Estimation of Walking Energy Expenditure using a Single Sacrum-Mounted IMU Based on Biomechanically-Informed Machine Learning

Energy expenditure (EE) estimation during walking has significant applications in healthcare, sports science, and rehabilitation, but remains challenging to measure in real-world settings. Existing wearable approaches often require complex multi-sensor systems or extensive training datasets, limiting their practical implementation. We propose a biomechanically-informed approach to estimate EE based on sagittal joint powers of the body segment, derived from a single sacrum-mounted inertial measurement unit (IMU). Scaling relationships between efficiency-weighted segmental joint mechanical power and whole-body EE were first established by regression analysis. Segmental analysis revealed that sagittal-plane joint mechanical power of the body segment, particularly the stance leg strongly correlates with whole-body joint mechanical power (R > 0.9 across subjects and walking speeds). Leveraging this relationship and a lightweight artificial neural network that predicts segmental joint dynamics from an IMU data, the whole-body EE was estimated from the stance-leg sagittal power with efficiency coefficients and the regression-based scale factor. The approach was validated in 13 healthy adults walking at multiple speeds on a treadmill, with ground-truth EE measured via indirect calorimetry. The results demonstrated remarkable consistency both within individuals across speeds and across different subjects (coefficient of variation < 2%), suggesting a robust biomechanical linkage. Furthermore, joint dynamics of the stance leg were accurately estimated from single sacrum-mounted IMU data incorporating a single-leg stance partition and gait speed information. The resulting stance-leg power estimates enabled accurate EE estimation (RMSE 0.69 W/kg) across an independent cohort. This study demonstrates that sagittal-plane joint mechanical power of the body segment particularly the stance leg serves as a reliable biomechanical surrogate for whole-body EE during walking which can be robustly inferred through the efficiency-weighting and regression-scaling. The proposed method offers a simple and practical solution for wearable EE monitoring, with potential applications in clinical rehabilitation, exercise prescription, and daily health tracking.