Dear CGA:
Two things about Lombard's paradox and Dr. Kirtley's reluctance to cover
the main muscles and their actions.
First, several years ago I placed a very large and bolded statement in
my
motor control course notes that the classic muscle action charts in
anatomy and kinesiology books are partially correct at best, and woefully
inaccurate at worst. Much data has been presented in the past 5-10
years or so (e.g., see Herzog's work) on task-specific muscle activation,
compartmentalization, and more; all of which suggest that our classic
notions
of muscle actions need rethinking.
Second, and in line with this thinking, was a presentation I attended
about using fMRI during real life tasks. The presenter showed leg
scans
of an individual doing submax squats and discussed at length the
technology and color-coding system depicting the level of muscle
activity. None of that interested me. The only thing I remember
was
that the vastus muscles were lit like a Christmas tree and the rectus femoris
was dark with inactivity (I can't remember what the hamstrings were doing).
One more explanation for Lombard's paradox?
Jeff
--
Jeffrey C. Ives, Ph.D.
Associate Professor
Dept. Exercise & Sport Sciences
Email: jives@ithaca.edu
Ithaca College
Phone: 607-274-1751
Ithaca, NY 14850 USA
Fax: 607-274-7055
Chris, I can't begin to comment authoritatively about your real question
here, but want to say that in the late 1960s, in my orthopedic residency
at Pitt, I learned--can't remember from whom--that if the leg/foot were
fixed[e.g. planted] that the gastroc heads could pull the femoral condyles
posteriorly--it made intuitive sense to me, and still does.
I also feel very leery of accepting computer modeling [of specific
postulated actions such as this] and think the models must be, as you
say, " extremely difficult to construct with any confidence." It makes
more sense to me to work toward imaging actual muscles in action, eg w
MRI when they get it 'miniaturized' etc. Surgically we see variations
in
muscle bulk, attachments, tendon width/thickness etc--how much do
these modify motions?
Mary Williams Clark MD
Pediatric Orthopedics
Sparrow Regional Children's Center
Suite 145, SPB
1200 E. Michigan Ave
Lansing MI 48909-7980
517-364-5434
Many of the people to whom we presented these findings
were skeptical of
them, and we were curious about whether these accelerations were artifacts
of our modeling assumptions, so we decided to construct a physical
model. A movie (3 MB .avi) showing the physical
model results may be found at
http://www.celos.psu.edu/kines488
The movie shows a horizontal double pendulum that was constructed to
represent the thigh and shank (same lengths, but 1/17 of the mass and
moment of inertia). A wire that passes behind the knee (roughly
representing the moment arms of semimembranosus) is pulled on, and
it is
clear that this action initially produces hip flexion rather than hip
extension. The way that this paradoxical acceleration arises
is through a
reaction force at the knee that passes anterior to the hip.
The existence
and magnitude of this phenomenon depends on the configuration of the
system, segment inertial parameters, and musculotendon geometry.
I
sometimes use the following thought experiment to explain this: Imagine
that you are sitting down and that your hamstrings attach near your
ankle
instead of near your knee. In this configuration the hamstrings
still
produce a hip extension moment, but it would not be hard to imagine
that a
hamstrings contraction would produce hip flexion rather than extension.
Best regards,
Steve Piazza
Assistant Professor
Departments of Kinesiology, Mechanical Engineering,
Bioengineering, and Orthopaedics & Rehabilitation
Center for Locomotion Studies
29 Recreation Building
The Pennsylvania State University
University Park, PA 16802
That's a great demonstration and great video!
I wonder if I could pin you down a bit and ask the following questions:
1. Does this behavior only apply to two-joint muscles - the Zajac review
seems to me to imply that it can happen with uni-articular muscles
too?
2. Is this the correct explanation for Lombard's paradox, or
do you
think that is a separate issue?
3. Is there any way to predict this behavior without resorting
to a full
biomechanical model/simulation? For example, I wonder if we could come
up with some basic rules for when it might be expected to happen?
Chris
--
Dr. Chris Kirtley MD PhD
>I wonder if I could pin you down a bit and ask the following questions:
>
>1. Does this behavior only apply to two-joint muscles - the Zajac
review
>seems to me to imply that it can happen with uni-articular muscles
too.
A uni-articular muscle can't produce an acceleration that doesn't
agree
with its moment at the joint it spans (e.g., soleus can't produce
ankle
dorsiflexion), but it is possible for uni-articular muscles to produce
motions at joints they do not span. For example, hip flexors
may produce
knee flexion during swing phase, and a rapid kicking motion produced
by
vasti action would also tend to plantarflex the ankle. I scanned
through
the Zajac review to find the wording to which you referred, but I didn't
see it.
