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Three-dimensional in vivo motion of adult hind foot bones
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Journal of Biomechanics 39 (2006) 726–733 www.elsevier.com/locate/jbiomech www.JBiomech.com
Three-dimensional in vivo motion of adult hind foot bones Brian Mattinglya, Vishwas Talwalkarb,c, Chester Tylkowskib,c, David B. Stevensb,c, Peter A. Hardya, David Pienkowskia,c, a
Center for Biomedical Engineering, University of Kentucky, Washington and Rose Streets, Lexington, KY 40507-0070, USA b Shriners Hospital for Children, 2800 Richmond Road, Lexington, KY 40502, USA c Department of Orthopaedic Surgery, School of Medicine, University of Kentucky, 740 South Limestone, Lexington, KY 40536-0284, USA Accepted 30 December 2004
Abstract Knowledge of hind foot bone motion is important for understanding gait as well as various foot pathologies, but the threedimensional (3D) motion of these bones remains incompletely understood. The purpose of this study was to quantify the motion of the talus, calcaneus, navicular, and cuboid in normal adult feet during open chain quasi-static uniplanar plantar flexion motion. Magnetic resonance images of the right feet of six normal young adult males were taken from which 3D virtual models were made of each hind foot bone. The 3D motion of these models was analyzed. Each hind foot bone rotated in the same plane about half as much as the foot (mean 0.541 of bone rotation per degree of foot motion, range 0.40–0.731 per degree of foot motion as measured relative to the fixed tibia). Talar motion was primarily uniaxial, but the calcaneus, navicular, and cuboid bones exhibited biplanar (sometimes triplanar) translation in addition to biaxial rotation. Net translational motions of these bones averaged 0.39 mm of bone translation per degree of foot motion (range 0.06–0.62 mm per degree of foot motion). These data reflect the functional anatomy of the foot, extend the findings of prior studies, provide a standard for comparison to patients with congenital or acquired foot deformities, and establish an objective reference for quantitatively assessing the efficacy of various hind foot therapies. r 2005 Elsevier Ltd. All rights reserved. Keywords: Talus; Calcaneus; Cuboid; Navicular; Hind foot
1. Introduction Knowledge of the three-dimensional (3D) motion of the hind foot bones is essential for a complete understanding of foot biomechanics. This knowledge will facilitate detection of various foot pathologies, quantify their severity, and provide an objective goal for function restoration. Previous studies have measured hind foot motion on live and cadaveric foot specimens by using externally applied goniometers, and based upon these data, have modeled hind foot motion by using combinations of simple hinges (Inman, 1991; Kitaoka Corresponding author. Department of Surgery, Division of Orthopaedic Surgery, School of Medicine, University of Kentucky, 740 South Limestone, Lexington, KY 40536-0284, USA. Tel.: +1 859 323 5533x240; fax: +1 859 323 2412. E-mail address: [email protected] (D. Pienkowski).
0021-9290/$ - see front matter r 2005 Elsevier Ltd. All rights reserved. doi:10.1016/j.jbiomech.2004.12.023
et al., 1995, 1997, 1998; Sammarco et al., 1973; Siegler et al., 1988). These models, however, were less than satisfactory because they failed to adequately describe the complex multiaxial motion of the hind foot. Magnetic resonance imaging and computer-aided analyses have recently been used to measure wrist (Gerlach et al., 2001; Snel et al., 1998) and foot (Hirsch et al., 1989, 1996, 2000; Udupa et al., 1998) motion. These techniques have enabled in vivo non-invasive quantification of 3D bone anatomy and motion. This offers the potential to generate new insight regarding the complex multiaxial motions of hind foot bones during gait and advance our knowledge of foot biomechanics. Therefore, the specific aim of the present study was to quantify the 3D translational and rotational motion of the talus, calcaneus, navicular, and cuboid bones of the normal adult hind foot during open chain quasi-static uniplanar plantar flexion–dorsiflexion motion.
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2. Methods Six male subjects (18–30 years) with normal foot and ankle motion and no known pathology or lower extremity trauma were examined by an Orthopaedic surgeon and recruited into an IRB approved study. Each subject reclined supine on the table of a 1.5 T S magnetic resonance imager and the right lower extremity was secured to a polymeric (CHAMCOTM, Miami, FL) non-weight bearing ankle motion device designed to rotate in the sagittal plane in 51 increments. This ankle motion device was placed on the gantry of the MR imager and constrained ankle motion to the sagittal plane in the field of view. The overall methodology employed follows the methods developed by Udupa et al. (1998). The foot was first secured in the positioning device and fixed at the neutral position, defined as the position at which a 901 angle is formed between the horizontal and the vertical platform against which the sole of the foot rests (Fig. 1). A 10-cm diameter radio frequency receive-only coil was placed directly underneath the foot. Scout images were acquired to locate the area from the distal tibia to the distal metatarsals. After identifying the areas of interest, a series of 64 MR images (slice thickness 1.5 mm) was obtained from the foot and ankle in the sagittal plane (pixel size ¼ 0.94 mm 0.94 mm) by using a Fast Low Angle Shot (FLASH) 3D protocol. The field of view was 240 mm 240 mm, with a 256 256 matrix and TR/TE/flip angle of 20 ms/6 ms/301. This imaging procedure was developed to optimize contrast and minimize imaging time. Imaging began with the subject’s foot at maximum dorsiflexion, and was repeated at successive 101 increments over the full range of uniplanar foot flexion motion. At maximum plantar flexion, the foot could sometimes not be flexed an
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additional 101; thus, a 51 final flexion increment was then obtained. Subjects were instructed not to actively contract the muscles controlling their foot, but to allow the ankle motion device to maintain foot position. 2.1. Image analysis Image analysis was performed by using 3DVIEWNIX, a custom-written Unix-based, X-Windows, C programming language software package (Udupa et al., 1994). The distal tibia, talus, calcaneus, navicular, and cuboid were identified and manually outlined in each MR slice by using a segmentation tool (paint). Paint allowed the margins of each bone to be smoothly traced and the perimeter accurately represented. No cartilage was included in any trace. After outlining, the area contained within each perimeter was automatically filled. Interpolation of the segmented object on each slice was performed to reconstruct the 3D structure of each bone. A 3D Gaussian filter was used to smooth the surface of the newly interpolated 3D image. Thresholding further clarified the reconstructed 3D bone image by assigning a binary 0 value to all cells whose gray scale intensity were less than 110 (on an arbitrary 256 point gray scale based on the MRI scan); all cells with gray scale intensity of 110 or greater received a binary 1 value. Since the entire tibia was not in the scanner’s field of view, care was taken to anatomically define the distal tibia by means of the epiphyseal scar. For each set of 64 sagittal slices, the slice containing the largest length of epiphyseal scar was identified and a straight line was drawn between the ends of this scar. This straight line was then used as the proximal border of the distal tibia for subsequent slices of the same foot, and the anterior, posterior, and distal borders were identified by the bony outline distal to this proximal border. This procedure was done to ensure that the ‘distal tibia’ could be identified and reproducibly outlined for each subject. 3D reconstruction of each bone was performed by interpolation, 3D Gaussian filtering and thresholding (Raya and Udupa, 1990; Udupa and Goncalves, 1993; Udupa et al., 1991). The resultant binary data consisted of reconstructed virtual images of each of the five bones, anatomically arranged for each imaged foot position. 2.2. Kinematic analyses
Fig. 1. Schematic illustration of commercially made foot positioning and motion constraining apparatus. The Velcro straps that secure the lower leg to the fixture and prevent motion of the tibia are not illustrated.
