| | Determination of subtalar joint axis location by restriction of talocrural joint motionReceived 15 November 2005; received in revised form 23 December 2005; accepted 3 January 2006. published online 03 February 2006. Abstract The location of the subtalar joint axis is an important determinant of the mechanical function of the foot. The moments of muscle forces and of the ground reaction force about the subtalar joint are dependent upon the location of this joint axis. There is substantial variation in subtalar axis location across subjects, but current methods for determining its location are often invasive or involve expensive imaging protocols. A novel technique for location of the subtalar axis is presented in which the talocrural joint is passively immobilized so that motion of the tibia relative to the calcaneus can be used to estimate the subtalar axis. This paper presents results of cadaver testing in which accuracy of the technique was assessed by comparing helical axes computed from calcaneus-tibia bone motions to axes computed from calcaneus-talus bone motions. Only small motions at the talocrural joint were observed, and good estimates of the subtalar axis (errors less than 15° and 2 mm) were achieved in four of six specimens. 1. Introduction  Abnormal subtalar joint moments can impair the function of the foot and lower extremity and may lead to a breakdown in foot structure and painful pathology. The position and orientation of the subtalar joint axis in three-dimensional space relative to the anatomical structures of the foot directly determine the subtalar joint moments of muscle, ligament and ground reaction forces. Determining the location of the subtalar axis in individual patients is an important goal because the axis location varies substantially from person to person [1], [2], [3], [4]. Non-invasive location of joint centers from measured motion of skin markers has been successfully achieved for the hip [5], [6], but there is a need for a similar method for locating the subtalar joint axis. Such a method would be useful for the creation of realistic musculoskeletal models, for accurate quantitative assessment of mechanics in the treatment of foot and lower extremity pathology and gait disorders [7]. Further, knowledge of the location of the subtalar axis would permit estimations of the moment about the subtalar joint in clinical gait analysis. Invasive in vivo [3] and in vitro [1], [2], [4], [8] techniques have been used to locate the subtalar joint axis by tracking the talus and calcaneus using bone-mounted markers. Image-based methods may prove useful for locating the subtalar axis [9], but a non-invasive method that utilizes skin-mounted markers may be better suited for clinical gait analysis in which such markers are already used. The use of skin-mounted markers for this purpose presents a problem because the talus cannot be tracked with skin-mounted markers. Measured in vivo ankle complex kinematics generally includes simultaneous motion about both the subtalar joint (between the calcaneus and talus) and talocrural joint (between the talus and tibia), which makes locating the axes of the individual joints difficult. Several methods suitable for use with clinical gait analysis have been proposed for locating the subtalar joint axis. Biaxial optimization methods [10], [11] involve using an optimization algorithm to estimate the location of two revolute axes based on measured motion across the joint complex. Estimates of both the talocrural and subtalar anatomical joint axes can be obtained; however, the accuracy of these estimates may be limited [12]. Methods involving palpation of the foot [13], [14] or visual location of points on the skin undergoing the least movement [15] have been proposed, but the accuracy of these methods has not been demonstrated. We propose a new technique for estimating the three-dimensional location of the subtalar joint axis in which subtalar motions are applied while attempting to passively and non-invasively immobilize the talocrural joint using a custom-designed device. With the talocrural joint effectively immobile, helical axis decomposition of measured calcaneus-tibia motion is used to estimate the location of the subtalar axis. The accuracy of the technique was assessed in cadaver specimens by comparing helical axes computed from calcaneus-tibia (CAL-TIB) bone motion to those computed from calcaneus-talus (CAL-TAL) bone motion (i.e., the true motion of the subtalar joint). The amount and nature of talocrural motion was also quantified. The ultimate goal of this work is the development and validation of a technique for determining the location of the subtalar axis that may be integrated into existing clinical gait analysis procedures. 