Introduction
Healthy adult humans can walk and run with ease, yet it takes years to develop stable
and economical locomotion. This apparent ease is the result of multiple degrees of
freedom at dozens of joints being controlled by hundreds of muscles, all recruited
and activated with precise timing and frequency by the neuromotor system (Turvey,
1990; Pandy and Andriacchi, 2010; Latash, 2012). Despite the multiple degrees of freedom
resulting from this abundance, as well as the variation across individuals, bipedal
gaits that emerge from this system (i.e., walking and running) are remarkably similar.
According to dynamical systems theory, these similarities in behavior emerge because
of attractors (Kelso et al., 1981; Kelso, 2012). Specifically, limit cycle attractors
may be primarily responsible for the convergence of joint motion to form the periodic
behavior in gait (Ijspeert, 2008; Broscheid et al., 2018).
Attractors represent coordination tendencies among system components (Davids et al.,
2008), can be identified at multiple levels and emerge from the self-organization
of the lower and higher-level components through circular causality (Haken, 1987).
This means that the behavior of components at a higher level will be influenced (i.e.,
constrained) in a bottom-up manner by the behavior of components at the lower level
and vice versa. With regards to locomotion, the two distinct human gaits, walking
and running, represent two attractors at the macroscopic level (Diedrich and Warren,
1995; Lamoth et al., 2009), relative to the joint coupling of the ankle, knee and
hip joints during these gaits that represents an attractor at a mesoscopic level (Diedrich
and Warren, 1995), relative to the rhythmic neural activity of the central pattern
generators that represents an attractor at a microscopic level (Cappellini et al.,
2006; Ijspeert, 2008; Minassian et al., 2017) (Figure 1). Please note that we use
micro-, meso- and macroscopic in relative terms, whereby the components at a mesoscopic
level are macroscopic level components relative to the microscopic components.
Figure 1
In bipedal gaits such as walking and running, gait, joint coupling and central pattern
generators (CPG) may represent limit cycle attractors (coordination tendencies that
cyclically repeat, simplified represented on the right in two dimensions based on
Kitano, 2004) at a macroscopic, mesoscopic and microscopic level relative to each
other when viewed from a top-down perspective, respectively. Internal and external
perturbations from for example fatigue or an uneven surface can lead to a phase transition
to another potentially less effective or less efficient (limit cycle) attractor. Large
perturbations may for example lead to problems such as falls during walking or an
ankle sprains while running. Training may increase the stability of attractors so
that perturbations of a larger magnitude or perhaps greater frequency or unpredictability
can be accommodated without a loss of stability.
Attractors in human locomotion may serve different purposes such as optimizing energetic
and mechanical efficiency (Selinger et al., 2015; Kung et al., 2018), minimizing mechanical
load (Kung et al., 2018), maintaining stability (Jordan et al., 2007) and increasing
the robustness of the motion to perturbations resulting from internal (physiology)
and external (environment) sources (Santuz et al., 2018). A decrease in stability
of an attractor and an increased variability can induce a spontaneous phase transition
to another attractor. An example of this in human locomotion is the walk to run transition,
whereby a decreased stability of phase relationships of walking gait and increased
variability in out-phase ankle-hip joint coupling with increasing walking speed results
in a sudden self-organized transition around a speed of 2 m/s to the more stable running
gait with a more in-phase joint coupling (Diedrich and Warren, 1995; Lamoth et al.,
2009; Kung et al., 2018).