The analysis used to quantify tarsal joint kinematics during foot dorsiflexion–plantar flexion motion follows portions of the methodology developed by Hirsch et al. (1996, 2000) and Udupa et al. (1998) The 3-D rotations and translations of the talus, calcaneus, navicular, and cuboid were measured relative to a coordinate system (c.f. red X-, Y-, Z-axis, Fig. 2), whose origin was fixed at one point on the distal tibia (Hirsch et al., 1996). Bone motion relative to the distal tibia was determined by
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using 3DVIEWNIX to first compute the shape and volume of each bone at each position, calculate the three principal moments of inertia, and then use these moments to establish a right-handed Cartesian coordinate system located at the geometric centroid of each bone (Udupa et al., 1998). Measurement of the distances between the centroids of individual bones and the centroid of the fixed distal tibia enabled translational motion to be quantified by using established vector analysis methods (Arfken, 1985). The primary axis of rotation was coincident with the first moment of inertia, the secondary axis was coincident with the second moment of inertia, and the tertiary axis resulted from the cross product of the first two (Fig. 2). Difficulties arise when trying to define a anatomic coordinate system or to establish a coordinate axis coincident with the true axis of rotation of a bone or joint. In this study, the rotational planes of bone motion did not truly coincide with the body planes of motion. The morphology of the user-outlined hind foot bones governed how the software established the three principal axes of rotation. After determination of bone volumes by user-steered segmentation, the 3DVIEWNIX software analyzed bone morphology to determine the three principal axes of rotation, each intersecting at the geometric centroid of each bone (Udupa et al., 1998). The software labeled the first, second, and third principal axes as ‘‘1’’, ‘‘2’’, and ‘‘3’’, respectively. These
Fig. 2. The distal tibia and hind foot bones. Embedded Cartesian coordinate systems with origins at the centroid were determined by 3DVIEWNIX, and renamed by the user as axes X (dorsiflexion–plantar flexion), Y (pronation–supination), and Z (inversion–eversion). The axes are shown for the distal tibia (red axes) and the navicular (black axes).
bone-embedded axes were visualized by the user for each image of the foot in the neutral position and those that were best aligned with the medial–lateral, volar–dorsal, and caudal–distal body axes, were simply renamed the X- (plantar flexion–dorsiflexion), Y- (pronation–supination), and Z-(inversion–eversion) axis, respectively (Fig. 2). No computational operations were performed to modify the position of the software-defined principal axes. These principal axes were simply renamed as noted in clinical terms, and the designation of these axes was held constant for each subsequent position of the foot. In this way bone rotation could be tracked during foot dorsiflexion–plantar flexion motion. Rotational kinematics were determined by first computing the directional cosines of the coordinate system embedded in each bone at each successive plantar flexion–dorsiflexion position, and then by using the Cardan angle sequence (a; b; and g) to quantify bone rotational motion (Arfken, 1985). Although the software-determined bone axes did not coincide perfectly with the anatomical body plane axes (Fig. 2), care was taken to name these bone axes so that they coincided as closely as possible with the anatomical body axes. Regardless of how the bone-embedded axes were defined and named, rotation of these axes was not necessarily confined to one plane. Due to these facts, the most clinically meaningful way to analyze rotation of tarsal bones relative to the fixed distal tibia appeared to be as a series of three orderdependent rotations of each bone about the global coordinate axes by the angles a; b; and g; representing dorsiflexion–plantar flexion, pronation–supination, and inversion–eversion rotations, respectively. The output from the 3DVIEWNIX kinematic analysis listed a set of directional cosine matrices that described the orientations of each bone at each position relative to the distal tibia. From the scalar entries of this direction cosine matrix, the angles of the anatomically relevant rotations, a; b; and g were determined. Because these rotations were order-dependent, calculation of the equations for the second rotation, b; depended on the angle of the first rotation, a: Similarly, the third rotation, g; depended on the 1st and 2nd rotations. Due to the cumulative error that could be induced by this dependence, care was taken to choose the first rotation about the most mobile axis of bone rotation, which usually coincided with gross rotation of the foot (the dorsiflexion–plantar flexion plane in this study). In theory, the third rotation calculation would be the most error-prone; thus to minimize error, this axis was designated to represent the least mobile rotation axis. Specifically, inversion–eversion was chosen as the third axis of rotation because this plane was the most secure in the ankle motion device and appeared to be least mobile during gross foot dorsiflexion–plantar flexion.
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2.3. Repeatability analysis A fresh frozen navicular was harvested, stripped of all soft tissue, fixed in formalin for 72 h, and then sealed with spray polyurethane to prevent contrast medium penetration. An MR contrast medium was prepared from an aqueous solution of 5% gelatin, heated, stirred, and poured into a 2 cm 2 cm 4 cm rectangular Plexiglas box. The estimated center of this navicular was suspended at the geometric center of the box until the gelatin solution hardened. The box was supported between two Plexiglas plates by using two nylon screws through the geometric centers of the box sides and the plates. This arrangement allowed pure rotation without translation. A protractor secured to one plate quantified rotation of the box and the navicular. The base plate of the rotational component of this fixture was affixed with two nylon screws with known thread diameter and pitch. Translation was determined from the pitch of the screw and the number of turns. A total of 22 different translated positions (ranging from 1 to 28 mm) and 46 different rotations (ranging from 11 to 801) of the navicular were imaged by using the same imaging protocol and field of view as that used for the subjects. Navicular translation and rotation were done in the plane of the MR image slices, and this optimized the accuracy of the motion measurements. For each displacement, the navicular was outlined in four separate trials by the same operator. Although the imaging protocol was the same as that used for the subjects, it is important to note that because conditions used for the repeatability study were ‘‘ideal’’ and do not directly reflect the actual events occurring during hind foot bone study in the human subjects; the repeatability study serves as a ‘‘best case’’ scenario. Mean differences in translation or rotation were calculated between the mechanically determined position of the navicular and the MR calculated position. Differences among these four sets of measurements were tested by using ANOVA with the Scheffe post hoc correction. In vivo measurements of absolute (relative to the fixed distal tibia) or relative (to another hind foot
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bone) movement of each bone were analyzed relative to the angular position of the foot by fitting a least-squares line to these data. The slopes of these lines were used to quantify the relative (to the angular foot position) motion of the individual bones and to eliminate minor inter-subject variability in total range of uniplanar foot motion. The motion of each bone was compared to zero by using a two-tailed t-test. p-values less than 0.05 were considered indicative of significant differences.