>2. Is this the correct explanation for Lombard's paradox, or do
you
>think that is a separate issue?
It seems like a separate issue, at least in the sit-to-stand
example you
have on the teach-in web site. I haven't done a simulation of
sit-to-stand
to answer this question definitively, but it seems to me that hamstrings
activation would produce a downward reaction force on the femur at
the hip
and thus act as a knee flexor at the beginning of the motion.
A guess as
to why hamstrings activation occurs is that it might help to stabilize
the
knee.
>3. Is there any way to predict this behavior without resorting to
a full
>biomechanical model/simulation? For example, I wonder if we could
come
>up with some basic rules for when it might be expected to happen?
Unfortunately I don't have a good answer to this question. Even
if you did
have a full-blown, muscle-actuated model, it's worth noting that there
are
many possible reasons that the behavior of such a model might not be
realistic: joints are typically modeled as frictionless, soft tissues
such
as skin are usually not modeled, etc. Perhaps the basic rules
you are
looking for could take the form of characteristic muscle-induced
acceleration profiles for common activities (such as normal
gait), but this
wouldn't be helpful if you were trying to determine whether paradoxical
accelerations were present in a pathological gait pattern.
Steve Piazza
Assistant Professor
Departments of Kinesiology, Mechanical Engineering,
Bioengineering, and Orthopaedics & Rehabilitation
Center for Locomotion Studies
29 Recreation Building
The Pennsylvania State University
University Park, PA 16802
Can I just comment on Stephen's model (Paolo Selber can actually do
this
with a folded bit of paper and a piece of thread but there must be
something about precisely how he makes the folds because despite a
desk
strewn with the little folded strips they never seem to work for me).
There seems to be a perception that this is "magic" or at the very best
that it can only be understood using complex mathematical techniques.
I
think, at least qualitatively, that the average mind can understand
what is
happening if we think about it in the correct way.
The important thing to recognise is that the hip is the joint connecting
the whole limb (and not just the thigh) to the pelvis. In considering
what
is happening at the hip we thus have to consider the movement of the
centre
of mass of the whole limb and not just the thigh. If the knee flexes
then
the CM of the whole limb moves posteriorly with respect to the thigh.
Consider doing this by isolated contraction of a uni-articular knee
flexor
(short head of biceps). No moment is exerted at the hip so Newtons
Laws say
that the centre of mass cannot move anteriorly or posteriorly. The
only way
this can occur is if, at the same time as the limb's CM moves posteriorly
with respect to the thigh, the thigh itself moves anteriorly by a
compensating amount, i.e. the hip must flex. The short head of the
biceps
is thus a hip flexor in this configuration!
Exactly the same is happening in Stephen's model except the hamstrings
are
also exerting a small extensor moment at the hip. This is the only
external
moment on the limb so the CM of the whole limb must move backwards.
The
knee flexion however causes a larger backwards moment of the CM with
respect to the thigh than is required by the hip moment so the hip
flexes
as described above (but less than it would do if the knee moment arose
purely from a uni-articular knee flexor). Because of the geometry of
the
knee joint and the hamstrings (and possibly because of the stop limiting
knee flexion in the physical model), as the knee flexes more and more,
further knee flexion brings about a smaller change in the
anterior-posterior position of the limb's CM and the effect of the
extensor
moment exerted at the hip starts to dominate. The initial hip flexion
has
thus reverted to hip extension by the end of the experiment.
Note that this explanation is based purely on consideration of the movement
of the CM of the whole limb. It is not dependent on any considerations
of
segment accelerations and would happen if the movements were performed
infinitesimally slowly. A fuller analysis must include inertial
terms, and
of course in real life nothing happens in the horizontal plane so gravity
is also acting. The fact that Stephen's model does behave as predicted
by a
consideration of the changing position of the CM within the limb suggests
that this is the key factor in explaining this "paradoxical" behaviour.
Anyone who is more deeply into the maths than I am like to comment?
Richard Baker PhD CEng
Gait Analysis Service Manager and Director of Research
Hugh Williamson Gait Laboratory, Royal Children's Hospital, Victoria
3052,
Australia
Tel: +61(0)3 9345 5354, Fax: +61(0)3 9345 5447
Adjunct Associate Professor, La Trobe University
Honorary Senior Fellow, University of Melbourne
When you think of it, these open and closed chains, there is not
a very exact distinction. In the open chain example, knee extension
also
moves the foot and can even give foot plantarflexion.
Thus: the action of a muscle STRONGLY depends on the relative
configuration of the limbs and on the interaction with the environment
(e.g. the floor) and, to a lesser degree and mainly in fast movements,
on
the mass distribution.
