Development of an anatomically based whole-body musculoskeletal model of the Japanese macaque (Macaca fuscata).код для вставкиСкачать
AMERICAN JOURNAL OF PHYSICAL ANTHROPOLOGY 139:323–338 (2009) Development of an Anatomically Based Whole-Body Musculoskeletal Model of the Japanese Macaque (Macaca fuscata) Naomichi Ogihara,1* Haruyuki Makishima,1 Shinya Aoi,2 Yasuhiro Sugimoto,2 Kazuo Tsuchiya,2 and Masato Nakatsukasa1 1 Laboratory of Physical Anthropology, Department of Zoology, Graduate School of Science, Kyoto University, Kyoto 606-8502, Japan 2 Department of Aeronautics and Astronautics, Graduate School of Engineering, Kyoto University, Kyoto 606-8501, Japan KEY WORDS locomotion; biomechanics; moment arm; endpoint force; motion analysis; registration ABSTRACT We constructed a three-dimensional whole-body musculoskeletal model of the Japanese macaque (Macaca fuscata) based on computed tomography and dissection of a cadaver. The skeleton was modeled as a chain of 20 bone segments connected by joints. Joint centers and rotational axes were estimated by joint morphology based on joint surface approximation using a quadric function. The path of each muscle was defined by a line segment connecting origin to insertion through an intermediary point if necessary. Mass and fascicle length of each were systematically recorded to calculate physiological cross-sectional area to estimate the capacity of each muscle to generate force. Using this anatomically accurate model, muscle moment arms and force vectors generated by individual limb muscles at the foot and hand were calculated to computationally predict Bipedal locomotion in Japanese macaques (Macaca fuscata) trained as bipedal performing monkeys has been thoroughly investigated in the field of physical anthropology, as this shift toward bipedalism for an inherently quadrupedal primate could be regarded to some extent as a modern analog for the evolution of human bipedal locomotion, thus offering an interesting model for understanding the emergence of human bipedalism (Hayama et al., 1992; Nakatsukasa, 2004; Hirasaki et al., 2006). For this reason, locomotor kinematics (Hirasaki et al., 2004; Ogihara et al., 2005b), kinetics (ground reaction force profile) (Ogihara et al., 2007), and energetics (Nakatsukasa et al., 2004, 2006) have recently been studied, and some unique characteristics of bipedal walking in Japanese macaques have been elucidated. Bipedal locomotion of Japanese macaques has also been analyzed by a group of locomotor neurophysiologists to clarify the physiological mechanisms of locomotor control in a higher primate (Mori et al., 2001, 2004; Nakajima et al., 2004; Mori et al., 2006). Although physiological studies on mammalian locomotion have concentrated on cats (e.g., Whelan, 1996), studies of monkey locomotion have gained attention recently (e.g., Courtine et al., 2005a,b; Xiang et al., 2007) in the hope that inferences gained by analyses of a phylogenetically and physiologically close primate might be more extensible to understand human locomotor mechanisms and associated clinical implications. Bipedal walking of Japanese C 2008 V WILEY-LISS, INC. muscle functions. Furthermore, three-dimensional whole-body musculoskeletal kinematics of the Japanese macaque was reconstructed from ordinary video sequences based on this model and a model-based matching technique. The results showed that the proposed model can successfully reconstruct and visualize anatomically reasonable, natural musculoskeletal motion of the Japanese macaque during quadrupedal/bipedal locomotion, demonstrating the validity and efficacy of the constructed musculoskeletal model. The present biologically relevant model may serve as a useful tool for comprehensive understanding of the design principles of the musculoskeletal system and the control mechanisms for locomotion in the Japanese macaque and other primates. Am J Phys Anthropol 139:323–338, 2009. V 2008 C Wiley-Liss, Inc. macaques has therefore been used as an important paradigm for understanding the evolution and neuro-control mechanisms of human bipedal walking. However, locomotion is a very complex mechanical phenomenon generated by coordinated dynamic interactions among the nervous system, musculoskeletal system, and environment. Activation of a large number of muscles must be controlled in a coordinated manner to generate appropriate external forces onto the ground at the feet to transport the body while maintaining stability. When trying to understand how the design of the musculoskeletal system biomechanically facilitates (or constrains) locomotor Additional Supporting Information may be found in the online version of this article. Grant sponsor: Japanese Ministry of Education, Culture, Sports, Science and Technology. *Correspondence to: Naomichi Ogihara, Laboratory of Physical Anthropology, Graduate School of Science, Kyoto University, Kitashirakawa-oiwakecho, Sakyo-ku, Kyoto, Kyoto 606-8502, Japan. E-mail: firstname.lastname@example.org Received 24 June 2008; accepted 9 October 2008 DOI 10.1002/ajpa.20986 Published online 29 December 2008 in Wiley InterScience (www.interscience.wiley.com). 324 N. OGIHARA ET AL. function and clarifying how the locomotor nervous system controls muscle activations in a coordinated manner to generate robust and adaptable locomotion, biomechanical analyses of locomotion based on an anatomically plausible mathematical model are indispensable. We describe herein the development of an anatomically based, whole-body musculoskeletal model of the Japanese macaque, with the aim of quantitative biomechanical analyses of locomotion. Using the model, moment arms of muscles and endpoint force vectors exerted due to the activation of muscles are calculated to predict muscle functions. Furthermore, the model is used to reconstruct three-dimensional (3D) whole-body musculoskeletal motion of a Japanese macaque from ordinary video camera sequences based on a model-matching method to demonstrate the validity and efficacy of the constructed musculoskeletal model. Biomechanical parameters such as inertial parameters of limb segments and muscular parameters have been reported for various species of macaque, including the rhesus macaque (M. mulatta) (Vilensky, 1979; Doyle et al., 1980; Cheng and Scott, 2000), crab-eating macaque (M. fascicularis) (Roy et al., 1984; Cheng and Scott, 2000), and Japanese macaque (Ishida, 1972; Hamada, 1983). For the Japanese macaque, a two-dimensional musculoskeletal model has also been constructed for estimating the internal mechanics of locomotion based on inverse dynamic calculations (Yamazaki et al., 1979; Hirasaki et al., 2000). However, no attempts have been made to construct an anatomically refined, 3D musculoskeletal model of a macaque for better understanding of whole-body mechanics during locomotion; although numerous 3D musculoskeletal models have been developed for humans (Delp et al., 1990; Andersen and Pandy, 2001; Holzbaur et al., 2005) and other animals such as cats (Burkholder and Nichols, 2004) and dogs (Shahar and Milgram, 2005). MATERIALS AND METHODS Specimens We used two fresh cadavers of adult Japanese macaques: one for whole-body computed tomography (CT) and the other for dissection. The male cadaver for whole-body CT was obtained from Suo Monkey Performance Association (Kumamoto, Japan). Body mass was about 10 kg at the time of death. This individual used to be a performing monkey, but had lived in retirement for more than 10 years. We gained a very rare opportunity to put the