3. Results The repeatability analysis of the 88 translation and 184 rotation measurements trials revealed that the mean difference between the known mechanical motion and that measured from imaging and reconstruction was 0.13 mm and 0.261 for translation and rotation, respectively. No significant differences in these values were observed among the four trials. A total of 9600 MR images (6 subjects 5 bones 5 foot positions 64 images per bone) were analyzed. Motion of each bone along each linear axis of motion (Table 1) and about each rotational axis (Table 2) was analyzed relative to the fixed tibia as a function of the angle of foot plantar flexion. Relative motion of the calcaneus, navicular and cuboid were also analyzed relative to the talus or the calcaneus as a function of the angle of plantar flexion (Table 3). Hind foot bone positions were plotted as a function of angular foot position as determined from the MR images and a least-squares line was fit to the data from each subject. Second and higher order lines were also fitted (data not shown), but no substantial improvements in fit were observed; therefore, the linear relationship was used. Fig. 3 is a representative sample of one of the plots used to obtain the tabularized data. Slopes of these lines reflect either the rotational or linear motion of a hind foot bone about (or along) the indicated axis versus the angle of foot plantar flexion. The mean range (7 std. dev.) of gross foot uniplanar motion was 40.174.91.
Table 1 Hind foot bone translation during foot plantar flexion
Talus Navicular Calcaneus Cuboid
Proximal–distal
Anterior–posterior
Medial–lateral
Resultant
0.0770.02* 0.3970.09* 0.2270.05* 0.4270.09*
0.0670.04* 0.2570.07* 0.2170.07* 0.3870.09*
0.0270.04 0.1970.05* 0.0770.08 0.2270.13*
0.1170.06* 0.5070.12* 0.3270.12* 0.6270.18*
Mean values (7std. dev.) for hind foot bone translation in the proximal–distal, anterior–posterior, or medial–lateral directions as well as the resultant (total spatial) translation, all expressed as mm of translation per degree of foot plantar flexion. Standard deviations primarily reflect subjectto-subject variability. *Denotes significant (po0:05) difference from zero. Negative signs denote linear motion in the proximal, anterior, or lateral directions. Resultant translation denotes the net translation in all three individual directions combined.
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Table 2 Rotation of the hind foot bones along the axes indicated relative to the fixed distal tibia
Talus Navicular Calcaneus Cuboid
Plantar flexion–dorsiflexion axis rotation
Inversion–eversion axis rotation
Pronation–supination axis rotation
0.4070.48* 0.5970.12* 0.4470.48* 0.7370.23*
0.0770.17 0.4570.21* 0.1870.08* 0.3870.17*
0.0270.16 0.0870.12 0.0570.21 0.0070.24
Mean (7 std. dev.) of individual bone rotation motions relative to the fixed tibia in each plane of rotational motion. Mean values are expressed as the ratio of degrees of indicated bone rotation per one degree of foot plantar flexion over the entire range of foot motion in this plane. Standard deviations primarily reflect subject-to-subject variability. * Denotes significant (po0:05) difference from zero. Negative signs denote plantar flexion, inversion, or pronation about each respective axis of rotation.
Table 3 Motion of the calcaneus, navicular, or cuboid relative to the talus or calcaneus
Talus–calcaneus Talus–navicular Calcaneus–cuboid
Plantar flexion–dorsiflexion axis rotation
Inversion–eversion axis rotation
Pronation–supination axis rotation
0.0470.10 0.0570.22 0.1170.30
0.0470.10 0.3370.27* 0.2770.13*
0.0270.24 0.0370.18 0.0970.21
Mean (7 std. dev.) angular rotation of one bone expressed relative to another as a function of foot plantar flexion angle. Units of motion are dimensionless degrees (individual bone motion) per degree (foot motion). Standard deviations primarily reflect subject-to-subject variability. * Denotes significant (po0:05) difference from zero. Negative signs denote plantar flexion, inversion, or pronation about each respective axis of rotation.
Fig. 3. Angular rotation (dorsiflexion–plantar flexion) of the talus as a function of angular rotation (same plane) of the foot. Each of these six lines represents the best linear fit of the individual talus position—foot angle data from each of the six subjects. Negative slopes of these lines indicate plantar flexion of the talus as the foot is plantar flexed.
Analyses of the translational motion of these hind foot bones as a function of foot plantar flexion angle (Table 1) showed that: (1) the talus has a small but
significant biplanar motion (e.g., 0.07 mm/deg foot motion ¼ 2.8 mm translation in the proximal–distal direction during 401 of foot plantar flexion); (2) the
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calcaneus also has biplanar motion but with a magnitude about three times that of the talus; (3) the navicular and the cuboid have triplanar motion and the amplitudes show a non-significant trend that is greater than those of the calcaneus. Compared to the distal tibia, most of the rotational motion of the hind foot bones occurred about the plane of foot motion (Table 2). In general, the hind foot bones rotated in this plane approximately one-half (53.8%) as much as the entire foot plantar flexed. The talus, for example, rotated 161 when the entire foot plantar flexed 401. While talar rotation was primarily uniaxial, motion of the navicular, the calcaneus, and the cuboid were biaxial: they also inverted while simultaneously plantar flexing (Table 2). These data permit individual bone rotation motions to be calculated based upon the overall foot motion. In addition to comparing hind foot bone motion relative to the fixed tibia, hind foot bone motion was also calculated relative to one another (Table 3). Note the virtual absence of relative motion between the calcaneus and the talus. Note also that the navicular inverts relative to the talus and the cuboid inverts relative to the calcaneus when the foot plantarflexes.
