The current study proposes the use of the αMω, which encapsulates a 3D angular relationship between the joint moment (M) and the joint angular velocity (ω) vectors, in an attempt to provide a “simple” measure of the function of intrinsic foot joints during gait. Our hypothesis was confirmed by the results which showed that the intrinsic foot joints are never fully propelling, resisting or stabilized, but instead adopt a stabilized-resistive configuration during most of the stance phase, with the exception of during pre-swing when all joints adopt a propulsive configuration. This stabilized-resistive configuration keeps the foot from collapsing while bearing weight, allowing stabilization of the foot and thus accomplishing the stability requirements of locomotion .
This study expanded the calculation of αMω from a lower limb model to a four-segment kinetic foot model. The αMω pattern of the Ankle joint found in this study was generally similar to that proposed by Dumas and Chèze (2008) . The most notable difference between the results of the two studies was that during loading response Dumas and Chèze (2008) found a stabilized configuration as opposed to the resistive configuration found in this study. The decomposition of αMω revealed that this discordance in configuration is likely to arise from different kinematic patterns, as Dumas and Chèze (2008) found a predominant combination of abduction and external rotation movements, whereas this study showed a combination of plantarflexion and eversion movements. It may be concluded that the observed differences may therefore come from the variation in foot kinematics between participants, since both studies used the same joint center, anatomical landmarks and reference frame to model the ankle joint.
A point of interest which deserves discussion is the critical role of the method by which the ankle complex is modelled. The simplified representation of the foot as a single functional segment is still widely used to quantify ankle joint kinetics in clinical biomechanical studies. The results showed that both peak power generation and absorption were lower in the Shank-Calcaneus joint than in the Ankle joint (Fig. 5). This is in accordance with previous gait studies for asympatomatic [29,30,31] and symptomatic  subjects. However, in terms of αMω and P/R% waveforms, the Shank-Calcaneus joint and the Ankle joint showed similar waveforms during the stance phase of gait.
As αMω is simply an extension of the joint power, it not possible to directly relate the propulsion/resistance or stabilization configuration to a particular anatomical structure crossing the joint. For instance, a resistance configuration does not systematically reveal an eccentric action of the muscles but the tension of tendons, ligaments, fascias and skin. Still, αMω can be interpreted with regards to the foot functional anatomy. Adding αMω to the computation of foot kinetics creating a four-segment foot model enabled the discovery of new insights into how the Chopart and Lisfranc joints are contributing to foot function from midstance to pre-swing. However, the interpretation of αMω of both joints during loading response should be undertaken with care, as the forefoot may not yet be in contact with the ground, and their respective joint moments were found to be close to zero. The computed αMω of both joints appear to correspond with their respective functional anatomy. The Lisfranc joint shows predominantly a stabilized configuration during midstance, possibly caused by the anatomical stiffness of the tarsometatarsal joints. The passive stability of the Lisfranc joint is largely provided by the plantar ligaments and the second metatarsal with its encased base between the cuneiforms. The peroneus longus tendon, inserted at the plantar aspect of the first metatarsal base, and the first cuneiform further contribute to the stabilization of the first ray in opposition to dorsiflexion moments that are commonly exerted by ground reaction forces acting plantar to the first metatarsal head . In contrast to the Lisfranc joint, the Chopart joint has considerably more freedom of movement and requires a resistive-stabilized configuration to control the deformation of the longitudinal arch under load, and to avoid collapsing during midstance and propulsion. Recent evidence suggests that the stability of the longitudinal arch is not only provided by the passive structures (e.g. plantar ligaments and plantar fascia), but also by contraction of the plantar intrinsic foot muscles . These muscles act as local stabilizers increasing the inter-segmental stability of the longitudinal arch. They have small cross-sectional areas and therefore produce small rotational moments . Flexor hallucis longus and tibialis posterior provide further substantial dynamic support to the medial longitudinal arch. These muscles provide both resistive and propulsive capabilities during gait [35, 36].
The foot’s rigidity in late stance is mainly attributed to the windlass and midtarsal locking mechanisms [37, 38]. The stiffening of the foot is required to resist the ground reaction forces and allow efficient propulsion of the body in late stance. At heel off, αMω and P&R % waveforms of the Ankle and Lisfranc joints are simultaneously adopting a propulsive configuration at terminal stance, which means that both joints are predominantly being driven by their respective plantarflexion moments, and thus contributing to power generation (Fig. 4-5). Recent studies suggest that this power generation at the Lisfranc joint during terminal stance is the result of the Windlass mechanism [11, 29, 39]. The activation of this mechanism results in tension the plantar fascia by winding it around the metatarsal heads as the toes dorsiflex in terminal stance . The power generated at the Lisfranc joint would then in turn result in the optimal repositioning of the bones around the Chopart joint . The reorientation of the midfoot bones were mainly characterized in our results by a plantarflexion moment combined with a dorsiflexion and inversion movement of the Chopart joint resulting in a resistive configuration. This phenomenon is often referred in the literature as the midtarsal locking mechanism [37, 41]. However, the term “locking” seems inappropriate as rotational movement at the Chopart joint was observed at terminal stance. It has also been suggested that the increased tension in the plantar fascia, and possibly other muscle-tendon structures, would result in a shortening and rise of the longitudinal arch through flexion and adduction of the metatarsals in combination with an inversion of the rearfoot [38, 42]. The longitudinal arch raise would then induce a first ray plantarflexion, an inversion of the Chopart joint, an inversion of the rearfoot, and Ankle dorsiflexion . At 65% of the stance, the resistive configuration adopted by the Chopart joint is converted into a propulsive configuration where the moments and angles show predominantly a plantarflexion inter-segmental action combined with a plantarflexion movement (Fig. 2-5). This configuration conversion allows the Chopart joint to contribute to power generation. Elastic recoil of the tibialis posterior as well as of the plantarflexors of the ankle and toes’ further add to power generation at the Chopart and ankle joints during terminal stance and pre-swing .
