorsal position of the wrist. We
defined downstroke as comprising 0 to 50 percent and upstroke as 50 to 100
percent of the wingbeat cycle. Empirically, downstroke occupied 48% of the
wingbeat cycle on average.
16
2.7 Wing membrane-opposed hindlimb motion
When ankle velocity is oriented opposite to the direction of wing
membrane tension on the ankle, then the wing membrane removes power from
ankle motion (motions of the ankle help drive wing membrane motion or
deformation). Conversely, when ankle velocity and wing membrane tension are
aligned, the wing membrane adds power to ankle motion (motions of the
membrane help drive ankle movement). To estimate whether the wing
membrane aided or opposed dorsoventral ankle motion, we calculated the
percentage of time that the dorsoventral (z) component of ankle velocity and
membrane tension, sin(θ), were opposed (i.e., one was positive, while the other
was negative). We did not consider the mediolateral (y) component because we
found that membrane tension exerted significant lateral, but not medial, force on
the ankle, which is likely due to an anatomical constraint (figure 2).
3. Results
3.1 Effect of speed and individual on the amplitude of ankle marker motion
Prior to carrying out statistical analysis of the relationship among speed,
amplitude, and individual, we removed one outlier from the measurements of
flexion/extension motion. We found no effect of speed, individual, or their
interaction on the flexion/extension amplitude of ankle motion (ANOVA; speed:
F1,14 = 1.859; p = 0.194; individual: F4,14 = 0.732; p = 0.211; interaction-term
(speed × individual): F4,14 = 0.645; p = 0.640) or on the abduction/adduction
17
amplitude of ankle motion (speed; F1,15 = 0.505; p = 0.488; individual: F4,15 =
0.653; p = 0.634; speed × individual: F4,15 = 0.664; p = 0.627). The results of our
analysis did not change significantly when the outlier was included.
3.1 Ankle marker kinematics
The path of motion traced by the ankle during a wingbeat cycle varied
considerably across the 25 wingbeats analyzed (figure 4B, C). Viewed from
behind the bat, ankle motion projected on the transverse (yz-) plane is a figure-8
pattern for 19 of 25 wingbeats and an elliptical pattern for the remaining six
wingbeats. Moreover, different starting and stopping locations were not
uncommon (figure 4C). The variation in these motion patterns indicated that the
mediolateral and dorsoventral motion are not entirely coupled.
The amplitude of ankle motion showed a similar high level of variation.
Flexion/extension amplitude ranged from 23˚ to 73˚, and was on average 2.4
times greater than abduction/adduction amplitude, which ranged from 6˚ to 34˚
(figure 4A). The position of the ankle was dorsal to the hip and shoulder markers
for 84 ± 3% (mean ± s.e.m.) of the wingbeat duration, and lateral to the hip and
shoulder markers for 96 ± 2% of the wingbeat duration.
Despite variability in ankle position during the wingbeat cycle, there was a
clear relationship between the direction of ankle motion and phase of the
wingbeat cycle. The ankle moved ventrally throughout the entire downstroke and
began moving dorsally almost synchronously with commencement of the
upstroke. However, the ankle moved ventrally before the commencement of
18
downstroke. Thus, ventral motion of the ankle occured over a longer portion of
the wingbeat cycle than that of the wrist, while ankle dorsal motion occured
rapidly, over a shorter period (figure 5A). In the mediolateral direction, the ankle
tended to move laterally during downstroke and medially during upstroke (figure
5B).
3.2 Trailing edge kinematics
We found a clear relationship between wingbeat cycle timing and trailing
edge length (figure 6A). The wing membrane lengthened quickly from ca. 65% to
85% of its maximum length over the first 15% of the wingbeat and then
lengthened gradually to its maximum length over the remainder of the
downstroke. Maximum length was reached and maintained during the
downstroke to upstroke transition, between 45% and 55% of the wingbeat
duration. The trailing edge then rapidly shortened to ca. 55% of its maximum
length between 55% and 90% of the wingbeat duration, at which point the wing
membrane proceeded to elongate again prior to the beginning of downstroke.
The orientation of the wing membrane trailing edge at its ankle attachment
(trailing edge angle, θ, in figure 6B) was also tightly correlated with the timing of
the wingbeat cycle. At the beginning of downstroke, the trailing edge was
oriented approximately dorsally (close to 90º), but as the downstroke progressed
and the membrane lengthened, the orientation of the trailing edge became more
lateral. During the downstroke to upstroke transition, between 45% and 55% of
the wingbeat duration, the median observed trailing edge angle changed from ca.
15˚ to 0˚. Near 70% of the wingbeat duration, the angle of the trailing edge
19
rapidly reoriented dorsally, and it began to decrease again at 90% of the
wingbeat duration.
3.3 Interactions between wing membrane tension and ankle motion
The dorsoventral components (z) of wing membrane tension and ankle
velocity were opposed throughout 71 ± 2% of the wingbeat. During these
periods, the wing membrane removed power from ankle motion. Considering
downstroke and upstroke separately, ventral ankle velocity opposed wing
membrane tension for 91 ± 3% (mean ± s.e.m.) of downstroke duration and was
only aligned during late downstroke. In contrast, these two vectors were opposed
for 48 ± 5% of upstroke duration and were most commonly aligned during the
middle third of upstroke.
4. Discussion
The physical attachment of the hindlimb to the wing membrane allows it to
influence wing shape. Hindlimb position affects both the chord- and spanwise
shape of the wing, and in turn, three-dimensional wing conformation strongly
influences the lift, drag, and pitching moment that the bat experiences. We found
that the ankle moved roughly in phase with the wingbeat cycle: during
downstroke, the ankle moved ventrally and laterally, and during the majority of
upstroke, the ankle moved dorsally and medially, with dorsoventral motion on
average being 2.4 times greater than mediolateral motion (figure 4; figure 5). The
dorsoventral component of ankle motion opposed wing membrane tension with a
20
high degree of consistency during downstroke (figure 7). This result is not
consistent with the hypothesis that passive wing membrane tension is sufficient
to explain the observed hindlimb motion. Therefore, we propose that hindlimb
muscle activity and/or inertial effects are responsible for powering hindlimb
movements. Whatever the proximate cause, ventral ankle motion during
downstroke increases wing angle of attack and modifies wing shape. This motion
is accompanied by flexion at the hip and/or knee, which adjust the overall wing
profile as well as lift, drag, and pitch produced by the wing.
4.1 Ankle marker kinematics
Few studies have examined hindlimb movements in bat flight (but see
Lindhe Norberg and Winter 2006, Wolf et al 2010, Adams et al 2012). Our
observations extend these studies by describing hindlimb movements with
improved spatial and temporal resolution, as well as increasing the number of
observations. Our results confirm some previous observations. In C. brachyotis,
the foot swept through a large arc in the parasagittal (xz-) plane (figure 4B), as
previously observed in Glossophaga soricina, a small-bodied nectar-feeding
phyllostomid (Lindhe Norberg and Winter 2006). We also found substantial
variation in the magnitude of ankle motion among wingbeats, as previously
observed in several bat species from diverse families (figure 4A) (see figure 2 in
Wolf et al 2010; figure 2 in Adams et al 2012). However, despite little consistency
among wingbeats between ankle position and wingbeat cycle timing, there is a
relationship between dorsoventral trajectory of ankle motion and wingbeat cycle
timing that is consistent among wingbeats and individuals (figure 5).
21
4.2 Interactions between wing membrane tension and ankle motion
Ankle motion was generally opposed by tension exerted by the wing
membrane. During downstroke, the dorsoventral component of force that the
wing membrane exerted on the ankle was directed dorsally (θ > 0 in figure 6B),
yet the ankle moved ventrally (figure 5A). In a few trials, the wing membrane
exerted force in the ventral direction at the end of downstroke, but the ventral
component of force was probably very small because the wing membrane pulled
in an almost purely lateral direction during this time (figure 6B).
Ankle motion was potentially aided by wing membrane tension during
approximately half of the upstroke duration. However, during this portion of the
wingbeat cycle, the wing membrane was either taut and pulled primarily laterally
(see first half of upstroke in figure 6), or relatively slack and pulled dorsally (see
second half of upstroke in figure 6). This pattern of movement arose from the
relative timing of wing membrane shortening and wing membrane reorientation.
During downstroke, the wing membrane elongated under tension, as
aerodynamic loading increased. Then, at the initiation of upstroke, the wing
membrane rapidly shortened, and throughout this period, orientation of wing
membrane tension at the ankle was primarily lateral. As the wing membrane
approached minimum length, the orientation of tension on the ankle rapidly
reoriented dorsally. Hence, although wing membrane tension was aligned with
ankle motion during a significant period of the upstroke, the magnitude of the
dorsally-oriented force exerted by the membrane on the ankle was low (figure 7).
22
The interactions between wing membrane tension and ankle motion imply
a primarily, if not purely, resistive role of wing membrane tension on ankle
motion. For dorsoventral ankle velocity to be consistently opposed by wing
membrane tension, hindlimb muscle forces and/or inertial effects must be aligned
with ankle velocity. One or both of these forces powers dorsoventral hindlimb
movements, and membrane tension dampens them.
4.3 Wing membrane elongation
The changes in trailing edge length that we documented were surprisingly
large (figure 6A). The wing membrane elongated almost 100% of the minimum
length observed during a typical wingbeat cycle. This would approach or exceed
the failure strain observed in many studies of mechanical behavior of vertebrate
skin (Swartz et al 1996). However, bat wing membrane skin is distinguished from
typical mammalian skin by the presence of large macroscopic elastin fiber
bundles (Holbrook and Odland 1978, Crowley and Hall 1994). Elastin can more
than double its resting length before yielding (Lillie and Gosline 2002, Hoeve and
Flory 1958), and mechanical tests have revealed similarly large failure strains for
bat wing membranes (Swartz et al 1996). We therefore suggest that these
measurements are realistic, and that future studies could employ additional
markers to further resolve the shape and motion of the trailing edge.
4.4 Aerodynamic consequences of hindlimb movement in bat flight
The bat hindlimb affects wing shape both by its movement dynamics and
anatomy. The effects will be greater on portions of the wing close to the hindlimb
23
and body and decrease distally, with little to no effect in the hand-wing. This
gradient in influence is caused by the attachment of the wing membrane
proximally to the lateral aspect of the body wall, thigh and leg, and more distally,
to digit V; at these attachments, the membrane must reflect the shape of the
skeletal elements to which it is affixed. Because the hindlimb defines part of the
boundary conditions for the wing membrane, it restricts how the wing membrane
deforms in response to aerodynamic load (Song et al 2008).
Varying boundary conditions significantly affects aeromechanics of wing
membranes (Stanford et al 2008, Hubner and Hicks 2011, Waldman and Breuer
2013). However, empirically quantifying magnitude of aerodynamic effects
caused by hindlimb motion is challenging. Wing shape is a function of both the
skeletal kinematics of the wingbeat cycle and aerodynamic loading. Bat wings
reconfigure, and thus change the boundary conditions of the wing membrane,
throughout the wingbeat cycle, which change the aeroelastic interactions with
airflow (Riskin et al 2008, Song et al 2008). Attributing changes specifically to the
hindlimb is impossible without detailed measurements of wing shape and
aerodynamic force. However, large-scale aerodynamic consequences of
hindlimb posture in bats have been explored with a physical modeling approach
using a fixed, membrane-wing model with hindlimbs capable of hip flexion
(Gardiner et al 2011). Angling the hindlimbs of the model relative to its body axis,
in a manner that mimicked ventral movement of the hindlimb, increased lift and
lift-to-drag ratio and reduced pitching moment in most configurations. Increased
lift and lift-to-drag ratio were attributed to increased angle of attack and camber,
24
while the reduced pitching moment was likely a result of limb flexion increasing
wing camber and/or shifting the relative location of maximum camber toward the
trailing edge (Abbott and von Doenhoff 1959, Leishman 2000).
The chordwise location of maximum wing camber provides a reasonable
estimate of the pitching moment of a thin wing section (Abbott and von Doenhoff
1959, Leishman 2000). In bats, wing profile, including the chordwise location of
maximum camber, changes proximodistally along the wingspan. It is relatively
straightforward to determine the chordwise wing profile where the wing
membrane is constrained at the body and hindlimb, and along digit V. At these
locations along the wingspan, maximum camber occurs at a ventral-flexing joint
in the wing skeleton (figure 2). This will most likely be at either the hip or knee;
the knee is a possibility because of the evolutionary reconfiguration of the hip,
which allows the knee to move the leg and ankle to a more ventral and cranial
position (figure 1). Thus, the anatomical orientation of the hip joint in bats and the
movement dynamics of the hindlimb are important in determining the threedimensional configuration of the wing, and hence in determining the
aerodynamics of bat flight.
5. Conclusions
Because the wing membrane is attached to the hindlimb, bats can change
wing shape by repositioning the hindlimbs. We found considerable variability in
ankle motion among wingbeats, yet the pattern of ankle motion was highly
25
predictable over wingbeat cycles as a whole. The temporal patterns of ankle
motion, length-changes of the wing membrane trailing edge, and orientation of
the trailing edge relative to the ankle led us to reject the hypothesis that the
motion of the hindlimb arises passively through tension in the wing membrane.
We therefore propose that hindlimb motion is generated directly by muscle
activity and/or inertial effects from vertical body oscillations and is resisted by
membrane tension. Further study is needed to distinguish among these
alternatives. Irrespective of the proximate cause, the observed hindlimb
movement must significantly influence three-dimensional wing conformation, and
thus affect aerodynamics in complex ways.
Acknowledgements
We thank Phil Lai for illustration help, Brock Fenton for photographic
contribution, Jose Iriarte-Díaz for assistance with data collection, and many
Brown University undergraduates who assisted in digitizing for this project. We
are grateful to Attila Bergou for many helpful discussions. We also thank Allyson
Walsh and the Lubee Bat Conservancy for access to bats for videography.
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Figure 1. Modifications to the bat hindlimb skeleton. Posterior view of the
pelvis and left femur in (A) a bat and (B) a tree shrew, illustrative of the ancestral
condition for bats. The arrow indicates the orientation of the acetabulum. The arc
indicates the angle between the acetabulum and the shaft of the femur. Modified
from Simmons (1994).
29
Figure 2. The hindlimb serves as a boundary condition for the wing
membrane. (A) Posterior view of Rousettus aegyptiacus (Family: Pteropodidae)
in flight; flight kinematics in this species are similar to those of Cynopterus
brachyotis (Riskin et al 2010). A plane transects the wing membrane adjacent to
the body, femur, and tibia. The wing profile approximates the geometry of these
elements where they directly support the skin. (B) A perspective-corrected wing
profile view. The orange circle indicates the left hip location. Photo courtesy of
Brock Fenton.
30
Figure 3. Illustration of the eight anatomical markers used in this study and
the parameters measured. The orange circle indicates the left hip marker
location. (A) Lateral view from late upstroke. F/E (blue) indicates the amplitude of
flexion/extension of the ankle marker in the parasagittal (xz-) plane. (B) Posterior
view from early downstroke. Inset, below: magnified view of the wing membrane
trailing edge attaching at the ankle. θ (magenta) indicates the angle of the trailing
edge at the ankle relative to the y-axis, in the transverse (yz-) plane.
31
Figure 4. Ankle position was variable among wingbeats. Variation in ankle
motion amplitude and path. Letters α-ε each represent a separate wingbeat. The
wingbeats are assigned alphabetically from greatest to smallest dorsoventral
amplitude. (A) Angular amplitude of the ankle relative to the hip for
flexion/extension (F/E) and abduction/adduction (Ab/Ad), separated by individual.