4. Discussion This study contributed new quantitative information regarding how the hind foot bones translate and rotate during controlled uniplanar foot motion. The talus, calcaneus, navicular and cuboid bones rotated in the dorsiflexion–plantar flexion plane about half as much as the entire foot rotated. The talus rotated about one axis and translated along two axes, the calcaneus rotated about two axes and translated along two axes, while the navicular and cuboid translated along three axes and rotated about two axes. Motion was virtually absent at the subtalar joint; this suggests that the talus and the calcaneus move as a unit during uniplanar foot plantar flexion. The rotational motion associated with the navicular and the cuboid was similar; the same was true for their translational motions. This supports the claim that these two bones also move as a unit. This did not occur in the talo-navicular joint; there significant inversion–eversion rotation was observed. These data are important because they: (1) provide insight into how the hind foot bones move in vivo during normal openchain motion; (2) provide a quantitative basis for comparing the results of subsequent studies of foot motion in patients with congenital or acquired foot deformities; and (3) establish a standard for normal motion in young male adults. Magnetic resonance imaging (Cahuzac et al., 2002) or computed tomography (Camacho et al., 2002) followed by 3D image reconstruction has been used by others to
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determine the spatial relationships among various bones in the hind feet of adults, normal children, and children with club foot. Kitaoka et al. (1995, 1997, 1998) have previously described the 3D kinematics of the adult hind foot by using a constrained cadaveric model with embedded radio-opaque markers. Motion of the tibiotalar, talonavicular, and subtalar joints was recorded and in found to be in agreement with the data from the present study. Udupa et al. (Stindel et al., 1999; Udupa et al., 1998) performed 3D MRI in vivo studies that partially described the motion of tarsal joints during constrained pronation–supination motion. While the data presented serve as a basis for classification of the architecture of normal and pathological feet, their motion data did not completely describe the clinically relevant 3D rotations of the tarsal bones. Lundberg et al. (1989) conducted an in vivo kinematic study of the loaded healthy adult foot moving in unconstrained dorsiflexion–plantar flexion while the subject was under local anesthesia. Foot motion was quantified by using roentgen stereophoto-grammetry to track the motions of at least three bone embedded tantalum markers. Although invasive and requiring radiation exposure, placement of tantalum beads allows a fixed invariant orthogonal coordinate system in each bone, which in turn permits calculation of order dependent rotations of one bone relative to a reference coordinate system. The Lundberg et al. study, however, reported a 601 range of dorsiflexion–plantar flexion foot motion versus the 401 range measured in the present study. Their greater range of motion may have been due to accompanying inversion–eversion or pronation–supination motions, which allow a greater arc of dorsiflexion–plantar flexion motion in the unconstrained foot (compared to the uniplanar motion-constrained by the foot-positioning fixture used here). Like the present data, virtually no subtalar motion was observed in the Lundberg study. In contrast, Lundberg et al. observed that the amount of talar dorsiflexion–plantar flexion rotation relative to the fixed tibia was about 11 per each 11 of foot plantar flexion (almost twice that of the present study). They also observed biplanar motion at the talonavicular joint rather than the uniplanar motion observed herein. Unlike the unloaded constrained foot motion of the present study, foot motion in the Lundberg study was made under load and unconstrained; this may account for the differences observed. 3D motion analyses formerly required external (skin) or bone-embedded radio-opaque markers, but offered the ability to provide more information than uniplanar radiographic goniometric measurements (Kitaoka et al., 1997; Lundberg et al., 1989). Although useful for live subjects, every external marker system is hampered by skin motion and variability in marker placement. Internal marker systems are invasive and expose subjects to ionizing radiation. Stereometry, magnetic tracking,
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and X-ray techniques can generate 3D bone motion data by using either type of marker. Computed tomography may provide better bony resolution, but MR-based techniques eliminate radiation exposure and offer the ability to clearly visualize cartilaginous anatomy. 3D MRI followed by computer analysis of joint kinematics offers the best of both worlds by objectively assigning ‘‘virtually determined’’ coordinate axes to each bone without ionizing radiation or invasive marker placement. Full dorsiflexion–plantar flexion motion of the foot is greater than the mean 401 recorded in the present study, but recall that this measurement was obtained by constraining motion to one plane. An unconstrained foot undergoing ‘‘similar’’ motion also slightly inverts and supinates and thus appears to present a greater range of motion. While the relationship of degrees of bone rotation per degree of foot plantar flexion was shown to be linear for positioning-device-constrained foot motion, this relationship could show higher order relationships if the extremes of true physiological motion were measured. Although the apparatus used in the present study induced a non-gait-relevant (constrained uniplanar) motion, its purpose was to ensure inter-subject uniformity as well as to hold the foot steady during imaging rather than to accurately imitate gait-relevant plantar flexion–dorsiflexion motion. A surprising finding was that although the foot was seemingly unable to move in the inversion–eversion plane, there was significant talonavicular and calcaneocuboid bone motion in this plane. Furthermore, these measurements were made with unloaded feet; gait-relevant axial loading during MR imaging requires equipment which was unavailable. The reproducibility study must be interpreted in light of several important factors. First, the procedure used was a ‘‘best case’’ scenario in which the navicular bone was surrounded by a contrast medium which reduced the variability in repeated bone outlining. Since one navicular was moved in one dimension, variability was optimized in the reproducibility study compared to the actual study involving biplanar and triplanar motion of four hind foot bones. Accuracy of the motion measurement may have also been enhanced by the fact that all motion (rotation and translation) in the reproducibility study was measured in the MR imaging plane, while considerable motion in one or two planes outside of the plane of imaging occurred in vivo. While reproducibility of the motion measurements were about 14 degree, the use of a mounted protractor to determine true rotation of the navicular bone suggests that the rotational accuracy of this technique was only as good as that enabled by the protractor measurement (typically 12 degree at best). Although the term motion is used throughout, it is worthy to note that the present study was not conducted
under conditions of true dynamic motion. All MR images of the hind foot were taken with the foot stationary: actual plantar flexion ‘‘motion’’ of the foot and constituent hind foot bones arose from a series of assembled static images. Weight bearing and active muscle contraction occurring during gait may cause the angular positions and rotations of the hind foot bones to be different than those presently reported. Despite these limitations, this study advances knowledge regarding the functional anatomy of the foot, shows why simple ‘‘hinged’’ models are inadequate, and provides a quantitative standard against which those with congenital or acquired foot deformities may be compared.