intact cadaver into a CT scanner before autopsy, but unfortunately did not have the opportunity to dissect this specimen. Hence, for measuring muscle dimensions, a female cadaver was obtained from the Primate Research Institute, Kyoto University. This monkey was euthanized for other research, but the postcranial musculoskeletal system remained intact and was stored frozen until our dissection. Body mass was 6.8 kg at the time of death. Representation of skeletal kinematics For a realistic representation of body motion, a total of 1,935 consecutive cross-sectional images of the adult male monkey were acquired using a TSX-002A/4I scanner (Toshiba Medical, Japan) in the Laboratory of Physical Anthropology, Kyoto University. Tube voltage and current were set to 120 kV and 100 mA, respectively. Pixel size of each image was 0.75 mm and slice interval American Journal of Physical Anthropology was 0.5 mm. Three-dimensional surface models of the entire body surface and skeleton were then constructed (see Fig. 1). Because of the insufficient spatial resolution of the whole-body scan (partial volume effect), adjacent bones were difficult to separate. Additional CT scans of the right elbow, hand, knee, and foot regions were thus taken at higher resolution (0.2 mm), and detailed joint surface models were created and registered to the wholebody skeletal model for clear separation of adjacent bones. The skeleton was divided into following bone segments: head (with cervical vertebrae); thorax; lumbus (lumbar vertebrae); pelvis; scapula; humerus; ulna; radius; hand (carpals and metacarpals); femur; tibia (with fibula); and foot (tarsals and metatarsals). For each bone segment, a bone-fixed coordinate system was defined by calculating principal axes. The xyz-axes generally corresponded to the long axes of the bone. The origin of the coordinate system was set to the centroid of the bone. This bone coordinate system was used for representing inertial parameters of limb segments and origin, insertion and intermediary points of muscles. Only the right limb bones were extracted, with corresponding left bones created as mirror images. In this study, the whole-body musculoskeletal system was modeled as a chain of rigid-body bone segments connected by revolute joints (Fig. 2A). Three torso joints connecting head, thoracic, lumbar, and pelvic segments (neck, lumbothoracic, and lumbopelvic joints, respectively) were modeled as triaxial (gimbal) joints. Joint centers were assumed to be at the center of the vertebral body. The hip joint was defined by approximating surfaces of the acetabulum and femoral head as concentric spheres. This joint was modeled by a gimbal joint. Each of the other limb joints was represented by a combination of hinges, joint centers, and rotational axes defined based on corresponding joint morphology. To achieve this, joint surfaces were approximated using a paraboloid surface by a least-squares method (see Fig. 3). The quadric function approximating a joint surface can be obtained by solving the following minimization problem for c1, c2, a, yy, yx, and yz: 2 xn 3 6 7 T 4 yn 5 ¼ Rðhy ; hx ; hz ; Þ ðvn aÞ zn X ðc1 x2n þ c2 y2n þ zn Þ2 ! min ð1Þ n where vn is the position vector of the nth point on the joint surface with respect to the bone coordinate system, c1 and c2 are curvatures at the apex of the fitted quadric surface, a is the position vector of the apex, yy, yx, and yz are the Eulerian angles defining the orientation of the fitted quadric surface with respect to the bone coordinate system, and R(yy, yx, yz) is the rotational matrix describing the orientation of the quadric surface, elements of which are represented by functions of yy, yx, yz. Superscript T denotes transpose matrix. Joint centers were then estimated from the position of the apex of the fitted paraboloids and the two principal radii of curvature at the apex. Rotational axes were determined from the principal directions in which the principal curvatures occur (i.e., rotational matrix, R). An advantage of using a paraboloid function is that the same equation can approximate both convex/concave and saddle-shaped surfaces by elliptical or hyperbolic paraboloids, respectively. MUSCULOSKELETAL MODEL OF JAPANESE MACAQUE Fig. 1. Three-dimensional representation of the entire body surface and skeleton of the Japanese macaque. Using the aforementioned joint surface approximation, the knee joint was modeled as a 1-degree-of-freedom (DOF) hinge joint. The proximal surface (distal articular surface of the femur) was approximated by the paraboloid, and the joint center and axis of rotation corresponding to flexion/extension were determined. These were also transformed to the tibia coordinate system when the femur and tibia were in the CT-scanned posture to define joint kinematic constraints. The talocrural (ankle) joint was modeled as a biaxial (universal) joint. Both proximal and distal articular surfaces were fitted by hyperbolic paraboloids to define the joint center and rotational axes (see Fig. 3). As the signs of c1 and c2 [Eq. (1)] are not equal, the two rotational axes do not intersect. Here, we introduce a virtual link to fill this gap between two joint locations (see Fig. 3 for more details). Fig. 2. Developed three-dimensional whole-body musculoskeletal model of the Japanese macaque. (A) Skeletal model. (B) Musculoskeletal model. Sagittal and frontal views are illustrated on the left and right sides, respectively. In addition to the 77 muscles listed in Table 2, sternomastoideus, longus capitis, splenius, and iliocostalis, longissimus are drawn. 325 Fig. 3. Joint surface approximation using a quadric function. The proximal and distal articular surfaces of the talocrural joint are approximated to calculate joint centers (black circles) and rotational axes (labeled a–d). Axis a is conformed to axis c to impose joint kinematic constraints. Dotted line segment represents the virtual link. Axis b is not used for modeling the joint. Scapular motion relative to the thorax has three DOFs: two translational along the surface of the thoracic cage and one rotational with respect to the axis normal to the surface. Herein, we constrained such scapular motion using a triaxial gimbal joint. To achieve this, the cranial portion of the thoracic wall corresponding to movement of the scapula was approximated by an elliptical paraboloid, and the rotational center was determined based on the apex and shorter radius of curvature (longer radius was too long and was not used). The three rotational axes were determined from the orientation of the quadric surface. Joint location and axes of rotation with respect to the scapula were determined as in knee modeling. The glenohumeral, humeroulnar (elbow), and radiocarpal (wrist) joints were modeled as triaxial, 1-DOF hinge, and biaxial joints, respectively. For these joints, both proximal and distal articular surfaces were fitted by el- Fig. 4. Skeletal posture of the model when all angles are zero. Sagittal and frontal views are illustrated on the left and right sides, respectively. American Journal of Physical Anthropology 326 N. OGIHARA ET AL. TABLE 1. Inertial parameters for body segments of the Japanese macaque model Position of COM (mm) Six elements of moment of inertia tensor (g mm2) Segment Mass (g) x y z Head Thorax Lumbar Pelvis Scapula Humerus Ulna Radius Carpus Femur Tibia Tarsus 814 2,806 1,121 1,776 253 320 100 101 60 557 268 101 1.7 5.2 27.9 22.7 0.0 28.2 5.8 25.2 22.4 21.6 26.7 25.7 0 0 0 0 0.9 2.2 3.2 1.9 23.2 2.4 1.5 20.6 