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Studying Primate Carpal Kinematics in Three Dimensions Using a Computed-Tomography-Based Markerless Registration Method.

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THE ANATOMICAL RECORD 293:692–709 (2010)
Studying Primate Carpal Kinematics in
Three Dimensions Using a ComputedTomography-Based Markerless
Registration Method
CALEY M. ORR,1,2* EVAN L. LEVENTHAL,3 SPENCER F. CHIVERS,4
MARY W. MARZKE,1 SCOTT W. WOLFE,5 AND JOSEPH J. CRISCO3
1
School of Human Evolution and Social Change, Arizona State University, Tempe, Arizona
2
Institute of Human Origins, Arizona State University, Tempe, Arizona
3
Department of Orthopedics, The Warren Alpert Medical School of Brown
University, Rhode Island Hospital, Providence, Rhode Island
4
Mayo School of Medicine, Mayo Clinic in Arizona, Scottsdale, Arizona
5
Department of Orthopedics, Weill Medical College of Cornell University, Hospital
for Special Surgery, New York, New York
ABSTRACT
The functional morphology of the wrist pertains to a number of important questions in primate evolutionary biology, including that of hominins. Reconstructing locomotor and manipulative capabilities of the wrist
in extinct species requires a detailed understanding of wrist biomechanics
in extant primates and the relationship between carpal form and function. The kinematics of carpal movement, and the role individual joints
play in providing mobility and stability of the wrist, is central to such
efforts. However, there have been few detailed biomechanical studies of
the nonhuman primate wrist. This is largely because of the complexity of
wrist morphology and the considerable technical challenges involved in
tracking the movements of the many small bones that compose the carpus. The purpose of this article is to introduce and outline a method
adapted from human clinical studies of three-dimensional (3D) carpal
kinematics for use in a comparative context. The method employs computed tomography of primate cadaver forelimbs in increments throughout
the wrist’s range of motion, coupled with markerless registration of 3D
polygon models based on inertial properties of each bone. The 3D kinematic principles involved in extracting motion axis parameters that
describe bone movement are reviewed. In addition, a set of anatomically
based coordinate systems embedded in the radius, capitate, hamate,
lunate, and scaphoid is presented for the benefit of other primate functional morphologists interested in studying carpal kinematics. Finally, a
brief demonstration of how the application of these methods can elucidate
the mechanics of the wrist in primates illustrates the closer-packing of
carpals in chimpanzees than in orangutans, which may help to stabilize
the midcarpus and produce a more rigid wrist beneficial for efficient hand
Additional Supporting Information may be found in the
online version of this article.
Grant sponsor: National Science Foundation (Doctoral
Dissertation Improvement Grant); Grant number: BCS-622515;
Grant
sponsor:
Wenner-Gren
Foundation
Dissertation
Fieldwork Grant; Grant number: 7484; Grant sponsor: Sigma
Xi Grant in Aid of Research; Arizona State University, School of
Human Evolution and Social Change; Graduate and
Professional Students Association of Arizona State University.
C 2010 WILEY-LISS, INC.
V
*Correspondence to: Caley M. Orr, School of Human Evolution and Social Change, Arizona State University, PO Box 2402,
Tempe, AZ 85287-2402. E-mail: caley.orr@asu.edu
Received 7 January 2010; Accepted 11 January 2010
DOI 10.1002/ar.21137
Published online in Wiley InterScience (www.interscience.wiley.
com).
PRIMATE CARPAL KINEMATICS
693
posturing during knuckle-walking locomotion. Anat Rec, 293:692–709,
C 2010 Wiley-Liss, Inc.
2010. V
Key words: wrist biomechanics; anatomical coordinate systems;
hand postures
The wrist plays a crucial role in facilitating mobility
and/or stability of the forelimb for a wide-range of locomotor and manipulative tasks in primates and other animals. Consequently, studies of wrist morphology and
biomechanics are important for reconstructing the functional capabilities of extant and extinct primates to
address a range of important questions in primate paleobiology and human evolution (e.g., Tuttle, 1967,
1969a,b,c, 1970; Marzke, 1971, 1983, 1997; Schön and
Ziemer, 1973; Jenkins and Fleagle, 1975; McHenry and
Corruccini, 1975; O’Connor, 1975, 1976; Corruccini,
1978; Jenkins, 1981; McHenry, 1983; Rose, 1984, 1988;
Sarmiento, 1988; Lewis, 1989; Heinrich et al., 1993;
Hamrick, 1996, 1997; Lemelin and Schmitt, 1998;
Marzke and Marzke, 2000; Richmond and Strait, 2000;
Ambrose, 2001; Richmond et al., 2001; Tocheri et al.,
2003, 2005, 2007, 2008; Orr, 2005; Carlson and Patel,
2006; Richmond, 2006; Wolfe et al., 2006; Patel and
Carlson, 2007; Lemelin et al., 2008; Kivell and Schmitt,
2009). Testing hypotheses about the relationship
between primate wrist form and function relies on an
understanding of carpal kinematics, including ranges of
motion and specific mechanisms that permit mobility or
enhance stability during the various locomotor and
manipulative tasks performed by primates. For example,
recent debates about the role of knuckle-walking in
human ancestry (Richmond and Strait, 2000; Corruccini
and McHenry, 2001; Dainton, 2001; Lovejoy et al., 2001,
2009a,b; Richmond et al., 2001; Begun, 2004; Orr, 2005;
Kivell and Schmitt, 2009), and the evolution of hominin
tool use (e.g., Ambrose, 2001; Wolfe et al., 2006) have
relied on inferences about wrist movement capabilities
in fossil species. However, there are very few quantitative data on carpal kinematics in extant species on
which to base these inferences, and it is not fully understood how the many individual joints of the wrist contribute to mobility and stability. Such information is
important for understanding the structural correlates of
mobility and interpreting the functional significance of
anatomical features of individual bones, which is critical
when studying isolated wrist elements in the fossil record. This lack of attention is primarily due to the complex morphology of the wrist and the considerable
technical challenges involved in tracking the movement
of its constituent elements. The purpose of this article is
to outline a noninvasive three-dimensional (3D) method
that we have adapted for analyzing carpal kinematics in
primates for use in comparative studies of the functional
morphology of the wrist.
Researchers have studied nonhuman primate carpal
kinematics and joint ranges of motion using one of a few
different methods: (1) planar radiography (Yalden, 1972;
Jenkins and Fleagle, 1975; Jenkins, 1981; Richmond and
Strait, 2000; Jouffroy and Medina, 2002; Daver et al.,
2009); (2) pins inserted into the proximal and distal carpal rows to track the movements of individual carpals
(Yalden, 1972; Sarmiento, 1985); and (3) in vivo wrist
function analysis during locomotion using cineradiography (Jenkins and Fleagle, 1975; Jenkins, 1981). Each of
these methods has its advantages, although the disadvantages are paramount. Planar radiography cannot
fully capture the complex suite of interactions that
occurs during wrist movement as is necessary to test
many functional hypotheses (Wolfe et al., 1997). Methods
involving the use of pins to track carpal movements are
of limited utility due to the disruption of the joint systems caused by pin insertion and by the necessary dissection involved. And, although cineradiographic work is
invaluable (and more studies are needed), the method is
limited in its ability to resolve the complexities of wrist
motion, and there are many logistic difficulties of working with live and conscious animals under the conditions
necessary to capture such data. In cineradiographic
studies of knuckle-walking (Jenkins and Fleagle, 1975)
and brachiation (Jenkins, 1981), the cineradiographs
were primarily used to show the gross positioning of the
hand and wrist, rather than the detailed mechanics of
the joints. This was particularly the case with the
knuckle-walking study because the carpals were not yet
ossified in the young juvenile chimpanzee subject. To
make more detailed inferences about the kinematics of
the bones, these studies relied on stationary planar radiographs of their subjects and other individuals to supplement the cineradiographic films [e.g., a frequently
displayed ‘‘knuckle-walking’’ hand from Jenkins and
Fleagle (1975) is from an anesthetized adult placed in a
simulated stance].