A given letter within an individual is for a single wingbeat, across the F/E and
Ab/Ad columns. When letters overlap, they are slightly offset along the horizontal
axis. (B, C) Ankle motion over the wingbeat cycle, for a single wingbeat from
each individual. Wingbeats were selected to convey the full range of kinematic
variation. The orange circle indicates the left hip location in the insets, which
provide expanded views. (B) Lateral view from late upstroke, (C) posterior view
from early downstroke.
32
Figure 5. Direction of ankle motion was consistent among wingbeats.
Angular velocity of the ankle with respect to the hip in (A) the parasagittal (xz-)
plane, with positive indicating dorsal extension, and (B) the frontal (xy-) plane,
with positive indicating abduction. Solid line is median; aqua shaded envelope is
bounded by the first and third quartiles over N = 5 individuals, 25 wingbeat
cycles. Downstroke is shaded in gray.
33
Figure 6. Wing membrane tension varied in a consistent pattern among
wingbeats. Proxies for magnitude and orientation of forcing of the ankle by the
wing membrane through the wingbeat cycle. (A) Length of the trailing edge
normalized by maximum length, a proxy for the magnitude of force. (B) Projected
on the transverse (yz-) plane, angle of the trailing edge at the ankle relative to the
y-axis (θ), a proxy for the direction of force. Solid line is median; aqua shaded
envelope is bounded by the first and third quartiles over N = 4 individuals, 17
wingbeat cycles. Downstroke is shaded in gray.
34
Figure 7. Ankle motion consistently resisted wing membrane tension. Left
ankle motion and approximate wing membrane tension through one wingbeat
cycle in the transverse (yz-) plane (view as in figure 3B). Filled markers indicate
movement during downstroke; open markers indicate movement during upstroke.
Blue arrows indicate direction and approximate magnitude of wing membrane
tension on the ankle, at 10% intervals across the wingbeat cycle. Black arrows
indicate direction of ankle motion. Orange circle indicates location of left hip.
Data is from individual 4, wingbeat β.
35
Chapter 2
Membrane muscle function in the compliant wings of bats
Jorn A Cheney1, Nicolai Konow1, Kevin M Middleton3,
Kenneth S Breuer2,1, Thomas J Roberts1, Erika L Giblin1,
and Sharon M Swartz1,2
1. Department of Ecology and Evolutionary Biology, Brown University, Providence, RI 02912
2. School of Engineering, Brown University, Providence, RI 02912
3. Department of Pathology and Anatomical Sciences, University of Missouri School of Medicine,
Columbia, MO 65212
Abstract
Unlike flapping birds and insects, bats possess membrane wings that are
more similar to many gliding mammals. The vast majority of the wing is
composed of a thin compliant skin membrane stretched between the limbs, hand,
and body. Membrane wings are of particular interest because they may offer
many advantages to micro air vehicles. One critical feature of membrane wings is
that they camber passively in response to aerodynamic load, potentially allowing
for simplified wing control. However, for maximum membrane wing performance,
tuning of membrane structure to aerodynamic conditions is necessary. Bats
possess an array of muscles, the plagiopatagiales proprii, embedded within the
wing membrane that could serve to tune membrane stiffness, or may have
alternative functions. We recorded the electromyogram (EMG) from the
plagiopatagiales proprii muscles of Artibeus jamaicensis, the Jamaican fruit bat,
in flight at two different speeds and found that these muscles were active during
downstroke. For both low- and high-speed flight, muscle activity increased
between late upstroke and early downstroke and decreased at late downstroke.
Thus, the array of plagiopatagiales may provide a mechanism for bats to
increase wing stiffness and thereby reduce passive membrane deformation.
These muscles also activate in synchrony, presumably as a means to maximize
force generation, because each muscle is small and, by estimation, weak. Small
differences in activation timing were observed when comparing low- and highspeed flight, which may indicate that bats modulate membrane stiffness
differently depending on flight speed.
36
1. Introduction
The evolution of bats, the only mammals capable of powered flight, has
led to unique wing morphologies, distinct from those of birds and insects.
Although mechanical function has been dramatically modified during bat
evolution, the component tissues that comprise all mammalian limbs form the
highly derived wings. Bat wings are framed by proportionally elongated bones
with many joints, controlled by skeletal muscles, and covered by skin that
provides the aerodynamic surface. Large expanses of compliant skin and muscle
between slender and poorly mineralized bones together result in a structural
design that lacks the intrinsic stiffness of bird and insect wings (Corning and
Biewener 1998, Combes and Daniel 2003, Swartz and Middleton 2008) and
morphs dramatically in flight.
Morphing in bat wings, although controlled in part by movements of wing
bones at joints, is significantly influenced by passive interactions between the
wing and the aerodynamic forces acting on it. Bat wings behave as membranes
due to the thinness and high compliance of wing skin relative to overall size of
the airfoil (Song et al 2008). The skin, which composes the majority of the wing
area, varies in thickness between 27 and 270 µm across a diversity of families
and body sizes (Studier 1972, Sokolov 1982, Crowley and Hall 1994, Swartz et al
1996). The elastic modulus of wing skin is approximately 3 MPa tested spanwise
to 30 MPa chordwise (Swartz et al 1996), approximately two to three orders of
magnitude less than that of insect wing cuticle (0.3 to 10.9 GPa; Smith et al
2000) or feather keratin (1.78 to 2.76 GPa; Bonser and Purslow 1995). Because
37
wing skin is thin and compliant, it has negligible bending stiffness (Song et al
2008). Thus, when a bat wing membrane experiences aerodynamic pressure, the
skin billows and deforms, increasing camber in the wing until tension generated
by deformation supports the pressure (Waldman and Breuer 2013).
Mechanically, this process is analogous to the inflation of an elastic balloon.
The musculoskeletal system of bat wings affords the potential to adjust
membrane deformations in several ways. The boundary of the membrane is set
by the articulated wing skeleton, which dictates membrane position and
orientation. In addition, a group of unusual muscles that might directly modulate
wing shape through interaction with the compliant skin are embedded within the
membrane. This array of long slender muscles running in the chordwise direction
is the plagiopatagiales proprii, henceforth referred to as plagiopatagiales
(singular: plagiopatagialis). These muscles have been hypothesized to directly
influence wing shape, in part because they both originate from and insert into the
connective tissues of the wing membrane skin, and, notably, not onto the wing
skeleton (Vaughan 1959, Gupta 1967, Quay 1970, Norberg 1972, Holbrook and
Odland 1978). However, in the absence of direct information concerning the
activity of these muscles, their functional significance remains speculative.
The architecture of the plagiopatagiales presents some clues to their
functional capacities and limitations in modulating three-dimensional shape in an
aerodynamically-loaded membrane (figure 1a). In the study species, Artibeus
jamaicensis, a medium-sized frugivorous bat, there are 27 plagiopatagiales in
each armwing. Each muscle belly is long relative to the wing chord, parallel38
fibered and has a relatively small cross-sectional area (mean length: 0.6 chord
lengths; approximate width x depth: 0.35 x 0.2 mm). Thus, the geometry of a
single plagiopatagialis muscle is well suited to large excursions but not to
generation of substantial force (Biewener 1998). The plagiopatagiales as a group
may be capable of generating considerable force if all muscles activate
synchronously, although the functional significance of the muscles’ considerable
length is not clear. There are no reports of obvious chordwise shortening of the
wing membrane in flight, which might be expected given their length.
Alternatively, some relatively small muscles in vertebrates are thought to function
primarily as stretch receptors rather than to generate force (Peck et al 1984).
Therefore, the plagiopatagiales may serve to provide sensory feedback over
large expanses of the wing instead of, or in addition to, playing a role in
controlling wing camber.
To better understand the role of the plagiopatagiales muscles in flight, we
used electromyography (EMG) to directly measure patterns of activation of
individual plagiopatagialis muscles during wind tunnel flight of A. jamaicensis.
Our aim was to test two hypotheses: 1) the plagiopatagiales are active in steady
flight and thus do not serve exclusively as stretch receptors; and 2) if the
plagiopatagiales are active during steady flight, multiple muscles activate
synchronously to increase force production, given the small cross-sectional area
of each muscle. Finally, to place plagiopatagiales function into the context of
wing membrane morphing, we related muscle activity to the wingbeat cycle and
flight speed. Based on our results, we developed a simple 1D model of
39
plagiopatagiales function to address the role of muscle and skin architecture and
the potential role of muscle length during active lengthening and isometric
contractions.
2. Materials and Methods
2.1 Bats and flight training
Three captive-bred male Jamaican fruit bats, Artibeus jamaicensis
(Chiroptera: Phyllostomidae), were housed in the Animal Care Facility at Brown
University and provided with food and nectar ad libitum under a reversed 12:12 h
dark:light cycle. All subjects underwent two weeks of wind tunnel training prior to
instrumentation and data collection. Following training, all animals flew
consistently within the wind tunnel. All experiments were conducted in
accordance with approved protocols (Brown University IACUC, Division of
Biomedical Research and Regulatory Compliance of the Office of the Surgeon
General of the U.S. Air Force).
2.2 Wind Tunnel
All flights occurred in a closed-loop wind tunnel with working section of 0.6
x 0.8 x 3.8 m (height x width x length). Mesh barriers limited test section length to
1.3 m for videography (see below) and to provide landing surfaces for bats
following each flight trial. Further wind tunnel characteristics are described by
Hubel and colleagues (2010).
40
2.3 Design and implantation of EMG electrodes
The bipolar electrode design was guided by the challenge of measuring
signals in very small muscles embedded in a rapidly flapping membrane. Bipolar
electrodes were constructed from 17 cm strands of 50.8 µm Evanohm alloy
(AMAX Specialty Metals Corp., Orangeburg, SC) with 615 ohms/m resistance.
For this electrode design, 1.5 mm of wire was bared along the length, not at the
tip, to form the electrode pole (figure 1c). The electrode was passed through a
2.5 x 1.5 mm rectangle latex film (thickness <0.75 mm, McMaster-Carr) so that
the latex reached the proximal edge of the pole, where it was affixed using
cyanoacrylate adhesive.
Reliably implanting EMG electrodes into the small plagiopatagiales proved
difficult. To maximize the rate of implantation success, we modified the approach
of Swartz and colleagues (2004) who sewed electrodes through the wing
membrane and used two sheets of latex to sandwich the membrane in order to
prevent the electrode from losing contact with the muscle.
For electrode implantation in an anesthetized animal, we pierced the wing
membrane and mid-belly of the muscle with a 33 Ga hypodermic needle (outer
diameter: 210 µm), entering from the ventral wing surface. This approach allowed
the electrode wire to be threaded into the bevel of the needle. The needle and
electrode were then retracted through the wing membrane until the affixed latex
square made contact with the dorsal membrane surface. Then, a second latex
rectangle was threaded onto the electrode from the ventral side and glued in
41
place, adjacent to the membrane. Finally, a small dab of electrode gel (SignaGel;
Parker Laboratories, Inc., Fairfield, NJ) was placed on the bared wire section to
enhance the contact between muscle and electrode. This process was then
repeated with the other wire strand to produce a bipolar electrode implant.
Finally, we affixed the ends of the electrode wires using a latex sheet and
cyanoacrylate adhesive. Electrode interpolar spacing was approximately 2 mm,
along the long axis of the muscle.
2.4 Camera setup and kinematic reconstruction
We recorded flight kinematics at 500 frames per second at 1024 x 1024
pixel resolution using three phase-locked high-speed cameras (Fastcam 1024
PCI; Photron USA, Inc., San Diego, CA). All cameras were placed beneath the
wind tunnel test section to image the ventral surface of the bat through optical
glass. Ventral oblique views were selected to minimize occlusion of markers
used to calculate 3D flight kinematics.
To calibrate the recorded volume, we determined intrinsic and extrinsic
camera properties using a series of 27 images of a 6 x 8 checkerboard taken
before each electrode implantation (Zhang 2000). From this calibration, 3D
positions of the wrist and sternum markers were calculated using Kalman filter
estimation by software described by Bergou and colleagues (2011).
2.5 Experimental protocol
Prior to electrode implantation, bats were anesthetized with isoflurane gas
(2%, 0.6 L/min O2 flow rate), and during implantation body temperature was
42
maintained using a heating pad. The plagiopatagiales muscles could be
visualized clearly by backlighting the membrane, and no incisions were
necessary. Following implantation (see above), electrode wires were secured
along the forearm using liquid latex (Osto-bond; Montreal Ostomy, VaudreuilDorion Quebec, Canada) and to tufts of fur on the back using cyanoacrylate
adhesive and small squares of latex film (figure 1b). Using a micro-connector
(ACH connector; JST, Waukegan, IL), the electrodes were then connected to a
lightweight, shielded, multi-stranded cable (#NMUF4/30-4046 J; Cooner Wire,
Chatsworth, CA), which exited the wind tunnel through an opening in the ceiling.
For kinematic analysis, a series of non-toxic acrylic paint markers was placed on
the sternum, wrist, wingtip, and wing membrane, as well as along the one or two
plagiopatagiales that were implanted. Each marker weighed ~0.5 mg, or 0.001%
subject body mass. Animals were anesthetized for approximately one hour and
allowed approximately 40 minutes to recover prior to flights.
We recorded three to four flights from each individual at two different wind
tunnel speeds (table 1); initial speed was pseudo-randomized. We designate
wind tunnel speeds of 1.0 m/s as low speed, and between 4 and 5 m/s as high
speed, although this species in nature can achieve higher flight speeds (Morrison
1980). After accounting for speed of the animal relative to flow in the wind tunnel
at low and high wind speed, average flight speed was 2.2 and 5.5 m/s,
respectively. Animals were held gently between trials to prevent electrode
damage.
43
We confirmed successful implantation by stimulation of the muscle
through the electrode both before and after data collection. If stimulation elicited
a visually observable contraction of the muscle, then we concluded that the
electrodes were well placed. Based upon this criterion, we collected EMG data
twice from a single plagiopatagialis muscle and twice from two plagiopatagiales
muscles simultaneously (table 1). We used three individuals, with one individual
recorded from twice. That individual had a rest period of 15 days, and we
recorded from different plagiopatagialis muscles in each trial. One individual
pulled out the electrode following high-speed recordings, prior to low-speed
recordings. In the two instances where two muscles were recorded from
simultaneously at both speeds, the recording sites were approximately 4 and 11
mm apart. The recorded muscle pairs were separated by at least two muscles,
and the muscles recorded from were those with the greatest diameter.
2.6 Signal processing
EMG signals were amplified 2000x with a 100-1000 Hz bandpass and a
60 Hz notch filter engaged (P511k; Grass Instruments, Warwick, RI). The signals
were A/D converted (NI-DAQ 6009; National Instruments, Austin, TX) and
sampled at 6000 Hz using a custom script in MATLAB (Mathworks, Natick, MA).
To minimize electrical noise, the recording PC laptop and A/D converter were
battery powered. EMG signals were synchronized with kinematics by recording
the TTL end-trigger from the cameras.
2.7 Kinematic analysis
44
We defined wingbeat cycles by digitizing points on the sternum and wrist,
and calculating vertical motion of the wrist relative to the sternum from the 3D
coordinates. To compare EMG activation across multiple wingbeats and speeds,
the time courses of downstroke and upstroke were normalized to their duration.
We defined downstroke and upstroke as each occupying half of the wingbeat
period. This definition closely approximates what we observed empirically: on
average, downstroke occupied 49.5% and 48.3% of the wingbeat cycle at low
and high speed, respectively.
2.8 Signal analysis
We only analyzed data recorded during wingbeats of steady flight. We
defined steady flight as a smooth, repeatable, cyclic motion of the wrist with
consistent amplitude (figure 2). Cycles that did not meet these criteria were
excluded from analyses. This process also excluded wingbeats occurring during
landing, turning, and interactions with the EMG cable.