24.9 12.6 25.8 3.3 28.2 9.4 28.6 1.9 219.7 16.1 1.6 212.6 Iyx Ixx 1.45 1.32 2.10 7.02 1.84 5.20 1.58 1.91 3.88 1.37 6.85 1.33 E E E E E E E E E E E E 106 107 106 106 105 105 105 105 104 106 105 105 0 0 0 0 22.03 917 21.46 2.35 2750 1.18 3.04 1.36 Iyy E 104 E 103 E 103 E 104 E 103 E 103 1.38 1.44 1.74 6.94 3.76 5.96 1.62 1.93 3.37 1.61 7.01 1.21 E E E E E E E E E E E E Izx 106 107 106 106 105 105 105 105 104 106 105 105 21.84 2.07 8.80 26.90 24.43 4.65 1.79 1.13 7.37 27.66 4.18 21.24 E E E E E E E E E E E E Izy 105 106 104 105 104 104 103 104 103 104 104 103 0 0 0 0 3.00 2.22 2.16 21.70 21.05 5.08 23.92 21.93 E E E E E E E E Izz 104 104 103 104 103 104 104 103 9.46 6.71 2.48 2.90 2.54 1.49 1.40 1.51 1.42 3.96 8.43 2.19 E E E E E E E E E E E E 105 106 106 106 105 105 104 104 104 105 104 104 COM, center of mass. liptical or hyperbolic paraboloids, and joint centers and rotational axes were determined and connected to each other as in ankle modeling. Virtual links were introduced at the glenohumeral and radiocarpal joints, as c1 and c2 are not equal. The radioulnar joint was modeled by a 1-DOF hinge joint, rotational axes of which were defined by a line connecting the center of the humeral capitulum as defined by approximation with a sphere and the point defined by quadric approximation of the ulnar notch and head. The joint center was defined to be the midpoint of the two locations. Mechanical interactions between the humerus and radius was not considered unlike the study by Pennestri et al. (2007) to avoid modeling of a closed-loop system as additional kinematic constraints of the closed-loop make kinematics and dynamics of the system particularly complex. Here, we summarize the joint type assumed for each of the joints. Joints connecting trunk segments (head, thorax, lumbar vertebrae, and pelvis) were represented as 3-DOF joints. Translational motion of the scapula along the rib cage was modeled using three revolute joints. Shoulder (glenohumeral), elbow, radioulnar, and wrist joints were modeled as 3-, 1-, 1- and 2-DOF joints, respectively. Hip, knee, and ankle joints were represented as 3-, 1- and 2-DOF joints, respectively. The total number of DOFs for the skeletal system was 47, and the total number of links in the model was 26 with 20 segments physically corresponding to the bones, and six virtual links at the glenohumeral, radiocarpal, and talocrual joints. Figure 4 shows the posture of the model when all joint angles are zero. Joint angles were defined as positive for extension, left lateral bending, and left axial rotation of the joints connecting the trunk segments; caudal rotation, caudal translation, and ventral translation of the scapulothoracic joint; retraction, adduction, and medial rotation of the glenohumeral joint; extension of the elbow; pronation of the forearm; palmar and radial flexion of the wrist; extension, adduction, and medial rotation of the hip; flexion of the knee; and plantar flexion and inversion of the ankle. Calculation of inertial parameters To calculate inertial properties necessary for biomechanical studies (i.e., mass, position of the center of mass of each segment, and inertial tensor about the center of mass), the body surface was divided into the segments by planes passing through the joint centers. One American Journal of Physical Anthropology exception was the scapular segment, which was separated from the thoracic volume by a rounded surface so as to include the muscles of the shoulder girdle. Each segmented surface was created and transformed to a free-form surface using 3D data-processing software (RapidForm2004; Inus Technology, Korea). The inertial properties of each segment were then numerically calculated using 3D computer-aided design software (Autodesk Inventor 9; Autodesk, USA), assuming homogeneous segment composition and a density of 1.0 g/cm3. Inertial tensors of trunk segments were symmetrized with respect to the sagittal plane, so Iyz 5 Izy 5 0 for trunk segments (Table 1). Representation of muscle architecture The female cadaver was dissected, and a total of 77 muscles (Table 1) were carefully exposed, removed, and weighed using a digital balance. Muscle fiber length (as fascicle length) was measured along the muscle fiber orientation using a digital caliper at three sites, and mean value was calculated. Physiological cross-sectional area (PCSA) of muscle was calculated as muscle mass/muscle density/muscle fiber length as described by Ogihara et al. (2005a). The capacity of the muscle to generate force was assumed to be proportional to PCSA and calculated by multiplying PCSA by the specific muscle tension (23 N/cm2) reported by Spector et al. (1980). Each muscle was basically modeled as a string connecting the origin and insertion points. In cases where the path of a muscle could not be described by a single line segment, an intermediary point was defined. These points were fixed to the corresponding bone coordinate systems. Calculation of moment arm Moment arm is the mechanical advantage of a muscle about the axis of joint rotation. Quantification of the moment arm is important for understanding how activation of an individual muscle is converted into moments generated around the joint rotational axes. Moment arm of the mth muscle about the jth revolute joint, dm,j, can be calculated using the following equation: dm;j ¼ vm ðaj 3 rm;j Þ ð2Þ where vm is the unit vector defining the direction of muscular force, aj is the unit vector defining the direction of the joint axis, and rm,j is the vector connecting MUSCULOSKELETAL MODEL OF JAPANESE MACAQUE the point of attachment of the muscle and the joint center. Moment arms calculated from the relationship between the change in muscle length versus joint angle (An et al., 1983; Hughes et al., 1998) were confirmed to be identical to those calculated from Eq. (2). Calculation of endpoint force Terrestrial locomotion is generated by exerting ground reaction forces at the hand/foot segments by the action of muscles. Estimation of the endpoint force vector exerted due to the activation of an individual limb muscle is therefore critical for assessing the functional roles of muscles in locomotion. When gravity and joint friction are ignored, the static equilibrium balance between endpoint force and muscular force can be written as follows: J Ti Fi ¼ GTi f i Fi ¼ ðJ Ti Þ1 GTi f brated space was 2.5 mm. The change in position of each coordinate over time was low-pass filtered at 12 Hz. To match the described musculoskeletal model to the temporal history of digitized marker coordinates, the model was first scaled to the size of the monkey in the video based on segment lengths. The scaling factor is given by averaging the eight scaling factors calculated for the upper arm, forearm, thigh, and shank segments of both sides. The model was then registered to the time history of marker coordinates by adjusting a total of 47 DOFs of vectors x and q such as to minimize the following: 1) the sum of distances between each motion-captured marker and the corresponding marker on the model, and 2) deviations of joint angles from the anatomically natural position, while 3) satisfying kinematic constraints due to the clavicle. For this, we solved the following minimization problem frame-by-frame: ð3Þ X where Fi is the 6 3 1 vector endpoint force and moment of ith endpoint on the carpus or tarsus segments, Ji is the Jacobian matrix relating joint displacement to the ith endpoint displacement, Gi is the moment arm matrix, and f is the vector of individual