- Email: [email protected]
The shifting of the torsion axis of the foot during the stance phase of lateral cutting movements
Journal of Biomechanics 45 (2012) 2680–2683
Contents lists available at SciVerse ScienceDirect
Journal of Biomechanics journal homepage: www.elsevier.com/locate/jbiomech www.JBiomech.com
The shifting of the torsion axis of the foot during the stance phase of lateral cutting movements Eveline S. Graf n, Darren J. Stefanyshyn University of Calgary, Human Performance Laboratory, Faculty of Kinesiology, 2500 University Drive NW, Calgary, AB, Canada T2N 1N4
a r t i c l e i n f o
a b s t r a c t
Article history: Accepted 15 August 2012
Previously, foot torsion has been studied with respect to peak angles during athletic movements. Athletic footwear often contains a torsion element that dictates a torsion axis of the shoe. The location of the axis of rotation of the foot is, however, unknown. Therefore, the purpose of this study was to describe the torsion axis location during the stance phase of lateral cutting movements. Thirty-nine subjects performed a barefoot lateral jab and 19 subjects performed a barefoot shuffle cut. Markers were placed on the fore- and rearfoot and their movement was quantified using a 3-D video system. The torsion axis location was determined using a modified finite helical axis approach during the stance phase while the torsion angle was calculated as the amount of rotation around the torsion axis. At the beginning of the stance phase, the axis was located on the medial aspect of the foot. During the stance phase, the axis shifted towards the lateral side of the foot before the axis moved back to the medial aspect of the foot at the end of stance. For both movements significant correlations between the axis location in the vertical and medio-lateral directions and the torsion angle were found. With larger torsion (forefoot inversion) angles the axis was in a more lateral and plantar location within the foot. With this knowledge, a shoe torsion system where the shoe torsion axis location is in agreement with the foot axis location could be developed. & 2012 Elsevier Ltd. All rights reserved.
Keywords: Foot Torsion Kinematics Finite helical axis Cutting
1. Introduction Torsion of the foot, which has been defined as the relative rotation between the forefoot and the rearfoot in the frontal plane, has been studied for athletic movements such as lateral cutting (Segesser et al., 1989; Stacoff et al., 1993). During lateral cutting movements, the foot typically touches the ground first with the forefoot, while the shank is at an angle of up to 331 to the vertical (Luethi et al., 1986). In order to keep the ankle joint stable, the rearfoot needs to stay aligned with the shank. This leads to torsion angles of up to 201 during lateral cuts (Davis et al., 2009). In an athletic setting, cutting movements are mainly performed wearing shoes. Therefore, the influence of footwear on foot torsion became of general scientific interest. It was found that torsional stiff shoes reduced the peak torsion angles, which may put the ankle at a higher risk of injury. Consequently, torsion shoes were introduced which contain a torsion bar in the outsole that reduces torsional stiffness while maintaining the midfoot bending stiffness (Segesser et al., 1989). The location of the torsion bar within the shoe was chosen according to estimates
n
Corresponding author. Tel.: þ1 403 220 2704; fax: þ 1 403 284 3553. E-mail address: [email protected] (E.S. Graf).
0021-9290/$ - see front matter & 2012 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.jbiomech.2012.08.025
based on foot anatomy; the location of the foot torsion axis, however, is unknown. The movement of a body segment relative to another body segment can be described with an axis that the body rotates around and translates along (Kinzel et al., 1972; Spoor and Veldpaus, 1980). This axis is referred to as the finite helical axis (FHA) because the movement of the body follows a helical motion. When there is no translation between the segments, which is a reasonable assumption for most human joints, the FHA approach determines the rotation axis. Calculating the actual rotation axis is an advantage over other methods that describe three-dimensional kinematics, e.g. Euler angles or angles calculated with a joint coordinate system, where the rotation is expressed about predefined axes (Zatsiorsky, 1998). However, the FHA is prone to error caused by noise or violations of the rigid body assumption especially when rotations are small (de Lange et al., 1990; Woltring et al., 1985). The finite helical axis has been used to describe the motion of various joints. Tuijthof et al. (2009) were able to determine differences in the helical parameters of the ankle joint between a healthy population and a patient with chronic ankle instability. A study by Arndt et al. (2004) found great differences between subjects in the helical axis orientation of the ankle joint during walking. The finite helical axis method was used to study the knee joint in order to further the understanding of knee kinematics
E.S. Graf, D.J. Stefanyshyn / Journal of Biomechanics 45 (2012) 2680–2683
(Sheehan, 2010; van den Bogert et al., 2008). van den Bogert et al. (2008) found that the shift of the helical axis, which resulted from a gliding movement between femur and tibia, was not dependent only on the amount of knee flexion. The helical axis was calculated for the two intervals before and after the transition from flexion to extension during running. The amount of knee flexion at the beginning of the first interval was equal to the amount of knee flexion at the end of the second interval. However, the axis during the flexion interval was located about 10 mm more anterior compared to the axis during the extension interval. A method to calculate the foot torsion axis based on the FHA method has previously been described (Graf et al., 2012). According to previous work describing the FHA for joints other than the midfoot (van den Bogert et al., 2008), it can be hypothesized that the torsion axis location moves during stance. Therefore, the purpose of this study was to describe the FHA location and orientation during the stance phase of a lateral jab and a shuffle cut. It was hypothesized that the axis location is dependent on the magnitude of the torsion angle.
