D.B. BURR, G. PIOTROWSKI, R.B. MARTIN, AND P.N. COOK a b. C. Fig. 1. The femur .... distally are higher than at midshaft, they don't approach the magnitude ...
T H E ANATOMICAL RECORD 202:419-429 (1982)
Femoral Mechanics in the Lesser Bushbaby (Galago senegalensis): Structural Adaptations to Leaping in Primates DAVID B. BURR, GEORGE PIOTROWSKI, R. BRUCE MARTIN, A N I ) P. NONG COOK Department of Anatomy and Orthopedic Research Laboratory, West Virginia University Medical Center, Morgantown, West Virginia 26506 (DB.B., R B.M.1; Department of Mechanical Engineering, University of Florida. Gainesuille, Florida 526'11 (G.P.);and Department of Diagnostic Radiology, University of Kansas Medical Center. Kansas City. Kansas 66103
ABSTRACT
One method used to examine the relationship between behavioral strategies and anatomical adaptation is to study the results of mechanical stress associated with a given behavior and compare this with skeletal adaptations to other behaviors. This comparative approach is appropriate for highlighting combinations of features that are specializations to specific types of behavior. The purpose of this paper is to compare femoral mechanics in Galago senegalensis with previously collected data for macaques and humans as a basis for discussing structural adaptations in the primate hindlimb to leaping. The stiffness and load carrying capabilities of the femoral diaphyses of 27 G. senegalensis were analyzed using the SCADS computer program. The data suggest that the galago femur is well adapted to sustain large sagittal plane compressive loads rather than large bending loads. The straightness of the femoral shaft and large midshaft area moments of inertia prevent buckling from these large compressive loads. Calculations indicate that the ratio of critical buckling load to body weight in galago is 31 times that in macaques and 55 times that in humans. The femur of this saltatory primate is morphologically adapted to resist buckling when subjected to large compressive loads, while those of macaques and humans are better adapted to resist bending moments caused by ground reaction forces acting on the extended limb. The differences between galago on the one hand and macaques and humans on the other suggest that relatively smaller moments about the hip and relatively larger moments about the knee accompany more quadrupedal and bipedal walking, while habitual leaping is associated with relatively larger moments about the hip. These data reinforce the apparent similarity of the mechanical effects of quadrupedal and biuedal locomotion on the femur and dissimilarity with femoral mechanics in habitually saltatory primates.
The focus of recent investigations of primate skeletal morphology has been the characterization of a relationship between behavioral strategies and anatomical adaptation (Fleagle, 1977a,b, 1978; Fleagle and Mittermeier, 1980; Rodman, 1979; Morbeck et al., 1979). One method used to examine this interaction is to study the results of mechanical stress associated with a given behavior and compare these with skeletal adaptations to other behaviors. This comparative approach may be the most appropriate for highlighting combinations of features that are mechanical specializations to specific types of behavior. The functional association between locomotor behavior and
0003-276X/82/2023-0419$03.500 1982 Alan R. Liss, Inc
anatomy can be shown best by investigating living species in which both behavior and anatomy can be established. The purpose of this paper is to further clarify functional patterns of mechanical adaptation in skeletal morphology to patterns of locomotion. This study concentrates on the adaptive correlates to leaping in the lesser bushbaby (Galago senegalensis), a primate well adapted to saltation. Movement patterns and musculoskeletal anatomy of G. senegalensis have been reasonably well established (Nayak, 1933; Hill, 1953; Hall-Craggs, 1964, 1965a.b; Stevens et Received February 17. 19x1: accepted November 2. 1981
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al., 1971, 1972; Jouffroy e t al., 1974; Jouffroy and Gasc, 1974; Petronis, 1978), but the mechanical, as opposed to morphological, adaptation of the skeletal system to these movement patterns has not been examined. Hindlimb dominance has been carried to an extreme in the lesser bushbaby (54%-60% forelimb lengthihindlimb length ratio) (Jouffroy and Lessertisseur, 1979). This represents an entirely different adaptive strategy than that studied previously in macaques, which are pronograde primates that exhibit little difference in limb proportion. Although both animals are capable of leaping, saltation in galagos is more specialized, subjects the skeleton to different