Because of these methodological limitations, quantitative data from past studies of primate wrist mechanics
have been limited to measuring ranges of motion of the
whole hand at the wrist (Tuttle, 1967, 1969b,c; Yalden,
1972; Ziemer, 1978; Richmond, 2006), or in a few cases
to taking individual measurements of ‘‘midcarpal’’ and
‘‘radiocarpal’’ ranges of motion (Yalden, 1972; Jenkins
and Fleagle, 1975; Sarmiento, 1985, 1988). However,
what is meant by ‘‘midcarpal’’ and ‘‘radiocarpal’’ motion
is not typically detailed, and an implicit assumption is
that the bones of the proximal row rotate together
throughout the global hand motion. From studies of
human carpal kinematics, it is known that although the
distal row mostly behaves as a single unit during wrist
motion (Garcia-Elias et al., 1994), the proximal row is
more loosely tethered by ligaments (Berger, 1996, 2001)
and the bones have a certain degree of kinematic independence from one another (Garcia-Elias et al., 1994;
Wolfe et al., 2000; Moojen et al., 2003). Consequently,
the suite of carpal motions that produce different hand
positions is highly complex, with different rotation magnitudes resulting for the scaphoid, lunate, and triquetrum. Thus, the more traditional methods of tracking
bone motion are inadequate for detailing the biomechanic complexities of wrist motion. For example, when
694
ORR ET AL.
TABLE 1. Specimen details and CT parameters
CT scanning parameters
Taxon
Pan troglodytes
Pan troglodytes
Pan troglodytes
Pongo pygmaeus
Pongo pygmaeus
Pongo pygmaeus
Pongo pygmaeus
Pongo pygmaeus
Papio anubis
Papio anubis
Papio anubis
Macaca mulatta
Macaca mulatta
Ateles geoffroyi
Colobus guereza
Segmentation
Sex
Agea
kvp
mAs
Field of
view (mm)
In-plane
resolution (mm)
Thresholdb
(HU)
F
F
M
F
F
M
F
F
F
F
M
M
M
M
M
Adult
Adult (48)
Adult (17)
Adult (38)
Adult
Adult (34)
Adult (55)
Adult (23)
Adult
Sub-adult (5)
Adult
Adult (11)
Adult (9)
Adult
Adult
140
140
140
140
140
140
140
140
120
120
140
120
120
120
120
240
240
240
240
240
240
240
240
300
300
240
300
300
300
300
120
120
120
150
120
150
120
140
100
120
120
100
80
80
100
0.234
0.234
0.234
0.293
0.234
0.293
0.234
0.273
0.195
0.234
0.234
0.195
0.156
0.156
0.200
611
610
450
700
656
450
650
450
600
600
500
600
700
700
550
a
Where known, the age in years is given in parantheses.
The initial threshold value used for segmentation measured in Hounsfield units (HU); see text for details.
b
studying wrist extension and flexion using planar radiography, the hand must be imaged in sagittal view and
the numerous bones of the wrist are superimposed on
one another, rendering it difficult or impossible to track
individual bone motion.
A number of orthopedic and bioengineering research
groups have used 3D methods for studying the kinematics of the human carpus in vitro and in vivo using medical imaging and computer-graphics techniques (e.g.,
Crisco et al., 1999; Feipel and Rooze, 1999; Moojen
et al., 2002a,b; Moritomo et al., 2003, 2004, 2006; Goto
et al., 2005; Kauffman et al., 2005, 2006). The use of a
noninvasive 3D method of studying carpal kinematics
has many benefits over traditional techniques used to
study the biomechanics of the primate wrist. These
advantages include the ability to: (1) track each of the
bones individually without disrupting the structural integrity of the wrist; (2) quantify motions with a high
degree of accuracy including out-of-plane rotations and
translations; (3) calculate the kinematics of a bone relative to any other bone of interest (e.g., the scaphoid relative to the radius or the scaphoid relative to the
capitate); and (4) clearly visualize carpal motions for an
intuitive means of study and to link movement patterns
with morphological features.
The general protocol for the method presented here
was developed in the Bioengineering Laboratory in the
Department of Orthopedics at Brown Medical School
and Rhode Island Hospital for use in human subjects
(Crisco et al., 1999, 2001, 2003, 2005; Neu et al., 2000,
2001; Wolfe et al., 2000; Coburn et al., 2007; Moore
et al., 2007; Rainbow et al., 2008). The approach is
quasi-dynamic in that it takes a series of static CTderived 3D models of the distal forelimb in various positions throughout the wrist’s range of motion and registers them to one another to derive a mathematical
description of the kinematics of the individual bones
within an anatomically defined set of coordinate systems. The mathematical description, coupled with 3D
computer visualization of bone motion, allows for a more
detailed analysis of wrist function. In this article, we
present the data collection protocol, review the general
mathematical foundations of the 3D kinematic analysis,
and describe anatomically based coordinate systems for
the wrist that can be used by primate functional morphologists. Accordingly, this article provides the ground
plan for our own work, and sets the stage for other
researchers interested in studying the biomechanics of
the wrist in primates.
SAMPLE AND RAW DATA COLLECTION
USING COMPUTED TOMOGRPAHY
Cadaveric Sample
The markerless bone registration method described
here was originally designed to study carpal kinematics
in vitro and in vivo in human subjects. Although there is
nothing inherent in the method that would prohibit
in vivo study of wrist function in nonhuman primates,
there are significant logistic obstacles for such work, and
we have thus far restricted our study of primate carpal
kinematics to using cadaver specimens (Table 1). The
forelimbs of 15 individuals from the following taxa have
been examined: Pan troglodytes (chimpanzee: two
females, one male), Pongo pygmaeus (orangutan: four
females, one male), Papio anubis (baboon: two females,
one male), Macaca mulatta (macaque: two males), Ateles
geoffroyi (spider monkey: one male), and Colobus guereza (black and white colobus: one male). Subspecific designations of the taxa are unknown. All individuals died
of natural causes at zoos, or were euthanized and
acquired secondarily following unrelated research activities at other institutions (see Acknowledgments). In all
cases, the specimens were free from external signs of pathology, and fresh frozen shortly after death with no
application of a preservative. The specimens were
thawed just prior to data collection, which proceeded at
room temperature. Previous researchers have demonstrated that such freezing and thawing has no significant effect on the mechanical properties of ligamentous
tissue (Viidik and Lewin, 1966; Woo et al., 1986). Ages of
individual specimens, when known, are given in Table 1.
With the exception of one female baboon, all specimens
were adults with complete fusion of the distal radius. In
PRIMATE CARPAL KINEMATICS
Fig. 1. Polycarbonate wrist-positioning jig. The hand is secured to
a grip that rotates on the platform to place the hand in flexion/extension. The grip also slides within a vertically oriented plastic arc to
position the hand throughout the radial/ulnar deviation range of
motion. Any number of flexion/extension plus radial/ulnar deviation
combinations are possible to situate the hand at angles that are
oblique to the standard anatomical planes. Goniometers in the flexion/
extension and radial/ulnar deviation planes provide measurement of
targeted wrist position for the specimen.
the subadult female baboon, the distal radial epiphysis
and all carpals and metacarpals were fully ossified, and
although fusion was not complete, it was relatively
advanced. The overall range of motion of this specimen
closely approximated that of the other baboons.