2. Methods Nineteen subjects (mean7std: 24.274.8 years; 186.176.6 cm; 83.379.1 cm) were recruited for this study and gave informed written consent. They were all free from lower extremity injuries for 6 months prior to data collection. The study protocol was approved by the institutional research ethics board. Each subject performed seven repetitions of a shuffle cut with bare feet at maximal effort. During the shuffle cut, the subjects performed a shuffle movement with a 1801 cut on the force plate (Fig. 1). The second movement was a lateral jab which consisted of a spring, a lateral side step with the right leg onto the force plate followed by a 451 cut towards the left side. The lateral jab movement was performed by an additional 20 subjects leading to a total of 39 subjects for this movement (mean7std: 24.774.6 years; 180.279.5 cm; 76.4710.8 kg). The additional 20 subjects were part of another study, which did not include the shuffle cut movement. Three retro-
Fig. 1. Schematic display of the performed movements; lateral jab: grey; shuffle cut: black.
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reflective markers were placed each on the forefoot and rearfoot: dorsal aspect of the first, second, and fifth proximal phalange, and medial, posterior, and lateral aspect of the calcaneus. Two additional markers were attached to the head of the first metatarsal and the head of the fifth metatarsal to approximate the metatarsophalangeal joint axis during a standing neutral trial. The marker trajectories were collected using a Motion Analysis system with eight high-speed digital cameras (Motion Analysis Corporation, Santa Rosa, CA, USA) with a sampling rate of 240 Hz. In order to define the stance phase, ground reaction forces were recorded using a Kistler force plate operating at 2400 Hz (Kistler AG, Winterthur, Switzerland). Before the analysis, the kinematic and kinetic data were filtered using a low-pass Butterworth filter (4th-order) with a cut-off frequency of 12 Hz and 50 Hz, respectively. The midfoot rotation axis location and orientation, which expressed the movement in the midfoot in all planes, were calculated using a modified finite helical axis approach at each percentile of the stance phase using Matlab software (Version 7.5, The MathWorks Inc., Natick, MA, USA) (Graf et al., 2012). The midfoot rotation axis location was approximated as the torsion axis location based on the assumption that rotations other than torsion in the midfoot are small. The axis location was expressed relative to the origin of the rearfoot coordinate system, which was at the marker placed on the posterior part of the heel. The orientation of the midfoot rotation axis was expressed through two angles, alpha 1 and alpha 2. Alpha 1 represented the inclination of the axis in the sagittal plane while alpha 2 was the angle of the axis from the sagittal plane towards the lateral side. The orientation of the torsion axis was predefined as perpendicular to the frontal plane of the rearfoot coordinate system. The torsion angle was determined as the rotation about the torsion axis. Pearson’s correlation coefficients and the significance of the correlations between the axis locations and the magnitude of the torsion angle were calculated with Matlab software (Version 7.5, The MathWorks Inc., Natick, MA, USA).
3. Results For both the lateral jab and the shuffle cut the axis was medial to and slightly above the rearfoot reference point at the beginning of the stance phase. It then moved to the lateral side and reached a peak lateral location of approximately 35 mm from the reference point during mid-stance. At the same time the axis moved to a lower location and reached a peak at around 10 mm below the reference point. Towards the end of stance, the axis moved back to the medial side of the foot (Figs. 2 and 3A). The axis trajectory for each subject was analysed and a similar shifting pattern was found for the majority of the subjects. The data of all subjects were normally distributed. Therefore, the shifting of the average axis over all subjects was analysed. The average axis of all subjects showed similar movement during the stance phase between the lateral jab and the side-shuffle cut (Figs. 2 and 3A). For the shuffle cut the peak lateral location reached earlier instance than for the lateral jab. During the lateral jab, at the beginning and end of the stance phase alpha 1 (the inclination of the axis in the sagittal plane) was larger than 51, but, between 29% and 61% of the stance time this angle was smaller than 51 indicating only very small amounts of
Fig. 2. Average torsion axis location (A) and average torsion angle (B) during the stance phase of a lateral jab (n¼ 39).