temporal and force thresholds, and consequently must exert qualitatively and quantitatively different mechanical demands on the skeleton than leaping or quadrupedalism in macaques. Unfortunately, there is no clear idea of what these demands are because the bushbaby skeleton has not been examined in terms of its load-carrying capability. This study concentrates on the stiffness and load-carrying capability of the femur for two reasons. First, i t satisfies the constraints of the comparative method. Previous work done on the macaque femur (Burr e t al., 1981) provides some comparative background. Second, if it is true that skeletal adaptation is sensitive to temporal and stress-related thresholds (Preuschoft, 1979; Oxnard, 1979a).then combinations of features that are mechanical specializations to leaping should be most evident in the femur. This is the primary load-carrying bone in the hindlimb and probably the one subjected to the largest joint-reaction forces. One need only observe the massive musculature surrounding the femur in galagos to realize that the thigh is the prime motivator in leaping and that large loads will therefore be sustained by the femur. Leaping in Galago: Behavioral observations Galagos are among the most saltatory of primates (Oxnard e t al., 1981a,b).They have been known to jump fourteen times their body length both vertically and horizontally (Jouffroy e t al., 1974) a t take-off velocities more than twice those found in other leaping animals (e.g., 380 cmisecond compared with 180 cmkecond in a frog) (Calow and Alexander, 1973). Hall-Craggs (1965a) has provided the most detailed observations of the mechanics of leaping in G. senegalensis. He states (pp. 2223):
The stance prior to jumping can be described as a Although the neck is extended the back is flexed and the longitudinal axis of the trunk forms an angle of approximately 30" to horizontal. The hind limbs are acutely flexed. the thigh lies alongside the trunk and the thigh, leg and foot are apparently tightly compressed against each other.
low crouch.
Movement begins as a progressive extension of the back and an extension of the trunk on the thigh, the thigh and the rest of the lower limb remaining virtually stationary during the first 0.03 second or so of the jump. The first apparent movement of the hind limb is a rotation forwards of the flexed thigh, leg and tarsus about the distal tarsus as dorsiflexion at the tarsometatarsal joint occurs. extension of the hind limb does not begin until 0.05 second after the trunk begins to rise. Extension of the trunk on the thigh continues and is joined at first by extension of the leg on the thigh. Extension at hip, knee and ankle joints lead to an alignment of trunk and lower limbs in the direction of the trajectory and the animal leaves the ground with trunk and hind limb lying almost along a straight line. Jouffroy e t al. (1974:823) provide additional observations on hindlimb mechanics during the symmetrical leap: The whole movement lasts 0.35 sec. It can be divided into a first, or preparatory phase of relatively long duration (0.26 sec.), and a very quick springing phase that lasts 0.09 sec. During the preparatory phase, the animal crouches with the feet in full plantigrade contact with the ground. The main movements occur at the femur and tibia levels. The femur undergoes a rotatory movement that diminishes the femoro-tibia1 angle in such a way that the pelvicifemoralarticulations are lower than the knees. before the end of this phase, the tibia moves towards the ground. The outcome of this movement is that it narrows even more t h e femoro-tibia1 angle. The springing phase straightens, in perfect alignment, all the hindlimb bone segments. 0.09 sec. before the launching, the heads of both femurs begin the ascent; at 0.05 sec. the tibiae follow the same ascending movement. Gross morphology of the femur The head of the femur in galago differs from that in nonsaltatory primates in being a cylindrically enlarged extension of the femoral neck rather than a well-defined spherical caput (Fig. la). The most spherical portion of the head projects anteriorly from the neck, while the posterior articular surface blends imperceptibly with the femoral neck. The femoral neck is rather short and indistinguishable from the head posteriorly and forms nearly a right angle
FEMORAL MECHANICS IN T H E LESSER BUSHBABY
