The Biodynamics of Arboreal Locomotion in the Gray Short
THE BIODYNAMICS OF ARBOREAL LOCOMOTION IN THE GRAY SHORT-
TAILED OPOSSUM (MONODELPHIS DOMESTICA)
A dissertation presented to
the faculty of
the College of Arts and Sciences of Ohio University
In partial fulfillment
of the requirements for the degree
Doctor of Philosophy
Andrew R. Lammers
August 2004
This dissertation entitled
THE BIODYNAMICS OF ARBOREAL LOCOMOTION IN THE GRAY SHORT-
TAILED OPOSSUM (MONODELPHIS DOMESTICA)
BY
ANDREW R. LAMMERS
has been approved
for the Department of Biological Sciences
and the College of Arts and Sciences by
Audrone R. Biknevicius
Associate Professor of Biomedical Sciences
Leslie A. Flemming
Dean, College of Arts and Sciences
LAMMERS, ANDREW R. Ph.D. August 2004. Biological Sciences
The biodynamics of arboreal locomotion in the gray short-tailed opossum (Monodelphis
domestica). (147 pp.)
Director of Dissertation: Audrone R. Biknevicius
Most studies of animal locomotor biomechanics examine movement on a level, flat trackway. However, small animals must negotiate heterogenerous terrain that includes changes in orientation and diameter. Furthermore, animals which are specialized for arboreal locomotion may solve the biomechanical problems that are inherent in substrates that are sloped and/or narrow differently from animals which are considered terrestrial.
Thus I studied the effects of substrate orientation and diameter on locomotor kinetics and kinematics in the gray short-tailed opossum (Monodelphis domestica). The genus
Monodelphis is considered the most terrestrially adapted member of the family
Didelphidae, but nevertheless these opossums are reasonably skilled at climbing.
The first study (Chapter 2) examines the biomechanics of moving up a 30° incline and down a 30° decline. Substrate reaction forces (SRFs), limb kinematics, and required coefficient of friction were measured. On sloped substrates, M. domestica moved more slowly with a higher duty factor, used more statically stable gaits (decline), and required a greater coefficient of friction to avoid slipping. These data suggest that a 30° slope is enough to perturb the opossums’ normal mode of locomotion, and they must therefore adjust their locomotor patterns to remain stable. On inclines, both limb pairs supported body weight equally, and the craniocaudal limb excursion increased; however, the forelimbs exerted greater propulsive impulse than hindlimbs. On the decline, the
forelimbs were brought to bear far more body weight and braking effort than the
hindlimbs; perhaps the greater forelimb protraction (at touchdown) was a way of
accommodating a more substantial load during downhill locomotion.
The second and third studies (Chapters 3 & 4) tested the effects of substrate diameter on locomotor kinetics and kinematics. On the arboreal substrate, many kinetic patterns were similar to those observed on the terrestrial. Forelimbs exhibited higher vertical impulse and peak vertical force than hindlimbs, and both limb pairs exerted a braking force followed by a propulsive force during each stride. However, the forelimbs exerted more than twice the braking and propulsive impulses than hindlimbs. The manus
was placed higher around the circumference of the branch than the pes. The shifts in
forces and limb placement resulted in a lower required coefficient of friction in the
forelimb. Thus, the forelimbs are probably more stable than the hindlimbs, and this may
explain why forelimbs have such a dominant role on the branch. Although vertical
impulses were lower on the terrestrial substrate than on the arboreal support, this was most likely due to speed effects because the opossums refused to move as quickly on the arboreal trackway. Vertical impulse decreased significantly faster with speed on the arboreal substrate because most of these trials were relatively slow, and stance duration decreased with speed more rapidly at these lower speeds.
A decrease in speed is a common behavioral adaptation to maintain stability.
Stride length, frequency, and duration were well-correlated with speed, but spatial variables were not. Thus it is possible that timing variables were affected by speed, while substrate affected mostly spatial variables (joint angles and limb placement). The distal elements of the forelimb were significantly more adducted on the arboreal substrate, but
otherwise there were few substrate effects on the forelimb. It is possible that the relatively stable placement of the manus permits the forelimb to make few kinematic adjustments for arboreal locomotion. In contrast, substrate had many significant effects on hindlimb kinematics. Like the forelimb, the distal elements of the hindlimb were significantly adducted on the arboreal trackway. On the arboreal trackway, the hindlimb was more protracted at touchdown and time of peak vertical force, and hip height was greater. The pelvic girdle of the opossums underwent lateral undulation regardless of substrate. The lack of crouching behavior on the branch may suggest that crouching behavior is not a universal adaptation to treacherous substrates. Finally, the posterior shift in weight support observed in Chapter 3 may be the result of relatively protracted hindlimbs on the arboreal trackway.
Approved: Audrone R. Biknevicius
Associate Professor of Biomedical Sciences
ACKNOWLEDGMENTS
I would like to thank my dissertation committee members: my advisor, Audrone
Biknevicius, and committee members Steve Reilly, Nancy Stevens, Nancy Taterek, and
Larry Witmer for their support during the completion of this dissertation. To Audrone, thank you for giving me this chance to work in your lab, for giving me a second chance when I needed it, and for your constant support, enthusiasm, and friendship. To Steve, thank you for sharing your excitement of science and of my research. To Nancy Stevens for many fruitful discussions about the biomechanical challenges of arboreal locomotion, and also for the possum poetry. To Larry, for showing me that anatomy is incredibly interesting – not only has it been enjoyable to teach human gross anatomy over the last three years, that knowledge and experience was in no small way responsible for landing my new job. To Nancy Taterek, thanks for your last-minute help and agreeing to serve on my committee on such short notice.
I would also like to acknowledge my indebtedness to Kay Earls, who taught me everything I know about designing and building force transducers and programming
Labview virtual instruments. I also thank former and current members of the Biknevicius lab, including Jen Hancock, Elicia Thompson, and Jeff Willey for their friendship and scientific discussion. Thanks also to all of the graduate students and faculty in the
Ecology and Evolutionary Biology program at Ohio University who have helped make the past five years a truly enjoyable experience, both professionally and personally.
I thank many undergraduates who spent tireless hours helping me collect data: Julie
Abbuhl, Amy Back, Emily Bevis, Trish Chalfant, Jessica Demidovich, Kevin Funk, Josh
Hill, Andy Parchman, ChiChi Peng, and Jen Tat. I thank Eric Lindner for his expert care
of the opossums, and Randy Mulford of the physics metal shop for building many
versions of the arboreal force transducers. Funding for this dissertation was provided by the Department of Biological Sciences, Ohio University, and a Sigma Xi Grant in Aid of
Research.
Finally, I thank my parents, Kenneth and Dorothy Lammers, and my brother Ben, for their never-ending support, and for providing a place to escape when I needed a break. Finally, thanks to my girlfriend, Darcy, whose love and support was essential to completing my dissertation and getting a job.
Table of Contents
List of Tables ...... 10 List of Figures...... 11 Chapter 1: The biomechanical challenges of arboreal locomotion ...... 15 1.1. Terrestrial locomotion...... 15 1.2. Arboreal substrates...... 16 Incline and decline...... 16 Diameter ...... 18 1.3. Relevance...... 20 1.4. References...... 21 Chapter 2: Locomotor kinetics and kinematics on inclines and declines in the gray short-tailed opossum (Monodelphis domestica) ...... 29 2.1. Summary...... 29 2.2. Introduction...... 30 2.3. Materials and Methods...... 34 Animals ...... 34 Force data acquisition ...... 34 High-speed videography ...... 36 Statistics ...... 37 2.4. Results...... 38 Kinematics...... 38 Kinetics ...... 40 Required coefficient of friction ...... 43 2.5. Discussion...... 44 Locomotor biodynamics on level substrates...... 44 Locomotor biodynamics on inclined substrates...... 46 Locomotor biodynamics on declined substrates...... 49 Synthesis...... 51 2.6. Acknowledgments...... 52 2.7. References...... 52 2.8. Tables and figures...... 59 Chapter 3: The effects of substrate diameter on locomotor kinetics in the gray short- tailed opossum (Monodelphis domestica) ...... 68 3.1. Summary...... 68 3.2. Introduction...... 69 3.3. Materials and methods ...... 72 Animals ...... 72 Kinetic data...... 72 Kinematic data...... 74 Calculating required coefficient of friction ...... 76 Statistical analyses...... 77 3.4. Results...... 78
Gait characteristics...... 78 Substrate reaction forces ...... 79 Limb placement and required coefficient of friction...... 81 3.5. Discussion...... 81 Behavioral adaptations for arboreal locomotion ...... 89 3.6. Acknowledgments...... 91 3.7. References...... 91 3.8. Tables and figures...... 97 Chapter 4: Limb kinematics on terrestrial and arboreal substrates in the gray short- tailed opossum (Monodelphis domestica) ...... 107 4.1. Summary...... 107 4.2. Introduction...... 108 4.3. Materials and methods ...... 110 Animals, landmark placement, and radiography...... 110 Kinematic data collection ...... 111 Statistical analyses...... 114 4.4. Results...... 115 General kinematics ...... 115 Forelimbs ...... 116 Hindlimbs...... 117 4.5. Discussion...... 119 Stability ...... 119 Broader implications on arboreal mechanics...... 123 4.6. Acknowledgments...... 125 4.7. References...... 125 4.8. Tables and figures...... 129 Chapter 5: Synthesis and future directions...... 139 5.1. Synthesis ...... 139 5.2. Future directions ...... 143 5.3. References...... 145
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List of Tables
Page Table 2.1. Limb kinematic parameters during stance phase. Protraction, 59 retraction, and adduction angles are measured in degrees. Shoulder and hip heights units are centimeters
Table 2.2. Least squares regression analyses of peak vertical force (BW s) vs. 60 speed (m s-1)
Table 2.3. Peak vertical force (BW units) and impulse (BW s) 61
Table 3.1. General kinematics. Shown are means±S.E.M., (minimum, maximum) 97
Table 3.2. Peak vertical force (BW units), and vertical, fore-aft and mediolateral 98 impulses (BW s). Means ± standard error, with minimum and maximum in parentheses
Table 3.3. Least squares regression results for vertical impulse (BW s) vs. speed 99 (m s-1)
Table 4.1. Fore-aft (y), vertical (z), and mediolateral (x) coordinates of the limb 129 joints relative to the shoulder and hip [mean (minimum, maximum)] at touchdown, time of peak vertical force, and liftoff. Shoulder and hip y and x coordinates were transformed to zero, and all other y and x coordinates were transformed accordingly. Positive values indicate a position anterior and/or medial to the shoulder or hip.Negative coordinates indicate posterior and/or lateral to the shoulder or hip. Vertical (z) coordinates indicate height above initial manus/pes contact.
Table 4.2. Limb angles [mean ( minimum, maximum)]. 131
Table 4.3. Shoulder and hip height from the contact of the limb on the substrate. 132
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List of Figures
Page Figure 1.1. A. Representation of a quadruped on an incline. Note that the line 26 of gravity (arrow) passing through the center of mass (black dot) very nearly passing outside the base of support. B. Limb retraction will cause the weight to be supported more evenly between fore- and hindlimbs. C. Crouching will decrease the risk of toppling, and also redistributes the weight between fore-and hindlimbs. The dashed line passing through the hindlimb in A. and C. is perpendicular to the substrate.
Figure 1.2. Diagram of the frontal view of a quadruped moving on a substrate 27 somewhat narrower than the body diameter of the animal. Forelimbs are shown in the same shade of gray as the rest of the body; hindlimbs are shown in dark gray. For clarity, only two or three limbs are shown at a time. A. Animal is in danger of toppling by falling because its weight (solid arrow) is not as well supported. B. Animal’s center of mass is now above the support, but it is still in danger of falling because of the torque generated by the limb in contact with the substrate. C. By maintaining a limb contact on both sides of the branch (in this case, a right forelimb and a left hindlimb), the animal reduces the likelihood of rolling. D. Identical to C., but the position of the manus and pes has shifted to decrease the likelihood of the limb sliding down the sides of the substrate. E. Identical to D., but the animal is also crouching to reduce the likelihood of rolling.
Figure 1.3. A. Monodelphis domestica, the gray short-tailed opossum. B. 28 Closeup of M. domestica, showing the hindfoot.
Figure 2.1. Data collection setup. A. Film from the cameras was uploaded and 62 analyzed using a personal computer. Voltage changes measured from the force platform were fed directly into the amplifier, converted from analog to digital, and then displayed by a LabVIEW virtual instrument. B. Digitized landmarks and the calculation of limb excursion angles. Protraction angle was measured at the beginning of stance phase, and retraction angle was measured at the end of stance stance phase. C. Likewise, adduction angle was also measured at the beginning and end of stance phase.
Figure 2.2. Gait plot of limb phase against hindlimb duty factor. Trot and 63 lateral sequence trot-like (i.e., diagonal couplet) classifications are denoted by dashed lines. Following the convention of Hildebrand (1976), the axes are reversed.
Figure 2.3. Summary of fore- and hindlimb touchdown and liftoff angles, and 64 dorsoventral, braking, and propulsive impulse. Angles are exaggerated to make differences between limbs and among substrates more visible. Note that
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braking (B) and propulsive (P) impulses, when shown, are approximately one order of magnitude smaller on the level than on the incline and decline.
Figure 2.4. Typical force traces for each limb and substrate type. A -D are 65 from the level trackway. A & B. were relatively fast trials, and C & D were relatively slow. A & C are forelimb traces, and B & D are hindlimb traces. E & F are fore- and hindlimb traces (respectively) from the inclined trackway. G & H are fore- and hindlimb traces (respectively) from the declined trackway. Craniocaudal force is shown in gray for clarity.
Figure 2.5. Relative effort (%) of dorsoventral, braking, and propulsive 66 impulses exerted by fore- and hindlimbs. Absolute values of total impulse (forelimb + hindlimb) are indicated to the right. Because the total propulsive impulse on the decline was extremely low, percent limb effort was not calculated.
Figure 2.6. Frictional issues in locomotion. A. Typical plot of the required 67 coefficient of friction in M. domestica running at 1.78 m s-1 on the level trackway. B. Box plots of median required coefficient of friction for each substrate and limb pair. The horizontal line in the middle of each box represents the median for each group, and each box on either side of the median encloses one-fourth of the data. Each whisker also represents one-fourth of the data. The asterisk indicates an outlier; the circle denotes an extreme outlier.
Figure 3.1. Arboreal locomotion in Monodelphis domestica. A. Resolution of 100 SRFs into normal and shear components (Fnormal, ML and Fshear, ML respectively) as illustrated for a forelimb and its mediolateral SRF (FML). XFL, YFL, ZFL = coordinates of the estimated center of forelimb pressure. B. Resolution of vertical SRFs into shear and normal components (Fnormal, V and Fshear, V respectively). C. Cropped representative image of M. domestica on the arboreal trackway illustrating the limb landmarks: (1) distal tip of the 3rd manual digit; (2) lateral aspect of the wrist joint; (3) distal tip of the 5th pedal digit; (4) lateral aspect of the metatarsophalangeal joint. Note that the heel (see arrow pointing to the ankle marker) was typically not in contact with the substrate during arboreal and terrestrial trials. Scale bar (4 cm) denotes the length and location of the arboreal force transducer.
Figure 3.2. Phylogeny of some American marsupials, based on Palma and 101 Spotorno (1999) and Nowak (1999). Although scansorial and arboreal locomotor adaptations evolved more than once in family Didelphidae, it is likely that the common ancestor was a terrestrial form. Furthermore, Nowak (1999) and Cartmill (1972) suggest that the terrestrial Monodelphis genus retains the primitive condition to the greatest degree.
Figure 3.3. A. Symmetrical gait plot for M. domestica during terrestrial and 102
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arboreal locomotion following Hildebrand (1976). Terrestrial and arboreal trials lie mostly within trots, although arboreal trials extend into smaller limb phases a(lateral-sequence diagonal- couplet gait). B. Relationship between stance duration and speed.
Figure 3.4. Representative substrate reaction force profiles from the terrestrial 103 and arboreal trackways (speed indicated on each plot). A, B. Slow terrestrial forelimb and hindlimb trials, respectively. C, D. Fast terrestrial trials for the forelimb and hindlimb, respectively. E, F. Forelimb and hindlimb arboreal trials. Negative craniocaudal forces indicate a braking effort and positive indicates propulsion. Negative mediolateral force designates a medially- directed SRF (laterally- directed limb force) and positive designates a medially-directed limb force. For clarity, craniocaudal force is shown in gray.
Figure 3.5. Relationship of kinetic variables vs. speed. A. Peak vertical force. 104 B. Vertical impulse. C. Braking impulse. D. Propulsive impulse. The sample ellipses emphasize substrate and limb groups. The dimensions of the ellipses were determined from the standard deviations of the y and x variables; sample covariance between y and x determine the orientation of the ellipse.
Figure 3.6. Box-and-whisker plots of net mediolateral impulse for each 105 substrate and extremity group. The line in the middle of each box plot represents the median; each box and each whisker corresponds to one- fourth of the data; asterisks designate outliers; circle denotes extreme outliers. Positive values indicate a medially-directed limb force (laterally- directed SRF), and negative values indicate a laterally-directed limb force. Substrates were significantly different (P<0.00001), but there were no differences between limbs within substrate groups.
Figure 3.7. A. Manus and pes placement about the arboreal trackway. 106 Location of the center of pressure of each foot is drawn to scale relative to branch cross- sectional shape. B. Representative required coefficient of friction data from M. domestica on the arboreal trackway (1.10 m s-1). High values occur at the foot touchdown and again at the end of the step. The hatched line indicates the median value for this record (0.528). C. Median required coefficient of friction for forelimbs and hindlimbs on horizontal terrestrial and arboreal substrates. Ellipses are used to make each group more clearly stand out, and are calculated as in Fig. 3.5.
Figure 4.1. A. Location of digitizing landmarks on the left side of M. 133 domestica; see text for further descriptions. B. Limb segments. C. Angles. Forelimb and hindlimb angles are shown by the dotted lines. D. 3-dimensional coordinate system. Negative x is lateral (coming out of the page), negative y is caudal, and negative z is ventral.
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Figure 4.2. Whole limb and joint angles during a typical stride cycle. A. 134 Forelimbs, arboreal substrate. B. Forelimbs, terrestrial substrate. C. Hindlimbs, arboreal substrate. D. Hindlimbs, arboreal substrate. Stance phase is shaded gray. 0% stride cycle = TD, dotted vertical lines indicate MS, and dashed vertical lines indicate LO.
Figure 4.3. Box and whisker plots of craniocaudal excursion angle. The white 135 boxes are forelimb touchdown (top) and liftoff (bottom) angles, and the gray boxes are hindlimbs. Arboreal trials are shown on the left, terrestrial on the right. Each box represents one-half of the data, with the median shown as a line in each box. Each whisker represents one-quarter of the data. Asterisks are outliers.
Figure 4.4. Lateral view of the sagittal limb kinematics during stance phase. 136 A. Forelimb, terrestrial substrate. B. Forelimb, arboreal substrate. C. Hindlimb, terrestrial substrate. D. Hindlimb, terrestrial substrate. Symbols represent joint coordinates through time. Gray ellipses represent limb segment (see Fig. 4.1B) at touchdown (left) and liftoff (right). The double- circle represents the manus or pes contact with the substrate. Negative values in the craniocaudal (y) axis indicate caudal to the manus of pes contact.
Figure 4.5. Dorsal view of the transverse limb kinematics during stance phase. 137 A. Forelimb, terrestrial substrate. B. Forelimb, arboreal substrate. C. Hindlimb, terrestrial substrate. D. Hindlimb, terrestrial substrate. Symbols represent joint coordinates through time. Plots progress from touchdown (left) to liftoff (right). The double-circle represents the manus or pes contact with the substrate. Negative values in the craniocaudal (y) and mediolateral (x) axes indicate caudal and lateral to the manus or pes contact, respectively.
Figure 4.6. Dorsal view of lateral undulation of the spine and pelvis. Shown is 138 the vertebral column and left hindlimb at touchdown (TD, dark gray) and liftoff (LO, light gray). Note that the pes is more lateral to the hip at LO compared with TD. Presuming minimal lateral movement of the pes during stance phase, this likely represents a shift of the pelvis toward the stance hindlimb at TD and a shift to toward the contralateral hindlimb at LO.
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Chapter 1: The biomechanical challenges of arboreal locomotion
1.1. Terrestrial locomotion
Great strides were made in the last half-century in describing and quantifying the biodynamics of terrestrial locomotion in tetrapods (reviewed in Reilly and Biknevicius
2003). For example, the summarization of symmetrical gaits by limb phase (timing of forelimb footfall relative ipsilateral hindlimb footfall) and duty factor (support duration relative to stride duration) enabled unambiguous kinematic classification of walks and runs (Hildebrand 1968, 1976). Similarly, the study of substrate reaction forces (SRFs) uncovered broad similarities in limb functions across (non-primate) mammals: forelimbs tend to support a greater proportion of body weight and are net braking whereas hindlimbs are net propulsive (Manter 1938; Budsberg et al. 1987; Biewener and Full
1992; Demes et al. 1994; Schmitt and Lemelin 2002). Finally, size-dependent changes among locomotor posture were found to explain moderate bone stress levels in terrestrial mammals (Biewener 1983, 1990): small mammals (0.001 – 0.1 kg) tend to have a crouched limb posture compared with larger mammals (0.1 – 300 kg).
