Predictive neuromechanical simulations indicate why walking performance declines with ageing

Baseline neuromechanical model

We adapt a previously proposed neuromechanical walking model that can generate diverse 3‐D human locomotion behaviours (Song & Geyer, 2015) and predict human responses during walking against a range of unexpected disturbances (Song & Geyer, 2017). The model represents the human body with a rigid body chain whose joints are actuated by Hill‐type muscles (Fig. 2). These muscle models combine an active, force‐producing element with passive series and parallel elasticities similar to human muscle–tendon units. The active elements are stimulated by feedback control circuits that simulate neural control circuits, relating sensory input from the muscle spindles and Golgi tendon organs (length and velocity of contractile elements, force of muscle–tendon units), from the vestibular system (trunk lean), and from mechanoreceptors underneath the feet (contact information as well as perceived leg loading) to the output of the α‐motoneurons. The resulting muscle contraction forces act through moment arms to produce joint torques, which together with the gravitational force and the ground reaction forces that the legs experience, generate walking in a physics‐based simulation of the human model. No human gait data are used in the simulation process, and the actual walking motion that emerges in the model depends solely on the values of its control parameters (such as the gain of a muscle's stretch reflex) and of its mechanical parameters (such as segment mass, maximum muscle force and contraction velocity).

We use the 2‐D sagittal plane portion of this model and add more physiological details relevant to the study of elderly gait. Specifically, the length and mass of skeletal segments (Winter, 2009), the strength and mass of muscles (Miller, 2014), and the range of joint motions (Roach & Miles, 1991) are further tuned. We also use a more detailed muscle activation dynamics model (the relationship between muscle excitation and contraction) (Thelen, 2003), and add sensory and motor noise (van der Kooij & Peterka, 2011), where the parameter values are all determined based on human experimental data.

Model modification on age‐related physiological properties

We modify the baseline model to represent healthy adults with an age of about 80 years. Pathological symptoms not observed in healthy elderly people, such as stooped posture (Hirose et al. 2004), are not considered. All modifications to the baseline model are presented in Table 1, where the specific values of changes are either adopted from previous modelling studies or estimated from available human data. The modifications are categorized into six groups based on the component of the model they apply to (Fig. 2). In the skeletal layer, the body mass distribution changes due to loss of leg muscles and gain of body fat (S ₁) (Jensen & Fletcher, 1994; Pavol et al. 2002), and the range of hip extension reduces due to muscle contracture (S ₂) (Roach & Miles, 1991; Kerrigan et al. 1998). In the muscular layer, the muscles lose strength (Thelen, 2003; Monaco & Micera, 2012) and mass, with much larger loss in the strength (M ₁) (Goodpaster et al. 2006; Delmonico et al. 2009), and a number of muscle properties change, where the most prominent change is that of becoming slower (M ₂) (Lexell, 1995; Thelen, 2003; Monaco & Micera, 2012; Nilwik et al. 2013). Since not much is known about how the control changes in elderly walking, we do not change the neural control structure, but we apply neural changes of reduced neural conductance speed (N ₁) (Bouche et al. 1993; Rivner et al. 2001) and increased sensory and motor noise (N ₂) (Goble et al. 2009). All changes are applied together to represent elderly people, and each change is applied individually to the baseline young model for further analysis.

Control parameter optimization

For each model with different physiological changes, we optimize the control parameters to minimize the cost

where T is the time duration, A _m is muscle activation, v _avg is the average walking speed, and v _tgt is the target walking speed. All of these values are calculated during the last six steady steps of the simulation. The first term, ${\displaystyle \frac{1}{T}\sum _{\mathrm{m}}\underset{T}{\int }{A_{\mathrm{m}}}^2\mathrm{d}t}$, represents muscle fatigue and has been commonly used in neuromechanical modelling studies of human locomotion (Thelen & Anderson, 2006; Ackermann & van den Bogert, 2010; Miller et al. 2012) as an optimization cost (Appendix A, ‘Optimization cost’). For all models, we search for solutions at 0.8, 1.0, 1.2, 1.4, 1.6 and 1.8 ms⁻¹, which covers the range of slow and fast walking speeds of healthy people (Murray et al. 1984).