with the axis of the femoral shaft. The head and lesser trochanter project about the same distance medially, the lesser trochanter fading gradually and disappearing about a quarter of the way down the shaft. There is no evidence of a third trochanter, such as is found in some lemurs and tree shrews, although Hill (1953) reports this as a distinguishing feature of the Galagidae. However, the distal portion of the greater trochanter projects laterally a good distance from the femoral shaft, and this may indicate a blending of the third trochanter with the greater trochanter. The diaphysis of the femur is very smooth, with no development of a linea aspera. The diaphysis thickens noticeably toward midshaft and narrows slightly distal to this (Fig. lb). The posterior aspect of the femur is quite flat, as are the medial and lateral aspects proximally, such that the cross section of the proximal femur appears to be nearly rectangular, rather than cylindrical. The distal portion of the galago femur appears nearly cylindrical, in contrast to the anteroposterior thickness and mediolateral narrowness reported by Stevens et al. (1971). The distal joint surfaces are elongated anteroposteriorly more than that found in nonsaltatory primates and tend to project sharply anterior to the shaft (Fig. lc). MATERIALS AND METHODS
The femora of 27 Lesser bushbabies (Galago senegalensis) were mechanically cleaned and air dried. The femora were each embedded in plaster of Paris in neutral rotation such that the major anatomical axes were parallel to the edges of the block mold. Blocks were cut out of the diaphysis at 26, 38, 50, 62, and 74% of femoral length using a Buehler Isomet lowspeed saw. The specimens were bathed in mineral spirits during these procedures. Each block was magnified 1 2 X and photographed under a 30 X 30 grid calibrated in 0.25 mm squares. The grid served as a scale with which the digitizer was calibrated and also permitted orientation of the photograph on the digitizing table. The x and y coordinates of each bone section were digitized using a Graf Pen digitizer interfaced to a PDP 11/04 minicomputer. Data were recorded on disc and later transferred to cards for input into the stress analysis program. The SCADS computer program permits the analysis of the mechanical properties of long bones based on cross sectional geometry of serial sections. The analyses performed, algorithms used and output generated have been
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extensively described by Piotrowski and Wilcox (1971) and Piotrowski and Kellman (1978). The program calculates the following variables: Cortical area (A) is one indication of the bone’s resistance to axial loads and can be used to measure the increase or decrease of bone tissue throughout the diaphysis. The area moments of inertia (Ixx, Iyy) are directly related to the stiffness of the bone in bending. The SCADS program defines Ixx as stiffness in the mediolateral plane and Iyy as stiffness in the anteroposterior plane. These definitions follow Crandall et al. (1972), although other investigators may reverse the meaning of these terms. The principal moments of inertia indicate the stiffest (Imax) and most flexible (Imin) axes through the cross section. The effective polar moment of inertia (Jeff)is related to the stiffness of noncircular cross sections of bone subjected to twisting moments and is computed from torsional rigidity calculations using the membrane analogy described by den Hartog (1952). The application of torque to a bone creates shear stress within the bone with the largest stresses along the periosteal border. Likewise, the application of a bending load to a bone creates compressive and tensile stress within the bone with the largest stresses found furthest from the axis about which bending occurs. Torsional shear stresses under a constant torque of 100 kgf.cm and bending stresses under a constant moment of 100 kgf.cm were computed for each cross section. Bending moments were applied in both anatomical planes and maximum bending stresses in each quadrant were calculated. Bending stresses calculated along the anterior and posterior aspects of the femur were based on bending about a mediolateral neutral axis through the cross section; bending stresses calculated along the medial and lateral aspects were based on bending about an anteroposterior neutral axis through the cross section. Outer and inner diameters in the anteroposterior and mediolateral planes were measured from data provided by the SCADS program. This permitted an assessment of the effects of the morphological variability in cortex thickness on the mechanical specialization of the femur in G. senegalensis. RESULTS
The cortical area available to support compressive axial loads in the galago femur declines sharply in the distal two thirds, such
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a
b
C Fig. 1. The femur of G. senegalensis. (a)Anterior view of the proximal femur; (b)anterolateral view of the whole femur; (c) lateral view of the distal femur.