More recently these biodynamic “rules” have been investigated further in order to assess whether or not they are truly ubiquitous, as it is acknowledged that laboratory runways designed with uniformly flat and level topography for steady-speed locomotion poorly represent real landscapes and locomotor behaviors (Weinstein and Full 2000;
Parchman et al. 2003). Studies of locomotion on inclined runways have uncovered some interesting contrasts with level locomotion. For example, animals as different as chameleons and cats appear to adapt kinematically to climbing up or down inclines by
16 adopting a more crouched posture (Peterson 1984; Carlson-Kuhta et al., 1998; Smith et al., 1998). It is at yet undetermined whether these postural changes are a response to increased stability or a strategy to maintain low levels of bone stress. Even modest inclines can boost locomotor effort, as indicated by the greater force generated by the gastrocnemius muscle in turkeys running up a 12° incline (Roberts et al., 1997).
Furthermore, arboreal substrates vary considerably in orientation and diameter, and small mammals must frequently negotiate such substrates. Thus, I explored how locomotor biomechanics in a small mammal are affected by slope and diameter changes.
1.2. Arboreal substrates
Arboreal substrates present several challenges to animals moving on or underneath them. These substrates vary dramatically in orientation (incline and decline), size (diameter), surface (coefficient of friction), and in stability (Bock and Winkler 1978;
Cartmill, 1974, 1985; Stevens, 2003a, b). My doctoral research examined behavioral and biomechanical adaptations that a terrestrial species undergoes to move on substrates that vary in orientation and diameter.
Incline and decline
When a quadruped moves up a sloped substrate, the line of gravity passing through the center of mass is drawn such that it intersects posteriorly with the base of support formed by the stance limbs (Fig 1.1A). Because of this shift in the direction of the weight vector, the hindlimbs of an animal moving uphill must accept relatively more weight than they do on a horizontal substrate, while forelimbs accept less. Thus, it is
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expected that the vertical impulse (which is responsible for resisting the pull of gravity on
the body) will adjust accordingly, increasing in hindlimbs and decreasing in forelimbs.
The opposite should occur on a decline.
A quadrupedal mammal may also have to adjust its limb kinematics or kinetics to
maintain stability on inclined and declined substrates because there is a greater possibility
of slipping down the slope or toppling (pitching). One way to maintain stability is to
move more slowly, allowing each limb to maintain contact with the substrate for a greater
percentage of each stride (i.e., increased duty factor). But decreased speed comes not
without cost. A rapidly moving animal may be dynamically stable, that is, the sequential
footfalls correct the tendency of the center of mass to fall. But when an animal decreases
its speed, it may have to make kinematic adjustments to enhance static stability, i.e.,
maintaining the weight vector within the base of support. This can be accomplished in
several ways. First, the animal can adjust the degree of protraction or retraction of its
limbs (Fig 1.1B). On an incline, both limbs (especially hindlimbs) can, on average,
maintain a more retracted posture so that the line of gravity passing through the center of
mass does not pass outside the base of support. On a decline, both limbs (especially forelimbs) may be more protracted relative to limb posture on a horizontal surface. A
second way to better maintain the line of gravity within the base of support is to crouch, because in this way the intersection of the weight vector with the base of support will be more centrally located (Fig 1.1C). This also has the effect of decreasing the likelihood that the animal will topple mediolaterally (rolling instability). Finally, an animal can modify its gait. Hildebrand (1980) demonstrated that a quadruped using a slow, lateral sequence singlefoot gait on a level substrate can keep the line of gravity enclosed in the
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base of support. If the limbs retract (on the incline) or protract (on the decline), then a lateral sequence gait may be useful to maintain static stability.
These adjustments are necessary to prevent the animal from toppling in the sagittal plane (pitch). But on sloped substrates, the animal must also prevent itself from sliding backward (on an incline) or forward (on a decline). Maintaining this form of stability is largely the role of the braking and propulsive impulses. On an incline, the propulsive impulses should increase to drive the animal up the slope and also prevent it from backsliding. Likewise, on the decline, the braking impulse should increase to
prevent the animal from sliding downslope. Propulsive and braking force can only be as
strong as the friction force between substrate and limb. Given that the coefficient of
friction is not expected to change, the friction force will be proportional to the
dorsoventral force, which in turn is closely related to vertical force. Thus, braking and
propulsive impulses are expected to be roughly proportional to vertical force.
Diameter
Unlike moving on inclines and declines, moving on a narrow substrate does not
shift the gravity vector relative to the animal. However, it is possible that there exist
greater challenges to stability because the animal can destabilize laterally and roll off the
branch or, if the manus or pes grip the sides of the branch, to slip downward (Fig 1.2A,
B). Strategies to increase stability include decreasing speed so that duty factor (time of
limb contact with the substrate relative to stride duration) can be easily increased. Speed
reduction may also have the consequence of decreasing stride frequency, which Demes et
al. (1990) suggested could help reduce branch oscillation. To counter the possibility of
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toppling, the animal can adjust its gait so that at least one pair of contralateral limbs is in
contact with the substrate at all times (Fig 1.2C). Appropriate gaits might include the trot, which provides contralateral limbs support, or the lateral-sequence singlefoot, which retains most perfectly the center of mass enclosed with the base of support (Hildebrand,
1980; Stevens, 2003a, b). Another possibility is the diagonal-sequence diagonal-couplet,
characteristic of primates at slow to moderate speeds; Prost (1972) and Hildebrand (1976)
suggested that these gaits maintain more frequent contralateral limb contacts. Indeed, some arboreal marsupials also employ this mode of walking on narrow supports
(Dromiciops australis: Pridmore 1994; Caluromys philander: Schmitt and Lemelin
2002). The animal can also adopt a crouching posture (Schmitt, 1999; Fig 1.2E), which reduces the moment arm length of any torque that might cause the animals to roll about the branch. To reduce the probability of slipping down the sides of the branch, the animal can keep its body more directly over the branch (Fig 1.2B) and reduce lateral undulation. Finally, by placing the manus and/or pes closer to the top surface of the branch (rather than on the sides; Fig. 1.2D), the animal can reduce the degree to which its weight will contribute to slipping. Thus, there are numerous kinematic adjustments that can be expected from an animal moving on a narrow support.
When kinematic adjustments occur, one should expect to find changes in limb function that are reflected by changes in substrate reaction forces (SRFs). For example,
Schmitt (2003) observed that primates tend to decrease the peak vertical SRF when moving on narrower supports; however, lower peak vertical forces are also expected if animals decrease speed. Many arboreal taxa (primates, woolly opossum) support a greater percentage of body weight with their hindlimbs (Schmitt and Lemelin, 2002).
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Although it has been suggested that this reduces the loading on flexible forelimbs
(Reynolds, 1985), it is possible that this “posterior weight shift” is a speed effect: at high speeds (on a terrestrial trackway) the animal should shift its weight anteriorly and maintain dynamic stability by moving its limbs fast enough to “catch” its anteriorly- displaced weight. But at the lower speeds expected on narrow supports, the animal may not shift its weight anteriorly as it would at high speeds. Finally, on narrow supports, it may be necessary for the animal to exert medially-directed limb forces (lateral SRFs) if the manus and/or pes are placed on the sides of the branch.
1.3. Relevance
At least 47% of extant non-volant, terrestrial mammals weigh less than 1 kg (Eisenberg
1981), yet most locomotor biodynamic studies have focused on mammals of much greater body mass. Furthermore, most small mammals are scansorial (capable of climbing) even if they are not arboreal specialists. By necessity, many small mammals are facultatively scansorial as they traverse the ground surface and scamper up or down vegetation with seemingly equal ease (Montgomery, 1980; Ladine and Kissell 1994).
This likely describes the locomotor behavior of primitive mammals as well (Jenkins
1971; Lee and Cockburn 1985; Schmitt and Lemelin 2002). But investigations into mammalian locomotion on arboreal substrates are still largely nascent (with the notable exception of primates). Because so little is known about the locomotor biodynamics of small mammals, it is difficult to make inferences about locomotor function in primitive mammals. These omissions have effectively neglected animals in the size range and inferred locomotor behavior of early mammals rendering inferences on primitive
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locomotor function tenuous at best. This study contrasts terrestrial and arboreal
locomotor kinematics and kinetics in a small generalized mammal, Monodelphis
domestica (gray short-tailed opossum; Fig. 1.3). M. domestica also retains many
characteristics of mammals which are considered primitive: for example, their body size
is small, their limb morphology is unspecialized, and they possess epipubic bones. I anticipate that the study will illuminate not only the challenges that animals face in arboreal habitats but also the challenges that small mammals encounter when moving on any uneven landscape.
1.4. References
Biewener, A.A. (1983). Allometry of quadrupedal locomotion: the scaling of duty factor,
bone curvature and limb orientation to body size. J. Exp. Biol. 105, 147-171.
Biewener, A.A. (1990). Biomechanics of mammalian terrestrial locomotion. Science
250, 1097-1103.
Biewener, A.A. and R.J. Full. (1992). Force platform and kinematic analysis. In
Biomechanics – structures and systems: a practical approach, edited by A.A.
Biewener. Oxford: IRL Press at Oxford University Press.
Bock, W.J. and H. Winkler. (1978). Mechanical analysis of the external forces on
climbing mammals. Zoomorphol. 91, 49-61.
Budsberg, S.C., M.C. Verstraete, and R.W. Soutas-Little. (1987). Force plate analysis
of the walking gait in healthy dogs. Amer. J. Vet. Res. 48, 915-918.
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Carlson-Kuhta, P., T.V. Trank, and J.L. Smith. (1998). Forms of forward quadrupedal
locomotion. II. A comparison of posture, hindlimb kinematics, and motor patterns
for upslope and level walking. J. Neurophys. 79, 1687-1701.
Cartmill, M. (1974). Pads and claws in arboreal locomotion. In: Primate locomotion,
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A. B.
C.
Figure 1.1. A. Representation of a quadruped on an incline. Note that the line of gravity (arrow) passing through the center of mass (black dot) very nearly passing outside the base of support. B. Limb retraction will cause the weight to be supported more evenly between fore- and hindlimbs. C. Crouching will decrease the risk of toppling, and also redistributes the weight between fore- and hindlimbs. The dashed line passing through the hindlimb in A. and C. is perpendicular to the substrate.
27
Figure 1.2. Diagram of the frontal view of a quadruped moving on a substrate somewhat narrower than the body diameter of the animal. Forelimbs are shown in the same shade of gray as the rest of the body; hindlimbs are shown in dark gray. For clarity, only two or three limbs are shown at a time. A. Animal is in danger of toppling by falling because its weight (solid arrow) is not as well supported. B. Animal’s center of mass is now above the support, but it is still in danger of falling because of the torque generated by the limb in contact with the substrate. C. By maintaining a limb contact on both sides of the branch (in this case, a right forelimb and a left hindlimb), the animal reduces the likelihood of rolling. D. Identical to C., but the position of the manus and pes has shifted to decrease the likelihood of the limb sliding down the sides of the substrate. E. Identical to D., but the animal is also crouching to reduce the likelihood of rolling.
28
A.
B.
Figure 1.3. A. Monodelphis domestica, the gray short-tailed opossum. B. Closeup of M. domestica, showing the hindfoot.
29
Chapter 2: Locomotor kinetics and kinematics on inclines and declines
in the gray short-tailed opossum (Monodelphis domestica)
2.1. Summary
Small terrestrial animals continually encounter sloped substrates when moving about their habitat. Therefore, it is important to understand the mechanics and kinematics of locomotion on non-horizontal substrates as well as on level terrain. To this end, I trained gray short-tailed opossums (Monodelphis domestica) to move along level, 30° inclined, and 30° declined trackways instrumented with a force platform to record substrate reaction forces. Vertical, craniocaudal, and mediolateral impulses, peak vertical forces and required coefficient of friction (µreq) were calculated. In addition, two high
speed video cameras (120 Hz) were used to measure whole limb protraction, retraction,
and adduction angles at limb touchdown and liftoff, as well as gait and timing variables.
Patterns on the level terrain were typical for non-primate quadrupeds in that the forelimbs
supported the majority of the body weight, forelimbs were net braking and hindlimbs net
propulsive, and both limb pairs exerted small laterally-directed impulses. On sloped
substrates, M. domestica moved more slowly with a higher duty factor, used a more
statically stable gait (lateral-sequence diagonal-couplet), and exhibited a higher
shear:normal force ratio. On inclines, both limb pairs were more protracted at touchdown and more retracted at liftoff. Fore- and hindlimbs had equal roles in body weight support, and forelimbs exerted greater propulsive impulse than hindlimbs. The
30
µreq was higher in the forelimbs than in hindlimbs. On declines, only the forelimbs were
more protracted at touchdown. Forelimbs also supported the great majority of body
weight, and they generated nearly all of the braking impulse. Despite the disparity in
fore- vs hindlimb function on the decline, the µreq was not significantly different between limbs. Thus, the opossum adjusts the base of support generated by its limbs to better support its body weight on the graded substrates (especially declines). The greater propulsive effort of the forelimbs on the incline may be due to the greater excursion of the limb pair. The expanded role of the forelimb on the decline suggests that a greater risk of injury may exist because the forelimbs must dissipate the great majority of the gravitational potential energy. Higher µreq on the graded substrates indicates a higher probability of slipping.
2.2. Introduction
Substrate reaction forces (SRFs) are the output of musculoskeletal effort during terrestrial locomotion. SRFs of individual limbs during walking and/or running have been examined in numerous tetrapods, including mammals (Budsberg et al., 1987;
Biewener, 1990; Demes et al., 1994), lizards (Christian, 1995), alligators (Willey et al.,
2004), and birds (Coor, 2003). Although differences among clades of mammals have been reported (Demes et al., 1994), the SRFs of most mammals follow a common pattern.
The vertical SRF is by far the largest in magnitude, and it is required to support the weight of the body. Because the center of mass of most mammals is located closer to the forelimbs than to the hindlimbs, forelimb vertical SRFs tend to exceed those of
31 hindlimbs. The craniocaudal (longitudinal) SRF is characterized by an initial braking component followed by a propulsive component; the braking component is typically larger than the propulsive component in the forelimbs whereas the hindlimbs are usually net braking. Mediolateral (transverse) forces tend to be very small, and, at least for cursorial mammals, they show no strong pattern of direction. Studies of terrestrial locomotor biomechanics predominately measure SRFs from animals moving along a flat, horizontal trackway, but locomotion on inclines and declines is ecologically relevant for most animals (Irschick and Jayne, 1999). Indeed, this may be especially true for small animals to which natural terrains appear particularly heterogeneous.
Stability is maintained during terrestrial locomotion (both level and graded substrates), in large part, by adjusting limb function (as reflected by SRFs), gait, and locomotor posture, including the degree of limb excursion. The inescapable effects of gravity necessitate shifts in limb function when moving on graded substrates. It is expected that uphill climbing should somewhat unload the forelimb while downhill climbing should enhance the forelimb’s load. It is further expected that both limbs must generate additional propulsive effort to raise the center of mass uphill whereas a greater braking effort is required when moving downhill to counter the acceleration due to gravity. Strategies to control the rate of ascent or descent incorporate shifts not only in
SRFs but frictional issues as well. In order to avoid slipping on a substrate, an animal must generate sufficient friction force by either: (1) increasing the normal force
(perpendicular to the substrate), (2) increasing the effective coefficient of friction between the limb contact and the substrate by engaging its claws, or (3) decreasing the
32
shear forces (parallel to the substrate) to reduce the required coefficient of friction (µreq) and/or required normal force.
At slower locomotor speeds, mammals may adjust their gait in order to maximize static stability, so that the line of gravity that passes through the animal’s center of mass lies more commonly within the base of support established by the animal’s supporting limbs. Static stability is more easily maintained with gaits having larger polygons of support (Hildebrand 1976). One the most stable gaits on horizontal substrates is the lateral-sequence singlefoot (Hildebrand 1976, 1980). This was also the gait observed in the largely terrestrial gray short-tailed opossums (Monodelphis domestica) when moving with a high duty factor along 45° inclined and declined branches (Lammers 2001). By contrast, primates and some arboreal marsupials use diagonal-sequence diagonal-couplets and several lateral-sequence gaits, including diagonal-couplet, singlefoot, and occasional lateral-couplet gaits during non-level locomotion (Reynolds, 1985; Vilensky et al., 1994;
Schmitt and Larson, 1995; Schmidt and Fischer, 2000; Schmitt and Lemelin, 2002). The diagonal-sequence diagonal-couplets gait has been interpreted as an adaptation for moving on narrow arboreal supports where contralateral limbs must exert opposing mediolateral SRFs to maintain stability (Hildebrand, 1976). Animals moving at faster speeds may create a dynamically stable situation by moving the limbs quickly enough to compensate when body weight passes outside the base of support.
Slope-climbing animals may also adjust their limb posture (Fig 1.1). During incline locomotion, the line of gravity intersects the substrate more posteriorly, and animals climbing uphill may increase the retraction of their limbs (especially hindlimbs) so that the support polygon is similarly drawn more posteriorly. Likewise, downhill
33 climbing animals are expected to increase the protraction of their limbs (especially forelimbs) as a means of drawing the support polygon more anteriorly to match the more anteriorly-placed line of gravity. These predictions are supported by hindlimb data collected from squirrel monkeys (Vilensky et al., 1994), cats (uphill only; Carlson-Kuhta et al., 1998), and lizards (Dipsosaurus dorsalis, Jayne and Irschick, 1999), by forelimb data from the slow loris (Loris tardigradus, Stevens, 2002) and cats (Smith et al., 1998), and both limb pairs in owl monkeys, lemurids, lorisids, and cheirogaleids (Stevens and
Larson, 1999; Stevens, 2003). Animals climbing slopes and/or arboreal substrates might also be predicted to shorten their effective limb lengths in order to decrease the rotational moment of the torso about the limbs. Decreased effective limb length may also cause the weight vector passing through the center of mass to intersect the base of support more centrally. Climbers often achieve this by actually shortening their limbs over evolutionary time (Losos and Sinervo, 1989) or by adopting an overall crouched limb posture (Cartmill, 1985; Carlson-Kuhta et al., 1998).
Although the effect of slope-climbing on gait and limb posture has been examined in some taxa, the manner by which limb function, as reflected by SRFs, adjusts to slope- climbing has only recently been explored (Dutto et al., 2002; David V. Lee, Harvard
University, pers. comm.). An examination of SRFs in climbing animals can also lead to a better understanding of the role of friction in locomotion. To test predictions of how substrate reaction forces, gait, and limb excursion angles change on inclines and declines versus horizontal trackways, I ran gray short-tailed opossums (Monodelphis domestica;
Wagner, 1842) on level, 30° inclined, and 30° declined trackways. M. domestica is a small, terrestrial marsupial with a generalized, primitive morphology (Lee and Cockburn,
34
1985; Novacek, 1992), and so it is likely that my findings will be applicable to many
mammalian taxa.
2.3. Materials and Methods
Animals
Locomotor biodynamics were assessed on a level trackway in six gray short-tailed
opossums (Monodelphis domestica) and on sloped trackways with five opossums (89-103
g). Prior to data collection, the opossums were trained to run on the trackways so that
they would be accustomed to the apparatus and run steadily in a straight line. The
carcasses of three additional M. domestica of comparable size (77-93 g) were used to
calculate the craniocaudal location of the center of mass using the reaction board method
(Özkaya and Nordin, 1999). All animal care and experimental procedures followed
Institutional Animal Care and Use Committee guidelines.
Force data acquisition
Two terrestrial trackways were constructed, a level trackway (48 cm long, 11 cm wide) and a 30° sloped trackway (36 cm long, 11 cm wide). The sloped trackway was stabilized through the use of extensive buttressing and base weighting. A force platform
was installed flush and parallel to the surface of each trackway (Fig. 2.1A). The force
platform was equivalent to the strain gage-based, spring-blade design described in
Parchman et al. (2003). Individual limb substrate reaction forces (SRFs) were obtained
as the first footfall (forelimb) and last footfall (hindlimb) on the platform surface. Trials
used to obtain fore- and hindlimb data did not differ significantly in speed. Analog
35
outputs from the force platforms captured at 1200 Hz (level trials) and 500 Hz (sloped
trials) for 3 – 6 s were amplified (SCXI 1000 and 1121, National Instruments, Austin,
TX), converted from analog to digital (NB-M10-16L, National Instruments), and
recorded using a LabVIEW (National Instruments) virtual instrument. The raw voltages
were then converted into three-dimensional SRFs oriented relative to the surface of the
platform (and the opossum’s body): dorsoventral (FDV), craniocaudal (FCC) and
mediolateral (FML). These forces were filtered using a Butterworth notch filter (56 ± 5
Hz for FDV and FCC; 97 ± 5 Hz for FML).
In spite of great effort to obtain equivalent forward speeds on the level and sloped
runways, the opossums moved significantly faster on the level trackway (1.51±
0.05 m s-1) than on the sloped trackways (incline, 0.87±0.03 m s-1; decline, 0.84±0.03 m
s-1; P<0.0001; no significant difference in speed between incline and decline trials).
Previous studies in other species also found that preferred speed decreases on non-level
substrates (e.g., Wickler et al., 2000). Only trials in which the opossum moved at a near
steady speed were evaluated further. This was determined either by calculating forward
speed at four intervals from the overhead videos or by integrating the whole body
craniocaudal acceleration over the entire force plate to estimate forward speed (Parchman
et al., 2003). If speed over the any part of the trial was 15% above or below step speed,
the trial was discarded.
The role of limbs in body weight support was assessed using vertical force (FV), computed as the vector sum of the vertical components of FDV and FCC. The function of
limbs in controlling forward impulsion was determined by the magnitude of braking and
propulsive components of the craniocaudal impulse. The net mediolateral impulse (sum
36
of medial and lateral impulses) reflected limb function in maintaining lateral stability. In
addition, time to peak FV and time to FCC = 0 (when the FCC profile switches from
braking to propulsive) were measured relative to support duration. The required
coefficient of friction (µreq) was calculated as the ratio of shear force (vector sum of FCC and FML) to normal force (FDV). Although µreq was determined over the entire stance
phase, only median values were evaluated; the median was used rather than the mean
because the median would be influenced less by the relatively large µreq at touchdown and
liftoff. Finally, impulses were calculated by integrating forces (FV, FCC, and FML) through time.