Before analysis of muscle activity patterns, each EMG signal was
processed using a custom written MATLAB script. The signal was bandpass
filtered between 100 and 750 Hz and rectified. From the rectified signal, the
linear envelope of the signal was calculated by applying a low-pass filter of 55
Hz, approximately five times wingbeat frequency. We subtracted baseline noise,
defined as signal below the 5th percentile from all signals, and used signal at the
95th percentile to normalize signal amplitude; this reduces effects of non-periodic
45
large amplitude transients. Muscle activity was defined as EMG intensity greater
than 33% of normalized peak amplitude.
To determine degree of synchronicity between pairs of plagiopatagialis
muscles, we cross-correlated EMG signal envelope pairs to determine the phase
shift required to reach maximum correlation. Because the overall shape of the
two waveforms forms the basis for comparison, this method provides a reliable
estimate of EMG synchronicity (Loeb et al 1987, Wren et al 2006, Konow et al
2010). Wingbeats were treated as individual samples and the maximum
permissible phase shift was ± one half-wingbeat. We used t-tests to address
whether phase shifts between the two muscle activation profiles differed between
two individuals and if the phase shift differed from zero. Although each wingbeat
has the potential to influence the next, wingbeats were treated as individual
samples due to our small sample size.
To address the effect of speed on plagiopatagiales activity, we compared
the two activation patterns. To compare relative timing of muscle activity in
relation to the wingbeat cycle, we cross-correlated the distributions at low and
high speed, and determined the phase lag at maximum correlation.
3. Results
3.1 EMG resolution
46
The signal-to-noise ratio of the EMG linear envelope, calculated as the
ratio of the signal at the 95th to that at the 5th percentile, averaged 7.3 ± 0.8
(mean ± s.e.m.; figure 2). Some trials showed non-periodic large amplitude
transient bursts in the EMG that were likely noise due to flapping and cable
movement. To be conservative, we retained these transients in our analyses,
because the frequency contained within these bursts contained the same
bandwidth as typically observed in bipolar fine-wire EMG.
3.2 Plagiopatagiales activation pattern
Plagiopatagiales muscles were most frequently active during downstroke
at both flight speeds (figure 3). We did not detect activity during every wingbeat,
but plagiopatagiales EMG was above threshold during the middle half of
downstroke in 58% of sampled wingbeats. EMG activity was sometimes
observed during upstroke. This was most frequent at the stroke transitions and
least frequent during the second quarter of upstroke, where EMG only was above
threshold in 10% of the wingbeats.
3.3 Effect of speed on kinematic timing and plagiopatagiales activity
Timing of wingbeat kinematics changed slightly between high and low
speed, but not to an extent that we considered meaningful for our analysis. At
high speed, mean wingbeat duration was 14% greater (48 vs. 41 ms), and
downstroke ratio was lower (48.3% vs. 49.5%) than at low speed. These
differences, although potentially biologically meaningful, were considered
47
relatively small, and further exploration of their possible functional significance is
left to future investigation.
High- and low-speed flights demonstrated similar plagiopatagiales activity
distributions, however, plagiopatagiales activity occurred earlier in the wingbeat
cycle at high speed (figure 3). Peak cross-correlation of EMG distributions for
low- and high-speed flight was found when the high-speed EMG distribution
preceded the low-speed EMG distribution by 3 ms, or 7% of the wingbeat cycle
(r2=0.95).
3.4 Synchronization among plagiopatagiales
Recordings of EMG from two plagiopatagialis muscle bellies in a single
individual indicated a strong pattern of synchronous activation (figure 4). No
difference in synchronicity was observed between experiments with muscle pairs
4 vs. 11 mm apart (two-sample t-test: t74=.65; p=0.52). Therefore, we pooled
phase shift data from both experiments, and determined that mean phase shift
between muscles was not significantly different from zero (one-sample t-test:
t75=-0.97; p=0.34).
4. Discussion
The goal of this study was to determine if bat wing membrane deformation
is purely passive or if the wing membrane is actively deformed by the array of
embedded plagiopatagiales muscles. Several authors have suggested that these
48
muscles function to control wing shape (Vaughan 1959, Norberg 1972, Holbrook
and Odland 1978). However, the small cross-sectional area of individual
plagiopatagiales limits the force generating capability of each muscle, so
synchronous activity of multiple muscles would likely be required to resist
aerodynamic loading. Since the articulated wing skeleton and non-linear stressstrain mechanics of wing membrane skin might provide bats with substantial
control of camber without muscle activity (Swartz et al 1996), it is also possible
that these muscles serve a purely sensory function.
We found regular, repeated patterns of plagiopatagiales activation during
steady flight at both low and high flight speeds (figures 2, 3). The observation of
cyclic and synchronous EMG activity during flight supports the hypothesis that
these muscles are involved in active force production and do not serve solely in a
sensory capacity. However, stretch reception could nonetheless be one of their
important functions. Further exploration of plagiopatagiales spindle density will
contribute to evaluating this possibility.
We observed greatest plagiopatagiales activity during downstroke for both
low- and high-speed flight. However, the exact timing and distribution of activity
varied between speeds. As hypothesized, simultaneous recordings from two
plagiopatagialis muscles showed highly synchronous activity (figure 4). This
observation suggests that when evaluating the potential force generating
capability of the plagiopatagiales in other bat species, where the number and
size of individual plagiopatagialis muscles differ (Gupta 1967), it may be more
49
appropriate to consider the combined force of the array, rather than the average
individual unit.
Our results are consistent with the hypothesis that the plagiopatagiales
muscles actively modulate wing membrane shape. Likely key determinants of
this behavior include the temporal patterns of plagiopatagiales activation, the
magnitude of force production by the muscle array, and the nature of interaction
between the plagiopatagiales and the wing membrane skin. These ideas are
further discussed below.
4.1 Limits to EMG resolution
We determined the distribution of plagiopatagiales muscle activity over the
course of a wingbeat cycle (figure 3) instead of quantifying the timing of activity
onset, duration and offset. We chose this method of analysis because significant
baseline noise made it difficult to identify distinct temporal landmarks of EMG
timing. We suspect that this noise resulted from cable vibrations induced by wing
flapping. When bats were stationary, electrical noise was well below the baseline
observed during flight. Therefore, we note that a potential caveat in our study is
the inability to rule out the possibility that the plagiopatagiales might be active
throughout the entire wingbeat cycle but are activated more intensely during
certain portions of the wingbeat.
4.2 Plagiopatagiales activation pattern
Our results indicate that, for both low- and high-speed flight, muscle
activity increases between late upstroke and early downstroke, then decreases at
50
late downstroke and remains at a low level through early upstroke (figure 3). This
activation pattern is consistent with the hypothesis that plagiopatagiales reduce
passive membrane deflections in A. jamaicensis.
Other evidence suggests that the pattern of plagiopatagiales muscle
activation we observed in Artibeus jamaicensis could be characteristic of many, if
not all, bat species. A decrease in plagiopatagiales force during late downstroke
to early upstroke was predicted by Song (2013), based on studies of a distantlyrelated bat species, Cynopterus brachyotis (Pteropodidae). Observations of C.
brachyotis revealed that wing membrane surface area increased during late
downstroke to early upstroke, although the elbow flexed and aerodynamic force
decreased during this portion of the wingbeat cycle, and both factors would tend
to decrease armwing membrane area. Song (2013) reasoned that an increase in
wing membrane surface area at a time of decreasing force indicated a decline in
wing membrane stiffness, possibly due to the relaxation of the plagiopatagiales.
This indirect line of evidence is consistent with the hypothesis that the observed
timing of plagiopatagiales relaxation could be similar in A. jamaicensis and C.
brachyotis, species whose evolutionary relationship is distant within bats (Teeling
et al 2005), and that this therefore may be a widespread pattern. Alternatively,
this pattern of muscle activity timing could have evolved multiple times
independently; further study of a greater diversity of bats will be required to
resolve this issue.
Plagiopatagiales activity increased at the upstroke to downstroke
transition, prior to the time of maximum membrane tension as estimated by
51
timing of maximum circulation, determined experimentally from wake
measurements of other bat species (Hubel et al 2010, 2012, Muijres et al 2011).
This raises the possibility that the muscles are actively lengthened early in the
wingbeat, which would result in high forces. Alternatively, muscles may shorten
early in the wingbeat, before significant tension is developed, to strain and tense
the wing membrane. If this shortening was followed by a period of isometric
contraction during wing loading, the process would be mechanically analogous to
establishing membrane pre-strain, the effect of which has been studied for
compliant wings (Song et al 2008, Rojratsirikul et al 2010, Timpe et al 2013,
Waldman and Breuer 2013), where pre-strain refers to membrane strain present
prior to aerodynamic loading.
4.3 Effect of speed on plagiopatagiales activity
We found that changes in EMG activity timing were associated with
changes in flight speed. In contrast to animals that walk and run, flying bats do
not demonstrate unambiguous gait transitions as locomotor speed increases
(Biewener 2003). Instead, flight kinematics change gradually with speed (Hubel
et al 2010, 2012, Riskin et al 2010, Wolf et al 2010, von Busse et al 2012). One
might expect a similarly graded response in plagiopatagiales activity patterns
because the aerodynamic pressure, which causes wing membrane deformation,
gradually increases with flight speed. For a passive compliant membrane wing, if
pressure distribution remains relatively constant, then increased aerodynamic
pressure is expected to result in increased camber. During high-speed flight,
plagiopatagiales activity occurred 7% earlier in the wingbeat cycle than during
52
low-speed flight. The earlier onset of activity might serve to resist passive camber
by providing increased membrane pre-strain (figure 3).
4.4 Plagiopatagiales force production
How the plagiopatagiales affect wing membrane mechanics depends on
whether they shorten, actively lengthen, or remain isometric. The contractile
behavior depends upon the magnitude of muscle force relative to membrane
tension. Active lengthening occurs if membrane tension is greater than muscle
force, while the other behaviors can only occur if plagiopatagiales force
production matches or exceeds membrane tension. Although neither in vivo
muscle force nor membrane tension is known, we can estimate both values to
assess whether the peak muscle force is of the correct order of magnitude to
allow for muscle shortening or isometric contraction. Peak specific tension in
vertebrate muscle is typically around 0.3 MPa (Wells 1965, Ker et al 1988). A.
jamaicensis has 54 plagiopatagiales and, based on physiological cross-sectional
area, we estimate that this array generates a total force equivalent to 2.3 body
weights in isometric contraction. Estimating the membrane tension requires a
number of simplifying parameterizations and assumptions. We used the
observed value of approximately 10% wing camber in flying pteropodid bats
(Riskin et al 2010). Furthermore, we assumed that only downstroke is
aerodynamically active, so average aerodynamic load is two times body weight.
Using these values in the theory developed by Song and colleagues (2008) and
Waldman and Breuer (2013) we estimate a membrane tension of 2.8 times body
weight, comparable to the above estimate of force generated by the
53
plagiopatagiales. Thus, despite the small size of the muscles, it is plausible that
the plagiopatagiales are capable of concentrically or isometrically contracting
against membrane tension.
4.5 Plagiopatagiales-wing membrane skin model
As researchers have sought to interpret the functional significance of the
distinctive features of the bat wing, it has been suggested that the
plagiopatagiales play a role in tensing the wing membrane and controlling wing
shape (Vaughan 1959, Norberg 1972, Holbrook and Odland 1978). Studies of
non-biological membrane wings have found that increasing membrane stiffness
or pre-strain decreases wing camber and lift (Song et al 2008, Rojratsirikul et al
2010, Timpe et al 2013). However, depending on aerodynamic conditions such
as Reynolds number, increased stiffness can also lead to increases in
parameters that affect wing efficiency, such as lift-to-drag ratio (Hays et al 2012).
To better understand the mechanical significance of plagiopatagiales activation,
we consider wing membrane stiffness when the muscles are active relative to
when they are passive under two scenarios: 1) plagiopatagiales undergoing
active lengthening (figure 5c, left); and 2) plagiopatagiales shortening to a
preferred length prior to tensile loading and maintaining this length (figure 5c,
right). Active lengthening occurs when membrane tension exceeds muscle
isometric force, whereas constant muscle length occurs when membrane tension
is equal to muscle isometric force.
54
In both scenarios, we consider how wing membrane stiffness changes as
a function of plagiopatagiales behavior. More complicated aeroelastic couplings
among plagiopatagiales activity, membrane stiffness, wing camber, and lift are
not considered here. Our simplifying assumptions for this 1D model are that: 1)
muscle passive stiffness is negligible relative to wing membrane stiffness; 2) skin
thickness is constant along the chord length; 3) elastic behavior of the membrane
tissue is linear; and 4) membrane tension is constant.
Wing membrane architecture places the plagiopatagiales both in series
and in parallel with the wing membrane, as the ventral and dorsal wing
membrane skin surround each muscle. In a chordwise slice of the wing
membrane under aerodynamic load, the wing membrane skin strains and
generates tension until it supports the aerodynamic load (figure 5a, b). Under
isometric as well as active lengthening conditions, wing membrane strain is
heterogeneous and will be less where skin is in parallel with the muscle (skin
overlying the muscle) than where skin is in series with muscle (anterior and
posterior to the muscles, toward the leading and trailing edge of the wing). This
strain reduction increases the effective Young’s modulus of the wing membrane.
In our 1D model, we calculate the change in Young’s modulus for the passive
wing membrane relative to the membrane-muscle composite during active
lengthening as:
Epassive
lpp
Tpp
=1−
×
Eactive
lc Tmem
and during isometric contractions as:
55
Epassive
lpp
εpp
= 1 − (1 −
);
Eactive
lc
εpassive
where
Epassive
Eactive
is the relative change in modulus when the muscles are inactive
relative to active;
lpp
lc
Tpp
is plagiopatagialis length relative to chord length; T
mem
tension generated by the muscle relative to the membrane tension; and
is
εpp
εpassive
is
muscle strain prior to isometric loading, relative to membrane strain without
muscle or in series with the muscle (figure 5c). This simplified formulation
provides a provisional interpretation of the effect of plagiopatagialis activity on
wing membrane mechanics. Further, the model highlights the role muscle length
plays in the function of the plagiopatagiales; relative muscle length is a significant
factor in modulating membrane stiffness in both contractile scenarios. This
observation is important because, although muscle length is not directly related
to muscle force, increases in relative muscle length reduce the amount of wing
membrane in series. Long muscles tend to generate large excursions, but in the
case of the plagiopatagiales, longer muscles will also tend to reduce wing
membrane strain. This analysis suggests that the answer to the question “Why
are the plagiopatagiales muscles so long?” may relate to minimizing the nonactuated portion of the wing membrane, which, in the absence of muscle would
strain substantially more than observed.
4.6 Broader implications
Bat wing membranes can respond mechanically to aerodynamic forces
through passive shape adaptation. However, in at least some flight behaviors,
56
such as steady forward flight, these deformations are not entirely passive. The
insertion of the plagiopatagiales into the connective tissue scaffolding of the wing
membrane skin suggests that these muscles act to modulate membrane stiffness
or tension, resulting in decreased wing camber. Modulating wing stiffness may
provide near-instantaneous tuning of otherwise passive wing membrane
properties to suit highly variable aerodynamic regimes (Hays et al 2012, Timpe et
al 2013). Under certain conditions, membrane wings enable softer stall at higher
angles of attack than rigid wings, and resist gusts due to their shallow lift curve at
high angles of attack, often passively, requiring no additional control (Lian and
Shyy 2007, Song et al 2008, Stanford et al 2008). Modulation of wing membrane
stiffness through activity of embedded muscles represents a relatively simple
control mechanism by which bats may be able to operate in a wider range of
conditions, resist excessive amounts of camber at high dynamic pressure, and
possibly allow for a thinner and lighter wing membrane, thus reducing the inertial
cost of flapping.
