Biomechanics

Quantitative Characterization of Human Mechanical Impedance

Mechanical impedance is a fundamental property of the human neuromuscular system that facilitates seamless, dynamic interactions with the physical environment. Specifically, it plays a crucial role when humans interact with unpredictable and/or destabilizing environments, complementing the slower actions that can be achieved through neural feedback.

Our lab utilizes robotic technologies to characterize mechanical impedance of human limbs and joints. The core challenges that we plan to address include the development of new robotic devices and system identification methods for multi-joint multi-DOF studies. Based on successful development of the devices and methods, we intend to identify intrinsic and reflexive mechanical impedance and their relative contribution during functionally relevant conditions.

Previous research includes the quantitative characterization of ankle, wrist, and elbow mechanical impedance.

Summary of Ankle Impedance during Walking

The human ankle joint plays a critical role during walking and understanding the biomechanical factors that govern ankle behavior and provides fundamental insight into normal and pathologically altered gait. Previous researchers have comprehensively studied ankle joint kinetics and kinematics during many biomechanical tasks, including locomotion; however, only recently have researchers been able to quantify how the mechanical impedance of the ankle varies during walking. The mechanical impedance describes the dynamic relationship between the joint position and the joint torque during perturbation, and is often represented in terms of stiffness, damping, and inertia. The purpose of this short communication is to unify the results of the first two studies measuring ankle mechanical impedance in the sagittal plane during walking, where each study investigated differing regions of the gait cycle. Rouse et al. measured ankle impedance from late loading response to terminal stance, where Lee et al. quantified ankle impedance from pre-swing to early loading response. While stiffness component of impedance increases significantly as the stance phase of walking progressed, the change in damping during the gait cycle is much less than the changes observed in stiffness. In addition, both stiffness and damping remained low during the swing phase of walking. Future work will focus on quantifying impedance during the ``push off'' region of stance phase, as well as measurement of these properties in the coronal plane.

Sex Differences in Ankle Impedance

Ankle stiffness has been known as one of the most important components contributing to the maintenance of lower body stability during postural balance and locomotion. It has been repeatedly shown that women have lower stability and increased risk of injury when compared to men participating in similar sports activities, yet sex differences in neuromuscular control of the ankle, including the modulation of ankle stiffness, and their contribution to stability remain unknown. To identify sex differences in human ankle stiffness, this study quantified multi-dimensional ankle stiffness in 20 young, healthy men and 20 young, healthy women over a range of ankle muscle contractions, from relaxed to 20% of maximum voluntary co-contraction of ankle muscles. A wearable ankle robot and a system identification method were used to reliably quantify ankle stiffness in a 2-dimensional space spanning the sagittal plane and the frontal plane. In all muscle activation levels, significant sex differences in ankle stiffness were identified in both the sagittal and frontal planes. In the given experimental conditions, ankle stiffness in males was higher than females up to 15.1 and 8.3 Nm/rad in the sagittal plane and the frontal plane, respectively. In addition, sex differences in the spatial structure of ankle stiffness were investigated by quantifying three parameters defining the stiffness ellipse of the ankle: area, aspect ratio, and orientation. In all muscle activation levels, a significant sex difference was identified in the area of stiffness ellipse as expected from the sex difference in the sagittal and frontal planes. However, no statistical sex difference was observed in the aspect ratio and orientation, which would be due to little differences in major anatomical configurations of the ankle joint between sexes. This study, in combination with future studies investigating sex differences during dynamic tasks (e.g. postural balance and locomotion) would serve as a basis to develop a risk assessment tool and sex-specific training programs for efficient ankle injury prevention or rehabilitation.

J. Trevino and H. Lee, Annals of Biomedical Engineering (2018)

Characterization of 2D Ankle Impedance

Multivariable dynamic ankle mechanical impedance in two coupled degrees-of-freedom (DOFs) was quantified when muscles were active. Measurements were performed at five different target activation levels of tibialis anterior and soleus, from 10% to 30% of maximum voluntary contraction (MVC) with increments of 5% MVC. Interestingly, several ankle behaviors characterized in our previous study of the relaxed ankle were observed with muscles active: ankle mechanical impedance in joint coordinates showed responses largely consistent with a second-order system consisting of inertia, viscosity, and stiffness; stiffness was greater in the sagittal plane than in the frontal plane at all activation conditions for all subjects; and the coupling between dorsiflexion–plantarflexion and inversion–eversion was small—the two DOF measurements were well explained by a strictly diagonal impedance matrix. In general, ankle stiffness increased linearly with muscle activation in all directions in the 2-D space formed by the sagittal and frontal planes, but more in the sagittal than in the frontal plane, resulting in an accentuated “peanut shape.” This characterization of young healthy subjects’ ankle mechanical impedance with active muscles will serve as a baseline to investigate pathophysiological ankle behaviors of biomechanically and/or neurologically impaired patients.

Characterization of 2D Wrist Stiffness

Because the dynamics of wrist rotations are dominated by stiffness, understanding wrist rotations requires a thorough characterization of wrist stiffness in multiple degrees of freedom. The only prior measurement of multivariable wrist stiffness was confined to approximately one-seventh of the wrist range of motion (ROM). Here, we present a precise nonlinear characterization of passive wrist joint stiffness over a range three times greater, which covers approximately 70% of the functional ROM of the wrist. We measured the torque–displacement vector field in 24 directions and fit the data using thin-plate spline smoothing optimized with generalized cross validation. To assess anisotropy and nonlinearity, we subsequently derived several different approximations of the stiffness due to this multivariable vector field. The directional variation of stiffness was more pronounced than reported previously. A linear approximation (obtained by multiple linear regression over the entire field) was significantly more anisotropic (eigenvalue ratio of 2.69+/- 0.52 versus 1.58 +/- 0.39; p < 0.001) though less misaligned with the anatomical wrist axes (12.1 +/- 4.6° versus 21.2 +/- 9.2°; p < 0.001). We also found that stiffness over this range exhibited considerable nonlinearity—the error associated with a linear approximation was 20–30%. The nonlinear characterization over this greater range confirmed significantly greater stiffness in radial deviation compared to ulnar deviation. This study provides a characterization of passive wrist stiffness better suited to investigations of natural wrist rotations, which cover much of the wrist’s ROM. It also provides a baseline for the study of neurological and/or orthopedic disorders that result in abnormal wrist stiffness.

A. Pando, H. Lee, W. Drake, S. Charles, and N. Hogan, IEEE Transaction on Biomedical Engineering (2014)

Treadmill Characterization for Biomechanics Studies

Non-ideal behavior of a treadmill depends on gait phase, speed, and weight

Noticeable differences exist between treadmill and overground walking; kinematics, kinetics, and muscle activation patterns differ between the two. Many previous studies have attributed the differences to changes in visual information, air resistance, and psychological effects such as fear. In this study, we demonstrate that no treadmill serves as an inertial frame of reference. Considering the linear momentum principle, the finite sampling rate of the controller, and the limited power of the treadmill motor, we predict that 1) the error of the treadmill speed periodically varies depending on the locomotion phase and 2) this non-ideal behavior becomes more evident as the locomotion speed or the weight of the walker increases. Experimental observation confirmed our predictions by quantifying the variation of the actual treadmill belt speed and the ground reaction force in the anterior–posterior direction for different locomotion speeds and subject weights. These results emphasize a need for design criteria like the minimum sampling rate and the minimum motor power that treadmill locomotion studies should consider.

A. Tielke, J. Ahn, and H. Lee, Scientific Reports (2019)

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