muscular force (muscle activation pattern). Superscript T denotes transpose matrix. The endpoint force vector Fi produced by muscular force vector f can be calculated by ð4Þ When endpoint force of a limb muscle is calculated, torso joints connecting the head, thoracic, lumbar and pelvic segments, and scapulothoracic joint are all assumed to be immobile. The rotational DOF of the glenohumeral joint is also fixed for the estimation of forelimb endpoint forces. Consequently, both fore- and hindlimb models have six DOFs, and Fi can be uniquely determined by solving the inverse matrix of JiT, provided this matrix is nonsingular (Asada and Slotine, 1986). Estimation of 3D musculoskeletal motion during locomotion If the musculoskeletal model described could be matched to ordinary video sequences, all body skeletal motion could be reconstructed as in video fluoroscopy. For this, in vivo whole-body motion data were collected from a male Japanese macaque (9 years old; body weight 10 kg) walking quadrupedally and bipedally on a treadmill at 3 km/h using four digital video cameras. The macaque had been trained to walk bipedally for 8 years. We used a sequence with quadrupedal, bipedal, and transient phases of locomotion to demonstrate the generalizability and robustness of the model matching method. A total of 16 reflective markers (8 on each side) were placed at the following positions: 1) head of the 5th metatarsal; 2) lateral malleolus of the fibula; 3) lateral epicondyle of the femur; 4) greater trochanter; 5) acromion; 6) lateral epicondyle of the humerus; 7) styloid process of the ulna; and 8) head of the 5th metacarpal. These markers were manually digitized frame-by-frame, and the coordinates of markers were calculated using 3D motion analysis software (Frame-DIAS II; DKH, Japan). Standard error of the mean accompanying each of the eight measured positions equally distributed in the cali- 327 i h 2 ji pi M k ðx; qÞk ct ri þcðq q0 Þ2 þd ðdR clÞ2 i þ ðdL clÞ2 ! min ð5Þ where pi is the measured position of the ith skin-fixed marker, kri is the position of the marker on the model fixed to the kth bone coordinate system, c is the scaling factor, Mk is the homogeneous transformation matrix of the kth bone coordinate system, elements of which were represented by functions of the vector of the position and orientation of head segment x and the vector of the 41 joint angles q, q0 is the vector of neutral joint angles (midpoints of the ranges of the joint rotations), d is the distance between points on the scapula and sternum where they articulate with the clavicle, l is the actual length of the clavicle (l 5 66.5 mm), and ji, c, and d are the weighting coefficients. Subscripts R and L denote right and left, respectively. The quasi-Newtonian method was used for this optimization. The range of joint rotation was estimated by rotating the corresponding joint of a fresh cadaver and approximated by a protractor. No markers were placed on the head segment, and therefore triaxial joint angles between the head and thorax were fixed in the present registration. Coefficient ji was determined as 3 for the markers on the hand and foot segments and 1 for the other proximal markers, and coefficients c and d were determined as 0.001 and 10, respectively, by referring to the order of magnitude of each of three terms. To evaluate the effects of coefficients on the resultant skeletal configuration, different sets of values were substituted, and changes in matching results were observed. RESULTS The constructed whole-body musculoskeletal model is presented in Figure 2B. For qualitative evaluation of the positions and orientations of joint axes and lines of muscle action, rotational motions of selected limb joints are displayed in Figure 5. The results suggest that this model successfully emulated actual joint articulation. The calculated kinematic and inertial parameters of the body segments and measured muscle parameters are listed in Tables 1 and 2, respectively. Comparisons of calculated inertial parameters of the upper arm, forearm, and hand segments with those estimated for M. mulatta American Journal of Physical Anthropology 328 N. OGIHARA ET AL. Fig. 5. Articular movements of selected limb joints. (A) Rotation of the scapula. (B) Rotation of the humerus with respect to the scapula. (C) Extension of the elbow. (D) Pronation of the forearm. (E) Palmar flexion of the wrist. (F) Extension of the hip. (G) Flexion of the knee. (H) Plantar flexion of the ankle. Fig. 7. Comparisons of moment arm curves for shoulder and elbow muscles using polynomial regression equations of moment arm to joint angle by Graham and Scott (2003). Definitions of joint angles match those given in Graham and Scott (2003). Joint angles are zero when the shoulder is abducted at 908 in the coronal plane and the elbow is fully extended. Joint angles were defined as positive for flexion. Flexion of the shoulder joint in Graham and Scott (2003) corresponds to adduction in the present model. The image shows the skeletal configuration of the model with the shoulder at 08 and the elbow at 908. American Journal of Physical Anthropology MUSCULOSKELETAL MODEL OF JAPANESE MACAQUE 329 Fig. 6. Estimated changes in moment arms for some selected muscles with respect to joint angles. Moment arm curves are calculated for each joint degree of freedom while all other joint degrees of freedom are fixed as in Figure 2. of the same body weight (10 kg) using linear regression equations (Cheng and Scott, 2000) indicated that our calculated moments of inertia appear generally consistent with estimated values (segment mass 5 367 g, 242 g, and 63 g, respectively; moment of inertia 5 4.00E 1 5 g mm2, 3.52E 1 5 g mm2, and 4.17E 1 4 g mm2, respectively). Table 3 shows comparisons of the present measurement with previously published reports for M. fuscata (Ishida, 1972; Hamada, 1983) and M. mulatta (Cheng and Scott, 2000) with respect to muscle fraction. The reported data are from dissections of both male and female individuals. Muscles were divided into those of the fore- and hind limb, and muscle fractions were calculated separately. American Journal of Physical Anthropology 330 N. OGIHARA ET AL. TABLE 2. Muscle parameters for a 6.8-kg female Japanese macaque 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 Rectus abdominis Obliquus abdominis externus Obliquus abdominis internus Pectoralis major capsulalis Pectoralis major sternalis Pectoralis minor Pectoralis abdominalis Trapezius cranial Trapezius caudal Latissimus dorsi Rhomboideus cervicis Rhomboideus dorsi Serratus anterior cervical Serratus anterior thoracic Deltoideus cleidoDeltoideus acromioDeltoideus spinoTeres minor Teres major Supraspinatus Infraspinatus Subscapularis Biceps brachii brevis Biceps brachii longus Brachialis Triceps brachii longum Triceps brachii laterale Triceps brachii mediale Pronator teres Flexor carpi radialis Palmaris longus Flexor carpi ulnaris Flexor digitorum sublimes Flexor digitorum profundus Brachioradialis Extensor carpi radialis longus Extensor carpi radialisbrevis Extensor digitorum communis Extensor carpi ulnaris Supinator Psoas major Iliacus Psoas minor Gluteus maximus Tensor fasciae latae Gluteus medius Gluteus minimus Piriformis Obturator internus Quadratus femoris Biceps femoris (femoral part) Biceps femoris (crural part) Semitendinosus Semimembranosus proprius Semimembranosus accessorius Gracilis Adductor longus Pectineus Adductor brevis Adductor magnus (mediale 1 laterale) Obturator externus Sartorius Rectus