2. Methods 2.1. Specimen preparation Six fresh-frozen cadaveric lower leg specimens were tested (donor ages 79, 56, 68, 74, 77, 56; sexes M, M, M, M, M, F; sides R, R, R, L, L, L). Specimens 2 and 5 appeared to be slightly cavus, and the remaining specimens appeared to have a normal arch posture. The specimens were thawed and sectioned approximately 35cm above the plantar surface of the foot. All soft tissues except for the Achilles tendon were removed from the most proximal 10cm of each specimen (Fig. 1). The fibula was fixed to the tibia proximally using a screw, while maintaining an interosseous gap. An aluminum and steel tibia rod assembly was attached to the proximal tibia using set screws. The tibia rod was aligned with the long axis of the tibia. 2.2. Device for applying subtalar motions A custom-designed device (Fig. 1) was used to apply motion about the subtalar joint while attempting to immobilize the talocrural joint passively (i.e., non-surgically). The tibia rod was fastened to the device with the foot hanging down. The three main components of the device were: (1) a 27cm medio-lateral forefoot bar, attached to the plantar surface of the forefoot using a nylon cable tie; (2) a 27cm control bar, approximately 50cm above and parallel to the forefoot bar, which rotated in the frontal plane about a fixed hinge; and (3) 1.5mm diameter flexible masonry cords that connected the bars to one another at their ends. (Trials were also performed with a deviated transverse plane orientation of the control bar and forefoot bar, but accuracy results were not consistently better or worse than those reported.) Prior to the motion trials, the vertical position of the specimen was adjusted to place the foot in approximately 5°–10° of ankle dorsiflexion. The superior surface of the talus that articulates with the tibia and fibula is wedge-shaped, with the anterior width being larger than the posterior width [1], [16]. Thus with the ankle in neutral position or dorsiflexed, the wider part of the talus is positioned within the ankle mortise, perhaps reducing the amount of motion possible at the talocrural joint in the frontal and transverse planes [17]. Further, passive tension in the Achilles tendon is increased in dorsiflexion, which increases the compressive forces within the talocrural joint and may further stabilize the talus. Clinicians often assess the subtalar joint in a slightly dorsiflexed ankle position due to reduced medio-lateral mobility in the talocrural joint [18]. The Achilles tendon was clamped in series with a spring scale and turnbuckle to the test device, and a tension of 25N was set prior to the testing. This magnitude was intended to roughly approximate the tendon tension that would be present in vivo with the foot in dorsiflexion (although in the pilot specimen, axis results were not affected substantially by the presence of Achilles force). Motion was applied manually by rotating the control bar, which rotated the forefoot. The tester could control only the speed and range of the motion through rotation of the control bar and could not control the actual movement path taken by the foot. The same tester applied motions for all specimens. Fig. 1 shows the orientation of the forefoot bar at the start of a trial, but during the motions this bar was free to change orientation (including in the transverse plane), and thus did not restrict foot motion to the frontal plane. 2.4. Testing protocol Anatomical landmarks were located (see Fig. 2) relative to the bone-fixed segment markers using a two-marker pointer during a series of static trials with the specimen held in an anatomically-neutral position. Subsequent motion trials involved rotating the control bar back and forth to induce motion of the foot relative to the tibia and measuring the motion of the tibia, talus, and calcaneus segment markers. A trial consisted of approximately six cycles of motion in 30s with the endpoints of rotational movement determined by the point where passive resistance was felt by the tester. Ten trials were performed for each specimen. Specimen 1 was a pilot specimen that underwent a slightly different testing protocol: five trials were performed; the specimen had all soft tissues except ligaments proximal to the midfoot removed; and the testing apparatus included a forefoot plate that was deviated so that it formed an angle of approximately 20° (directed posteromedially) with the frontal plane instead of being purely medio-lateral. 