Page 150 - Biomedical Engineering and Design Handbook Volume 1, Fundamentals

BIOMECHANICS OF HUMAN MOVEMENT 127

(at any given time) for each muscle that we will call muscle activation, α , and it will be mathemati-
i
cally represented as a value between 0 and 1. Hence, if it is to be estimated from EMGs, additional
steps are needed to transform EMGs to muscle activation.
Musculotendon dynamics govern the transformation of muscle activation, α , to muscle force, F . i
i
Once the muscle begins to develop force, the tendon (in series with the muscle) begins to carry load
as well. Depending upon the kinetics of the joint, the relative length changes in the tendon and the
muscle may be very different. For example, this is certainly the case for a “static contraction.” (This
commonly used name is an oxymoron, as something cannot contract, i.e., shorten, and be static at
the same time. Hence, the tendon must lengthen as the muscle shortens if the joint is not to move!).
The force in each musculotendonous unit contributes toward the total moment about the joint.
The musculoskeletal geometry determines the moment arms of the muscles. (Since muscle force is
dependent upon muscle length, i.e., the classic muscle “length-tension curve,” there is feedback
between joint angle and musculotendon dynamics.) It is important to note that the moment arms of
muscles are not constant values, but change as a function of joint angles. Also, one needs to keep in
mind the multiple degrees of freedom of each joint, as a muscle may have multiple actions at a joint,
depending on its geometry. Finally, it is important to note that the joint moment, T , is determined
i
from the sum of the contributions for each muscle. If not all muscles are included in the process, the
joint moment will be underestimated. The output of this transformation is a moment for each joint
(or, more precisely, each degree of freedom).
From the joint moments, multijoint dynamics can be used to compute the accelerations, velocities,
and angles for each joint of interest. On the feedback side, the neural command is influenced by
muscle length (via muscle spindles) and tendon force (via Golgi tendon organs). Many other sensory
organs play a role in this as well, but these two are generally the most influential.
There are several limitations of the forward dynamics approach. First, it requires estimates of
muscle activation. EMG methods have been used to this end, but the high variability in EMG signals
has made this difficult, especially during dynamic conditions. Second, the transformation from
muscle activation to muscle force is difficult, as it is not completely understood. Most models of this
(e.g., Zajac, 1989) are based on phenomenological models derived from A. V. Hill’s classic work
(Hill, 1938) or the more complex biophysical model of Huxley’s (Huxley, 1957; Huxley and
Simmons, 1971), such as Zahalack’s models (Zahalack, 1986, 2000). One way around the problem
of determining force from EMGs is to employ optimization methods to predict muscle forces directly
(bypassing these first two limitations). However, the choice of a proper cost function is a matter of
great debate. Scientists doing research in human motor control find it surprising that biomechanical
engineers replace their entire line of study (and indeed, the entire central nervous system), with a
simple, unverified equation. Nevertheless, some cost functions provide reasonable fits of the data
when addressing specific questions. Another limitation is that of determining musculoskeletal
moment arms. These are difficult to measure in cadavers and even harder to determine with any
accuracy in a living person. Finally, joint moments can easily be underestimated. Using forward
dynamics, small errors in joint torques can lead to large errors in joint position.

6.2.2 Inverse Dynamics

Inverse dynamics approaches the problem from the opposite end. Here we begin by measuring
position and the external forces acting on the body (Fig. 6.2). In gait analysis for example, the
position of tracking targets attached to the segments can be recorded using a camera-based system
and the external forces can be recorded using a force platform.
The relative position of tracking targets on adjacent segments is used to calculate joint angles.
These data are differentiated to obtain velocities and accelerations.
The accelerations and the information about other forces exerted on the body (e.g., the recordings
from a force plate) can be input to the equations of motion to compute the corresponding joint
reaction forces and moments.
If the musculoskeletal geometry is included, muscle forces can then be estimated from the joint
moments and, from these it may be possible to estimate ligament and joint compressive forces.
As with forward dynamics, inverse dynamics has important limitations. First, in order to estimate
joint moments correctly, one must know the inertia of each body segment (this is embedded in the