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that there is 20% less cortical bone at 74% of femoral length than at 26% of length (Fig. 2). This suggests an enhanced ability to sustain axial loads proximally and decreased ability to withstand such loads distally. This variation in cross sectional area has no direct effect on the structural strength of the femur in bending or torsion, as shown below.
The distal decline in cortical area can be attributed primarily to relative medullary expansion in the sagittal plane (Fig. 3). Widening of the marrow space is accompanied by cortical thinning in the sagittal plane. Cortical thickness in the coronal plane, however, does not change markedly throughout the femur since increased inner width is paralleled by increased
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Fig. 3. Variation in anteroposterior and mediolateral outer and inner diameters proximal to distal in the femoral diaphysis. Numbers above and below symbols refer t o standard errors.
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outer diameter at most levels. A slight decrease in both outer diameters occurs between 62% and 74% of femoral length and further contributes to the decline in cross-sectional area. At the most distal level, coronal and sagittal plane outer widths are the same and inner diameters differ by less than 10%. The anteroposterior thickness and mediolateral narrowness of the distal femur of Galago reported by Stevens et al. (1971) was not observed. Examination of Figure 4 indicates that the femur of G. senegalensis is much stiffer in bending in the anteroposterior plane (Iyy)than the mediolateral plane (Ixx) in the proximal diaphysis, and that this difference in stiffness gradually declines until stiffness in the two planes is nearly the same in the distal diaphysis. Stiffness in the anteroposterior plane is highest proximally, declines slightly a t midshaft, and declines considerably distally. In contrast, stiffness in the mediolateral plane is highest at midshaft and lowest proximally, along with a small decline in mediolateral rigidity below midshaft. Large torsional stiffness (Jeff) is also found at femoral midshaft, with low stiffnesses both proximal and distal to this. Maximum bending rigidity (Imax)within each section parallels patterns found in the an-
teroposterior plane. Largest values are found in the proximal 50% of the diaphysis, but decline somewhat between 62% and 74% of length. Lowest values of minimum stiffness (Imin) are found at both proximal and distal ends of the shaft, with the highest values of Imin found at midshaft. Large values of Imax, Imin, and Jeff at midshaft indicate that the stiffness of the bone as a whole in all planes is largest at midshaft. The cross sections of the galago femur tend to be elongated, with widely discrepant bending stiffnesses in each plane. Imax is more than 40% greater than Imin in the proximal quarter of the diaphysis and is 24% greater in the distal femur. The much larger bending ridigity in the anteroposterior than the mediolateral plane proximally is illustrated by the fact that Iyy is about 35% greater than Ixx in the most proximal section and 15% larger at midshaft. Although the cortical area available to support loads in the galago femur declines sharply from 38% down the shaft distally, this variation in area is not closely correlated to structural properties of the femoral shaft in bending or torsion (c.f. Fig. 4). Stiffness in the anteroposterior plane shows very little decline from proximal to distal and mediolateral stiffness
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Fig. 4. Variation in cross sectional moment of inertia in the mediolateral (Ixx)and anteroposterior (Iyy)planes, principal moments of inertia (Imax, Imin). and the effective polar moment of inertia (Jeff)in the femoral diaphysis of G. senegalensis. Numbers above and below symbols refer to standard errors.