Scanning Protocol
The scanning protocol is described here as an example,
but the details of raw data acquisition may vary according
to the specific needs of the researcher based on available
equipment and the questions involved. For the present
research, the forelimb specimens were secured in a custom-designed polycarbonate positioning jig (Fig. 1). The jig
is outfitted with goniometers that situate the hand in
positions throughout the wrist’s range of motion. The
specimen in the jig was scanned using a Siemens SOMATOM Sensation 64-detector CT scanner (Siemens Medical
Solutions, Malvern, PA). The scans were made between
120 and 140 kVp and 240 and 300 mAs with a slice thickness of 0.6 mm, scan interval of 0.3 mm, and field of view
between 80 and 150 mm. Scanning parameters were optimized within these ranges for each specimen’s size and
cortical thickness and produced high resolution slice
images with in-plane resolution between 0.156 mm and
0.293 mm. With a Z dimension (the slice thickness) of
0.6 mm, this resulted in voxel dimensions between 0.156
mm 0.156 mm 0.6 mm and 0.293 mm 0.293 mm 0.6 mm, which is a scan resolution higher than most currently published studies on human carpal kinematics. By
comparison, a recent study by Crisco et al. (2005) had
voxel dimensions of between 0.2 mm 0.2 mm 1.0 mm
and 0.9 mm 0.9 mm 1.0 mm. The specific scan parameters for individual specimens are provided in Table 1.
Each specimen was scanned beginning with the clinically defined neutral position (dorsal aspect of the hand
flush with the dorsal aspect of the radius/ulna) and then
specific positions were targeted throughout the wrist’s
695
full range of motion. Once scanned and processed, the
actual global wrist position was determined by tracking
third metacarpal position (details below). The first scan
of the forelimb with the wrist in its neutral position
spanned from the elbow to just distal to the metacarpal
heads to produce a full model of the radius for establishing the radius-based anatomical coordinate system (see
below). For subsequent positions, shorter scans spanning
from approximately the distal fifth of the antebrachium
to just distal to the metacarpal heads were made to facilitate processing by producing smaller image files. These
subsequent scans targeted every 10 throughout the
entire range of motion. The positions of maximum extension, flexion, ulnar deviation, and radial deviation were
also scanned and determined as the points at which the
wrist exhibited firm resistance to further motion (following Tuttle, 1969b; Richmond, 2006; Calfee et al., 2008).
Contiguous scans were produced at these sampling
intervals throughout flexion/extension and radial/ulnar
deviation. Although we have chosen an interval of 10 at
which to sample wrist position, the sampling protocol
can be altered as needed by the researcher.
Production of 3D Wrist Models
The radius, ulna, carpals [scaphoid, centrale (when
present), lunate, triquetrum, capitate, hamate, trapezium,
trapezoid, and pisiform], and five metacarpals were segmented into individual binary ‘‘masks’’ from DICOM-formatted CT images (see Zollikofer and Ponce de León,
2005, for a review of this format) using the Mimics 11.11
software package (Materialise, 2007, Leuven, Belgium).
Segmentation is the process of selecting voxels that make
up a given object within a CT image (Zollikofer and Ponce
de León, 2005), and the mask is a binary (white-on-black)
representation of those voxels within the CT volume. The
thresholding algorithm in Mimics was used to produce an
initial mask by separating bone from the surrounding soft
tissue and other scanning artifacts based on the X-ray
densities recorded within the particular pixels as measured in Hounsfield units. Initial thresholds were set
between 450 and 650 Hounsfield units (Table 1). Although
specific protocols have been developed for thresholding CT
images to minimize measurement error (e.g., Ulrich et al.,
1980; Coleman and Colbert, 2007), such methods were not
used here, because the complexity of the images (hundreds of slices imaging multiple bones with numerous
joint spaces and tissue interfaces) renders an optimal
threshold level for the entire CT volume effectively impossible to define. Instead, thresholds were determined visually based on the need to separate the cortical shells of
the bones efficiently and thereby minimize the necessity
for manual segmentation (see below), which is the primary source of error for the kinematic registration process. Thresholding was based on segmenting only cortical
bone; internal trabecular bone was ultimately removed
from the constructed 3D models as described below.
From the initial mask (comprising all bones), the
region growing algorithm in Mimics was used to isolate
the individual bones into their own masks. Region growing identifies individual objects by selecting all voxels in
the original mask which are directly connected to the
initial selection (Zollikofer and Ponce de León, 2005). If
the initial thresholding step separated the individual
bones as distinct regions within the initial mask, then
696
ORR ET AL.
each region-growing step produced a new mask for each
bone. However, in some cases, when the joint-spacing
between two bones was small, the initial thresholding
could not distinguish between the bone and the surrounding cartilage and ligamentous tissue due to resolution-imposed constraints. In such instances, manual
editing of the certain parts of the initial mask was
required to separate the bones before region growing
could be applied. Editing of the masks was done using
the erase and draw functions in Mimics to delete pixels
from the masks where necessary, thereby defining the
bone outline. Adjustment of the contrast values in the
CT slices allows the contours of the bones to be seen
more easily, and care should be taken to follow these
contours throughout the editing process to minimize segmentation errors. To enable the calculation of bone centroids and inertial properties (see below), all bone masks
were filled in and made solid to remove internal structures. Solid models reduce error due to slight differences
in the segmentation of low-density trabeculae. When
completed, the masks of the individual bones were used
to create 3D polygon models exported in an appropriate
file format. We use the VRML (Virtual Reality Modeling
Language) format (a text file containing the vertices and
edges of the polygon representation of the object).
Because the full radius and ulna were not scanned
(except for the full scan of the neutral position used to
generate the anatomical coordinate system), inadvertent
sliding of the jig on the scanner bed resulted in models
for these bones that did not always include the same
length of the shaft for each position. Consequently, the
position of the bone’s centroid (its geometric center or
center of ‘‘mass’’) and the orientation of inertial axes (a
system of three orthogonal axes passing through the
centroid that describe how the ‘‘mass’’ of the object is
distributed, i.e., the same definition of inertial axes as
used in basic mechanics) of the two long bones used for
model registration (see next section) would not be comparable across scans within an individual specimen. Discrepancies between the models for these long bones were
accounted for by substituting the 3D models produced
for the radius and ulna in the neutral position for their
counterparts in every other position using surfacematching algorithms in GeomagicV Studio 9.0 (2006,
Geomagic, Research Triangle Park, NC). These surface
matching algorithms allow the registration of partial
models using best-fit algorithms that minimize the overall distance between the models. In this way, the neutral-position models for the radius and ulna were
registered to their corresponding non-neutral models.
Occasionally, one or more metacarpals were similarly
cut short due to errors in setting the window for the CT
scanner or because the chosen field of view was ultimately too small to capture the full length of the hand
at certain goniometer angles. Consequently, a full 3D
model was not available for the metacarpals in those
positions. In these cases, the neutral-position metacarpals were substituted for the relevant position using a
similar registration step in Geomagic.
R
MODEL REGISTRATION AND BONE
TRANSFORMATIONS
Following Crisco et al. (1999), the centroids and principal inertial axes of each 3D bone model were used to
register each bone in each position to the same bone in
the neutral position. The process aligns the centroids
and inertial axes for the bones in two different positions
and then calculates the transformation that describes
the differences in position assuming rigid-body kinematics (i.e., that no deformation of the bones occurs during
the motions). The methods here follow manipulations
derived from the field of theoretical kinematics, including Chasles’ Theorem (Chasles, 1830), which states that
the most general rigid-body displacement is one that
involves a translation and a rotation. A summary of the
matrix algebra involved in computing the mathematical
transformations that are used to describe bone motion in
those terms is provided below. A number of authors provide full treatment of the mathematical foundations of
modern kinematics (proofs and derivations) and the
reader is referred to their works (Bottema and Roth,
1979; Beggs, 1983; McCarthy, 1990; Zatsiorsky, 1998).