2.5. Data processing The static trial data were used to compute the position of each anatomical landmark, establish body-fixed anatomical coordinate systems based on these landmarks (see Fig. 2), and compute the invariant positions of the segment markers relative to these coordinate systems. The motion data were filtered in Matlab using a fourth order, low-pass Butterworth filter with a cut-off frequency of 10Hz and then systematically resampled to change the sampling frequency from 100 to 10Hz. Global rigid-body kinematics of the anatomical coordinate systems were computed from the motion data using a least-squares method [19]. Finite helical axes were computed [20] for both the CAL-TAL and the CAL-TIB relative motions for every possible pair of time frames. Inclination angle and deviation angle of helical axes were defined relative to the calcaneus anatomical coordinate system, with the inclination angle measured from the xc–zc plane (superior–anterior being positive) and the deviation angle measured from the xc–yc plane (medial–anterior being positive). A mode (i.e., the most frequently occurring) helical axis was computed for both the CAL-TAL and CAL-TIB motions, for each trial. The mode was used due to the skewed nature and outliers present in the helical axes [21]. Four parameters (the minimum number required) were computed that fully defined each individual axis. The first two parameters were the coordinates of the intersection of the axis with a reference plane that was positioned at the posterior heel point with its normal pointing in the direction computed by adding all the helical axis unit direction vectors together. The third and fourth parameters were the inclination and deviation angles of the axis. Using histogram bin sizes of 1mm for the two positional parameters and 1° for the two orientation parameters, each axis was effectively binned by rounding each of its four parameters to the nearest millimeter or degree. The mode axis was then determined by finding the most frequently occurring set of the four (rounded) parameters. Intraspecimen repeatability in the orientations of these mode axes was assessed by computing the intraclass correlation coefficient for the inclination and deviation angles. The CAL-TIB mode axis location was compared to the CAL-TAL axis location to assess the accuracy of the CAL-TIB axis as an estimate of the subtalar joint axis location. The comparison resulted in three orientation differences (the angle between the axes, difference in inclination angles, and difference in deviation angles) and one position difference. The position difference was computed as the minimum distance between the axes within a region beginning at the posterior heel and extending to 10cm anterior from this point. Rotations about the talocrural joint were quantified by decomposing the rotation submatrix of the transformation matrices that described the motion of the talus relative to the tibia. Using a Z–X–Y fixed (with respect to tibia) angles convention, three angles, α, β, and γ, which described motion in the sagittal, frontal, and transverse planes of the tibia, respectively, were computed for each frame. Thus, for each frame the talus orientation could be reconstructed by: (1) rotating α degrees about the (fixed) tibia zt; (2) rotating β degrees about xt; and (3) rotating γ degrees about yt. Additionally, the translation components x, y, and z were taken directly from the transformation matrix. Ranges in α, β, γ, x, y, and z during a trial indicated the amount of talus movement relative to the tibia. It should be noted that translations x, y, and z were affected by the choice of how the anatomical coordinate systems were established. 3. Results The angle between the CAL-TIB and the CAL-TAL axes ranged from 1.7° to 27.4° across the six specimens (Fig. 3). The minimum distance ranged from 0.2 to 5.2mm (Fig. 4). These differences were less than 15° and 2mm for all trials of four specimens, and less than 4° and 2mm for two of these same four. The intraspecimen standard deviations in the inclination and deviation angles ranged from 0.3° to 1.5° for the CAL-TIB axes and 0.0° to 0.8° for the CAL-TAL axes (Table 1). The intraclass correlation coefficients were greater than 0.98 for the inclination and deviation angles for both axes, indicating that 98% of the variation in these angles was due to interspecimen differences. | a Three degrees was subtracted from the deviation angles of Inman [1] in order for them to be approximately measured from a sagittal plane passing through the second metatarsal (assuming that adjacent metatarsal heads were separated by 6°). |