We anticipate that the discovery of muscle activity within the wing
membrane will inspire renewed efforts to integrate passive dynamics of
membrane wings (Song et al 2008, Rojratsirikul et al 2010, Timpe et al 2013)
with active membrane deformation (Pawlowski et al 2003, Hays et al 2012) and
sensation (Xu et al 2003). Although this challenge is significant, biological
models, of which bat wings may be exemplars, could inform development and
design.
57
5. Conclusions
During the downstroke of steady flight, bats activate the plagiopatagiales
proprii, a group of muscles embedded within the wing membrane. Recordings
from pairs of plagiopatagiales suggest synchronous activation. This pattern is
consistent with expectations based on the force-generating capabilities of
individual muscles, any one of which would have little effect relative to
aerodynamic load on the wing compared with the force that can be generated by
the whole muscle array functioning together. The evidence of activation in this
muscle array during downstroke is consistent with, and necessary for, the
hypothesis that these muscles influence wing membrane mechanics by
modulating membrane stiffness or pre-strain. Periodic muscle activation refutes
the hypothesis that these muscles serve exclusively as stretch receptors, but
stretch reception could still be critical to their function.
The plagiopatagiales were active during steady flight at slow and
moderately high speed. The overall activation patterns did not differ dramatically,
but plagiopatagiales activation occurred earlier during downstroke at the higher
speed. This result suggests that plagiopatagiales activity is likely speeddependent.
Activation of embedded musculature as a control mechanism in a
compliant membrane wing is intriguing in the context of membrane wing
aerodynamics and aeromechanics. Bats and micro air vehicles are expected to
perform well in a wide range of highly variable flow conditions. Passive dynamics
58
of membrane wings have great potential benefits (reviewed in Stanford et al
2008), but without the capacity to modulate pre-strain or stiffness, a given
compliant membrane wing will operate most effectively only under a limited range
of aerodynamic conditions (Timpe et al 2013). Based on our results, we propose
that bats modulate wing membrane pre-strain/stiffness to extend the range of
aerodynamic conditions under which they can achieve high flight performance.
Acknowledgements
We thank Rye Waldman for many helpful discussions concerning membrane
wing mechanics. We are also grateful to Cosima Schunk for technical assistance.
We appreciate Brown University undergraduates, especially Rosalyn PriceWaldman, for assistance with digitizing. This work was supported by the Air
Force Office of Scientific Research (F49620-01-1-0335 to SMS and KSB and
FA9550-12-1-0301 to SMS and TJR) and the National Science Foundation (IOS
1145549 to SMS).
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62
Table 1. Summary of successful experiments. We recorded from plagiopatagiales
of three individuals. Each bat had one or two muscles recorded from, and
performed three or four flights at two different wind speeds. Average flight speed
was 2.2 m/s at the lower wind speed and 5.5 m/s at the higher wind speed. The
wingbeats column lists total number of wingbeats sampled at each flight speed per
experiment.
muscles
recorded
bat
1
2
3
1
2
2
1
flights
2.2 m/s
3
4
3
0
5.5 m/s
3
4
4
3
63
wingbeats
2.2 m/s
13
21
20
0
5.5 m/s
26
17
18
16
Figure 1. (a) Illustration of lateral view of flying bat at beginning of downstroke indicating
location and orientation of the plagiopatagiales muscles. Dashed rectangle is location of
plagiopatagiales photo, below, from a large pteropodid bat (Eidolon helvum; ~275 g). (b)
Artibeus jamaicensis experimental subject following EMG electrode implantation. The
electrode was anchored to the back and forearm. At the forearm, the electrode wire was
looped to allow for strain-free displacement. During experiments, the electrode was
connected to a shielded cable running to an amplifier. Dashed rectangle is location of
higher magnification photo below. (c) Design of EMG electrode as implanted in a wing
cross-section.
64
Figure 2. Measurements from a representative flight trial. Wingbeat cycle is defined by
vertical position of the wrist; gray bars indicate downstroke. EMG from plagiopatagiales
were amplified 2000x and bandpass filtered (Raw EMG). The signal was further filtered
and rectified (Filtered/rectified EMG) before it was low-pass filtered and normalized to
produce the EMG envelope (Processed EMG). Activity is indicated by EMG envelope
being greater than threshold (horizontal dashed line). Data collected in the diagonal
striped region was excluded from analysis because of wingbeat unsteadiness, as
defined by wrist motion.
65
Figure 3. Rose plot of activity distribution over the wingbeat cycle at low- (left) and high(right) speed flight (mean 2.2 and 5.5 m/s, respectively). Column height indicates
percentage of wingbeats that displayed activity during that portion of the wingbeat cycle.
Gray columns indicate downstroke.
66
Figure 4. Recording of pairs of plagiopatagiales show little variation in phase, and thus
synchronous activation. Histogram of lag between paired activation of plagiopatagiales.
Lag is calculated as percent wingbeat cycle. Average lag was not significantly different
from zero (p=0.34).
67
Figure 5. Schematic of hypothesized plagiopatagiales function. (a,b) Chordwise wing
membrane cross-section containing a plagiopatagialis muscle at (a) rest, (b) under
aerodynamic load. (c) Plagiopatagiales function in two 1D mechanical scenarios. Wing
skin is modeled as a spring. The models begin unloaded, as in (a), and end in a loaded
state, as in (b), but differ based on muscle contractile behavior. Under the active
lengthening scenario (left), muscle is active, but membrane tension is greater than
muscle force. Both muscle and skin stretch, but skin anterior and posterior to muscle (in
series) stretches more than skin ventral and dorsal (in parallel). Under the concentric
then isometric contraction scenario (right), muscle undergoes a concentric contraction,
prior to substantial aerodynamic loading, and then maintains constant length by
matching its tension to membrane tension. The initial concentric contraction does not
allow skin ventral and dorsal to the muscle (in parallel, not shown) to stretch.
68
Chapter 3
A wrinkle in flight: the role of elastin fibers in the
mechanical behavior of bat wing membrane
Jorn A Cheney1, Nicolai Konow1, Andrew Bearnot1, and
Sharon M Swartz1,2
1. Department of Ecology and Evolutionary Biology, Brown University, Providence, RI 02912
2. School of Engineering, Brown University, Providence, RI 02912
Abstract
Bats fly using a thin wing membrane composed of compliant anisotropic
skin. Wing membrane skin deforms dramatically as bats fly, and the threedimensional configurations depend in large part on the mechanical behavior of
the tissue. Large macroscopic elastin fibers are an unusual mechanical element
found in the skin of bat wings. We characterize the fiber orientation and
demonstrate that elastin fibers are responsible for the distinctive wrinkles in the
surrounding tissue of the membrane, which we refer to as matrix. Following this,
uniaxial mechanical testing is performed on wing membrane parallel and
perpendicular to elastin fibers to study the contribution of elastin and the
surrounding matrix to mechanical behavior. We find that matrix is isotropic within
the plane of the membrane and responsible for bearing load at high stress,
wheras elastin fibers are responsible for membrane anisotropy and only provide
notable contribution to load bearing at very low stress. Further, the architecture of
elastin fibers is what provides the extreme extensibility of the wing membrane.
We relate these findings to flight with membrane wings and discuss the
aeromechanical significance of elastin fiber pre-stress, membrane excess length,
and how these parameters may aid bats in resisting gusts and preventing
membrane flutter.
69
1. Introduction
Skin plays an important role in the locomotion of many vertebrates. The
expansion of the skin connecting adjacent skeletal elements of limbs was an
important adaptation in all flying and gliding mammals and many aquatic
vertebrates (Dudley et al 2007). This skin expansion increases surface area and
allows the skeletal structure of a limb to be exapted for novel use to generate
fluid-dynamic force, as a paddle or wing. Bats, the only mammals capable of
powered flight, fly using a wing membrane comprising skin that spans the hands,
arms, legs, and trunk. The skin of the wing is extremely thin, roughly an order of
magnitude thinner than body skin (Madej et al 2013). The thinness and
compliance of bat wing skin has important consequences for the aeromechanics
of bat wings.
The slenderness of bat wings (here used to refer to thickness relative to
length) makes them behave mechanically as elastic membranes which lack
bending stiffness and therefore cannot maintain a pre-determined threedimensional wing form. Membrane wings deflect when they experience
aerodynamic loading, naturally adopting a cambered shape, and support the
aerodynamic load through tension in the membrane (Song et al 2008; figure 1a).
Thus membrane wings of both bats and human-engineered devices experience
considerable passive shape change with aerodynamic loading (Rojratsirikul et al
2010, Song et al 2013, Timpe et al 2013, Waldman and Breuer 2013). Among
the potential benefits of this aeroelastic coupling are that passive shape change
requires no additional energy input from the bat, can provide rapid mechanical
70
response to varying flow conditions, delays stall to higher angles of attack,
enhances lift, and can alleviate the effects of gusts (Hu et al 2008, Song et al
2008).
Relative to the basal condition for mammalian skin, bat wing membrane
skin possesses distinctive morphological traits that may relate directly to flying
with membrane wings. Although bat wing membrane is exceptionally thin, it
contains an array of muscles (Schöbl 1871, Morra 1899) along with macroscopic
(approx. 0.1 mm) fiber bundles composed primarily of elastin fibrils (figure 1b)
(Bhangoo and Church 1976, Holbrook and Odland 1978, Crowley and Hall
1994). Many of the wing membrane muscles likely modulate membrane stiffness
and consequently shape during flight (Cheney et al 2014). Although the effect of
the unusually large elastin fibers on membrane mechanics remains unclear, it is
possible that elastin fibers aid wing folding and/or provide membrane
reinforcement (Holbrook and Odland 1978, Crowley and Hall 1994, Swartz et al
1996). Additionally, presence of elastin fibers is correlated with prominent
corrugation or wrinkles in bat wing membranes (Bhangoo and Church 1976,
Holbrook and Odland 1978, Crowley and Hall 1994).
Mechanical testing of wing membranes in a number of bat species found
that the membrane is mechanically anisotropic (Swartz et al 1996). The
membrane is most compliant along the wingspan and tissue compliance is
correlated with orientation of wing wrinkles or corrugations (figure 3a). Further
study of wing membrane mechanical properties will provide insight into the
aeromechanic behavior of bat wings. To this end, we seek to develop a tractable
71
model of the wing membrane. Because the tissue is a fiber-composite, we use
the traditional material science term “matrix” to refer to tissue not consisting of
elastin fibers. This is not to be confused with the extracellular matrix. Our goal is
to understand how elastin fibers, wrinkles, and matrix affect wing membrane
mechanical behavior. From this model, we can better understand how each
architectural feature contributes to wing shape configurations.
Elastin is known to be responsible for the compliant “toe” of the J-shaped
stress-stretch behavior in a multitude of biological tissues (Roach and Burton
1957, Hoeve and Flory 1958, Oxlund et al 1988). Elastin performs this specific
mechanical role, discrete from its stiffer surrounding constituents, because it is
pre-stretched relative to those components, which are essentially buckled (Brown
1973, Lanir 1979, Daly 1982, Caves et al 2010). In this configuration, as tissue is
loaded in tension, elastin bears load at low stresses until buckled components
elongate to an extent that allows them to begin bearing load. Despite that the
organization of elastin with respect to other skin constituents is quite different in
bat wing membranes, elastin fibers likely still contribute to compliance in wing
membrane skin.
We hypothesize that wing membrane anisotropy arises from the highly
oriented elastin fibers, not collagenous elements of the membrane; stiff wing
membrane collagen appears randomly oriented within the plane of the tissue
(Crowley and Hall 1994), but elastin fibers show preferential orientation
consistent with a major role in dictating anisotropy. We further hypothesize that
the macroscopic elastin fibers in bat wings are pre-stretched relative to the
72
ventral and dorsal layers of the skin, placing surrounding matrix in compression
when the skin is resting, or unloaded. Compressive loading of the slender wing
membrane results in the matrix buckling and producing the characteristic
wrinkles. The strong anisotropic response arises from wrinkles delaying onset of
stretch and stress in the surrounding matrix until they have unfurled.
To address these hypotheses, we first characterize the architecture of
elastin fibers, and then test if elastin fibers are responsible for matrix wrinkling.
Subsequently, we quantify wing membrane stress-stretch behavior, both parallel
and perpendicular to elastin fibers, normalized to 1) a relaxed configuration and
2) a high-stress configuration. Finally, because this wrinkled architecture should
allow for greater tissue stretch parallel to elastin fibers, we measured wing
membrane extensibility parallel and perpendicular to elastin fibers.
2. Materials and methods
2.1 Tissue
Tissue used for mechanical testing was excised from the wing membranes
of three male phyllostomid bats, Carollia perspicillata (body mass: 17.1, 18.4,
18.9 g). We selected this species because of their availability in our colony and
because phyllostomid bats are among the best-studied with respect to function of
wing membranes in flight (e.g. Swartz et al 1996, Cheney et al 2014). Each
individual was euthanized using carbon dioxide and tissue samples were
73
collected and placed within a humid storage chamber. Mechanical testing began
immediately to minimize the effects of tissue desiccation and breakdown.
Additional tissue used for dissection was taken from naturally deceased
individuals of C. perspicillata. Individuals were frozen after death, and thawed
prior to dissection. Tissue was manually hydrated as needed.
All experiments were conducted in accordance with approved protocols
(Brown University IACUC, Division of Biomedical Research and Regulatory
Compliance of the Office of the Surgeon General of the U.S. Air Force).
2.2 Elastin fiber orientation and removal
Elastin fibers in bat wings exhibit strain birefringence, so cross-polarizers
were used to determine elastin fiber orientation. Wings were illuminated using a
light box covered with linear polarizing film (TechSpec; Edmund Optics Inc.,
Barrington, NJ). Wings were imaged with a SLR with a lens-mounted circular
polarizing filter (Nikon Inc., Melville, NY). Elastin fibers could be more clearly
discriminated from wing membrane muscles under cross-polarized lighting than
standard backlighting.
To determine whether elastin fibers are the cause of wing membrane
wrinkling, we carried out a microdissection experiment. Prior to dissection, we
photographed a wing sample to document degree of wrinkling. We then removed
the elastin fibers and visualized degree of wrinkling following fiber removal. To
remove elastin fibers, we first carefully separated the ventral and dorsal layers of
the wing membrane. An incision was made from the elbow, along the forearm,
74
over the wrist, and down digit V, to form a triangular flap of tissue. The two skin
layers were then separated by blunt dissection. Some elastin fibers were
removed by separation of the two layers, and the rest were dissected away. For
imaging, the wing was lit at a shallow angle to highlight the peaks and troughs of
tissue wrinkles.
2.3 Sample preparation for mechanical testing
Fifteen samples underwent mechanical testing. Two to three tissue
samples were taken from each wing for uniaxial testing. Samples were oriented
either parallel or perpendicular to elastin fibers and taken from both arm- and
handwing (figure 2a). Each wing was gently extended until the membrane was
flat but still compliant, and far from the point of plastically deforming. We
determined fiber orientation by visualizing the wing membrane with crosspolarizing filters. Before excising wing tissue samples, a pair of rectangular, diecut, adhesive-backed paper frames was placed on the ventral and dorsal
surfaces (.0008” Carpet Tag; RippedSheets.com; Benton City, WA). These
frames served to keep the material flat, simplifying tissue handling and
preventing crumpling in response to elastin pre-stress. Frames were carefully
aligned and oriented either parallel or perpendicular to elastin fibers (figure 2c).
