Patterns of asymmetry and energy cost generated from predictive simulations of hemiparetic gait

Hemiparesis, defined as unilateral muscle weakness, often occurs in people post-stroke or people with cerebral palsy, however it is difficult to understand how this hemiparesis affects movement patterns as it often presents alongside a variety of other neuromuscular impairments. Predictive musculoskeletal modeling presents an opportunity to investigate how impairments affect gait performance assuming a particular cost function. Here, we use predictive simulation to quantify the spatiotemporal asymmetries and changes to metabolic cost that emerge when muscle strength is unilaterally reduced and how reducing spatiotemporal symmetry affects metabolic cost. We modified a 2-D musculoskeletal model by uniformly reducing the peak isometric muscle force unilaterally. We then solved optimal control simulations of walking across a range of speeds by minimizing the sum of the cubed muscle excitations. Lastly, we ran additional optimizations to test if reducing spatiotemporal asymmetry would result in an increase in metabolic cost. Our results showed that the magnitude and direction of effort-optimal spatiotemporal asymmetries depends on both the gait speed and level of weakness. Also, the optimal speed was 1.25 m/s for the symmetrical and 20% weakness models but slower (1.00 m/s) for the 40% and 60% weakness models, suggesting that hemiparesis can account for a portion of the slower gait speed seen in people with hemiparesis. Modifying the cost function to minimize spatiotemporal asymmetry resulted in small increases (~4%) in metabolic cost. Overall, our results indicate that spatiotemporal asymmetry may be optimal for people with hemiparesis. Additionally, the effect of speed and the level of weakness on spatiotemporal asymmetry may help explain the well-known heterogenous distribution of spatiotemporal asymmetries observed in the clinic. Future work could extend our results by testing the effects of other neuromuscular impairments on optimal gait strategies, and therefore build a more comprehensive understanding of the gait patterns observed in clinical populations.Author summary: Hemiparesis is muscle weakness that occurs primarily on one side of the body and can occur in a range of different clinical populations. Individuals with hemiparesis tend to walk with an asymmetrical motion and expend more energy while walking than other age-matched individuals. We still do not understand how each specific change to the neuromuscular system is linked with changes in walking patterns, in part because it is difficult to test one change at a time in people. Instead, we can use a mathematical model of the musculoskeletal system that represents the individual changes to the muscular system that occur in people with hemiparesis. In this study, we modeled how a weakness on one side of the body can impact walking patterns. We found that the level of weakness and the walking speed affect the asymmetrical walking patterns of our models, but do not change the total energy cost. Overall, our study is one step towards better understanding how neuromuscular impairments affect walking patterns. This knowledge could be applied to identify rehabilitation strategies that are most likely to improve walking in people with hemiparesis.