Other factors such as training (Zanone and Kelso, 1992; Kostrubiec et al., 2012),
fatigue and aging (Stergiou and Decker, 2011) may also affect the magnitude of variability
or the stability of the movement system and thereby induce a phase transition to a
less optimal systems behavior. This may lead to reduced performance, injuries and
pain. As effective locomotion is key to success in many sports, but also a necessity
for functioning in daily life, understanding how the stability of the movement system
in walking and running can be improved through training to enhance performance and
reduce fatigue and injury would be beneficial. With the above points in mind, we propose
that dynamical systems theory provides a framework for understanding locomotion and
improving the effectiveness of interventions in locomotion-related problems. In this
opinion article, we discuss two locomotor-related problems in populations of very
different capacities, namely, falls among older adults and ankle sprain injuries in
runners, and discuss how the application of dynamical systems theory can lead to novel
approaches to intervention. Specifically, we hypothesize that applying small perturbations
during locomotion may be effective for modifying the stability of specific locomotor
attractors. Although using variability to improve performance is not novel [see studies
on the variability of practice hypothesis (Schmidt, 1975), contextual interference
effect (Magill and Hall, 1990) or differential learning (Beckmann and Schöllhorn,
2003; Schöllhorn et al., 2010; Serrien et al., 2018)], studies on these topics have
mostly investigated discrete skills such as football kicking and shot-put and induced
variability by practicing different movements rather than applying small unexpected
perturbations during the actual movement to be improved. The use of small unexpected
perturbations during movement may represent an effective way to further enhance performance.
Dynamical Systems Theory and Ankle Sprain Injuries in Running
Running is a gait fundamental to many sports, but also an activity that is associated
with a high injury incidence. A significant proportion of individuals participating
in running or running-based sports sustain acute injuries such as ankle sprains (Van
Gent et al., 2007; Fong et al., 2009). An ankle sprain can occur when high impact
forces induce rapid inversion during ground contact, in particular when running on
an irregular surface such as grass, sand or uneven sidewalks, or when changing direction.
This inversion results in excessive stretch of the lateral ligaments that may lead
to large strains or rupture (Fong et al., 2009).
Traditional approaches to ankle injury prevention and rehabilitation have applied
training such as balancing on a wobble board or on one leg with the eyes closed (Schiftan
et al., 2015). Although these approaches have been shown to be effective at preventing
re-injuries in individuals with a history of ankle sprains, the evidence is less conclusive
for ankle sprain prevention in individuals with no prior injury (Schiftan et al.,
2015). Up to 70% of individuals with ankle sprain injuries report incomplete recovery
and are therefore at a higher risk of re-injury (Anandacoomarasamy and Barnsley, 2005).
One reason for the less conclusive evidence regarding primary prevention and incomplete
recovery following an ankle sprain may be the different ways in which perturbations
are corrected in traditional balance training and high-intensity movements such as
running. According to the dynamical systems theory, a phase transition may occur from
a combined reflex and preflex based correction of perturbations during tasks with
no or minimum time pressure (e.g., traditional balance training on an unstable surface
or slow walking) to a more preflex dominant correction in tasks with high time pressure
such as the ground contact during high-speed running on uneven grass (Bosch, 2015).
Reflexes may be strong and fast enough to correct smaller perturbations during traditional
balance training, whereas they may be too slow and insufficient to prevent the effects
of perturbations during (high-speed) running. Indeed, using a computational model
of ankle inversion, DeMers et al. (2017) showed that reflexes took at least 80 ms
to partly correct the perturbation, but failed to fully prevent excessive inversion.
In contrast, moderate to high levels of co-activation were able to correct the perturbation
within 60 ms due to the force-length-velocity properties of the muscle fiber and tendon
elasticity, also known as preflexes (Loeb et al., 1999).
Applying small perturbations during running could potentially improve the robustness
of running gait and in particular the motions of the ankle to perturbations by modifying
the stability of the attractor via mechanisms such as alterations in step width and
muscle activation at a mesoscopic level (Santuz et al., 2018). In the long-term, these
acute mechanisms may translate into a more robust running gait pattern that is more
prone to injuries via alteration in contact times and stride frequencies. We hypothesize
that applying small perturbations during running may therefore be more effective for
prevention and rehabilitation of ankle sprains compared to traditional balance training
without time pressure, although further research is required to substantiate this
notion. Also note that both approaches can complement each other and are not necessarily
mutually exclusive.