High-speed videography
Prior to each experiment, the opossums’ limbs were shaved and white 1.3 x 1.7 mm beads were applied onto darkened skin overlying major limb joints (wrist, glenohumeral joint, lateral metatarsophalangeal joint, and greater trochanter of the hip).
Simultaneous high-speed video recordings (JVC GR-DVL 9800, Yokohama, Japan), recording at 120 Hz, shutter speed 1/250 s, were obtained for all trials (Fig. 2.1A). One camera provided detailed images of either fore- or hindlimb strikes on the force platform; an additional camera (level trackway) or two (sloped trackway) supplied a broad view for evaluating footfalls and forward speed. A single angled mirror was placed behind the trackway so that contralateral footfall timing could be measured. Three strobe lights
(Monarch-Nova, Amherst, NH) provided lighting (233.3 Hz).
Images from the cameras were uploaded using U-lead VideoStudio 4.0 (Ulead,
Taipei, Taiwan) and three-dimensional coordinates for all landmarks were determined
37
using APAS (Ariel Dynamics, San Diego, CA). Stride duration was calculated as the time from initial contact of the hindlimb to the next contact of the same hindlimb.
Hindlimb duty factor was computed as stance duration/stride duration. Gait was
determined by limb phase (Hildebrand, 1976), calculated as the elapsed time between
hindlimb footfall and ipsilateral forelimb footfall divided by stride duration.
Angular data were obtained for the fore- and hindlimb (Fig. 2.1B, C). Protraction
angle at touchdown and retraction angle at liftoff were measured for each limb pair. For
the forelimb, these angles were calculated from the coordinates of the shoulder, wrist, and
a point projected directly posterior to the shoulder joint (parallel to the substrate surface).
In the hindlimb, the protraction and retraction angles were calculated from the hip,
metatarsophalangeal joint, and a point projected directly posterior to the hip joint
(parallel to the substrate surface). Adduction angles at touchdown and liftoff were
calculated for fore- and hindlimbs by projecting a point lateral to the shoulder or hip
markers (parallel to the trackway surface), respectively. Shoulder and hip heights relative
to trackway surface were measured at touchdown, midstance and liftoff. These were
calculated by measuring the perpendicular distance between the shoulder and wrist joint
and between the hip and metatarsophalangeal joints, respectively; the latter measure is an
appropriate measurement of hip height because the opossums’ heels rarely contacted the substrate (Chapter 3, Fig. 3.1).
Statistics
Force data were adjusted for body weight to account for difference in body size across the sample. Data from all individuals were pooled, and the Systat 9.0 (Point
38
Richmond, CA) statistical package was used for all analyses. Limb excursion angle data
were compared among groups (incline, level, and decline) and between limbs (fore- and
hindlimb) using two-way fixed-factor analysis of variance (ANOVA); because different
animals were used between level and non-level trials, I did not use repeated measures
ANOVA. The sequential Bonferroni technique (Rice, 1989) was used to determine significance level (alpha = 0.05). When significant differences among substrates were found, a Bonferroni post-hoc test was used to determine which substrates were significantly different from each other. Few significant correlations were found between the kinetic parameters and speed using least squares linear regressions, thus, two-way
ANOVA was used for these comparisons as well as for angular limb excursion data.
2.4. Results
The center of mass of M. domestica was determined to lie 37.0±1.8%
(mean±S.E.M.) of the distance between the glenohumeral and hip joints (i.e., closer to the
glenohumeral joint).
Kinematics
The animals moved significantly faster on the level trackway (mean±S.E.M. =
1.511±0.051 m s-1) than on the sloped trackways (incline, 0.874±0.027 m s-1; decline,
0.835±0.029 m s-1; P<0.00001). There was no significant difference in speed between
incline and decline trials. Furthermore, trials used to obtain fore- and hindlimb data did
not differ significantly in speed. Incline trials had the highest duty factor (39.9±1.3 %),
followed by declines (34.4±1.0 %) and then level (30.2±0.9 %; P≤0.012; Fig. 2.2). Gait,
39
determined by limb phase, was also affected by substrate slope (P≤0.001): limb phase
was significantly lower on decline trials (38.7±1.2 %) than on the incline (46.8±1.6 %) or level trials (51.1±1.1 %; P≤0.001; no significant difference between incline and level).
Therefore, the opossums kinematically trotted during the level and incline trials whereas
the decline trials are primarily lateral-sequence diagonal-couplets, a four-beat trot-like
gait (Fig. 2.2).
Kinematic data (craniocaudal and mediolateral limb angles, shoulder and hip height) are shown in Table 2.1. Because the two-way ANOVA for each of the three
within-step intervals (touchdown, midstance, liftoff) showed a significant interaction
between limb pair (shoulder, hip) and substrate (P≤0.0028), each factor was tested separately. Hip height was always greater than shoulder height (P<0.0001) on all substrates. During stance phase, shoulder height was lower at touchdown and midstance on the incline in comparison to the level and decline (P≤0.0196; no significant difference in shoulder height between decline and level substrates). By comparison, hip height was always significantly lower on the decline substrates than on incline or level substrates
(P≤0.0195; no significant differences in hip height between incline and level substrates).
Shoulder and hip heights (relative to the trackway surface) changed cyclically on all trackway orientations, so that shoulders and hips reached their lowest position at midstance. Because this pattern is consistent with spring-mass (bouncing) mechanics
(Cavagna et al., 1976), and because duty factor reliably fell below 0.5, it is likely that the animals typically utilized bouncing mechanics.
Angular data are summarized in Table 2.1 and Fig. 2.3. On all sloped trials, fore- and hindlimbs were significantly more protracted at touchdown than they were on the
40
horizontal trackway (P≤0.0001). There was no significant difference in degree of protraction at touchdown between incline and decline trials. In comparison to the level
trackway, forelimbs were significantly more retracted at liftoff on the incline (P≤0.0018)
but not on the decline. A different pattern emerged in the hindlimb retraction angle at
liftoff: level and incline trials had equivalent retraction angles, but on the decline the
hindlimbs were significantly less retracted at liftoff (P≤0.0022). Thus, the total
craniocaudal excursion of both limb pairs was greatest on the incline trackway.
Protraction and retraction angles were usually not correlated with speed. The exception
was retraction angle at liftoff, which was negatively correlated with speed for downhill
hindlimb trials (P=0.0035, r2=0.483) and level forelimb trials (P=0.0369, r2=0.224), i.e.,
there is a weak tendency for these limbs to undergo greater retraction at higher speeds.
Finally, hindlimb adduction angle did not change significantly between limb touchdown and liftoff. Nor did adduction angles for the forelimb typically change, the exception being forelimbs on the sloped substrates: during the incline and decline trials, the
forelimbs became significantly more adducted between touchdown and liftoff
(P≤0.0171).
Kinetics
Few speed-dependent relationships were found among the kinetic parameters.
While significant correlations were determined for peak vertical force in forelimbs on
declines and hindlimbs on all substrates (Table 2.2), only a single significant difference
in regression slope was found (hindlimb peak vertical force on level versus on decline;
P=0.0080). Sample force traces are shown in Fig 2.4.
41
Locomotor kinetic results are summarized in Table 3 and Fig 2.5. Vertical
impulse and peak vertical force of forelimbs exceed those of hindlimbs during level and
decline trials (P<0.00001). Consequently, forelimbs support over 65% of the body weight when the opossums ran on the horizontal trackway and about 82% of body weight when they ran downhill. By contrast, fore- and hindlimbs take on subequal roles in body weight support during the incline trials. Vertical forces of forelimbs are greatest on level trials, intermediate on downhill trials, and least on uphill trials (P<0.00001). Hindlimbs largely follow an inverse relationship: the greatest mean values were obtained during level and uphill running and smaller vertical forces were recorded during downhill trials
(P<0.00001; level and uphill trials did not differ significantly).
On the level trackway, peak vertical force occurred earlier in the stance phase of hindlimbs (43.4±3.2%) than in forelimbs (58.3±3.1%; P=0.01800). There were no significant differences in the timing of peak vertical force between limb pairs on the sloped trackways, where peak occurred at 54.5±2.2% of stance. But when limb pairs were considered separately, there was a small substrate effect for the forelimb: relative timing of the peak vertical force was significantly earlier on the decline (40.5±2.8%) and later on the incline (70.9±2.6%) compared with the level (P≤0.04089; not significant with the sequential Bonferroni technique). There were no significant substrate effects when hindlimbs were considered separately.
Craniocaudal impulses on the horizontal trackway were typical for terrestrial quadrupeds, in that an initial braking impulse was followed by a propulsive impulse.
Braking impulse was significantly higher in the forelimbs than in the hindlimbs
(P=0.0003), such that the forelimbs generated nearly 78% of the total braking impulse.
42
However, there was no significant difference between limb pairs with respect to
propulsive impulse (P=0.31), although the hindlimb mean was higher than the forelimb
mean. The transition between braking and propulsive phases occurred significantly
earlier in the forelimbs (62.0±2.1% of stance duration) than in the hindlimbs (33.3±3.7%;
P<0.0001).
On inclines, braking impulse was trivially small, and time of braking-to-
propulsion transition was effectively at touchdown in both limb pairs. Both fore- and
hindlimbs produced substantial propulsive impulse, approximately an order of magnitude
greater than that exerted on the level, although forelimbs provided approximately 57.7% of the total propulsive impulse (P=0.001). On declines, braking impulse was substantial for both limb pairs, although forelimbs generated approximately 81.8% of the total braking impulse (P≤0.0001). The braking impulse generated by the forelimb on the decline trackway was the greatest of any craniocaudal impulse. Fore- and hindlimbs produced virtually no propulsive impulse on the decline, so that in almost all trials there existed no braking-propulsion transition.
Mediolateral impulses of fore- and hindlimbs for level and inclined trials were equivalent in magnitude and orientation, and they consistently indicated a net medial substrate reaction impulse (i.e., laterally directed limb force) within each limb.
Mediolateral impulses on level trials were fairly substantial, on the order of the craniocaudal impulses, whereas those on incline trials were substantially smaller than the craniocaudal impulses. While medially-directed impulses were obtained for the forelimbs during downhill running, the hindlimbs indicated net lateral impulses, so that limbs pairs on the decline exerted oppositely-directed and significantly different net
43
mediolateral impulses (P≤0.0001). Across substrates, forelimbs consistently yielded net medial impulses that were smallest during uphill running (P=0.01352) and subequal on level and downhill trials. Hindlimbs during level and incline trials exerted equivalent net medial impulses whereas decline trials had net lateral impulses (P<0.05 for level versus decline means).
Required coefficient of friction
The overall shape of the required coefficient of friction (µreq) curve was largely
the same across substrates or between limb pairs (Fig. 2.6A): µreq was typically highest at
the beginning of the stance phase and then fell and remained at lower values until just
before liftoff when the values rose again. Median µreq was usually uncorrelated with speed. On the level, median µreq of fore- and hindlimbs were statistically
indistinguishable (0.211±0.021 and 0.254±0.022, respectively) and their values were
lower than either of the two sloped substrates (P≤0.0001; Fig. 2.6B). Although median
µreq was not significantly different between inclined and declined substrates, a significant
substrate–limb interaction term was found in the two-way ANOVA (P≤0.00001). When
limb pairs were evaluated separately using T-tests it was found that forelimbs had a
significantly higher µreq than hindlimbs on inclines (forelimb 0.694±0.018, hindlimb
0.478±0.028, P=0.00015), whereas the reverse pattern existed on the declined trackway
(forelimb 0.540±0.019, hindlimb 0.651±0.0228, P=0.00673).
44
2.5. Discussion
Locomotor biodynamics on level substrates
Monodelphis domestica preferentially trot on the level substrate (Reilly and
White, 2003; this study). The vertical fluctuations in its shoulder and hip suggest that the
limbs are compressing during stance phase as they accept the body weight. This implies
that the animals are most likely using bouncing mechanics (Cavagna et al. 1977), where
spring elements in the limbs (potentially tendons, ligaments and muscles) and belly
(Reilly and White, 2003) absorb external mechanical energy between touchdown and
midstance and then release the stored elastic strain energy between midstance and liftoff.
This is consistent with a study of whole-body mechanics on M. domestica moving on a
level trackway at comparable speeds that found that kinetic and gravitational potential
energies of the center of mass rise and fall in phase with each other (Parchman et al.,
2003).
Limb function during terrestrial locomotion, as reflected by SRF patterns and
limb kinematics, has best been characterized on level substrates (Demes et al., 1994;
Schmitt and Lemelin, 2002), and the general pattern found for M. domestica is typical for
terrestrial quadrupedal mammals. Given that body weight support is reflected by the
magnitudes of vertical SRFs or impulses, then the forelimbs of M. domestica on level
substrates support the majority of the body weight. The unremarkable explanation for
this is that the center of mass of M. domestica is closer to the forelimbs than to the hindlimbs (37% of the gleno-acetabular distance). This is also a common feature among
non-primate mammals (Schmitt and Lemelin, 2002).
45
Forward impulsion is controlled by the craniocaudal SRFs and impulses. Because
both limb pairs have braking and propulsive components, neither fore- nor hindlimbs are
exclusively responsible for decelerating or accelerating the center of mass forward with
every step on level substrates. The forelimbs of M. domestica are net braking whereas
the hindlimbs are net propulsive, as is typical for terrestrial quadrupeds (Demes et al.,
1994). It is noteworthy, however, that while the forelimbs take on a larger share of
overall braking effort, forelimbs and hindlimbs share more equally the propulsive effort.
This may be due to the greater range of motion of the forelimbs in M. domestica.
However, most mammals have greater excursion angles in the forelimb compared with the hindlimb (Larson et al., 2001). Alternatively, the opossums in the sample may have been, on average, slightly accelerating during forelimb trials and slightly decelerating during the hindlimb trials, despite my best efforts to eliminate trials in which the opossums did not move at a steady speed.
Mediolateral forces control yaw. Mediolateral impulses were medially directed in
M. domestica, reflective of laterally-directed limb forces. The most striking feature of the mediolateral impulses is their magnitude: mediolateral impulses are nearly equivalent
to craniocaudal impulses. By contrast, most terrestrial mammals, and especially those
that are cursorial, have mediolateral forces are so negligible that they are ignored (e.g.,
Bertram et al., 2000). While the mediolateral impulses of M. domestica are relatively
higher in comparison to a cursorial mammal with erect limb posture, forces in M.
domestica were relatively low for vertebrates with more sprawled limb postures (lizards,
Christian, 1995; alligators, Willey et al., 2004). Indeed, M. domestica maintains a
46
moderately abducted limb as commonly found in non-cursorial mammals (Jenkins,
1971).
Locomotor biodynamics on inclined substrates
Although the efficiency of moving up a surface gradient is inversely related to
body size (Taylor et al., 1972), moving uphill represents a biomechanical challenge even
to small mammals. For example, muscle activity is more intense on inclines compared
with level locomotion in rats (Gillis and Biewener, 2002). The results of the present
study similarly demonstrate that both limb pairs of M. domestica exert considerable effort
to drive the animal up an inclined substrate. Braking forces during uphill locomotion are
negligible while the propulsive impulses are about an order of magnitude greater than
they are on the level. This reflects the work performed by the opossums against gravity.
Craniocaudal excursion also increases in concert with these changes in craniocaudal
forces. Both fore- and hindlimbs are significantly more protracted at touchdown
compared with level locomotion, and the forelimbs (but not hindlimbs) are also more
retracted at liftoff. Other studies on quadrupeds (Vilensky et al., 1994; Carlson-Kuhta et
al., 1998; Jayne and Irschick, 1999) and bipeds (Iversen and McMahon, 1992) have noted
comparable increases in limb excursion during climbing. Because the craniocaudal
forces are virtually exclusively propulsive in M. domestica, these shifts in limb excursion
suggest that the opossum uses its limbs to pull and then push itself up a graded substrate.
Thus, at even a modest 30° upward gradient, M. domestica is truly climbing. The greater
retraction of the forelimb compared with the hindlimb may occur simply because the
47 pectoral girdle is more mobile than the pelvic girdle, with the scapula capable of contributing greatly to overall forelimb excursion (Fischer et al., 2002).
The opossums modified their locomotor behavior in several other ways when moving uphill. First, they moved significantly more slowly. A slower preferred speed on inclined substrates has also been reported in horses and humans (Warncke et al., 1988;
Wickler et al., 2000; Paradisis and Cooke, 2001). In these large mammals, the reduction in metabolic cost of locomotion associated with moving more slowly helps to counter the additional metabolic energy consumption of moving up a gradient. Moving with slower preferred speed (and higher duty factors) in M. domestica may also be an adaptation to improving overall stability. Second, the hindlimbs take on a greater role in body weight support compared with level locomotion. The explanation is this finding is that the line of gravity from the center of mass shifts relatively caudally (closer to the center of pressure of the pes) when the opossum stands on an incline substrate.
In spite of changes in limb function and excursion angles, M. domestica continued to move primarily at a trot, albeit at slower speeds. Furthermore, shoulder and hip movements (perpendicular to the surface of the trackway) continue to exhibit the
“bouncing” pattern similar to that described on the level trackway. This kinematic result suggests that the opossums may still be able to recover some external mechanical energy through bouncing mechanics on the incline substrate. Indeed, peak stresses measured from the tendons of leg muscles in guinea fowl and tammar wallabies moving on level and incline trackways suggest that elastic energy storage increases (in the guinea fowl) or remains unchanged (in tammar wallabies) on inclines (Daley and Biewener, 2003;
Biewener et al., 2004). Thus, some level of mechanical energy recovery through elastic
48
elements in the limbs may be common when animals move up inclines, although this
manner of energy recovery may be limited in small mammals (Biewener and Roberts,
2000).
Animals moving across a surface will not slip as long as their applied shear force is less than friction force and the required coefficient of friction (µreq) is less than the true
coefficient of friction. The true coefficient of friction between the opossum’s feet and the
trackway was not determined in this study; however, Kinoshita et al. (1997) calculated
that the coefficient of friction between 220-grit sandpaper and human skin (thumb and
index finger) to be above 1.5, substantially greater than µreq computed for M. domestica
on the sandpaper-covered trackways. Cartmill (1979) estimated coefficients of static
friction between the volar skin of primates and a plastic surface to be above 5. In M.
domestica, the median µreq is significantly higher in both limb pairs on the inclined
trackway than it is on the level. This is consistent with data on humans walking on gradients (McVay and Redfern, 1994). The likelihood of slipping increases as the required coefficient of friction (µreq) approaches the true coefficient of static friction. On
the inclined trackway, propulsive impulse and µreq are significantly greater in the
forelimbs than in the hindlimbs, so the forelimbs are at greater risk of slipping compared
to the hindlimb.
The increased function of the forelimb in controlling forward impulsion on the
incline was unexpected. Given that the hindlimbs of most mammals provide the majority
of propulsive effort on the level and that body weight shifts towards the hindlimbs on
inclines, I expected that the hindlimbs would simply take on an even greater role in the
propulsive effort when the opossums moved up a gradient. Interestingly a similar pattern
49
of enhancing propulsive function was found when M. domestica moved over a horizontal
branch about half the diameter of the animal’s body: forelimbs increased their propulsive
effort such that they generated about three times the propulsive impulse than the
hindlimbs (Chapter 3; Lammers and Biknevicius, in review).
Locomotor biodynamics on declined substrates
The challenges of moving down a gradient include avoiding excessive acceleration due to gravity while maintaining stability and not toppling forward. Because gravity supplies a substantial propulsive effect, the fore- and hindlimbs of M. domestica function largely in braking forward impulsion. On a decline, the center of mass of the opossum is located much closer to the forelimbs than to the hindlimbs simply because of the animal’s orientation on the substrate. Consequently, the forelimbs are responsible for approximately 82% of body weight support.
Adjustments in locomotor behavior for stabilizing the descent include limb excursion, gait, and posture. Both fore- and hindlimbs of M. domestica are more
protracted at touchdown when descending an incline than on the level. This serves to enhance the braking effectiveness of the limbs. It is noteworthy that the forelimbs in M.
domestica are especially protracted at touchdown, similar to the condition found in the
slow loris on declined substrates (Stevens, 2002). The forelimbs of a quadruped likely
function to dissipate much of the gravitational potential energy as the animal descends, as
was suggested for the lower limbs of humans moving downhill (Buczek and Cavanagh,
1990). Increased protraction may serve to elongate stance duration so that energy can be
dissipated over a longer time. Changes in protraction angles at touchdown have also
50
been observed in other species (e.g., slow loris; Stevens, 2002) but are not ubiquitous.
For example, cats on declines do not protract their hindlimb at touchdown on a decline
(Smith et al., 1998). Gait is a second way that M. domestica adjusts it locomotor behavior for descending a substrate. Rather than retaining the trot of the level and incline trials, the opossums tend to prefer the lateral-sequence diagonal-couplet, a four-beat trot- like gait. This gait has a greater degree of static stability because the forelimb-hindlimb diagonal couplets are sufficiently dissociated in footfall timing that periods of tripodal support occur. Finally, hip height is significantly reduced at touchdown, midstance, and liftoff in comparison to the other substrates. Increased hindlimb crouching during substrate descent was similarly reported for squirrel monkeys (Vilensky et al., 1994) and desert iguanas (Higham and Jayne, 2004). Because M. domestica did not crouch with its
forelimbs on the decline (as deduced from shoulder height), the opossums maintained a
low rotational moment about the shoulder, thereby, reducing the likelihood of toppling
over the forelimb. Together, these kinematic adjustments may enhance the ability of M.
domestica to maintain its stability on a descent. The relatively extreme kinematic
adjustments, the considerable loading on the forelimbs, and the claws (which most likely
are less effective on the decline) strongly suggest that the risk of slipping and/or injury is
probably greatest while moving on a decline in comparison to moving on a level or
inclined surface. Studies of human locomotion support this hypothesis in that they have
demonstrated that injuries occur more often on declined slopes and descending stairs than
on other substrates (Mizrahi et al., 2000; Christina and Cavagna, 2002).
