To Jonas, Ton, Richard, Young-Hoo:

them according to topic areas:

SCALAR NATURE OF WORK AND POWER
Richard, you may remember asking a similar question a couple of years ago,
regarding the scalar nature of kinetic energy. I responded then with a
thought experiment that leads to physically meaningful information (see
BIOMCH-L archives, 23 March 2000). Briefly, each term (not component) in
the dot product equation for work can be used to determine changes in
kinetic energy for motion along its respective reference axis. This step is
perfectly consistent with the scalar nature of work and the relationships
stated in the work/energy theorem (i.e., the work done on a rigid body
equals its change in kinetic energy). It seems to me that a problem would
arise only if we tried to perform vector addition using the terms of the dot
product. Since my thought experiment didn't do that, nor does it need to,
there is no problem assigning physical meaning to work (or power) terms.

In this regard, I agree with Ton. Individual terms in the dot product for
joint power do have physical meaning, and are useful in understanding motion
of a multi-link system. (I could even argue that, in the general case, all
six degrees-of-freedom would be useful, but in deference to Ton, I'll keep
the discussion focused on three rotational degrees-of-freedom, only.)

JOINT POWER VERSUS MUSCLE POWER
Regarding the present discussion, I have long since stopped equating "joint
power" with "muscle power" when these are derived through Inverse Dynamics.
(Important qualifier, see below.) I'll skip details of my learning curve,
and focus on the gait analyses we perform on children with cerebral palsy.
A good example involves a child who goes into recurvatum at the knee
approximately at mid-stance. It is typical to see a profound intrinsic knee
flexion moment at this time, in the presence of power absorption. Often,
there is also knee flexor EMG activity, but not always. When knee flexor
EMG is absent, the moment arises due to deformation of soft tissues in the
joint capsule and muscle/tendon unit; in extreme cases, it may arise from
bone-to-bone contact.

It seems to me that the terms "joint moment" and "joint power" are always
correct. They express two mechanical characteristics of the joint motion.
On the other hand, since it is likely that passive contributions to the
moment are always present in addition to active muscle contributions, the
terms "muscle moment" and "muscle power" are less likely to be accurate when
obtained via Inverse Dynamics.

INVERSE DYNAMICS, INDUCED ACCELERATIONS, & MUSCLE MODELING
I have more experience in the first of these than in the other two.
However, I see them this way:

INVERSE DYNAMICS essentially describes motion that we've already observed,
strictly as an engineering mechanics problem. Yes, we use anthropometry to
define some inertial characteristics, but once we've done that, the
equations we write would be the same for a person walking as they would be
for a machine. The joint moments describe the NET effect of all moments
that arise from active and passive structures, and in this regard, they do a
fine job of describing why we saw the observed motion.

Unfortunately, they only describe the local joint, and we must use
subjective reasoning to infer interactions with other joints.

INDUCED ACCELERATIONS provide greater objectivity with regard to
mechanical interactions among joints. Once net joint moments have been
calculated through inverse dynamics, they can be isolated and studied
individually. Forward dynamics, over very brief periods, are used to see
the effects of a single joint moment on all links of the system. Again,
this is essentially a mechanics problem. It really doesn't matter whether
joint moments arise from active muscles, passive tissues, or a combination
of the two. The net moment simply has the effects we calculated on all

We know more about interactions, but we are still missing a sizeable amount
of the biology.

MUSCLE MODELING can be achieved numerous ways, to many of which I remain
naive. In concept, it seems to me that we begin with first principles, with
the very smallest force generators within muscles. These are grouped in
muscle/tendon units that have specific origins, insertions, force/length and
force/velocity properties, etc. When the body is placed in positions known
to have occurred through motion capture, optimization techniques can be used
to either produce the body kinematics, or the net joint moments. By far the
more difficult problem, muscle modeling finally gives us the elusive "muscle
moments" by assigning forces to muscle/tendon units in the presence of known
moment arms.

SUMMARY (As Richard said, provided you actually get this far...)
I think there is very useful information contained in inverse dynamics
because the net joint moments and powers help us begin to understand why a
person moved the way we observed. Induced accelerations can add objectivity
to interactions among joints, and therefore have value in the understanding
of root causes, voluntary compensations, and involuntary consequences. Some
day, perhaps muscle modeling will become accurate enough to definitively
identify mechanics attributed to individual structures, whether passive or
dynamic.

Best regards,
FB

Frank L Buczek Jr, PhD
President-Elect, Gait & Clinical Movement Analysis Society
Director, Motion Analysis Laboratory
Shriners Hospitals for Children
1645 West 8th Street, Erie PA, 16505, USA
(814) 875-8805 voice, (814) 875-8756 facsimile
fbuczek@shrinenet.org

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