Subjects

The cross-sectional study was carried out on active and healthy adults (18-60 years old; min. two sport activities per week) who were free from any musculoskeletal complaints or acute infections, had had no surgery on the lower extremities during the previous 12 months and did not perform any intensive training session the day before the examination. All participants signed an informed consent and ethics approval for the study was retrieved from the Ethics Committee of the Canton of Bern (KEK-No. 052/15). Twenty-two participants were included and examined but only the data from 20 persons were eligible for further analysis due to data acquisition errors in two cases. One subject was additionally excluded from further statistical analysis in addition because this person presented an atypical and non-representative walking pattern, characterized by making initial contact with the midfoot and a lacking heel rocker phase [4]. Subjets’ antropometric data is presented in Table 1.

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Table 1. Subjets’ anthropometric data [Mean (SD)].

https://doi.org/10.1371/journal.pone.0208175.t001

Measurement procedure

Foot kinematics were measured using a three-dimensional motion capture system with 10 cameras (Vicon Motion Systems, Ltd, Oxford, UK; 8x Bonita 3 and 2x Bonita 10 cameras at 200 Hz) that provided a measurement volume of (4 x 1.5 x 1.5) m³). Ground reaction forces were measured with a force plate (AMTI OR6, AMTI Inc., Watertown, USA; sampling frequency 1 kHz) and served for initial contact and toe off identification (threshold at 25 N) to subsequently extract the kinematics during stance. While the participants were walking at self-selected speed, the kinematics of the right foot were simultaneously captured by a set of four markers to quantify the navicular mobility in terms of cranio-caudal (NCC) and medio-lateral translation (NML) of the navicular tuberosity (Fig 1b) [17] and by the Oxford Foot Model (OFM) [18] to measure forefoot to hindfoot (FFtoHF), hindfoot to tibia (HFtoTBA) and global hindfoot rotations (HFL) (Fig 1). The foot’s longitudinal axis was the bisecting line of the MPM-MPL-CA triangle. The X-Y plane was calibrated to be parallel with the foot’s planar surface based on a static bipedal standing trial and defined via the plane spanned by MPM-MPL-CA markers. NML was measured parallel to the x-axis and NCC was measured parallel to the z-axis. The 3D rotations output by the OFM were reported as Euler angle sequence of 1) sagittal plane rotations (plantar-/dorsalflexion), 2) transversal plane rotations (adduction/abduction for FFtoHF angles; internal/external rotation for HFtoTBA and HFL angles) and 3) frontal plane rotations (pro-/supination for FFtoHF angles; inversion/eversion for HFtoTBA and HFL angles). The software Vicon Nexus version 1.8.5 was used for measurement and version 2.5 for 3D point reconstruction, marker labelling, gait event detection and in the case of the OFM to calculate the model outputs. The Vicon PlugInGait Lowerbody model is a prerequisite for the OFM and the OFM markerset was applied in addition to the PluginGait Lowerbody markerset. The PlugInGait Lowerbody model is part of Nexus by default and the OFM is available as plug-in from Vicon. The joint kinematics from the PlugInGait Lowerbody model and the OFM were calculated within Nexus while the navicular translation parameters were calculated with custom-made software in Matlab (Version 2017a, The MathWorks Inc., Natick, USA). The .c3d file format (www.c3d.org) and the btk-Toolkit [19] were used to access the measurement data from Matlab. Spherical skin surface markers with a diameter of 16 mm were used for the PluginGait Lowerbody model and of 14 mm diameter for the Oxford and navicular mobility foot models. Using smaller markers for the measurement of foot kinematics was necessary to properly resolve the intrinsic foot motion within the given measurement volume. An experienced physical therapist palpated the anatomical landmarks and applied the reflective markers by means of double-face adhesive tape while the participants were in bipedal upright standing pose (Fig 1).

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Fig 1.

Skin-surface markers used for measuring right foot kinematics (a) and description of the 4-marker foot model (b). (a) Markersets for the OFM and the 4-marker foot model applied to the right foot. The markers at the middle of the dorsal calcaneous (CA), the lateral caput of the 5^th metatarsal bone (MPL) and the medial caput of the 1^st metatarsal bone (MPM) were shared by both models. The marker at the tuberosity of the navicular bone (NA) was applied in addition for the 4-marker foot model. (b) 4-marker foot model to measure cranio-caudal (NCC) and medio-lateral (NML) navicular displacement.