The finding of substantial mediolateral impulses in the forelimbs of M. domestica
during substrate descent is curious and, as yet, unexplained. Although the forelimbs tend
51 to be somewhat more abducted on decline trials, they are not significantly more abducted than they were on the level or incline substrates. The medially-directed impulses, reflective of laterally-directed limb forces, may be countering locomotor parameters that were outside the scope of this study, such as rolling of the torso.
Synthesis
The data collected in this study suggest that a 30° slope forces these small mammals to adopt consistent climbing behaviors. While the limbs typically exert braking and propulsive impulses on level substrates, the limbs exerted only propulsive impulse on the incline and only braking on the decline. Futhermore, the animals adopted a consistent crouching pattern which resulted in making the body more level. Finally, the limb pair which was most elevated (forelimbs on the incline, hindlimbs on the decline) tended to have a significantly greater craniocaudal angular excursion.
Regardless of substrate, the opossums virtually always used a trotting footfall pattern. This is a dynamically stable gait, common among virtually all tetrapods
(Hildebrand, 1976), and so it is likely that the opossums’ use of the trot is simply a retention of the primitive pattern. Yet, Reilly and White (2003) suggest an intriguing alternative explanation. They observed that the muscles spanning from the femur and epipubic bone on one side of the animal to the contralateral forelimb are active during the stance phase of the limbs to which the muscles connect. Reilly and White (2003) suggest that opossums in the family Didelphidae (including M. domestica) are limited to using a trotting gait because these muscles provide an anatomical constraint. Previous gait data collected by Pridmore (1992) and Lammers (2001), however, show that M. domestica
52 does indeed use non-trotting gaits at low speeds (singlefoot gait) and high speeds (gallop or bound).
2.6. Acknowledgments
I thank Amy Back, Emily Bevis, Kevin Funk, Andy Parchman, and Chi Chi Peng for assistance with data collection. John Bertram and David Lee designed and constructed the force platform and the data acquisition and conversion LabVIEW programs. Kay
Earls created the LabVIEW filtering program, and Steve Reilly programmed the analysis virtual instrument. Audrone Biknevicius, Ron Heinrich, Steve Reilly, Nancy Stevens,
Nancy Tatarek, and Larry Witmer provided insightful comments on the manuscript.
Funding was provided by a Sigma Xi Grant-in-Aid of research (to A.R.L.), an Ohio
University Post-doctoral Fellowship award (to A.R.B.), and NSF grants IBN 9727212 and IBN 0080158 (to A.R.B. and Steve Reilly).
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59
2.8. Tables and figures
Table 2.1. Limb kinematic parameters during stance phase. Protraction, retraction, and adduction angles are measured in degrees. Shoulder and hip heights units are centimeters. Angle type Limb Level Incline Decline Substrate differences Shoulder height, TD FL 2.59±0.09* 2.28±0.08* 2.40±0.09* L>U, L=D, U=D Shoulder height, MS FL 2.17±0.09* 2.02±0.07* 2.14±0.08* L=U, L=D, U=D Shoulder height, LO FL 2.49±0.09* 2.18±0.08* 2.38±0.08* L>U, L=D, U=D Hip height, TD HL 3.76±0.10 3.81±0.13 3.21±0.10 L=U, L>D, U>D Hip height, MS HL 3.44±0.09 3.30±0.11 2.82±0.09 L=U, L>D, U>D Hip height, LO HL 3.62±0.09 3.66±0.12 3.12±0.10 L=U, L>D, U>D Protraction, TD FL 101.36±2.00* 107.46±1.71 114.81±1.84 LU, L=D, U
60
Table 2.2. Least squares regression analyses of peak vertical force (BW s) vs. speed (m s-1). Substrate Limb Slope 95% confidence interval R2 P-value Level Fore ------0.25 Level Hind 0.935 0.529, 1.341 0.629 0.00025 Incline Fore ------0.44 Incline Hind 1.263 0.234, 2.291 0.481 0.02286 Decline Fore 0.940 0.241, 1.639 0.269 0.01121 Decline Hind 0.293 0.094, 0.492 0.416 0.00756
61
Table 2.3. Peak vertical force (BW units) and impulse (BW s). Impulses and Limb Level Incline Decline Substrate forces differences Peak vertical FL 1.528±0.043* 0.843±0.038 1.342±0.040* L>U, L>D, force U
62
Gait camera A.
High view camera
Lateral view Force plate camera
APAS software
Amplifier, analog LabVIEW to digital converter programs
B. C.
Figure 2.1. Data collection setup. A. Film from the cameras was uploaded and analyzed using a personal computer. Voltage changes measured from the force platform were fed directly into the amplifier, converted from analog to digital, and then displayed by a LabVIEW virtual instrument. B. Digitized landmarks and the calculation of limb excursion angles. Protraction angle was measured at the beginning of stance phase, and retraction angle was measured at the end of stance stance phase. C. Likewise, adduction angle was also measured at the beginning and end of stance phase.
63
0
25 Lateral sequence trot-like
50 Trot
75 30E Decline 30E Incline Level
100 10075 50 25 0 Duty factor (%)
Figure 2.2. Gait plot of limb phase against hindlimb duty factor. Trot and lateral sequence trot-like (i.e., diagonal couplet) classifications are denoted by dashed lines. Following the convention of Hildebrand (1976), the axes are reversed.
64
Level Incline Decline
P
B BP
Direction of locomotion
B P B P
Dorsoventral Craniocaudal impulse impulse (braking and propulsion)
Figure 2.3. Summary of fore- and hindlimb touchdown and liftoff angles, and dorsoventral, braking, and propulsive impulse. Angles are exaggerated to make differences between limbs and among substrates more visible. Note that braking (B) and propulsive (P) impulses, when shown, are approximately one order of magnitude smaller on the level than on the incline and decline.
65
1.5 Vertical A. B. 1.0
Vertical 0.5 Craniocaudal Craniocaudal 0.0 Mediolateral Mediolateral -0.3 1.5 D. Vertical C. Vertical 1.0
0.5 Craniocaudal Craniocaudal 0.0 Mediolateral Mediolateral -0.5
1.0 Vertical E. Vertical F. 0.5 Craniocaudal Craniocaudal 0.0 Mediolateral Mediolateral
-0.5 1.4 Vertical G. H. 1.0 Mediolateral
0.5
Vertical 0.0 Mediolateral Craniocaudal -0.5 Craniocaudal -0.8
0.000.02 0.04 0.06 0.080.00 0.02 0.04 0.06 0.08 Time (s) Time (s) Figure 2.4. Typical force traces for each limb and substrate type. A -D are from the level trackway. A & B. were relatively fast trials, and C & D were relatively slow. A & C are forelimb traces, and B & D are hindlimb traces. E & F are fore- and hindlimb traces (respectively) from the inclined trackway. G & H are fore- and hindlimb traces (respectively) from the declined trackway. Craniocaudal force is shown in gray for clarity.
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Forelimb Hindlimb
67.2% 32.8% Level (0.07079 BW s)
Vertical Incline (0.08631 BW s) impulse 50.8% 49.2%
{ 82.1% 17.9% Decline (0.09599 BW s)
77.8% 22.2% Level (0.00413 BW s)
Braking 52.7% 47.3% Incline (0.00029 BW s) impulse { 81.8% 18.2% Decline (0.04377 BW s)
44.0%56.0% Level (0.00557 BW s) Propulsive 42.3% Incline (0.04214 BW s) impulse 57.7% { Decline (0.00001 BW s)
Figure 2.5. Relative effort (%) of dorsoventral, braking, and propulsive impulses exerted by fore- and hindlimbs. Absolute values of total impulse (forelimb + hindlimb) are indicated to the right. Because the total propulsive impulse on the decline was extremely low, percent limb effort was not calculated.
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1.0 A. 0.8
0.6
0.4
0.2
0.0 0.00 0.01 0.02 0.03 0.04 0.05 0.06 Time (s)
1.0
0.9 B.
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1 FL HL FL HL FL HL
Level30E incline 30E decline
Figure 2.6. Frictional issues in locomotion. A. Typical plot of the required coefficient of friction in M. domestica running at 1.78 m s-1 on the level trackway. B. Box plots of median required coefficient of friction for each substrate and limb pair. The horizontal line in the middle of each box represents the median for each group, and each box on either side of the median encloses one-fourth of the data. Each whisker also represents one-fourth of the data. The asterisk indicates an outlier; the circle denotes an extreme outlier.
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Chapter 3: The effects of substrate diameter on locomotor kinetics in
the gray short-tailed opossum (Monodelphis domestica)
3.1. Summary
Effects of substrate diameter on locomotor biodynamics were studied in the gray
short-tailed opossum (Monodelphis domestica). Two horizontal substrates were used: a flat “terrestrial” trackway with a force platform integrated into the surface and a cylindrical “arboreal” trackway (20.3 mm diameter) with a force-transducer instrumented region. On both terrestrial and arboreal substrates, forelimbs exhibited higher vertical impulse and peak vertical force than hindlimbs. Although vertical limb impulses were lower on the terrestrial substrate than on the arboreal support, this was most likely due to speed effects because the opossums refused to move as quickly on the arboreal trackway.
Vertical impulse decreased significantly faster with speed on the arboreal substrate because most of these trials were relatively slow, and stance duration decreased with speed more rapidly at these lower speeds. While braking and propulsive roles were more segregated between limbs on the terrestrial trackway, forelimbs were dominant in both braking and propulsion on the arboreal trackway. Both fore- and hindlimbs exerted equivalently strong, medially-directed limb forces on the arboreal trackway and laterally- directed limb forces on the terrestrial trackway. I propose that the modifications in substrate reaction force on the arboreal trackway are due to the differential placement of the limbs about the dorsolateral aspect of the branch. Specifically, the pes typically made contact with the branch lower and more laterally than the manus, which may
69
explain the significantly lower required coefficient of friction in the forelimbs relative to
the hindlimbs.
3.2. Introduction
Substrate reaction forces (SRFs) are often used to summarize limb function
during terrestrial locomotion, and a single pattern characterizes most quadrupeds
(summarized in Demes et al., 1994). Body weight support is reflected by the vertical
component of the SRF, and, because the center of mass of most mammals is cranially-
displaced, the vertical SRF is most commonly greater in the forelimbs than the hindlimbs.
The craniocaudal force has two active parts: a braking component followed by a
propulsive component. During terrestrial locomotion, braking impulse (area under the
force-time curve) is typically greater than propulsive impulse in the forelimb; by contrast,
the hindlimb tends to be net propulsive. Mediolateral force and impulse are considered
negligible for cursorial animals moving along a straight path (Biewener, 1990).
However, sprawling tetrapods commonly generate a more substantial medially-directed
SRF (laterally-directed limb force) so that their mediolateral impulse is comparable in
magnitude to craniocaudal impulse (Christian, 1995; Willey et al. 2004).
Quadrupeds adapted to arboreal locomotion display an altered pattern of SRF
(Kimura, 1985; Ishida et al., 1990; Demes et al., 1994; Schmitt, 1994, 1999; Schmitt and
Lemelin, 2002): peak vertical forces tend to be reduced, hindlimbs commonly take on a greater role in body weight support, and the limbs exert strong laterally-directed SRF
(medially-directed limb force). Differences between the terrestrial and arboreal SRF patterns have been related to differences in substrates. For example, lowered peak
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vertical forces observed in primates moving on horizontal, narrow supports may help
reduce branch oscillations (Demes et al., 1990; Schmitt, 1999).
To date, studies on arboreal locomotor kinetics have concentrated almost
exclusively on primates. Yet virtually any small mammal must negotiate heterogeneous terrain that includes some non-terrestrial substrates. For example, many species of
rodents (Montgomery, 1980) and the didelpid marsupial Didelphis virginiana (Ladine
and Kissell, 1994) utilize fallen logs and branches on the forest floor as arboreal runways.
Terrestrial mammals navigating an arboreal substrate are likely to adapt their locomotor
behavior in an attempt to enhance stability on this curved substrate, and some of these
strategies may result in observable differences in limb function and thus SRFs. Such
strategies might include adjustments in speed, limb placement, and gait (Fig. 1.2).
Terrestrial mammals may choose to move more slowly on arboreal supports; decreased
speed is generally associated with lower peak vertical forces (Demes et al., 1994; Schmitt
and Lemelin, 2002). Limb placement about a curved substrate will affect the potential
for slipping off of the sides of a branch. When limb contacts occur on the top of the
branch (or anywhere on a flat substrate), then the shear force is the vector sum of the
mediolateral and craniocaudal forces while the normal force is equivalent to the vertical
force. But vertical and mediolateral forces will each contribute shear and normal
components when contact occurs on any other part of the branch (Fig 3.1A, B).
Therefore, the relative proportions of the three-dimensional SRFs may be altered to avoid
excessive shear forces. It is also possible that the limb force could be reoriented toward
the centroid of the branch, which would increase the normal reaction force. Finally, it is
possible that gait (defined by Hildebrand, 1976, as timing and duration of foot contacts
71 relative to stride duration) shifts may occur between terrestrial and arboreal locomotor bouts. A gait that is dynamically stable (where stability is provided by motions through conditions which are statically unstable) on a terrestrial substrate may be be inadequate on arboreal substrates, particularly if speeds are reduced. Animals may switch to more statically stable gait (e.g., toward a singlefoot gait) (Hildebrand, 1976).
The aim of this study was to determine if and how limb function, as reflected by
SRFs, differ in terrestrial and arboreal locomotion in a non-arboreal specialist. I used
Monodelphis domestica (Wagner, 1842), the gray short-tailed opossum, as our model. M. domestica is a small terrestrial marsupial (Cartmill, 1972; Nowak, 1999) that is readily capable of moving on narrow substrates (Lammers, 2001). Although arboreality has evolved several times within family Didelphidae, terrestrial habitation is most likely primitive (Fig. 3.2). Furthermore Monodelphis is considered the most terrestrial genus within the family (Nowak, 1999). In this chapter, I address the mechanics of arboreal locomotion through two primary questions. First, do terrestrial mammals necessarily adopt SRF patterns observed in arboreal specialists? Arboreal specialists such as
Caluromys philander have morphological as well as behavioral adaptations for arboreal habitation and locomotion (Schmitt and Lemelin, 2002). But the terrestrial M. domestica presumably must rely much more on behavioral modifications in order to move on arboreal substrates. Thus it is likely that M. domestica will move along a branch differently than would an arboreal specialist. Secondly, how does limb placement about a curved substrate affect stability on a branch?
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3.3. Materials and methods
Animals
I used six adult male Monodelphis domestica (gray short-tailed opossums) for all
experiments (body mass: 0.105 – 0.149 kg), and all procedures were approved by the
Ohio University Animal Care and Use Committee. Animals were anaesthetized prior to
each experiment by placing them and approximately 0.3 – 0.4 ml of isoflurane (Abbott
Laboratories, North Chicago, IL) into a plastic container (about 2 minutes). The fur
covering the lateral aspect of the left fore- and hindlimb was shaved and white 1.3 X 1.7
mm beads were glued to the skin overlying bony landmarks. Landmarks used in this
study include: distal tip of the third manual digit, the lateral aspect of the wrist, distal tip
of the fifth pedal digit and fifth metatarsophalangeal joint (Fig. 3.1C). The animals typically awoke within 2 min and appeared to suffer no ill effects.
Kinetic data
Force transducers for recording SRFs were constructed based on the spring-blade design described in Biewener and Full (1992) and Bertram et al. (1997). The terrestrial trackway was 160 cm long, with a 48 X 11 cm force platform integrated in the middle and was covered with 60-grit sandpaper for traction. This force platform was initially developed to evaluate whole body mechanics, so its length necessitated capturing individual fore- and hindlimb SRFs in separate trials. Forelimb data were obtained as the first footfall on the platform whereas hindlimb data represent the last limb off the platform. The arboreal trackway was constructed from 2.03 cm diameter aluminum tubing (including 60-grit sandpaper covering); the trackway, therefore, corresponded to
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approximately one-half body width. This trackway was 151 cm long, with a 4 cm force
transducer instrumented section. Because the force transducer was short in the arboreal trackway, sequential fore-and hindlimb SRFs were obtained in each trial. Animals were encouraged to run toward a wooden box placed at the end of each trackway. Force transducer calibration protocol followed Bertram et al. (1997). Briefly, the vertical
transducers were calibrated by placing known weights on the platform or hanging
weights from the pole; craniocaudal and mediolateral directions were calibrated by
hanging weights through a pulley apparatus.
SRF data were collected at 1200 Hz for 3 to 6 s. Analog outputs from the force
transducers were amplified (SCXI-1000 and 1121, National Instruments, Austin, TX),
converted to a digital format (National Instruments, NB-M10-16L), and recorded as
voltage changes with a LabVIEW 5.1 (National Instruments) virtual instrument data
acquisition program. Voltage changes were then converted into forces (in N) using
calibration scaling factors. All force traces were filtered with Butterworth notch filters at
60 Hz, 53 ± 5 Hz, and 87 ± 5 Hz for the terrestrial trials and at 60 Hz, 120 ± 5 Hz, and
300 ± 5 Hz for the arboreal trials.
Only trials that approximated steady speed over the force transducers were
analyzed. This was determined in the arboreal trials by comparing the total braking
impulse of both fore- and hindlimbs to the total craniocaudal impulses [(braking
impulse)/(craniocaudal impulse) * 100%]; see below for description of impulse
calculations. If this percentage fell between 45 – 55%, then the trial was considered to be
steady-speed. A different criterion for steady speed was developed for the terrestrial
trials. Whole body SRFs were obtained as the animals crossed the force platform. The
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craniocaudal SRFs were divided by mass and then integrated to obtain craniocaudal
velocity profiles; the integration constant was set as mean speed determined
videographically over three 12 cm intervals. Terrestrial trials were accepted as steady
speed when braking and propulsive components of the whole body velocity were
balanced. I made every effort to obtain steady-speed trials at a large range of speeds on
each substrate, but despite our persistance only one slow terrestrial trial (0.724 m s-1) was acceptable.
Kinetic data include peak vertical force, time to peak vertical force, vertical impulse, braking impulse, propulsive impulse and net mediolateral impulse for fore- and hindlimbs. A fourth LabVIEW virtual instrument was used to calculate impulse by integrating the force/time curve separately for each limb and each orthogonal direction
(vertical, craniocaudal, mediolateral). In this study, “impulse” refers to the impulse generated by individual limbs, rather than the change in momentum of the body (Bertram et al., 1997). Substrate reaction forces were divided by the animal’s body weight to account for the 0.105 – 0.149 kg range in mass; forces and impulses were therefore analyzed in units of Body Weight (BW) and BW s, respectively.
Kinematic data
The trackways were illuminated with three 233.3 Hz strobe lights (Monarch-
Nova, Amherst, NH) as two high-speed 120 Hz digital cameras with a 1/250 s shutter speed (JVC GR DVL 9800; Yokohama, Japan) captured footfall patterns and limb movement. The first camera obtained a lateral view of the left side of the animal and the second obtained a dorsolateral view. These videos were uploaded to a computer using U-
75 lead Video Studio 4.0 (Ulead, Taipei, Taiwan), and then the APAS motion analysis system (Ariel Dynamics, San Diego, CA) was used synchronize the kinematic events from the two camera views, digitize the landmarks and convert each two-dimensional set of digitized data into three-dimensional coordinates for each landmark.
The center of pressure for each foot was estimated using the landmarks. Because the forelimb assumed a fully plantigrade posture on both arboreal and terrestrial substrates, the center of pressure of the manus was estimated as the geometric midpoint between the wrist and 3rd manual digit landmarks. Because the heel did not contact either substrate, the center of pressure of the pes was set as the geometric midpoint between the metatarsophalangeal and 5th pedal digit landmarks. Given that the distance between manual and pedal landmarks was short (15.7 and 6.8 mm, respectively), placing the center of pressure at the midpoint between proximal and distal contacts was not unreasonable. This estimate also assumes that the manus and pes contact the substrate without gripping, which is reasonable for the forelimb because the manus in M. domestica is short and lacks opposable digits. Although the pes is longer than the manus and has an opposable hallux, the diameter of the substrate is considerably greater than the span of the grip of the pes and the grit of the sandpaper did not offer much claw penetration. Furthermore, because the heel did not touch the substrate, only a small part of the pes was used to connect with the branch.
Timing variables (speed, stance duration, stride frequency, stride length) were also measured from the videos. Gaits were identified using limb phase, which is percentage of stride duration that the left forelimb contacted the substrate after the left hindlimb contact (Hildebrand, 1976). Hildebrand (1976) divided limb phase into octiles
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of equal size. A limb phase close to 50% (between 43.75 and 56.25%) indicates a
kinematic trot; limb phases greater than 56.25% indicate different lateral sequence gaits,
and below 43.75% indicate diagonal sequence gaits. (See Hildebrand (1976) for further
detail). Duty factor of the hindlimb (ratio of stance duration to stride duration) was also
calculated. Differences between arboreal and terrestrial duty factor and limb phase were
determined by t-test.
