Analysis of mechanical characteristics of walking and running foot functional units based on non-negative matrix factorization

Objective: To explore the characteristics of Non-Negative Matrix Factorization (NNMF) in analyzing the mechanical characteristics of foot functional units during walking and running. Methods: Eighteen subjects (9 males and 9 females) were recruited, and the ground reaction force curves of each foot region during walking and running were collected using a plantar pressure measurement system. NNMF was used to extract the mechanical features of different foot regions and to determine the number of foot functional units. The differences between the base matrices of walking and running were compared by traditional t-tests, and the differences in coefficient matrices were compared by one-dimensional statistical parameter mapping. Results: 1) When the number of foot functional units for walking and running were both 2, the Variability Accounted For (VAF) by the matrix exceeded 0.90 (VAF (walk) = 0.96 ± 0.02, VAF (run) = 0.95 ± 0.04); 2) In foot functional unit 1, both walking and running exhibited buffering function, with the heel region being the main force-bearing area and the forefoot also participating in partial buffering; 3) In foot functional unit 2, both walking and running exhibited push-off function, with the middle part of the forefoot having a higher contribution weight; 4) In foot functional unit 1, compared to walking, the overall force characteristics of the running foot were greater during the support phase of the 0%–20% stage, with the third and fourth metatarsal areas having higher contribution weights and the lateral heel area having lower weights; 5) In foot functional unit 2, compared to walking, the overall force was higher during the beginning and 11%–69% stages of running, and lower during the 4%–5% and 73%–92% stages. During running, the thumb area, the first metatarsal area and the midfoot area had higher contribution weights than during walking; in the third and fourth metatarsal areas, the contribution weights were lower during running than during walking. Conclusion: Based on the mechanical characteristics of the foot, walking and running can both be decomposed into two foot functional units: buffering and push-off. The forefoot occupies a certain weight in both buffering and push-off functions, indicating that there may be a complex foot function transformation mechanism in the transverse arch of foot. Compared to walking, running completes push-off earlier, and the force region is more inclined towards the inner side of the foot, with the hallux area having a greater weight during push-off. This study suggests that NNMF is feasible for analyzing foot mechanical characteristics.