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Estimation of ankle joint parameters in typically developed adults using functional calibration methods
Gait & Posture 77 (2020) 95–99
Contents lists available at ScienceDirect
Gait & Posture journal homepage: www.elsevier.com/locate/gaitpost
Estimation of ankle joint parameters in typically developed adults using functional calibration methods
T
Firooz Salamia, Sebastian I. Wolfa,*, Jan Simonb, Julien Lebouchera, Daniel W.W. Heitzmanna, Thomas Dreherc, Marco Götzea a
Universitätsklinikum Heidelberg, Centre of Orthopedics and Trauma Surgery, Heidelberg, Germany Universitätsklinikum Heidelberg, Institute of Physiology and Pathophysiology, Heidelberg, Germany c University Children's Hospital Zurich, Department of Pediatric Orthopedics, Zurich, Switzerland b
A R T I C LE I N FO
A B S T R A C T
Keywords: Ankle joint parameters Functional methods Functional calibration
Background: Despite of many attempts to determine or correct hip and knee joint parameters via non-invasive techniques such as regression or functional methods, in conventional gait models the position of the ankle joint center still is assumed at the center point between malleoli. Research question: The aim of this study was to estimate the ankle joint parameters using a functional approach. Methods: To this aim, we used data of 23 typically developed adults performing two different calibration motions. Subsequently, we applied functional approaches to determine the functional joint center and axis. Results: The results show significant differences for ankle joint parameters in all directions for both calibration motions applied with respect to the malleoli line. Most prominently, we find a shift of the ankle joint center of 7 % of the foot length anteriorly to the malleoli mid-point when applying functional calibration. Conclusion: These significant alterations of the ankle joint center and axis indicate the importance of accurate determination of ankle joint parameters and consequently their influence on the clinical outcome.
1. Introduction Estimating human body joint parameters (joint centers and axes) via non-invasive, accurate and feasible methods always has been a struggling challenge for researchers and clinicians. In this regard, several approaches such as predictive [1,2] or functional methods [3,4] are proposed during the years, though these methods have their shortcomings. Predictive methods are dependent on accurate skin marker placement while functional methods depend on performing specific motions in adequate ranges of motion (RoM). However, both methods are sensitive to soft tissue artifacts (STA) [2,5]. Many studies used these methods for evaluating hip and knee joint parameters [2,6,7] but there are a few studies focusing on the ankle joint in this regard [8–10]. The reason for this may be that among the main joints in the lower extremities, the ankle joint complex, as the name suggests, has the most complicated structure. Anatomically, ankle motion is realized by a combination of three joints acting together, namely the talo-calcaneal (sub-talar), the tibio-talar (talo-crural) and the talo-calcaneo-navicular (transverse-tarsal) joint [11]. Therefore, evaluating the ankle joint parameters is more complicated than in the hip and the knee joint but it will help to provide more insight into the ⁎
function of the ankle joint complex and its biomechanics. The early studies addressing the ankle joint parameters in the 1960s introduced two different ankle axes of rotation according to foot plantar flexion (flexion with slight supination) and dorsal flexion (flexion with slight adduction and supination) with obliquity of the joint to the sagittal plane for tibio-talar joint [12,13]. Iceman and Inman calculated the ankle joint parameters for 46 specimens and their results widely have been referred to in other studies [14]. Later in 1989, Lundberg et al. calculated the tibio-talar axis of rotation with different dorsi-plantar flexion RoM in vivo using x-ray and stereo-photogrammetry techniques. They noticed the importance of locating the center of rotation for the tibio-talar joint [15]. Recently, several studies have applied image techniques and computer modelling to improve the precision of the ankle joint complex parameters [16,17]. Makki et al. calculated ankle joint complex orientations of the axes of rotations and its position during active and passive motions using MRI data [18]. Siegler et al. similarly calculated the tibio-talar and the talo-calcaneal axis and their positions in seven healthy subjects and eight vitro specimens using MRI data and in conclusion they questioned the reliability of skin marker results [19]. Bruening et al. proposed a correction on the conventional gait models’
Corresponding author at: Centre of Orthopedics and Trauma Surgery, Schlierbacher Landstr. 200a, 69118, Heidelberg, Germany. E-mail address: [email protected] (S.I. Wolf).
https://doi.org/10.1016/j.gaitpost.2020.01.016 Received 4 June 2019; Received in revised form 20 December 2019; Accepted 17 January 2020 0966-6362/ © 2020 Elsevier B.V. All rights reserved.
Gait & Posture 77 (2020) 95–99
F. Salami, et al.
ankle joint center as the mid-point between the malleoli [20,1], for retrospective data of 30 patients using their radiographic images [21]. In another study Lewis et al. applied an optimization method while assuming the ankle complex joint as a two revolute linkage trying to locate the ankle axis of rotation. However, the results showed that their assumption was not that accurate [22]. In respect of using functional approaches to determine lower limb joint parameters, the number of studies for the ankle joint is much smaller in comparison of the ones about the hip and knee joint [23]. We could find only one study which tests the reliability of ankle joint center during walking using two functional and conventional methods by comparing their kinematics results during walking though they did not report on the joint parameters [24]. In the conventional gait model, which in a key publication by Kadaba et al. in 1990 was titled “an algorithm for computing lower extremity joint motion”, all joints are assumed as simple ball joints despite the complexity of the underlying anatomy specifically of the ankle joint [20]. In clinical application, the ankle joint center is determined most typically by rather simple methods from landmarks of the malleoli [1]. However, bony prominences may be misleading in the determination of function. Even though the model assumption of a ball and socket joint may have shortcomings for the ankle, the way to estimate the joint center by functional calibration may actually be the best approach given the simplicity of the model. To the best of our knowledge, there is no study calculating the ankle joint parameters using a functional method supported by specific calibration motion in vivo directly. To this aim, we calculated both the functional center of the ankle joint complex (fAJC) and the tibio-talar joint (ankle) axis (fAJA) in a group of typically developed adults and compared it to the location and orientation of the malleolar line as given by markers on the medial and the lateral malleolus.
