EMG & Joint Moment: What people said...

EMG is not directly proportional to the muscle force. It is only an indicator
of muscle activiation level. You need to consider the length-tension relationship.

Bing Yu, Ph.D.
Assistant Professor
Division of Physical Therapy
The University of North Carolina at Chapel Hill


Might your paradox simply be the result of the non-linear tension/length
relationship of the gastroc muscle.  With increased plantar flexion, the
gastroc is shortened and therefore goes down the ascending limb of the
tension/length curve.  More motor units are recruited to counteract this
decrease in force producing capability. This is more important that the
reduction in moment arm.  It would also be important to examine knee
kinematics to get a more complete picture of gastroc activity.  As the
gastroc crosses the knee joint, flexion of the knee joint may further
reduce the length of the muscle and therefore exasperate the situation.

Ben Sidaway


It may be as the plantarflexors contract and shorten they are in a
less favorable length tension relationship (i.e. less cross bridges)
and therefore, more motor-units are required.  Additionally, I
believe the moment for the plantar flexors is also decreasing.

Kind Regards,

Bob Streb,M.S.,P.T.
Department of Physical Therapy
Health Science Center
State University of New York at Stony Brook
Stony Brook, New York 11794-8201
fax 516-444-7621
e-mail rstreb@epo.hsc.sunysb.edu

In their analysis, the decrease in moment arm from the
ankle joint to the point of force application on the forefoot
was described.  Another variable that changes is the moment arm of
the gastrocnemius which also decreases as the foot plantarflexes
from the neutral position.  Depending on how the two
moment arms vary together, it may take more muscle force to
generate a balancing moment.
Also, as Dr. Yu mentioned, the force-length relationship
is an important consideration.  As the ankle plantarflexes, the
gastroc will shorten and may be operating on a less than optimal
portion of the force-length curve.  This would also affect the
recruitment (and EMG) of the muscle.
Laura Miller
Northwestern University
Prosthetics Research Laboratory

Hello Readers,

So far I had been a silent observer, but the proposed problems/questions
are so tempting that I decided to write down what I think. (I hope I send
this to the right address...)

I try to answer Chris's question about the increasing EMG signal of the
medial gastrocnemius while the joint moment falls as the subject raised
himself up.

I think the sarcomer's length-tension relationship explains the findings.
The moment decreases (which has to be balanced by the contracting muscle),
but at the same time the muscle also shortens and therefore more muscle
activity is needed. If the moment was decreasing at the same rate as the
muscle has to increase it's action to generate that moment, then the EMG
would remain constant during the acrobatic "kunst". The fact that the EMG
increased shows that (in the ankle joint at least) the reduction in the
needed moment is smaller then the increase in muscle activity in order to
generate the moment, to maintain equilibrium.

To me this experiment also explains well the commonly known fact that the
intensity of EMG is not necessarily proportional to the force generated.
Other factors are also involved, like sarcomer length etc.

Chris, the mailing list and the Web page are excellent!


PS: I have just received some replies for the same problem! Anyway, I send

Dr. Gabor Barton
GJBarton@compuserve.com  or  106545.3576@compuserve.com
Gait Laboratory
Alder Hey Children's Hospital


My thanks to Bing Yu, Ben Sidaway, Bob Streb, Laura Miller & Gabor Barton
for their quick repsonse to the Teach-in on EMG & Joint Moment. 

I'm also awaiting the verdict of Rolf Moe-Nilssen's students, who are doing
the exercise today in Bergen, Norway!

Basically, we're all in agreement that there are two possibilities:

1. The length-tension relationship of the gastrocnemius causes more work to
be done as it shortens, even though the load is decreasing;


2. The moment arm of the gastrocnemius changes (decreases) as the ankle
plantarflexion angle increases, so increasing the load on the muscle (even
though the external moment is decreasing).

I think we now need some numbers! Someone out there must know what is the
resting length of the medial gastroc. and something about it's
length-tension relationship (since this was an isometric test, we thankfully
don't need to worry about force-velocity!) I confess that I find (2) hard to
believe, but I'd also be interested to know how the moment arm changes with
joint angle. As I remember, Felix Zajac's group have done a lot of work on this.

I still find it hard to believe that the efficiency of the muscle falls so
much that the reduction in external moment is more than compensated for,
such that the EMG steadily rises. But I also have no other explanation. It
strikes me that this phenomenon might be another reason why Aristotle's
philosophy of movement persisted for so long - when we raise ourselves up we
FEEL that it the force is greater the higher we go.