Specimens 1 and 2, the specimens with the smallest axis location errors, exhibited smaller amounts of rotation of the talus with respect to the tibia than did the other specimens in both the sagittal and frontal planes (Table 2, Fig. 5). For all specimens, rotations were greater in the sagittal plane than in the other two planes. Sagittal rotations, averaged across intraspecimen trials, ranged from 2.8° to 7.1° in the six specimens, while rotations in the frontal and transverse planes ranged from 0.5° to 4.2° and 0.6° to 6.6°, respectively. 4. Discussion The CAL-TIB axis determined by these tests was a good approximation of the subtalar (CAL-TAL) axis in some of the specimens (Fig. 3, Fig. 4). In four of six specimens, orientation differences between the CAL-TIB and CAL-TAL axes were considerably less than previously measured interspecimen variability in subtalar axis orientation angles (Inman [1] reported that the two angles of the axis relative to anatomical planes had interspecimen ranges of 43° and 48°), suggesting that this technique is potentially useful for subject-specific axis location. Given these ranges, angular errors of 5° and positional errors of 3–5mm in axis location are reasonable goals for applications in clinical gait analysis and musculoskeletal modeling. Such levels of accuracy were met in Specimens 1 and 2, but improvements are required for the others. Repeatability across intraspecimen trials in determining both the CAL-TIB and CAL-TAL axes was good (Table 1). The orientations of the CAL-TAL axes are similar to those previously reported [1], [2] (Table 1). The inclination angle of the CAL-TIB axis was consistently lower than that of the CAL-TAL axis, likely because the CAL-TIB axis was influenced by small amounts of motion that occurred about the more horizontal talocrural joint. The talocrural joint was nearly immobilized in Specimens 1 and 2 (Table 2), and the most accurate estimates of the subtalar axis by the CAL-TIB axis were found for these specimens (Fig. 3, Fig. 4). Rotations in the frontal and transverse planes were generally small for all specimens. Sagittal plane rotations, however, were larger than these (Table 2). The motion at the ankle complex involved primarily subtalar motion because (1) the center of the forefoot bar (and thus the forefoot) was held approximately at the same vertical height during the motions, and (2) compliance in the talocrural joint may have been reduced because the foot was in slight dorsiflexion. Current efforts to improve the technique are focused on reducing sagittal plane movements at the talocrural joint. These were the largest talocrural rotations we observed (Table 2), perhaps because the sagittal plane moment about the talocrural joint varied during foot movements. The forces applied to the forefoot (via the cords and forefoot bar) to hold the ankle in dorsiflexion varied during the motion and were unknown and uncontrolled. This uncontrollability, combined with anatomical differences between specimens, likely led to the differences between specimens in accuracy of the technique and amount of movement about the talocrural joint. The primary limitation of the present study is that the technique was implemented on a cadaver model to simulate implementation in vivo. The Achilles tendon was tensioned but there was no plantar heel load, and the general lack of physiological loading that accompanies in vitro testing may have affected the results. Non-invasive in vivo implementation would involve tracking skin-mounted markers (instead of bone-mounted markers), which would likely negatively affect accuracy of the technique. A single fixed axis was fit, whereas the actual subtalar axis varies for different types of movements [3], [8] and during these movements [2], [3], [4]. Alternative methods have been proposed for computing a single representative axis [22] but were not employed in this study. Further, alternatives to the hinge model of the subtalar joint, such as the pes acetabulum model [23] may be more suitable for some persons or applications. In assessing intraspecimen repeatability, all trials were performed in one session and without taking out and replacing the specimen into the testing device. The repeatability may have also been influenced by the discretization that followed from the use of the mode. Further work is underway to develop a modified device that applies a constant talocrural moment during the applied subtalar motions. Such improvements may further reduce sagittal plane talocrural rotations and improve the accuracy of estimates of the subtalar axis from CAL-TIB motion. Future work should also involve assessing accuracy of the method in vivo with skin-mounted markers. Acknowledgments The authors would like to thank Andrea Cereatti for valuable discussions. This work was supported by grant number BES-0134217 from the National Science Foundation. References [1]. [1]Inman VT. The joints of the ankle. Baltimore: Williams and Wilkins; 1976;. [2]. [2]van Langelaan EJ. A kinematical analysis of the tarsal joints. An X-ray photogrammetric study. Acta Orthop Scand Suppl. 1983;204:1–269. MEDLINE [3]. [3]Lundberg A, Svensson OK. The axes of rotation of the talocalcaneal and talonavicular joints. Foot. 1993;3:65–70. [4]. [4]Leardini A, Stagni R, O’Connor JJ. Mobility of the subtalar joint in the intact ankle complex. J Biomech. 2001;34:805–809. Abstract | Full Text |
Full-Text PDF (146 KB)
|
CrossRef
[5]. [5]Cappozzo A. Gait analysis methodology. Hum Mov Sci. 1984;3:27–50.