femoris Vastus lateralis Vastus medialis Vastus intermedius Gastrocnemius medial Gastrocnemius lateral Soleus Plantaris American Journal of Physical Anthropology Abbreviation Mass (g) FL (mm) PCSA (cm2) RA OAE OAI PMAcap PMAstern PMI PA TRPcra TRPcau LAT RHOcerv RHOdorsi SEAcer SEAtho DELcleido DELacro DELspino TEmi TEma SUPR INFS SUBS BBb BBl BRC Tblong Tblat Tbmed PT FCR PALL FCU FDS FDPu BRR ECRl ECRb EDC ECU SUPI PSOmaj ILI PSOmin GLUmax TFL GLUmed GLUmin PIR OBTin QF BIFb BIFl STE SMEpro SMEacc GRA ADL PEC ADB ADMmed OBTex SAR REF VASlat VASmed VASint GCm GCl SOL PLT 32.0 27.5 12.0 10.0 19.9 7.1 5.3 10.1 8.2 33.3 4.4 4.4 5.1 18.8 6.2 9.1 4.3 1.7 11.6 10.1 14.7 21.6 7.6 15.4 10.2 23.3 20.5 12.8 4.0 4.1 2.2 10.0 6.4 19.1 9.7 3.7 5.4 3.4 2.8 2.5 18.4 12.5 4.1 21.6 6.3 54.8 6.5 6.0 8.1 6.5 24.7 49.1 20.1 24.8 23.8 21.7 4.0 1.9 4.4 56.4 7.5 10.4 19.9 56.6 15.3 13.1 9.7 9.7 11.9 3.8 33 70 34 80 80 58 107 49 44 150 50 50 40 55 54 25 41 14 51 22 25 15 57 50 34 28 42 47 18 24 20 24 31 29 105 59 26 24 22 10 46 52 26 54 36 47 26 22 21 36 84 115 151 105 164 155 46 33 37 102 24 197 28 35 35 28 27 27 14 16 9.3 3.7 3.4 1.2 2.4 1.2 0.5 2.0 1.8 2.1 0.8 0.8 1.2 3.2 1.1 3.5 1.0 1.2 2.1 4.3 5.7 14.1 1.3 2.9 2.9 8.0 4.7 2.6 2.1 1.6 1.1 4.0 2.0 6.2 0.9 0.6 2.0 1.3 1.2 2.5 3.8 2.3 1.5 3.8 1.7 11.2 2.4 2.6 3.7 1.7 2.8 4.1 1.3 2.2 1.4 1.3 0.8 0.5 1.1 5.3 3.0 0.5 6.8 15.3 4.1 4.4 3.4 3.4 7.8 2.2 (continued) TABLE 2. (Continued) Abbreviation 71 72 73 74 75 76 77 Flexor hallucis longus Flexor digitorum longus Tibialis posterior Tibialis anterior Extensor digitorum longus Peloneus longus Peloneus brevis FHL FDL TP TA EDL PELL PELB Mass (g) FL (mm) PCSA (cm2) 8.3 4.5 3.1 9.7 3.7 6.9 4.1 28 26 11 38 28 24 22 2.9 1.7 2.6 2.4 1.3 2.8 1.8 FL, muscle fiber length; PCSA, physiological cross-sectional area of muscle. TABLE 3. Comparisons between the present model and previously published reports with respect to muscle fraction Mass fraction of forelimb (%) Latissimus dorsi Deltoideus cleido Deltoideus acromio Deltoideus spino Teres minor Teres major Supraspinatus Infraspinatus Subscapularis Biceps brachii brevis Biceps brachii longus Brachialis Triceps brachii longum Triceps brachii laterale Triceps brachii mediale Brachioradialis Extensor carpi radialis longus Extensor carpi radialis brevis Total This study Cheng and Scott (2000) Hamada (1983) 15.0 2.8 4.1 1.9 0.8 5.2 4.6 6.7 9.8 3.4 7.0 4.6 10.5 9.3 5.8 4.4 1.7 2.4 100.0 14.6 2.9 3.8 2.6 0.7 5.8 5.0 5.6 8.1 4.5 6.9 4.3 10.7 9.3 5.4 5.3 2.3 2.3 100.0 12.9 9.3 0.8 5.3 5.3 6.8 10.5 9.8 4.0 26.7 4.6 3.9 100.0 Mass fraction of hindlimb (%) This study Iliopsoas Gluteus maximus Tensor fasciae latae Gluteus medius Gluteus minimus Piriformis Obturator internus Quadratus femoris Biceps femoris (femoral part) Bı́ceps femoris (crural part) Semitendinosus Semimembranosus proprius Semimembranosus accessorius Gracilis Adductor longus Pectineus Adductor brevis Adductor magnus (mediale 1 laterale) Obturator externus Sartorius Rectus femoris Vastus lateralis Vastus medialis Vastus intermedius Gastrocnemius medial Gastrocnemius lateral Soleus Plantaris Flexor hallucis longus Flexor digitorum longus Tibialis posterior Tibialis anterior Extensor digitorum longus Peloneus longus Peloneus brevis Total 6.1 3.8 1.1 9.6 1.1 1.0 1.4 1.1 4.3 8.6 3.5 4.3 4.1 3.8 0.7 0.3 0.8 9.8 1.3 1.8 3.5 9.9 2.7 2.3 1.7 1.7 2.1 0.7 1.4 0.8 0.5 1.7 0.6 1.2 0.7 100.0 Ishida (1972) Hamada (1983) 7.0 3.3 1.5 9.2 1.3 0.9 1.6 1.1 6.8 3.0 1.2 8.7 1.8 1.2 1.8 1.4 10.9 10.0 3.4 3.0 – 4.0 0.8 0.5 0.9 13.0 1.6 1.5 3.9 9.0 2.8 2.1 3.5 2.7 3.4 3.8 1.7 0.6 1.0 8.0 2.1 1.5 3.9 9.4 2.9 2.6 4.3 3.8 1.9 0.9 2.0 1.1 0.7 3.0 0.8 1.3 0.7 100.0 2.3 0.9 2.0 1.4 0.8 2.6 1.0 1.5 0.9 100.0 332 N. OGIHARA ET AL. Although variability is present, muscle fractions were generally consistent with those previously reported, as demonstrated in Table 3. Sexual influence on muscle fractions of limb musculature seems to be minor as also reported by Ishida (1972) and Hamada (1983). However, there is a certain degree of sexual dimorphism in Japanese macaques (average body mass in male 5 11.0 kg and in female 5 8.0 kg; Smith and Jungers, 1997), and body composition is also different between sexes with adult males having a lower fat mass fraction than females (Hamada et al., 2003). Therefore, absolute muscle mass of an adult male is expected to be much larger than that of female of the same body weight. To adjust this size difference, absolute masses of 18 forelimb muscles listed in Table 2 were compared with those estimated for M. mulatta of the same body weight (6.8 kg) using linear regression equations (Cheng and Scott, 2000) constructed based on one female and five male specimens. Mean ratio (6standard deviation) of estimated to measured muscle mass was 1.59 6 0.25, indicating that the female cadaver dissected in this study had small muscles if compared with male macaque of the same body weight. Furthermore, the CT-scanned male specimen was 1.47 times heavier than the dissected cadaver. Accordingly, PCSA values listed in Table 2 must be adjusted for size when substituted into the model. In this study, PCSA values were scaled by a factor of 1.76 [i.e., (1.59 3 1.47)0.667], assuming a simple allometric relationship between body mass and PCSA for the sake of simplicity. Problems that may arise from this simple assumption will be addressed in the ‘‘Discussion’’ section. The calculated changes in moment arms of selected muscles are presented in Figure 6. Signs of calculated moment arms agreed well with the qualitative description of muscular actions for M. mulatta in Hartman and Straus (1969) (no experimental data has yet been published for M. fuscata for comparison). Exceptions were the gluteus maximus (GLUmax), gracilis (GRA), and sartorius (SAR), which were predicted to represent hip flexor (protractor), lateral rotator of the thigh and knee flexor, respectively, in this study, but vice versa in Hartman and Straus (1969). However, the muscular paths of the above three muscles seem to be consistent with the signs of the predicted moment arms. We also compared predicted moment arms with the values reported by Graham and Scott (2003), who experimentally measured flexion/extension moment arms of the shoulder and elbow muscles in the M. mulatta and reported moment arm regression equations (see Fig. 7). We do not know the exact orientation of the scapula with respect to the thorax in their experiment, but we configured the skeletal posture of the model with reference to Graham and Scott (2003) to a maximum extent as in Figure 7 to calculate moment arms of the muscles. Calculated changes in moment arm with joint angle tended to resemble those reported in the literature, indicating that the model successfully emulated the geometry and mechanics of the musculoskeletal system in M. fuscata (see Fig. 7). Figure 8 illustrates the calculated endpoint force vectors of some selected muscles when skeletal posture is configured as in Figure 2. Here, we defined the palmar side of the heads of the third metacarpal and metatarsal as the endpoints on the carpal and tarsal segments, respectively, for the calculation of endpoint force vectors. Triceps brachii lateralis (Tblat) was estimated to generate the largest endpoint force at the hand (see Fig. 8). American Journal of Physical Anthropology Fig. 8. Calculated endpoint force vectors of muscles when the skeletal posture is configured as in Figure 2. Sagittal and transverse (frontal) views are illustrated on the left and right sides respectively. Forelimb muscles