Effects of a Semi-Active Two-Keel Variable-Stiffness Prosthetic Foot (VSF-2K) on Prosthesis Characteristics and Gait Metrics: A Model-Based Design and Simulation Study

Background/Objectives: Semi-active prosthetic feet present a promising solution that enhances adaptability while maintaining modest size, weight, and cost. We propose a semi-active Two-Keel Variable-Stiffness Foot (VSF-2K), the first prosthetic foot where both the hindfoot and forefoot stiffness can be independently and actively modulated. We present a model-based analysis of the effects of different VSF-2K settings on prosthesis characteristics and gait metrics. Methods: The study introduces a simulation model for the VSF-2K: (1) one sub-model to optimize the design of the keels of VSF-2K to maximize compliance, (2) another sub-model to simulate the stance phase of walking with different stiffness setting pairs and ankle alignment angles (dorsiflexion/plantarflexion), and (3) a third sub-model to simulate the keel stiffness of the hindfoot and forefoot keels comparably to typical mechanical testing. We quantitatively analyze how the VSF-2K’s hindfoot and forefoot stiffness settings and ankle alignments affect gait metrics: Roll-over Shape (ROS), Effective Foot Length Ratio (EFLR), and Dynamic Mean Ankle Moment Arm (DMAMA). We also introduce an Equally Spaced Resampling Algorithm (ESRA) to address the unequal-weight issue in the least-squares circle fit of the Roll-over Shape. Results: We show that the optimal-designed VSF-2K successfully achieves controlled stiffness that approximates the stiffness range observed in prior studies of commercial prostheses. Our findings suggest that stiffness modulation significantly affects gait metrics, and it can mimic or counteract ankle angle adjustments, enabling adaptation to sloped terrain. We show that DMAMA is the most promising metric for use as a control parameter in semi-active or variable-stiffness prosthetic feet. We identify the limitations in ROS and EFLR, including their nonmonotonic relationship with hindfoot/forefoot stiffness, insensitivity to hindfoot stiffness, and inconsistent trends across ankle alignments. We also validate that the angular stiffness of a two-independent-keel prosthetic foot can be predicted using either keel stiffness from our model or from a standardized test. Conclusions: These findings show that semi-active variation of hindfoot and forefoot stiffness based on single-stride metrics such as DMAMA is a promising control approach to enabling prostheses to adapt to a variety of terrain and alignment challenges.