2. Material and method Gait data of 23 healthy adults, taken along with the development of the Heidelberg Foot Measurement Method (HFMM) [25] during the years 2002–2008, were used for this analysis. The protocol had been approved by the institutional ethics committee at Heidelberg University and each participant had provided informed, written consent. All data had been captured using a Vicon 9 camera system and with foot marker set and placement described in this reference [25]. Due to marker occlusions and other technical shortcomings, data of one right foot and three left feet could not be considered, so 22 right feet and 19 left feet were included for further analysis, respectively (see details in Table 1). Participants have performed two different functional calibration movements with bare feet as follows: In single limb stance the subjects performed repetitive active plantar/dorsiflexion (PF) of the unloaded foot (RoM: 72.7 ± 6.81°, 6.4 ± 2.8° and 15.8 ± 5.3° in the sagittal, frontal and transverse planes respectively) and subsequently a circular motion, including subtalar motion (Cir) (RoM: 69.3 ± 8.9°, 11.8 ± 3.8° and 40.7 ± 8.1° in the sagittal, frontal and transverse planes, respectively), again with their unloaded foot. Each movement was performed at least three times for the left and right foot separately (Fig. 1). An anatomically oriented coordinate reference system (ACS) for the hindfoot was defined on the basis of the three markers on the calcaneus, namely the medial, the lateral, and the dorsal calcaneus marker using
Fig. 1. Calibration motions: plantar flexion (PF) and Circle (Cir).
the Heel Alignment Device (HAD) developed earlier (Fig. 2A) [25]. For each calibration movement, the motion of these three calcaneus markers was monitored in relation to the tibia using the algorithm by Schwartz and Rozumalski allowing to determine a centre of rotation and an average axis of rotation for ball and hinge like joints, respectively, at the presence of multiple degrees of freedom (DOF) [3,4] under two differing model assumptions which we made for testing:
Table 1 Demographics. The primary group included 23 subjects which it reduced to 22 right and 19 left feet. Subject
Number
Male
Female
Age (year)
Body mass (kg)
Height (cm)
Right foot Left foot All
22 19 23
11 8 11
11 11 12
36.8 ± 9.4 37.2 ± 9.8 37.4 ± 9.6
72.4 ± 16.7 70.1 ± 16.5 71.4 ± 17.1
175.9 ± 10.8 175.1 ± 10.6 175.2 ± 11.1
96
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Fig. 2. A: Defining ACS according to the calcaneus (Medial, lateral and central) and 2nd metatarsal markers using the Heel Alignment Device (HAD) [29]. B: Normalizing the fAJCs according to the foot length (the longitude distance between central Calcaneus and Hallux markers), the ankle width (the horizontal distance between central and lateral Malloli markers) and the ankle height (the vertical distance between the MM and mid point at the medial-lateral calcaneus line) in the X, Y and Z directions respectively.
monitored qualitatively. An approximate sphere with the diameter of the distance between the malleoli markers centered at the midpoint of the malleolar axis was assumed as a reasonable area for the fAJC location. For all feet monitored (22 right and 19 left), the fAJCs were located within this sphere for the both PF and Cir movement. Also, if the orientation of the fAJA in any direction was deviating by more than 45 degrees from the malleolar axis, we considered this to be out of a reasonable orientation. Applying these criteria, it turned out that in five right feet and two left feet the orientation of the ankle joint axis exceeded this limits and were therefore completely excluded from final statistics. One-way ANOVA and Bonferroni Post-hoc tests were performed on the data of the normalized fAJCs (according to Fig. 2B) by comparing locations derived from the two calibration movements (Cir and PF) with the position of the MM for both sides, respectively. Similarly, the fAJAs obtained from the PF were compared to the orientation of the MA to find significant differences (P-value = 0.05).
1) The ankle joint is a ball joint (3DOF) and the fAJC is calculated for the PF and the Cir movements, respectively. 2) The ankle joint is a hinge joint (1DOF) and subsequently the fAJA is calculated for the PF movement. The ACS of the foot (as a whole) was defined by the following construct: The X-axis is defined by the direction from heel (dorsal calcaneus) to toe (2nd metatarsal) marker. The XY plane is defined as a plane crossing the lateral and medial calcaneus as well as the toe marker. The Y-axis is then defined perpendicular to the X-axis crossing the lateral calcaneus marker. Finally, the (vertical) Z-axis is defined perpendicular to the X- and the Y-axis, crossing their intersection. The fAJC and fAJA were subsequently determined for each subject using Visual3d software (Copyright © 2016 C-Motion, Inc. U.S.A). The malleolar line (MA) defined as a line crossing the medial and lateral malleoli markers as well as its mid-point (MM) served as an anatomic reference [26], also sometimes regarded as dorsiplantar flexion axis [11]. The fAJCs were normalized for each subject in units of foot length (the longitudinal distance between the the heel marker and the Hallux marker), ankle width (the medio-lateral distance between the medial and the lateral malleolus marker), and ankle height (vertical distance between the malleolar midpoint (MM) and the mid-point of the medial and lateral calcaneus markers (Fig. 2B). Before any further calculations and analysis, the results were
3. Results Table 2 presents the normalized fAJC and MM mean values in X (+/−: anterior/posterior), Y (+/−: Medial/Lateral) and Z (+/−: superior/inferior) direction for the left, the right, and both sides averaged, respectively. Note that the origin of the ACS of the foot is positioned dorsally in the hindfoot and at the sole of the foot as indicated in
Table 2 Mean and std values for the normalized fAJCs and MM locations in X, Y and Z directions (regarding to ACS). (P-value = 0.05). Center location in relation to ACS Cir (%) PF (%) MM (%) Cir vs. MM PF vs. MM Cir vs. PF
Num
X Mean (Std)
41 41 41
20.6 (2.4) 20.3 (2.2) 13.6 (2.4)
Y Mean (Std)
P-value
P-value
22.1 (5.8) 16.9 (10.3) 11.1 (5.2) < 0.001 < 0.001 0.6
P-value
88.8 (8.3) 93.2 (8.6) 98.5 (6.8) < 0.001 < 0.001 0.002
97
Z Mean (Std)
0.001 0.04 0.013
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Fig. 3. The locations (mean values) of the right foot fAJCs, MM, fAJA and MA. The frontal plane (left), MM: upper circle (green), PF: mid circle (blue) and Cir: lower circle (red). MA: upper axis (green) and PF axis: lower axis (blue). The transverse plane (right), MM: lower circle (green), PF: upper circle (blue) and Cir: upper circle left (red). MA: lower axis (green) and PF axis: upper axis (blue). the transverse (right) planes. The foot images are from the Visual3d library and they are scaled between 0 and 1 for each direction according to the normalization criteria. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article).