A last point of interest is the functioning of the First Metatarso-phalangeal joint during propulsion, which tends to absorb relatively more power than the joints distal to the Ankle joint (Fig. 5). The Ankle and the First Metatarso-Phalangeal joints, among all joints of the foot, undergo the largest ranges of motion in the sagittal plane, while moving in opposite directions during the majority of the stance phase of gait. Both joints are crossed by the tendon of flexor hallucis longus, which acts as a plantarflexor of the ankle and a joint-stabilizer of the First Metatarso-Phalangeal joint. Further active stabilization of the hallux against the ground is provided by the flexor hallucis brevis, adductor and abductor hallux muscles which exert a plantar flexion moment. Evidence suggests that this power absorption observed at the First Metatarso-Phalangeal joint could be the result of the pressing down action of the intrinsic foot muscles and the flexor hallucis longus to stabilize the hallux against the ground and to counteract the dorsiflexion and eversion moments externally produced by the ground reaction forces [43, 44]. Kelly et al. (2014) further suggested that the intrinsic foot muscles also served to decrease the stress on passive elements, such as the plantar ligaments, plantar fascia and plantar plate, crossing the First Metatarso-Phalangeal joint . It may therefore be concluded that the resistive configuration adopted by the First Metatarso-Phalangeal joint at terminal stance and pre-swing is in accordance with earlier findings describing the mechanisms countering the ground reaction forces.
There are several limitations to this study. A first issue concerns the estimation of the center of pressure and resultant ground reaction forces for each foot segment, derived from combining force and pressure data. The use of a proportionality scheme was originally validated for the calculation of joint kinetics of a three segment foot model and not for a four segment foot model . Validity of the proportionally scheme was assessed by comparing the predicted shear forces obtained from the same experimental setup as the present study with the measured shear forces obtained by asking the participants to adopt a 3 step controlled foot placement approach on two adjacent force plates during a walking trial. Mean differences of less than 3% between the shear force measured by 2 adjacent force plates and the shear force predicted by the proportionality scheme in the hindfoot and forefoot segments were found in a paediatric population. Recently, Eerdekens et al. (2019) has further investigated the clinical applicability of the proportionality scheme in subjects suffering from ankle and hindfoot osteoarthritis . Their results revealed insignificant over- and underestimation errors in multi-segment foot kinetics by comparing estimated shear forces with measured shear forces obtained by an adjacent force plate method. However, these results should be viewed with care as errors in the determination of the point of force application have been found towards force plate edges . Therefore, the results of the current study should be considered as an estimation and further research is needed.
A second limitation is the use of skin markers to estimate joint centers and segmental kinematics. Estimation of movement of foot bones using skin markers, especially in complex joints such as the Chopart and Lisfranc joints, is a challenging process complicated by the small size of the foot bones as well as the relatively small motions occurring at these joints. Over the last decade, multi-segment kinematic foot models using skin markers have been proposed to estimate the kinematic behaviour of foot joints by grouping foot bones into segments (e.g. hindfoot, midfoot, forefoot), the clinical value of which has been shown through the detection of intrinsic foot mobility impairments [1, 47]. However, this approach can lead to inaccuracies in foot joint kinematic and kinetic estimations as these models do not account for individual bone-to-bone motion and therefore may violate rigid-body assumptions [2, 8]. In addition, soft-tissue artefacts must be considered in segmental foot analysis [2, 6, 8]. To overcome these challenges, methods using bone-anchored markers and biplanar videoradiography have been used to provide more accurate measures of foot joint motion, which can be difficult to discern with skin mounted markers [2, 6,7,8]. However, the invasive/ ionising nature of these alternative methods precludes their use in routine clinical analysis. To assess the errors in experimental data due to violation of the rigid-body assumption, studies have compared bone-mounted markers with skin-mounted markers [2, 8], which found no systematic error pattern in the degree of skin motion over the underlying foot bones. They also reported that the degree of error varied between subjects and between anatomical sites and found maximum differences of 3 to 9 degrees between skin and bone-mounted marker data [2, 8]. Recently, Kessler et al. (2019) compared foot motion measured by biplanar videoradiography and optical motion capture . They found good agreement between the two systems for foot motion in the sagittal plane, and reported soft-tissue artefacts of 3.29 mm on the surface of the foot . However, the impact of these errors on the estimation of foot joint moments, angular velocity and powers is difficult to assess. Therefore, the results of the current study should be considered as an estimate, and further research using emerging technologies such as biplanar videoradiography is needed to provide a more detailed insight into the kinetic behavior of foot joints.
A third limitation concerns the recruitment of asymptomatic participants, which does not mean that all feet were entirely free of degenerative changes in foot structure (e.g. clinical osteoarthritic changes). Studies have shown that a sizeable percentage of asymptomatic individuals may present abnormal findings of soft tissues on magnetic resonance imaging [48, 49]. Finally, since walking speed results in different foot kinetics, the effect of walking speed on αMω should be further investigated in future studies .