Calculating required coefficient of friction
The required coefficient of friction (µreq), the ratio of shear force to normal force,
is one way of estimating the ability of an animal to generate friction with its limbs. If the
limb does not slip when it makes contact with the substrate, then the true coefficient of
friction is greater than the required coefficient of friction. As noted above, on the flat
terrestrial substrate, shear force is the vector sum of craniocaudal and mediolateral forces
and normal force is the vertical force. On the arboreal substrate, the animal’s limbs
contacted the pole between its lateral aspect to its dorsalmost surface. Thus, while
craniocaudal forces continue to contribute exclusively to shear force in the arboreal
trackway, vertical and mediolateral forces each contribute to both shear and normal
forces (Fig. 3.1A, B).
To calculate µreq on the arboreal substrate, the components of the vertical, craniocaudal and mediolateral SRFs contributing to shear and normal forces were computed as:
2 2 0.5 Shear force component = [(FML sin θ - FV cos θ ) + (FCC) ]
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Normal force component = (FML cos θ) + (FV sin θ)
where FV, FCC and FML are vertical, craniocaudal, and mediolateral force, respectively,
and θ is the angle formed by the coordinates of the limb contact, the center of the pole,
and the horizontal (Fig. 3.1A, B). FV was always in the same direction, but when FML
was occasionally medially directed, this component of the SRF was given a negative sign
so that the same calculations could be used throughout.
Statistical analyses
Data from all individuals were pooled, and Systat 9.0 (Point Richmond, CA) was
used for all analyses. Least squares regression was used to determine the correlation of
forces and impulses with speed for each substrate and limb pair grouping. Because most
of the regressions of vertical impulse versus speed were significant, a two-way analysis
of covariance (ANCOVA) with speed as the covariate was used to determine differences
among groups with respect to vertical impulse. However, because peak vertical force and
remaining impulses were typically not significantly correlated with speed, a two-way
repeated measures analysis of variance (ANOVA) was used to determine significant differences between substrates and limbs. The sequential Bonferroni technique (Rice,
1989) was used to determine statistical significance (alpha = 0.05). Data are reported as mean ± standard error of the mean.
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3.4. Results
Gait characteristics
Locomotor speed was significantly lower on the arboreal trackway (arboreal:
1.00±0.03 m s-1; terrestrial: 1.51±0.05 m s-1; P<0.00001). Because we used similar methods to encourage the animals to move quickly across the trackway, it is likely that the speeds we obtained on the arboreal trackway approached the animals’ maximal efforts. Attempts to obtain slower trials on the terrestrial trackway yielded unacceptable acceleration or deceleration within trials.
The animals predominantly used kinematic trotting (diagonal couplet) gaits on both terrestrial and arboreal substrates (limb phase range: 34.7 - 57.1%; Fig. 3.3A).
However, arboreal trials had a significantly lower limb phase than terrestrial trials (t-test,
P=0.0003), where 22.7% of the arboreal trials were classified as a lateral-sequence diagonal couplet gait (a trot-like gait with limb phase between 31.25 - 43.75%).
Duty factor was significantly larger in arboreal trials (arboreal: 42.4±0.8%; terrestrial: 30.2±1.0%; t-test, P<0.00001; Fig. 3.3A). Stance duration decreased with speed in a concave-up manner (Fig. 3.3B). The slope of stance duration versus speed was significantly steeper in the arboreal trials than in terrestrial trials (one-way ANCOVA,
P=0.00621). Stride frequency increased linearly with speed, and there was no significant difference in slope with respect to limb pair or substrate (two-way ANCOVA, P=0.8).
However, the arboreal trials had a significantly higher stride frequency than the terrestrial trials (Least squares means: arboreal, 6.92±1.01 Hz; terrestrial, 6.02±1.26 Hz;
P=0.00012).
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Substrate reaction forces
Sample force traces from the arboreal and terrestrial trackways are shown in Fig.
3.4. Two patterns were observed in the terrestrial trials. At the slowest speeds on the terrestrial substrate (below 1.5 m s-1), forelimb vertical force had a double-peak (Fig.
3.4A). This double peak also occurred in the terrestrial hindlimbs at the slowest speed
recorded (1.25 m s-1; Fig. 3.4B). All faster speeds on the terrestrial trackway in both the
fore- and hindlimbs yielded single peak vertical force profiles (Fig. 3.4 C,D). Vertical
force profiles on the arboreal trackway always yielded single peaks (Fig. 3.4 E,F).
Peak vertical force was not correlated with speed for any substrate/limb pair
except for terrestrial hindlimbs. Forelimbs had significantly higher peak vertical force
than hindlimbs on each substrate (two-way ANCOVA, P=0.00015; Fig. 3.5A). Peak
vertical forces of fore- and hindlimbs were higher in the terrestrial trials than in arboreal
trials (P<0.00001). Interaction was also significant (P=0.01006), so that the substrate
effect on peak vertical force was significantly more pronounced in the forelimbs than in
hindlimbs. Relative to percent stance duration, peak vertical force occurred significantly
earlier in hindlimbs than in forelimbs, regardless of substrate (two-way ANOVA,
P<0.00001). Furthermore, this peak occurred significantly earlier in arboreal trials than
in terrestrial trials (P=0.00753) (Fig. 3.4 E,F). The ratio of forelimb to hindlimb peak
vertical forces was higher for the terrestrial substrate (1.702) than the arboreal substrate
(1.617; ratios were calculated using mean peak vertical forces for each limb and
substrate).
Vertical impulse decreased significantly with speed in all substrate/limb groups except for the terrestrial hindlimb group (Fig. 3.5B, Table 2). Slopes were significantly
80 different from each other (two-way ANCOVA, P=0.00003), and in both fore- and hindlimbs the slope of vertical impulse versus speed was steeper on the arboreal substrate than on the terrestrial. On each substrate, the vertical impulse of forelimbs had significantly higher y-intercepts means than that of hindlimbs (least squares linear regression, 95% confidence intervals to determine slope and y-intercept differences,
P<0.00001). Arboreal forelimb and hindlimb slopes were not significantly different. On the terrestrial substrate, forelimb vertical impulse was negatively correlated with speed, while terrestrial hindlimb vertical impulse was not correlated with speed. (P<0.00001).
The ratio of forelimb:hindlimb vertical impulse was 2.047 on the terrestrial substrate and
1.727 on the arboreal.
Regardless of substrate, craniocaudal force traces were characterized by a braking phase followed by a propulsive phase (Fig. 3.4). Braking and propulsive impulses were typically not correlated with speed (with the exception of forelimb braking impulse and hindlimb propulsive impulse on the arboreal substrate; P≤0.00349). On the terrestrial substrate, the forelimbs usually exerted a net braking impulse and the hindlimbs a net propulsive impulse. However, when propulsive impulse was considered alone, there was no significant difference between forelimb and hindlimbs on the terrestrial substrate. On the arboreal substrate, forelimbs exerted braking and propulsive impulses that were both strong and not significantly different from each other (Fig. 3.5 C,D). Hindlimbs similarly generated braking and propulsive impulses which were equal, but these impulse magnitudes were significantly lower than those produced by the forelimbs (P=0.00017).
The net fore-aft impulse of fore- and hindlimbs on the arboreal substrate was nearly zero.
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Within each substrate, there were no significant differences between limb pairs with respect to net mediolateral impulse (Fig. 3.6). On the terrestrial substrate, both limb pairs produced strong medially-directed SRFs. Among the arboreal trials, the limbs generated strong medially-directed limb force (laterally-directed SRFs). Differences between substrates were highly significant (P<0.00001).
Limb placement and required coefficient of friction
On the arboreal trackway, the pes was usually placed considerably lower on the branch than manus (Fig. 3.7A). The required coefficient of friction (µreq) at foot touchdown for all trials on both substrates was initially high, but quickly dropped for most of stance phase, only to rise again at the end of the step (Fig. 3.7B). The highest values were typically found at touchdown. Because we used the filtered data for these calculations, it is unlikely that these high values were the result of impact noise. The median µreq was significantly higher in the arboreal trials than in terrestrial trials
(P<0.00001; Fig. 3.7C). In arboreal trials hindlimbs had significantly higher median µreq than forelimbs (P=0.0008). No significant difference in µreq was found between limb pairs in the terrestrial trials (t-test, P=0.172).
3.5. Discussion
In this study Monodelphis domestica predominantly trotted on both terrestrial and arboreal substrates, with occasional lateral-sequence diagonal couplet trials observed on the arboreal trackway. (Note that I used Hildebrand’s (1976) definitions of gaits, which rely only on duty factor and relative fore- and hindlimb phase relationship. Some
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workers (e.g., Lee and Farley, 1998) define gait by the mechanical behavior of the limb and center of mass, i.e., inverted pendular walking or bouncing mechanics). This largely
conforms to kinematic gaits reported previously for this species (Pridmore, 1992;
Lemelin et al., 2003; Parchman et al., 2003) although the present study analyzed fewer lateral-sequence walks on the terrestrial trackway simply because slower trials often failed to meet the steady speed criterion. While more arboreally-adapted opossums
(brush-tailed opossum, Trichosurus vulpecula; monito del monti, Dromecips australis; woolly opossum, Caluromys philander;) also trot, they shift to diagonal sequence gaits at slower locomotor speeds (White, 1990; Pridmore, 1994; Lemelin et al., 2003). This observation led Pridmore (1994) to conjecture that diagonal sequence gaits are an arboreal adaptation in marsupials, a suggestion that parallels the arboreal, “fine-branch” explanation for diagonal sequence gaits in primates (e.g., Cartmill, 1972). That M. domestica did not resort to a diagonal sequence gait when moving along arboreal substrates (Lemelin et al., 2003; this study) supports the contention that terrestrial animals may not have the same locomotor response to curved and more narrow substrates as have arboreal specialists.
Substrate diameter does appear to have some affect on locomotor behavior in M. domestica. Narrow substrates (<12.5 mm) clearly challenge the species’ stability, as individuals were observed to frequently falter and fall (Pridmore, 1994). Once habituated to the 20 mm arboreal trackway, M. domestica in the present study appeared quite capable of freely traversing the 1.5 m trackway but we were unable to entice animals to travel at steady speeds higher than 1.32 m s-1. Thus, it appears that speed is an important
behavioral adaptation to moving on a more treacherous substrate.
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M. domestica relies more heavily on the forelimbs than on the hindlimbs to support its body weight on both terrestrial and arboreal trackways. The vertical component of the SRF reflects limb function in body weight support. Peak vertical forces in terrestrial trials of M. domestica conform to the pattern of typical terrestrial mammals, namely, forelimb values exceed hindlimb values (Demes et al., 1994; Schmitt and Lemelin, 2002; this study). The most likely explanation for this finding is that the center of mass in M. domestica lies closer to the forelimbs than to the hindlimbs (about
40% of the distance between the shoulder and hip joints; Lammers, unpubl. data).
Forelimbs continue to dominate in body mass support when M. domestica moved along the arboreal trackway, but the ratio of forelimb to hindlimb peak vertical force drops.
This occurs largely because hindlimbs display somewhat higher than expected peak vertical forces relative to speed (as displayed by an extrapolation of the terrestrial hindlimb slope into the arboreal speed range; Fig. 5A). This shift in body weight support between fore and hindlimbs is relatively small in comparison to the pattern exhibited by the arboreal C. philander (Schmitt and Lemelin, 2002): whereas peak vertical force on arboreal substrates for the hindlimbs are comparable in the two species (0.5-0.9 BWU in
M. domestica; 0.6-1.0 in C. philander), C. philander’s forelimb forces (0.5-0.8 BWU) fall below the range observed in M. domestica (0.8-1.3 BWU).
Comparisons of peak vertical force beyond the marsupials fail to uphold a strict terrestrial-arboreal dichotomy. Although most primates are hindlimb-dominant in body weight support (Demes et al., 1994), the highly arboreal slow loris (Nycticebus coucang) and common marmoset (Callithrix jacchus) display higher forelimb peak vertical forces when moving pronograde (over the branch) on an arboreal trackway (Ishida et al., 1990;
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Schmitt, 2003a). Furthermore, the more terrestrial chipmunk and the more arboreal
squirrel are both forelimb dominant in body mass support when moving over a terrestrial
trackway (Biewener, 1983).
The effect of substrate curvature on peak vertical force does, however, appear to
be consistent across arboreal specialist and more terrestrial species. Primates and
marsupials alike typically apply lower peak vertical forces when switching from a
terrestrial trackway to an arboreal one (Schmitt, 1994, 1999, 2003b; Schmitt and
Lemelin, 2002; this study). Furthermore, there is a significant reduction in peak vertical
force as primates move on progressively smaller arboreal substrates (Schmitt, 2003b). A
benefit for reducing vertical forces on arboreal substrates might be a concomitant
reduction in branch oscillation (Demes et al., 1994; Schmitt, 1999). Therefore, while
hindlimb dominance in body weight support is not a prerequisite for moving along an
arboreal support, reduction in vertical force application relative to terrestrial values does appear to be an inescapable consequence of arboreal locomotion, especially if arboreal speeds are slow. To support body weight, however, these lower forces must then be distributed over a longer interval. This could be accomplished with greater stance duration and/or stride frequency on the arboreal substrate (as was the case in this study).
These data suggest that there was a small posterior weight shift, i.e., the time relative to stance duration that the peak vertical force occurred was significantly delayed in both limb pairs on the arboreal substrate. Furthermore, the forelimb:hindlimb ratio of peak vertical force (BW) and vertical impulse (BW s) was higher on the terrestrial substrate than on the arboreal substrate. This finding further suggests a posterior weight shift because the time at which peak vertical force occurs is closely associated with the
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time that a limb is supporting the greatest amount of body weight. If the center of mass is
effectively moved posteriorly relative to the base of support, then both fore- and
hindlimbs will support the greatest weight at a later portion of the stance phase. Posterior
weight shift has been found for most primate species, whether on arboreal or terrestrial
substrates (Schmitt and Lemelin, 2002). Furthermore, this posterior weight shift tends to
be exaggerated when arboreal specialists move on arboreal substrates.
I noted that at lower speeds on the terrestrial trackway, the vertical force trace
yielded two peaks (Fig. 4A,B), whereas at higher speeds there was a single peak. The
same pattern exists in sheep and dogs (Jayes and Alexander, 1978) and horses (Biewener
et al., 1983). A double-peaked vertical force is normally indicative of a mechanical walk
– that is, the animal is exchanging kinetic and gravitational potential energy via an
inverted pendulum mechanism (Enoka, 2002). However, I doubt that the opossums are
recovering energy via the inverted pendulum mechanism. First, Parchman et al. (2003)
found that the same species recovered about 3.4% of mechanical energy by using walking
mechanics, and that this was the case over a range of speeds between <0.5 to >1.5 m s-1.
Second, these force traces are from single limb contacts. Determining whole-body mechanics is more accurate when using the sum of all limb contacts during a stride, or during a couplet if the animal uses a trotting gait (as was nearly always the case in M. domestica).
Limb differences in vertical impulse largely parallel those of peak vertical force in
M. domestica, except that vertical impulse tends to decrease with speed as is common in mammals moving with symmetrical gaits. The decrease in vertical impulse with speed is driven primarily by a speed-dependent reduction in stance duration more so than any
86
increase in peak vertical force. A concave-up negative relationship between support
duration vs. speed is typical for terrestrial locomotion (e.g., Demes et al., 1990;
Abourachid, 2001), a pattern that may reflect the need to move more cautiously in order to remain stable at slower speeds. The particularly long stance durations in the slower arboreal trials in M. domestica may indicate an increased perception of hazard by the animals when moving on an arboreal substrate. Because vertical impulse, which is responsible for body weight support, decreases with speed faster on the arboreal trackway, the higher stride frequency on the arboreal trackway may be a way of compensating so that body weight support is adequately maintained.
Craniocaudal forces control forward impulsion, and all mammals moving at steady speed on a terrestrial substrate rely on the hindlimbs to provide most of the
propulsive force (Demes et al., 1994). Although craniocaudal forces fluctuate from an
initial braking action to a final propulsive action in both fore- and hindlimbs, hindlimbs
generate greater propulsive impulses than do forelimbs. Previous studies on arboreal
specialists report similar functions for locomotion on arboreal trackways (Ishida et al.,
1990; Schmitt 1994). Shifting between terrestrial and arboreal substrates resulted in
either no significant changes in craniocaudal force (Schmitt, 1994) or smaller propulsive
forces on arboreal substrates (forelimbs only were evaluated; Schmitt, 1999). By
contrast, results reported here suggest that terrestrial mammals may shift a greater role in
forward propulsion to the forelimbs when moving on an arboreal support.
Most terrestrial mammals generate small and erratic mediolateral forces (e.g.,
Hodson et al., 2001), yet mediolateral forces in M. domestica are often substantial, with
magnitudes that rival the craniocaudal forces (Fig. 3.4) and the net direction of the
87
mediolateral SRF is medial (reflective of a laterally-directed limb force). This is
consistent with SRF data on terrestrial animals that use a more sprawled and semi-erect posture such as lizards and alligators (Christian, 1995; Willey et al., 2004). A similar
orientation (but lesser magnitude) was also reported for higher primates (Schmitt, 2003c).
The polarity of mediolateral forces switches to reflect medially-directed limb forces when
M. domestica moved along the arboreal trackway. Not surprisingly, this is also the
primary orientation for most other mammals when moving on arboreal substrates
(Schmitt, 2003c). Thus, on the terrestrial substrate, the mediolateral SRFs are “tipping,”
whereas on the arboreal substrate they are “gripping.”
Thus, compared with more arboreally-adapted mammals, M.domestica appears to
retain forelimb dominance in body weight support and to shift a greater role in forward impulsion to the forelimbs when moving on an arboreal substrate. I believe that the
explanation of the dominance of the forelimb during arboreal locomotion lies in the
differences in limb placement about the curved substrate. This is best illustrated by a
consideration of friction. Kinoshita et al. (1997) estimated that the coefficient of static
friction (µs) between 220-grit sandpaper and human skin is 1.67±0.24 (index finger) and
1.54±0.27 (thumb); Cartmill (1979) estimated values of µs in excess of 5 between the
volar skin of primates and a plastic surface. It is likely that the values of µs in this study
are well above those calculated by Kinoshita et al. (1997) because: (1) I used 60-grit
sandpaper, which is rougher than 220-grit, and (2) the claws and the palmar tubercles on
the manus and pes of the opossums may improve the degree of interlocking between foot
and substrate (as per Cartmill, 1974), and (3) the limbs did not demonstrably slip
(implying that the true coefficient of static friction is higher than the mean µreq).
88
The values for the median µreq, and thus the potential for slipping, was significantly higher in both fore- and hindlimbs in the arboreal trials than in terrestrial trials, which verifies the more precarious nature of arboreal locomotion. The reason for this may be two-fold. First, vertical force was significantly lower on the arboreal substrate than on the terrestrial (in both limbs), so that there simply was less vertical force to contribute to the generation of normal force (although see the section above). The normal force is the stabilizing force for maintaining the position of the manus and pes on the substrate. Second, some percentage of vertical force results in a shear force across the surface of arboreal substrates because of the placement of the manus and pes laterally off the top of the branch. Consequently, a smaller percentage of vertical force is available to contribute to the normal force during arboreal locomotion.
Similarly, the positioning of manus and pes can explain the significantly greater
µreq of hindlimbs on the arboreal trackway. Hindlimbs were nearly always placed lower and more laterally on the branch than forelimbs, and they supported significantly less body weight than the forelimbs. The difference in µreq and foot placement between fore- and hindlimbs on the arboreal trackway may also serve to explain why the forelimbs were apparently so dominant in body weight support, braking, and propulsion. By placing the manus closer to the top of the branch, the forelimbs were more stable than the hindlimbs and so they were recruited to assume a greater role in propulsion than is normally found during terrestrial locomotion. The hindlimbs, with their more lateral placement on the branch and their smaller role in body weight support, were perhaps less able to exert significantly higher propulsive forces without slipping.
89
Behavioral adaptations for arboreal locomotion
The results of this paper suggest that there are three important factors that animals
may regulate in order to maintain stability during locomotion: speed, kinematic gait, and limb placement. I propose that all three of these factors should be analyzed when conducting locomotor analyses, especially if different substrates are used.
This study examines arboreal locomotion in a terrestrial mammal with a primitive, generalized morphology and behavior (Lee and Cockburn, 1985), in the context of
comparing terrestrial generalists and arboreal specialists. Although some animals move
within arboreal habitats with impressive skill and speed (e.g., squirrels, many primates),
many arboreal specialists apparently use speed reduction to maintain stability on
branches and to reduce detection by predators (e.g., slow loris, woolly opossum,
chameleon). Thus, speed reduction may serve as a common behavioral adjustment to
arboreal locomotion.
On the terrestrial and arboreal substrates, M. domestica almost always
kinematically trotted, although this species tended somewhat to dissociate the diagonal
couplets and list toward the lateral sequence trot-like gait on arboreal trackways
(Hildebrand, 1976). That this gait shift may be reflective of a need to increase stability is
supported by data from Lammers (2001) that indicate that opossums use lateral sequence
trot-like and singlefoot gaits at slow speeds and/or on narrow (one-fourth body diameter)
supports. In contrast, most primates and the woolly opossum (Lemelin et al., 2003) use a
diagonal sequence trot-like gait on both arboreal and terrestrial substrates. It appears that
divergent kinematic gait patterns exist between arboreal specialists and terrestrial
generalists.