Looking forward to seeing some numbers put to this interesting problem.

Chris Kirtley


The answer, as I understand it, is:
There are less cross bridges available.  As the sarcomere shortens
opposing  action filaments will overlap each other as well as the 
under lying myosin filament.  The actin filament from one side 
interfere with the actin filaments from the opposite side.  
Therefore less myosin heads can form cross bridges and less force is 
produced.  The overlap increses as the shortening continues.

Gordon, Huxley, & Julian, 1966, The variation in isometric tension 
with sarcomere length in vertebrate muscle fibers. J. of Physiology, 
184, 170-192. [11]

Lieber, Skeletal Muscle Structure and Function, 1992 Williams & 

McComas, Skeletal Muscle, Form and Function 1996, Human 

Kandel, Schwartz and Jessill, Principles of Neural Science, 3rd 
edition, 1991, Appleton & Lange   (nothing new here but they do a 
nice job of explaining)
Kind Regards,

Bob Streb,M.S.,P.T.
Department of Physical Therapy
Health Science Center
State University of New York at Stony Brook
Stony Brook, New York 11794-8201


   No, I am afraid my class didn't come up with more revolutionary results
than pointing to the fact that the length-tension relationship may play a
part in understanding the problem. 
  My own trifling contribution is speculative: May be the relative
shortening of m. soleus is greater than that of the gastro with increased
plantar flextion of the foot, thus leaving more of the work to be done by
the gastro - or may be for some other reason there is a changing
relationship in tension and/or activation betweeen the various bellies of
m. triceps surae as the angle of the ankle joint changes. If so, it my seem
somewhat simplistic to relate the moment round the ankle joint to the EMG
activity from one belly of the gastro only. 
   My reason for responding to Chris and now to the whole list - is to
express my admiration as to the important work Chris is doing. I find it
thrilling to print out exellent colour illustrations from Vienna and show
them locally to a group of people the very same day, not to mention the
case of the week and all the other informative stuff on the Web. What
puzzles me though, is that I still cannot find the reference to the Froude
number (used for scaling) which Chris promised would be there. Keep up your
enthusiastic and brilliant work Chris, I am sure I am not the only one who
have promised you a free beer!
   As always this time of the year, regards from wintry Norway

Rolf Moe-Nilssen, MS, PT, Research fellow, Division for Physiotherapy Science
Department of Public Health and Primary Health Care, University of Bergen 
Ulriksdal 8c, N-5009 Bergen, Norway, email: Rolf.Moe-Nilssen@isf.uib.no
voice: +47 55 58 61 70, fax: +47 55 58 61 39 


I agree Ben Sidaway and Laura Miller that there can be an influence from
the force-length (FL) and musculoskeletal geometry (MSG) in this study.  

However, an empiracally-based SIMM model, which considers these factors
together, shows a peak in plantar flexor strength near 15 degrees.  (see
Delp et al., IEEE transactions on Biomedical Engineering, 37:757-767,
1990).  I do not see you going that much past 25 degrees from the pictures,
so I'm not sure that FL and MSG can be the entire answer.  

Was this as high as you could go?  If so, perhaps I can offer a possible
alternative: passive structures.  In order to rise, you are resisting more
and more the skin and ligamentous structures.  Bones are also reaching
joint limits.

Mansor and colleagues have done some work in this area, trying to
characterize and model the passive contributions that we modeling people
often ignore:

Yoon, Y.S., J. M. Mansour  (1982)  Passive Elastic Moment at the Hip.
Journal of Biomechanics.  15:905-910.

Mansour, J. M., M. L. Audu  (1987)  Passive Elastic Moment at the Knee and
its Influence on Human Gait.  Journal of Biomechanics.  19:51-58.

Esteki, A., J. M. Mansour  (1996)  An experimentally based nonlinear
Viscoelastic model of joint passive moment.  Journal of Biomechanics.

My question to the group is: is anyone aware of a good paper that does
characterize the passive viscoelastic properties of the ankle?  I realize
that the ankle is a more difficult joint due to its complex nature.

By the way, this paradigm looks painful for the foot! [... it was: all in the name of science! - Chris]

 Jim Patton

Doctoral Candidate,        645 N Michigan Av 
Biomedical Engineering     Suite 1100       
Northwestern U.            Chicago, IL 60611 
EMAIL: j-patton@nwu.edu    (312)908-6785LAB 


If the force required of the muscle did not increase as it passed into
progressively more equinus then a particularly difficult control problem
arises in that the ankle would actually be unstable in plantarflexion. As
soon as the ankle starts plantarflexing it actually requires less force than
is already being generated in the muscle to move further into plantarflexion.