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Journal of Biomechanics 39 (2006) 726–733 www.elsevier.com/locate/jbiomech www.JBiomech.com
Three-dimensional in vivo motion of adult hind foot bones Brian Mattinglya, Vishwas Talwalkarb,c, Chester Tylkowskib,c, David B. Stevensb,c, Peter A. Hardya, David Pienkowskia,c, a
Center for Biomedical Engineering, University of Kentucky, Washington and Rose Streets, Lexington, KY 40507-0070, USA b Shriners Hospital for Children, 2800 Richmond Road, Lexington, KY 40502, USA c Department of Orthopaedic Surgery, School of Medicine, University of Kentucky, 740 South Limestone, Lexington, KY 40536-0284, USA Accepted 30 December 2004
Abstract Knowledge of hind foot bone motion is important for understanding gait as well as various foot pathologies, but the threedimensional (3D) motion of these bones remains incompletely understood. The purpose of this study was to quantify the motion of the talus, calcaneus, navicular, and cuboid in normal adult feet during open chain quasi-static uniplanar plantar flexion motion. Magnetic resonance images of the right feet of six normal young adult males were taken from which 3D virtual models were made of each hind foot bone. The 3D motion of these models was analyzed. Each hind foot bone rotated in the same plane about half as much as the foot (mean 0.541 of bone rotation per degree of foot motion, range 0.40–0.731 per degree of foot motion as measured relative to the fixed tibia). Talar motion was primarily uniaxial, but the calcaneus, navicular, and cuboid bones exhibited biplanar (sometimes triplanar) translation in addition to biaxial rotation. Net translational motions of these bones averaged 0.39 mm of bone translation per degree of foot motion (range 0.06–0.62 mm per degree of foot motion). These data reflect the functional anatomy of the foot, extend the findings of prior studies, provide a standard for comparison to patients with congenital or acquired foot deformities, and establish an objective reference for quantitatively assessing the efficacy of various hind foot therapies. r 2005 Elsevier Ltd. All rights reserved. Keywords: Talus; Calcaneus; Cuboid; Navicular; Hind foot
1. Introduction Knowledge of the three-dimensional (3D) motion of the hind foot bones is essential for a complete understanding of foot biomechanics. This knowledge will facilitate detection of various foot pathologies, quantify their severity, and provide an objective goal for function restoration. Previous studies have measured hind foot motion on live and cadaveric foot specimens by using externally applied goniometers, and based upon these data, have modeled hind foot motion by using combinations of simple hinges (Inman, 1991; Kitaoka Corresponding author. Department of Surgery, Division of Orthopaedic Surgery, School of Medicine, University of Kentucky, 740 South Limestone, Lexington, KY 40536-0284, USA. Tel.: +1 859 323 5533x240; fax: +1 859 323 2412. E-mail address: [email protected] (D. Pienkowski).
0021-9290/$ - see front matter r 2005 Elsevier Ltd. All rights reserved. doi:10.1016/j.jbiomech.2004.12.023
et al., 1995, 1997, 1998; Sammarco et al., 1973; Siegler et al., 1988). These models, however, were less than satisfactory because they failed to adequately describe the complex multiaxial motion of the hind foot. Magnetic resonance imaging and computer-aided analyses have recently been used to measure wrist (Gerlach et al., 2001; Snel et al., 1998) and foot (Hirsch et al., 1989, 1996, 2000; Udupa et al., 1998) motion. These techniques have enabled in vivo non-invasive quantification of 3D bone anatomy and motion. This offers the potential to generate new insight regarding the complex multiaxial motions of hind foot bones during gait and advance our knowledge of foot biomechanics. Therefore, the specific aim of the present study was to quantify the 3D translational and rotational motion of the talus, calcaneus, navicular, and cuboid bones of the normal adult hind foot during open chain quasi-static uniplanar plantar flexion–dorsiflexion motion.
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2. Methods Six male subjects (18–30 years) with normal foot and ankle motion and no known pathology or lower extremity trauma were examined by an Orthopaedic surgeon and recruited into an IRB approved study. Each subject reclined supine on the table of a 1.5 T S magnetic resonance imager and the right lower extremity was secured to a polymeric (CHAMCOTM, Miami, FL) non-weight bearing ankle motion device designed to rotate in the sagittal plane in 51 increments. This ankle motion device was placed on the gantry of the MR imager and constrained ankle motion to the sagittal plane in the field of view. The overall methodology employed follows the methods developed by Udupa et al. (1998). The foot was first secured in the positioning device and fixed at the neutral position, defined as the position at which a 901 angle is formed between the horizontal and the vertical platform against which the sole of the foot rests (Fig. 1). A 10-cm diameter radio frequency receive-only coil was placed directly underneath the foot. Scout images were acquired to locate the area from the distal tibia to the distal metatarsals. After identifying the areas of interest, a series of 64 MR images (slice thickness 1.5 mm) was obtained from the foot and ankle in the sagittal plane (pixel size ¼ 0.94 mm 0.94 mm) by using a Fast Low Angle Shot (FLASH) 3D protocol. The field of view was 240 mm 240 mm, with a 256 256 matrix and TR/TE/flip angle of 20 ms/6 ms/301. This imaging procedure was developed to optimize contrast and minimize imaging time. Imaging began with the subject’s foot at maximum dorsiflexion, and was repeated at successive 101 increments over the full range of uniplanar foot flexion motion. At maximum plantar flexion, the foot could sometimes not be flexed an
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additional 101; thus, a 51 final flexion increment was then obtained. Subjects were instructed not to actively contract the muscles controlling their foot, but to allow the ankle motion device to maintain foot position. 2.1. Image analysis Image analysis was performed by using 3DVIEWNIX, a custom-written Unix-based, X-Windows, C programming language software package (Udupa et al., 1994). The distal tibia, talus, calcaneus, navicular, and cuboid were identified and manually outlined in each MR slice by using a segmentation tool (paint). Paint allowed the margins of each bone to be smoothly traced and the perimeter accurately represented. No cartilage was included in any trace. After outlining, the area contained within each perimeter was automatically filled. Interpolation of the segmented object on each slice was performed to reconstruct the 3D structure of each bone. A 3D Gaussian filter was used to smooth the surface of the newly interpolated 3D image. Thresholding further clarified the reconstructed 3D bone image by assigning a binary 0 value to all cells whose gray scale intensity were less than 110 (on an arbitrary 256 point gray scale based on the MRI scan); all cells with gray scale intensity of 110 or greater received a binary 1 value. Since the entire tibia was not in the scanner’s field of view, care was taken to anatomically define the distal tibia by means of the epiphyseal scar. For each set of 64 sagittal slices, the slice containing the largest length of epiphyseal scar was identified and a straight line was drawn between the ends of this scar. This straight line was then used as the proximal border of the distal tibia for subsequent slices of the same foot, and the anterior, posterior, and distal borders were identified by the bony outline distal to this proximal border. This procedure was done to ensure that the ‘distal tibia’ could be identified and reproducibly outlined for each subject. 3D reconstruction of each bone was performed by interpolation, 3D Gaussian filtering and thresholding (Raya and Udupa, 1990; Udupa and Goncalves, 1993; Udupa et al., 1991). The resultant binary data consisted of reconstructed virtual images of each of the five bones, anatomically arranged for each imaged foot position. 2.2. Kinematic analyses
Fig. 1. Schematic illustration of commercially made foot positioning and motion constraining apparatus. The Velcro straps that secure the lower leg to the fixture and prevent motion of the tibia are not illustrated.