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E.S. Graf, D.J. Stefanyshyn / Journal of Biomechanics 45 (2012) 2680–2683
Fig. 3. Average torsion axis location (A) and average torsion angle (B) during the stance phase of a shuffle cut (n ¼19).
Table 1 Pearson’s correlation coefficient r and p-value of correlation for comparison of axis location with torsion angle. No. of subjects column includes number of subjects that showed a significant correlation (po 0.05) in the same direction as the mean correlation and in brackets the number of subjects with a significant correlation in opposite direction of the mean correlation.
Lateral jab (n¼ 39) Shuffle cut (n¼ 19)
Vertical Medio-lateral Vertical Medio-lateral
r
p-Value
No. of subjects
0.692 0.467 0.737 0.541
o 0.001 o 0.001 o 0.001 o 0.001
22 (10) 31 (3) 13 (2) 14 (1)
ad-/abduction. If there is no ad-/abduction, alpha 1 is 01, while alpha 1 is 901 if there is only ad-/abduction and no torsion. Consequently, small angles for alpha 1 indicate small ad-/abduction angles. Alpha 2 (the angle from the sagittal plane towards lateral) was smaller than 51 throughout the entire stance and smaller than 11 for the first 52% of stance. During the shuffle cut, alpha 1 was below 51 at all times except for the first 5% of the stance phase and alpha 2 was below 11 throughout the entire stance indicating the axis was mainly oriented along the foot length axis. The correlations between the torsion angle (Figs. 2 and 3B) and the axis locations (in the medio-lateral and vertical directions) (Figs. 2 and 3A) were calculated for the average data of all subjects (total mean) and the average data of each individual subject (individual mean). The correlation coefficients as well as the p-values for the comparisons of the total mean data are shown in Table 1. Table 1 also shows how many individual subjects had a significant correlation between the axis locations and the torsion angle. The axis location (both in the vertical and medio-lateral directions) showed highly significant correlations with the torsion angle for the lateral jab and the shuffle cut. With larger torsion angles (larger forefoot inversion) the axis was located more plantar and lateral. When analysing the correlations for the individual means it was found that for the vertical axis location during the lateral jab, 10 of the 39 subjects had a significant correlation that was in the opposite direction to the mean correlation. For the other direction and movement, only between one and three subjects showed an opposite trend and can be assumed to be outliers.
4. Discussion The location of the torsion axis of the foot during the stance phase has not previously been reported. Therefore, the purpose of
this study was to describe the axis location during the stance phase of a lateral jab and a shuffle cut and to determine if there is a relationship between the axis location and the magnitude of the torsion angle. The movement of the axis was larger in the medio-lateral direction than it was vertically (Figs. 2 and 3A). It is assumed that this difference in range of motion is a result of the foot anatomy. With the midfoot being wider than it is high more joints lay beside each other in the medio-lateral direction compared to the vertical. Therefore, the axis can shift more in the medio-lateral direction. The torsion axis location showed significant correlations with the torsion angle. The pattern of a more lateral location with higher angles could be explained based on foot anatomy. The tarsal bones are arranged and connected in a way that the medial side of the foot is more rigid than the lateral part (Debrunner, 1985; Kapandji, 1970). This could explain why at the beginning of stance, the axis is more medial as the medial side is the more rigid element around which the flexible, lateral part rotates. Forefoot inversion causes a loosening of the connection between the bones, also on the medial side (Bojsen-Møller, 1979). BojsenMøller (1979) described that the cuboid can rotate with respect to the calcaneus in a pivoting motion. However, the dorsal aspect of the calcaneus overhangs the cuboid and limits the amount of relative rotation. In addition, calcaneocuboid ligaments tighten through the relative rotation between the bones. This could result in a more rigid lateral aspect of the foot with increased torsion that could cause the medial part of the foot to rotate about the lateral aspect. This would cause the torsion axis to shift to the lateral side when large torsion angles are present. In the vertical direction, a negative correlation between the axis location and the torsion angle was observed meaning a more plantar position with higher torsion angles. The vertical axis shifting could be a direct consequence of the medio-lateral shifting. The medial side of the foot is typically higher than the lateral side due to the transverse arch (McMinn et al., 1996). Therefore, a rotation about the medial aspects of the foot would occur about an axis that is higher than a rotation axis that is located on the lateral side of the foot. The midfoot is a complex structure with multiple articulating surfaces and numerous ligaments and muscles. It is, therefore, likely that a number of anatomical factors affect the shifting of the torsion axis location during stance. In order to determine the contribution of the individual joints and test the above proposed mechanism for axis shifting, the kinematics of the single bones would need to be quantified using invasive measurement or imaging techniques. Some subjects showed significant correlations between the locations and the angle that were in the opposite direction than
