Angular damping coefficient of the in vivo human knee joint.

THE ANGULAR DAMPING COEFFICIENT OF THE IN VIVO HUMAN KNEE
JOINT
Steve McFaull 1 and Mario Lamontagne 1,2
School of Human Kinetics 1 and Department of Anatomy and Neurobiology 2
University of Ottawa, Ottawa, Ontario, Canada
INTRODUCTION
Muscle force prediction models (e.g., Davy and Audu, 1987) are constructed in an
attempt to predict the force contribution of individual muscles crossing a joint during a
specific movement pattern. It has been hypothesized that the passive structures spanning a
joint may also contribute to or oppose the net joint moment and possibly should be included
in a model to enhance its fidelity (Winter, 1990; Hatze, 1976). Omission of the passive
moments may be acceptable during the midrange of joint motion, however as the mechanical
limits of a joint are approached the passive moments become increasingly important.
Very little data exists in the literature regarding the moments which arise due to the
viscosity of the passive structures spanning the knee joint during full range flexion-extension.
Hatze (1975a) determined the angular damping coefficient of the knee joint for one male
subject using the small oscillation technique. The damping coefficient was found to be a
nonlinear function (parabolic) of the knee joint angle.
The purpose of the present investigation was to determine the angular damping
coefficient of the knee joint as a function of knee joint angle for a sample of normal subjects.
METHODS
Seventeen male subjects between the ages of 22 and 31 years volunteered for this
study. The small oscillation method as described by Hatze (1975, 1975a) was used to
determine the damping coefficient of the knee at joint angles of 10º, 45º, 90º, 110º, and
130º. The length of the biarticular muscles was held constant by fixing the hip joint at 90º
and the ankle joint at 0º (neutral). To ensure the passive state the surface EMG activity of
the main extensors and flexors of the leg was recorded during the testing. Five oscillation
trials were recorded from each subject at each knee angle. A strain gage loadcell
(Intertechnology) was used to record the amplitude decay of the oscillations. The loadcell
signal was A/D converted at 500 Hz and subsequently low pass filtered (f c =4 Hz). The time
period and logarithmic decrement of the underdamped oscillations were determined and the
equations given by Hatze (1975) were used to calculate the damping coefficients. The elastic
stiffness data was obtained from a separate experiment (refer to the abstract by the same
authors also included in these proceedings).
RESULTS AND DISCUSSION
Figure 1 depicts the mean damping function within the ± 1 standard deviation
envelope. The angular damping function is approximately quadratic in nature. On average,
the damping coefficient reaches a minimum at 90º, although some subjects (4) exhibited
minimum values at 45º. Overall, the data of Hatze (1975a) is somewhat larger in magnitude
than the average data observed in this investigation; although
considerable variation exists in the data of the present study especially at 130º. The quadratic
nature of the damping function is most likely due to the fact that passive
structures (ligaments, joint capsule, etc.) are being added and/or strained as the limits of the
joint are approached. The moments produced by the viscosity of the joint are determined by

multiplying the damping coefficient
by the angular velocity of the leg
(in rad/s). For example, if the
angular velocity is 10 rad/s the
passive viscous moment at 10º
would be about 13 N.m. Sincel the
small oscillation method is a linear
approximation, the values of the
damping coefficients presented in
this study probably represent the
upper limits since at higher
velocities the viscosity of the
passive tissues decreases due to the
nonnewtonian (thixotropic)
characteristics of biological tissues
and fluids (Fung, 1981).
In summary, the passive
moments which arise due to the
viscosity of the knee joint may be
significant in magnitude especially
for movements in which the knee
joint approaches its limits and the
magnitude of the net joint moment
is relatively small - such as during
the late swing phase of gait. If a
portion of the observed net joint
Figure 1. Mean angular damping coefficient of
the knee joint as a function of joint angle.
Dotted lines are ± 1 S.D.
moment could be satisfied passively, this will have implications in the magnitudes of the
predicted muscle forces.
REFERENCES
Davy, D.T., and Audu, M.L. (1987). Journal of Biomechanics, 20(2), 187-202.
Fung, Y.C. (1981). Biomechanics: Mechanical Properties of Living Tissues. New York:
Springer-Verlag.
Hatze, H. (1975). European Journal of Applied Physiology, 34, 217-226.
Hatze, H. (1975a). Ph.d. Thesis. University of South Africa.
Hatze, H. (1976). Mathematical Biosciences, 28, 99-135.
Winter, D.A. (1990). Biomechanics and Motor Control of Human Movement (2 nd ed.).
New York: John Wiley and Sons.
ACKNOWLEDGEMENTS
This study was partly funded by the Natural Sciences and Engineering Council and
the Research Committee of the University of Ottawa.