Either the factors already highlighted by the other contributors actually
mean that force rises as plantarfleion increases which allows a sensible
control strategy, or some other mechanism is required to control the
movement. Have you considered checking activity in the antagonists ?

Richard Baker
Gait Analysis Service Manager
Musgrave Park Hospital


I have just read Richard Baker's reply to the CGA mailing list regarding
the subject.

I think that the force does not necessarily rise (EMG activity does rise,
but the force can fall during that, as in a fatigue test where maintaining
the same force leads to increased EMG due to more motor unit recruitment).
During plantarflexion the external moment is reduced, the moment arm
reduces, and so most likely the force also reduces. Yes, the ankle is
unstable in plantarflexion. I know that this is not a scientific reference,
but at the medical university I was taught that more ankle sprains occur in
women on high heels (equinus). The more sound explanation by my anatomy
textbook was that in plantarflexion the narrower section of the Trochlea
Tali is between the malleoli making the joint a bit lose. The point
highlighted by Richard gives an other explanation for the empirical finding
that the ankle is unstable in dorsiflexion.

(Does the moment arm really decrease?)

Gabor Barton
Gait Laboratory
Alder Hey Children's Hospital
Liverpool, UK


I have been reading the replies to the ankle problem with interest 
and I would also agree that the length of the muscles and the 
antagonist contribution are important.
I have run a simple simulation in SIMM with the standard lower limb 
model and it is clear that because the fibres of the soleus and med. 
and lat. gastrocs are very short near full plantarflexion the force 
produced by those muscles is minimal. In fact, although we assign 
full activation, the force of the soleus is almost zero from 30 to 18 
deg of plantarflexion and increases after that. Those three muscles 
produce their maximum force after neutral and during dorsiflexion and 
this force is almost constant throughout dorsiflexion.
The ankle moment during plantarflexion is generated mainly by the 
other P/F (Tib.Post etc) which have very small moment arms and 
therefore their length (and therefore force in isometric conditions) 
changes very little over plantar and dorsi flexion.
Another fact to consider is the change in pennation angle at the 
different positions. We are currently doing some measurements using 
ultrasonography and there are large changes in pennation angle with 
contraction at the different joint angles, indicating that 
despite maximum activation, less force is transmitted to the tendon. 
Furthermore, apart from changes in pennation angle we also observed a 
change in aponeuroses distance for Lat. Gastroc and Soleus although 
muscle thickness remained the same for the Med. Gastroc and we would 
welcome any comments and explanation on this observation.
The values for optimal fibre length used in the SIMM model are 
0.030 m for soleus and 0.045 and 0.0640 for the med. and lat. 
gastroc. respectively. I could provide the length of the muscles 
during the motion together with moment arms etc from the simulation 
output for those who are interested in the actual values.

I hope this helps. Best wishes

V. Baltzopoulos
Biomechanics Group
Manchester Metropolitan University

Fax: +44 161 247 6375
Tel: +44 161 247 5659


The debate on ankle EMG and moments has up to now focussed on two 
possibilities.  I would like to add a third view, which is completely 

Firstly I have been puzzled by various anamolies concerning moments 
around the ankle using simplified pin-jointed models.  The typical 
model can be found in the book "Human Walking" by Inman, Ralston and 
Todd, (1st Edition) and the second edition by Rose and Gamble.  The 
walking cycle is described in a sequence of pictures.  A gnome is 
standing (perched) of the leg in the region of the calf, holding 
ropes representing the muscles, one attached to the heel, the other 
to the top of the foot. The foot is a single rigid lever attached to 
the leg by a simple hinge.  

The first picture shows the heel on the ground, foot elevated 
while the gnome lowers the foot onto the ground.  The en the gnome 
releases the anterior rope, and begins to pull the heel chord up.  
This is the manner in which we are supposed to walk, yet it does not 
explain how the foot is elevated in the first place, because if yopu 
try this from a standing start, you fall over backwards.  As I see 
it, the mechanics of this system are entirely with the sentiments 
expressed so far in this debate, the role of the calf muscles being 
to raise the heel.  

However, Chris's data does not quite fit this model.  