E.S. Graf, D.J. Stefanyshyn / Journal of Biomechanics 45 (2012) 2680–2683
the correlation of the mean data of all subjects. This was primarily the case for the vertical location during the lateral jab: with increasing torsion angles, the axis moved upwards. While the torsion angles are fairly consistent between subjects, the difference in correlation is an effect of altered axis shifting. The reasons that cause this shifting are still to be determined. It can be speculated that subject specific differences in the way the movement is performed could contribute to the variation in axis movement (e.g. more midfoot transverse plane rotation, which affects the axis location). The modified FHA approach was used to calculate the midfoot helical axis and approximate the torsion axis location. While the orientation of the torsion axis is defined as perpendicular to the frontal plane, the helical axis can have a different orientation. The helical axis orientation is determined by the global rotation occurring in different planes. During mid-stance the helical axis was mainly oriented along the foot length axis and, therefore, closely represents the torsion axis. During the final part of the stance phase of the lateral jab, forefoot adduction was occurring, which was represented by a positive alpha 1 angle. Therefore, the location of the helical axis was not solely influenced by the torsion movement. However, alpha 1 was always smaller than 301 which showed that torsion was always greater than ad-/ abduction and, therefore, the main influence on the axis location. A limitation of the study is the dependence of the axis location on the reference coordinate system. The axis location is expressed relative to the marker placed on the proximal side of the heel. Therefore, possible variations in marker placement between subjects reduced the comparability of the data. In order to reduce this effect, the markers were placed by one examiner only. Also, even though the quantitative comparison between subjects might be limited, the qualitative description of the shifting pattern is not affected by this aspect. Another limiting factor was that the measurement of foot kinematics was based on markers placed on the skin of the heel and the forefoot. It has been shown that markers placed on the skin do not represent the movement of the underlying bone exactly due to relative movement between the skin and the bone (Nester et al., 2007). However, the extent of this relative movement between marker and underlying bone for the dynamic lateral movements performed in this study has not been quantified in previous studies. This study describes the location of the torsion axis of the foot over the course of the stance phase of a lateral jab and a shuffle cut. At the beginning and end of stance the axis is located in the medial aspect of the foot. As the torsion angle (forefoot inversion) increased, the axis shifted towards the lateral side and reached a peak lateral location at around the time of the peak torsion angle. Significant correlations were reported between the axis location and the torsion angle. Future work that quantifies the movement of the individual bones is necessary to provide a definitive explanation for the observed axis shifting. Knowledge of the foot torsion axis location could allow locating a shoe torsion element in a way so that the shoe torsion axis location coincides with the foot torsion axis. As the torsion axis is shifting during stance, a shoe torsion element where the axis location is dependent on the amount of torsion would be necessary. It has been speculated that in such a shoe the foot would not be forced to torque about the
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shoe axis and could, therefore, follow its natural path of torsion. Future research should focus on testing this hypothesis.
Conflict of interest statement This study was funded by Adidas International. Adidas was not involved in any aspects of the study such as study design, data collection and analysis.
Acknowledgements The authors would like to thank Adidas International for financial support. References Arndt, A., Westblad, P., Winson, I., Hashimoto, T., Lundberg, A., 2004. Ankle and subtalar kinematics measured with intracortical pins during the stance phase of walking. Foot and Ankle International 25 (5), 357–364. Bojsen-Møller, F., 1979. Calcaneocuboid joint and stability of the longitudinal arch of the foot at high and low gear push off. Journal of Anatomy 129 (1), 165–176. Davis, E.M., Landry, S.C., Nigg, B.M., 2009. Torsion of the foot in low cut basketball shoes in four cutting movements. Footwear Science 1 (S1), 65–67. Debrunner, H.U., 1985. Biomechanics of the Foot. Enke, Stuttgart. de Lange, A., Huiskes, R., Kauer, J.M.G., 1990. Effects of data smoothing on the reconstruction of helical axis parameters in human joint kinematics. Journal of Biomechanical Engineering 112 (2), 107–113. Graf, E.S., Wright, I.C., Stefanyshyn, D.J., 2012. Effect of relative marker movement on the calculation of the foot torsion axis using a combined Cardan angle and helical axis approach. Computational and Mathematical Methods in Medicine /http://www.hindawi.com/journals/cmmm/aip/368050S. Kapandji, I.A., 1970. The Physiology of the Joints: Volume II: Lower Limb. Churchill