https://doi.org/10.1371/journal.pone.0208175.g001

Data analysis

Data analysis was carried out in Matlab and included the extraction and normalization of stance phase time-series (0-100% stance phase; 200 samples/stance phase) and averaging among the trials from each participant. Between 6 and 15 walking trials from each participant were averaged to retain representative stance phase kinematics for further analysis. An analysis was made of how the two navicular mobility measures related to each other and to the forefoot to hindfoot (FFtoHF), the hindfoot to tibia (HFtoTBA) and the hindfoot to laboratory (HFL) angles. Translational (NCC, NML) and rotational (FFtoHF, HFtoTBA, HFL) displacements from initial contact to toe off were considered in the analysis. The following relationships were explored further qualitatively by displacement-displacement plots and quantitatively by cross-correlation coefficients at zero phase shift (X_c) [5, 10]: (i) NCC to NML, (ii) NCC and NML to FFtoHF plantar-/dorsiflextion, adduction/abduction and pro-/supination, (iii) NCC and NML to HFtoTBA internal/external rotation and inversion/eversion, and (iv) NCC and NML to HFL inversion/eversion. The cross-correlation coefficients were calculated with the cross-correlation function xcorr() from Matlab’s Signal Processing Toolbox (normalization option ‘coeff’ to normalize the cross-correlation sequence so that X_c ∈ [−1, 1]). In accordance with Pohl et al. [5], the following conventions were used for interpreting the degree of the relationships between the model outputs:

• Strong: −1 ≤ X_c ≤ −0.8 and 0.8 ≤ X_c ≤ 1
• Moderate: −0.8 < X_c ≤ −0.3 and 0.3 ≤ X_c < 0.8
• Weak: −0.3 < X_c < 0.3

Compared to Pohl et al. [5], who considered ≥ 0.7 (or ≤ −0.7) as strong, the thresholds used in this study for classifying a relationship as strong were more restrictive. The ranges of motion (RoMs) must be taken into account when interpreting relationships based on cross-correlation coefficients because ranges of motion [10] below measurement errors may lead to large cross-correlation values and hence to an overinterpretation that two kinematic time-series are strongly related even if one or both movements were not substantial. We therefore adopt an error threshold of 3° mentioned by Wolf et al. [10] for the angular displacements and use an error threshold of 2 mm for the navicular displacements (RMSE estimate of 1 mm [17]), which the RoMs must exceed to classify a relation as valid.

In addition to looking at the whole stance phase, the analysis of the relationships between the various foot kinematic measures was subdivided into phases of power absorption and generation ( and , respectively) based on the anterior-posterior ground reaction force, which represents the two phases related to the body center of mass in the direction of progression. This was done to explore the relationships more closely to the two fundamental functional requirements of foot function, on the one hand, providing flexibility for shock absorption and balance and, on the other hand, stiffness for effective propulsion during push-off [3, 4]. The two phases were discriminated by the direction of the anterior-posterior ground reaction force component, which turns from posterior to anterior at around 50% of stance as the body center of mass is moved from behind to the front of the foot fixed to the ground during normal walking [4].

Relationship between cranio-caudal and medio-lateral navicular translation

The navicular translation parameters showed a pattern of caudal dropping while deviating medially up to a deflection point around 75% stance phase where the pattern turned into rising cranially and shifting laterally (Fig 2a). In addition, the NML showed a deflection around 20% stance phase, which was not apparent in NCC. Patterns similar to NCC were already observed by others, who studied the navicular drop during walking [20, 21]. The cranial rise exceeded the initial contact level at toe off. While the RoMs during absorption were similar, the RoM of NCC was more than twice as high as the RoM of NML during generation. The pattern is reflected in the displacement-displacement diagram (Fig 2b) and also in the cross-correlation coefficients which were primary classified as moderate and strong (Fig 2d) resulting in a relationship for the stance phase at the transition from moderate to strong (-0.79). Looking at the absorption and generation phases separately, the relationships became stronger. The mean RoMs were above the error threshold of 2 mm (Table 2), which indicates valid relationships.

Relationships to forefoot to hindfoot kinematics

Sagittal and transversal plane kinematic waveforms of the forefoot with respect to the hindfoot showed similar patterns. The forefoot dorsiflexed while it abducted during approximately the first 75% of stance, and from then on it started to plantarflex and adduct until toe off. In contrast, this pattern did not become evident in the pronation/supination movement, where the maximum pronation was reached around 20% stance phase by subsequent forefoot supination. Nevertheless, all waveforms of the FFtoHF kinematics were consistent with observations that were also made with the Oxford Foot Model in healthy adults [22] and children [23]. The similarities of sagittal and transversal FFtoHF kinematics with the cranio-caudal and medio-lateral navicular displacements became evident qualitatively from the linear patterns in the displacement-displacement diagrams and quantitatively from the cross-correlation values (Fig 3, Table 3). A clear association could be observed between the FFtoHF plantar/dorsiflexion and the NCC displacement with median cross-correlation coefficients above 0.90 and more than 60% classified as strong in all phases (Table 3, Fig 3d) and a distinct linear pattern (Fig 3b left). The navicular bone dropped as the forefoot dorsiflexed and vice versa. The relationship with the NML displacement was close to the moderate to strong transition (0.78), which indicated that the navicular bone deviated medially as the forefoot dorsiflexed and vice-versa. The strength of the relationship between FFtoHF abduction/adduction and NCC and NML was similar (median cross-correlation around 0.80), although somewhat stronger for the absorption phase in the case of NML (-0.98), but which might be overestimated due to the relatively small RoM in FFtoHF abduction during absorption (Table 2). Basically, the forefoot abducted while the navicular bone dropped caudally and drifted medially and adducted while the navicular bone rised cranially and shifted laterally. The FFtoHF pronation/supination was only moderately linked to the cranio-caudal navicular displacement but showed a strong relationship to the medio-lateral navicular displacement with a median cross-correlation of -0.90 and more than 57.9% classified as strong in all phases (Table 3). The relationship was especially pronounced during the absorption phase (-0.98). Hence, the navicular bone deviated medially as the forefoot pronated and vice versa.