CrossRef
[6]. [6]Leardini A, Cappozzo A, Catani F, Toksvig-Larsen S, Petitto A, Sforza V, et al. Validation of a functional method for the estimation of hip joint centre location. J Biomech. 1999;32:99–103. Abstract | Full Text |
Full-Text PDF (95 KB)
|
CrossRef
[7]. [7]Kirby KA. Subtalar joint axis location and rotational equilibrium theory of foot function. J Am Podiatr Med Assoc. 2001;91:465–487. MEDLINE [8]. [8]Engsberg JR. A biomechanical analysis of the talocalcaneal joint—in vitro. J Biomech. 1987;20:429–442. MEDLINE |
CrossRef
[9]. [9]Siegler S, Udupa JK, Ringleb SI, Imhauser CW, Hirsch BE, Odhner D, et al. Mechanics of the ankle and subtalar joints revealed through a 3D quasi-static stress MRI technique. J Biomech. 2005;38:567–578. Abstract | Full Text |
Full-Text PDF (575 KB)
|
CrossRef
[10]. [10]Sommer HJ, Miller NR. A technique for kinematic modeling of anatomical joints. J Biomech Eng. 1980;102:311–317. MEDLINE |
CrossRef
[11]. [11]van den Bogert AJ, Smith GD, Nigg BM. In vivo determination of the anatomical axes of the ankle joint complex: an optimization approach. J Biomech. 1994;27:1477–1488. MEDLINE |
CrossRef
[12]. [12]Lewis GS, Sommer HJ III, Piazza SJ. In vitro assessment of a motion-based optimization method for locating the talocrural and subtalar joint axes. J Biomech Eng, in press. [13]. [13]Kirby KA. Methods for determination of positional variations in the subtalar joint axis. J Am Podiatr Med Assoc. 1987;77:228–234. MEDLINE [14]. [14]Phillips RD, Lidtke RH. Clinical determination of the linear equation for the subtalar joint axis. J Am Podiatr Med Assoc. 1992;82:1–20. MEDLINE [15]. [15]Scott SH, Winter DA. Talocrural and talocalcaneal joint kinematics and kinetics during the stance phase of walking. J Biomech. 1991;24:743–752. MEDLINE |
CrossRef
[16]. [16]Barnett CH, Napier JR. The axis of rotation at the ankle joint in man. Its influence upon the form of the talus and the mobility of the fibula. J Anat. 1952;86:1–9. MEDLINE [17]. [17]McMaster M. Disability of the hindfoot after fracture of the tibial shaft. J Bone Joint Surg Br. 1976;58:90–93. [18]. [18]In: Greene WB editors. Essentials of musculoskeletal care. Rosemont, IL: American Academy of Orthopaedic Surgeons; 2001;. [19]. [19]Challis JH. A procedure for determining rigid body transformation parameters. J Biomech. 1995;28:733–737. Abstract |
Full-Text PDF (554 KB)
|
CrossRef
[20]. [20]Spoor CW, Veldpaus FE. Rigid body motion calculated from spatial co-ordinates of markers. J Biomech. 1980;13:391–393. MEDLINE |
CrossRef
[21]. [21]Schwartz MH, Rozumalski A. A new method for estimating joint parameters from motion data. J Biomech. 2005;38:107–116. Abstract | Full Text |
Full-Text PDF (274 KB)
[22]. [22]Gamage SS, Lasenby J. New least squares solutions for estimating the average centre of rotation and the axis of rotation. J Biomech. 2002;35:87–93. Abstract | Full Text |
Full-Text PDF (388 KB)
|
CrossRef
[23]. [23]Mosca VS. The child's foot: principles of management. J Pediatr Orthop. 1998;18:281–282. MEDLINE a Department of Mechanical and Nuclear Engineering, 29 Recreation Building, The Pennsylvania State University, University Park, PA 16802, USA b California School of Podiatric Medicine, Oakland, CA 94609, USA c Department of Kinesiology, The Pennsylvania State University, University Park, PA 16802, USA d Department of Orthopaedics and Rehabilitation, The Pennsylvania State University, Hershey, PA 17033, USA  Corresponding author. Tel.: +1 814 865 3413; fax: +1 814 863 4755.
PII: S0966-6362(06)00004-X doi:10.1016/j.gaitpost.2006.01.001 © 2006 Elsevier B.V. All rights reserved. | |
|
FULL TEXT