Dynamical Systems Theory and Falls Prevention in Older Adults
Walking is an essential gait for daily life but is also accompanied with an increased
risk of falls with increasing age (Berg et al., 1997; Talbot et al., 2005). If we
exclude environmental influences, we can address an individual's falls risk by looking
either at the stability of their steady-state gait or at their behavior when they
are brought out of balance to the extent that the locomotor behavior is altered. The
latter has been the focus of much research, as many falls occur due to slipping or
tripping (Berg et al., 1997; Talbot et al., 2005). Research on perturbation-based
balance training has proliferated recently, during which the recovery reactions to
sudden perturbations to balance or gait are trained (Mansfield et al., 2015; Okubo
et al., 2016; Gerards et al., 2017; McCrum et al., 2017). However, as well as studying
the reactive responses following balance loss, it is important to consider how the
balance loss comes about, and if the robustness of the gait pattern to perturbations
can be improved. In this context, rather than just using large perturbations that
bring people out of balance, dynamical systems theory would suggest that applying
smaller perturbations during gait that do not require a complete switch of locomotor
behavior (phase transition in attractors) may also lead to positive improvements in
gait stability via an increased robustness of the movement patterns. Both coping with
small perturbations without a significant change in gait behavior and with large perturbations
that do require some explicit recovery movements have previously been suggested as
key requirements for stable gait (Bruijn et al., 2013), and both show significant
declines with increasing age (Maki and Mcilroy, 2006; Süptitz et al., 2013; Terrier
and Reynard, 2015; McCrum et al., 2016). The importance of studying stability during
steady-state gait, in addition to reactive stability during larger perturbations,
is supported by evidence of the relationship between decreased stability during steady-state
gait and falls incidence (Hausdorff et al., 2001; Van Schooten et al., 2016; Bizovska
et al., 2018).
Through the application of small perturbations during steady-state walking, the stability
of specific locomotion attractors may be modified. One study has demonstrated alterations
in motor primitives while walking and running on uneven, compared with even surfaces,
creating activation patterns that were more robust to the perturbations (Santuz et
al., 2018). If the basins of attraction of limit cycle attractors could be modified
in older adults, this could mean that perturbations of a larger magnitude (or perhaps
greater frequency or unpredictability) could be accommodated without significant loss
in dynamic stability. For example, while walking over uneven ground, more frequent
or larger undulations in the surface could be negotiated without loss of dynamic stability
and without the need for subsequent large reactive balance corrections. One recent
study had older participants walk on a treadmill with stable and unstable (water)
loads in a backpack (Walsh et al., 2018). As would be expected, step variability was
increased, and mediolateral dynamic stability decreased in the unstable load condition
and electromyography activity was also increased to cope with the load (Walsh et al.,
2018). If practiced over longer time periods, a more robust gait pattern may be the
result via alterations such as step width or time, joint moments at the ankle to control
center of mass velocity and muscle activation and motor primitives at a mesoscopic
level. Further research is needed to examine the training effects of walking with
small continuous unexpected perturbations and whether this translates to a more robust
response to large perturbations and subsequently reduced falls risk, but such training
represents one interesting avenue for future falls prevention interventions.
Conclusion
Human locomotion can be conceptualized as a behavior of a dynamical system, with attractors
that serve different purposes such as optimizing energetic and mechanical efficiency,
minimizing mechanical load, maintaining stability and increasing the robustness of
the motion to perturbations resulting from internal (physiology) and external (environment)
sources. We have proposed that through the application of small perturbations during
walking and running, the basin of attraction for specific locomotion attractors may
be modified, which may have benefits for both maintaining gait stability and for reducing
injury risk. Further research is required to elucidate the effectiveness of such interventions
in different populations.
Author Contributions
BVH and CM: Conception of the work; drafted the article. BVH: Prepared figure. All
authors participated in discussions of the literature and concepts, reviewed and revised
the article and approved the final version of the article.
Conflict of Interest Statement
The authors declare that the research was conducted in the absence of any commercial
or financial relationships that could be construed as a potential conflict of interest.
The handling editor declared a shared affiliation, though no other collaboration,
with one of the authors CM.