Frames enclosing tissue samples were then cut away from the wing and
mounted in the mechanical testing apparatus. Once mounted, the sides of the
frame were removed. The region of each membrane sample subjected to testing
was sample thickness x 5 x 20 mm. We placed an array of white paint markers
on each sample for video-based analysis of sample length change, but found the
75
reliability of such measurements inadequate for our purposes, and do not report
them here (see section 2.4).
2.4 Uniaxial tensile testing
We tested wing membrane using a uniaxial mechanical testing apparatus
(Mini Bionix II; MTS; Eden Prairie, MN). Tensile force was measured using a 1N
load cell (ULC-1N; Interface Inc.; Scottsdale, AZ), and recorded from an A/D
converter (USB 6218-BNC; National Instruments Corp.; Austin, TX) using a
custom MATLAB script (Mathworks Inc.; Natick, MA). Sample length was
measured from device crosshead position because wing membrane wrinkling
and twisting made digitizing from video-based length measurements unreliable.
Prior to testing tissue samples, we determined the length range over
which cyclic tests would be performed. Our aim was to test each sample from
lengths corresponding to untensioned, to that at approximately one body weight
of tension. To determine these critical lengths, first, all pre-stretch in the sample
was removed by reducing crosshead height until wing membrane displaced out
of plane, indicating a relaxed state. We then slowly stretched the sample to
approximately one body weight of tension, 0.18 N, and ascertained sample
length at this load. Each sample was then returned to the relaxed state and
allowed to recover for five minutes to minimize loading history-dependent effects
on subsequent tests.
We selected minimum and maximum tension values to contain a
biologically meaningful loading range as well as to ensure that our model
assumptions were met. In vivo, skin is often under tension in its natural
76
configuration (Ridge and Wright 1966, Jor et al 2011), therefore studying skin
from a fully relaxed starting configuration may not be necessary. However, we
reasoned that our test of bat wing membrane skin should capture a fully relaxed
configuration because bats fold their wings, compressing the large wing surface
area into a small volume, potentially placing the wing membrane in a tension-free
state. We could not estimate a single typical maximum in vivo tension value with
confidence. Instead, we selected a value that was likely well above the normal
biological range. We chose a value high enough to ensure that the contribution of
elastin to tensile load bearing was negligible relative to the contribution by matrix,
which allowed us to test for matrix isotropy.
Sample testing occurred over seven stretch-relaxation cycles at constant
elongation rate, each with a cycle period of 100 s (Supplemental figure 1). Tissue
was elongated slowly to minimize viscous contributions to stress. We found that
tissue texture and elasticity did not noticeably change over the test duration, and
rate-dependent effects at this speed were small enough to not affect our model
assumptions. We analyzed the elongation portion of the seventh cycle only and
consider the previous six cycles to serve as preconditioning of the tissue. The
stress-stretch response changed little over cycles two through six (Supplemental
figures 1 and 2).
2.5 Signal processing
Wing membrane is very compliant and relatively little tissue area can be
tested, therefore the measured forces and signal-to-noise ratio are low. Load and
displacement measurements were therefore digitally filtered to better resolve
77
tissue mechanical response compared to electrical noise. We smoothed the
recorded signal using a moving window that applied a first-order polynomial over
a window size of one second of data collection. We tested alternative
approaches to smoothing and filtering, and these did not change the conclusions
of the study.
2.6 Wing membrane thickness estimation
Uniaxial tensile force was converted to stress by normalizing by wing
membrane sample cross-sectional area. We estimated wing membrane
thickness by sectioning four wing membrane samples from the arm- and
handwing. After flash freezing, each sample was sectioned on a cryostat and
membrane thickness was measured using imageJ (Schneider et al 2012).
Because wing thickness bulges locally wherever there are muscles or elastin
fibers, thickness measurements were taken from regions between these
structures. All arm- and handwing tension measurements were normalized to
their respective average thickness values.
2.7 Mechanical behavior equations
We describe mechanical behavior of the wing membrane using stressstretch properties and anisotropy of the tangent modulus. Mathematically stretch
is merely the sum of one plus the engineering strain. Strain is traditionally
reserved for small-scale deformations and carries with it many implicit
assumptions invalid for large deformations. We calculate stretch as:
λ=
𝐿
𝐿𝑟𝑒𝑓
78
;
where 𝐿 is the deformed length and 𝐿𝑟𝑒𝑓 is sample length at the reference
configuration. Then using engineering stress, σ, tissue stiffness is:
𝐸=
𝛿σ
𝛿σ
= 𝐿𝑟𝑒𝑓 ∗ ;
𝛿λ
𝛿𝐿
where 𝐸 is the tangent modulus. From the tangent modulus, we quantify tissue
anisotropy as an index of the stiffness parallel to elastin fibers (𝐸║ ) relative to
perpendicular to elastin fibers (𝐸┴ ) at equal stress as:
𝛿σ
]║
= 𝛿λ .
𝐸┴ [𝛿σ]
𝛿λ ┴
𝐸║
[
If elastin fibers are pre-stressed, then by definition their resting length is
shorter than that of the surrounding matrix. Therefore, to understand the
mechanical behavior of both constituents we must consider two different
reference configurations. In the case of bat wing membranes, the high-frequency,
large-amplitude wrinkles in the resting configuration demonstrate that matrix
length likely far exceeds the length of elastin fibers. Accounting for matrix length
in excess of the fiber length is necessary for accurately assessing its mechanical
behavior. The two reference configurations (Lref) we employ are a relaxed
configuration, the most common normalization approach for mechanical studies
(which we designate L0 MPa); and a high-stress configuration (discussed below in
section 2.9, which we designate L1 MPa: as in the configuration at 1 MPa stress).
The high-stress configuration is designed to account for matrix excess length
parallel to elastin fibers by placing the stiff matrix at an equal state of stretch,
79
regardless of sample orientation. The two reference configurations are further
discussed below.
2.8 Low-stress-referenced mechanical behavior
To describe mechanical behavior of the wing membrane of our study
species at the tissue level, we carried out tests in which sample length was
normalized to the length at 5 kPa, the approximate resolution of our load cell.
After normalization, we compared stress-stretch behavior of all wing membrane
samples.
2.9 High-stress-referenced mechanical behavior
To test for isotropy in the wing membrane matrix itself, we had to account
for elastin’s contribution to stress and the wrinkling of the matrix. Matrix wrinkling
is important because it indicates excess matrix length, and therefore, that the
measured stretch in the elastin-matrix composite (parallel to elastin fibers) is
greater than matrix stretch. To account for these contributions to the stressstretch behavior, we normalized sample length to the length at a high-stress
configuration, i.e., at stress = 1 MPa. This length was chosen because we
expected that at this stress level, the contribution by elastin to bearing load would
be negligible. Consistent with this, at 1 MPa stress, tangent modulus falls within
the range of typical skin values (Ashby et al 1995). If load bearing by elastin is
negligible, then when samples of differing orientations are at equal stress, the
matrix component would be at equal stretch. We compared stress-stretch
behavior of wing membrane samples and measured the anisotropy within the
80
plane of the membrane with respect to stress (see below, 2.10 surface
anisotropy).
2.10 Surface anisotropy
We calculate anisotropy within the plane of the wing membrane, also
referred to as surface anisotropy (Lanir and Fung 1974), as an index describing
the ratio of the tangent moduli measured parallel to elastin fibers relative to that
perpendicular to elastin fibers. The anisotropic index was calculated for sample
pairs taken from a single individual and from the same wing region, i.e., armwing,
handwing between digits IV and V, and handwing between digits III and IV (figure
2a). Seven pairs of samples were used to calculate mean ± standard error for the
anisotropic index over the stretch domain occupied by all samples. We calculated
anisotropic index for samples at the same state of stretch, as well as for samples
at the same state of stress.
2.11 Effect of elastin fiber orientation on membrane elongation
To address whether elastin fibers increase extensibility of wing membrane
as a composite material, we compared the extensibility of wing membrane with
contribution from elastin fibers (tested parallel to elastin fibers) and without
contribution from elastin fibers (tested perpendicular to elastin fibers). We
measured the stretch required to deform samples from a relaxed state to a highstress state, 1 MPa. The ratio of average extensibility parallel relative to
perpendicular to elastin fibers described the effect of elastin and tissue wrinkling
on wing extension.
81
3. Results
3.1 Wing membrane thickness
Wing membrane thickness varied by wing region. Membrane thickness in
the distal armwing was 0.03 mm. Membrane thickness in the handwing was 0.02
mm.
3.2 Elastin fiber orientation and influence on wing membrane wrinkling
Using polarized light, we determined that elastin fibers are arranged in a
generally parallel array in the wing membrane of C. perspicillata, along the axis
of wing unfolding, approximately spanwise (figure 2b). Exceptions included small
regions of the wing membrane directly adjacent to wing bones and where elastin
fibers branched frequently, specifically between metacarpals IV and V. Samples
for mechanical testing were not taken from regions with branching fiber
architecture, and thus contained fiber arrays that were close to completely
parallel (figure 2c). The elastin fiber network was highly similar in both wings of
all three individuals tested (Supplemental figure 3).
We found elastin fibers caused the natural wrinkled state of the relaxed
wing membrane. After removing the ventral epidermis, the remaining dermis and
dorsal epidermis of the wing membrane remained wrinkled parallel to the elastin
fibers. However, after elastin fiber removal, the dorsal epidermis no longer
exhibited high spatial-frequency wrinkling; instead, it exhibited disorganized low
82
spatial-frequency buckling modes (figure 3). We found similar results when we
removed the dorsal epidermis instead of the ventral epidermis.
3.3 Stress-stretch mechanical behavior: low-stress configurations
Stress-stretch behavior of the wing membrane was nonlinear. In addition,
comparison of stress-stretch curves among samples demonstrates both that the
membrane is anisotropic and that variation in curves among samples was
relatively high when data are presented in reference to a relaxed configuration
(figure 4; Supplemental figure 4). For all samples, the wing membrane was
compliant at low stretch and stiffened with increasing stretch in a non-linear
fashion. Samples tested parallel to elastin fibers remained compliant over a
greater range of stretch than samples tested perpendicular to elastin fibers. The
stretch required to reach one body weight of tension was highly variable.
3.4 Stress-stretch mechanical behavior: high-stress configuration
Stress-stretch behavior of the wing membrane was similar in tests
conducted parallel and perpendicular to elastin fibers when results are
referenced to sample length at 1 MPa stress (figure 5). For stress exceeding 0.1
MPa, stretch in all samples was similar (standard deviation <1.1% stretch). At
lower stresses, at a given stretch, stress was greater in samples tested parallel to
elastin fibers than those tested in the perpendicular configuration (figure 5a
inset). Wing membrane anisotropy was not discernible above 0.34 MPa (figure
5b).
3.5 Elastin fiber effect on extensibility
83
Extension of wing membrane was much greater in samples tested parallel
to elastin fibers compared with samples perpendicular to elastin fibers: on
average, samples tested parallel to elastin fibers elongated 289% more over the
studied range than samples tested perpendicular to elastin fibers. Samples
tested perpendicular to elastin fibers elongated 13 ± 2% (mean ± S.E.M) from the
low- to high-stress configuration, and samples tested parallel to elastin fibers
elongated 37 ± 4% under the same load.
4. Discussion
The mechanical behavior of bat wing membranes depends upon a number
of structural features including wing membrane wrinkles, elastin fibers, and the
surrounding matrix. We found that wrinkles result from pre-stretched elastin
fibers, which compress and buckle the slender wing membrane (figure 3).
Parallel and perpendicular to the elastin fibers and wrinkles, bat wing membrane
was anisotropic, exhibiting greater extensibility and compliance parallel to the
fibers (figure 4). We found that anisotropy was not a result of the matrix, as its
stress-stretch behavior was isotropic once normalized to approximately the same
state of matrix stress/stretch (figure 5). Therefore, elastin fibers are responsible
for wing membrane anisotropy, and provide the wing membrane skin with its
dramatic spanwise extensibility and initial compliance.
Our results provide a simple and tractable model for wing membrane,
considering it a two-element composite in which parallel, pre-stretched, compliant
elastic fibers are embedded in a stiffer but buckled isotropic matrix when the wing
84
is unloaded. With this architecture, elastin fibers provide an initial compliant
phase when wing membrane is loaded in tension, until the wrinkles in the
isotropic matrix are unfolded. When the stretch at which the wrinkles have
dissipated is reached, the stiffer matrix dominates wing membrane mechanical
behavior, and the higher stiffness portion of the curve is reached. Below, we
address the biphasic behavior of bat wing membrane parallel to elastin fibers,
and discuss evidence to suggest the extent to which this provisional
interpretation of wing membrane mechanics is applicable to other bat species.
Finally, we discuss how this wing membrane architecture may relate to the
dynamics of the wing membrane during bat flight.
4.1 Elastin fibers: orientation and effect on wing wrinkling
Elastin fibers are necessary for the characteristic wrinkling of wing
membranes: following their removal, the wrinkles dissipate (figure 3). This
demonstrates that membrane wrinkles are not part of the intrinsic structure of the
matrix. Instead, wrinkles result from compressive buckling imposed on the thin
matrix by elastin fibers. Although the pattern of skin wrinkling observed in bat
wings is unique, our interpretation of elastin architecture, that it is pre-stretched
relative to its surrounding matrix, is consistent with its architecture in the skin of
other mammals (Daly and Odland 1979, Oxlund et al 1988). It is because elastin
is pre-stretched relative to the matrix that makes elastin responsible for the
stress-stretch behavior at low stress in bat wing membrane (Roach and Burton
1957). Further, because the fibers and wrinkles have a distinct orientation, the
85
matrix wrinkles create an abundance of excess length along the length of the
fibers which must be accounted for when measuring the degree of anisotropy.
The pattern of spanwise-oriented elastin fibers is likely broadly, possibly
universally, distributed among bats. All bats must undergo large spanwise
deformations during wing retraction during flight, which would be aided by the
extensibility provided by elastin. Spanwise elastin fibers have been reported in
bats from diverse families, including Vespertilionidae, Rhinolophidae,
Pteropodidae, and Molossidae (Schöbl 1871, Morra 1899, Schumacher 1931,
Church and Warren 1968, Holbrook and Odland 1978). However, many of these
species have not been described in detail, so there may be exceptions to this
pattern at a species-specific level, in particular anatomical regions of the wing,
such as the elastin fiber “web” between metacarpals IV and V in C. perspicillata
(figure 2b), or parts of the armwing in Tadarida brasiliensis (Holbrook and Odland
1978). Regardless, the wing membranes of all bats studied to date are more
extensible spanwise, consistent with elastin fibers and their associated wrinkles
running in a similar orientation, in an evolutionarily conserved pattern (Swartz et
al 1996).
4.2 Stress-stretch behavior: anisotropic effect of elastin at low-stress
configurations
The stress-stretch behavior of wing membrane exhibited substantial
anisotropy within the plane of the membrane when data were referenced to a
relaxed configuration (figure 4). In particular, samples tested parallel to elastin
fibers display compliance over a larger range of stretch values than samples of
86
perpendicular fiber orientation. The observed stress-stretch behavior of samples
tested parallel to elastin fibers was close to biphasic, and, after an extended
compliant phase, behaved much like that of samples tested perpendicular to
elastin fibers. This biphasic behavior is consistent with a typical role of elastin in
biological materials: contracting the resting state of the material and providing a
compliant phase over the contracted length (Roach and Burton 1957, Hoeve and
Flory 1958, Oxlund et al 1988). In bat wing membranes, elastin fibers perform
this role by buckling and wrinkling the wing matrix in the unloaded state, such
that it must first be unwrinkled before it can bear load. Hence, comparison of
relaxed membrane mechanical behavior in perpendicular vs. parallel orientations
is functionally a comparison of mechanical behavior of matrix to elastin fibers,
testing elastin fibers and not the wrinkled matrix in the first case, and testing
matrix in the second. Therefore, sample length parallel to elastin fibers is
approximately elastin fiber length and is an underprediction of the matrix length,
until higher loads are reached and the matrix unwrinkles.