We use covariance matrix adaptation evolution strategy (CMA‐ES) (Hansen, 2006) with the actual optimization cost constructed as multiple stages (Song & Geyer, 2015) that first search for steady and stable walking solutions with all joint angles within the range of motion, and then minimize eqn (1). A single trial of CMA‐ES is set to run for 400 generations with a population size of 16 and takes about 1 day on a modern desktop machine. To ensure convergence and to avoid bad local minima, we chain multiple CMA‐ES trials by initializing a new run (with a new unbiased covariance matrix) with a previous solution until the solutions do not improve and by starting new trials with different initial parameters. We continue this optimization process until most of the monitored walking features of a model, such as J (eqn (1)), COT, step length and trunk lean, show qualitatively smooth trends across all walking speeds. On average, the optimization process for one set of control parameters involved five CMA‐ES trials.

Metabolic energy consumption

The simulations show that the combined modifications produce gait consistent with elderly walking. Like young and elderly people (Kerrigan et al. 1998; Monaco et al. 2009; Schmitz et al. 2009), the young and elderly models walk with more or less similar time trajectories of the joint angles and torques, the ground reaction forces, and the muscle activations. However, the elderly model has also adapted in ways common to elderly gait. It has more pelvic tilt with less hip extension throughout the gait cycle (Kerrigan et al. 1998; Monaco et al. 2009) and a smaller ankle plantarflexion torque during stance (Kerrigan et al. 1998; Monaco et al. 2009; Monaco & Micera, 2012) (Fig. 3). Most importantly, the metabolic cost has shifted as known from human experiments. It is, on average, 16% higher than in the young model across all walking speeds, and the walking speed that minimizes COT remains about the same in both models as observed in humans (compare Fig. 4 A and Fig. 1).

When the modifications are applied one by one, the simulations reveal that the increase in COT is triggered mainly by the loss of muscle strength and mass (M ₁). Applying M ₁ to the young model results in a substantial increase in the average COT (16%), while applying any of the other modifications does not (<5%) (Fig. 4 B). Further analysis of the muscle metabolic energy consumption model ($E_{\mathrm{m}}=m_{\mathrm{m}}(h_{\mathrm{A},\mathrm{M}}+h_{\mathrm{s}})+w_{\mathrm{M}}$, where m _m is the muscle mass, h _{A, M} is the activation and maintenance heat, h _s is the shortening heat, and w _M is the mechanical work) points to two factors that mainly and about equally contribute to the COT increase (in Appendix A, ‘Metabolic energy calculations’). The first factor is the decline in muscle quality. Ageing muscles weaken more than they lose mass (Goodpaster et al. 2006; Delmonico et al. 2009) (Table 1, M ₁), which results in more energy consumed per amount of force produced due to the increase in activation and maintenance heat rate. Second, the size principle of motor unit recruitment amplifies the energy consumption of weaker muscles. Motor unit recruitment progresses from slow‐twitch muscle fibres at low activations to metabolically more expensive fast‐twitch fibres at higher activations (Martin et al. 1992; Bhargava et al. 2004), which is captured in the activation and maintenance heat rate of the metabolics model and further amplifies the energetic cost of producing the same force.

Our simulation results suggest training muscle strength and mass may be the only effective way to enhance metabolic economy in elderly walking. While it is known that physical training can reverse muscular changes and enhance walking performance in elderly people, the effects of different training regimes vary and it remains unclear which one is optimal (Lopopolo et al. 2006). Our results suggest that a training regime which focuses on restoring muscle strength and mass (M ₁) may be most effective, and that reversing other physiological changes matters less (S ₁, M ₂, N ₁) or not at all (S ₂, N ₂).

Preferred walking speed

Neither in human experiments nor in our computer simulations can the metabolic cost of transport explain the slower speed at which elderly people prefer to walk, but we find evidence that another criterion based on muscle fatigue can. Muscle fatigue is often studied in the elderly with regard to balance control and fall risk (dos Santos et al. 2017). Its effect on the preferred speed of walking is not well understood; however, fatigue of the tibialis anterior muscle has been shown to lower the speed at which humans prefer to transition from walking to running (Segers et al. 2007). We find that, when combined in a performance criterion similar to the COT, minimizing muscle fatigue suggests preferred walking speeds observed in young adults and elderly people. Specifically, we define the fatigue of transport (FOT) as the fatigue accumulated by all muscles over the distance travelled, ${\displaystyle \frac{1}{d}\sum _{\mathrm{m}}\underset{T}{\int }{A_{\mathrm{m}}}^2\mathrm{d}t}$, where the squared muscle activations is a gauge of fatigue commonly used in neuromechanical models (Appendix A, ‘Muscle fatigue calculations’) (Ackermann & van den Bogert, 2010). We then compute the FOT from our simulation data and find it is minimal at 1.49 ms⁻¹ in the young model and at 1.21 ms⁻¹ in the elderly model (Fig. 4 C). The two minima are consistent with the preferred walking speeds of young and elderly people (Himann et al. 1988; Lauretani et al. 2003), supporting the hypothesis that muscle fatigue could govern a person's preference on speed. The result may also explain the observation that fatigued young and elderly people do not change walking speed by much (Helbostad et al. 2007; Granacher et al. 2010), as their gait seems already optimal in this regard.

