Parametric Modeling of Human Gradient Walking for Predicting Minimum Energy Expenditure

A mathematical model to predict the optimum gradient for a minimum energetic cost is proposed, based on previous results that showed a minimum energetic cost when gradient is −10%. The model focuses on the variation in mechanical energy during gradient walking. It is shown that kinetic energy plays a marginal role in low speed gradient walking. Therefore, the model considers only potential energy. A mathematical parameter that depends on step length was introduced, showing that the optimal gradient is a function of that parameter. Consequently, the optimal negative gradient depends on the individual step length. The model explains why recent results do not suggest a single optimal gradient but rather a range around −10%

Parametric modeling of human gradient walking for predicting minimum energy expenditure

A mathematical model to predict the optimum gradient for a minimum energetic cost is proposed, considering previous results that show a minimum energetic cost when gradient is -10%. The model focus on the variation of mechanical energy during gradient walking. It is shown that kinetic energy has a marginal role in low speed gradient walking. Therefore, the model takes in consideration only potential energy. A mathematical parameter that depends on step length is introduced, showing that the optimal gradient is a function of that parameter. Consequently, the optimal negative gradient depends on the individual step length. The model explains why recent results do not suggest a single optimal gradient but rather a range around -10%

Modelización biomecánica de la locomoción bípeda en humanos y homininos

[spa] La locomoción bípeda humana es un importante hito evolutivo. Los humanos aprendemos a caminar a temprana edad, aunque no por ello los procesos mecánicos involucrados son simples. Fuerzas y energía deben sincronizarse creando un equilibrio dinámico complejo. Ejemplo de ello es que el mínimo consumo energético en locomoción en gradiente se de con una pendiente negativa aproximada del -12% o bien que la trayectoría que minimiza el consumo energético entre dos puntos no necesariamente sea la más recta. Esta tesis presenta un modelo teórico de análisis biomecánico a fin de servir de marco conceptual en el que desarrollar los análisis energéticos de la locomoción bípeda en gradiente. De dicho modelo se extraen conclusiones como el rol dominante de la energía potencial gravitatoria en el balance energético, y emerge un parámetro adimensional, K, que gobierna el proceso de optimización del consumo energético determinando para cada valor de K un gradiente óptimo. Con el marco teórico desarrollado, se pueden explicar algunos de los resultados experimentales conocidos en aparente contradicción. A continuación y dada la relevancia del parámetro K, la tesis realiza una medición experimental en humanos modernos para determinar los rangos fisiológicamente permitidos para el parámetro K. Dicha medición se realiza en humanos adultos y adolescentes, hallando resultados consistentes. Se halla también un dimorfismo sexual entre mujeres y hombres adultos en el valor del parámetro K en el rango de valores naturales. Finalmente la tesis compara el valor de K para humanos modernos con el de diferentes homininos haciendo estimaciones de registros fósiles como los de Roccamonfina (Italia), Laetoli (Tanzania), Ileret (Kenia) o Happisburgh (Reino Unido). Basándonos en los valores hallados para humanos modernos se puede concluir que no todos los homininos estudiados tienen un valor del parámetro K dentro del rango de valores de los humanos modernos, y en consecuencia, podemos determinar que su grado de bipedismo no era mecánicamente igual al de nuestros contemporáneos.[eng] Human bipedal locomotion is a huge evolutionary milestone. Human children learn to walk very young, nonetheless, the mechanical processes involved are anything but simple. Energy and forces must synchronize creating a complex dynamic balance. The fact that the minimum energy consumption in gradient walking is achieved for a negative gradient of -12% or that the path that minimizes the energy consumption between two points is not always the straight one are two known examples of the complexity of gradient walking. This thesis presents a theoretical biomechanical model to set a conceptual framework in which the energetic analysis for human gradient walking can be developed. From this model some outstanding conclusions can be drawn such as the fact that the gravitational potential energy has a main role in the global mechanical energy balance or that a dimensionless parameter, K, is the key to minimize the energy expenditure in gradient walking, having a certain optimal gradient for each value of K. With the developed theoretical framework several known experimental results, apparently in contradiction, can be explained. Given the importance of K parameter, experimental measures of its value in modern human have been done, either for adult and sub adult, showing consistent results for both groups. It has been shown that a sexual dimorphism exists in human adults, having women a slightly but significantly bigger K parameter within the natural walking scenario. Finally the thesis compares the K value found for modern human against the estimated value for different hominins fossil registers such as Roccamonfina (Italy), Laetoli (Tanzania), Ileret (Kenya) or Happisburgh (United Kingdom). Based on the values found, it is shown that not all hominins had a K value within the range of values found for modern humans, thus it can be determined that their evolutionary stage of bipedism was not mechanically the same than the one achieved by modern humans

Parametric modeling of human gradient walking for predicting minimum energy expenditure

A mathematical model to predict the optimum gradient for a minimum energetic cost is proposed, considering previous results that show a minimum energetic cost when gradient is -10%. The model focus on the variation of mechanical energy during gradient walking. It is shown that kinetic energy has a marginal role in low speed gradient walking. Therefore, the model takes in consideration only potential energy. A mathematical parameter that depends on step length is introduced, showing that the optimal gradient is a function of that parameter. Consequently, the optimal negative gradient depends on the individual step length. The model explains why recent results do not suggest a single optimal gradient but rather a range around -10%