Livingstone, Edinburgh. Kinzel, G.L., Hall, A.S., Hillberry, B.M., 1972. Measurement of the total motion between two body segments—I. Analytical development. Journal of Biomechanics 5, 93–105. Luethi, S.M., Frederick, E.C., Hawes, M.R., Nigg, B.M., 1986. Influence of shoe construction on lower extremity kinematics and load during lateral movements in tennis. International Journal of Sport Biomechanics 2, 166–174. McMinn, R.M.H., Hutchings, R.T., Logan, B.M., 1996. Color Atlas of Foot and Ankle Anatomy. Mosby-Wolfe, London. Nester, C., Jones, R.K., Liu, A., Howard, D., Lundberg, A., Arndt, A., Lundgren, P., Stacoff, A., Wolf, P., 2007. Foot kinematics during walking measured using bone and surface mounted markers. Journal of Biomechanics 40 (15), 3412–3423. Segesser, B., Stuessi, E., Stacoff, A., Kaelin, X., Ackermann, R., 1989. Torsion—a new concept in sport shoe construction. Sportverletzung Sportschaden 4, 167–182. Sheehan, F.T., 2010. The instantaneous helical axis of the subtalar and talocrural joints: a non-invasive in vivo dynamic study. Journal of Foot and Ankle Research 3 (13), 1–10. Spoor, C.W., Veldpaus, F.E., 1980. Rigid body motion calculated from spatial coordinates of markers. Journal of Biomechanics 13, 391–393. Stacoff, A., Steger, J., Stuessi, E., 1993. The control of the rearfoot in lateral cutting movements in sports. Sportverletzung Sportschaden 7, 22–29. Tuijthof, G.J.M., Zengerink, M., Beimers, L., Jonges, R., Maas, M., van Dijk, C.N., Blankevoord, L., 2009. Determination of consistent patterns of range of motion in the ankle joint with a computed tomography stress-test. Clinical Biomechanics 24 (6), 517–523. van den Bogert, A.J., Reinschmidt, C., Lundberg, A., 2008. Helical axes of skeletal knee joint motion during running. Journal of Biomechanics 41 (13), 1632–1638. Woltring, H.J., Huiskes, R., de Lange, A., 1985. Finite centroid and helical axis estimation from noisy landmark measurements in the study of human joint kinematics. Journal of Biomechanics 18 (5), 379–389. Zatsiorsky, V.M., 1998. Screw (helical) motion. In: Hooper-Davenport, L.M. (Ed.), Kinematics of Human Motion. Human Kinetics, Champaign, pp. 52–60.
Contents lists available at SciVerse ScienceDirect
Journal of Biomechanics journal homepage: www.elsevier.com/locate/jbiomech www.JBiomech.com
The shifting of the torsion axis of the foot during the stance phase of lateral cutting movements Eveline S. Graf n, Darren J. Stefanyshyn University of Calgary, Human Performance Laboratory, Faculty of Kinesiology, 2500 University Drive NW, Calgary, AB, Canada T2N 1N4
a r t i c l e i n f o
a b s t r a c t
Article history: Accepted 15 August 2012
Previously, foot torsion has been studied with respect to peak angles during athletic movements. Athletic footwear often contains a torsion element that dictates a torsion axis of the shoe. The location of the axis of rotation of the foot is, however, unknown. Therefore, the purpose of this study was to describe the torsion axis location during the stance phase of lateral cutting movements. Thirty-nine subjects performed a barefoot lateral jab and 19 subjects performed a barefoot shuffle cut. Markers were placed on the fore- and rearfoot and their movement was quantified using a 3-D video system. The torsion axis location was determined using a modified finite helical axis approach during the stance phase while the torsion angle was calculated as the amount of rotation around the torsion axis. At the beginning of the stance phase, the axis was located on the medial aspect of the foot. During the stance phase, the axis shifted towards the lateral side of the foot before the axis moved back to the medial aspect of the foot at the end of stance. For both movements significant correlations between the axis location in the vertical and medio-lateral directions and the torsion angle were found. With larger torsion (forefoot inversion) angles the axis was in a more lateral and plantar location within the foot. With this knowledge, a shoe torsion system where the shoe torsion axis location is in agreement with the foot axis location could be developed. & 2012 Elsevier Ltd. All rights reserved.
Keywords: Foot Torsion Kinematics Finite helical axis Cutting
1. Introduction Torsion of the foot, which has been defined as the relative rotation between the forefoot and the rearfoot in the frontal plane, has been studied for athletic movements such as lateral cutting (Segesser et al., 1989; Stacoff et al., 1993). During lateral cutting movements, the foot typically touches the ground first with the forefoot, while the shank is at an angle of up to 331 to the vertical (Luethi et al., 1986). In order to keep the ankle joint stable, the rearfoot needs to stay aligned with the shank. This leads to torsion angles of up to 201 during lateral cuts (Davis et al., 2009). In an athletic setting, cutting movements are mainly performed wearing shoes. Therefore, the influence of footwear on foot torsion became of general scientific interest. It was found that torsional stiff shoes reduced the peak torsion angles, which may put the ankle at a higher risk of injury. Consequently, torsion shoes were introduced which contain a torsion bar in the outsole that reduces torsional stiffness while maintaining the midfoot bending stiffness (Segesser et al., 1989). The location of the torsion bar within the shoe was chosen according to estimates
n
Corresponding author. Tel.: þ1 403 220 2704; fax: þ 1 403 284 3553. E-mail address: [email protected] (E.S. Graf).