exerting forces mainly in the ventral (downward) direction were triceps brachii (Tblat and Tbmed), while those in the dorsal (upward) direction were brachialis (BRC). Rotator cuff muscles such as subscapularis (SUBS), supraspinatus (SUPR) and infraspinatus (INFS), and acromio-deltoideus (DELacro) were estimated to generate forces directed cranioventrally, while that of triceps brachii longus (Tblong) was directed caudoventrally. For hind limb endpoint force, vastus lateralis (VASlat) was estimated to generate the largest force. The hind limb muscles exerting forces mainly in the ventral direction were vastus muscles (VAS), while the muscle exerting force mainly in the dorsal direction was the crural head of biceps femoris (BIFl). Soleus (SOL) and rectus femoris (REF) were estimated to exert forces in a cranioventral direction, whereas gluteus medius (GLUmed), adductor magnus (ADMmed), and the femoral head of biceps femoris (BIFb) exerted force in the caudoventral direction. Gastrocnemius (GC) and MUSCULOSKELETAL MODEL OF JAPANESE MACAQUE TABLE 4. Effects of changes in coefficients on results of model matching A B C D Coefficient Matching bias (mm) Clavicular distance (mm) c d Mean SD Mean SD 0.001 0.001 0 0 10 0 0 10 9.2 9.0 5.0 5.2 4.5 4.4 3.6 3.6 62.9 68.6 122.9 62.6 0.4 9.7 33.9 0.1 SD, standard deviation. semimembranosus proprius (SMEpro) were predicted to generate forces directed cranially and caudally, respectively. Figure 9 illustrates the results of model-based matching, indicating that whole-body skeletal kinematics of the Japanese macaque in transition from quadrupedal to bipedal walking were successfully reconstructed. Matching bias of markers averaged over time was 9.2 mm 6 4.5 mm (mean 6standard deviation), indicating that the skeletal model was successfully registered to the marker trajectories and that matching precision was reasonably accurate. Table 4 summarizes the effects of changes in coefficients on the results of model-matching by comparing the matching bias of markers and clavicular distance (d). Case A in Table 4 represents the original setting for coefficients. Snapshots of matching results corresponding to the four different cases in Table 4 are shown in Figure 10. Comparisons of matching results show that matching with c 5 0 (Cases C and D), i.e., omission of the second term in Eq. (5), gives anatomically impossible, unsatisfactory reconstructed results (see Fig. 10) despite a relatively low matching bias (Table 4). In matching with d 5 0 (Cases B and C), i.e., omission of the third term, mean clavicular distance differs from actual clavicle length (cl 5 62.5 mm) and the standard deviation is large, indicating that the reconstructed shoulder movements do not satisfy the kinematic constraint of the clavicle due to omission of the third term. Anatomically reasonable skeletal motions were reconstructed only for c [ 0 and d [ 0. Figure 11 displays the estimated changes in some joint angles in the Japanese macaque while in transition from quadrupedal to bipedal walking. In this locomotor sequence, the monkey walked quadrupedally from 0 to 1.5 s, then stood on the hind limbs so that lumbopelvic and hip joints were extended at around 2 s to make the upper body straighten up, before finally walking bipedally (after 2.5 s). Although not displayed, changes in muscular length during locomotion can also be estimated, since these values are represented as functions of joint angles. DISCUSSION Development of musculoskeletal model We have described the construction of the first anatomically based, whole-body musculoskeletal model of the Japanese macaque for comprehensive mechanofunctional analyses of locomotion based on CT and dissection. One unique feature of the model is that the locations of joint centers and orientations of rotational axes were defined based on joint morphology to approximate actual kinematic constraints of the skeletal system. The axes are thus not mutually perpendicular as shown in Figure 333 2, unlike in robots. Our assumption that joint rotational axes are fixed with bones does not hold in a precise sense, but such joint translation can be considered negligible due to the ligamentous structure and muscles around joints. At the same time, mathematical formulation of the skeletal system becomes more feasible if the system is represented by a chain of segments connected only by revolute joints, providing clearer prospects for morphofunctional analyses of this complex musculoskeletal system. Description of the body kinematics as explained previously thus seems legitimate. Nevertheless, other factors that kinematically constraint joint motion such as viscoelastic properties of articular cartilage, joint capsule, and ligaments were not considered in the present model. Such anatomical components should be investigated for more precise modeling. Another unique feature of the present model was the incorporation of the scapular segment because of the fact that the relationship between scapula and forelimb was suggested to be functionally equivalent to that of the femur and hind limb, thus representing an important element for propulsion in quadrupedal walking (Fischer, 2001). Kinematic modeling of the shoulder complex structured as a closed chain mechanism by thorax, clavicle and scapula is actually very challenging, but here we tried to simplify this modeling by defining the kinematic constraints only between the thorax and scapula using a triaxial revolute joint based on shape approximation of the thoracic cage, leaving the clavicle out of consideration. Although this gives the first approximation of the wide range of scapular motion, two main problems result from this simplified modeling. First, distance between the sternoclavicular and acromioclavicular joints is not kept constant in the model, but is always constant in actual shoulder movements due to kinematic constraint from the clavicle. Second, the center of the right scapulothoracic joint is located on the left side of the body and vice versa, because the joint is located distant to the scapula to emulate quasi-planar movement of the scapula using a gimbal joint, and force transmission between the right forelimb and thorax therefore occurs unrealistically on the left side in the present model. Nevertheless, these limitations could be overcome if the motion to be analyzed was specified and the model amended accordingly. For instance, the principal motion of the scapula during quadrupedal locomotion in a terrestrial primate (Cercopithecus aethiops) is rotation, and translation seems relatively small (Whitehead and Larson, 1994). Consequently, two translational DOFs of the scapulothoracic joint may be eliminated in quadrupedal locomotion, and location of the joint center could be moved onto the plane of scapular rotation where the clavicular constraint is satisfied. One methodological weakness in the model construction was that we used two different specimens for the skeletal and muscular aspect of the model; the size adjustment of the PCSAs was hence necessary, but the scaling conducted here based on geometric similarity might not be an appropriate assumption. Alexander et al. (1981) found that muscle force generating capacity (5 PCSA) is proportional to body mass raised to the power of 0.8 in mammals in general, inferring that the simple allometric relationship between body mass and PCSA does not hold in a precise sense. Furthermore, such allometric relationship seems to differ from one muscle to another (Alexander et al., 1981; Cheng and