90
When arboreal specialists move on branches that are narrower than their body diameter, but too wide to grasp with opposable digits, do they place manus and pes on branches in different locations than terrestrial generalists? Data and/or tracings of images
indicate that like M. domestica, the lesser mouse lemur (Microcebus murinus), fat-tailed
dwarf lemur (Cheirogaleus medius), slow loris (Nycticebus caucang), and the brown
lemur (Eulemur fulvus) may place their manus relatively dorsally on the branch and the
pes more laterally (Cartmill, 1974; Jouffroy and Petter, 1990; Larson et al., 2001).
However, illustrations of chameleon (Chameleo spp.) locomotion suggest that the manus
and pes contact the branch in approximately the same location around a large arboreal
support (manus: Peterson, 1984; pes: Higham and Jayne, 2004). The common opossum
(Didelphis marsupialis) places its manus slightly laterally to the pes on narrow supports
(Cartmill, 1974). Finally, the aye-aye (Daubentonia madagascariensis) contacts
branches in a wide variety of locations (Krakauer et al., 2002). It is not yet possible to
determine whether the kinetic and kinematic patterns observed in the present study
represent a general behavioral adaptation to the challenges of arboreal locomotion by
terrestrial mammals or simply a solution specific for this species.
3.6. Acknowledgments
I thank Audrone Biknevicius, Jennifer Hancock, Ron Heinrich, Steve Reilly,
Daniel Schmitt, Nancy Stevens, Nancy Tatarek, Larry Witmer, and two anonymous
reviewers for their critics on the manuscript. John Bertram, Kay Earls, David Lee, and
Steve Reilly programmed the LabVIEW virtual instruments and assisted with the design
and construction of the force transducers. I am grateful to Emily Bevis, Josh Hill, Andy
91
Parchman, and ChiChi Peng for their long hours collecting data. I also thank Don Miles for his statistical expertise, Randy Mulford for machining the transducer parts, and Eric
Lindner for animal care. Supported by NSF IBN 9727212 & IBN 0080158 to ARB.
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3.8. Tables and figures
Table 3.1. General kinematics. Shown are means±S.E.M., (minimum, maximum) Arboreal Terrestrial Speed (m s-1) 1.00±0.02 (0.74, 1.31)* 1.51±0.05 (0.72, 2.18) Limb phase (%) 46.0±0.6 (34.7, 52.8)* 50.1±0.7 (41.3, 57.1) Duty factor (%) 44.6±0.8 (35.2, 58.2)* 33.9±1.0 (24.0, 51.7) * = Significant difference (using sequential Bonferroni technique) between substrates (P≤0.0003).
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Table 3.2. Peak vertical force (BW units), and vertical, fore-aft and mediolateral impulses (BW s). Means ± standard error, with minimum and maximum in parentheses.
Arboreal Terrestrial Forelimb Hindlimb Forelimb Hindlimb Peak vertical 1.010 ± 0.0285 0.625 ± 0.0290 1.528 ± 0.0724 0.898 ± 0.0565 force (0.821, 1.309) (0.383, 0.897) (0.901, 2.075) (0.577, 1.241) Vertical impulse 0.0423 ± 0.00186 0.0239 ± 0.00186 0.0519 ± 0.00157 0.0216 ± 0.00292 (0.0378, 0.0663) (0.0180, 0.0420) (0.0333, 0.0645) (0.0126, 0.0321) Braking impulse 0.00362 ± 0.00031 0.00163 ± 0.00029 0.00322 ± 0.00040 0.00092 ± 0.00017 (0.0014, 0.0065) (0.0003, 0.0053) (0.0008, 0.0069) (0.0002, 0.0029) Propulsive 0.00368 ± 0.00041 0.00164 ± 0.00028 0.00245 ± 0.00028 0.00312 ± 0.00058 impulse (0.0003, 0.0080) (0.00000, 0.0042) (0.0005, 0.0043) (0.0008, 0.0079) Net fore-aft 0.00006 ± 0.00058 0.00000 ± 0.00052 -0.00077 ± 0.00054 0.00221 ± 0.00066 impulse (-0.0047, 0.0066) (-0.0053, 0.0039) (-0.0064, 0.0017) (-0.0007, 0.0074) Net 0.00444 ± 0.00053 0.00450 ± 0.00044 -0.00496 ± 0.00159 -0.00310 ± 0.00107 mediolateral (-0.0021, 0.0096) (0.0008, 0.0107) (-0.0158, 0.0085) (-0.0121, 0.0050) impulse
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Table 3.3. Least squares regression results for vertical impulse (BW s) vs. speed (m s-1).
Slope 95% confidence R2 P-value intervals Arboreal forelimbs -0.0472 -0.0581, -0.0362 0.791 < 0.00001 Arboreal hindlimbs -0.0303 -0.0471, -0.0134 0.383 0.00126 Terrestrial forelimbs -0.0179 -0.0258, -0.0010 0.599 0.00026 Terrestrial hindlimbs ------0.60063
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A. Z axis
FL FL FL Fnor mal, ML (X , Y , Z )
2
FML
Fsh ear, M L 2 Branch centroid X axis (X, Y, Z)
FV B.
2 Fsh ear, V Fnor mal, V
Z axis
2 Branch centroid X axis (X, Y, Z)
C.
2 1 4 3
Figure 3.1. Arboreal locomotion in Monodelphis domestica. A. Resolution of SRFs into normal and shear components (Fnormal, ML and Fshear, ML respectively) as illustrated for a forelimb and its mediolateral SRF (FML). XFL, YFL, ZFL = coordinates of the estimated center of forelimb pressure. B. Resolution of vertical SRFs into shear and normal components (Fnormal, V and Fshear, V respectively). C. Cropped representative image of M. domestica on the arboreal trackway illustrating the limb landmarks: (1) distal tip of the 3rd manual digit; (2) lateral aspect of the wrist joint; (3) distal tip of the 5th pedal digit; (4) lateral aspect of the metatarsophalangeal joint. Note that the heel (see arrow pointing to the ankle marker) was typically not in contact with the substrate during arboreal and terrestrial trials. Scale bar (4 cm) denotes the length and location of the arboreal force transducer.
101
DidelphisPhilander Chironectes Metachirus MarmosaMonodelphis Caluromys Rhyncholestes Caenolestes
Semi- Aquatic
Mixed: arboreal and terrestrial species Arboreal
Family Didelphidae
Terrestrial
Figure 3.2. Phylogeny of some American marsupials, based on Palma and Spotorno (1999) and Nowak (1999). Although scansorial and arboreal locomotor adaptations evolved more than once in family Didelphidae, it is likely that the common ancestor was a terrestrial form. Furthermore, Nowak (1999) and Cartmill (1972) suggest that the terrestrial Monodelphis genus retains the primitive condition to the greatest degree.
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0 A.
25 Lateral sequence trot-like gait
50 Trot
75
100 100 75 50 25 0 Duty factor (%)
150 B. 125
100
75
50
25
0 0.5 1.0 1.5 2.0 2.5 Speed (m s-1)
Arboreal forelimbs Terrestrial forelimbs Arboreal hindlimbs Terrestrial hindlimbs
Figure 3.3. A. Symmetrical gait plot for M. domestica during terrestrial and arboreal locomotion following Hildebrand (1976). Terrestrial and arboreal trials lie mostly within trots, although arboreal trials extend into smaller limb phases a(lateral-sequence diagonal- couplet gait). B. Relationship between stance duration and speed.
103
Forelimbs Hindlimbs 1. 5 A. B. Speed = Speed = 0. 916 m s-1 0. 916 m s-1
1. 0 Vertical Vertical
0. 5
Mediolateral Mediolateral 0. 0
Craniocaudal Craniocaudal -0.3
1. 5 C. D. Speed = Speed = -1 -1 Vertical 1. 784 m s Vertical 1. 617 m s
1. 0
0. 5
Craniocaudal
Craniocaudal 0. 0
Mediolateral -0.3 Mediolateral
1. 5 E. Speed = F. Speed = 1. 146 m s-1 1. 246 m s-1 Vertical
1. 0
Vertical 0. 5
Craniocaudal Craniocaudal
0. 0 Mediolateral Mediolateral -0.3 0. 00 0. 01 0. 02 0. 03 0. 04 0. 05 0. 06 0. 07 0. 08 0. 09 0. 00 0. 01 0. 02 0. 03 0. 04 0. 05 0. 06 0. 07 0. 08 0. 09 Time (s) Time (s)
Figure 3.4. Representative substrate reaction force profiles from the terrestrial and arboreal trackways (speed indicated on each plot). A, B. Forelimb and hindlimb arboreal trials. C, D. Fast terrestrial trials for the forelimb and hindlimb, respectively. E, F. Slow terrestrial forelimb and hindlimb trials, respectively. Negative craniocaudal forces indicate a braking effort and positive indicates propulsion. Negative mediolateral force designates a medially-directed SRF (laterally- directed limb force) and positive designates a medially-directed limb force. For clarity, craniocaudal force is shown in gray.
104
2.2 0.07 A. B.
0.06 1.8
0.05 1.4
0.04
1.0 0.03
0.6 0.02
0.2 0.01
0.008 0.008 C. D. 0.007 0.007
0.006 0.006
0.005 0.005
0.004 0.004
0.003 0.003
0.002 0.002
0.001 0.001
0.000 0.000 0.5 1.0 1.5 2.0 2.5 0.5 1.0 1.5 2.0 2.5 Speed (m s-1) Speed (m s-1)
Arboreal forelimbs Terrestrial forelimbs Arboreal hindlimbs Terrestrial hindlimb s
Figure 3.5. Relationship of kinetic variables vs. speed. A. Peak vertical force. B. Vertical impulse. C. Braking impulse. D. Propulsive impulse. The sample ellipses emphasize substrate and limb groups. The dimensions of the ellipses were determined from the standard deviations of the y and x variables; sample covariance between y and x determine the orientation of the ellipse.
105
0.02
0.01 Medial limb force (lateral substrate reaction force) 0.00 Lateral limb force (medial substrate reaction force) -0.01
-0.02 FLHL FL HL
Arboreal Terrestrial
Figure 3.6. Box-and-whisker plots of net mediolateral impulse for each substrate and extremity group. The line in the middle of each box plot represents the median; each box and each whisker corresponds to one- fourth of the data; asterisks designate outliers; circle denotes extreme outliers. Positive values indicate a medially-directed limb force (laterally- directed SRF), and negative values indicate a laterally-directed limb force. Substrates were significantly different (P<0.00001), but there were no differences between limbs within substrate groups.
106
1.5 cm Forelimbs A.
1.0 cm
0.5 cm
Hind- 0.0 cm limbs
2.0 B. Figure 3.7. A. Manus and pes placement about the arboreal 1.5 trackway. Location of the center of pressure of each foot is drawn to scale relative to branch cross- 1.0 sectional shape. B. Representative required coefficient of friction data from M. domestica on the arboreal trackway (1.10 m s-1). 0.5 High values occur at the foot touchdown and again at the end of the step. The hatched line 0.0 indicates the median value for this 0.00 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 record (0.528). C. Median Time (s) required coefficient of friction for 4 forelimbs and hindlimbs on C. horizontal terrestrial and arboreal substrates. Ellipses are used to 3 make each group more clearly stand out, and are calculated as in Fig. 3.5.
2
1
0 0.5 1.0 1.5 2.0 2.5 Speed (m s-1)
Arboreal forelimbs Terrestrial forelimbs Arboreal hindlimbs Terrestrial hindlimbs
107
Chapter 4: Limb kinematics on terrestrial and arboreal substrates in
the gray short-tailed opossum (Monodelphis domestica)
4.1. Summary
Small mammals (< 1 kg) encounter heterogeneous substrates regularly, and many
species use low or fallen tree branches as “arboreal trackways” in order to move on a
relatively obstacle-free pathway. To understand how animals modify their limb kinematics to adjust to branch-like substrates, locomotor kinematics in the gray short- tailed opossum (Monodelphis domestica) were examined on a simulated horizontal branch (diameter: 2.03 cm, approximately one-half the diameter of the animal’s body) for comparison with a flat terrestrial trackway. The opossums moved significantly slower on the arboreal trackway, and stride length, frequency, and duration were well-correlated with speed. The forelimb was significantly more adducted on the arboreal substrate, but otherwise there were few substrate effects on the forelimb. In contrast, on the arboreal trackway, the hindlimb was more protracted at touchdown and midstance, hip height was
greater, and, like the forelimb, the distal elements of the hindlimb were significantly
adducted. The pelvic girdle of the opossums underwent lateral undulation on both
substrates. Speed affected mostly timing variables, while substrate affected spatial
variables (limb angles and limb placement). The opossums did not crouch on the
arboreal trackway, which suggests that crouching behavior may not be a universal adaptation to treacherous substrates. Finally, the posterior weight shift observed by
Lammers and Biknevicius (in review; also see Chapter 3) may be the result of relatively
protracted hindlimbs on the arboreal trackway.
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4.2. Introduction
Small vertebrates living along the forest floor customarily develop trackways to move efficiently between safe places (Mattingly and Jayne, 2002). These trackways extend along the surface of the ground (terrestrial trackways) as well as along low or fallen branches or limbs (arboreal trackways; Montgomery, 1980; Ladine and Kissell,
1994). Consequently, the capacity for both terrestrial locomotion and scansoriality
(climbing) is key to these animals’ survival. As such, even in an animal which is classified as “terrestrial”, it is ecologically relevant to understand the biodynamics of locomotion on arboreal substrates.
Several studies suggest that animals adjust their limb kinematics in order to maintain stability on a branch-like (rounded) support. The first strategy is simply to adopt a lower preferred speed (compared with speed on a flat, horizontal substrate with no obstacles) and to adjust locomotor gait. Lower speeds on terrestrial substrates are often accompanied by higher duty factors (Demes et al. 1994), so that the support duration is longer relative to stride duration. At slower speeds, there is also a tendency for animals to shift toward gaits in which a greater number of limbs contact the substrate at any given time (Hildebrand, 1976; Stevens, 2003). For example, on terrestrial substrates, the lateral-sequence singlefoot tends to maintain most regularly a tripod of support and the line of gravity (passing through the center of mass of the animal) is most often located within the base of support (Hildebrand, 1980). Other gaits may be more appropriate on arboreal supports (i.e., more stable, or allowing more efficient propulsion), such as a diagonal-sequence diagonal-couplet found in some primates and marsupials
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(Schmitt and Lemelin, 2002) or occasional lateral-sequence lateral-couplet gaits observed in lorisids (Demes et al., 1990).
Stability on an arboreal support might also be enhanced by adopting a crouched limb posture (Cartmill 1985). By drawing the center of mass closer to the branch, the leverage for lateral instability is reduced and thus the likelihood of rolling off the support decreases. However, crouching comes with some unfortunate biomechanical consequences, such as increasing anti-gravity muscle activity (Biewener, 1990) and decreasing effective limb length. Nevertheless, many species crouch (Higham and Jayne,
2004) or utilize a compliant gait (Schmitt, 1999), in which the limbs are less stiff during stance phase, when moving on arboreal supports.
A third strategy for maintaining stability while moving along an arboreal support is to increase stride length as a means for reducing the number of steps taken along the less stable substrate. Moving with lower stride frequencies may reduce oscillations of narrower, more compliant branches (Demes et al., 1990; Stevens, 2003). Increases in limb protraction and/or retraction in arboreal mammals (Larson et al., 2000; 2001) may be an adaptation to obtain lower stride frequencies without greatly compromising speed.
Finally, depending on the diameter of the arboreal support, placement of the manus and pes on the substrate may significantly affect mediolateral stability. Limb adduction may be accomplished by adducting the distal limb elements without effecting the proximal elements (Higham and Jayne, 2004) or by abducting the proximal elements while adducting the distal elements (Schmitt, 1994). The latter strategy may also increase the degree of limb crouch or compliance.
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In this paper, I explore limb kinematics on terrestrial and arboreal trackways in
Monodelphis domestica (gray short-tailed opossum) in order to determine how a primarily terrestrial species adapts to differing substrate diameters. Four predictions were tested on mechanisms to maintain stability when moving on an arboreal substrate: (1)
decreased preferred speed, (2) increased crouching, (3) increased protraction at
touchdown and retraction at liftoff, and (4) increased adduction during stance phase.
This study is one of the first to detail arboreal kinematics in a locomotor generalist.
4.3. Materials and methods
Animals, landmark placement, and radiography
I used six adult male gray short-tailed opossums (Monodelphis domestica;
Wagner, 1842) for all experiments (body mass: 0.105 – 0.149 kg) and all procedures
were approved by the Ohio University Animal Care and Use Committee. Animals were
anaesthetized prior to each experiment by placing them and 0.3 – 0.4 ml of isoflurane
(Abbott Laboratories, North Chicago, IL) into a plastic container (about 2 minutes). The
fur covering the lateral aspect of the left fore- and hindlimb was shaved and white 1.3 X
1.7 mm beads were glued to the skin overlying bony landmarks. Landmarks used in this
study include: (1) distal tip of the third manual digit, (2) the lateral aspect of the wrist, (3)
mid-forearm, (4) glenohumeral joint, (5) distal tip of the fifth pedal digit, (6) lateral side
of the fifth metatarsophalangeal joint, (7) lateral malleolus, (8) mid-shank, (9) greater
trochanter, and (10) anterior superior iliac spine (Fig. 4.1A, Table 4.1). Angles of the
glenohumeral joint and of the scapula were not recorded, as they could not be visualized
with these methods. The approximate midpoint of the forearm and shank (markers 3 and
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8) were used to calculate the position and angles of the elbow and knee, respectively.
The animals typically awoke from the anesthetic within 2 min and appeared to suffer no ill effects.
Each anesthetized animal was also radiographed in a sagittal plane using Kodak diagnostic film (Insight pediatric film IP-1). A portable radiograph unit (Soyee, Inc. SY-
31-90P) was used to expose the film for 0.1 s at 50 kV, 30 mA. Lengths of the forearm and shank were then measured to the nearest 0.1 mm with digital calipers (Mitutoyo absolute digimatic). The forearm was measured from the center of the carpal bones to the center of the trochlea of the humerus. The shank was measured from the center of the trochlea of the astralagus to the center of the femoral condyles (which is close to the center of rotation of the knee). These lengths were used with other markers coordinates to calculate the coordinates of the elbow and knee joints (see below for further details concerning angular calculations).
Kinematic data collection
I used two horizontal trackways in the experiments. The terrestrial trackway was constructed of wood, and it measured 160 cm long and 11 cm wide. Round aluminum tubing was used to construct the arboreal trackway, which was 151 cm long and 2.03 cm in diameter. This diameter corresponds to approximately one-half the animal’s thoracic body diameter. Each trackway was covered by 60-grit sandpaper to provide traction.
These trackways also had force transducer instrumented regions so that kinetic data could be collected simultaneously (see Chapter 3; Lammers and Biknevicius, in review).
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Only trials that approximated steady speed were analyzed. This was determined by analyzing the substrate reaction force (SRF) traces which were obtained at the same time as the kinematic data (see Chapter 3 for further detail concerning the collection of force data). In arboreal trials, I compared the total braking impulse of both fore- and hindlimbs to the total craniocaudal impulses [(braking impulse)/(craniocaudal impulse) *
100%]. If this percentage fell between 45 – 55%, then the trial was considered to be steady-speed. A different criterion for steady speed was developed for the terrestrial trials because only forelimb or hindlimb data were obtained in each trial. For the arboreal trials, whole body SRFs were obtained as the animals crossed the force platform. The craniocaudal SRFs were then divided by mass and then integrated to obtain craniocaudal velocity profiles; the integration constant was set as mean speed determined videographically over three 12 cm intervals. Terrestrial trials were accepted as steady speed when braking and propulsive components of the whole body velocity were balanced. Despite every effort to obtain steady-speed trials at a large range of speeds on each substrate, the mean speed of arboreal trials (1.00 m s-1) was lower than those of terrestrial trials (1.5 m s-1).
The trackways were illuminated with three Monarch-Nova (Amherst, NH) strobe lights (233.3 Hz) as two high-speed digital cameras (JVC GR DVL 9800; recording at
120 Hz) captured footfall patterns and limb movement. The first camera obtained a lateral view of the left side of the animal and the second obtained a dorsolateral view .
These videos were uploaded to a computer using U-lead Video Studio 4.0, and then the two camera views were synchronized using kinematic events in the Trimmer module of the APAS program (Ariel Dynamics, San Diego, CA). Landmarks from the
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synchronized camera views were digitized in the Digitize module of APAS (Fig. 4.1A).
The Transform module was used to convert each two-dimensional set of coordinates into
a single set of three-dimensional coordinates for each landmark (x, y, and z reflect
mediolateral, craniocaudal, and dorsoventral or vertical positions, respectively).
Coordinates of the limb joints were then transformed such that the y and x coordinates
(craniocaudal and mediolateral axes) of the shoulder and hip joints were 0,0 (Higham and
Jayne, 2004). The z-coordinates were transformmed into height from the contact of the
manus or pes with the substrate. A polarity for the coordinates was established such that
negative values indicate lateral (x) and caudal (y) relative to the shoulder or hip (Fig
4.1.D). Three-dimensional angles of the elbow and knee joints (Fig 4.1.C) were
computed at the beginning of stance phase (touchdown, TD), the time at which peak
vertical force occurred (midstance, MS), and end of stance phase (liftoff, LO). Total
forelimb and hindlimb craniocaudal excursion angle (Fig 4.1.C ) were also calculated at
these events. Craniocaudal forelimb excursion was the angle between the wrist, shoulder,
and a line drawn posteriorly behind the shoulder; the wrist joint contacts the substrate at
the beginning of stance phase, but it lifts off before the limb loses contact with the
substrate. Likewise, the adduction angle of the forelimb was the angle formed by the
wrist, shoulder, and a line drawn medially from the shoulder point. Hindlimb angles
were formed similarly, using the metatarsophalangeal joint and hip markers. On both
arboreal and terrestrial substrates, the heel rarely made contact with the trackway surface,
but the metatarsophalangeal joint was in contact with the substrate throughout the
majority of stance phase, until shortly before LO.