Matrix manipulations discussed for the method were calculated using customized scripts written in MATLABV
(2007, The Mathworks, Natick, MA).
The inertial properties of each bone used for motion
capture are defined by the shape of the bone, and constitute a system of orthogonal vectors with the centroid as
the origin. The bone centroids and orientations of the
principal inertial axes for each 3D bone model can be
calculated using an application of Gauss’s divergence
theorem (Messner and Taylor, 1980; Eberly et al., 1991;
Gonzalez-Ochoa et al., 1998). In brief, the divergence
theorem allows for calculation of the volume of an
enclosed polygon object by way of numerical integration
over the surface. From that integrated surface, and
assuming a uniform density, the object’s centroid (or center of ‘‘mass’’) and principal inertial axes (which describe
how that ‘‘mass’’ is distributed about the centroid) can
be derived (see Gonzalez-Ochoa et al., 1998). For a bone
in a given position, the vector ~
c provides the position of
the bone’s centroid, and matrix I provides the orientation of the three principal inertial axes in the global
coordinate space of the CT scanner. The vectors are
defined as the following:
R
2
3
c1
c ¼ 4 c2 5
c3
*
(1)
where the elements of ~
c are the global coordinates for
the centroid, and
2
i1
I ¼ 4 i2
i3
j1
j2
j3
3
k1
k2 5
k3
(2)
where the elements of I are the direction cosines of the
^ for the inertial axes.
unit vectors ^i, ^j, and k
From these bone parameters, a rigid-body transformation (rotations and translations) is calculated that
describes the positional difference for a given bone’s
centroid and inertial axes between the neutral scan and
the secondary wrist position. A three-dimensional transformation accounting for all rotations and translations
can be summarized using a 3 3 rotation matrix R of
direction cosines and a 1 3 translation vector ~
t
PRIMATE CARPAL KINEMATICS
697
(Zatsiorsky, 1998). The rotation matrix is calculated as
the product of the 3 3 transposed matrix I1, whose columns are the unit vectors of the inertial axes for the
neutral position, and 3 3 matrix I2, whose columns
are the unit vectors for the inertial axes of the secondary
position:
Rbone ¼ I2 IT
1
(3)
The rotation matrix provides the description of the
change in orientation of the inertial axes for the motion.
The translation vector expresses the positional difference
between the centroid of the neutral position (~
c1 ) and the
centroid for the object’s secondary position (~
c2 ). When
Rbone is known,
~
c2 Rbone~
c1
tbone ¼ ~
(4)
The rotation matrix and translation vector provide the
raw kinematic data for analyzing carpal bone motions in
the global coordinates, which can be mapped into local
anatomical coordinate frames and summarized using
helical axes of motion (described below).
Before the registration of primary interest (using the
principal inertial axis method to obtain the bone kinematics), it was necessary to account for the previously
discussed shifts in the position of the forelimb during the
scanning process. Correcting such shifts was done by
applying the rotation and translation obtained for the radius to all the bones in a given position to bring each 3D
model into the same relative space within the global coordinate system of the CT scanner. With all bones registered to the radius within the scanner’s coordinate
system, the transformations describing the carpal and
metacarpal motions can be mapped subsequently into a
local coordinate frame based on the anatomy of the wrist.
Accuracy Studies of the Inertial-Properties
Registration Method for Kinematic Analysis
The inertial-properties-based registration method used
to derive the bone transformations and motion axis properties is highly accurate. To validate the inertial-properties registration technique, Neu et al. (2000) used
models produced from CT scans of a dissected human
cadaver wrist with multiple ceramic spheres of high-tolerance diameters (specified to 0.002 mm) glued to each
bone. Using spheres of known size allowed for highly
accurate calculation of centroid position for each sphere.
A least-squares method (Veldpaus et al., 1988) was then
used to register the sphere centroids in one wrist position with the models in secondary positions—thereby
establishing a ‘‘gold standard.’’ Following inertial-properties-based registration of the bones, error in the motion
parameters for a given bone was estimated as deviations
from the rigid-body transformations of the bone’s associated sphere. Most of the carpals had errors of <2 for
the rotation component and <0.5 mm for the translation
component. Furthermore, the helical axes of motion
(detailed below) for most of the bones (including those of
primary interest for our primate work) demonstrated
errors of 5 for the orientation and 0.5 mm for its
position. Only the trapezoid, trapezium, and pisiform
Fig. 2. Accuracy of the bone inertial-properties registration method
for four motion parameters calculated during the kinematic analysis
(Neu et al., 2000).
have higher error values (Fig. 2). Registration error
occurs primarily due to errors in segmentation of the
individual bones from the CT volume, because this
impacts the calculation of the centroid position and the
orientation of the inertial axes. The trapezium and trapezoid are both somewhat pyramidal in shape, whereas
the pisiform (in humans) is small and round. Therefore,
slight errors in segmentation appear to have a disproportionately larger effect on the orientation of the inertial axes for these bones from position to position.
Segmentation error may also be higher in the trapezoid
and trapezium, because the tight joint spacing frequently required manual editing of the images to produce separate masks for the bones. A similar study
evaluating other inertial-properties based registration
methods found comparable results (Pfaeffle et al., 2005).
ANATOMICAL COORDINATE SYSTEMS
We have established anatomically based coordinate
systems, which are necessary to quantify carpal motion
in ways that can be understood in terms of the morphology and overall hand position. These anatomical coordinate systems allow the transformation for each bone—
initially calculated in the global coordinate system of the
CT scanner [Eqs. (3) and (4)]—to be described in terms
of coordinate frames constructed from local properties of
the bones themselves. The magnitudes of the bone rotations and translations as calculated relative to a ‘‘fixed’’
bone are independent of the coordinate system in use,
but motion axis orientation and position in space is
always described relative to the chosen coordinate frame
(see section below on helical axes of motion). By mapping the global coordinate description of the motions
into a local anatomical framework, the motion of a bone
can be quantified relative to any other bone in the wrist.
This allows individual carpal joint kinematics within the
wrist (e.g., the scaphocapitate joint tracked as the scaphoid relative to a ‘‘fixed’’ capitate) to be studied as functions of the global wrist position (as tracked by the third
metacarpal).
For our purposes, we have set up five anatomical
coordinate systems embedded in the radius, capitate,
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ORR ET AL.
hamate, lunate, and scaphoid. These bones provide a
good basis for examining motions within the radiocarpal
and midcarpal joints, which have been the focus of our
investigations. Future research can expand the set of
coordinate systems as needed to address other questions
(e.g., if a researcher wanted to examine trapeziometacarpal kinematics, a coordinate system could be set up for
the trapezium). We have opted for a homology-based
approach to defining the anatomical coordinate systems,
and construct coordinate frames from osteologic landmarks, which allow for descriptions of bone motions in a
comparative context. A coordinate system could be established for any bone of the wrist, and in fact, the inertial
axes of any bone can be used as a coordinate system
(e.g., Coburn et al., 2007). However, given that the inertial axes are mathematically defined (without regard to
morphology), such coordinate systems do not always fit a
criterion of morphologic homology when compared across
primate species. For example, the mathematically
defined long axis of the capitate does not necessarily correspond to the morphologically defined proximodistal
axis as recognized by comparative anatomists.
