Predictive musculoskeletal simulations reveal the mechanistic link between speed, posture and energetics among extant mammals

A fundamental question in biology is understanding the relationship between body size and locomotor performance. Across mammals, a curious pattern emerges: the fastest animals are of intermediate size, neither the largest nor the smallest. This pattern, while observed in quadrupedal mammals, lacks a clear mechanistic explanation. The diversity in animal shape makes identifying the underlying mechanisms challenging. This study uses computational modeling to address this question, leveraging the ability to maintain consistent morphology while varying body size. Existing detailed musculoskeletal models, often based on hominin form, provide a framework for exploring the effects of size on speed and energetics. The significant variation in hominin body size throughout history, ranging from the small *Australopithecus afarensis* to the larger *Homo erectus*, and the existence of exceptions like *Homo naledi* and *Homo floresiensis*, further highlight the need for a mechanistic understanding of the size-speed relationship. This research directly tackles the question of why intermediate body size is optimal for speed in mammals by employing predictive musculoskeletal simulations across a wide range of body masses.

Previous research extensively explored the relationship between body mass and maximum running speed in mammals, consistently revealing the curvilinear relationship where intermediate-sized animals achieve the highest speeds. However, the mechanisms behind this pattern remain elusive. Studies on quadrupedal mammals have documented this relationship, but the diversity in morphology hampers a comprehensive understanding. Computational modeling offers a unique opportunity to explore this by systematically varying body size while holding morphology constant. Several prior theoretical models attempted to explain this phenomenon, focusing on either muscle power demands at smaller sizes or muscle work capacity at larger sizes. Some suggest that no single limiting factor applies across all body sizes. Studies on hominins show significant variation in body mass over time, providing a rich context for examining the impact of size on locomotion. Existing work on the relationship between posture and locomotor energetics in mammals shows a trend towards crouched postures in smaller animals and more upright postures in larger animals. This suggests that posture may play a key role in mediating the relationship between size and speed.

This study utilized a full-body OpenSim musculoskeletal model with 29 degrees of freedom, 92 muscle-tendon units, and 6 contact spheres per foot. The model, initially representing a generic human, was scaled across a body mass range of 0.1 kg to 2000 kg using geometric similarity principles. Segment mass, inertia, and linear dimensions were scaled according to established allometric relationships (m^1.0, m^1.67, and m^0.33, respectively). Maximum isometric force (F_max) was scaled with m^0.67, reflecting the proportionality to cross-sectional area. Linear dimensions of skeletal segments and muscle-tendon properties were scaled with m^0.33. Pennation angle and V_max remained size-invariant. The study employed an optimal control framework to simulate steady-state gaits (left-right symmetry) at different speeds, solving for muscle excitations that minimized a multi-objective cost function considering metabolic energy rate, muscle activity, joint accelerations, passive joint torques, and arm excitations. Direct collocation methods were used to solve the optimal control problem. Maximum gait speed for each body size was defined as the highest speed for which a feasible solution was found (within 10,000 iterations), characterized by distinct ground contact and aerial phases. The simulations provided data on stride parameters, ground reaction forces, cost of transport (COT), joint range of motion, muscle forces, activation, and strain rates. Safety factors (ratio of maximal muscle stress to observed muscle stress) for hip, knee, and ankle extensors were calculated. Effective mechanical advantage (EMA) was computed as the ratio of ground reaction force impulse to muscle force impulse during stance. Minimum COT was determined by analyzing the relationship between COT and speed for each body mass using generalized additive models. To explore the impact of athleticism, an "athletic" model was created by adjusting muscle strengths in the 60 kg model to match the hypertrophied musculature of elite sprinters, based on MRI data. Finally, experiments involving seven healthy adults walking and running on an instrumented treadmill were conducted to gather empirical data on stride parameters. Generalized additive models (GAMs) were used to analyze the non-linear relationships between variables and body size. Confidence intervals were estimated using simulations based on the model coefficients and covariance matrix.

The simulations revealed a curvilinear relationship between body mass and maximum running speed, mirroring that observed in real-world quadrupedal mammals. A 60 kg model was the fastest, achieving 6.3 m/s. The estimated optimal body mass maximizing speed was ~47 kg (95% CI 33–63 kg). The simulations demonstrated a decrease in COT with increasing body mass up to 700 kg, followed by a rapid increase. This is consistent with patterns observed in mammals. Smaller models adopted crouched postures, larger models upright postures. Analysis of safety factors indicated that muscle force limits speed in larger animals (low safety factors for hip and ankle extensors), while ground reaction force limitations constrain speed in smaller animals. Smaller models compensate for reduced contact time by adopting a crouched posture, increasing contact time and allowing the production of relatively larger impulses. There's a trade-off between stance time and stride frequency; increased stance time necessitates decreased stride frequency, impacting speed. Incorporating an "athletic" phenotype into the model resulted in a relatively small increase in speed (0.3 m/s) compared to a generic human model, suggesting that other factors beyond muscle size contribute to elite sprinting performance. The close match between simulated and empirical data on the relationship between body mass and locomotion patterns across both quadrupedal and bipedal animals is remarkable.

This study provides a mechanistic explanation for the observed curvilinear relationship between body mass and maximum running speed in mammals. The simulations demonstrate that speed limitations arise from an interaction between body mass and two different factors: muscle force production for larger animals and ground reaction force production for smaller animals. The intermediate optimum size reflects an optimal trade-off between these two constraints. The findings highlight the importance of considering both mechanical and energetic factors in understanding locomotor performance across a range of body sizes. The consistency of results across bipedal and quadrupedal gaits suggests the identified mechanisms represent general principles governing locomotion in mammals, rather than being specific to gait type. This study overcomes some limitations of previous studies by using a comprehensive musculoskeletal model and a wide range of body masses.

This study demonstrates that predictive musculoskeletal simulations can effectively reveal the mechanistic links between speed, posture, and energetics across a wide range of body sizes in mammals. The findings support the hypothesis that maximum speed is limited by muscle force in large animals and ground reaction force in small animals, with an intermediate body size representing an optimal trade-off between these constraints. This research emphasizes the power of computational modeling in uncovering fundamental biological principles and suggests directions for future research involving exploring the impacts of anatomical variability across diverse populations and in individuals with musculoskeletal diseases.

While the model incorporates many physiological details, some simplifications exist. The scaling exponents used might differ from empirical data due to a lack of robust data across the entire body size range examined, particularly in hominins. The study's focus on geometric similarity may not fully capture all complexities of allometric scaling. The model does not incorporate factors such as muscle fiber type composition or the detailed force-velocity relationship of skeletal muscle, aspects which could contribute to elite sprinting performance. The relatively small increase in speed observed with the "athletic" model highlights the multifaceted nature of elite athletic performance.