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Development of an anatomically based whole-body musculoskeletal model of the Japanese macaque (Macaca fuscata).

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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: ogihara@anthro.zool.kyoto-u.ac.jp
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.
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