A challenge with studying a multiple-link kinematic
chain such as the wrist is that any coordinate axis (other
than that for the radius) will deviate from the global anatomical axes as the hand moves through its range of
motion. Because the ultimate goal for primate functional
morphologists interested in the wrist is to relate motions
of the carpals to aspects of carpal morphology on a local
scale (i.e., for particular joints), we suggest a standardized terminology for discussing these movements to
facilitate the explanation of local kinematics. Thus, we
use ‘‘pronation/supination,’’ ‘‘flexion/extension,’’ and
‘‘radial/ulnar deviation’’ to describe rotations about the
local coordinate axes defined on anatomical grounds
regardless of the bone’s global position vis-à-vis the forearm. For example, ‘‘supination about the capitate’’ refers
to motion about the anatomical proximodistal axis of the
capitate, regardless of whether the capitate itself is in
the standard neutral position (relative to the radius/
ulna) or is ulnarly deviated.
Three landmarks (a, b, and c) were used to construct
each coordinate frame, and these were selected directly
from the 3D polygon models using the ‘‘Create Datum’’
function in Geomagic. One landmark defines the origin
of the system in the global coordinate space, and the orientations of the axes are constructed as follows. For
each
! coordinate system, two landmarks define a vector
ab , which serves as the first axis. The second
axis is
!
defined as a vector that is orthogonal to ab and that
lies within
! a plane abc (i.e., calculated as the cross-product of ab and !
ac ). The third axis is defined as a vector
that!is orthogonal to the first two (i.e., the cross product
of ab and the second axis). Once the orientations are
determined, the axis that runs proximodistally is
assigned as the pronation-supination axis (x), the axis
that runs in a radio-ulnar direction is the flexion-extension axis (y), and the final axis running dorsovolarly is
the radial/ulnar deviation axis (z). The landmarks used
to construct the coordinate systems for each of the five
bones are described in Table 2 and shown visually in
Fig. 3 (for the radius), Fig. 4 (capitate and hamate), and
Fig. 5 (scaphoid and lunate).
The repeatability of coordinate frame construction was
estimated by conducting three trials of landmark selec-
TABLE 2. Landmarks used for coordinate
system construction
Bone
Radius
Capitate
Hamate
Lunate
Scaphoid
Landmark
Point a: Midpoint of the distal edge of the
ulnar notch (origin)
Point b: Medial-most point on the proximal
head of the radius
Point c: Tip of the styloid process
Point a: The dorsal corner of the notch on the
ulnar side of the third metacarpal articular
surface (origin)
Point b: The proximal-most point on the
hamate articular facet
Point c: The dorsal corner of the notch on the
radial side of the third metacarpal articular
facet
Point a: The radiovolar corner of the fourth
metacarpal articular facet (origin)
Point b: The ulnar-volar corner of the fifth
metacarpal articular facet
Point c: The proximal-most point on the
capitate articular surface
Point a: The volar-most point on the radial
edge of the capitate articular facet
Point b: The dorsal-most point on the radial
edge of the capitate articular facet
Point c: The proximal-most point on the radial
edge of the capitate articular facet (origin)
Point a: The proximal-most point on the lunate
articular surface (origin)
Point b: The distal horn of the capitate
articular surface (or the equivalent where the
centrale would articulate in primates with a
free centrale)
Point c: The volar corner of the lunate
articular surface
tion (for all 15 specimens) and recalculating the position
of the origin and the orientation of the x, y, and z axes
for each trial. For each specimen, the Euclidean distance
between the origins for each pairwise comparison of trials was used as an estimate of the positional error (i.e.,
Trial 1 was compared to Trial 2 and Trial 3, and Trial 2
was compared to Trial 3). To estimate the orientation
error, the yaw (about the x-axis), pitch (about the yaxis), and roll (about the z-axis) angles were derived
from the rotation matrix giving the difference in orientation for the two trials being compared. The mean of the
three pairwise comparisons for each specimen was used
as the error for that specimen, and the mean of all specimen errors reported as the error for the bone in question
(Figs. 6 and 7). The errors for most bones were low for
both the origin position and orientation, indicating that
the coordinate frames can be applied reliably. However,
the lunate and scaphoid exhibited somewhat larger orientation errors than the other bones (Fig. 7), suggesting
that analyses relying on the orientation of the lunate
and scaphoid coordinate frames should be interpreted
with more caution (e.g., when the analysis requires
decomposing the motion into the x, y, and z rotation components, in which case the orientation of the motion axis
relative to the coordinate frame must be known). The
higher orientation errors for the scaphoid and lunate
stem from the closer proximity of the landmarks on
these bones (there are fewer options for suitable landmarks than the other bones); errors in their placement
PRIMATE CARPAL KINEMATICS
699
Fig. 3. Radius coordinate system from ulnovolar, distal, volar, and
ulnar views. Shown in this figure are the landmarks and the coordinate
axis frames constructed from those points. See Table 2 for descriptions of the landmark locations and the text for details about how the
coordinate system is constructed. The open arrows indicate pronation
(about x-axis), flexion (about y-axis), and ulnar deviation (about z-axis).
The radius coordinate system is used to track global hand position as
well as the motion of any bone relative to the radius.
have a greater relative impact on the calculation of axis
orientation. Similarly, the error in the origin position
was slightly higher for the radius and scaphoid (but still
<1.0 mm; see Fig. 6), likely because the origin landmarks used on these bones are sometimes not well
defined. Error in the origin position is relevant when an
analysis requires knowing something about distances
involved (e.g., the position in space of the motion axis).
forelimb could not be imaged due to concerns about the
subjects’ radiation dosage. Thus, only the distal end of
the radius was CT scanned and the ‘‘long-axis’’ of the radius, which serves as the x-axis was calculated as a
least-squares line fit to the centroids of the CT slice
images. Although this arrangement works for human
subjects, due to their almost completely straight radial
diaphyses, the line-fitting method does not capture the
long axis of the radius for other primates, because most
have shafts that are more highly curved in the mediolateral plane (Aiello and Dean, 1990; Swartz, 1990; Patel,
2005; Galtés et al., 2009). Thus, the alternative landmark-based method was used to define the long axis of
the antebrachium for our system. The radius coordinate
frame can be constructed with little error (Figs. 6 and
7); it is used to describe any bone motion relative to the
Radius Coordinate System
It should be noted that the radius coordinate system
we have established here (Fig. 3) differs from that used
for humans following the original method by Coburn
et al. (2007) after Kobayashi et al. (1997). Because the
original system was intended for in vivo work, the entire
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ORR ET AL.
Fig. 4. Capitate and hamate coordinate systems. The top boxes display the landmarks used to establish the coordinate system, and the lower boxes display the constructed axis frames. Table 2 describes
the landmark locations. The open arrows indicate pronation (about x-axis), flexion (about y-axis), and ulnar deviation (about z-axis).
radius, as well as to define hand position based on third
metacarpal position (Fig. 8). Describing the motions of
bones relative to the radius follows the standard anatomical directions: flexion/extension, radial/ulnar deviation, and pronation/supination.
Capitate and Hamate Coordinate Systems
The capitate and hamate coordinate system (Fig. 4)
can be applied reliably with little estimated error (Figs.
6 and 7). These coordinate frames are useful for quantifying motions within the midcarpal joint complex. For
our work, we have quantified scapho-centrale-capitate,
lunatocapitate, and carpometacarpal joint motions relative to the capitate coordinate system and the triquetrohamate joint motions relative to the hamate’s frame. As
discussed earlier, for describing motion of the carpals (in
words), we use the axes of the fixed bone’s coordinate
frame regardless of that bone’s position relative to
the radius. However, verbal description of individual
bone motions when there are bones proximal and distal
to the fixed bone (as when examining the midcarpal and
carpometacarpal joint complexes) is less straightforward.