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actually increases in this range. The slight decline in outer diameter and thinning of the cortex in the sagittal plane between 62% and 74% of femoral length does contribute to the decline in anteroposterior rigidity in the distal femur. The relationship between femoral rigidity and cortical width and thickness is well demonstrated by these data. A 17% increase in anteroposterior medullary cavity diameter coupled with no change in outer width accounts for a 7% decline in Iyy between 2690 and 6290 of femoral length. However, only a 4.8370decrease in outer diameter coupled with but a slight increase in inner diameter accounted for greater than 20% decline in Iyy between 62% and 74% of femoral length. Changes in outer diameter have larger effects on the bending stiffness, as characterized by the area moments of inertia (I),than equally large changes in inner diameter. What appears on first inspection to be a minor change in geometry actually has a significant mechanical effect on femoral function and underscores the fallacy behind using cortical width alone as an indicator of the mechanical adaptation of bone. The
increasingly tubular nature of the galago femur, which results in similar stiffnesses in each plane at the most distal level, is illustrated in Figure 3 as well. The maximum bending stresses within each quadrant a t each of the five sectional levels under constant moment of 100 kgf.cm are shown in Figure 5. These data indicate that the femur is configured to reduce bending stresses in all planes at femoral midshaft. Higher stresses are found both proximally and distally. Highest stresses in the mediolateral plane are found proximally, and although stresses distally are higher than at midshaft, they don’t approach the magnitude of those found proximally. The opposite pattern is found anteroposteriorly, i.e., highest stresses are found distally, with somewhat lower stresses proximally. This again indicates the adaptation of the femur to support bending loads in the anteroposterior plane proximally and the adaptation to support higher mediolateral bending loads distally than proximally. Because Ixx is smaller than Iyy, higher stresses are found mediolaterally than anteroposteriorly a t all levels,
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Fig. 5. Maximum bending stresses developed proximal to distal within each quadrant (m.1.a.p)of the femoral diaphysis under a constant moment of 100 kgfxm. Numbers above and below symbols refer to standard errors.
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with one minor deviation from this posteriorly at the most distal section. The adaptation of the femur in G. senegalensis is toward a reduction of anteroposterior bending stresses. A similar pattern of torsimal stress is found in the femoral diaphysis of G. senegalensis (Fig. 6 ) .Lowest stresses are found at midshaft with somewhat higher stresses both proximally and distally. The trend is not so pronounced mediolaterally, however. Torsional stresses along the medial aspect remain at low levels distally, while stresses along the lateral aspect compensate by marked increase just distal to midshaft. Maximum torsional stresses are found along the posterolateral aspect of the femur at all cross sectional levels. DISCUSSION
There are two fundamental differences in the mechanics of leaping and walking locomotion. First, leaping is a much more dynamic activity requiring much larger accelerations of the body center of gravity. This implies that peak forces acting on and within the body will be far
greater than those that would be required to walk at a nearly constant velocity. Second, the trunk is flexed on the thigh during leaping so that the body's center of gravity is placed forward of the ground support point. This increases the horizontal component of the ground reaction force, which must act through the body's center of gravity. This causes the ground reaction force to have a longer moment arm about the hip in leaping than it does in bipedal or quadrupedal walking. Thus, mechanical principles imply that leaping produces larger muscle and ground reaction forces, and larger moments about the hip joint, than does walking. These differences in the mechanics of leaping and walking are supported by the structural adaptations found in the femora of leapers and walkers. The cross sectional moments of inertia of the galago femoral diaphysis are large both proximally and in the sagittal plane, indicating that sagittal plane bending moments are relatively greater near the hip than near the knee. This also corresponds to behavi-
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Fig. 6. Torsionasl shear stresses developed proximal to distal within each quadrant Im.1.a.p) of the femoral diaphysis and maximum stresses (M) under a constant torque of 100 kgf.cm. Numbers above and below symbols refer to standard errors.
