A viscoelastic model has been
developed for the dynamic behavior of a muscle
and tendon pair suitable for use as an actuator
in neuromusculoskeletal control simulation.
This model accounts for the steady-state force
generator characteristics of the musculotendon
unit, such as force variation with length, velocity
with length and velocity with load, as well as
accounting for the transient behavior of the
system in response to dynamic changes in
activation and loading. This model is
formulated as a bond graph in a manner to be
implemented with standard system simulation
software. A careful and thorough section on
parameter estimation from available
physiologic data is included. The bond graph is
compatible with inclusion into an anatomically
more comprehensive model, based on its
inherent hierarchic capability for system
building.

INTRODUCTION

The static and dynamic characteristics
of skeletal muscles and their accompanying
tendons define the properties of the actuators in
the neuromusculoskeletal system. Each
musculotendon unit is similar in structure but
has individual characteristics that tend to suit its
particular role in producing the joint torques
that ultimately cause skeletal motion. For
example, muscles with a larger physiologic
cross-sectional area are able to develop more
total force, while muscles with a higher
percentage of fast fiber composition are able to
achieve a faster contraction velocity (Winters,
1988).
The musculotendon unit also provides
feedback corresponding to the mechanical state
of the muscle and tendon. Anatomically, these
feedback transducers are the muscle spindles
and the Golgi tendon organs. They are
embedded within the musculotendon unit so as
to experience the same relative length changes
as the individual muscle and tendon. The
feedback from these proprioceptors is

MUSCULOTENDON ACTUATOR MODEL

The model should be complex enough to
account for commonly accepted behavior of
muscle, yet be simple enough to be defined as a
macro function for the actuators in a
neuromusculoskeletal control simulation.
As an actuator, the musculotendon unit
receives an activation level as an input and
produces as outputs a force and velocity at the
junction between the tendon and the load. Live
muscle preparations are commonly tested invitro
under isotonic and isometric conditions.
Measurements made with these types of tests
include the static tension versus length, velocity
versus length at a constant load and velocity
versus load. These types of tests characterize
the force generator characteristics of the
contractile unit after transient effects have
decayed. Typical observations include the
following.
The active force developed by the
muscle reaches a maximum at the optimal
length of the muscle and then declines as the
muscle becomes shorter or longer than this
length. Also, the developed active force sums
with the passive force (Zajac, 1989). At a very
light load, the velocity of contraction is constant
in the midrange of sarcomere lengths. The
velocity decreases at lengths below the
midrange and increases at lengths beyond the
midrange (Edman, 1979). The velocity of
contraction is inversely related to load (Wilkie,
1950).
Other tests, such as the quick-release
experiment, impose a sudden change in load to
measure the transient response of the muscle.
The results from these dynamic tests show that
upon sudden change in the magnitude of the
load, the muscle responds with a very rapid