0021-9290/$ - see front matter & 2012 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.jbiomech.2012.08.025
based on foot anatomy; the location of the foot torsion axis, however, is unknown. The movement of a body segment relative to another body segment can be described with an axis that the body rotates around and translates along (Kinzel et al., 1972; Spoor and Veldpaus, 1980). This axis is referred to as the finite helical axis (FHA) because the movement of the body follows a helical motion. When there is no translation between the segments, which is a reasonable assumption for most human joints, the FHA approach determines the rotation axis. Calculating the actual rotation axis is an advantage over other methods that describe three-dimensional kinematics, e.g. Euler angles or angles calculated with a joint coordinate system, where the rotation is expressed about predefined axes (Zatsiorsky, 1998). However, the FHA is prone to error caused by noise or violations of the rigid body assumption especially when rotations are small (de Lange et al., 1990; Woltring et al., 1985). The finite helical axis has been used to describe the motion of various joints. Tuijthof et al. (2009) were able to determine differences in the helical parameters of the ankle joint between a healthy population and a patient with chronic ankle instability. A study by Arndt et al. (2004) found great differences between subjects in the helical axis orientation of the ankle joint during walking. The finite helical axis method was used to study the knee joint in order to further the understanding of knee kinematics
E.S. Graf, D.J. Stefanyshyn / Journal of Biomechanics 45 (2012) 2680–2683
(Sheehan, 2010; van den Bogert et al., 2008). van den Bogert et al. (2008) found that the shift of the helical axis, which resulted from a gliding movement between femur and tibia, was not dependent only on the amount of knee flexion. The helical axis was calculated for the two intervals before and after the transition from flexion to extension during running. The amount of knee flexion at the beginning of the first interval was equal to the amount of knee flexion at the end of the second interval. However, the axis during the flexion interval was located about 10 mm more anterior compared to the axis during the extension interval. A method to calculate the foot torsion axis based on the FHA method has previously been described (Graf et al., 2012). According to previous work describing the FHA for joints other than the midfoot (van den Bogert et al., 2008), it can be hypothesized that the torsion axis location moves during stance. Therefore, the purpose of this study was to describe the FHA location and orientation during the stance phase of a lateral jab and a shuffle cut. It was hypothesized that the axis location is dependent on the magnitude of the torsion angle.
2. Methods Nineteen subjects (mean7std: 24.274.8 years; 186.176.6 cm; 83.379.1 cm) were recruited for this study and gave informed written consent. They were all free from lower extremity injuries for 6 months prior to data collection. The study protocol was approved by the institutional research ethics board. Each subject performed seven repetitions of a shuffle cut with bare feet at maximal effort. During the shuffle cut, the subjects performed a shuffle movement with a 1801 cut on the force plate (Fig. 1). The second movement was a lateral jab which consisted of a spring, a lateral side step with the right leg onto the force plate followed by a 451 cut towards the left side. The lateral jab movement was performed by an additional 20 subjects leading to a total of 39 subjects for this movement (mean7std: 24.774.6 years; 180.279.5 cm; 76.4710.8 kg). The additional 20 subjects were part of another study, which did not include the shuffle cut movement. Three retro-
Fig. 1. Schematic display of the performed movements; lateral jab: grey; shuffle cut: black.
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reflective markers were placed each on the forefoot and rearfoot: dorsal aspect of the first, second, and fifth proximal phalange, and medial, posterior, and lateral aspect of the calcaneus. Two additional markers were attached to the head of the first metatarsal and the head of the fifth metatarsal to approximate the metatarsophalangeal joint axis during a standing neutral trial. The marker trajectories were collected using a Motion Analysis system with eight high-speed digital cameras (Motion Analysis Corporation, Santa Rosa, CA, USA) with a sampling rate of 240 Hz. In order to define the stance phase, ground reaction forces were recorded using a Kistler force plate operating at 2400 Hz (Kistler AG, Winterthur, Switzerland). Before the analysis, the kinematic and kinetic data were filtered using a low-pass Butterworth filter (4th-order) with a cut-off frequency of 12 Hz and 50 Hz, respectively. The midfoot rotation axis location and orientation, which expressed the movement in the midfoot in all planes, were calculated using a modified finite helical axis approach at each percentile of the stance phase using Matlab software (Version 7.5, The MathWorks Inc., Natick, MA, USA) (Graf et al., 2012). The midfoot rotation axis location was approximated as the torsion axis location based on the assumption that rotations other than torsion in the midfoot are small. The axis location was expressed relative to the origin of the rearfoot coordinate system, which was at the marker placed on the posterior part of the heel. The orientation of the midfoot rotation axis was expressed through two angles, alpha 1 and alpha 2. Alpha 1 represented the inclination of the axis in the sagittal plane while alpha 2 was the angle of the axis from the sagittal plane towards the lateral side. The orientation of the torsion axis was predefined as perpendicular to the frontal plane of the rearfoot coordinate system. The torsion angle was determined as the rotation about the torsion axis. Pearson’s correlation coefficients and the significance of the correlations between the axis locations and the magnitude of the torsion angle were calculated with Matlab software (Version 7.5, The MathWorks Inc., Natick, MA, USA).
