Eva Dorschky ¹ Marlies Nitschke ¹ Matthias Mayer ¹ Ive Weygers ² Heiko Gassner ^3,4 Thomas Seel ² Bjoern M Eskofier ^1,5 Anne D Koelewijn ^1,6*

• ¹ Machine Learning and Data Analytics Lab, Faculty of Engineering, Friedrich-Alexander-University Erlangen-Nürnberg, Erlangen, Bavaria, Germany
• ² Institute of Mechatronic Systems, Faculty of Mechanical Engineering, Leibniz University Hannover, Hannover, Lower Saxony, Germany
• ³ Department of Molecular Neurology, University Hospital Erlangen, Erlangen, Bavaria, Germany
• ⁴ Fraunhofer Insititute for Integrated Circuits (IIS), Erlangen, Bavaria, Germany
• ⁵ Institute of AI for Health, Helmholtz Center München, Helmholtz Association of German Research Centres (HZ), Neuherberg, Bavaria, Germany
• ⁶ Chair of Autonomous Systems and Mechatronics, Faculty of Engineering, Friedrich-Alexander-Universität Erlangen-Nürnberg, Erlangen, Bavaria, Germany

Estimating spatiotemporal, kinematic, and kinetic movement variables with little obtrusion to the user is critical for clinical and sports applications. One possible approach is using a sparse inertial sensor setup, where sensors are not placed on all relevant body segments. Here, we investigated if movement variables can be estimated similarly accurate from sparse sensor setups as from a full lower-body sensor setup. We estimated the variables by solving optimal control problems with sagittal plane lower-body musculoskeletal models, in which we minimized an objective that combined tracking of accelerometer and gyroscope data with minimizing muscular effort. We created simulations for 10 participants at three walking and three running speeds, using seven sensor setups with between two and seven sensors located at the feet, shank, thighs, and/or pelvis. We found that differences between variables estimated from inertial sensors and those from optical motion capture were small for all sensor setups. Including all sensors did not necessarily lead to the smallest root mean square deviations (RMSDs) and highest coefficients of determination. Setups without a pelvis sensor led to too much forward trunk lean and inaccurate spatiotemporal variables. Mean RMSDs were highest for the setup with two foot-worn inertial sensors (largest error in knee angle during running: 18 deg vs. 11 deg for the full lower-body setup), and ranged between 4.8-18 deg for the joint angles, between 1.0-5.4 BW BH % for the joint moments, and between 0.03 BW-0.49 BW for the ground reaction forces. We found strong or moderate relationships (R2 > 0.5) on average for all kinematic and kinetic variables, except for the hip and knee moment for five of the seven setups. The large range of the coefficient of determination for most kinetic variables indicated individual differences in simulation quality. Therefore, we conclude that we can perform a comprehensive sagittal-plane motion analysis with sparse sensor setups as accurately as with a full sensor setup with sensors on the feet and on either the pelvis or the thighs. Such a sparse sensor setup enables comprehensive movement analysis outside the laboratory, by increasing usability of inertial sensors.