knee joint in the recent years to improve gait results with respect to inverse kinematics and kinetics [1]. To the best of our knowledge, evaluating joint parameters using a functional approach was never followed for the ankle. In trying to replicate the assumptions of conventional gait modelling, we calculated the functional ankle joint center and the (talo-crural) joint axis for a group of typically developed adults using two different calibration motions (PF and Cir). The functional approach showed that the ankle joint center is located anteriorly-medially-distally in respect to the MM in the foot (Fig. 3). This result is in line with the work of Isman and Inman who determined the talo-crural axis location to be anteriorly-inferiorly in relation to the MA [14] and also Makki et al. showed that talo-crural and calcaneal-tibial joints forming the complex ankle joint, translate anteriorly-inferiorly during passive or active motions [18]. It turns out that the functional calibration results obtained by the Cir movement and by the PF movement, respectively, are slightly different and it is not per se clear which result is the more reliable. Intuitively, one would assume the functional calibration results obtained by the Cir movement to be more reliable as it provides more RoM in all directions during the calibration motion when compared to the PF movement. However, based on the data we obtained we cannot give preference to any of the two calibration movements. Nevertheless, the PF and the Cir movements coincide in results. With both methods, the relative distance between the average fAJC (located at 21 % of the foot length) and the anatomic MM (located at 14 % of the foot length) is almost 7 % of foot length with the fAJC located more anteriorly (comp. Table 2). This shift is considerably high (around 1.7 cm for an average foot length of 24 cm) and may have a high impact on the biomechanics of the ankle joint and foot. Referring to Davis et al and Kadaba et al, the conventional ankle joint center is defined with regard to the lateral malleolus marker only in medio-lateral direction meaning that the MM is typically located slightly more superior to the conventional ankle joint center [1,20] therefore, the average fAJC in the frontal plane in the Z direction may be slightly closer to the conventional ankle center. Our results regarding the fAJA and the MA in the frontal plane are in agreement with previous findings obtained via imaging techniques and regression methods [14,16,21]. In the transverse plane, the projected fAJA is almost parallel to the horizontal line (Fig. 3) and it is in
Table 3 Mean and std values for the projections of the fAJAs and MA (degree) on the frontal and the transverse planes. (P-value = 0.05). Frontal plane
Transverse plane
Axis angle
Num
Mean (Std)
P-value
Mean(Std)
P-value
PF°
34
vs. MA (< 0.001)
34
−0.11 (1.06) 0.75 (0.66)
Vs. MA (< 0.001)
MA°
6.73 (3.78) 4.04 (0.76)
Fig. 3. Further, Table 3 presents the average values for the fAJA and the MA projections onto the frontal (+/−: inversion/eversion), and the transverse (+/−: external/internal rotation) planes. The results for the fAJC show significant differences in location for both the Cir and the PF movements when comparing to the location of the MM in all three directions. On group average, the fAJC in the X direction is located 7 % (Cir movement) and 6 % (PF movement) anteriorly in relation to the MM, respectively, i.e. 1.73 cm and 1.48 cm for the average foot length of 24.7 cm. In the Y direction, the fAJC is located 11 % (Cir) and 6 % (PF) medially in relation of the MM respectively, i.e. 1.00 cm and 0.54 cm for the average ankle width of 9.1 cm. In the Z direction, the fAJC is located more distally in relation to the MM by 9 % (Cir) and 5 % (PF), respectively, i.e. 0.44 cm and 0.25 cm for the average ankle height of 4.9 cm. Also, there are significant differences for the fAJC results between the two different calibration movements Cir and PF in the Y and Z directions (see Table 2). Further, the orientation of the fAJA differed when comparing to the MA, both in the projection to the frontal and the transverse plane, respectively (Table 3). 4. Discussion The ankle joint has a complex structure and therefore the reduction to a ball joint is a rather drastic simplification, but is nevertheless standard assumption in conventional clinical gait analysis. However, in standard procedures the ankle joint center is defined via anatomical landmarks and not via functional methods as is done for the hip and the 98
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the shank and thereby have an indirect effect also on the knee flexion angle. Although applying image techniques for calculating the joint parameters may be more reliable and more accurate than other noninvasive methods, they are not always feasible in clinical application, besides they are expensive. Hence we hope that this study may help for refining conventional gait models with regards to foot and ankle biomechanics in a clinical setting.
agreement with the Lundberg’s results [18]. The tilt of the fAJA in the frontal plane indicates a complimentary fact that the assumption of a pure hinge joint is flawed to some extent, though it seems that in the transverse plane this assumption is more acceptable. It should be noticed that these studies calculated the axis angles in relation to the tibias’ long axis while our fAJA angle is the projection on the frontal plane, therefore the results may be slightly smaller but on the other hand our method is more adequate when deformity comes into play since then the long axis of the foot may be distorted by mid and forefoot deformities. However, in presence of foot deformities, determination of the ankle joint parameters in general is more difficult. Besides reducing marker placement accuracy, the boney structure of the ankle joint complex such as misplacement of the calcaneus in flat feet or limited mobility of the tarsal and ankle joints in the Charcot-Marie-Tooth feet influence the location and orientation ankle joint parameters [27,28]. In this case, a functional approach may be superior, given that there is an adequate range of motion for calibration. There are mainly two potential factors that could influence our functional outcomes. The first factor is given by the fact that the ankle anatomically neither is a pure hinge nor a pure ball joint. This per se limits the accuracy and precision, but may in fact be the best solution given that one want’s to apply this outcome in a model with a ball joint as done in standard clinical gait modelling. The second factor is STA. The subjects performed the calibration motions in unloaded conditions and hence the influence of STA onto the markers placed on the hindfoot should be rather low. Calibration with loaded movements (e.g. walking) may be more appropriate but this will increase the STA and further limit the available RoM which may further negatively affect the joint parameter outcomes. A better outcome using an approach in loaded condition is therefore not self-evident and may be made subject of a consecutive study. Nevertheless, the relatively high inter-individual precision of the joint center determination indicates that the influence of STA is rather small. Further also the optimization algorithm may have its shortcomings. In fact, 7 out of 41 feet investigated showed results for the fAJA which were outside the region of expectation (i.e. off in orientation of the axis) when using the PF movement for calibration. Also with careful analysis we could not determine if this originates from insufficient or inadequate data input for calibration or from a weakness of the applied algorithm. Nevertheless, for the fAJC the algorithm of Schwartz and Rozumalski reliably led to consistent results. Also in previous studies this method has been proven reliable [29,30]. According to Ehrig et al. [3], one of the big issues with this method backs to the computational cost which after more than a decade of introducing the method the computation cost would not be felt that much as it was and we did not experience it during our calculations. Also, using movements not in the plane (e.g. the frontal plane) along with the STA, the algorithm is in principle able to determine the functional center regarding 1DOF hinge like joint or 1DOF calibration motion in practice [4].
