Effective leg stiffness increases with speed to maximize propulsion energy Dynamics & Energetics of Human Walking Seyoung Kim and Sukyung Park, “Leg stiffness increases with speed to modulate gait frequency and propulsion energy”, Journal of Biomechanics, Vol.44(7): , 2011 Human Gait Research Seyoung Kim, PhD

Model based balance & gait analysis 2 Mechanical model-based human gait analysis – Periodic gait cycle [ Mcgeer 1990; Garcia et al ] – Lateral stability [ Kuo 1999 ] – Advantage of curved foot [ Adamczyk et al ] – Collision dynamics [ Jin and Park 2011 ] Research background [ Kuo 2001 ] [ Geyer et al ]

Model based balance & gait analysis Spring-like leg behavior to human gait dynamics 3 Lower limb stiffness was introduced in order to account for walking dynamics. spring-like leg mechanics [ Geyer et al. 2006; Whittington and Thelen 2009; Kim and Park 2011 ] Leg stiffness The relationship between Leg stiffness change w/ speed and energetic benefit Has not been investigated.

Model based balance & gait analysis 4 Objective : – We examined whether humans may benefit from spring-like leg mechanics during walking. Hypothesis : [1] Human walking may take advantage of resonance characteristics of the spring-like leg. [2] Humans may change their leg stiffness to obtain maximum propulsion energy as walking speed changes. Research objective

Model based balance & gait analysis Subjects – Eight healthy young (7M/1F, 23 ± 2y) – 1.68 ± 0.06 m / 66.7 ± 10.9 kg Protocols – Three sets of four randomly ordered frequency – Self-selected natural speed and maximum walking speed Measurement – Kinematics : sacrum and both ankles by Motion capture system – Kinetics : Ground reaction forces (GRFs) by three force plates Center of mass (CoM) estimation – Twice integrating the accelerations obtained from the GRFs data [ Donelan et al. 2002b; Yeom and Park 2010 ] Walking experiment Biomimetics Lab

Model based balance & gait analysis Compliant walking model 6 M : body mass R : curved foot radius θ : leg angle L : spring leg length K : spring constant C : damping constant [ Equation of motion ] Heel-strike force Motion Push-off force

Model based balance & gait analysis Model equation: Lagrangian formulation 7

Model based balance & gait analysis Double support phase (DS) – DS begins when the leading leg ( L 1 ) hits the ground. – DS continues until the trailing leg ( L 2 ) spring reaches its slack length ( L 0 ), where the single support phase begins. – During the DS, the CoM motion is constrained by two compliant legs. Single support phase (SS) – The trailing leg is repositioned ahead of the body’s CoM at a given inter- leg angle and becomes the leading leg for the next step. – When the leading leg hits the ground, i.e., touchdown, SS is finished. Mechanism of the walking model 8 L1L1 L2L2

Model based balance & gait analysis 9 Spring and damping constants from an optimization (Matlab®) that minimized the least square error between the GRF data and the model simulation over one step gait cycle, which consists of double and single support phases. Estimation of leg stiffness by model simulation [ Compliant walking model ] [ Vertical leg stiffness ]

Model based balance & gait analysis 10 Fitting results Model parameter change with gait speed Mechanical resonance characteristics Mechanical energy analysis Results and Discussion

Model based balance & gait analysis 11 Fitting result: goodness of fit (avg. 0.81±0.06) [ S. Kim and S. Park, Journal of Biomechanics (2011) ]

Model based balance & gait analysis Model parameter ( K,  ) change with gait speed 12 A B Humans increase joint stiffness as gait speed increases. The increase in joint stiffness could be achieved by increased muscle forces that reduce the range of joint motion. [ S. Kim and S. Park, Journal of Biomechanics (2011) ] Why the leg stiffness increases with gait speed ? Is there any energetic or dynamic benefit ?