The proximal and distal bones (e.g., lunate and third
PRIMATE CARPAL KINEMATICS
701
Fig. 5. Lunate and scaphoid anatomical coordinate systems. The top boxes display the landmarks
used to establish the coordinate system, and the lower boxes display the constructed axis frames. Table 2
describes the landmark locations. The open arrows indicate pronation (about x-axis), flexion (about y-axis),
and ulnar deviation (about z-axis).
metacarpal, respectively) will rotate in the opposite
direction relative to the capitate or hamate, but we may
consider both motions to be either ‘‘flexion’’ or ‘‘extension.’’ Thus, for motions relative to the capitate and
hamate we use the following convention regardless of
whether the moving bone is proximal or distal: rotation
toward the volar aspect of the fixed bone ¼ ‘‘flexion’’;
rotation toward the dorsal aspect of the fixed bone ¼
‘‘extension’’; rotation toward the ulnar side ¼ ‘‘ulnar
deviation’’; rotation toward the radial side ¼ ‘‘radial
deviation.’’ Because pronation and supination occur
about the proximodistal axis, they are the same for
bones proximal and distal to the capitate and unaffected
by this issue.
Lunate and Scaphoid Coordinate Systems
The lunate and scaphoid coordinate frames (Fig. 5)
have been used primarily for examining motions
between the bones of the proximal carpal row (scapholunate and triquetrolunate joints). The attribution of rotation ‘‘sense’’ follows the same rule as for the capitate and
hamate (above). We have also used the scaphoid coordinate frame to track motions of the centrale relative to
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ORR ET AL.
Fig. 6. Repeatability error for establishing the origin of the anatomical coordinate systems in the primate sample used for the current
study (see Table 1). The bar indicates the mean, and whiskers are 1
standard deviation.
Fig. 8. Tracking global hand position in flexion/extension and radial/
ulnar deviation. Global position of the hand was tracked as the position
of the third metacarpal’s long axis (as defined by its first principal inertial axis; dotted red line) relative to the axis of the radius coordinate
system (defined by its first principal inertial axis; solid red line).
tion of the chosen anatomical coordinate system, and
~
tref is the origin vector for that system (e.g., the midpoint of the ulnar notch for the radius coordinate system). Given these coordinate frame parameters, the
trel )
rotation matrix (Rrel) and translation vector (~
describing the displacement of the bone of interest relative to the reference frame are calculated as follows:
Rrel ¼ RT
ref Rbone
(5)
~
~
~
trel ¼ RT
ref ðtbone tref Þ
(6)
and
Fig. 7. Repeatability error for establishing the orientation of the anatomical coordinate systems in the nonhuman primate sample used
for the current study (see Table 1). The bar indicates the mean, and
whiskers are 1 standard deviation.
the scaphoid. However, the construction of these coordinate frames is associated with somewhat more error
than those of the capitate and hamate (Figs. 6 and 7);
consequently, our analyses have mostly focused on the
magnitudes of total rotation and translation (which are
independent of the coordinate system’s position and orientation), rather than orientation of the motion axes.
Mapping the Bone Transformations into the
Anatomical Coordinate Frames
The global-coordinate description of a bone motion can
be mapped into a local anatomically based coordinate
frame by using the global-coordinates transformation
tbone from Eqs. (3) and (4), respectively]
[Rbone and ~
along with the rotation matrix and translation vector for
tref ). The columns
the appropriate local frame (Rref and ~
of Rref are the three unit vectors describing the orienta-
The resulting rotation and translation are used as the
full description of the motion of interest. For example,
the centrale motion can be described relative to the scaphoid’s coordinate frame. In that case, the Rbone and
~
tbone provide the centrale’s transformation in global
tref provide the transformation of the
space, Rref and ~
scaphoid’s inertial axis frame in global space, and the
trel give the centrale’s rotation and
resulting Rrel and ~
translation relative to the scaphoid. Finally, such relative motion is summarized by using helical axes of
motion as detailed in the following section.
KINEMATIC ANALYSIS USING HELICAL
AXES OF MOTION
Because six-degrees-of-freedom kinematics using the
translation vector and rotation matrix is difficult to
interpret and visualize, the analysis of 3D kinematic
data can be facilitated by calculating the parameters of
helical axes of motion (HAM) associated with the carpal
motions of interest. Helical axes (or ‘‘screw axes’’) are
703
PRIMATE CARPAL KINEMATICS
body occurs and along which that body translates (Fig.
9); thus, the motion can be summarized as a translation
and a single rotation rather than a series of rotations (as
is the case with the transformation matrix in which the
component rotations are expressed as functions of the
Euler angles about the coordinate axes). If no translation
occurs, the motion is a pure rotation about the axis and
vice versa. The parameters of the HAM for particular
motions provide the primary variables of interest for
examining joint functions in the carpus. Here, we review
the calculation of these parameters, which include the
following (after Panjabi et al., 1981):
Fig. 9. Helical axis of motion (HAM). The 3D motion of a rigid body
from Position 1 to Position 2 (which we calculate by registering the inertial axes) can be described as a rotation (U) and translation along
(tham), a unique axis in space. If ktham k ¼ 0, then the motion is a pure
rotation, and if U ¼ 0, then the motion is a pure translation. The orien^, and its position in space
tation of the HAM, described by the vector n
(established by finding an arbitrary point q through which the HAM
passes) is described in terms of the fixed anatomical coordinate frame
being used (see text for details).
the 3D extension of the 2D instantaneous center of rotation (Zatsiorsky, 1998). In other words, a HAM represents
a unique axis in 3D space about which rotation of a rigid
n21 versU þ cos U
M ¼ 4 ðn1 n2 versU þ n3 sinUÞ
ðn3 versU n2 sinUÞ
2
sin U ¼
^ ¼ k^
n
Rrel n
Rrel ð3; 3Þ n23
1 n23
(9)
Rrel ð1; 3Þ n1 n3 ð1 cosUÞ
n2
(10)
In rare cases, where the HAM is parallel to one of
the local anatomical coordinate axes, the relationships
used above to find cos U and sin U will be undefined
because it will necessitate dividing by zero. For example, if the HAM is parallel to the anatomical z-axis,
_
then n ¼ ½ 0 0 1 T , and neither cos U nor sin U can
be calculated because the denominators of Eqs. (9)
and (10) would be zero. In such cases, these relation-
(7)
2. Magnitude of the rotation: Expressed as a single
angle phi (U)—the rotation component of the motion
^ . To calculate U, the rotation matrix Rrel
about n
[Eq. (5)] can be expressed as matrix M in terms of U
^ by transforming Rrel into a
and the elements of n
^ (see the apcoordinate frame with one axis fixed as n
pendix in Panjabi et al., 1981 for a derivation of M
following Kinzel et al., 1972a,b):
ðn1 n2 versU n3 sinU
Þ
n22 versU þ cosU
ðn2 n3 versU n1 sinUÞ
where vers 1 cos By equating two appropriate elements of Rrel with
the corresponding elements of M, cos and sin can be found and the rotation calculated in turn.
Primarily we have used the elements Rrel(1,3) and
Rrel(3,3) as found in Eq. (5) to establish these
relationships:
cos U ¼
^ defined
1. HAM orientation: A normalized unit vector n
as [nx ny nz]T along the positive direction of the HAM,
whose elements are the direction cosines that describe
^ is calculated as
the HAM’s orientation. The vector n
the eigenvector of the rotation matrix Rrel [as calculated in Eq. (5) for the coordinate system of choice].