Declaration of Competing Interest There is no conflict of interest. Acknowledgement Financial Funding by the Else-Kröner-Fresenius-Stiftung, Grant 2017_A06, is gratefully acknowledged. References [1] R.B. Davis IIIet al., A gait analysis data collection and reduction technique, Hum. Mov. Sci. 10 (5) (1991) 575–587. [2] H. Kainz, et al., Estimation of the hip joint centre in human motion analysis: a systematic review, Clin. Biomech. 30 (4) (2015) 319–329. [3] R.M. Ehrig, et al., A survey of formal methods for determining the centre of rotation of ball joints, J. Biomech. 39 (15) (2006) 2798–2809. [4] M.H. Schwartz, A. Rozumalski, A new method for estimating joint parameters from motion data, J. Biomech. 38 (1) (2005) 107–116. [5] M. Sangeux, A. Peters, R. Baker, Hip joint centre localization: evaluation on normal subjects in the context of gait analysis, Gait Posture 34 (3) (2011) 324–328. [6] R.M. Ehrig, et al., A survey of formal methods for determining functional joint axes, J. Biomech. 40 (10) (2007) 2150–2157. [7] B.A. MacWilliams, A comparison of four functional methods to determine centers and axes of rotations, Gait Posture 28 (4) (2008) 673–679. [8] P. Procter, J. Paul, Ankle joint biomechanics, J. Biomech. 15 (9) (1982) 627–634. [9] L. Nofrini, et al., Evaluation of accuracy in ankle center location for tibial mechanical axis identification, J. Investig. Surg. 17 (1) (2004) 23–29. [10] R.A. Siston, et al., Evaluation of methods that locate the center of the ankle for computer-assisted total knee arthroplasty, Clin. Orthop. Relat. Res. 439 (2005) 129–135. [11] C.L. Brockett, G.J. Chapman, Biomechanics of the ankle, Orthop. Trauma 30 (3) (2016) 232–238. [12] J. Hicks, The mechanics of the foot: II. The plantar aponeurosis and the arch, J. Anat. 88 (Pt 1) (1954) 25. [13] T. Wyller, The axis of the ankle joint and its importance in subtalar arthrodesis, Acta Orthop. Scand. 33 (1–4) (1963) 320–328. [14] R.E. Isman, V.T. Inman, P. Poor, Anthropometric studies of the human foot and ankle, Bull. Prosthet. Res. 10 (11) (1969) 97–129. [15] A. Lundberg, et al., The axis of rotation of the ankle joint, J. Bone Joint Surg. Br. 71 (1) (1989) 94–99. [16] L. Claassen, et al., The geometrical axis of the talocrural joint—suggestions for a new measurement of the talocrural joint axis, Foot Ankle Surg. (2018). [17] E. Montefiori, et al., An image-based kinematic model of the tibiotalar and subtalar joints and its application to gait analysis in children with Juvenile Idiopathic Arthritis, J. Biomech. (2019). [18] K. Makki, et al., In vivo ankle joint kinematics from dynamic magnetic resonance imaging using a registration-based framework, J. Biomech. 86 (2019) 193–203. [19] S. Siegler, et al., Mechanics of the ankle and subtalar joints revealed through a 3D quasi-static stress MRI technique, J. Biomech. 38 (3) (2005) 567–578. [20] M.P. Kadaba, H. Ramakrishnan, M. Wootten, Measurement of lower extremity kinematics during level walking, J. Orthop. Res. 8 (3) (1990) 383–392. [21] D.A. Bruening, A.N. Crewe, F.L. Buczek, A simple, anatomically based correction to the conventional ankle joint center, Clin. Biomech. 23 (10) (2008) 1299–1302. [22] G.S. Lewis, K.A. Kirby, S.J. Piazza, Determination of subtalar joint axis location by restriction of talocrural joint motion, Gait Posture 25 (1) (2007) 63–69. [23] G.S. Lewis, et al., In vivo tests of an improved method for functional location of the subtalar joint axis, J. Biomech. 42 (2) (2009) 146–151. [24] R.W. Graydon, et al., The test-retest reliability of different ankle joint center location techniques, Foot Ankle J. 1 (11) (2015). [25] J. Simon, et al., The Heidelberg foot measurement method: development, description and assessment, Gait Posture 23 (4) (2006) 411–424. [26] G. Wu, et al., ISB recommendation on definitions of joint coordinate system of various joints for the reporting of human joint motion—part I: ankle, hip, and spine, J. Biomech. 35 (4) (2002) 543–548. [27] M. Medhat, H. Krantz, Neuropathic ankle joint in Charcot-Marie-Tooth disease after triple arthrodesis of the foot, Orthop. Rev. 17 (9) (1988) 873–880. [28] R. Donatelli, Abnormal biomechanics of the foot and ankle, J. Orthop. Sports Phys. Ther. 9 (1) (1987) 11–16. [29] M.B. Pohl, C. Lloyd, R. Ferber, Can the reliability of three-dimensional running kinematics be improved using functional joint methodology? Gait Posture 32 (4) (2010) 559–563. [30] M.A. Robinson, J. Vanrenterghem, An evaluation of anatomical and functional knee axis definition in the context of side-cutting, J. Biomech. 45 (11) (2012) 1941–1946.