Model based balance & gait analysis The duration of single support phase ≈ the period from damped natural frequency of the leg. The duration of the single support phase and the period of oscillation of the compliant leg 13 [ S. Kim and S. Park, Journal of Biomechanics (2011) ] ∆t∆t [ Video clip uploaded by moogyxo,Youtube.com (2007) ] Driving frequency: 1Hz Natural frequency: 1.6, 1, 0.63 Hz Human walking may take advantage of resonance ?  Analysis in the view of mechanical energy

Model based balance & gait analysis Parameter study: energetic benefits of human walking 14 Propulsion energy as a function of leg stiffness (14 ~ 28 kN/m) and walking speed (0.8 ~ 2.2 m/s)

Model based balance & gait analysis Leg stiffness to store max. propulsion energy 15 [ S. Kim and S. Park, Journal of Biomechanics (2011) ]

Model based balance & gait analysis Humans emulate spring-like leg mechanics, and modulate the apparent stiffness at a given walking speed. Conclusion 16 Leg stiffness increases with speed to modulate gait frequency and propulsion energy. Application: Quantifying parameter changes among different walking condition and/or subject groups Gait performance assessment for the elderly or patients Development of walking assist device Multi-joint stiffness to whole leg stiffness

Model based balance & gait analysis 17 The compliant walking model does not require an energy input mechanism to maintain steady walking. However, human walking requires active positive and negative muscle work [ Donelan et al., 2002 ]. Multi-joint stiffness characteristics were lumped into whole- leg stiffness. Thus, the compliant walking model does not specify how changes in leg stiffness might be attributed to changes at each joint. Limitations

Model based balance & gait analysis Funds – Postural control study was supported by a Basic Research Fund of the Korea Institute of Machinery and Materials, the second stage of the Brain Korea 21 Project, and a National Institute on Aging. – Walking research was supported by the Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education, Science and Technology (# ) and the Unmanned Technology Research Center (UTRC) at the Korea Advanced Institute of Science and Technology (KAIST), originally funded by DAPA, ADD. Collaborators – Fay B. Horak (Oregon Health & Science University) – Patricia Carlson-Kuhta (Oregon Health & Science University) – Chris G. Atkeson (Carnegie Mellon University) Acknowledgement 18

Model based balance & gait analysis 19 Special thanks to… Advisor: Sukyung Park, PhD

Model based balance & gait analysis 20

The oscillatory behavior of the CoM facilitates mechanical energy balance between push-off and heel strike Dynamics & Energetics of Human Walking Seyoung Kim and Sukyung Park, “The oscillatory behavior of the CoM facilitates mechanical energy balance between push-off and heel strike”, Journal of Biomechanics, Vol.44(7): , 2011 Human Gait Research Seyoung Kim, PhD

Model based balance & gait analysis 22 The least costly gait is achieved when the push-off propulsion fully compensates for the collision loss during the double support phase, during which the redirection of the center of mass (CoM) occurs [ Jin and Park 2011; Kuo 2002 ]. The duration of the CoM redirection can also be defined based on changes in work or velocity, and those durations are greater than that of the double support phase. The purpose of this study was to examine whether different definitions of the step-to-step transition (SST) would affect the mechanical energy balance between push-off and heel strike during gait. Introduction [ Adamczyk and Kuo 2009 ]

Model based balance & gait analysis 23 Mechanical energy balance btw PO and HS

Model based balance & gait analysis 24 The observed robustness of energetic optimality may be attributable to the seemingly symmetric oscillatory behavior of the CoM during the step-to-step transition. – Recent studies have described the motion of the CoM of the body during the gait cycle as the oscillation of the inertia on a compliant leg. – Due to the intrinsic symmetry of the mechanical power of an oscillatory mechanism around the minimum and maximum heights of the CoM, the mechanical powers of the mass before and after the mid point of the double support phase are approximated to be the same in magnitude but opposite in sign, showing energetic symmetry. Conclusion

Model based balance & gait analysis Funds – This research was supported by the Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education, Science and Technology (# ) and the Unmanned Technology Research Center (UTRC) at the Korea Advanced Institute of Science and Technology (KAIST), originally funded by DAPA, ADD. Acknowledgement 25

Model based balance & gait analysis 26