4.3 Matrix: Isotropic and stiff
Stress-stretch tests of bat wing membrane referenced to a high-stress
configuration demonstrate that the matrix is approximately isotropic. Normalizing
sample length to that at moderately high stress (1 MPa) accounts for the
compliant phase of elastin fibers as well as matrix unwrinkling. Employing this
approach, we found that the nonlinear stress-stretch behavior of samples tested
perpendicular and parallel to elastin fibers were strikingly similar (figure 5).
Difference in mechanical behavior between the two sets of samples remained
87
only at low stress or stretch, where the contribution of elastin to load bearing was
not negligible (figure 5). Matrix isotropy suggests that internal elements, such as
collagen, are likely randomly oriented. A lack of preferential orientation in load
bearing elements in the matrix would produce the kind of uniform response that
we observed.
Elastin typically dominates mechanical behavior at low stress in a variety
of tissues (Roach and Burton 1957, Hoeve and Flory 1958, Oxlund et al 1988),
and we used this expectation to guide our analytical approach to identifying
matrix isotropy, although elastin is not found in large homogeneous bundles
within skin outside of bat wing membranes. Our approach hypothesized that the
contribution by elastin fibers was negligible at moderately high stress and
employed sample length normalization instead of accounting for elastin fiber
contribution explicitly. Had anisotropy at the high-stress configuration been
found, we could not have distinguished whether it arose from anisotropy in the
membrane matrix and/or from elastin fibers. However, our measurements relative
to the high-stress configuration, demonstrate that load bearing by elastin fibers
can be considered negligible at higher stresses and that the matrix is
mechanically isotropic (figure 5).
It is not surprising that the mechanical role of elastin at higher stresses is
small in bat wing membrane skin. Elastin is one to two orders of magnitude more
compliant than mammalian skin as a whole (Ashby et al 1995), and its fiber
volume fraction in skin is relatively low (Meyer et al 1994). However, although the
large, macroscopically visible fibers in bat wing membranes are composed
88
predominantly of elastin, they possess a small fraction of collagen, located inside
and around the periphery of the fiber bundle (Madej et al 2013, Holbrook and
Odland 1978). The function of this collagen is unknown: the collagen fibrils could
subtly modulate the stress-stretch behavior at a finer scale than our present
methodology can resolve, or serve another function, such as increasing fiber
yield strength. Further analyses, including more detailed study of tear
propagation and failure in wing membranes could address this latter hypothesis.
4.4 Elastin contribution to stretch
Elastin fibers delay the onset of stretch in the matrix, which suggests that
a key role of elastin fibers is to enhance membrane elongation. By imposing
buckling on the matrix component of the wing membrane, elastin fibers form high
spatial-frequency wrinkles (figure 3), allowing the wing to collapse its large
surface area into a relatively small volume (supplemental figure 5). This, in turn,
allows the unfurling wing membrane to stretch much more parallel than
perpendicular to elastin fibers. Human-engineered composites often utilize a
similar design to allow a wrinkled/buckled element to undergo displacements
without deforming and failing, such as in some forms of flexible electronics
(Khang et al 2006). As a consequence of bat wing elastin fiber architecture, wing
membrane at the whole tissue level may be able to achieve larger stretch than
yield stretch of the matrix alone.
4.5 The role of elastin in wing membrane aeromechanics
The wrinkles of the bat wing membrane result from the length of the matrix
exceeding the length of the elastin fibers. This architecture is essentially
89
analogous to matrix slack, but we describe it as excess length following
Rojratsirikul and colleagues (2010). The effect of excess length in membrane
aeromechanics is to increase membrane deflection, which can manifest as
various wing reconfigurations depending upon how the wing membrane is
anchored along the edges (Hu et al 2008; Rojratsirikul et al 2010). If the leading
and trailing edges are anchored, the result is increased camber (Song et al 2008,
Waldman and Breuer 2013). However, if the trailing edge is free to deflect, like in
the armwing of bats, the wing will twist which can result in decreased lifting
efficiency and have the beneficial effect of reducing sensitivity to gusts
(Abudaram 2009). Thus, the interaction between elastin fibers and matrix may be
critical determinants of three-dimensional shapes adopted by the wing and thus
aerodynamic performance of bats during flight.
Elastin fibers may also have important roles other than interaction with the
wing membrane matrix. The fiber-matrix interaction dictates that elastin fibers
within the wing membrane are under greater stretch than the surrounding matrix,
and can experience net tension even when the surrounding matrix is buckled in
compression (figure 3). As a result of elastin pre-tension and its overall
compliance, the wing membrane can stretch notably more parallel to elastin
fibers than perpendicular to them, almost three-fold for 1 MPa stress. Thus, when
the wing matrix buckles as the wing is retracted during upstroke, elastin fibers
maintain a low level of tension in the wing membrane over much, if not all, of this
part of the wingbeat cycle. Increased spanwise tension in membrane wings with
free trailing edges results in an overall decrease in membrane deflection, but
90
perhaps more importantly, a decrease in flutter (Timpe et al 2013). This may be
critically important for bats because fluttering can dramatically decrease
aerodynamic performance of a membrane wing (Hu et al 2008).
5. Conclusions
Bat wing membrane skin is an unusual fiber composite. It consists of a
spanwise array of large and well-organized elastin fibers (figure 2), which are
more compliant than the surrounding matrix. These fibers are pre-stretched and
compressively load the slender membrane, inducing high spatial-frequency
buckling in the form of wrinkles (figure 3). By placing the majority of the wing
membrane in a buckled configuration, elastin fiber organization enables dramatic
extensibility in bat wings and allows efficient packing and unfurling of the excess
wing matrix length. This mechanical architecture may apply broadly to all bat
species, given that the wing membrane of all bats studied to date is similarly
anisotropic (Swartz et al 1996) and possess a spanwise array of elastin fibers
(Schöbl 1871, Morra 1899, Schumacher 1931, Holbrook and Odland 1978,
Church and Warren 1968). Regardless, the architecture of bat wing membranes
suggests that during downstroke the matrix may possess substantial slack, and
during upstroke, the elastin fibers may keep spanwise tension on the membrane.
These features have been shown to be beneficial in human-engineered wing
membranes (Rojratsirikul et al 2010, Timpe et al 2013). Finally, this structural
model of bat wing membrane is simple and many details have yet to be
accounted for. However, our first step provides insight into this functionally
91
important tissue by demonstrating that wing membrane, as a whole, acts as a
composite of an isotropic, nonlinearly elastic matrix with excess length, due to
embedded pre-stretched elastic fibers (figure 6). From this starting point, the role
of each of these units in aeromechanics can be better understood through future
studies.
Acknowledgements
We thank Beth Brainerd and Christian Franck for their considerate advice
on data analysis. We appreciate assistance from Erika Giblin for her significant
role in maintaining the health of our bats. Also, we thank Cosima Schunk, Kenny
Breuer, Phil Lai, Rye Waldman, and Alyssa Skulborstad for many helpful
discussions. This work was supported by the National Science Foundation (IOS1145549 to SMS) and the Air Force Office of Scientific Research (F49620-01-10335, monitored by D. Smith, to SMS).
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Figure 1. Bat wing membranes support and deform in response to
aerodynamic load. (a) A phyllostomid bat in flight with the right wing strongly
cambered, in part due to wing compliance. (b) Macroscopic structure of a bat
wing membrane, hypothesized to play a role in wing compliance. Array of nearly
homogeneous, approximately spanwise-oriented elastin fibers indicated by *;
chordwise-oriented muscles in armwing indicated by †.
96
Figure 2. Elastin fibers form a parallel array, allowing uniaxial testing
parallel and perpendicular to the fibers (a) Polarized light image of C.
perspicillata wing. Elastin fibers run primarily along the wing unfolding axis,
approximately spanwise. The more intensely birefringent muscles in the armwing
run orthogonal to elastin fibers. Digits III-V are labeled. Rectangles illustrate
location of sampling for specimens with elastin fibers parallel (image left, bat’s
right wing) and perpendicular (image right, bat’s left wing) to predominant elastin
fiber orientation. (b) Diagrammatic representation of the elastin fiber network in
the hand- and armwing illustrating generally parallel organization except between
metacarpals IV and V and directly adjacent to bones. Striped area of schematic
was not studied. (c) Wing membrane samples framed and excised. Samples
were tested along the designated uniaxial tension axis, and either parallel or
perpendicular to the principal elastin fiber network orientation. Samples are 20 x
5 mm. Sample flatness is indicated for configurations at relaxation and under
moderate-high stress.
97
Figure 3. Elastin fibers are necessary for wing wrinkling. Ventral view of
distal armwing. Elbow is at the left, digit V to the right. (a) Wing membrane
wrinkles run parallel to elastin fibers. Shallow raking light reveals illuminated and
shadowed faces of the high spatial-frequency wrinkles. (b) Removal of elastin
fibers by dissection eliminates wing wrinkling. Ventral epidermis is also removed.
Wing wrinkling still occurs where residual elastin fibers remain (region around *).
98
Figure 4. Wing membrane mechanical behavior was nonlinear and
anisotropic, when referenced to relaxed configuration. Representative
stress-stretch data for uniaxial mechanical testing parallel (black) and
perpendicular to (gray) elastin fibers. Wing membrane samples were stretched
slowly to one body weight of tension over a period of 100 s. Stretch was
normalized to an approximately relaxed sample configuration. Mechanical
behavior of samples tested parallel to elastin fibers appeared biphasic, with an
initial compliant phase, which was then followed by a stiff phase similar to the
mechanics of wing membrane tested perpendicular to elastin fibers. λ*
designates the stretch required for each sample to reach 1 MPa and varies
substantially with sample orientation.
99
Figure 5. Wing membrane tested both parallel and perpendicular to elastin
fibers behaves isotropically at higher stretch and stress, when referenced
to sample length at 1 MPa; whereas its behavior is anisotropic at very low
stretch and stress. (a) Stress-stretch behavior, normalized to sample length at 1
MPa, of samples tested parallel (black line) and perpendicular (gray line) to
elastin fibers. (b) Surface anisotropy for samples from the same individual and
wing region, but opposite wings. Anisotropic index is defined as the ratio of
tangent modulus parallel to elastin fibers relative to perpendicular to elastin
fibers. Solid line is mean, shaded region delineates the standard error envelope,
and gray dashed line indicates isotropy. The wing membrane initially exhibits
surface anisotropy, but becomes increasingly isotropic with increasing stress.
100
Figure 6. Bat wing membrane is an anisotropic composite of spanwise prestressed compliant elastic fibers embedded in an isotropic stiff matrix with
excess length parallel to the fibers. Samples tested perpendicular to elastin
fibers display stiff non-linear stress-stretch behavior dominated by matrix (left
gray line). Samples tested parallel to elastin fibers, undergo a similar stiff phase,
but first must proceed through a compliant phase dominated by elastin (black
line), which then transitions into matrix dominated mechanical behavior (black
line transitions into right gray line). Once excess matrix length has unfurled,
mechanical behavior is approximately isotropic.
101
Supplemental figure 1. Measurements from representative mechanical
testing trial. Samples were tested at a constant rate of elongation. Range of
lengths tested began with the sample at complete relaxation (displacement=0)
and ended with the sample supporting approximately one body weight of tension,
0.18 N (displacement=L*).
102
Supplemental figure 2. Effects of preconditioning are minor after cycle 1.
Representative stress-stretch plot of seven consecutive stretches. The first
stretch is noticeably different from stretches two through seven. Plot is
normalized to sample length at 1 MPa.
103
Supplemental figure 3. The elastin network was similar across wings, both
within and among individuals. Four wings imaged with cross-polarizers. Top
image shows the left and right wings from one individual, bottom images are from
two additional individuals. Elastin fibers can be identified as thin fibers of
moderate contrast, running approximately along the axes of wing spreading (see
figure 2b for schematic of elastin architecture).
104
Supplemental figure 4. Wing membrane mechanical behavior was
nonlinear, anisotropic, and highly variable when referenced to relaxed
configuration. Fifteen wing membrane samples were stretched slowly to one
body weight of tension over a period of 100 s. Stretch was normalized to an
approximately relaxed sample configuration. Stress-stretch behavior of wing
membrane tested parallel (black) and perpendicular (gray) to elastin fibers
(armwing: solid; handwing: dashed). The stretch required to reach 1 body weight
of tension varied substantially. However, all samples stretched parallel to elastin
fibers remained compliant over a larger range of stretch than samples stretched
perpendicular to elastin fibers.
105
Supplemental figure 5. Bat wings can collapse their large surface area into
a tightly packed volume. Images are of back-illuminated wings from the same
individual.
106
Chapter 4
Bat wing membrane architecture: the elastin network and
muscles of the plagiopatagium
Jorn A Cheney1, Justine J Allen1, and Sharon M Swartz1,2
1. Department of Ecology and Evolutionary Biology, Brown University, Providence, RI 02912
2. School of Engineering, Brown University, Providence, RI 02912
Abstract
Bat wings are composed of thin skin embedded with large elastin fibers
and muscles. The large elastin fibers increase extensibility of wing membrane
skin when it is subjected to tension, whereas active wing membrane muscle
reduces extensibility. A more thorough understanding of the effect of muscle and
elastin fibers requires greater knowledge of the architecture of these
components. Current information about the morphological pattern of elastin and
muscle distribution in bat wings suggests that it varies greatly among species,
and one species may not represent many others. Here we develop an imaging
approach using cross-polarized light to study elastin fiber and muscle geometry
and distribution within the wing membranes of 130 species from sixteen families.
Elastin fibers run predominantly along the axes of wing spreading, whereas, wing
membrane muscle morphology varies substantially, but is usually similar among
closely related species. Finally, we demonstrate that the wing membrane
muscles anchor to the dermal matrix by means of unusual tendon composed of
elastin at the core and collagen at the periphery, the latter of which has
numerous insertions into the matrix.
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1. Introduction
Bats fly using membrane wings of considerable structural complexity. In
addition to the typical constituents of mammalian skin, bat wing membranes
contain large (on the order of tens of microns in diameter) elastin fibers and
skeletal muscles (Quay 1970, Crowley and Hall 1996). Elastin fibers are found in
the plagiopatagium and dactylopatagium, whereas membrane muscles are found
only in the plagiopatagium (figure 1b). These structures are thought to be
important for flight performance and the three-dimensional form adopted by the
wing during flight (Holbrook and Odland 1978, Cheney et al 2014a, b).
The architecture of elastin fibers and wing membrane muscles determines
how they affect wing form. Along their long axes, elastin fibers increase wing skin
extensibility, whereas active wing membrane muscles decrease wing skin
extensibility. For both elastin fibers and muscle, the magnitude of effect depends
on the length relative to the surrounding matrix (Cheney et al 2014a, b). Thus
their architecture will influence flight performance by modulating the extensibility
and effective stiffness, thereby changing the properties of the wing as a dynamic
airfoil.