5. Conclusion With the use of functional joint center calibration we could deduce the location of the ankle joint center to be slightly more medially and more distally to the malleolar midpoint and markedly more anteriorly. The results were consistent in all feet with little variation making this method promising for further use. Specifically when determining a fAJA from the PF movement, a few foot samples with numerically fAJAs far outside the region of orientation (7 out of 41 feet, respectively) were excluded from further analysis without yet having a rigorous explanation for the deviation. However, in all samples both calibration movements locate the AJC significantly anterior to the MM with consequences for clinical gait data obtained by standard modelling for both joint kinematics and kinetics. Given the validity of our results, which was not yet tested in this study, these effects would not be limited to the ankle only, but would have an influence on the segment definition of 99
Contents lists available at ScienceDirect
Gait & Posture journal homepage: www.elsevier.com/locate/gaitpost
Estimation of ankle joint parameters in typically developed adults using functional calibration methods
T
Firooz Salamia, Sebastian I. Wolfa,*, Jan Simonb, Julien Lebouchera, Daniel W.W. Heitzmanna, Thomas Dreherc, Marco Götzea a
Universitätsklinikum Heidelberg, Centre of Orthopedics and Trauma Surgery, Heidelberg, Germany Universitätsklinikum Heidelberg, Institute of Physiology and Pathophysiology, Heidelberg, Germany c University Children's Hospital Zurich, Department of Pediatric Orthopedics, Zurich, Switzerland b
A R T I C LE I N FO
A B S T R A C T
Keywords: Ankle joint parameters Functional methods Functional calibration
Background: Despite of many attempts to determine or correct hip and knee joint parameters via non-invasive techniques such as regression or functional methods, in conventional gait models the position of the ankle joint center still is assumed at the center point between malleoli. Research question: The aim of this study was to estimate the ankle joint parameters using a functional approach. Methods: To this aim, we used data of 23 typically developed adults performing two different calibration motions. Subsequently, we applied functional approaches to determine the functional joint center and axis. Results: The results show significant differences for ankle joint parameters in all directions for both calibration motions applied with respect to the malleoli line. Most prominently, we find a shift of the ankle joint center of 7 % of the foot length anteriorly to the malleoli mid-point when applying functional calibration. Conclusion: These significant alterations of the ankle joint center and axis indicate the importance of accurate determination of ankle joint parameters and consequently their influence on the clinical outcome.
1. Introduction Estimating human body joint parameters (joint centers and axes) via non-invasive, accurate and feasible methods always has been a struggling challenge for researchers and clinicians. In this regard, several approaches such as predictive [1,2] or functional methods [3,4] are proposed during the years, though these methods have their shortcomings. Predictive methods are dependent on accurate skin marker placement while functional methods depend on performing specific motions in adequate ranges of motion (RoM). However, both methods are sensitive to soft tissue artifacts (STA) [2,5]. Many studies used these methods for evaluating hip and knee joint parameters [2,6,7] but there are a few studies focusing on the ankle joint in this regard [8–10]. The reason for this may be that among the main joints in the lower extremities, the ankle joint complex, as the name suggests, has the most complicated structure. Anatomically, ankle motion is realized by a combination of three joints acting together, namely the talo-calcaneal (sub-talar), the tibio-talar (talo-crural) and the talo-calcaneo-navicular (transverse-tarsal) joint [11]. Therefore, evaluating the ankle joint parameters is more complicated than in the hip and the knee joint but it will help to provide more insight into the ⁎
function of the ankle joint complex and its biomechanics. The early studies addressing the ankle joint parameters in the 1960s introduced two different ankle axes of rotation according to foot plantar flexion (flexion with slight supination) and dorsal flexion (flexion with slight adduction and supination) with obliquity of the joint to the sagittal plane for tibio-talar joint [12,13]. Iceman and Inman calculated the ankle joint parameters for 46 specimens and their results widely have been referred to in other studies [14]. Later in 1989, Lundberg et al. calculated the tibio-talar axis of rotation with different dorsi-plantar flexion RoM in vivo using x-ray and stereo-photogrammetry techniques. They noticed the importance of locating the center of rotation for the tibio-talar joint [15]. Recently, several studies have applied image techniques and computer modelling to improve the precision of the ankle joint complex parameters [16,17]. Makki et al. calculated ankle joint complex orientations of the axes of rotations and its position during active and passive motions using MRI data [18]. Siegler et al. similarly calculated the tibio-talar and the talo-calcaneal axis and their positions in seven healthy subjects and eight vitro specimens using MRI data and in conclusion they questioned the reliability of skin marker results [19]. Bruening et al. proposed a correction on the conventional gait models’
Corresponding author at: Centre of Orthopedics and Trauma Surgery, Schlierbacher Landstr. 200a, 69118, Heidelberg, Germany. E-mail address: [email protected] (S.I. Wolf).
https://doi.org/10.1016/j.gaitpost.2020.01.016 Received 4 June 2019; Received in revised form 20 December 2019; Accepted 17 January 2020 0966-6362/ © 2020 Elsevier B.V. All rights reserved.
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ankle joint center as the mid-point between the malleoli [20,1], for retrospective data of 30 patients using their radiographic images [21]. In another study Lewis et al. applied an optimization method while assuming the ankle complex joint as a two revolute linkage trying to locate the ankle axis of rotation. However, the results showed that their assumption was not that accurate [22]. In respect of using functional approaches to determine lower limb joint parameters, the number of studies for the ankle joint is much smaller in comparison of the ones about the hip and knee joint [23]. We could find only one study which tests the reliability of ankle joint center during walking using two functional and conventional methods by comparing their kinematics results during walking though they did not report on the joint parameters [24]. In the conventional gait model, which in a key publication by Kadaba et al. in 1990 was titled “an algorithm for computing lower extremity joint motion”, all joints are assumed as simple ball joints despite the complexity of the underlying anatomy specifically of the ankle joint [20]. In clinical application, the ankle joint center is determined most typically by rather simple methods from landmarks of the malleoli [1]. However, bony prominences may be misleading in the determination of function. Even though the model assumption of a ball and socket joint may have shortcomings for the ankle, the way to estimate the joint center by functional calibration may actually be the best approach given the simplicity of the model. To the best of our knowledge, there is no study calculating the ankle joint parameters using a functional method supported by specific calibration motion in vivo directly. To this aim, we calculated both the functional center of the ankle joint complex (fAJC) and the tibio-talar joint (ankle) axis (fAJA) in a group of typically developed adults and compared it to the location and orientation of the malleolar line as given by markers on the medial and the lateral malleolus.