Relationships to hindfoot kinematics

The waveform observed for the HFtoTBA external/internal rotation, which showed external rotation until around 20% stance phase followed by subsequent internal rotation, differed from those of HFtoTBA and HFL eversion/inversion which presented eversion until around the absorption/generation transition, followed by inversion. Nevertheless, both patterns were consistent with the literature [22]. HFtoTBA external/internal rotation was poorly related to NCC (0.15) and rather moderately to NML (-0.38), in which case the cross-correlation for the absorption phase was noticeably higher (-0.88) compared with the generation phase (0.10), although no linear pattern became apparent from the displacement-displacement diagram. This can be explained by the common shapes of NML and HFtoTBA external/internal rotation with distinct deflection points around 20% stance phase. Hence, the hindfoot rotated externally relative to the tibia (i.e. the tibia rotated internally relative to the hindfoot) as the navicular bone deviated medially during approximately the first 20% of the stance phase, but the navicular bone did not reverse the medial motion as the hindfoot reversed its direction of rotation towards internal during the remaining generation phase. For the generation phase relationships of HFtoTBA external/internal rotation, the cross-correlation values were heterogeneous among the participants and broadly spread from strong negative to strong positive (Fig 4f). Hence, the resulting median relationships were weak (0.10) although only for 21.1% of the participants the relationships were classified as weak (Fig 4g Table 3). HFtoTBA eversion/inversion was moderately (0.74), even if close to the strong transition, related to NCC and strongly related (-0.83) to NML, whereas in both cases the relationships were strong when considering the absorption and generation phases separately. The relationships of NCC and NML to the global hindfoot eversion/inversion were only moderate (0.44 and -0.44, respectively). The high cross-correlation of -0.94 for the absorption phase in the case of the relationship to NML cannot be classified as valid because the RoM of hindfoot inversion/eversion did not exceed the error threshold. That a strong relationship to HFtoTBA internal/external rotation was only found for the medio-lateral translation during absorption suggests that there is no systematic coupling between foot pronation and tibia rotation. The hindfoot eversion/inversion (i.e. the calcaneal angle) did not present any relationship to the navicular parameters but it turned out that the eversion/inversion of the hindfoot relative to the tibia (i.e. the Achilles tendon angle) led to relatively high cross-correlations. Hence, taking the frontal plane tibia motion in addition to the calcaneal angle into account seemed to highly increase the relationship between hindfoot motion and foot pronation. In fact, the frontal plane curves of the hindfoot and the hindfoot relative to the tibia did not represent substantial shape differences (Fig 4a). Therefore, the increase in cross-correlation coefficients must be attributed to the higher angular range due to the tibia motion and not to more similarity with the navicular translation curves. Hence, the relationship between navicular translation and hindfoot motion is suggested to be rather weak.

Limitations

We included participants complying with the criteria of being asymptomatic but did not classify feet according to morphological criteria. This may explain the occasionally large spreads of cross-correlation coefficients. The results might differ in low- or high-arch, even though symptom-free, subgroups and the representativeness of the present study might be therefore limited. The results are limited to walking gait and might not be directly transferred to situations like walking on stairs or running. The cross-correlation analysis is limited to the fact that the coefficients capture only linear relationships between two signals. Hence, small values may result, even if two signals were strongly related but in a non-linear fashion (e.g. quadratic). When interpreting cross-correlation coefficients, which are in fact Pearson correlations in function of a phase shift between the two vectors under consideration, it must be born in mind that they are sensitive to the range of the vector values. Hence, larger cross-correlation coefficients might results from increased ranges of values rather than actually more similarity of curve shapes. In addition, the interpretation of the strength of relationships is dependent from the cross-correlation levels used for classification. Since cross-correlation coefficients are relative estimates on how much of the variance in a dependent variable can be explained by an independent variable, there is no absolute rule from when on a relationship can be said to be strong. However, we set this limit at 0.8 and are more restrictive in this respect than previous examinations [5]. Limitations due to soft tissue artifacts must always be borne in mind when applying skin surface marker based methods. Nevertheless, skin-based markers represent real life conditions in clinical gait analysis settings.