3. Results For both the lateral jab and the shuffle cut the axis was medial to and slightly above the rearfoot reference point at the beginning of the stance phase. It then moved to the lateral side and reached a peak lateral location of approximately 35 mm from the reference point during mid-stance. At the same time the axis moved to a lower location and reached a peak at around 10 mm below the reference point. Towards the end of stance, the axis moved back to the medial side of the foot (Figs. 2 and 3A). The axis trajectory for each subject was analysed and a similar shifting pattern was found for the majority of the subjects. The data of all subjects were normally distributed. Therefore, the shifting of the average axis over all subjects was analysed. The average axis of all subjects showed similar movement during the stance phase between the lateral jab and the side-shuffle cut (Figs. 2 and 3A). For the shuffle cut the peak lateral location reached earlier instance than for the lateral jab. During the lateral jab, at the beginning and end of the stance phase alpha 1 (the inclination of the axis in the sagittal plane) was larger than 51, but, between 29% and 61% of the stance time this angle was smaller than 51 indicating only very small amounts of
Fig. 2. Average torsion axis location (A) and average torsion angle (B) during the stance phase of a lateral jab (n¼ 39).
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E.S. Graf, D.J. Stefanyshyn / Journal of Biomechanics 45 (2012) 2680–2683
Fig. 3. Average torsion axis location (A) and average torsion angle (B) during the stance phase of a shuffle cut (n ¼19).
Table 1 Pearson’s correlation coefficient r and p-value of correlation for comparison of axis location with torsion angle. No. of subjects column includes number of subjects that showed a significant correlation (po 0.05) in the same direction as the mean correlation and in brackets the number of subjects with a significant correlation in opposite direction of the mean correlation.
Lateral jab (n¼ 39) Shuffle cut (n¼ 19)
Vertical Medio-lateral Vertical Medio-lateral
r
p-Value
No. of subjects
0.692 0.467 0.737 0.541
o 0.001 o 0.001 o 0.001 o 0.001
22 (10) 31 (3) 13 (2) 14 (1)
ad-/abduction. If there is no ad-/abduction, alpha 1 is 01, while alpha 1 is 901 if there is only ad-/abduction and no torsion. Consequently, small angles for alpha 1 indicate small ad-/abduction angles. Alpha 2 (the angle from the sagittal plane towards lateral) was smaller than 51 throughout the entire stance and smaller than 11 for the first 52% of stance. During the shuffle cut, alpha 1 was below 51 at all times except for the first 5% of the stance phase and alpha 2 was below 11 throughout the entire stance indicating the axis was mainly oriented along the foot length axis. The correlations between the torsion angle (Figs. 2 and 3B) and the axis locations (in the medio-lateral and vertical directions) (Figs. 2 and 3A) were calculated for the average data of all subjects (total mean) and the average data of each individual subject (individual mean). The correlation coefficients as well as the p-values for the comparisons of the total mean data are shown in Table 1. Table 1 also shows how many individual subjects had a significant correlation between the axis locations and the torsion angle. The axis location (both in the vertical and medio-lateral directions) showed highly significant correlations with the torsion angle for the lateral jab and the shuffle cut. With larger torsion angles (larger forefoot inversion) the axis was located more plantar and lateral. When analysing the correlations for the individual means it was found that for the vertical axis location during the lateral jab, 10 of the 39 subjects had a significant correlation that was in the opposite direction to the mean correlation. For the other direction and movement, only between one and three subjects showed an opposite trend and can be assumed to be outliers.