^ satisfies the equation
That is, n
3
ðn1 n3 versU þ n2 sinUÞ
5
ðn2 n3 versU n3 sinU
Þ
n23 versU þ cosU
(8)
ships must be derived using different elements of Rrel
and M—as advised by Panjabi et al., (1981). Once cos
U and sin U are known, the angle of rotation about
the HAM can be found in degrees as
sinU 180
U ¼ atan2
cosU
p
(11)
To avoid confusion regarding the direction of rotation, the computing function atan2 is preferable to the
functions arccosine or arcsine of U. The atan2 function
returns the calculation of U as a counterclockwise
rotation about the HAM with a range of p to p (i.e.,
between 0 and 180 ). To avoid confusion, and following
convention (e.g., Zatsiorsky, 1998), when U is nega^ , U,
tive, we force it to a positive value by negating n
tham is shown in Eq. (12) below].
and ~
tham [~
3. Magnitude of the translation: This is the magnitude
of the bone’s translation along the
HAM
(i.e., parallel
^ ), given as a linear distance (~
to n
tham ). The translation vector ~
tham is defined as [tx ty tz]T and is calculated by projecting the translation vector ~
trel onto an
axis parallel to the HAM by the relationship
704
ORR ET AL.
*
~
^
tham ¼ t rel n
(12)
The magnitude of ~
tham is calculated as
qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
~
tham ¼ t2x þ t2y þ t2z
(13)
4. HAM’s position in space: Expressed as a point q,
through which the HAM passes and whose position
vector ~
q is defined as [qx qy qz]T. The point q provides the HAM’s position as described by the coordinates of the chosen anatomical frame. To calculate ~
q,
first ~
trel is decomposed into a vector component that
^ (the HAM translation vector, ~
is parallel to n
tham
^ (a vector ~
discussed above) and orthogonal to n
e).
^ in planar fashFor the rotation U, ~
e rotates about n
ion (i.e., in pure rotation), and ~
q is the vector that
describes the position of the instantaneous center of
^ . The orthogonal vector ~
rotation for ~
e about n
e is
found as
^ Þ^
~
n
e ¼ trel ðtrel n
(14)
^,
As derived by Panjabi and White (1971), given ~
e, n
and U, the position vector of q is calculated as
~
^ ~
e
n
e
!
q ¼ þ
2 2tan U=
2
(15)
^ , the HAM is fully described, givCombined with n
ing the orientation relative to the anatomical coordinate frame and its position in the same coordinate
system.
The HAM’s orientation and position can be described
relative to the coordinate system of any of the other
bones depending on the question. The phi rotation values can be decomposed into their ‘‘flexion/extension,’’
‘‘radial/ulnar deviation,’’ and ‘‘pronation/supination’’
vector components as follows
Ui ¼ Un2i
(16)
^ correwhere ni is the direction cosine element of n
sponding to the coordinate axis of interest (e.g., if the
flexion/extension vector component is of interest, ny is
used).
When tracking bone motions relative to the radius,
the orientation of the HAM can be understood strictly
in terms of the standard anatomical planes. When its
position and orientation are calculated relative to a
bone other than the radius, the descriptive terms follow the conventions outlined in the section on anatomical coordinate systems using the fixed bone as the
reference (see previous section). Visualization of the
motions and written descriptions of the HAMs and
their relationships to the morphology are useful for
clarification. As noted previously, the magnitude of
the total rotation (U) and the translation component
(~
tham ) relative to a fixed bone is independent of the
coordinate frame in which the orientation and position
of the HAM are described.
Visualization of Carpal Kinematics
and Anatomy
A benefit of the method used here to study carpal kinematics is the ability to visualize carpal movements
using computer graphics techniques. Still and animated
images allow detailed study of carpal joint positioning
throughout the wrist’s range of motion as well as visualization of the HAMs involved. This not only provides an
intuitive method of validating the quantitative results of
carpal movements, but is invaluable in its own right for
understanding the complex mechanisms at work in the
wrist. The 3D models produced from the CT images in
Mimics can be visualized in packages such as Open
InventorV (2007, Mercury Computer Systems, Chelmsford, MA) or AutodeskV Maya. We make use of a custom
Wrist Vizualizer program developed by one of us (Evan
L. Leventhal). In animating the bones from one scanned
position to another to visualize particular movements we
use a 10-frame linear interpolation to smooth the
motions between positions.
R
R
APPLICATION
The kinematics of the carpals is complex and is an
understudied topic in primate functional morphology.
The protocol we outline here for tracking bone motions
sets the stage for morphologists to address a number of
hypotheses about form and function in the wrist. Our
own collaborative efforts have focused on mechanisms
underlying mobility and stability in the radiocarpal and
midcarpal joints in relation to the habitual locomotor
hand postures exhibited by different anthropoids and
their implications for hominin evolution. In particular,
we have been interested in testing hypotheses about the
biomechanics and associated morphology of the wrist in
the knuckle-walking African apes (e.g., Tuttle, 1967;
Richmond et al., 2001; Orr, 2005).
One goal of this research program (e.g., Orr et al.,
2009) has been to test hypotheses about the relative efficacy of the midcarpal screw-clamp mechanism in maintaining joint stability in primates (MacConnaill, 1941).
Under this model (the screw-clamp mechanism), within
the proximal carpal row, the scaphoid is analogous to
the stable block against which the loosely tethered
lunate is pinned by a screw action of the triquetrohamate joint. Lewis (1989) attributed such a mechanism to
use of the hand in suspensory behavior, but noted that a
screw-clamp mechanism in the suspensory orangutans
was not as well developed. Alternatively, the screwclamp mechanism could accommodate terrestrial
knuckle-walking hand postures. Chimpanzees and gorillas are highly terrestrial (Schaller, 1963; van LawickGoodall, 1968; Tuttle and Watts, 1985; Hunt, 1992), and
knuckle-walking is the predominant mode of progression
at an early age (Doran, 1992, 1993, 1997). During
knuckle-walking, the African apes employ a rigid hand
and wrist as a lever during the stance phase (Tuttle,
1967; Tuttle and Basmajian, 1974; Jenkins and Fleagle,
1975; Wunderlich and Jungers, 2009), and mechanisms
to produce a more rigid wrist may allow for more
efficient use of the hand during the stance phase (Tuttle,
1967; Jenkins and Fleagle, 1975; Richmond and Strait,
2000; Richmond et al., 2001; Begun, 2004; Orr, 2005).
Orangutans, on the other hand, are highly arboreal and
PRIMATE CARPAL KINEMATICS
705
Fig. 10. Kinematics of the midcarpus in a chimpanzee (Pan) and an orangutan (Pongo) during wrist extension (neutral position to maximum extension). For each bone, the total phi rotation about the helical axes relative to the global hand position (position of the MC3 in extension) is shown along with the percentage of
the maximum phi that is composed of supination, extension, and ulnar deviation. See text for discussion.
suspensory and spend very little time on the ground
(Rodman, 1973; MacKinnon, 1974a,b; Cant, 1987;
Thorpe and Crompton, 2005, 2006; Thorpe et al., 2007).
They appear to have more mobile wrists than the African apes and use a wide array of hand postures both in
the trees and on the ground, including fist-walking on
the dorsal aspects of the proximal phalanges and
extended-wrist palmigrade positions (Tuttle, 1967,
1969a; Susman, 1974; Sarmiento, 1985, 1988; Thorpe
et al., 2007). As an example of an application of the
method outlined here, we briefly describe the kinematics
of the midcarpal joint complex in a chimpanzee and an
orangutan in the context of the screw-clamp model.