2. Material and method Gait data of 23 healthy adults, taken along with the development of the Heidelberg Foot Measurement Method (HFMM) [25] during the years 2002–2008, were used for this analysis. The protocol had been approved by the institutional ethics committee at Heidelberg University and each participant had provided informed, written consent. All data had been captured using a Vicon 9 camera system and with foot marker set and placement described in this reference [25]. Due to marker occlusions and other technical shortcomings, data of one right foot and three left feet could not be considered, so 22 right feet and 19 left feet were included for further analysis, respectively (see details in Table 1). Participants have performed two different functional calibration movements with bare feet as follows: In single limb stance the subjects performed repetitive active plantar/dorsiflexion (PF) of the unloaded foot (RoM: 72.7 ± 6.81°, 6.4 ± 2.8° and 15.8 ± 5.3° in the sagittal, frontal and transverse planes respectively) and subsequently a circular motion, including subtalar motion (Cir) (RoM: 69.3 ± 8.9°, 11.8 ± 3.8° and 40.7 ± 8.1° in the sagittal, frontal and transverse planes, respectively), again with their unloaded foot. Each movement was performed at least three times for the left and right foot separately (Fig. 1). An anatomically oriented coordinate reference system (ACS) for the hindfoot was defined on the basis of the three markers on the calcaneus, namely the medial, the lateral, and the dorsal calcaneus marker using
Fig. 1. Calibration motions: plantar flexion (PF) and Circle (Cir).
the Heel Alignment Device (HAD) developed earlier (Fig. 2A) [25]. For each calibration movement, the motion of these three calcaneus markers was monitored in relation to the tibia using the algorithm by Schwartz and Rozumalski allowing to determine a centre of rotation and an average axis of rotation for ball and hinge like joints, respectively, at the presence of multiple degrees of freedom (DOF) [3,4] under two differing model assumptions which we made for testing:
Table 1 Demographics. The primary group included 23 subjects which it reduced to 22 right and 19 left feet. Subject
Number
Male
Female
Age (year)
Body mass (kg)
Height (cm)
Right foot Left foot All
22 19 23
11 8 11
11 11 12
36.8 ± 9.4 37.2 ± 9.8 37.4 ± 9.6
72.4 ± 16.7 70.1 ± 16.5 71.4 ± 17.1
175.9 ± 10.8 175.1 ± 10.6 175.2 ± 11.1
96
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Fig. 2. A: Defining ACS according to the calcaneus (Medial, lateral and central) and 2nd metatarsal markers using the Heel Alignment Device (HAD) [29]. B: Normalizing the fAJCs according to the foot length (the longitude distance between central Calcaneus and Hallux markers), the ankle width (the horizontal distance between central and lateral Malloli markers) and the ankle height (the vertical distance between the MM and mid point at the medial-lateral calcaneus line) in the X, Y and Z directions respectively.
monitored qualitatively. An approximate sphere with the diameter of the distance between the malleoli markers centered at the midpoint of the malleolar axis was assumed as a reasonable area for the fAJC location. For all feet monitored (22 right and 19 left), the fAJCs were located within this sphere for the both PF and Cir movement. Also, if the orientation of the fAJA in any direction was deviating by more than 45 degrees from the malleolar axis, we considered this to be out of a reasonable orientation. Applying these criteria, it turned out that in five right feet and two left feet the orientation of the ankle joint axis exceeded this limits and were therefore completely excluded from final statistics. One-way ANOVA and Bonferroni Post-hoc tests were performed on the data of the normalized fAJCs (according to Fig. 2B) by comparing locations derived from the two calibration movements (Cir and PF) with the position of the MM for both sides, respectively. Similarly, the fAJAs obtained from the PF were compared to the orientation of the MA to find significant differences (P-value = 0.05).
1) The ankle joint is a ball joint (3DOF) and the fAJC is calculated for the PF and the Cir movements, respectively. 2) The ankle joint is a hinge joint (1DOF) and subsequently the fAJA is calculated for the PF movement. The ACS of the foot (as a whole) was defined by the following construct: The X-axis is defined by the direction from heel (dorsal calcaneus) to toe (2nd metatarsal) marker. The XY plane is defined as a plane crossing the lateral and medial calcaneus as well as the toe marker. The Y-axis is then defined perpendicular to the X-axis crossing the lateral calcaneus marker. Finally, the (vertical) Z-axis is defined perpendicular to the X- and the Y-axis, crossing their intersection. The fAJC and fAJA were subsequently determined for each subject using Visual3d software (Copyright © 2016 C-Motion, Inc. U.S.A). The malleolar line (MA) defined as a line crossing the medial and lateral malleoli markers as well as its mid-point (MM) served as an anatomic reference [26], also sometimes regarded as dorsiplantar flexion axis [11]. The fAJCs were normalized for each subject in units of foot length (the longitudinal distance between the the heel marker and the Hallux marker), ankle width (the medio-lateral distance between the medial and the lateral malleolus marker), and ankle height (vertical distance between the malleolar midpoint (MM) and the mid-point of the medial and lateral calcaneus markers (Fig. 2B). Before any further calculations and analysis, the results were
3. Results Table 2 presents the normalized fAJC and MM mean values in X (+/−: anterior/posterior), Y (+/−: Medial/Lateral) and Z (+/−: superior/inferior) direction for the left, the right, and both sides averaged, respectively. Note that the origin of the ACS of the foot is positioned dorsally in the hindfoot and at the sole of the foot as indicated in
Table 2 Mean and std values for the normalized fAJCs and MM locations in X, Y and Z directions (regarding to ACS). (P-value = 0.05). Center location in relation to ACS Cir (%) PF (%) MM (%) Cir vs. MM PF vs. MM Cir vs. PF
Num
X Mean (Std)
41 41 41
20.6 (2.4) 20.3 (2.2) 13.6 (2.4)
Y Mean (Std)
P-value
P-value
22.1 (5.8) 16.9 (10.3) 11.1 (5.2) < 0.001 < 0.001 0.6
P-value
88.8 (8.3) 93.2 (8.6) 98.5 (6.8) < 0.001 < 0.001 0.002
97
Z Mean (Std)
0.001 0.04 0.013
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Fig. 3. The locations (mean values) of the right foot fAJCs, MM, fAJA and MA. The frontal plane (left), MM: upper circle (green), PF: mid circle (blue) and Cir: lower circle (red). MA: upper axis (green) and PF axis: lower axis (blue). The transverse plane (right), MM: lower circle (green), PF: upper circle (blue) and Cir: upper circle left (red). MA: lower axis (green) and PF axis: upper axis (blue). the transverse (right) planes. The foot images are from the Visual3d library and they are scaled between 0 and 1 for each direction according to the normalization criteria. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article).
