Walking and running represent the most basic modes of human locomotion. They are not only integral to our daily lives but also serve as popular forms of exercise due to their cost-effectiveness and accessibility. While walking and running may appear simple on the surface, they involve complex biomechanics and intricate interactions with the ground. The foot, as the primary point of contact with the ground during these activities, plays a crucial role in bearing body weight, absorbing and releasing energy, dampening ground impact, and facilitating propulsion. Consequently, understanding the functional aspects of the foot during walking and running is of paramount importance. One of the most commonly employed methods for analyzing foot function is through the measurement of foot pressure. This approach allows researchers and clinicians to gain insights into how the foot supports the body, how pressure is distributed across its various regions, and how it contributes to balance, stability, and motion control. Foot pressure analysis has found applications in rehabilitation programs, sports training, foot function evaluation, and sports shoe development. Traditionally, the plantar surface of the foot is divided into four major zones: the toe zone, metatarsal zone, midfoot zone, and heel zone. These zones can be further subdivided based on anatomical features. Functional analysis of the foot is typically carried out by examining metrics such as impulse, maximum pressure, maximum pressure intensity, and force loading rate in different regions of the foot. However, this approach, while informative, has limitations. It tends to focus on anatomical divisions, potentially overlooking shared mechanical properties among different regions of the foot. Additionally, traditional plantar pressure analysis methods often fail to account for the spatiotemporal characteristics of foot mechanics, limiting the exploration of dynamic mechanical features.
To address these limitations, a new study published in the peer-reviewed Journal Frontiers in Bioengineering and Biotechnology, led by PhD candidate Xiaotian Bai and Dr. Jingmin Liu from Tsinghua University, in collaboration with Dr. Hongfeng Huo from Hebei Normal University, the authors investigated the mechanics of human walking and running, with a particular focus on the functional analysis of the foot during these fundamental forms of human movement. The authors employed Non-Negative Matrix Factorization (NNMF), a data analysis method designed for processing complex non-negative data. NNMF breaks down the original data matrix into a base matrix reflecting the weight of each element and a coefficient matrix representing the overall characteristics of each element. This allows the extracted data to exhibit clustering and temporal characteristics. While NNMF has been widely used in sports science to analyze Surface Electromyographic Signals (sEMG) and explore muscle coordination during complex human actions, it also finds applications in the medical field, such as predicting drug-disease relationships or tumor distribution based on magnetic resonance imaging. In the context of foot mechanics, some researchers have successfully applied NNMF to functional partitioning of the foot. However, traditional statistical methods struggle to analyze the continuous data model of the coefficient matrix generated by NNMF. To overcome this challenge, the authors incorporated One-Dimensional Statistical Parameter Mapping (SPM1D), a technique rooted in random field theory, for topological analysis of continuous data models. This approach has been used in one-dimensional biomechanical data analysis, such as torque and angle studies. By combining SPM1D with NNMF, the researchers achieved quantitative analysis of the decomposed matrix and address the shortcomings of traditional plantar pressure analysis methods.
The study began by determining the number of foot functional units during walking and running. Through analysis, it was observed that when the number of foot functional units is set to 2, the Variance Accounted For (VAF) of the reconstruction matrix is more than 0.90 for both walking and running. The VAF remains consistent even when the number of foot functional units exceeds 2. Consequently, the study selects 2 foot functional units for analysis during both walking and running. Following the determination of foot functional units, the study proceeds to examine the characteristics of these units during walking and running. The analysis revealed that during walking, the two foot functional units primarily reflect distinct phases of the support period. The first unit, associated with cushioning and weight-bearing buffering, focuses on the heel region and the mid-forefoot region, specifically the second, third, and fourth metatarsal bones. This unit corresponds to the early phase (around 15% to 35%) of the stance phase when the foot undergoes dorsiflexion and knee joint flexion to decelerate the body’s forward motion. Notably, the heel and mid-forefoot regions dominate this phase, with the overall force characteristics concentrated around 20% and 80% of the stance phase. The second unit, related to push-off, aligns with the later stage (around 60% to 80%) of the stance phase during walking. In this phase, the posterior muscles of the lower leg and the muscles of the foot undergo plantar flexion to initiate push-off, while the thigh and buttock muscles begin exerting force, extending the knee joint and propelling the body forward. The primary force application area during this phase is the middle forefoot region, specifically the metatarsal bones M2 to M4.
Similar to walking, running also exhibits two foot functional units, representing cushioning and push-off phases. During running, the first unit, associated with cushioning, is characterized by the heel region and the second and third metatarsal bones. The overall force characteristics of this unit are concentrated around 10% to 30% of the stance phase. In contrast, the second unit, linked to push-off, places emphasis on the medial and central parts of the forefoot and the toes, with the force concentrated prior to 40% and between 40% to 60% of the stance phase. Comparing walking and running, it becomes evident that the primary force application areas in these units remain consistent, with the heel, mid-forefoot, and medial forefoot regions playing prominent roles. However, the timing and distribution of forces differ, with running completing the push-off phase earlier in the stance phase than walking.
To quantitatively assess the differences between foot function units during walking and running, the authors conducted comparisons of the coefficient matrices and basic matrices within these units. In the first foot functional unit, during the initial 20% of the support period, the overall force characteristics of the foot are higher in running than in walking. Additionally, the contribution weights of the second and third metatarsal regions are higher in running, while the weight of the lateral part of the heel region is lower in running, suggesting that running places greater impact on the forefoot during the buffering phase of rearfoot landing. In the second foot functional unit, walking exhibits lower overall force characteristics than running during the support phase from 11% to 69%. However, during the support phase from 73% to 92%, walking demonstrates higher overall force than running. Further analysis of the basic matrices reveals that running places higher weight on the heel and forefoot regions compared to walking during specific phases of the stance.
The findings of Xiaotian Bai and colleagues hold several important implications for understanding foot mechanics during walking and running. Notably, the application of NNMF and SPM1D techniques provides a novel approach to explore the dynamic mechanical characteristics of the foot during these activities. NNMF proves to be a valuable tool for simplifying the analysis of complex foot mechanical data. Its ability to extract features from multidimensional data while preserving temporal and spatial variations enhances our understanding of foot function. The study offered a more detailed functional division of the foot based on mechanical features. It highlights the roles of different regions of the foot during specific phases of the gait cycle, such as the heel’s importance in buffering during weight-bearing and the middle forefoot’s significance in push-off. The authors highlighted the importance of the transverse arch of the foot in both cushioning and push-off phases. It suggests that the arch area plays a crucial role in transitioning from elastic buffering to rigid lever function, particularly during push-off. In conclusion, the new study contributes to our understanding of foot function and have potential applications in sports science, rehabilitation, and the development of sports footwear. Future research can build upon these insights to explore foot mechanics in diverse populations and during complex movements.
Bai X, Huo H, Liu J. Analysis of mechanical characteristics of walking and running foot functional units based on non-negative matrix factorization. Front Bioeng Biotechnol. 2023;11:1201421. doi: 10.3389/fbioe.2023.1201421.