The analysis used to quantify tarsal joint kinematics during foot dorsiflexion–plantar flexion motion follows portions of the methodology developed by Hirsch et al. (1996, 2000) and Udupa et al. (1998) The 3-D rotations and translations of the talus, calcaneus, navicular, and cuboid were measured relative to a coordinate system (c.f. red X-, Y-, Z-axis, Fig. 2), whose origin was fixed at one point on the distal tibia (Hirsch et al., 1996). Bone motion relative to the distal tibia was determined by
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using 3DVIEWNIX to first compute the shape and volume of each bone at each position, calculate the three principal moments of inertia, and then use these moments to establish a right-handed Cartesian coordinate system located at the geometric centroid of each bone (Udupa et al., 1998). Measurement of the distances between the centroids of individual bones and the centroid of the fixed distal tibia enabled translational motion to be quantified by using established vector analysis methods (Arfken, 1985). The primary axis of rotation was coincident with the first moment of inertia, the secondary axis was coincident with the second moment of inertia, and the tertiary axis resulted from the cross product of the first two (Fig. 2). Difficulties arise when trying to define a anatomic coordinate system or to establish a coordinate axis coincident with the true axis of rotation of a bone or joint. In this study, the rotational planes of bone motion did not truly coincide with the body planes of motion. The morphology of the user-outlined hind foot bones governed how the software established the three principal axes of rotation. After determination of bone volumes by user-steered segmentation, the 3DVIEWNIX software analyzed bone morphology to determine the three principal axes of rotation, each intersecting at the geometric centroid of each bone (Udupa et al., 1998). The software labeled the first, second, and third principal axes as ‘‘1’’, ‘‘2’’, and ‘‘3’’, respectively. These
Fig. 2. The distal tibia and hind foot bones. Embedded Cartesian coordinate systems with origins at the centroid were determined by 3DVIEWNIX, and renamed by the user as axes X (dorsiflexion–plantar flexion), Y (pronation–supination), and Z (inversion–eversion). The axes are shown for the distal tibia (red axes) and the navicular (black axes).
bone-embedded axes were visualized by the user for each image of the foot in the neutral position and those that were best aligned with the medial–lateral, volar–dorsal, and caudal–distal body axes, were simply renamed the X- (plantar flexion–dorsiflexion), Y- (pronation–supination), and Z-(inversion–eversion) axis, respectively (Fig. 2). No computational operations were performed to modify the position of the software-defined principal axes. These principal axes were simply renamed as noted in clinical terms, and the designation of these axes was held constant for each subsequent position of the foot. In this way bone rotation could be tracked during foot dorsiflexion–plantar flexion motion. Rotational kinematics were determined by first computing the directional cosines of the coordinate system embedded in each bone at each successive plantar flexion–dorsiflexion position, and then by using the Cardan angle sequence (a; b; and g) to quantify bone rotational motion (Arfken, 1985). Although the software-determined bone axes did not coincide perfectly with the anatomical body plane axes (Fig. 2), care was taken to name these bone axes so that they coincided as closely as possible with the anatomical body axes. Regardless of how the bone-embedded axes were defined and named, rotation of these axes was not necessarily confined to one plane. Due to these facts, the most clinically meaningful way to analyze rotation of tarsal bones relative to the fixed distal tibia appeared to be as a series of three orderdependent rotations of each bone about the global coordinate axes by the angles a; b; and g; representing dorsiflexion–plantar flexion, pronation–supination, and inversion–eversion rotations, respectively. The output from the 3DVIEWNIX kinematic analysis listed a set of directional cosine matrices that described the orientations of each bone at each position relative to the distal tibia. From the scalar entries of this direction cosine matrix, the angles of the anatomically relevant rotations, a; b; and g were determined. Because these rotations were order-dependent, calculation of the equations for the second rotation, b; depended on the angle of the first rotation, a: Similarly, the third rotation, g; depended on the 1st and 2nd rotations. Due to the cumulative error that could be induced by this dependence, care was taken to choose the first rotation about the most mobile axis of bone rotation, which usually coincided with gross rotation of the foot (the dorsiflexion–plantar flexion plane in this study). In theory, the third rotation calculation would be the most error-prone; thus to minimize error, this axis was designated to represent the least mobile rotation axis. Specifically, inversion–eversion was chosen as the third axis of rotation because this plane was the most secure in the ankle motion device and appeared to be least mobile during gross foot dorsiflexion–plantar flexion.
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2.3. Repeatability analysis A fresh frozen navicular was harvested, stripped of all soft tissue, fixed in formalin for 72 h, and then sealed with spray polyurethane to prevent contrast medium penetration. An MR contrast medium was prepared from an aqueous solution of 5% gelatin, heated, stirred, and poured into a 2 cm 2 cm 4 cm rectangular Plexiglas box. The estimated center of this navicular was suspended at the geometric center of the box until the gelatin solution hardened. The box was supported between two Plexiglas plates by using two nylon screws through the geometric centers of the box sides and the plates. This arrangement allowed pure rotation without translation. A protractor secured to one plate quantified rotation of the box and the navicular. The base plate of the rotational component of this fixture was affixed with two nylon screws with known thread diameter and pitch. Translation was determined from the pitch of the screw and the number of turns. A total of 22 different translated positions (ranging from 1 to 28 mm) and 46 different rotations (ranging from 11 to 801) of the navicular were imaged by using the same imaging protocol and field of view as that used for the subjects. Navicular translation and rotation were done in the plane of the MR image slices, and this optimized the accuracy of the motion measurements. For each displacement, the navicular was outlined in four separate trials by the same operator. Although the imaging protocol was the same as that used for the subjects, it is important to note that because conditions used for the repeatability study were ‘‘ideal’’ and do not directly reflect the actual events occurring during hind foot bone study in the human subjects; the repeatability study serves as a ‘‘best case’’ scenario. Mean differences in translation or rotation were calculated between the mechanically determined position of the navicular and the MR calculated position. Differences among these four sets of measurements were tested by using ANOVA with the Scheffe post hoc correction. In vivo measurements of absolute (relative to the fixed distal tibia) or relative (to another hind foot
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bone) movement of each bone were analyzed relative to the angular position of the foot by fitting a least-squares line to these data. The slopes of these lines were used to quantify the relative (to the angular foot position) motion of the individual bones and to eliminate minor inter-subject variability in total range of uniplanar foot motion. The motion of each bone was compared to zero by using a two-tailed t-test. p-values less than 0.05 were considered indicative of significant differences.
3. Results The repeatability analysis of the 88 translation and 184 rotation measurements trials revealed that the mean difference between the known mechanical motion and that measured from imaging and reconstruction was 0.13 mm and 0.261 for translation and rotation, respectively. No significant differences in these values were observed among the four trials. A total of 9600 MR images (6 subjects 5 bones 5 foot positions 64 images per bone) were analyzed. Motion of each bone along each linear axis of motion (Table 1) and about each rotational axis (Table 2) was analyzed relative to the fixed tibia as a function of the angle of foot plantar flexion. Relative motion of the calcaneus, navicular and cuboid were also analyzed relative to the talus or the calcaneus as a function of the angle of plantar flexion (Table 3). Hind foot bone positions were plotted as a function of angular foot position as determined from the MR images and a least-squares line was fit to the data from each subject. Second and higher order lines were also fitted (data not shown), but no substantial improvements in fit were observed; therefore, the linear relationship was used. Fig. 3 is a representative sample of one of the plots used to obtain the tabularized data. Slopes of these lines reflect either the rotational or linear motion of a hind foot bone about (or along) the indicated axis versus the angle of foot plantar flexion. The mean range (7 std. dev.) of gross foot uniplanar motion was 40.174.91.