knee joint in the recent years to improve gait results with respect to inverse kinematics and kinetics [1]. To the best of our knowledge, evaluating joint parameters using a functional approach was never followed for the ankle. In trying to replicate the assumptions of conventional gait modelling, we calculated the functional ankle joint center and the (talo-crural) joint axis for a group of typically developed adults using two different calibration motions (PF and Cir). The functional approach showed that the ankle joint center is located anteriorly-medially-distally in respect to the MM in the foot (Fig. 3). This result is in line with the work of Isman and Inman who determined the talo-crural axis location to be anteriorly-inferiorly in relation to the MA [14] and also Makki et al. showed that talo-crural and calcaneal-tibial joints forming the complex ankle joint, translate anteriorly-inferiorly during passive or active motions [18]. It turns out that the functional calibration results obtained by the Cir movement and by the PF movement, respectively, are slightly different and it is not per se clear which result is the more reliable. Intuitively, one would assume the functional calibration results obtained by the Cir movement to be more reliable as it provides more RoM in all directions during the calibration motion when compared to the PF movement. However, based on the data we obtained we cannot give preference to any of the two calibration movements. Nevertheless, the PF and the Cir movements coincide in results. With both methods, the relative distance between the average fAJC (located at 21 % of the foot length) and the anatomic MM (located at 14 % of the foot length) is almost 7 % of foot length with the fAJC located more anteriorly (comp. Table 2). This shift is considerably high (around 1.7 cm for an average foot length of 24 cm) and may have a high impact on the biomechanics of the ankle joint and foot. Referring to Davis et al and Kadaba et al, the conventional ankle joint center is defined with regard to the lateral malleolus marker only in medio-lateral direction meaning that the MM is typically located slightly more superior to the conventional ankle joint center [1,20] therefore, the average fAJC in the frontal plane in the Z direction may be slightly closer to the conventional ankle center. Our results regarding the fAJA and the MA in the frontal plane are in agreement with previous findings obtained via imaging techniques and regression methods [14,16,21]. In the transverse plane, the projected fAJA is almost parallel to the horizontal line (Fig. 3) and it is in
Table 3 Mean and std values for the projections of the fAJAs and MA (degree) on the frontal and the transverse planes. (P-value = 0.05). Frontal plane
Transverse plane
Axis angle
Num
Mean (Std)
P-value
Mean(Std)
P-value
PF°
34
vs. MA (< 0.001)
34
−0.11 (1.06) 0.75 (0.66)
Vs. MA (< 0.001)
MA°
6.73 (3.78) 4.04 (0.76)
Fig. 3. Further, Table 3 presents the average values for the fAJA and the MA projections onto the frontal (+/−: inversion/eversion), and the transverse (+/−: external/internal rotation) planes. The results for the fAJC show significant differences in location for both the Cir and the PF movements when comparing to the location of the MM in all three directions. On group average, the fAJC in the X direction is located 7 % (Cir movement) and 6 % (PF movement) anteriorly in relation to the MM, respectively, i.e. 1.73 cm and 1.48 cm for the average foot length of 24.7 cm. In the Y direction, the fAJC is located 11 % (Cir) and 6 % (PF) medially in relation of the MM respectively, i.e. 1.00 cm and 0.54 cm for the average ankle width of 9.1 cm. In the Z direction, the fAJC is located more distally in relation to the MM by 9 % (Cir) and 5 % (PF), respectively, i.e. 0.44 cm and 0.25 cm for the average ankle height of 4.9 cm. Also, there are significant differences for the fAJC results between the two different calibration movements Cir and PF in the Y and Z directions (see Table 2). Further, the orientation of the fAJA differed when comparing to the MA, both in the projection to the frontal and the transverse plane, respectively (Table 3). 4. Discussion The ankle joint has a complex structure and therefore the reduction to a ball joint is a rather drastic simplification, but is nevertheless standard assumption in conventional clinical gait analysis. However, in standard procedures the ankle joint center is defined via anatomical landmarks and not via functional methods as is done for the hip and the 98
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the shank and thereby have an indirect effect also on the knee flexion angle. Although applying image techniques for calculating the joint parameters may be more reliable and more accurate than other noninvasive methods, they are not always feasible in clinical application, besides they are expensive. Hence we hope that this study may help for refining conventional gait models with regards to foot and ankle biomechanics in a clinical setting.
agreement with the Lundberg’s results [18]. The tilt of the fAJA in the frontal plane indicates a complimentary fact that the assumption of a pure hinge joint is flawed to some extent, though it seems that in the transverse plane this assumption is more acceptable. It should be noticed that these studies calculated the axis angles in relation to the tibias’ long axis while our fAJA angle is the projection on the frontal plane, therefore the results may be slightly smaller but on the other hand our method is more adequate when deformity comes into play since then the long axis of the foot may be distorted by mid and forefoot deformities. However, in presence of foot deformities, determination of the ankle joint parameters in general is more difficult. Besides reducing marker placement accuracy, the boney structure of the ankle joint complex such as misplacement of the calcaneus in flat feet or limited mobility of the tarsal and ankle joints in the Charcot-Marie-Tooth feet influence the location and orientation ankle joint parameters [27,28]. In this case, a functional approach may be superior, given that there is an adequate range of motion for calibration. There are mainly two potential factors that could influence our functional outcomes. The first factor is given by the fact that the ankle anatomically neither is a pure hinge nor a pure ball joint. This per se limits the accuracy and precision, but may in fact be the best solution given that one want’s to apply this outcome in a model with a ball joint as done in standard clinical gait modelling. The second factor is STA. The subjects performed the calibration motions in unloaded conditions and hence the influence of STA onto the markers placed on the hindfoot should be rather low. Calibration with loaded movements (e.g. walking) may be more appropriate but this will increase the STA and further limit the available RoM which may further negatively affect the joint parameter outcomes. A better outcome using an approach in loaded condition is therefore not self-evident and may be made subject of a consecutive study. Nevertheless, the relatively high inter-individual precision of the joint center determination indicates that the influence of STA is rather small. Further also the optimization algorithm may have its shortcomings. In fact, 7 out of 41 feet investigated showed results for the fAJA which were outside the region of expectation (i.e. off in orientation of the axis) when using the PF movement for calibration. Also with careful analysis we could not determine if this originates from insufficient or inadequate data input for calibration or from a weakness of the applied algorithm. Nevertheless, for the fAJC the algorithm of Schwartz and Rozumalski reliably led to consistent results. Also in previous studies this method has been proven reliable [29,30]. According to Ehrig et al. [3], one of the big issues with this method backs to the computational cost which after more than a decade of introducing the method the computation cost would not be felt that much as it was and we did not experience it during our calculations. Also, using movements not in the plane (e.g. the frontal plane) along with the STA, the algorithm is in principle able to determine the functional center regarding 1DOF hinge like joint or 1DOF calibration motion in practice [4].