If muscle fatigue indeed governs the preferred speed, then the FOT calculations for the model variants with individual age‐related modifications show that restoring walking speed is more difficult than restoring metabolic economy. Similarly to the increase in metabolic costs, a shift of the minimum FOT towards slower walking speed in the elderly model results from the loss of muscle strength and mass (M ₁, −0.32 ms⁻¹). Yet, in contrast to the results for metabolic costs, the shift also results from the redistribution of the segment masses (S ₁, −0.31 ms⁻¹) and from the lower speed of muscle contraction (M ₂, −0.18 ms⁻¹) (Fig. 4 D). These results suggest that increasing the preferred walking speed would require a training that addresses all three changes simultaneously. However, the changes are connected at least in part by the age‐related atrophy of fast twitch fibres (Nilwik et al. 2013), which is associated with loss and slowdown of leg muscles and a related shift in mass distribution. A training that focuses on reversing this atrophy would thus seem most effective.

Limitations

As with any simulation study, ours is based on assumptions that may limit its predictive capabilities. First, our model simplifies the neuromuscular structure of the human locomotor system. Although we have tried to include in this structure the parts that previous studies have suggested to influence elderly gait, any missing part may have an effect as well. For instance, we estimated the metabolic energy consumption of young and elderly muscles following the same formulation (Bhargava et al. 2004), but the validity of this assumption has not been tested. Second, we rely on a hypothesized neural control circuitry and an optimization criterion to identify walking gaits in our model. Although neither has been validated in human experiments, the optimization criterion we use is commonly applied in many studies on human locomotion performance (Thelen & Anderson, 2006; Ackermann & van den Bogert, 2010; Miller et al. 2012), and we find no qualitative differences in model outcome with alternative criteria of muscle fatigue and metabolic energy (Appendix A, ‘Optimization cost’). The control circuitry of the model has at least been demonstrated to predict human leg kinematics, kinetics and muscle activations in steady walking (Song & Geyer, 2015) and human responses to unexpected disturbances (Song & Geyer, 2017). An alternative to assuming a specific neural control circuitry would be to directly optimize the muscle stimulation patterns for obtaining walking gaits (Ackermann & van den Bogert, 2010; Miller et al. 2012). However, this alternative approach implies the human controller has no underlying structural constraints. Moreover, when muscle stimulation patterns are directly optimized, it is difficult to include the effects of control‐related changes, such as neural transmission delays (N ₁), and sensory and motor noise (N ₂).

Conclusion

We have investigated the physiological origins of the age‐related decline in walking performance with a predictive neuromechanical model. In simulations of this model with physiological changes known to affect elderly people, we have found that their increased metabolic cost of walking is caused mainly by the loss of muscle strength and mass. In addition, we have found that the slower preferred walking speed of elderly people would emerge if humans adapt to muscle fatigue rather than energy economy, and that this adaptation occurs in response to several muscle‐related changes in physiology. The results suggest that reversing these changes is the only effective way to enhance the performance of elderly walking. Physical training has been shown to achieve such a reversion, although it remains unclear precisely which training regimes work well (Lopopolo et al. 2006). A regime with a focus on restoring the fast‐twitch muscle fibres (Pyka et al. 1994; Nilwik et al. 2013) may be most effective.

Competing interests

None declared.

Author contributions

Both authors designed the research and drafted the article. S.S. conducted the simulation studies. Both authors approved the final version of the manuscript, agreed to be accountable for all aspects of the work, and qualify for authorship. All those who qualify for authorship are listed.

Funding

This work is supported in part by the Richard King Mellon Foundation Presidential Fellowship in the Life Sciences at Carnegie Mellon University.