Scott, 2000). For more reliable scaling, clarification of American Journal of Physical Anthropology 334 N. OGIHARA ET AL. Fig. 9. Graphical representation of reconstructed whole-body musculoskeletal kinematics of a Japanese macaque in transition from quadrupedal to bipedal walking. The figure is displayed every 0.167 s from 0.67 s to 3 s in Figure 11. See additional Supporting Information. the allometric relationship between body mass and PCSA in the Japanese macaque is essential. In addition, the hand and foot is modeled as a single segment in spite of the fact that the midcarpal and midtarsal joints play important roles during primate locomotion because the mass and inertia of these segments become too small for forward dynamic simulation, and kinematics of these joints are quite complex and not sufficiently understood for modeling. However, inclusion of these joints is certainly desirable for analyzing functional roles of these segments and will be addressed in future studies. The other crude assumption made in the present modeling was that we used the density value of 1.0 g/cm3 for all the segments; although the human cadaveric study by Dempster (1955) demonstrated that density of human limb segment is about 10% larger than 1.0 and that of the thorax segment is about 10% less depending on difference in segment composition. These values could be used as best estimates of the segment densities, but we did not do so as we do not know how close the human values are with those of Japanese macaques. Finding accurate segment densities is another important issue remained to be investigated. Nevertheless, if the masses and moments of inertia are provided based on the density value of 1.0, recalculation of these parameters are very easy when more appropriate data become available. This study demonstrated that this model can predict how moment arms change with joint angles. The moment arm is a factor of transformation from muscular American Journal of Physical Anthropology Fig. 10. Snapshots of matching results with the four different sets of coefficients. (A) Original setting (g 5 0.001 and d 5 10); (B) g 5 0.001 and d 5 0; (C) g 5 0 and d 5 0; (D) g 5 0 and d 5 10. Sagittal and frontal views are illustrated on the upper and lower rows, respectively. MUSCULOSKELETAL MODEL OF JAPANESE MACAQUE 335 force into joint moment. The present model thus allows estimation of moment-generating capacity of muscles around joints, experimental measurement of which is quite impossible for nonhuman primates. This sort of anatomically based mathematical model of the human musculoskeletal system is able to successfully predict experimentally measured maximum isometric joint moments (e.g., Holzbaur et al., 2005). The present model for the Japanese monkey will hopefully be able to predict moment-generating capacities of muscles accordingly. Furthermore, the model allows us to computationally predict endpoint force vectors of the fore- and hind limb muscles that are useful for morphofunctional analyses of primate locomotion. Although comparisons of the predicted endpoint force vectors with those experimentally measured by intramuscular stimulation are certainly desirable for validation of the model, the endpoint forcegenerating capacity of a muscle seems to be fundamentally determined by the geometrical constraints of the musculoskeletal system (Nijhof and Gabriel, 2006), so musculoskeletal models are often used for prediction (e.g., Hof, 2001). We plan to analyze how the orientations and magnitudes of endpoint force vectors change with joint angles and how these values correlate to joint configurations during actual walking from now on. The advantage of this anatomical musculoskeletal model of the Japanese macaque is the ability to predict how changes in the morphology and structure of the musculoskeletal system could alter force-generating capacity at the endpoint. For example, the ways in which changes in the line of muscle could affect endpoint force-generating capacity following modification of muscular disposition or skeletal morphology can be estimated. Virtual deformation of skeletal morphology may be possible using a morphing technique as applied by Ogihara et al. (2006). Such predictive studies will enhance the understanding of causal relationships between morphology of the musculoskeletal system and locomotor habits in primates. In addition, if a set of equations of motions for the described musculoskeletal system is derived, internal forces such as forces generated in muscles and joints during locomotion could be estimated based on inverse dynamic calculation (e.g., Crowninshield and Brand, 1981) that are very difficult to measure in vivo. Such model-based biomechanical analyses would offer a promising approach to clarifying the biomechanics and hence the design principles underlying the musculoskeletal system and the control mechanisms of locomotion in Japanese macaques. Fig. 11. Changes in selected joint angles and muscle lengths of the Japanese macaque in transition from quadrupedal to bipedal walking. Angles are positive for: extension (E) and left lateral bending (B) of lumbothoracic (LT) and lumbopelvic (LP) joints; caudal rotation (CR), caudal translation (CT), and ventral translation (VT) of the scapulothoracic joint; retraction (R), adduction (AD), and medial rotation (MR) of the glenohumeral joint; extension of the elbow; pronation (P) of the forearm; plantar flexion (PF) of the wrist; extension, adduction and medial rotation of the hip; flexion (F) of the knee; and plantar flexion and inversion (I) of the ankle. The MR of the glenohumeral joint means the internal rotation of the humerus around its long axis with respect to the scapula. The same applies to the MR of the hip joint. RH 5 stance phase of the right hind limb, RF 5 stance phase of the right forelimb. American Journal of Physical Anthropology 336 N. OGIHARA ET AL. Another application of this musculoskeletal model is a simulation study of locomotion with a physiological model of the sensorimotor neuro-control system (e.g., Taga, 1995; Ogihara and Yamazaki, 2001; Ekeberg and Pearson, 2005). If a neuro-control mechanism that can spontaneously generate adaptive locomotion could be constructed and incorporated with the musculoskeletal model, dynamics of bipedal locomotion in the Japanese macaque could be thoroughly investigated in a virtual environment. What would be more interesting for the field of physical anthropology is the predictive simulation of locomotion (Sellers et al., 2003). For instance, changes in kinematics, kinetics, and energetics of locomotion in accordance with modification in the musculoskeletal system as above might be predictable, allowing in-computer generation and testing of hypotheses about the origin and evolution of human bipedalism. The importance of computer simulation studies based on biologically relevant neuromusculoskeletal modeling has been highlighted in recent years for truly elucidating the control mechanisms underlying the emergence of adaptive locomotion in animals (Frigon and Rossignol, 2006; Pearson et al., 2006). A synthetic study using the present model will also hopefully contribute to understanding of the sophisticated control mechanisms in primate locomotion. Reconstruction of musculoskeletal kinematics during locomotion Using the newly constructed musculoskeletal model and model-based matching technique, this study successfully reconstructed whole-body skeletal kinematics of a Japanese macaque in transition from quadrupedal to