Unfortunately, anatomical descriptions of wing membrane architecture are
difficult to reconcile. Two patterns of elastin fiber networks have been described
in bat wing membrane skin. It has been reported that elastin fibers run
approximately spanwise in the dactylopatagium and plagiopatagium in a number
of vespertilionids, Rhinolophus ferrumequinum, Eidolon helvum, and Carollia
perspicillata. (Schöbl 1876; Morra 1899; Schumacher 1932; Church and Warren
108
1968; Cheney et al 2014b), or that elastin fibers run spanwise in the
dactylopatagium, but in the plagiopatagium they form an approximately biorthogonal grid in Tadarida brasiliensis and Pteropus poliocephalus (Holbrook
and Odland 1978; Crowley and Hall 1994; Swartz et al 1996).
Reports of wing membrane muscles also vary. Wing membrane muscles
originate from the hindlimb, trunk, humerus, and insert into the skin of the wing
membrane. Muscles are named not as individual muscle bellies, but as arrays of
muscle bellies. Comparisons of muscle morphology across studies are
complicated by the fact that the arrays have been named and categorized
differently in many of the anatomical studies. However, within studies, wing
membrane muscles are described as varying in innervation, presence, number,
and length (Schöbl 1871, MacAlister 1872, Morra 1899, Schumacher 1932,
Vaughan 1959, Gupta 1976).
In this study, we sought to better understand the architecture of elastin
and muscle in bat wing membrane skin. Identifying architectural similarities and
differences across taxa informs whether mechanical function of elastin fibers and
wing membrane muscles may be similar across taxa. Our approach was to
develop a methodology for differentiating wing membrane muscle and elastin
fibers in whole bat wings using relatively rapid non-invasive imaging. This would
allow us to study the diverse museum collections and identify any consistent
morphological patterns in muscle and/or elastin. We identify orientation of elastin
fibers, and a number of wing membrane muscle characters, such as orientation,
relative muscle length, and number. We validate this technique using histology.
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The region studied was carefully selected to reflect how elastin and muscle
interact. Combined, this work provides a synthesis of wing membrane functional
anatomy at varying morphological scales.
2. Materials and methods
2.1 Tissue and bats
Tissue used for histology was excised from the wing membranes of
Artibeus lituratus (Family: Phyllostomidae). This species was selected because
functional studies of elastin fibers and plagiopatagiales proprii have been
performed for other related phyllostomid bats, and because A. lituratus is a
relatively large species simplifying the imaging (~65 g; Tacutu et al 2012). Tissue
from one individual of A. lituratus was donated from the American Museum of
Natural History.
Imaging of whole-mount wings were from alcohol-preserved collections at
the American Museum of Natural History, New York; the National Museum of
Natural History, Washington D.C.; and the Field Museum, Chicago. A total of
sixteen of the seventeen recognized families were imaged (Teeling et al 2005). In
total 130 species were studied, which represents on average 38% of family-level
diversity (Table 1). Species numbers are from Wilson and Reeder (2005).
2.2 Validation: differentiating elastin fibers and muscle using cross-polarized light
Polarized light differentiates birefringent from non-birefringent tissues.
Neither muscle nor elastin are birefringent, but both are ensheathed in
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birefringent collagen (Holbrook and Odland 1978). Further, elastin exhibits
birefringence under strain and imaging the whole wing requires the wing to
unfold, placing the elastin fibers under strain (Cheney et al 2014b). Both
structures are expected to illuminate under cross-polarized light, but the intensity
of the illumination may be sufficient to differentiate the two tissues.
We compared images collected using polarized light imaging to 1)
previous anatomical descriptions, and 2) histological sections of the wing
membrane. Anatomical descriptions of the wing membrane existed for a species
within the genus Rhinolophus, and for two species within Vespertilionidae
(Schöbl 1871, Morra 1899). Histolological sections were taken from an area of
the wing that captured two distinct populations of structures with differing
birefringence. These sections were then stained to differentiate muscle and
elastin (Section 2.3).
2.3 Histology
The wing was fixed in 70% ethanol and four samples (approximately 3 x 2
mm each) of the junction between plagiopatagiales proprii and tendon were
excised from surrounding tissue (figure 2a,b). Samples were dehydrated in an
ethanol series before being infiltrated with, and embedded in, polyester wax.
Serial sections of six µm were cut with a rotary microtome (Leica Biosystems;
Buffalo Grove, IL) parallel with or perpendicular to the length of the
plagiopatagiales proprii muscles (sagittal or transverse sections) and then
mounted on subbed glass slides (Weaver 1955). Slides were then stained for
elastin, collagen, and muscle using modified Verhoeff’s and van Gieson’s stains
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(Garvey et al 1991), imaged with a microscope (Axioskop; Carl Zeiss AG;
Oberkochen, Germany) and mounted digital camera (EOS 5D Mark II; Canon
U.S.A., Inc., Melville, NY).
2.4 Muscle naming
The literature contains multiple conflicting names for many of the wing
membrane muscles. We synthesized the various names and followed the origininsertion convention. This convention has been the most frequently used for the
wing membrane muscles, and preserves the names of the most commonly
discussed muscles. In general, the muscle origins appeared variable and our
names reflect a general region of the origin.
2.5 Whole-wing imaging
Wings were illuminated using a light box covered with linear polarizing film
(TechSpec; Edmund Optics Inc., Barrington, NJ). A single wing from each
species was stretched out by hand underneath the camera and rotated until
different muscle groups could be imaged. Often multiple images were taken
because different muscle groups illuminate relative to the orientation of the crosspolarizers. Our imaging focused on the plagiopatagium and the dactylopatagium
between digits III-V. Our imaging could often not clearly resolve the uropatagium
(tailwing) and the small region of the dactylopatagium between digits II and III,
and so descriptions of those regions are excluded from our analysis. All imaging
was performed with an SLR and a lens-mounted circular polarizing filter (Nikon
Inc., Melville, NY).
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2.6 Wing membrane descriptions
We described the architecture of elastin fibers and wing membrane
muscles based on patterns observed at the taxonomic level of the family. We
describe elastin orientation, muscle orientation, muscle length, and muscle
number. These traits were chosen because they are believed to play important
roles in wing membrane function (Cheney et al 2014a, Cheney et al 2014b).
When multiple individuals within a species were sampled, there was no
substantial variation in the traits described.
3. Results
3.1 Cross-polarized wing imaging and previous wing dissections
Imaging of the wing membrane identified two distinct populations of fibers:
thin weakly birefringent fibers, and thick strongly birefringent fibers. When
comparing those fiber populations to published anatomical illustrations of the
wing membrane, the thin weakly birefringent fibers fit descriptions of elastic
fibers, and the thick strongly birefringent fibers were consistently structures
previously identified as muscles (figure 1).
3.2 Histological validation of cross-polarized wing imaging
Histology of a region of skin containing plagiopatagiales proprii muscles in
a phyllostomid bat confirmed that the thin weakly birefringent fibers were elastin
fibers and the thick strongly-birefringent fibers were muscles. Muscle fibers were
identified both by presence of characteristic striations and by differential staining
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(purple); elastin fibers were darkly stained by Voerhoff’s stain (black/dark purple)
(Figure 2).
3.3 Muscle nomenclature
We propose muscle nomenclature that employs an origin-insertion
convention to aid identification of muscles that insert within the plagiopatagium.
We found that the origins of these muscles are often broad, including multiple
bones, although their extent varies among families. For these reasons, we
ascribe origins to an anatomical area and not a single localized source (figure 3).
We found muscles originating from the 1) dorsum of the trunk, 2) axilla, which
presumably originates from the coracoid (as described by Schumacher 1932,
Vaughan 1959), 3) plagiopatagium, 4) cubital region (elbow), and 5) vicinity of
the tibia, including distal femur and proximal foot. We designate these muscles
the mm. dorsoplagiopatagiales, mm. coracoplagiopatagiales, mm.
plagiopatagiales proprii, mm. cubitoplagiopatagiales, and mm.
tibioplagiopatagiales, following Schumacher (1932) in the first three cases.
3.4 Elastin orientation in the dactylopatagium and plagiopatagium
Within the dactylopatagium of all bats examined, elastin fibers run in a
predominantly parallel array along the axes of digit spreading. Specifically,
between digits III and IV, and IV and V, elastin fibers run approximately
perpendicular to the digits (figures 4 and 5). Elastin fiber patterning includes
regions of primarily parallel organization, as well as branching and coalescence
or reticulation, which can produce a honeycomb-like pattern. This reticulation is
114
most prevalent in Pteropodidae, and between metacarpals IV and V in
Phyllostomidae and Myzopodidae (figure 4a).
Within the plagiopatagium, elastin fibers always run along the wing
spreading axes, approximately spanwise, but, on occasion we found a second
population of fibers, perpendicular to the first (figure 5). Fibers in the
perpendicular population run approximately rostrocaudally, occur only rostral to
the plagiopatagiales proprii, and appear to be tendinous extensions of these
muscle (figures 5c and 6). The two populations of fibers form a cross-hatched
network of elastin fibers and were observed in Molossidae, Emballonuridae,
Pteropodidae, and within a subset of the Rhinolophidae (all three species
sampled from Hipposideros, but no species sampled from Rhinolophus). In all
other taxa, plagiopatagiales proprii appeared to insert on the either spanwise
elastin fibers or in the dermal matrix in which the muscles and elastin fibers are
embedded.
3.5 Muscle insertion site architecture
Plagiopatagiales proprii muscles run in series with elastin fibers. We
observed a single elastin fiber originating from each plagiopatagialis proprius
muscle. At a finer scale, fibrils of individual elastin fibers originate from each
myofiber within the muscle (figure 6b-d). Surrounding elastin fibers were collagen
fibrils running along the length. These peripheral collagen fibrils were highly
organized compared to the collagen within the dermis. At numerous points along
the length of elastin fibers, we observed the peripheral collagen diverging from its
parallel arrangement and anchoring to the surrounding dermis (figure 7).
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3.6 Muscle architecture in bat wing membranes
We summarize findings on diversity of muscle architecture in Table 2.
Below we discuss each muscle group, each of which was identified based on its
location within the wing membrane.
Coracoplagiopatagiales
The coracoplagiopatagiales enter the wing membrane approximately from
the axilla. A single muscle belly exits, but in some species, it branches into
multiple muscles. The muscles run approximately caudally and terminate near
the trailing edge. They form the boundary between the proximal
dorsoplagiopatagiales and the distal plagiopatagiales proprii (figure 3). We
observed these muscles in all families except Mystacinidae, in which skin in the
axillary region is exceptionally thick and unusually wrinkled, which obscured
imaging.
Dorsoplagiopatagiales
The dorsoplagiopatagiales enter the wing membrane from the thorax and
abdomen. They typically run laterally and caudally. The overall density of these
muscles is typically similar to that of the plagiopatagiales proprii and, like the
density of plagiopatagiales proprii (see below), varies substantially. We observed
these muscles in all families.
Plagiopagatagiales proprii
The plagiopatagiales proprii originate and insert within the plagiopatagium.
They run rostrocaudally. We most commonly observed plagiopatagiales proprii
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running the majority of the rostrocaudal length of the plagiopatagium, but in
species with high muscle number, the muscles adjacent to digit V were often very
short (~10% of the chord length). Muscle number varied substantially, from a
minimum of four, spaced between the elbow and digit V, to a tightly packed
dense array that approximates a continuous sheet of muscle. We observed
plagiopatagiales proprii muscles in all species.
Tibioplagiopatagiales
The most common site of origin of the tibioplagiopatagiales is the leg, but
muscles in this group also appear to originate from the distal femur or proximal
portions of the foot. They run laterally and, when of substantial length, rostrally.
When these muscles were present, they were: 1) very short (5-10% of
plagiopatagium length), 2) of moderate length, extending to the elbow, or 3) long,
extending almost the length of the plagiopatagium. The number of individual
muscles in this group varied from a minimum of seven to a maximum of 25, a
considerably smaller range of variation than that observed for the
plagiopatagiales proprii. In seven of the sixteen families of bats studied, we did
not observe tibioplagiopatagiales.
Cubitoplagiopatagiales
The cubitoplagiopatagiales enter the wing membrane skin from the elbow
region in all families sampled in this study. When present, we observed between
one and four cubitoplagiopatagiales muscles per wing. The muscles run laterally
and were frequently short, spanning less than a fourth of the distance from the
elbow to digit V. When only a single muscle occurred, it frequently originated
117
from the elbow in combination with a neurovascular bundle. In three of the
sixteen families of bats studied, we did not observe cubitoplagiopatagiales.
4. Discussion
4.1 Cross-polarized light imaging for bat wings
We found cross-polarized light imaging to be an effective method of
differentiating elastin from muscle in bat wings (figures 1, 2). Elastin fibers
displayed moderate contrast to the surrounding matrix, and muscles were usually
much brighter. The birefringence of muscle was also less consistent along the
length of the structure, and the end-to-end path was generally more tortuous than
that of elastin fibers, which were straighter on average.
This approach to imaging the whole wing membrane enables efficient and
effective visualization of structural architecture in specimens. It does not require
destructive sampling, nor significant cost. Further, it is generally superior to
brightfield imaging, a common technique employed in previous studies of bat
wing membranes (Gupta 1967; Holbrook and Odland 1978; Swartz et al 1996).
Cross-polarized light was inferior to brightfield imaging, however, for very large
bats (>250g). In these large bats, which are primarily Pteropodidae, elastin fibers
show low contrast.
Cross-polarized light imaging was invaluable for sampling in this study, but
its limitations must be taken into account. For elastin fibers and muscles,
magnitude of illumination depends upon the orientation of the fiber axis relative to
the cross-polarizers. Fibers that appear bright in one configuration may appear
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dim in another, and failure to fully explore the range of polarizer orientations
could lead to omission of birefringent structures. Further, as in any technique that
employs back-illumination, cross-polarized imaging requires light to penetrate the
tissue to arrive at the camera sensor. This requirement makes visualization
adjacent to the opaque body and arms difficult. Regions of dense hair can create
further imaging challenges. Because of these limitations, using this technique, we
cannot discern conclusively if muscle is absent from a particular region of the
wing membrane or if the technique has lacked the sensitivity to detect muscle
that may be present but are small or obscured.
4.2 Elastin fiber architecture
Elastin fibers consistently run along the wing spreading axes in all bats
(figure 5). Previous anatomical studies of the wing membrane have also
observed elastin fibers in this orientation (Schöbl 1876; Morra 1899; Schumacher
1932; Church and Warren 1968; Holbrook and Odland 1978; Crowley and Hall
1994; Swartz et al 1996; Cheney et al 2014b). However, a few of these studies
observed a second population of elastin fibers running perpendicular to the first
and concluded that elastin fibers predominantly form a bi-orthogonal grid
(Holbrook and Odland 1978; Crowley and Hall 1994; Swartz et al 1996). We do
observe a grid pattern, but only in a limited subset of species and then only
rostral to the plagiopatagiales proprii (figure 5c). To characterize wing membrane
skin as possessing a grid pattern of elastin fiber architecture overall is imprecise
and somewhat misleading.
119
The similarities in elastin fiber architecture among all bats sampled
indicates that the mechanical effect of elastin fibers is likely comparable in all
species. Elastin fibers cause increased tissue extensibility by means of wrinkling
the surrounding, stiffer components of skin, resulting in tissue anisotropy
(Cheney et al 2014b). The predominance of elastin fibers running along the
length of the wing suggests that all species have anisotropic wing membranes,
which would be more compliant parallel to the fibers. These resulting mechanics
are most significant when the wing membrane is under low levels of tension,
such as when it is relaxed or during the upstroke (Cheney et al 2014b). When the
wing membrane is relaxed, elastin fibers buckle the large surface area of the
membrane and aid its efficient packing into a small volume. During upstroke,
elastin fibers maintain tension in the wing membrane which may resist
membrane flutter (Cheney et al 2014b, Hu et al 2008).