Table 1 Hind foot bone translation during foot plantar flexion
Talus Navicular Calcaneus Cuboid
Proximal–distal
Anterior–posterior
Medial–lateral
Resultant
0.0770.02* 0.3970.09* 0.2270.05* 0.4270.09*
0.0670.04* 0.2570.07* 0.2170.07* 0.3870.09*
0.0270.04 0.1970.05* 0.0770.08 0.2270.13*
0.1170.06* 0.5070.12* 0.3270.12* 0.6270.18*
Mean values (7std. dev.) for hind foot bone translation in the proximal–distal, anterior–posterior, or medial–lateral directions as well as the resultant (total spatial) translation, all expressed as mm of translation per degree of foot plantar flexion. Standard deviations primarily reflect subjectto-subject variability. *Denotes significant (po0:05) difference from zero. Negative signs denote linear motion in the proximal, anterior, or lateral directions. Resultant translation denotes the net translation in all three individual directions combined.
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Table 2 Rotation of the hind foot bones along the axes indicated relative to the fixed distal tibia
Talus Navicular Calcaneus Cuboid
Plantar flexion–dorsiflexion axis rotation
Inversion–eversion axis rotation
Pronation–supination axis rotation
0.4070.48* 0.5970.12* 0.4470.48* 0.7370.23*
0.0770.17 0.4570.21* 0.1870.08* 0.3870.17*
0.0270.16 0.0870.12 0.0570.21 0.0070.24
Mean (7 std. dev.) of individual bone rotation motions relative to the fixed tibia in each plane of rotational motion. Mean values are expressed as the ratio of degrees of indicated bone rotation per one degree of foot plantar flexion over the entire range of foot motion in this plane. Standard deviations primarily reflect subject-to-subject variability. * Denotes significant (po0:05) difference from zero. Negative signs denote plantar flexion, inversion, or pronation about each respective axis of rotation.
Table 3 Motion of the calcaneus, navicular, or cuboid relative to the talus or calcaneus
Talus–calcaneus Talus–navicular Calcaneus–cuboid
Plantar flexion–dorsiflexion axis rotation
Inversion–eversion axis rotation
Pronation–supination axis rotation
0.0470.10 0.0570.22 0.1170.30
0.0470.10 0.3370.27* 0.2770.13*
0.0270.24 0.0370.18 0.0970.21
Mean (7 std. dev.) angular rotation of one bone expressed relative to another as a function of foot plantar flexion angle. Units of motion are dimensionless degrees (individual bone motion) per degree (foot motion). Standard deviations primarily reflect subject-to-subject variability. * Denotes significant (po0:05) difference from zero. Negative signs denote plantar flexion, inversion, or pronation about each respective axis of rotation.
Fig. 3. Angular rotation (dorsiflexion–plantar flexion) of the talus as a function of angular rotation (same plane) of the foot. Each of these six lines represents the best linear fit of the individual talus position—foot angle data from each of the six subjects. Negative slopes of these lines indicate plantar flexion of the talus as the foot is plantar flexed.
Analyses of the translational motion of these hind foot bones as a function of foot plantar flexion angle (Table 1) showed that: (1) the talus has a small but
significant biplanar motion (e.g., 0.07 mm/deg foot motion ¼ 2.8 mm translation in the proximal–distal direction during 401 of foot plantar flexion); (2) the
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calcaneus also has biplanar motion but with a magnitude about three times that of the talus; (3) the navicular and the cuboid have triplanar motion and the amplitudes show a non-significant trend that is greater than those of the calcaneus. Compared to the distal tibia, most of the rotational motion of the hind foot bones occurred about the plane of foot motion (Table 2). In general, the hind foot bones rotated in this plane approximately one-half (53.8%) as much as the entire foot plantar flexed. The talus, for example, rotated 161 when the entire foot plantar flexed 401. While talar rotation was primarily uniaxial, motion of the navicular, the calcaneus, and the cuboid were biaxial: they also inverted while simultaneously plantar flexing (Table 2). These data permit individual bone rotation motions to be calculated based upon the overall foot motion. In addition to comparing hind foot bone motion relative to the fixed tibia, hind foot bone motion was also calculated relative to one another (Table 3). Note the virtual absence of relative motion between the calcaneus and the talus. Note also that the navicular inverts relative to the talus and the cuboid inverts relative to the calcaneus when the foot plantarflexes.