bipedal walking on a treadmill. To determine the spatial position and orientation of any bone segment, six DOFs have to be defined. As a result, 16 marker coordinates are certainly insufficient for reconstructing the complete posture of bone segments. However, this study exploited an anatomically relevant skeletal model, joint movements of which were kinematically constrained based on joint morphology, and this skeletal model was registered so as to satisfy another two morphological constraints expressed in Eq. (5). By incorporating such constraints in both the model and the registration method, this study successfully yielded anatomically reasonable, natural skeletal motion from the limited number of external markers. Unrealistic solutions such as dislocation and collision were thus avoided. Therefore, this successful reconstruction itself demonstrated the validity of the anatomical musculoskeletal model. To understand form and function relationships in locomotor apparatuses in primates, accurate kinematics of the musculoskeletal system in motion has to be obtained, and the mechanical interplay of muscular forces must be analyzed. The proposed reconstruction of the musculoskeletal movements is certainly useful for this end. The 3D visualization of the whole-body musculoskeletal movements contributes to intuitive understanding of dynamical behaviors and interactions of each element constituting the musculoskeletal system during locomotion. From this reconstructed skeleton, changes in 3D anatomical joint angles defined between adjacent bone coordinate systems as well as state variables of muscles such as length and contractile velocity during locomotion can be estimated. Furthermore, such anatomical representation of the skeletal kinematics and muscle orientation American Journal of Physical Anthropology enables more realistic estimation of joint torque and muscular forces based on calculation of inverse dynamics, allowing better comprehension of dynamical mechanisms of locomotion in the Japanese macaque. The estimated hip, knee, and ankle extension/flexion angles of the bipedal sequence in Figure 11 were very consistent with the corresponding published data (Hirasaki et al., 2004; Ogihara et al., 2005b), indicating that joint angles were appropriately estimated in this study. Besides, the present method allows additional quantification of adduction/abduction and axial rotation angles of the hip joint, which have never been measured previously. Furthermore, angle profiles of invisible joints such as scapulothoracic joint during quadrupedal and bipedal walking could also be determined. Estimated joint angle profiles during quadrupedal walking were also reasonably consistent with published reports. For example, maximum lateral bending of the lumbopelvic joint was estimated to occur approximately at touchdown of the ipsilateral foot, as actually observed in some prosimian primates (Shapiro et al., 2001). Furthermore, the scapula was estimated to be cranially rotated at touchdown of the hand and the range of scapular rotation was about 308, comparable with values observed in the velvet monkey (Whitehead and Larson, 1994). Retraction/protraction of the humerus with respect to the scapula was much smaller in this digitized sequence when compared with that for the velvet monkey; although this discrepancy may be attributable to the relatively slow speed of the treadmill. The estimated musculoskeletal motion thus appears anatomically feasible. The present model-matching method certainly displays some limitations. First, external markers were assumed to be fixed to the corresponding bones, but relative movements of markers with respect to the bones (i.e., skin/fur motion artifacts) exist just as in conventional human gait analyses, hindering accurate estimation of bone movements. Positioning and digitization of external markers attached to the joints themselves could also represent a potential source of error in estimated kinematics. Second, the musculoskeletal model was matched with marker trajectories by simple isometric scaling in the present method, even though the body proportion (relative relationship in size between body segments) of the walking subject did not perfectly coincide with that of the model. The model was not tailored to the exact specifications of the monkey in the video here as detailed measurements of the body dimension of the macaque were not available for individualizing the model. Third, the number of joint DOFs of the skeletal system was confined to 41, but this may be insufficient for accurate description of skeletal kinematics, particularly involving the trunk. Estimated musculoskeletal movements in this study were certainly not perfectly accurate. Nevertheless, direct measurements of true spatial movements of bones using bone pins as in Lafortune et al. (1992) and Reinschmidt et al. (1997) are usually not applicable because of the high invasiveness of the technique. Cineradiography represents an ideal tool for visualizing the skeletal kinematics of animals during walking and has been used for analysis of limb movements, particularly for that of scapula movement in primate locomotion (e.g., Jenkins et al., 1978; Whitehead and Larson, 1994; Schmidt and Fischer, 2000; Schmidt, 2005), but the field of view of a fluoroscope is relatively narrow for capturing whole-body movements of large primates and the technique is still invasive. The proposed MUSCULOSKELETAL MODEL OF JAPANESE MACAQUE easy-to-apply, noninvasive method for 3D reconstruction of musculoskeletal motion seems to offer a good compromise between accuracy and practicability. Although some limitations exist, the proposed method may offer tremendous morphofunctional insights into complex musculoskeletal mechanics in primate locomotion, since time-varying 3D relative movements of bones and muscles were quantified and visualized. As the next step, the precise kinematics of bipedal/quadrupedal locomotion in Japanese macaques will be analyzed based on the proposed model-based registration method. Furthermore, the proposed 3D reconstruction method should be expanded for application in field studies in which cameras cannot be fixed and calibrated. Although size estimation of a video-taped subject is theoretically impossible without calibration, 3D kinematic profiling of the musculoskeletal system and graphical representation should be feasible, provided a realistic 3D bone model like the one used here is available for registration. We hope to be able to develop such techniques for 3D reconstruction of musculoskeletal motion for non-human primates in wild environments. ACKNOWLEDGMENTS The authors sincerely thank Prof. Hideki Endo, for allowing us to dissect the specimen, and all the staff at the Suo Monkey Performance Association for their generous collaboration in the experiment. We are also grateful to Sugio Hayama, Eishi Hirasaki, Hidemi Ishida and Nobutoshi Yamazaki for their continuous guidance and support throughout the course of the present study, and anonymous reviewers for their constructive and thoughtful comments. This study was supported by a Grant-in-Aid for Scientific Research on Priority Areas ‘‘Emergence of Adaptive Motor Function through Interaction between Body, Brain and Environment’’ from the Japanese Ministry of Education, Culture, Sports, Science and Technology. LITERATURE CITED Alexander RM, Jayes AS, Maloiy GMO, Wathuta EM. 1981. Allometry of the leg muscles of mammals. J Zool 194:539–552. 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