FEMORAL MECHANICS IN T H E LESSER BUSHBABY
oral observations that leaping in galagos is achieved with a two-legged symmetrical stance in which sagittal plane bending moments in the femur should be created by hip and knee extension (Hall-Craggs, 1965a; Jouffroy et al., 1974). In contrast, cross sectional moments of inertia in macaque and human femurs are largest in the frontal plane and increase distally (Miller and Piotrowski, 1977; Burr et al., 1981), suggesting relatively larger moments near the knee. The principal bending loads in human and macaque femurs are in the frontal plane and, in humans, result from abductor forces necessary for balancing on one leg during the swing phase of locomotion (McLeish and Charnley, 1970). When the distal joint reaction force acts at an angle to the femur it applies a bending moment to the bone causing it to deflect. Although it is clear that large anteroposterior bending moments are developed proximally in the galago femur during leaping the diaphysis of G . senegalensis is not nearly as curved anteroposteriorly as that of humans and other nonsaltatory primates. Frost (1964) has hypothesized that if a long bone bears significant radial loads (i.e., loads perpendicular to the longitudinal axis of the shaft)that create bending moments in the shaft, the shaft will remodel into a curved shape. The curvature is such that compressive loads are eccentric to the midshaft and create bending moments opposing those of the radial loads. The degree of curvature is inversely proportional to the amount of compressive stress. This would explain the anteroposterior curvature in the human femur since, during several portions of the gait cycle, the ground reaction force acts through or anterior to the knee (Elftman, 1951) bending the femur in the anteroposterior plane. This bending by perpendicular loads at the knee is opposed by compressive muscle loads acting in conjunction with the anteroposterior curvature. Hall-Craggs (1965a) showed that in galago, however, ground reaction forces pass behind the knee and across the femoral shaft during the leap. Consequently, bending loads perpendicular to the shaft should be relatively small. Also the leaping galago generates large forces in its hamstring and quadriceps muscle groups as it extends the hip and knee simultaneously from the initial flexed position. This must produce compressive forces in the femur that are relatively much greater than those in nonsaltatory primates. Because of the large compressive loads less curvature of the femoral shaft is necessary to compensate bending loads.
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High compressive loads in the galago femur would be more likely to cause buckling if the femoral diaphysis were curved. In general, bones of smaller animals are more slender than those of larger animals because of the allometric relationship of body weight and cross sectional moment of inertia. The shaft of the galago femur is, however, proportionately more robust than human and macaque femora. The ratio of periosteal diameter to length is 0.10 in galago and 0.065 in both macaques and humans. The critical buckling load (Pc)may be defined as
where E is the modulus of elasticity, Imin is the mean value at femoral midshaft, and L is femoral length. The ratio of critical buckling load to body weight in Galago is 31 times that in macaques and 55 times that in humans. (These calculations assume the elastic moduli of femoral bone to be equal in the three species and use mean data for males and females.) Thus, the femur of this saltatory primate is morphologically adapted to resist buckling when subjected to large compressive loads, while those of macaques and humans need not be as well adapted to compressive loads since compressive forces required for walking are much less. The cortical walls of the femur in Galago are thin in an absolute sense but are thick relative to body weight and femoral length. The absolutely thin cortical walls and small body weight allow speed of movement, while the allometric relationships of cross sectional geometry, femoral length, and body weight prevent buckling when the femur is subjected to large loads. These data reinforce the apparent similarity of the mechanical effects of quadrupedal and bipedal locomotion on the femur and dissimilarity with femoral mechanics in habitually saltatory primates. The mechanics of leaping in arboreal and terrestrial species differ (Oxnard, 1979b),and it is therefore not surprising that femoral mechanics in G. senegalensis are markedly different than femoral mechanics in macaques (Burr et al., 1981). Although some of these differences could be taxonomic, the very specialized mechanical adaptation of the bushbaby femur to its particular type of locomotion suggests that these differences are basic to its saltatory mode of progression. These data satisfy Oxnard’s (1979a) third method of separating spurious morphology-behavior associations from true functional complexes -the nature of