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Gaits were identified kinematically by calculating limb phase, the percentage of
stride duration that the left forelimb contacted the substrate after the left hindlimb contact
(Hildebrand, 1976). Hindlimb duty factor was also computed as the ratio of stance
duration to stride duration.
Statistical analyses
Data from all individuals were pooled, and Systat 9.0 (Point Richmond, CA) was
used for all analyses. Because stride frequency, length, and stance duration were correlated with speed, two-way analysis of covariance (ANCOVA) was used to test for
differences between substrates and between limbs with speed as the covariate. Least
squares regression was used to determine whether the angular or coordinate variables (at
TD, MS, and LO) were correlated with speed on each substrate and for each limb pair.
Because these variables were rarely correlated with speed, a two-way fixed-factor
repeated measures analysis of variance (ANOVA) was used to determine differences between substrates (terrestrial and arboreal) and among events (TD, MS, and LO).
Differences between arboreal and terrestrial limb phase and duty factor were determined
by t-test. In all tests, significance was determined using the sequential Bonferroni
technique (Rice, 1989; alpha = 0.05). Unless otherwise noted, forelimbs and hindlimbs
were tested separately because of the difficulty in making paired comparisons: for
example, the elbow and knee joints are serially homologous structures, but functionally
they are rather different (Fischer et al. 2002). Data are reported as mean (minimum,
maximum) unless otherwise indicated.
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4.4. Results
General kinematics
Speed was significantly lower among arboreal trials [arboreal: 1.00 (0.74, 1.32) m s-1; terrestrial: 1.51 (0.72, 2.18) m s-1; P<0.00001]. In general, most of the timing variables (e.g., duty factor, stride frequency) were well correlated with speed, while the spatial variables (e.g., limb joint coordinates and angles) were poorly correlated with speed. As reported in Chapter 3, the opossums primarily used lateral-sequence diagonal- couplet gaits (see Fig. 3.2.A). Arboreal trials had a significantly higher limb phase [46.0
(34.7-52.8)%, lateral-sequence diagonal-couplets and trots] than terrestrial trials [51.1
(43.6, 57.1)%, almost exclusively trots; P=0.00031]. Duty factor was significantly greater on the arboreal trackway [42.4 (35.2, 47.8)%] vs. the terrestrial [30.2 (24.0,
36.7)%; P<0.00001]. Stance duration decreased in a continuous, nonlinear manner relative to speed (see Fig. 3.2.B). Among arboreal trials, the negative slope of stance duration vs. speed is more steep than among terrestrial trials.
Stride frequency was positively correlated with speed, and there was no significant difference in least squares regression slope between substrates (one-way fixed-factor ANCOVA, P=0.28). But least squares means of stride frequency differed significantly between substrates (arboreal least-squares mean±S.E.M. = 6.86±0.12 Hz; terrestrial, 6.11±0.15 Hz; P=0.00106). Stride length was highly correlated with speed, but two-way ANCOVA found no significant differences between substrates or limb pairs
(P≥0.059). Step length (i.e., craniocaudal excursion of the distal limb joint during stance phase) was not correlated with speed, and there were no significant differences between limb pairs (P=0.057). However, step length was significantly longer on the arboreal
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substrate [5.1 (2.9, 6.4 ) cm] relative to the terrestrial [4.5 (2.5, 6.8) cm; two-way
ANOVA, P=0.00081].
Forelimbs
The vertical, fore-aft, and mediolateral positions of the limb joints at the three events (TD, MS, and LO) are summarized in Table 4.1; elbow and forelimb angles at these events are summarized in Table 4.2.
Assessment of the degree of protraction/retraction revealed no significant substrate effect on the craniocaudal forelimb angle at TD, MS, or LO (P=0.28; see Fig.
4.2 A, B; Fig. 4.3). Despite the lack of significant differences in forelimb angle, on the arboreal trackway the wrist joint was significantly more anterior at TD (P<0.00001), and the elbow joint was more posterior at LO (P=0.00610) in comparison to the terrestrial trackway (Fig. 4.4 A,B for representative).
Limb compliance and degree of crouching was assessed with elbow angle and shoulder height. There were no substrate effects observed for the elbow angle (Fig. 4.2
A,B). Shoulder height decreased significantly between TD and MS, and then increased between MS and LO (Table 4.3; P=0.00015) on both terrestrial and arboreal supports, but there was no difference between substrates (P=0.57). On both substrates, elbow height increased significantly between TD and MS (P<0.00001); it then decreased somewhat between MS and LO (but not significantly: P=0.087).
The degree of overall forelimb adduction (wrist relative to shoulder) was significantly greater on the arboreal substrate at all events (P<0.00001). On the terrestrial trackway, the wrists and elbows were positioned laterally relative to the shoulder, with
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the elbow more lateral than the wrist (Fig. 4.5A). Thus, the entire forelimb (brachium
and antebrachium) was abducted throughout stance phase on the terrestrial trackway. On
the arboreal trackway, the wrist was located slightly medial to the shoulder throughout
stance phase, while the elbow was lateral to the shoulder (Fig. 4.5B). Therefore, the wrist and shoulder were in nearly the same sagittal plane throughout stance, while the elbow was laterally displaced. In other words, the brachium was abducted whereas the antebrachium was adducted. When the mediolateral location of individual limb joints were compared between substrates (relative to shoulder position), the wrist joints were significantly more lateral on the terrestrial trackway than on the arboreal throughout stance (P<0.00001), but the mediolateral placement of the elbow joints were not significantly different between substrates when the sequential Bonferroni technique was applied (P=0.02673).
Hindlimbs
Hindlimb positional data are summarized in Table 4.1, and knee and total hindlimb angle data in Table 4.2.
Overall hindlimb angle at TD, MS, and LO was always significantly more protracted on the arboreal trackway than on the terrestrial (P<0.00001; Fig. 4.3 C, D).
Furthermore, the y-coordinates of the metatarsophalangeal and ankle joints were more anterior (relative to the hip) on the arboreal trackway at TD and MS (P<0.00001; Fig. 4.4
C,D). At LO, only the metatarsophalangeal joint was relatively more anterior on the arboreal substrate (P<0.00001). There was no significant difference in craniocaudal position of the knee joint between terrestrial and arboreal substrates (P=0.057).
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On the arboreal trackway the knee joint was significantly more extended at TD and LO but more flexed at MS compared with the terrestrial angles (substrate effect:
P=0.00413; substrate * time interaction: P=0.00316; see Fig. 4.2 C, D). The height of the ankle increased throughout stance phase on both substrates (P<0.00001), and, because there was a significant interaction term between substrate and time in ankle height
(P<0.00001), substrate was tested separately at TD, MS, and LO (Fig. 4.4 C, D). At TD and MS, the ankle height was greater on the arboreal substrate (P≤0.00073), but ankle height was lower on the arboreal substrate at LO (P=0.00106). On both substrates, knee height decreased significantly between TD and MS (P<0.00001), but there was no change between MS and LO (P=0.8). However, there were no differences in knee height between substrates (P=0.01448, not significant with the sequential Bonferroni correction) nor was there a significant substrate * time interaction term (P=0.8). Hip height (Table
4.3) also decreased significantly between TD and MS (P≤0.00425) and then remained constant on both arboreal and terrestrial trials. At each event, hip height was significantly greater on the arboreal substrate (P=0.00021). To explain why hip height was greater on the arboreal substrate than on the terrestrial, effective hindlimb length at TD, MS, and LO was computed as the distance between the metatarsophalangeal joint and the hip. At TD and MS, the effective hindlimb length was longer in arboreal trials, although this was not significant with the sequential Bonferroni correction (P=0.01756). However, hindlimb length was shorter in arboreal trials at LO (interaction term, P<0.00001).
The hindlimb was more adducted on the arboreal substrate than on the terrestrial
(P=0.00127). On both substrates, the hindlimb abducted between MS and LO
(P<0.00001). Regardless of substrate and event, the ankle was medial to the
119 metatarsophalangeal joint and the knee was lateral to both of these joints (Fig. 4.5 C, D).
On both arboreal and terrestrial trackways, the hip, ankle, and knee moved medially relative to the metatarsophalangeal joint during stance (i.e., the distal limb elements became more abducted relative to the hip throughout stance phase; Fig. 4.5 C,D). There was no apparent difference in the magnitude of this displacement among any of these joints relative to the metatarsophalangeal joint (interaction term P≥0.074), and so the hindlimb elements abducted about the same amount during stance due to the abduction of the hip joint. Although the movement of the hindlimb joints were similar on both substrates, the placement relative to the hip differed significantly between substrates in the metatarsophalangeal and ankle joints (P<0.00001). On the arboreal trackway, metatarsophalangeal and ankle joints were medial to the hip at the beginning of stance phase, and they then moved such that they were in approximately the same sagittal plane as the hip at LO. On the terrestrial trackway, the metatarsophalangeal and ankle joints were in the same sagittal plane as the hip at TD, and both joints then moved laterally throughout stance (P<0.00001).
4.5. Discussion
Stability
Locomotor speed, degree of crouching, limb excursion, and limb adduction are factors that may, at least in theory, affect an animal’s stability on arboreal supports.
While these locomotor parameters have been observed in arboreal species (e.g., Cartmill
1985; Schmitt, 1999; Stevens, 2003), their presence in the locomotor behavior of a generalized mammal moving along an arboreal support is not well established. Hence,
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the data presented here on M. domestica provide a valuable contrast to arboreal
specialists.
One of the most important locomotor differences between arboreal and terrestrial
substrates is the significant reduction in speed on the arboreal trackway. Speed reduction
is a common behavioral response to animals moving on non-level (arboreal) and non- horizontal (graded) substrates (Losos and Sinervo, 1989; Sinervo and Losos, 1991;
Wickler et al., 2000; Chapter 3). Changes in speed necessarily modified limb kinematics
(e.g., Watson and Ritzmann, 1998; Reilly, 2000): speed-dependent changes in stride
frequency (increased) and stance duration (decreased) occur when M. domestica moves
along arboreal and terrestrial supports alike. Thus, it appears that timing variables, along
with stride length, are significantly affected by speed. By contrast, most of the spatial
variables, such as joint coordinates and angles, are poorly correlated with speed. Watson
and Ritzmann (1998) report similar findings in the death head cockroach (Blaberus
discoidalis). While gait (limb phase) was not correlated with speed, there was a tendency
for arboreal trials (which, on average, were slower) to more frequently use the lateral-
sequence diagonal-couplet compared with the trot most commonly used in the terrestrial
trials. Hildebrand (1976) demonstrated that at low speeds, the lateral-sequence diagonal-
couplet gait tends to be more stable than the trot because the legs form a tripod of support
more frequently within a stride.
Several studies demonstrate that animals moving along an arboreal support
assume a more crouched (flexed limb) posture. For example, chameleons and Anolis
sagrei both moved with more crouched hindlimbs on branches (Higham and Jayne, 2004;
Spezzano and Jayne, 2004) whereas some primates crouch their forelimbs (Schmitt,
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1999). M. domestica moves arboreally with yet another crouching pattern: whereas
shoulder height does not differ between substrates, hindlimbs are actually less crouched on the arboreal substrate. Elevated hip height was enabled, in part, by moving with more extended knees. Therefore, M. domestica fails to take advantage of this simple postural
adjustment to reduce rotational moments of the torso about the limbs. Furthermore, both
fore- and hindlimbs retain the same degree of compliancy on the arboreal substrate as
they have on the terrestrial substrate, that is, shoulder and hip heights are highest at
touchdown and liftoff and lowest at midstance and they descend by about the same
percentage of limb length on both substrates. This has also been demonstrated in some
prosimian species (Stevens, 2003).
Arboreal animals that reduce stride frequency may be better able to control branch
oscillations (Demes et al., 1990; Stevens, 2003). One way to do this would be to increase
limb excursion, i.e., taking fewer but longer steps. Schmitt (1999) hypothesized that
primates on narrow supports would move with forelimbs that are more protracted at TD
and more retracted at LO (although Schmitt’s [1994] protraction and retraction data do
not appear to support this hypothesis). Indeed, greater limb protraction and/or retraction
is commonly found in arboreal primates (Schmidt and Fischer, 2000; Larson et al., 2001).
The present study demonstrates that M. domestica does not adopt a lengthened limb
excursion strategy when moving on an arboreal support, nor does it decrease its stride
frequency. Schmitt (1999) further suggested that compliant limb posture would be
advantageous for reducing the oscillation of branches and for reducing impact forces.
Given that the opossums did not make use of a more compliant limb posture, it may be
122 that these biomechanical adaptations are of little use to the opossums moving on the rigid
2-cm-diameter arboreal substrate that was used in my experiments.
Adduction of the manus and pes on narrow arboreal substrates enables the limbs to grasp these narrow supports. Primates and arboreal lizards also adduct their limbs when moving on narrow supports (Schmitt, 1994, 1999; Higham and Jayne, 2004;
Spezzano and Jayne, 2004). In M. domestica, virtually all distal limb joints are significantly more medial and the limbs are more adducted during stance phase on the arboreal substrate. This is not surprising because, on the arboreal trackway, the manus and pes are constrained to contact a substrate which was considerably narrower than the diameter of the body. On the terrestrial trackway, there was no such constraint, and so the animals could (and did) abduct their limbs somewhat. On the arboreal trackway, the opossums consistently abducted the brachium and thigh and adducted the antebrachium and shank, such that the knee and elbows were laterally displaced. Previous work on lizards and primates has shown that this limb posture is common (Schmitt, 1994; Higham and Jayne, 2004; Spezzano and Jayne, 2004), but not ubiquitous (Schmitt, 1994).
In summary, the opossums do not adopt all of the hypothesized strategies for maintaining (or increasing) stability on the arboreal substrate. While M. domestica decreases forward speed and adducts the limbs when moving arboreally, they do not crouch or increase the craniocaudal excursion of their limbs. Therefore, it is likely that a branch about half the diameter of the body challenged the opossums somewhat, but perhaps not as much as a narrower or more slippery substrate would have done. A rough sandpaper (60 grit) was used on all surfaces in this study, thus the animals could generate
123 adequate friction at low speeds. Furthermore, the branch was probably wide enough that when an opossum did slip, its body would land on the branch instead of toppling from it.
Broader implications on arboreal mechanics
Parchman et al. (2003) found that M. domestica recover very little energy via walking mechanics. Their data showed that the fluctuations of kinetic and gravitational potential energies of the moving opossums were in phase (i.e., each reaching its minimum at approximately the same time), which suggests bouncing mechanics. The present study shows that the opossums had compliant limbs on both terrestrial and arboreal substrates, as demonstrated by the changes in shoulder and hip heights during stance (higher at touchdown and liftoff than at midstance). It would be interesting to determine, but out of the scope of the present study, to what degree these small mammals can store and recover mechanical energy in the elastic elements of their limbs and whether or not this changes on an arboreal substrate.
Crouching during locomotion has other locomotor consequences besides stability
(Higham and Jayne, 2004). The effective mechanical advantage of limb muscles typically decrease when an animal crouches, so that more muscular force is required to maintain that posture (Biewener, 1990). Thus, it is possible that crouching behavior is not necessarily advantageous during arboreal locomotion, and our data (and also primate locomotor data by Stevens, 2003) suggest that crouching may not be as universal as is commonly thought.
Pridmore (1992), using cineradiographic data, described lateral undulations of the spine in M. domestica on both flat and arboreal (6.3 mm wooden dowel rod) substrates,
124 and these undulations occurred mainly in the anterior lumbar vertebrae. The present study supports this finding: the hindlimb exhibits evidence of lateral undulation, the forelimbs do not. Specifically, the mediolateral position of metatarsophalangeal joint appears to move laterally between touchdown and liftoff, yet, assuming that the foot is not moving substantially on the substrate during stance phase, this apparent shift is more likely due to a shift of the pelvis away the supporting foot (Fig. 4.6). The lateral undulation of the pelvis may contribute to the increased protraction of the hindlimb on arboreal supports, similar to that described in some primates (Demes et al., 1990).
In the previous chapter, timing of peak vertical force and magnitudes of vertical impulse between fore- and hindlimbs suggested that a posterior weight support shift occurred on the arboreal trackway. Similar results were obtained in studies of primate locomotion on horizontal terrestrial and arboreal supports (Schmitt, 1999). A possible explanation for this finding in M. domestica may be the more anterior placement of the hindlimbs (along with the more protracted hindlimb angle). This would cause the base of support to be shifted anteriorly relative to the center of mass so that the line of gravity passing through the animal's center of mass would then intersect the base of support relatively more posteriorly, i.e., a posterior weight shift. It is true that if the hindlimbs were, on average, more anteriorly displaced, then the center of mass would be moved slighly more anteriorly. But because the mass of the limbs (especially the distal-most parts) is very small relative to the mass of the body, it is likely that the anterior shift in the center of mass has a negligible effect on the posterior shift of weight support.
On the arboreal trackway, both manus and pes are placed on the side of the branch, although this is especially true for the pes. Simultaneously, the elbow and knee
125 are displaced more laterally (relative to the distal limb elements, not the shoulder and hip) during stance. This orientation of the distal limb elements may also allow these terrestrial animals to more effectively exert normal force on the branch, necessary for developing adequate static frictional force to avoid slipping off the support. Most arboreal primates and at least some arboreal lizards also abduct the elbow and knee joints when on branches (Schmitt, 1994; Stevens, 2003; Higham and Jayne, 2004; Spezzano and Jayne, 2004; contra Schmitt, 1994), and so this might be a common biomechanical means for increasing the normal force of the manus and pes on the branch.
4.6. Acknowledgments
I thank Audrone Biknevicius, Jen Hancock, Steve Reilly, Nancy Stevens, Nancy Tatarek, and Larry Witmer for critical reviews of the manuscript. Emily Bevis, Josh Hill, and Chi
Chi Peng assisted with data collection. Funding was provided by a Sigma Xi Grant-in-
Aid of research (to A.R.L.), an Ohio University Post-doctoral Fellowship award (to
A.R.B.), and NSF grants IBN 9727212 and IBN 0080158 (to A.R.B. and Steve Reilly).
4.7. References
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Larson, S.G., Schmitt, D., Lemelin, P., and Hamrick, M. (2000). Uniqueness of
primate forelimb posture during quadrupedal locomotion. Am. J. Phys. Anthrop.
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Larson, S.G., Schmitt, D., Lemelin, P., and Hamrick, M. (2001). Limb excursion
angle during quadrupedal walking: how do primates compare to other mammals?
J. Zool. (Lond). 255, 353-365.
Losos, J.B., and Sinervo, B. (1989). The effects of morphology and perch diameter on
spring performance of Anolis lizards. J. Exp. Biol. 145, 23-30.
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ecomorphs of Anolis lizards. Integ. Comp. Biol. 42, 1274.
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(Schreber). Mammal. Rev. 10, 189-195.
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patterns of locomotion in a semi-erect mammal. J. Exp. Biol. 206, 1379-1388.
Pridmore, P.A. (1992). Trunk movements during locomotion in the marsupial
Monodelphis domestica (Didelphidae). J. Morphol. 211, 137-146.
Reilly, S.M. (2000). Locomotion in the quail (Coturnix japonica): the kinematics of
walking and increasing speed. J. Morphol. 243, 173-185.
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during quadrupedal walking in the brown lemur (Eulemur fulvus, Primates:
Lemuridae). Am. J. Phys. Anthrop. 111, 245-262.
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Schmitt, D. (1999). Compliant walking in primates. J. Zool. (Lond.) 248, 149-160.
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the woolly opossum. Am. J. Phys. Anthop. 118, 231-238.
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on the hindlimb kinematics of an arboreal lizard (Anolis sagrei). J. Exp. Biol. 207,
2115-2131.