Declaration of Competing Interest There is no conflict of interest. Acknowledgement Financial Funding by the Else-Kröner-Fresenius-Stiftung, Grant 2017_A06, is gratefully acknowledged. References [1] R.B. Davis IIIet al., A gait analysis data collection and reduction technique, Hum. Mov. Sci. 10 (5) (1991) 575–587. [2] H. Kainz, et al., Estimation of the hip joint centre in human motion analysis: a systematic review, Clin. Biomech. 30 (4) (2015) 319–329. [3] R.M. Ehrig, et al., A survey of formal methods for determining the centre of rotation of ball joints, J. Biomech. 39 (15) (2006) 2798–2809. [4] M.H. Schwartz, A. Rozumalski, A new method for estimating joint parameters from motion data, J. Biomech. 38 (1) (2005) 107–116. [5] M. Sangeux, A. Peters, R. Baker, Hip joint centre localization: evaluation on normal subjects in the context of gait analysis, Gait Posture 34 (3) (2011) 324–328. [6] R.M. Ehrig, et al., A survey of formal methods for determining functional joint axes, J. Biomech. 40 (10) (2007) 2150–2157. [7] B.A. MacWilliams, A comparison of four functional methods to determine centers and axes of rotations, Gait Posture 28 (4) (2008) 673–679. [8] P. Procter, J. Paul, Ankle joint biomechanics, J. Biomech. 15 (9) (1982) 627–634. [9] L. Nofrini, et al., Evaluation of accuracy in ankle center location for tibial mechanical axis identification, J. Investig. Surg. 17 (1) (2004) 23–29. [10] R.A. Siston, et al., Evaluation of methods that locate the center of the ankle for computer-assisted total knee arthroplasty, Clin. Orthop. Relat. Res. 439 (2005) 129–135. [11] C.L. Brockett, G.J. Chapman, Biomechanics of the ankle, Orthop. Trauma 30 (3) (2016) 232–238. [12] J. Hicks, The mechanics of the foot: II. The plantar aponeurosis and the arch, J. Anat. 88 (Pt 1) (1954) 25. [13] T. Wyller, The axis of the ankle joint and its importance in subtalar arthrodesis, Acta Orthop. Scand. 33 (1–4) (1963) 320–328. [14] R.E. Isman, V.T. Inman, P. Poor, Anthropometric studies of the human foot and ankle, Bull. Prosthet. Res. 10 (11) (1969) 97–129. [15] A. Lundberg, et al., The axis of rotation of the ankle joint, J. Bone Joint Surg. Br. 71 (1) (1989) 94–99. [16] L. Claassen, et al., The geometrical axis of the talocrural joint—suggestions for a new measurement of the talocrural joint axis, Foot Ankle Surg. (2018). [17] E. Montefiori, et al., An image-based kinematic model of the tibiotalar and subtalar joints and its application to gait analysis in children with Juvenile Idiopathic Arthritis, J. Biomech. (2019). [18] K. Makki, et al., In vivo ankle joint kinematics from dynamic magnetic resonance imaging using a registration-based framework, J. Biomech. 86 (2019) 193–203. [19] S. Siegler, et al., Mechanics of the ankle and subtalar joints revealed through a 3D quasi-static stress MRI technique, J. Biomech. 38 (3) (2005) 567–578. [20] M.P. Kadaba, H. Ramakrishnan, M. Wootten, Measurement of lower extremity kinematics during level walking, J. Orthop. Res. 8 (3) (1990) 383–392. [21] D.A. Bruening, A.N. Crewe, F.L. Buczek, A simple, anatomically based correction to the conventional ankle joint center, Clin. Biomech. 23 (10) (2008) 1299–1302. [22] G.S. Lewis, K.A. Kirby, S.J. Piazza, Determination of subtalar joint axis location by restriction of talocrural joint motion, Gait Posture 25 (1) (2007) 63–69. [23] G.S. Lewis, et al., In vivo tests of an improved method for functional location of the subtalar joint axis, J. Biomech. 42 (2) (2009) 146–151. [24] R.W. Graydon, et al., The test-retest reliability of different ankle joint center location techniques, Foot Ankle J. 1 (11) (2015). [25] J. Simon, et al., The Heidelberg foot measurement method: development, description and assessment, Gait Posture 23 (4) (2006) 411–424. [26] G. Wu, et al., ISB recommendation on definitions of joint coordinate system of various joints for the reporting of human joint motion—part I: ankle, hip, and spine, J. Biomech. 35 (4) (2002) 543–548. [27] M. Medhat, H. Krantz, Neuropathic ankle joint in Charcot-Marie-Tooth disease after triple arthrodesis of the foot, Orthop. Rev. 17 (9) (1988) 873–880. [28] R. Donatelli, Abnormal biomechanics of the foot and ankle, J. Orthop. Sports Phys. Ther. 9 (1) (1987) 11–16. [29] M.B. Pohl, C. Lloyd, R. Ferber, Can the reliability of three-dimensional running kinematics be improved using functional joint methodology? Gait Posture 32 (4) (2010) 559–563. [30] M.A. Robinson, J. Vanrenterghem, An evaluation of anatomical and functional knee axis definition in the context of side-cutting, J. Biomech. 45 (11) (2012) 1941–1946.
5. Conclusion With the use of functional joint center calibration we could deduce the location of the ankle joint center to be slightly more medially and more distally to the malleolar midpoint and markedly more anteriorly. The results were consistent in all feet with little variation making this method promising for further use. Specifically when determining a fAJA from the PF movement, a few foot samples with numerically fAJAs far outside the region of orientation (7 out of 41 feet, respectively) were excluded from further analysis without yet having a rigorous explanation for the deviation. However, in all samples both calibration movements locate the AJC significantly anterior to the MM with consequences for clinical gait data obtained by standard modelling for both joint kinematics and kinetics. Given the validity of our results, which was not yet tested in this study, these effects would not be limited to the ankle only, but would have an influence on the segment definition of 99