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the morphological differences is biomechanically related to the function in question, i.e., leaping. Distribution of cortical area in both macaques and bushbabies are superficially similar in that area is high proximally and declines distally. However, the percentage decline is more than twice as large in Galago as in Macaca. While this distal decline in cortical area was offset in Macaca by increases in bending stiffness distally, this is clearly not the case in Galago, a t least in the anteroposterior plane. While stiffness in the macaque femur was greatest distally in most planes and was generally lower at midshaft, the stiffness of the galago femur was generally high a t midshaft, and decreased toward the distal end. Moreover, stiffness is high in galagos in the sagittal plane while stiffnesses were higher mediolaterally in macaques. These patterns of rigidity are reflected in stress patterns in each group: stresses in the anterior and posterior quadrants were highest in Macaca and lowest in Galago. Also the midshaft decline in stress found in Galago is not found in the femur of Macaca. This analysis indicates that there is a very specific functional complex of traits that define the femoral mechanics of leaping primates and that this complex of traits differs from functional complexes found in animals less specialized for leaping. As Fleagle (1979) points out, paleoanthropological and paleoprimatological reconstruction is limited by our ability to predict behavior from anatomy. This analysis demonstrates that the biomechanical techniques used here can be useful for discriminating anatomical specializations to different behaviors based on a single aspect of morphology. These techniques can be expected to be more sensitive to subtle behavioral differences when applied to more than one morphological structure and when used in conjunction with other biomechanical techniques. Fleagle (1979) suggested that the articular surfaces of the long bones provide more information about the mechanics of movement of an animal than do other parts of the bone. While this may be true, it is also true that other parts of the skeletal anatomy may hold information which can only now be extracted using techniques which have not been applied to such analyses in the past. This analysis of femoral mechanics in a leaping primate indicates that a great deal of information about the locomotion of a given animal can be extracted from the femoral diaphysis alone. I t further extends the analyses carried out by Hall-Craggs (1965a.b)in demonstrating
the adaptation of one aspect of the skeletal system of G. senegalensis to a very specialized form of behavior. Further comparative data using these techniques on animals less dissimilar than Macaca and Galago are needed to demonstrate the sensitivity of the techniques in functional anatomical investigations, and to further improve the difficult task of interpreting the complexities of morphologyibehavior interactions. ACKNOWLEDGMENTS
This research was supported by a University of Kansas Medical Center Committee on Research grant and by the Department of Anatomy. I am greatly indebted to Dr. Duane Haines, Department of Anatomy, West Virginia University, for providing the galagos used in this study. LITERATURE CITED Amtmann, E. (1971) Mechanical stress, functional adaptation and the variation structure of the human femur diaphysis. Ergeb. Anat. Entwickl. 44. Springer-Verlag, Berlin. Burr, D.B.. G. Piotrowski, and G. Miller (1981) Structural strength of the macaque femur. Am. J. Phys. Anthropol.. 54:305-3 19. Calow. L.J. and R. McN. Alexander (1973) A mechanical analysis of a hind leg of a frog (Rana temporaria). J. Zool. Lond.. 171:293-321. Crandall. S.H.. N.C. Dahl. and T.J. Lardner (1972) An Introduction t o the Mechanics of Solids, ed. 2. McGraw-Hill, New York. den Hartog. J.P. (1952) Advanced Strength of Materials. McGraw-Hill, New York. Elftman, H. (1951) The basic pattern of human locomotion. Ann. N.Y. Acad. Sci.. 51:1207-1212. Fleagle, J.P. (1977a) Locomotor behavior and muscular anatomy of sympatric Malaysian leaf-monkeys (Presbytis obscura and Presbytis melalophos). Am. J. Phys. Anthropol., 46297-308. Fleagle, J.P. (1977b) Locomotor behavior and skeletal anatomy of sympatric Malaysian leaf-monkeys (Presbytis obscura and Presbytis meldophos). Yrbk. Phys. Anthropol., 20:440-453. Fleagle, J.P. (1979) Primate positional behavior and anatomy: Naturalistic and experimental approaches. In: Environment Behavior, and Morphology: Dynamic Interactions in Primates. M.E. Morbeck. H. F’reuschoft, and N. Gomberg. eds. Gustav Fischer. New York. Fleagle, J.P. and R.A. Mittermeier (1980) Locomotor behavior, body size, and comparative ecology of seven Surinam monkeys. Am. J. Phys. Anthropol., 52301-314. Frost, H.M. (1964) The Laws of Bone Structure. C.C. Thomas, Springfield. 111. Gray. J. (1953) How Animals Move. Cambridge University Press, Cambridge. Hall-Craggs, E.C.B. (1964)Thejump of the bushbaby, a photographic analysis. Med. Biol.. 14:170-174. Hall-Craggs, E.C.B. (1965a)An analysis of the jump of the Lesser Galago (Galago senegalensis). J. 2001..14720-29. Hall-Craggs. E.C.B. (1965b) An osteometric study of the hind limb of the Galagidae. J. Anat. Lond.. 99:119-126.
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