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4.8. Tables and figures
Table 4.1. Fore-aft (y), vertical (z), and mediolateral (x) coordinates of the limb joints relative to the shoulder and hip [mean (minimum, maximum)] at touchdown, time of peak vertical force, and liftoff. Shoulder and hip y and x coordinates were transformed to zero, and all other y and x coordinates were transformed accordingly. Positive values indicate a position anterior and/or medial to the shoulder or hip.Negative coordinates indicate posterior and/or lateral to the shoulder or hip. Vertical (z) coordinates indicate height above initial manus/pes contact. Coordinate Limb joint Stance time Arboreal (cm) Difference Terrestrial (cm) Fore-aft (y) Wrist TD 0.86 ( 0.18, 1.60) > 0.58 (-0.53, 1.65) MS -3.05 (-3.88, -2.04) n.s. -3.01 (-4.06, -1.97) LO -4.08 (-4.62, -2.75) n.s. -3.74 (-4.45, -2,96) Elbow TD -1.12 (-1.91, 0.35) n.s. -1.32 (-2.16, -0.49) MS -3.12 (-3.96, -2.04) n.s. -2.93 (-3.80, -2.03) LO -4.08 (-4.62, -2.75) < -2.70 (-3.41, -1.44) Metatarso- TD 2.12 ( 0.95, 3.06) > 0.17 (-0.91, 2.02) phalangeal MS -0.60 (-1.76, 0.94) > -1.52 (-2.94, -0.21) LO -3.17 (-3.68, -2.49) > -4.45 (-5.51, -3.72) Ankle TD 1.72 ( 0.62, 2.65) > -0.25 (-1.15, 1.50) MS -0.88 ( 0.17, -1.91) > -1.82 (-0.73, -3.24) LO -3.01 (-4.73, -2.40) > -2.85 (-3.52, -2.08) Knee TD 1.77 ( 1.33, 2.31) > 1.05 ( 0.41, 1.55) MS 0.97 ( 0.20, 1.67) > 0.36 (-1.01, 1.25) LO -0.60 (-0.87, -0.36) n.s. -0.37 (-1.88, 1.60) Vertical (z) Wrist TD 0 n.s. 0 MS 0.50 (-0.47, 0.88) n.s. 0.53 (-0.03, 1.15) LO 0.83 (-0.02, 1.32) < 1.02 ( 0.41, 1.85) Elbow TD 0.62 (-0.81, 1.46) n.s. 0.86 ( 0.24, 1.86) MS 2.42 (-0.50, 3.13) n.s. 2.62 ( 1.89, 3.50) LO 2.36 (-0.51, 3.32) n.s. 2.94 ( 2.58, 3.67) Metatarso- TD 0 n.s. 0 phalangeal MS 0.26 (-0.10, 1.13) n.s. 0.36 (-0.78, 1.10) LO 0.36 (-0.41, 1.13) < 0.47 ( 0.04, 1.54) Ankle TD 0.53 (-0.02, 1.43) > 0.33 (-0.60, 1.06) MS 0.89 ( 0.41, 1.33) n.s. 0.84 (-0.55, 1.60) LO 1.11 (-0.25, 1.80) < 1.48 ( 0.47, 1.93) Knee TD 2.77 ( 2.35, 3.27) n.s. 2.55 ( 3.50, 0.89) MS 2.25 ( 1.70, 2.80) n.s. 2.28 ( 1.49, 3.28) LO 2.40 ( 2.07, 2.77) < 2.56 ( 1.80, 2.91) Mediolateral (x) Wrist TD 0.16 (-0.44, 0.77) > -0.27 ( -0.90, 0.19) MS 0.11 (-0.47, 0.72) > -0.37 ( -1.07, 0.52) LO 0.15 ( -0.27, 0.55) > -0.40 ( -1.47, 0.20) Elbow TD -0.43 ( -0.90, 0.02) n.s. -0.91 ( -1.53, -0.14) MS -0.66 ( -1.31, 0.22) n.s. -0.77 ( -1.46, -0.17) LO -0.64 ( -1.54, 0.40) n.s. -0.73 ( -1.54, 0.34) Metatarso- TD 0.68 ( 0.23, 1.27) > -0.22 ( -1.18, 0.33) phalangeal MS 0.35 ( -0.12, 1.17) > -0.54 ( -2.00, 0.37) LO -0.19 ( -0.74, 0.37) > -0.83 ( -1.97, 1.18) Ankle TD 0.92 ( 0.53, 1.55) > 0.09 ( -0.78, 0.87) MS 0.60 ( 0.04, 1.27) > -0.05 ( -0.89, 0.78) LO -0.07 ( -0.76, 0.61) > -0.44 ( -1.24, 1.25) Knee TD -0.55 ( -0.98, 0.04) n.s. -0.53 ( -1.67, 1.77) MS -0.93 ( -1.30, -0.23) n.s. -1.01 ( -1.97, -0.01) LO -1.06 ( -1.74, -0.51) n.s. -1.40 ( -2.47, -0.29)
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(Table 4.1 continued)
< or > indicates significance with the sequential Bonferroni correction (Rice, 1989); n.s. = not significant.
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Table 4.2. Limb angles [mean ( minimum, maximum)]. Limb or joint angle Stance Arboreal Substrate Terrestrial time (degrees) differences (degrees) Forelimb TD 108 ( 94, 123) n.s. 101 ( 76, 121) (craniocaudal) MS 36 ( 27, 50) n.s. 36 ( 26, 52) LO 25 ( 18, 33) n.s. 24 ( 17, 34) Forelimb TD 93 ( 78, 105) >>> 92 ( 87, 97) (adduction) MS 92 ( 84, 100) >>> 84 ( 72, 97) LO 92 ( 87, 97) >>> 85 ( 67, 93) Elbow TD 75 ( 57, 97) n.s. 70 ( 52, 90) MS 82 ( 40, 106) n.s. 87 ( 66, 118) LO 108 ( 74, 134) n.s. 101 ( 87, 120) Hindlimb TD 116 (101, 129) >>> 92 ( 76, 114) (craniocaudal) MS 81 ( 66, 97) >>> 64 ( 46, 87) LO 51 ( 46, 57) >>> 41 ( 31, 49) Hindlimb TD 98 ( 93, 104) >>> 87 ( 78, 95) (adduction) MS 95 ( 89, 105) >>> 85 ( 71, 95) LO 87 ( 80, 94) >>> 82 ( 71, 106) Knee TD 110 ( 90, 133) >> 93 ( 63, 112) MS 86 ( 70, 98) n.s. 91 ( 66, 139) LO 116 ( 86, 136) >> 103 ( 69, 141) << or >> indicates P≤0.01; <<< or >>> indicates P≤0.001; n.s. = not significant. There was significant interaction between substrate and stance time effects for the knee angle (P=0.0032), and so arboreal and terrestrial substrates were tested separately (one-way ANOVA). Arb = arboreal, Ter = terrestrial.
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Table 4.3. Shoulder and hip height from the contact of the limb on the substrate. Stance time Arboreal (cm) Difference Terrestrial (cm) Shoulder height Touchdown 2.66 ( 2.06, 3.53) n.s. 2.59 ( 2.08, 3.02) Peak vertical force 2.31 ( 1.91, 2.90) n.s. 2.27 ( 1.81, 2.85) Liftoff 2.49 ( 2.00, 3.29) n.s. 2.50 ( 1.86, 3.10) Hip height Touchdown 4.25 ( 3.70, 4.88) >>> 3.76 ( 3.03, 4.69) Peak vertical force 3.95 ( 3.29, 4.25) >>> 3.42 ( 2.49, 4.40) Liftoff 4.22 ( 3.38, 4.95) >>> 3.71 ( 3.00, 4.54) >>> indicates P≤0.001; n.s. = not significant.
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A. 10 9 4 3 8 2 1 7 6 5
B. Pelvis
Thigh Brachium Shank
Manus Antebrachium Pes
C.
Hindlimb Forelimb Knee Elbow
-y D. -x
-z
Figure 4.1. A. Location of digitizing landmarks on the left side of M. domestica; see text for further descriptions. B. Limb segments. C. Angles. Forelimb and hindlimb angles are shown by the dotted lines. D. 3-dimensional coordinate system. Negative x is lateral (coming out of the page), negative y is caudal, and negative z is ventral.
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Arboreal Terrestrial
TDMS LO TDMS LO 130 A. B. 110
90
70
50
Elbow 30 Forelimb
TDMS LO TDMS LO 130 C. D. 110
90
70
50 Knee 30 Hindlimb
0 20 40 60 80 100 0 20 40 60 80 100 Time (% stride cycle) Time (% stride cycle)
Figure 4.2. Whole limb and joint angles during a typical stride cycle. A. Forelimbs, arboreal substrate. B. Forelimbs, terrestrial substrate. C. Hindlimbs, arboreal substrate. D. Hindlimbs, arboreal substrate. Stance phase is shaded gray. 0% stride cycle = TD, dotted vertical lines indicate MS, and dashed vertical lines indicate LO.
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150
125
100 Touchdown
75
50
Liftoff 25
0
Arboreal Terrestrial
Figure 4.3. Box and whisker plots of craniocaudal excursion angle. The white boxes are forelimb touchdown (top) and liftoff (bottom) angles, and the gray boxes are hindlimbs. Arboreal trials are shown on the left, terrestrial on the right. Each box represents one-half of the data, with the median shown as a line in each box. Each whisker represents one-quarter of the data. Asterisks are outliers.
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Direction of locomotion
5 A. C. 4
3
2
1
0
-1
5 B. D. 4
3
2
1
0
-1 -4 -3-2-10 1 2 3 4 5 -4 -3-2-10 1 2 3 4 5 Craniocaudal (y) axis (cm)
Figure 4.4. Lateral view of the sagittal limb kinematics during stance phase. A. Forelimb, terrestrial substrate. B. Forelimb, arboreal substrate. C. Hindlimb, terrestrial substrate. D. Hindlimb, terrestrial substrate. Symbols represent joint coordinates through time. Gray ellipses represent limb segment (see Fig. 4.1B) at touchdown (left) and liftoff (right). Negative values in the craniocaudal (y) axis indicate caudal to the shoulder or hip. Contact with the substrate occurs at coordinates (0,0).
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Direction of locomotion
-2 A. Lateral -1 to footfall
0 Shoulder Medial to 1 Elbow footfall Wrist 2
-2 B. Figure 4.5. Dorsal view of -1 the transverse limb kinematics during stance 0 phase. A. Forelimb, terrestrial substrate. B. 1 Forelimb, arboreal substrate. C. Hindlimb, 2 terrestrial substrate. D. Hindlimb, terrestrial -2 C. substrate. Symbols represent joint coordinates -1 through time. Plots progress from touchdown 0 (left) to liftoff (right). The double-circle represents the 1 substrate/manus or substrate/pes contact 2 (located at x,y coordinates 0,0). Negative values in the -2 D. craniocaudal (y) and mediolateral (x) axes -1 indicate caudal and lateral to the shoulder or hip, 0 respectively. Hip 1 Knee Ankle
2 -4 -3-2-10 1 2 3 4 5 Craniocaudal (y) axis (cm)
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TD Vertebral column
LO
Figure 4.6. Dorsal view of lateral undulation of the spine and pelvis. Shown is the vertebral column and left hindlimb at touchdown (TD, dark gray) and liftoff (LO, light gray). Note that the pes is more lateral to the hip at LO compared with TD. Presuming minimal lateral movement of the pes during stance phase, this likely represents a shift of the pelvis toward the stance hindlimb at TD and a shift to toward the contralateral hindlimb at LO.
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Chapter 5: Synthesis and future directions
5.1. Synthesis
My doctoral research investigated the effects of substrate slope and diameter on the biomechanics of locomotion in a small, quadrupedal mammal (Monodelphis domestica, the gray short-tailed opossum). First, I established base-line kinetic patterns
(based on substrate reaction forces) on level, flat substrates. These were found to be typical for non-primate quadrupeds in that the forelimbs supported the majority of the body weight, forelimbs were net braking and hindlimbs net propulsive, and both limb pairs exerted small laterally-directed impulses.
In the first study (Chapter 2), I examined how moving up a 30° incline and down a 30° decline affects these substrate reaction force (SRF) patterns, as well as limb kinematics and required coefficient of friction. On sloped substrates, M. domestica moved more slowly with a higher duty factor, used more statically stable gaits (decline), and required a greater coefficient of friction to avoid slipping. These data suggest that a
30° slope is enough to perturb the opossums’ normal mode of locomotion, and they must therefore adjust their locomotor patterns to remain stable. On inclines, both limb pairs supported body weight equally, and the craniocaudal limb excursion increased. But the forelimbs exerted greater propulsive impulse than hindlimbs, which was something of a recurring theme in my studies. On the decline, the forelimbs were brought to bear far more body weight and braking effort than the hindlimbs; perhaps the greater forelimb protraction (at touchdown) was a way of accommodating a more substantial load during downhill locomotion.
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In the second and third studies (Chapters 3 & 4), I tested the effects of substrate
diameter on locomotor kinetics and kinematics. On the arboreal substrate, many kinetic
patterns were similar to those observed on the terrestrial. Forelimbs exhibited higher
vertical impulse and peak vertical force than hindlimbs, and both limb pairs exerted a
braking force followed by a propulsive force during each stride. However, the forelimbs
exerted more than twice the braking and propulsive impulses than hindlimbs. The manus
was placed higher around the circumference of the branch than the pes. The shifts in
forces and limb placement resulted in a lower required coefficient of friction in the
forelimb. Thus, the forelimbs are probably more stable than the hindlimbs, and this may
explain why forelimbs have such a dominant role on the branch. Although vertical
impulses were lower on the terrestrial substrate than on the arboreal support, this was most likely due to speed effects because the opossums refused to move as quickly on the arboreal trackway. Vertical impulse decreased significantly faster with speed on the arboreal substrate because most of these trials were relatively slow, and stance duration decreased with speed more rapidly at these lower speeds.
A decrease in speed is a common behavioral adaptation to maintain stability
(Warncke et al., 1988; Losos and Sinervo, 1989; Sinervo and Losos, 1991; Chickering,
1995; Wickler et al., 2000; Paradisis and Cooke, 2001). Stride length, frequency, and
duration were well-correlated with speed, and I hypothesize that for the most part, timing
variables were affected by speed, while substrate affected mostly spatial variables (joint
angles and limb placement). The distal elements of the forelimb were significantly more
adducted on the arboreal substrate, but otherwise there were few substrate effects on the
forelimb. It is possible that the relatively stable placement of the manus permits the
141 forelimb to make few kinematic adjustments for arboreal locomotion. On the other hand
(or limb, rather), substrate had many significant effects on hindlimb kinematics. Like the forelimb, the distal elements of the hindlimb were significantly adducted on the arboreal trackway. On the arboreal trackway, the hindlimb was more protracted at touchdown and time of peak vertical force, and hip height was greater. The pelvic girdle of the opossums underwent lateral undulation regardless of substrate. I was surprised that the opossums did not crouch on the arboreal trackway. This suggests that crouching behavior may not be a universal adaptation to treacherous substrates (Stevens, 2003). Finally, the posterior weight shift observed in Chapter 3 may be the result of relatively protracted hindlimbs on the arboreal trackway.
One interesting finding, consistent on sloped and narrow substrates, is the expanded role of the forelimbs. On the inclined trackway, the forelimbs took on the majority of the propulsive effort (as measured by propulsive impulse). This was unexpected for two reasons. First, on horizontal, flat surfaces, the forelimbs are net braking, while the hindlimbs are net propulsive. Given the propulsive role of the hindlimbs, it might be expected that hindlimbs would expand their propulsive role rather than the forelimbs. Second, the weight support roles of fore- and hindlimbs on the incline were equal. As such, the normal force (and correspondingly, the friction force) of the forelimbs was most likely no greater than the friction force generated by the hindlimbs. If generation of friction is equal between limb pairs, then there is no a priori reason to assume that one limb pair would have a greater propulsive role (on an incline) than another limb pair. On the decline, the forelimb role was expanded even more: forelimbs exerted 81% of the body weight support role and 82% of the braking effort (as
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indicated by vertical and braking impulses, respectively). Finally, on the narrow-
diameter trackway, forelimbs exerted significantly more braking and propulsive effort
than the hindlimbs. While the braking effort was not higher than expected, the great
propulsive effort was surprising. This leads me to the question: Are forelimbs just more adaptable than hindlimbs? Many mammals tend to use the manus in different ways from the pes. For example, raccoons, otters, some marsupials, and many primate species use the manus for manipulation and/or grasping of arboreal supports (McClearn, 1992;
Nowak, 1999; Larson et al., 2001; Hamrick, 2001). Even cockroaches use their forelimbs to explore the environment, relegating propulsive effort to their hind and middle leg
pairs, so that the kinematics of the forelimbs are somewhat irregular in comparison to
more caudal legs (Full et al., 1991; Watson et al., 2002). Two (as yet untested) possible
reasons why opossums may be able to expand the functions of its forelimbs more readily
than the hindlimbs: (1) The forelimbs usually display a greater range of motion due to
their more mobile, flexible joints (e.g., glenohumeral joint) and the highly mobile scapula
(Fischer et al., 2002). (2) The forelimbs are affected by their close proximity to the head, on which the special senses are clustered, i.e., they are ideally placed for detailed
manipulation of the environment.
Another consistent observation across all substrates was the consistency of the
opossums’ gait: they virtually always used a trotting footfall pattern. This is a
dynamically stable gait, common among virtually all tetrapods (Hildebrand, 1976), and
so it is likely that the opossums’ use of the trot is simply a retention of the primitive
pattern. Yet, Reilly and White (2003) suggest an intriguing alternative explanation.
They observed that the muscles spanning from the femur and epipubic bone on one side
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of the animal to the contralateral forelimb are active during the stance phase of the limbs to which the muscles connect. Reilly and White (2003) suggest that opossums in the family Didelphidae (including M. domestica) are limited to using a trotting gait because
these muscles provide an anatomical constraint. Previous gait data collected by Pridmore
(1992) and Lammers (2001), however, show that M. domestica does indeed use non-
trotting gaits at low speeds (singlefoot gait) and high speeds (gallop or bound). As such,
the hypothesis of Reilly and White (2003) must be further tested by comparing the
opossum data to other taxa which have a primitive, generalized morphology, but no
epipubic bones or cross-couplet muscle activity.
5.2. Future directions
These studies that comprise my doctoral research examined separately the effects
of substrate slope and diameter. I have also collected substrate reaction forces and limb
kinematics from opossums moving up and down a 30° sloped arboreal trackway, which
gives me the unique opportunity to examine how the interaction between slope and
diameter affects locomotor biomechanics. Indeed, these are the first force data to be
collected from a sloped arboreal trackway. Preliminary analyses indicate that when the
opossums moved up the incline, the hindlimbs supported a greater percentage of body
weight than the forelimbs (as indicated by vertical impulse). This differs from the pattern
observed on the sloped “flat” trackway, where fore- and hindlimbs had equal roles in
supporting body weight. However, when the opossums moved down the arboreal
trackway, the forelimb vertical impulse was approximately three times greater than
hindlimb vertical impulse. This is closer to the pattern of weight support roles between
144 fore- and hindlimbs on the “flat” declined trackway. I intend to explore the relationship between slope, diameter, and locomotor biodynamics further.
I am also am interested in calculating work. Because work takes distance into account, this might have been a way to evaluate the efforts exerted for weight-support, propulsive, and mediolateral stability without the confounding speed effects. Donelan et al. (2002) described a method of calculating work which uses force records from individual limbs (“individual limbs method”), which may be applicable to my data sets.
Their technique takes into account the negative work done at the beginning of stance phase in order to change the direction of the center of mass, as well as the positive work done during the remainder of stance phase. It would be interesting to determine if total work varies between inclines and declines.
I am also interested in determining the effects of substrate friction on locomotor substrate reaction forces and kinematics. Given that the animals did not slip in the trials, and the required coefficient of friction (µreq) was sometimes around 2, it is likely that the coefficient of static friction (µs) is greater than 2 (see also Kinoshita et al., 1997). I would also like to experimentally measure the actual µs by using dead specimens.
Lowering the µs or increasing gradient so that the animals can still move without slipping should result in more dramatic modifications in force production and movement.
Parameters could be adjusted until animals fail to progress, indicating a discrete limit to their locomotor performance.
Finally, this study of locomotor biomechanics in a mammal which retains many primitive characters (Lee and Cockburn, 1985; Novacek, 1992) could be expanded by comparing the results obtained herein to other mammals which retain a relatively
145
primitive morphology. For example, like M. domestica, hedgehogs (family Erinaceidae)
and rats (Rattus norvegicus) are quadrupeds with a rather generalized, primitive-like body
plan. By making comparisons to these animals, it may be possible to draw conclusions
about how primitive mammals must have moved on non-level and narrow substrates. In
turn, by understanding how primitive mammals move, one can better understand the
evolution of locomotor characteristics in more derived taxa – primates, for example.
In summary, this dissertation is the first study to describe in detail how a generalized, terrestrial mammal adapts its locomotor biodynamics to arboreal supports. I have also demonstrated the apparent mechanical adaptability of forelimbs in this generalized species. Thus, the research lays an excellent foundation for future research in comparative locomotor biomechanics, as well as expanding into energetics and the
effects of fricton.
5.3. References
Chickering, J.G. (1995). Scaling of skeletal adaptation, locomotor performance and
muscular morphology in Sciurids (Mammalia: Rodentia). Ph.D. dissertation,
Brown University. 155pp.
Donelan, J.M., Kram, R., and Kuo, A.D. (2002). Simulataneous positive and negative
external work in human walking. J. Biomech. 35, 117-124.
Fischer, M.S., Schilling, N., Schmidt, M., Haarhaus, D., and Witte, H. (2002). Basic
limb kinematics of small therian mammals. J. Exp. Biol. 205, 1315-1338.
Full, R.J., Blickhan, R, and Ting, L.H. (1991). Leg design in hexapedal runners. J. Exp.
Biol. 158, 369-390.
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Hamrick, M.W. (2001). Morphological diversity in digital skin microstructure of
didelphid marsupials. J. Anat. 198, 683-688.
Hildebrand, M. (1976). Analysis of tetrapod gaits: general considerations and
symmetrical gaits. In: Neural Control of Locomotion Vol. 18. (ed. Herman, R.M.,
Grillner, S., Stein, P. and Stuart, D.G.). pp. 203-206. Plenum. New York.
Kinoshita, H., Bäckström, L., Flanagan, J.R., and Johansson, R.S. (1997). Tangential
torque effects on the control of grip forces when holding objects with a precision
grip. J. Neurophysiol. 78, 1619-1630.
Lammers, A.R. (2001). The effects of incline and branch diameter on the kinematics of
arboreal locomotion. Am. Zool. 41, 1500.
Larson, S.G., Schmitt, D., Lemelin, P., and Hamrick, M. (2001). Limb excursion
angle during quadrupedal walking: how do primates compare to other mammals?
J. Zool. (Lond). 255, 353-365.
Lee, A.K. and A. Cockburn. (1985). Evolutionary ecology of marsupials. Cambridge:
Cambridge University Press.
Losos, J.B. and Sinervo, B. (1989). The effects of morphology and perch diameter on
sprint performance of Anolis lizards. J. Exp. Biol. 145, 23-30.
McClearn, D. (1992). Locomotion posture and feeding behavior of kinkajous, coatis and
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