4.3 Muscle insertion site architecture
We found that the plagiopatagiales proprii run in series with elastin fibers,
making these fibers architecturally analogous to tendons (figure 6). Although our
observations are specific to the plagiopatagiales proprii, they echo those of Morra
(1899), who described elastin fiber tendons for all of the wing membrane
muscles. However, elastin fibers differ compositionally and mechanically from
typical tendon. Tendon is normally 75-85% collagen and less than three percent
elastin; whereas elastin fibers found in bat wings are 25-33% collagen and 5066% elastin (Holbrook and Odland 1978, Holzapfel 2001). These compositional
differences mean that typical mammalian tendon is stiff, approximately 1 GPA,
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over the majority of its elongation (Ker et al 1988, Pollock and Shadwick, 1994).
In contrast, elastin fibers are extremely compliant (Cheney et al 2014b). They are
structurally similar to ligamentum nuchae in ungulates (Holbrook and Odland
1978), which is three orders of magnitude more compliant than tendon over the
majority of elongation (~1 MPa; Dimery et al 1985). We are aware of no other
tendon composed primarily of elastin. With tendons composed primarily of long
and compliant fibers, muscles would be incapable of substantial force generation
due to limitations arising from muscle force-length properties (see Appendix).
The plagiopatagiales proprii contract in flight, thus it is extremely unlikely that
their tendons inhibit force generation (Cheney et al 2014a). So how do wing
membrane muscles function with such unusual tendons?
Our histological data suggests that treating the tendon as a compliant
linear elastic material may be inappropriate. Although elastin fibers are compliant
over substantial elongation (Cheney et al 2014b), the colinear collagen fibrils
surrounding the elastin fibers will substantially increase fiber stiffness once
sufficient elongation has occurred to engage them (figure 6; Hoeve and Flory
1958, Carton et al 1962, Gosline and Shadwick 1996). Thus based on this
tendon architecture, we would predict plagiopatagiales proprii activation to occur
when the wing membrane is under load and has substantially deformed, ie.,
during downstroke. This is consistent with their EMG profile (Cheney et al
2014a).
Further resistance to muscle contraction can be provided by the collagen
fibrils anchoring elastin fibers to the matrix (figure 7). These attachment points
121
could allow the matrix to operate in parallel with the fibers, which would allow the
whole wing membrane to bear muscle tension. Though membrane is still
compliant compared to tendon (~30 MPa vs 1 GPa; Swartz et al 1996, Dimery et
al 1985), the sheer quantity of it could provide sufficient stiffness to allow for
efficient muscle contraction.
4.4 Variation in architecture of wing membrane muscles
Within bats, there is substantial variation in wing membrane architecture.
For example, plagiopatagiales proprii numbered from a few to hundreds, and
tibioplagiopatagiales varied in length from 5% of the plagiopatagium to spanning
the whole of it. The cause of muscle variation is unclear, but it was not strongly
correlated with ecology, as was hypothesized by Gupta (1967). We observed
frequent convergent evolution of similar morphological patterns that are not
consistent with ecotype. One example was the sheet-like morphology of
dorsoplagiopatagiales and plagiopatagiales proprii that occurred in Epomops
franqueti (Pteropodidae), Anoura geoffroyi (Phyllostomidae), and all molossids
(figure 8), but was not observed in other Pteropodidae or Phyllostomidae. E.
franqueti is a large fruit bat with wings of average aspect ratio (body mass: 109 g,
aspect ratio: 6.5); A. geoffroyi is a small feeding generalist with average aspect
ratio wings (body mass: 14 g, aspect ratio: 7.2); and Molossidae are moderate to
large-sized specialist aerial hawkers with generally high aspect ratio wings (body
mass: 11 to 136 g, aspect ratio: 7.3 to 14.3) (Norberg and Rayner 1987). We
suggest that there are considerable phylogenetic patterns in membrane muscle
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morphology in bats, but we also see instances of convergent evolution whose
purpose, if any, is unclear.
4.5 Number of wing membrane muscles
Muscle number varied substantially in the dorsoplagiopatagiales and
plagiopatagiales proprii, both within and among families. We propose that there
may be little functional significance to this variation. The plagiopatagiales proprii
contract as an array and not as single muscles, and for this reason, the total
cross-sectional area of the group may be the critical parameter (Cheney et al
2014a). We observed that species with sheet-like muscle morphology generally
possessed thinner muscles than comparably sized bats within their respective
families. Thus the increase in number may not come with a concomitant increase
in muscle area and force capacity.
Despite the large variation in muscle number, the patterns in one muscle
group sometimes extended to others. Large numbers of muscles in any of the
rostrocaudally-oriented muscle groups (dorsoplagiopatagiales,
coracoplagiopatagiales, or plagiopatagiales proprii) was correlated with relatively
high counts in the other two groups. These muscles may all share development
origins which would explain the observed correlation. It has been shown that the
coracoplagiopatagiales and plagiopatagiales proprii share a developmental
origin, but details of dorsoplagiopatagiales development are still unknown (Tokita
et al 2012).
4.6 Length of wing membrane muscles
123
For wing membrane muscles, it is thought that the less plagiopatagium in
series, the greater the effect on membrane stiffness and thus shape (Cheney et
al 2014a). Thus relatively long muscles are more effective than relatively short
ones. The dorsoplagiopatagiales, coracoplagiopatagiales, and plagiopatagiales
proprii, are all always relatively long and extend over the majority of the
chordwise plagiopatagium. In contrast, the tibioplagiopatagiales and
cubitoplagiopatagiales varied between extremely short to extending over almost
the whole plagiopatagium (contrast tibioplagiopatagiales in figure 5a vs 5c). Such
varying muscle morphology suggests that there exists dramatic differences in the
effectiveness of muscle actuation. The short tibioplagiopatagiales in Molossidae,
Natalidae, and Noctilionidae, represent such a small percentage of the spanwise
length of the plagiopatagium that they may be wholly ineffective as membrane
actuators (Table 1).
Wing membrane muscles have been proposed to function as stretch
sensors in addition to, or instead of, exerting force (Cheney et al 2014a). Such a
sensory role would provide bats with the degree to which muscle, and thus wing
skin, are deformed by aerodynamic forces. Integration of membrane length and
skeletal position of the bones framing the plagiopatagium, would provide an
indirect measure of the three-dimensional configuration of the plagiopatagium. If
muscle stretch reception is critical to bat flight, we expect that these short
muscles may be the most likely to relay this information, given their hypothesized
reduced functional capacity.
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5. Conclusions
Imaging bat wing membranes with cross-polarized light provides a means
to differentiate elastin fibers from wing membrane muscles that is both relatively
quick and does not involve destructive sampling. It is also generally superior to
brightfield imaging. Though it cannot replace the detailed histological information
provided by sectioning or scanning electron microscopy, it can be used to place
those findings into a broader context, both within the heterogeneous architecture
of the wing membrane and across taxa.
Using cross-polarized light, we found that wing membranes have multiple
arrays of muscles, potentially allowing for tremendous capacity to modulate
three-dimensional wing form. We identified five arrays of muscles that insert into
the plagiopatagium, originating from the regions of the tibia, trunk, scapula,
elbow, and within the plagiopatagium itself. Among species, muscle number and
length varied. This variation appeared to show a phylogenetic signal, but more
detailed analysis is required.
The tendons of the plagiopatagiales proprii are elastin fibers, or more
precisely, fibers composed of colinear elastin and collagen fibrils. These fibers
anchor to the surrounding membrane by means of collagen fibrils. The collagen
fibrils may be key to providing a stiff insertion site for the plagiopatagiales proprii,
as without them, muscle function could be impaired.
Finally, we found that elastin fibers run along the wing spreading axes in
every species studied. A second population forming a grid was observed, but
125
only in a subset of species and a small portion of the wing membrane. Thus
given the architectural similarities in most species, the mechanical contribution to
wing membrane mechanics by elastin fibers is likely similar in all bats.
Further study of wing membrane architecture is needed at multiple levels.
We have demonstrated that there is unusual architectural arrangements at the
microscopic level, dramatic heterogeneity within the wing membrane, and
variability among taxa. Data at one level, without a broader perspective, can lead
to improperly drawn conclusions. We hope that this work inspires future
integrative studies.
Acknowledgements
We would like to thank Andrew Bearnot, Rosalyn Price-Waldman, Elissa
Johnson, and Caleb Anderson for their help photographing specimens. Roger T.
Hanlon, Alan M. Kuzirian, and George R. R. Bell provided equipment, laboratory
space, and assistance with histology. Beth Brainerd provided helpful discussion
that greatly benefitted the manuscript.
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Figure 1. Tissues illuminate under cross-polarized light in a manner
consistent with anatomical description. (a) Image of plagiopatagium
illuminated with cross-polarized light for species Rhinolophus alcyone. (b)
Anatomical drawing of Rhinolophus ferrumequinum (adapted from Morra 1899).
Thin lines are described as elastic fibers, thick bands are muscle. (a,b)
Anatomical drawing suggests brightly illuminated structures to be muscle and
moderate contrast thin bands to be elastic fibers under cross-polarized light.
129
Figure 2. Validation of crosspolarized light imaging using
histology. (a) Image of wing
membrane under cross-polarized light.
Yellow rectangle denotes approximate
region of wing studied. (b) Left,
representative image of tissue region
sampled. Each region was
hypothesized to contain the tip of a
plagiopatagialis proprius muscle, as
well as elastin fibers running
perpendicular and parallel to the
muscle. Purple dashed line
approximates the tissue section shown
in (c). Right, schematic of hypothesized
architecture; muscle is light purple and
elastin fibers are dark purple. (c)
Sagittal section of plagiopatagialis
proprius and tendon. Elastin fibers runs
in series with the muscle. Tissue is
differentiated with modified Verhoeff’s
and van Gieson’s stains. (b,c)
Abbreviations: muscle (m), elastin fiber
in cross-section (e┴), elastin fiber in
longitudinal section (e║).
130
Table 1. Summary of imaged bats sorted by family. We sampled sixteen of
the seventeen families, as defined by Teeling and colleagues (2005). In total, 130
species were imaged, representing on average, 34% of family level diversity.
Right, family-level phylogeny (Teeling et al 2005).
131
Figure 3. Schematic of the muscles of the plagiopatagium. Muscle
architecture varies, but five muscle groups are consistently found inserting into
the skin of the plagiopatagium. Naming adapted from Schumacher (1932).
132
Figure 4. Schematic of elastin network. (a) Cross-polarized light image of
whole wing of Artibeus jamaicensis (Phyllostomidae) showing elastin fibers and
vasculature. Muscles have been removed by chemical digestion. Wing is
mounted on steel wire frame. (b) Illustration of elastin fibers. Vertically striped
regions not studied.
133
Figure 5. Elastin fibers
run along the wing
spreading axis, but
some regions contain
a second population of
elastin fibers. (a,b)
Elastin fibers run
predominantly along the
spreading axes. (c) The
region rostral to the
plagiopatagiales proprii,
(indictaed by +) contains
a second population of
elastin fibers, orthogonal
to the dominant axis.
Inset captures magnified
view of this region. (a)
Natalus tumidirostris
(Natalidae); (b)
Pteronotus davyi
(Mormoopidae); (c)
Hipposideros diadema
(Rhinolophidae). (a-c)
scale bar: 5 cm.
134
1
2
3
Table 2. Summary of muscles observed in bats. Bat phylogeny is included on the right for reference (Teeling et al
2005). The range of morphologies observed is included in each cell. Each cell contains morphological data on number
and/or length. The most commonly observed morphologies are indicated in parentheses.
4
135
Figure 6. Elastin fibers are
analogous to muscle
tendons. (a) Schematic of
plagiopatagium and
plagiopatagiales proprii
(orange). Sampled region is
marked by green rectangle. (bd) Brightfield images of sections
of the rostral end of
plagiopatagialis proprius stained
with modified Verhoeff’s and
van Gieson’s stains.
Abbreviations: c, collagen; e+c,
elastin wrapped in collagen; m,
plagiopatagialis proprius
muscle. (b) Sagittal section
showing junction between
muscle (dark purple with visible
z-bands) and elastin fibers
wrapped in collagen (dark
purple and pink). (c-d)
Transverse section showing the
ends of the myofibers (purple)
transitioning to elastin fibers
wrapped in collagen (dark
purple and pink). (d) Higher
magnification image showing
detail in elastin fiber (black/dark
purple) wrapped in collagen
(pink) and the ends of the
plagiopatagialis proprius muscle
in cross section (purple). Scale
bars: (a) 1mm; (b-c) 100μm; (d)
10μm.
136
Figure 7. Collagenous periphery of elastin fibers anchors to the
surrounding matrix. (a,b) Sagittal sections of plagiopatagialis proprius muscle
and elastin fibers stained with modified Verhoeff’s and van Gieson’s stains.
Upper elastin fiber has been sectioned in cross, lower elastin fiber has been
sectioned longitudinally. Lower elastin fiber runs in-series with muscle. Collagen:
pink, elastin: dark purple, muscle: purple. Green arrows denote collagenous
anchor points. Abbreviations: e, elastin; m, plagiopatagialis proprius muscle.
137
Figure 8. Convergent sheet-like muscle
morphology in the plagiopatagiales
proprii. (a-c) Elbow can be identified in
upper-left corner of images. Distal portion of
the plagiopatagium is right. (a) Brightfield
image of Epomops franqueti
(Pteropodidae). (b) Cross-polarized light
image of Anoura geoffroyi (Phyllostomidae).
(c) Cross-polarized light image of Otomops
martiensseni (Molossidae).
138
Appendix
Compliant tendons can increase the number of functional roles of muscle,
but they can also hinder muscle function. Muscles with compliant tendons can
function as power amplifiers and attenuators (reviewed in Roberts and Azizi
2011). However, too much compliance may limit a muscle’s capability to
generate maximum force. Because muscle and tendon are in series, muscle
force must equal the tensile force in the tendon. Tendon must stretch to bear
these loads and if the change in length, corresponding to maximum muscle force,
exceeds the sum of maximum joint excursion and muscle length contraction,
then tendon will limit muscle force. This hypothetical limitation would almost
certainly be met if muscles force was borne by slender elastin tendons.
Fixed-end compliance analysis demonstrates that extremely compliant
tendons do not transmit muscle loads efficiently unless they are relatively short
and/or thick (Roberts 2002). This analysis describes percent muscle length
change during maximal force contractions in which the combined length of
muscle and tendon remains constant. Typical change in muscle length is less
than 30% (Roberts 2002). Fixed-end compliance depends upon the relative
𝐿
resting length of a muscle and its tendon ( 𝐿𝑚), relative cross sectional area of the
𝑡
𝐴
muscle and tendon ( 𝐴𝑚 ), and the ratio of peak muscle stress to tendon stiffness
𝑡
𝜎
( 𝐸𝑚 ) and is described with the following inequality:
𝑡
𝐿𝑡
𝐴𝑚 𝜎𝑚
∗
∗
< 0.3
𝐿𝑚
𝐴𝑡
𝐸𝑡
139
Using approximate values for the stiffness of elastin (1 MPa; Hoeve and Flory
1958) and peak stress capacity in mammalian muscle (0.3 MPa, Ker 1988), we
find that relative muscle area must be less than relative muscle length:
𝐴𝑚 𝐿𝑚
<
𝐴𝑡
𝐿𝑡
This inequality demonstrates that a tendon composed entirely of compliant
elastin can only allow typical muscle length changes, if relative to the muscle it is
extremely short or extremely thick. Neither of which describes elastin fibers.
Thus, given that the plagiopatagiales proprii do activate in flight, we must
carefully look at the architecture of these fibers to understand which assumptions
used in this model are likely to be invalid.
140