4. Discussion The location of the torsion axis of the foot during the stance phase has not previously been reported. Therefore, the purpose of
this study was to describe the axis location during the stance phase of a lateral jab and a shuffle cut and to determine if there is a relationship between the axis location and the magnitude of the torsion angle. The movement of the axis was larger in the medio-lateral direction than it was vertically (Figs. 2 and 3A). It is assumed that this difference in range of motion is a result of the foot anatomy. With the midfoot being wider than it is high more joints lay beside each other in the medio-lateral direction compared to the vertical. Therefore, the axis can shift more in the medio-lateral direction. The torsion axis location showed significant correlations with the torsion angle. The pattern of a more lateral location with higher angles could be explained based on foot anatomy. The tarsal bones are arranged and connected in a way that the medial side of the foot is more rigid than the lateral part (Debrunner, 1985; Kapandji, 1970). This could explain why at the beginning of stance, the axis is more medial as the medial side is the more rigid element around which the flexible, lateral part rotates. Forefoot inversion causes a loosening of the connection between the bones, also on the medial side (Bojsen-Møller, 1979). BojsenMøller (1979) described that the cuboid can rotate with respect to the calcaneus in a pivoting motion. However, the dorsal aspect of the calcaneus overhangs the cuboid and limits the amount of relative rotation. In addition, calcaneocuboid ligaments tighten through the relative rotation between the bones. This could result in a more rigid lateral aspect of the foot with increased torsion that could cause the medial part of the foot to rotate about the lateral aspect. This would cause the torsion axis to shift to the lateral side when large torsion angles are present. In the vertical direction, a negative correlation between the axis location and the torsion angle was observed meaning a more plantar position with higher torsion angles. The vertical axis shifting could be a direct consequence of the medio-lateral shifting. The medial side of the foot is typically higher than the lateral side due to the transverse arch (McMinn et al., 1996). Therefore, a rotation about the medial aspects of the foot would occur about an axis that is higher than a rotation axis that is located on the lateral side of the foot. The midfoot is a complex structure with multiple articulating surfaces and numerous ligaments and muscles. It is, therefore, likely that a number of anatomical factors affect the shifting of the torsion axis location during stance. In order to determine the contribution of the individual joints and test the above proposed mechanism for axis shifting, the kinematics of the single bones would need to be quantified using invasive measurement or imaging techniques. Some subjects showed significant correlations between the locations and the angle that were in the opposite direction than
E.S. Graf, D.J. Stefanyshyn / Journal of Biomechanics 45 (2012) 2680–2683
the correlation of the mean data of all subjects. This was primarily the case for the vertical location during the lateral jab: with increasing torsion angles, the axis moved upwards. While the torsion angles are fairly consistent between subjects, the difference in correlation is an effect of altered axis shifting. The reasons that cause this shifting are still to be determined. It can be speculated that subject specific differences in the way the movement is performed could contribute to the variation in axis movement (e.g. more midfoot transverse plane rotation, which affects the axis location). The modified FHA approach was used to calculate the midfoot helical axis and approximate the torsion axis location. While the orientation of the torsion axis is defined as perpendicular to the frontal plane, the helical axis can have a different orientation. The helical axis orientation is determined by the global rotation occurring in different planes. During mid-stance the helical axis was mainly oriented along the foot length axis and, therefore, closely represents the torsion axis. During the final part of the stance phase of the lateral jab, forefoot adduction was occurring, which was represented by a positive alpha 1 angle. Therefore, the location of the helical axis was not solely influenced by the torsion movement. However, alpha 1 was always smaller than 301 which showed that torsion was always greater than ad-/ abduction and, therefore, the main influence on the axis location. A limitation of the study is the dependence of the axis location on the reference coordinate system. The axis location is expressed relative to the marker placed on the proximal side of the heel. Therefore, possible variations in marker placement between subjects reduced the comparability of the data. In order to reduce this effect, the markers were placed by one examiner only. Also, even though the quantitative comparison between subjects might be limited, the qualitative description of the shifting pattern is not affected by this aspect. Another limiting factor was that the measurement of foot kinematics was based on markers placed on the skin of the heel and the forefoot. It has been shown that markers placed on the skin do not represent the movement of the underlying bone exactly due to relative movement between the skin and the bone (Nester et al., 2007). However, the extent of this relative movement between marker and underlying bone for the dynamic lateral movements performed in this study has not been quantified in previous studies. This study describes the location of the torsion axis of the foot over the course of the stance phase of a lateral jab and a shuffle cut. At the beginning and end of stance the axis is located in the medial aspect of the foot. As the torsion angle (forefoot inversion) increased, the axis shifted towards the lateral side and reached a peak lateral location at around the time of the peak torsion angle. Significant correlations were reported between the axis location and the torsion angle. Future work that quantifies the movement of the individual bones is necessary to provide a definitive explanation for the observed axis shifting. Knowledge of the foot torsion axis location could allow locating a shoe torsion element in a way so that the shoe torsion axis location coincides with the foot torsion axis. As the torsion axis is shifting during stance, a shoe torsion element where the axis location is dependent on the amount of torsion would be necessary. It has been speculated that in such a shoe the foot would not be forced to torque about the
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shoe axis and could, therefore, follow its natural path of torsion. Future research should focus on testing this hypothesis.
Conflict of interest statement This study was funded by Adidas International. Adidas was not involved in any aspects of the study such as study design, data collection and analysis.
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