4. Discussion This study contributed new quantitative information regarding how the hind foot bones translate and rotate during controlled uniplanar foot motion. The talus, calcaneus, navicular and cuboid bones rotated in the dorsiflexion–plantar flexion plane about half as much as the entire foot rotated. The talus rotated about one axis and translated along two axes, the calcaneus rotated about two axes and translated along two axes, while the navicular and cuboid translated along three axes and rotated about two axes. Motion was virtually absent at the subtalar joint; this suggests that the talus and the calcaneus move as a unit during uniplanar foot plantar flexion. The rotational motion associated with the navicular and the cuboid was similar; the same was true for their translational motions. This supports the claim that these two bones also move as a unit. This did not occur in the talo-navicular joint; there significant inversion–eversion rotation was observed. These data are important because they: (1) provide insight into how the hind foot bones move in vivo during normal openchain motion; (2) provide a quantitative basis for comparing the results of subsequent studies of foot motion in patients with congenital or acquired foot deformities; and (3) establish a standard for normal motion in young male adults. Magnetic resonance imaging (Cahuzac et al., 2002) or computed tomography (Camacho et al., 2002) followed by 3D image reconstruction has been used by others to
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determine the spatial relationships among various bones in the hind feet of adults, normal children, and children with club foot. Kitaoka et al. (1995, 1997, 1998) have previously described the 3D kinematics of the adult hind foot by using a constrained cadaveric model with embedded radio-opaque markers. Motion of the tibiotalar, talonavicular, and subtalar joints was recorded and in found to be in agreement with the data from the present study. Udupa et al. (Stindel et al., 1999; Udupa et al., 1998) performed 3D MRI in vivo studies that partially described the motion of tarsal joints during constrained pronation–supination motion. While the data presented serve as a basis for classification of the architecture of normal and pathological feet, their motion data did not completely describe the clinically relevant 3D rotations of the tarsal bones. Lundberg et al. (1989) conducted an in vivo kinematic study of the loaded healthy adult foot moving in unconstrained dorsiflexion–plantar flexion while the subject was under local anesthesia. Foot motion was quantified by using roentgen stereophoto-grammetry to track the motions of at least three bone embedded tantalum markers. Although invasive and requiring radiation exposure, placement of tantalum beads allows a fixed invariant orthogonal coordinate system in each bone, which in turn permits calculation of order dependent rotations of one bone relative to a reference coordinate system. The Lundberg et al. study, however, reported a 601 range of dorsiflexion–plantar flexion foot motion versus the 401 range measured in the present study. Their greater range of motion may have been due to accompanying inversion–eversion or pronation–supination motions, which allow a greater arc of dorsiflexion–plantar flexion motion in the unconstrained foot (compared to the uniplanar motion-constrained by the foot-positioning fixture used here). Like the present data, virtually no subtalar motion was observed in the Lundberg study. In contrast, Lundberg et al. observed that the amount of talar dorsiflexion–plantar flexion rotation relative to the fixed tibia was about 11 per each 11 of foot plantar flexion (almost twice that of the present study). They also observed biplanar motion at the talonavicular joint rather than the uniplanar motion observed herein. Unlike the unloaded constrained foot motion of the present study, foot motion in the Lundberg study was made under load and unconstrained; this may account for the differences observed. 3D motion analyses formerly required external (skin) or bone-embedded radio-opaque markers, but offered the ability to provide more information than uniplanar radiographic goniometric measurements (Kitaoka et al., 1997; Lundberg et al., 1989). Although useful for live subjects, every external marker system is hampered by skin motion and variability in marker placement. Internal marker systems are invasive and expose subjects to ionizing radiation. Stereometry, magnetic tracking,
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and X-ray techniques can generate 3D bone motion data by using either type of marker. Computed tomography may provide better bony resolution, but MR-based techniques eliminate radiation exposure and offer the ability to clearly visualize cartilaginous anatomy. 3D MRI followed by computer analysis of joint kinematics offers the best of both worlds by objectively assigning ‘‘virtually determined’’ coordinate axes to each bone without ionizing radiation or invasive marker placement. Full dorsiflexion–plantar flexion motion of the foot is greater than the mean 401 recorded in the present study, but recall that this measurement was obtained by constraining motion to one plane. An unconstrained foot undergoing ‘‘similar’’ motion also slightly inverts and supinates and thus appears to present a greater range of motion. While the relationship of degrees of bone rotation per degree of foot plantar flexion was shown to be linear for positioning-device-constrained foot motion, this relationship could show higher order relationships if the extremes of true physiological motion were measured. Although the apparatus used in the present study induced a non-gait-relevant (constrained uniplanar) motion, its purpose was to ensure inter-subject uniformity as well as to hold the foot steady during imaging rather than to accurately imitate gait-relevant plantar flexion–dorsiflexion motion. A surprising finding was that although the foot was seemingly unable to move in the inversion–eversion plane, there was significant talonavicular and calcaneocuboid bone motion in this plane. Furthermore, these measurements were made with unloaded feet; gait-relevant axial loading during MR imaging requires equipment which was unavailable. The reproducibility study must be interpreted in light of several important factors. First, the procedure used was a ‘‘best case’’ scenario in which the navicular bone was surrounded by a contrast medium which reduced the variability in repeated bone outlining. Since one navicular was moved in one dimension, variability was optimized in the reproducibility study compared to the actual study involving biplanar and triplanar motion of four hind foot bones. Accuracy of the motion measurement may have also been enhanced by the fact that all motion (rotation and translation) in the reproducibility study was measured in the MR imaging plane, while considerable motion in one or two planes outside of the plane of imaging occurred in vivo. While reproducibility of the motion measurements were about 14 degree, the use of a mounted protractor to determine true rotation of the navicular bone suggests that the rotational accuracy of this technique was only as good as that enabled by the protractor measurement (typically 12 degree at best). Although the term motion is used throughout, it is worthy to note that the present study was not conducted
under conditions of true dynamic motion. All MR images of the hind foot were taken with the foot stationary: actual plantar flexion ‘‘motion’’ of the foot and constituent hind foot bones arose from a series of assembled static images. Weight bearing and active muscle contraction occurring during gait may cause the angular positions and rotations of the hind foot bones to be different than those presently reported. Despite these limitations, this study advances knowledge regarding the functional anatomy of the foot, shows why simple ‘‘hinged’’ models are inadequate, and provides a quantitative standard against which those with congenital or acquired foot deformities may be compared.
Acknowledgments We thank Kosair Charities, Inc. of Louisville, KY, the Shriners Hospitals for Children, the Center for Biomedical Engineering and the Department of Orthopaedic Surgery at the University of Kentucky for their support. We also thank Christin Minter for technical help. References Arfken, G., 1985. Mathematical Methods for Physicists. Academic Press, New York. Cahuzac, J.P., Navascues, J., Baunin, C., Salles De Gauzy, J., Estivalezes, E., Swider, P., 2002. Assessment of the position of the navicular by three-dimensional magnetic resonance imaging in infant foot deformities. Journal of Pediatric Orthopaedics—Part B 11 (2), 134–138. Camacho, D.L., Ledoux, W.R., Rohr, E.S., Sangeorzan, B.J., Ching, R.P., 2002. A three-dimensional, anatomically detailed foot model: a foundation for a finite element simulation and means of quantifying foot-bone position. Journal of Rehabilitation Research and Development 39 (3), 401–410. Gerlach, D., Blazar, P.E., Lawton, J.L., Pienkowski, D., 2001. In vivo three-dimensional motion of the carpus is more complicated than previously described. 47th Annual Meeting of the Orthopaedic Research Society, San Francisco, CA. Hirsch, B.E., Udupa, J.K., Roberts, D., 1989. Three-dimensional reconstruction of the foot from computed tomography scans. Journal of the American Podiatric Medical Association 79 (8), 384–394. Hirsch, B.E., Udupa, J.K., Samarasekera, S., 1996. New method of studying joint kinematics from three-dimensional reconstructions of MRI data. Journal of the American Podiatric Medical Association 86 (1), 4–15. Hirsch, B.E., Udupa, J.K., Stindel, E., 2000. Tarsal joint kinematics via 3d imaging. Critical Reviews in Diagnostic Imaging 41 (6), 403–449. Inman, V.T., 1991. Joints of the Ankle. Williams & Wilkins, Baltimore. Kitaoka, H.B., Lundberg, A., Luo, Z.P., 1995. Kinematics of the normal arch of the foot and ankle under physiologic loading. Foot and Ankle 16 (8), 492–499. Kitaoka, H.B., Luo, Z.P., An, K.N., 1997. Three-dimensional analysis of normal ankle and foot mobility. American Journal of Sports Medicine 25 (2), 238–242.
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