Under the screw-clamp model, it is expected that the
scaphoid, lunate, and triquetrum in the chimpanzee
should cease rotating at an earlier point in the overall
wrist extension movement, which would be indicated by
a lower overall phi (U) rotation for these bones. Because
the intercarpal mobility for the bones of the proximal
row is known to be substantial in humans (Garcia-Elias
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ORR ET AL.
et al., 1994; Wolfe et al., 2000; Moojen et al., 2003),
chimpanzees, and orangutans (Orr et al., 2009; Orr,
unpublished observations), the proximal and distal carpal rows must be stabilized by an interlocking mechanism. Under the screw-clamp model, this might occur
by: (1) more pronounced supination of the scaphoid onto
the dorsum of the capitate head, which should result in
a firmer clasp on the neck of the capitate and set up the
stable, radial-side block (a motion that would also interpose the scaphoid between its articulation with the radius and the capitate head and facilitate load
transmission in a semiextended wrist position); (2) rotation of the lunate relative to the capitate that occurs primarily as extension, resulting in a closer approximation
of the scaphoid and lunate as the motion proceeds; and
(3) a spiraling rotation of the triquetrum on the hamate
(evidenced by an increased supinatory rotation component for the triquetrum relative to the hamate’s x-coordinate axis) that ‘‘screws’’ the triquetrum into the lunate
and tightens their intercarpal ligaments, thereby stabilizing the lunate between the scaphoid and triquetrum.
As the wrist is moved from the neutral position to its
position of maximum extension, the total rotation for
each bone is captured by its phi (U) calculated relative to
the capitate (for the scaphoid and lunate) or to the
hamate (for the triquetrum). The phi angle can then be
decomposed using Eq. (16) to obtain the pronation/supination, flexion/extension, and radial/ulnar deviation components. Relative to the capitate or hamate, the motions
of the three bones occur as a combination of supination,
extension, and ulnar deviation in both taxa, although the
relative contributions of each component differ between
chimpanzee and orangutan. In Fig. 10, the phi rotation
as function of third metacarpal position (i.e., hand position in extension) for each joint is plotted along with the
percentage of the peak rotation that occurs as supination,
extension, and ulnar deviation. Note that the three joints
show higher phi values in the orangutan (Pongo), which
has a higher overall range of motion of the hand as demonstrated by its third metacarpal extension angle (Fig.
10A,C,E). Also, note that the chimpanzee (Pan) exhibits
scaphoid and triquetral motions in which supination
occurs as a greater proportion of the peak maximum phi
angle (Fig. 10A,F) and that the lunate almost exclusively
extends on the capitate (Fig. 10D).
Visualization of these two specimens shows that the
scaphoid’s HAM in the chimp (Fig. 11A) is oriented more
obliquely to the capitate’s flexion-extension axis (running
mediolaterally) than in the orangutan (Fig. 11B), resulting in a higher supination component for the rotation
values. This produces a rapid engagement of the scaphoid with the capitate neck and a rigid radial-side carpal arrangement that may be facilitated by the os
centrale’s fusion to the scaphoid in the African apes (Orr
et al., 2008; Orr, unpublished observations). Consequently, the scaphoid reaches its ‘‘close-packed’’ position
at a lower total degree of wrist extension and rotates
into close proximity with the lunate. On the ulnar side
of the wrist, the triquetrum’s obliquely oriented HAM
indicates its supination on the hamate in the chimp
(Fig. 11C), which may tighten the lunotriquetral ligaments (Berger, 1996) and ‘‘twist’’ triquetrum and lunate
together, pinning the lunate between the other two
bones of the proximal row, consistent with the screwclamp model.
Fig. 11. Orientations of the helical axes of motion (HAMs) in a
chimpanzee (A and C) and an orangutan (B and D) for the scaphoid
and lunate as calculated relative to the capitate (A and B) and the triquetrum calculated relative to the hamate (C and D). Bones of the
right carpus are shown in dorsal view with the distal end oriented toward the top of the page. See text for discussion. Also, see the supplemental videos online, which demonstrate how the combination of
these rotations close pack the lunate between the scaphoid and triquetrum (and subsequently the proximal row to the distal row) in Pan
versus a looser packing through the full motion in Pongo. The videos
are shown with motion relative to a fixed lunate.
In contrast to the chimpanzee, in the orangutan the
scaphoid HAM is oriented approximately midway
between the flexion-extension and radial-deviation axes,
such that when the hand is extended, it is mainly extension and ulnar deviation that occurs at the scaphocapitate joint. As such, the scaphoid rides more radially
along the capitate head and does not rapidly engage
with the neck. In addition, the triquetrum’s HAM about
the hamate is not obliquely inclined as in the chimp
(Fig. 11C,D), and it aligns approximately with those of
the scaphoid and lunate (Fig. 11B), such that there is no
evidence of significant supination as seen in the chimpanzee at this joint. This rotational pattern suggests the
orangutan midcarpus may not function as an effective
screw clamp, and consequently the midcarpal complex
does not become close-packed until a higher angle of
global hand extension at the wrist in the orangutan. The
resulting rotational pattern pinning the lunate is clearest when motion is viewed relative to a fixed lunate, and
two videos (one for Pan and one for Pongo) are provided
as supplemental online material. These videos show the
dorsal rotation of the scaphoid onto the capitate head in
the chimpanzee and its closer approximation to the
lunate as extension proceeds, and the apparent screw
action of the triquetrum. Viewers will note the ‘‘twisting’’
of the scaphoid and triquetrum on either side of the
lunate and what appears to be a closer packing of the
PRIMATE CARPAL KINEMATICS
bones in the chimp than in the orangutan. The resulting
close-packing of the wrist may help to stabilize the midcarpus and produce a more rigid wrist that could be of
benefit for efficient use of the hand during knuckle-walking. However, whether or not the chimpanzee pattern
observed here is distinctive of African apes or is common
to quadrupedal primates that use other hand postures
(digitigrady and palmigrady) is the subject of on-going
research using these techniques.
CONCLUSION
The methods outlined in this article provide a means
for detailed examination of carpal kinematics in primates by quantifying wrist joint motion and visualizing the
movements involved. The kinematic principles involved
in studying wrist mechanics in 3D were outlined, a system of anatomically based coordinate frames established
to facilitate comparative work, and an example provided
of how this system can be used to describe carpal motion
quantitatively, verbally, and visually to aid analysis. We
hope that it establishes some useful conventions, and
that other functional morphologists will follow suit to
tackle questions involved in understanding the complex
mechanics, anatomy, and evolution of the wrist in
primates.
ACKNOWLEDGMENTS
The authors thank the following people and institutions for providing primate specimens: Carol Allen and
Rickie Bass (Yerkes National Primate Research Center),
Michelle Bowman (Cheyenne Mountain Zoo), Doug
Broadfield (Florida Atlantic University), Lora Daniels
(Oregon National Primate Research Center), Jo Fritz
(Primate Foundation of Arizona), Jerilyn Pecotte (Southwest National Primate Research Center), Kathy Orr
(Phoenix Zoo), Lori Perkins (Zoo Atlanta), Frank Ridgley
(Miami Metro Zoo), and Joe Smith (Fort Wayne Children’s Zoo). They also thank Doug Moore, Michael Rainbow, and Kerry Knodel for technical assistance, and
Sondra Menzies, Samuel Larson, and Carol Ward’s
many students for segmenting CT scans. In addition,
their work has benefited from many conversations about
carpal morphology and 3D methods with Matt Tocheri,
who also provided critical comments on an earlier version of this manuscript. Comments from Mark Spencer
on a chapter of C.M. Orr’s dissertation and critiques by
two anonymous reviewers also improved the document.
Finally, they appreciate the efforts of Jason Organ and
Qian Wang in editing this special issue on primate functional morphology and for organizing the symposium
that inspired it.
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