What Lombard has to do with it is, as it seems, mainly that he
has already anticipated such effects, not so much that he has
predicted
them. On this subject I can only recommend Art Kuo's masterly chapter
10 "The action of two-joint muscles: the legacy of W.P. Lombard." in
"Classics in Movement Science" ed. by Latash and Zatsiorsky, Human
Kinetics (2001). It is a tough piece of math, but worth while.
In an isometric task, it is found that the action of a muscle,
which of course consists of of a force on the environment, has in a
certain configuration a definite direction. This direction is constant
and
the magnitude of the delivered force is linearly proportional to the
respective muscle force. This is not so difficult to see, I wrote a
paper on
this isometric case in J.Biomech 34:1085-1089 (2001). Kuo makes a major
step further. In a movement the result of the action, usually the
acceleration of segments, has also in a certain configuration
a definite
direction(s). This direction is constant and the magnitude is again
linearly proportional to the respective muscle force. If you look very
carefully, you can see this also in Zajac I's formula's. This direction
is not
the same as the force direction in the isometric case, which is relatively
easy to predict, because of the different segment masses. Monoarticular
muscles around some joint all have the same force or movement
direction. Biarticular muscles have directions between the monoarticular
ones, which vary with the ratio of their moment arms. Their presence
thus provides the body with additional force or movement directions.
Finally, about Jeff Ives remark:
Second, and in line with this thinking, was a presentation I attended
about using fMRI during real life tasks. …… The only thing I remember
was that the vastus muscles were lit like a Christmas tree and the
rectus
femoris was dark with inactivity.
I can refer to a very recent finding by Anand Nene et al.: "Is rectus
femoris really a part of quadriceps?" Gait & Posture 16:
S121 (2002). The
answer, obtained with intramuscular EMG, is: "……functionally RF is
a
different muscle and does not belong with Quadriceps."
Yours,
At Hof
Institute of Human Movement Sciences &
Laboratory of Human Movement Analysis AZG
University of Groningen
A. Deusinglaan 1, room 321
postal address:
PO Box 196
NL-9700 AD GRONINGEN
THE NETHERLANDS
Tel: (31) 50 363 2645
Fax: (31) 50 363 3150
e-mail: a.l.hof@med.rug.nl
http://www.ppsw.rug.nl/~ibw/
Surface EMG showed clear monophasic activity of the vasti (late
swing and
early stance) and biphasic activity of the rectus (with the
vasti and also
in late stance and early swing). Most of us have been taught that this
is
normal rectus and vasti activity and if you look through most of the
standard texts tracing surface EMG data to Inman, Sutherland, Winters
or
others this pattern is clearly described.
However fine wire showed monophasic activity in both groups.
Vasti were
active in late swing and early stance as expected. Rectus however was
ONLY
active during late stance and early swing. Comparison of the data from
fine
wire and surface EMG made a convincing case that the late swing/early
stance activity is in fact cross-talk from the vasti being picked
up by the
rectus electrode. I've got a lot of respect for the use of EMG at Enschede
and if Anand is getting this I'm pretty sure that we all are. True
to form
Perry is the only one who hasn't been hoodwinked by those dodgy surface
electrodes. Page 96 of Gait Analysis: Normal and Pathological function
clearly shows monophasic rectus activity at the same phase of the gait
cycle as Anand recorded it.
Anand's abstract is pretty heavily oriented to muscle function (rectus'
primary function during gait is as a hip flexor) but the message I
take out
of it is more related to electrode function (surface EMG, even when
performed carefully, does not reliably record rectus activity). The
relevance to the Lombard paradox is clear. Is the observation a result
of
inaccurate recordings of rectus activity? A combination of activity
in
vasti (extending the knee) with hamstrings (augmenting hip extension
once
the knee is stabilised by the vasti) is a perfectly sensible combination
of
muscles to use to perform this activity (I assume the gluts are working
as
well). Certainly any examination of the department's skeleton shows
that
with the hip flexed 90 degress the hamstrings are ideally suited to
act as
hip extensor and there's no real need to resort to SIMM to identify
this.
How did Lombard record rectus activity? (The copy of the American Journal
of Physiology for January 1907 that normally sits on the shelf behind
me is
inexplicably missing!) Do we believe him?
Richard Baker PhD CEng
Gait Analysis Service Manager and Director of Research
Hugh Williamson Gait Laboratory, Royal Children's Hospital, Victoria
3052,
Australia
Tel: +61(0)3 9345 5354, Fax: +61(0)3 9345 5447
Adjunct Associate Professor, La Trobe University
Honorary Senior Fellow, University of Melbourne