Studying Primate Carpal Kinematics in Three Dimensions Using a Computed-Tomography-Based Markerless Registration Method.код для вставкиСкачать
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: firstname.lastname@example.org 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, 698 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 700 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 702 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 706 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. 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