Optimization of modularity during development to simplify walking control across multiple steps

Abstract

Introduction: Walking in adults relies on a small number of modules, reducing the number of degrees of freedom that needs to be regulated by the central nervous system (CNS). While walking in toddlers seems to also involve a small number of modules when considering averaged or single-step data, toddlers produce a high amount of variability across strides, and the extent to which this variability interacts with modularity remains unclear.

Methods: Electromyographic activity from 10 bilateral lower limb muscles was recorded in both adults (n = 12) and toddlers (n = 12) over 8 gait cycles. Toddlers were recorded while walking independently and while being supported by an adult. This condition was implemented to assess if motor variability persisted with reduced balance constraints, suggesting a potential central origin rather than reliance on peripheral regulations. We used non-negative matrix factorization to model the underlying modular command with the Space-by-Time Decomposition method, with or without averaging data, and compared the modular organization of toddlers and adults during multiple walking strides.

Results: Toddlers were more variable in both conditions (i.e. independent walking and supported by an adult) and required significantly more modules to account for their greater stride-by-stride variability. Activations of these modules varied more across strides and were less parsimonious compared to adults, even with diminished balance constraints.

Discussion: The findings suggest that modular control of locomotion evolves between toddlerhood and adulthood as the organism develops and practices. Adults seem to be able to generate several strides of walking with less modules than toddlers. The persistence of variability in toddlers when balance constraints were lowered suggests a link with the ability to explore rather than with corrective mechanisms. In conclusion, the capacity of new walkers to flexibly activate their motor command suggests a broader range of possible actions, though distinguishing between modular and non-modular inputs remains challenging.

Keywords: development; modularity; muscle synergies; toddlers; variability; walking.

Figure 1

Illustration of stride events taken by the toddler. Events identified by the coder are shown with a grey background.

Figure 2

Illustration of the analyzed properties of the modular organization. Depicted are modular organizations of two spatial and temporal modules. At the center of each figure 8 activation coefficients are depicted (one for each stride). The variation of these coefficients defines the properties of consistency and selectivity. (A) example of a consistent and selective modular organization (activation coefficients show low variability and are significantly higher for given pairs of spatial and temporal module). (B) example of a modular organization with a high IRV (activation coefficients show high variability across strides). (C) example of a modular organization with a low IRS (activation coefficients are equivalent for each possible pair of spatial and temporal modules).

Figure 3

Control conditions. (A) Computational control. Raw adult signals are retrieved (this signal is a zoom from Figure 4) and step events are randomly shifted to verify that a difference between adults and toddlers is not due to difficulties to detect step events in toddlers. (B) Experimental control. Toddlers were recorded during stepping on a treadmill on the same day that they were recorded during walking in order to verify that variability in toddler was not mainly due to feedback regulations following new balance issues.

Figure 4

EMG and basic kinematic parameters in adults and toddlers and for control conditions. (A) Raw EMG in a representative adult. Preprocessed EMG are depicted at the right of the figure, in blue for this representative adult and in red for the control condition (randomly shifted detection of gait event, see Figure 3A). The black lines represent the average signal of the corresponding muscle in this participant after preprocessing while colored lines represent the signal of the corresponding muscle in each stride for the same participant. (B) Raw EMG for a representative toddler. Preprocessed EMG are depicted at the right of the figure, in green for walking and in yellow for the control condition (stepping in the same participant, see Figure 3B). (C) Basic kinematic and EMG parameters. From left to right: Stride duration, Variability of stride duration, Proportion of phases across the gait cycle, and Index of EMG Variability. Squares and points are individual data (for adults and toddlers respectively, with one color for each subject). Stars show significant differences after post-hoc tests (*p < 0.05; **p < 0.01; ***p < 0.001). Black stars are for the main analysis and color stars are for repeated analyses with control conditions.

Figure 5

Quality of reconstruction index (VAF) and number of modules. Color code is the same as in Figure 4: Adults and Toddlers primary conditions are, respectively, depicted in blue and green whereas computational control is depicted in red and experimental control in yellow. Squares and points are individual data (for adults and toddlers respectively, with one color for each subject). (A) results from variant I. The plot shows the resulting VAF in adults and toddlers when EMG signals were preprocessed either averaged across strides or not and then factorized into four spatial and temporal modules. Stars show significant differences after post-hoc tests (*p < 0.05; **p < 0.01; ***p < 0.001). Black stars are for the main analysis and color stars are for repeated analyses with control conditions. (B) results from variant II. 2 to 8 modules were extracted from non-averaged data. The plot shows the resulting VAF in adults and toddlers. The dotted line represents the threshold for a good quality of reconstruction (i.e., averaged VAF obtained in adults with four modules). More than 6 modules are necessary on average in toddlers to reach this threshold VAF. (C) Number of modules in primary and control conditions.

Figure 6

Properties of the modular organization of adults and toddlers. (A) Result of the factorization in a representative adult. Adult factorization is depicted for four spatial and temporal modules based on literature. (B) Result of the factorization in a representative toddler. Toddler factorization is depicted for six spatial and temporal modules, which was the minimum number of modules in this individual to cross the threshold VAF. In each figure, spatial modules are displayed on the left, and muscle weighting are represented in the following order: rectus femoris (RF), tibialis anterior (TA), biceps femoris (BF), soleus (So) and gluteus medius (GM) for the right side then for the left side. Temporal modules are depicted on the top of each figure. They represent 200 time points from the beginning of swing to the end of stance (considering phases of the right lower-limb). Activation coefficients are depicted in the center of each figure. Each bar represents the activation coefficient corresponding to one stride. An activation coefficient represents the concurrent activation of the corresponding pair of spatial and temporal modules during one stride. In each subplot, the y axis represents the amplitude of activation (arbitrary units). (C) Comparison of the modular organization properties in toddlers and adults. The Index of Recruitment Variability (top) indicates how variables activation coefficients are across the 8 steps in each population and condition. The index of Recruitment Selectivity (bottom) indicates how selectively distributed are those activation coefficients (i.e., exclusively activated with a given spatial or temporal modules or distributed across several ones). Results were verified with a fixed number of modules (stripped bars) to ensure that the effect was not due to methodological choices. Stars show significant differences (*p < 0.05; **p < 0.01; ***p < 0.001). Squares and points are individual data (for adults and toddlers respectively, with one color for each subject).