I would suggest that the model is incorrect.  In the first edition of 
"Human Walking" there is an interesting calculation of the power flow 
in the leg.  Careful inspection of this data reveals a disturbing 
trend.  During parts of the gait cycle, the power USED to power the 
walk precedes its SUPPLY.  The anomaly is particularly apparent at 
the ANKLE!  It does not make sense that the power is used before it 
is supplied.  Perhaps because of this "nonsensical data", it has been 
omitted in the 2nd edition; yet the gnome model has been retained.  

Furthermore, in the article by David Winter: Mechanical Power in 
Human Movement: Generation, Absorption and Transfer.  (Med. Sports 
Sci 25:34-45, 1987), he notes that during swing phase (when the foot 
is not on the ground) power transfer calcualtions are nearly 100% 
accurate.  But large error occur during stance, particularly, again, 
at the ankle joint!

I would suggest that the simple joint moment calculations about the 
ankle, are wholely unrepresentative of the actual roles of the 
muscles, and this needs to be considered as a third reason for the 
puzzling data.  

Anatomical Engineer

With respect to the length-tension issue.  Maximal isometric tension 
is produced at sarcomere lengths of ~ 2.0 to 2.25 um.  As sarcomere's 
shorten (overlapping of the thin filaments at opposite ends of the 
sarcomere) tension falls off slowly and that rapidly. At sarc. 
lengths of 1.65um the thick filaments abut the Z line, then you get 
a rather sharp decline in force produced. At this point the muscle 
would need more motor-units and thus an increase in EMG activity.  
See Basic Biomechanics of the Musculoskeletal System 2nd edition 
1989, Nordin and Frankel.

Robert Strep


The discussion on the plantar flexion EMG has reminded me of the following.

A few years ago I tried to find the best position to test the gluteus
maximus during a maximum voluntary effort (MVE). My subject was lying prone
with the legs hanging off the table. I measured the EMG during a MVE while
the hip was in 90, 60, 45, 30, and 0 degrees flexion.  Each measurement was
done isometrically! The EMG output increased almost linearly (a vague S
curve to be more exact) from the 90 to the 0 degrees despite the fact that
the subject was requested to give their maximum effort in each of these hip

I could not explain this finding but decided to test in the hip position
that was most like the experimental situation.

Since this phenomenon seems to have reappeared in the calf, it looks like
there is a Length-EMG relation opposite to the Length-Force relation.  It
would be interesting to repeat the plantar flexion experiment using maximum
voluntary effort to see whether the pattern emerges again. This may mean
that moment arms and other such biomechanical factors are not the main
cause for the occurrence of this phenomenon.  Does the CNS make adjustments on the basis of length or force feedback from the muscle receptors?


Robert van Deursen


I enjoyed Richard Baker's comments on control, V Baltzopoulos' 
comments on pennation angle and C Nevin's comments on the validity of 
the simple model. It strike me that all these contributions allude to 
the same problem and that is the ankle model.

Quite clearly the ankle isn't a simple pivot; the ankle joint (i.e 
the talo-crural joint) does not even have any muscle connections to 
it, only across it! The action of antogonists is also clearly 
important especially if when we  consider the subtalar joint's 
and the mid-tarsal joint's influence on the situation. This is 
clearly a VERY 3-D problem! The simple models are clearly 
insifficient to explain the sitiuation - I saw some graphs (i think 
Inman's) which show power generation in the anterior muscles during 
roll-over, which have led some to summise that the anterior tibialis 
actually "pulls" the shank forward!!!

Keep the discussion going - this is fascinating

Jeremy Linskell
Manager, Gait Analysis Laboratory 
Co-Ordinator, Electronic Controls Service
Dundee Limb Fitting Centre
Dundee, DD5 1AG, Scotland 
tel +1382-730104, fax +1382-480194
email: j.r.linskell@dth.scot.nhs.uk


Dear all those interested in the ankle EMG problem,

    I took a week of vacation, and on return, when tidying up
my mailbox, I found a heated debate was going on about an
experiment on EMG and muscle moment at the ankle in rising on
the toes. It took me some time to read all of this, and to try
downloading some photographs from Vienna. The latter has not
succeeded until now, but this has to do with an overloaded
fileserver over here. Next time it may better to present the
results in a small table, instead of in a set of vague photos,
also to protect the environment of bit-pollution.
    In the distant past I have done some work on the EMG-force
relation of the triceps surae (refs 1 - 4 see below), I even
did practically the same experiment, see (3), fig 6 left.
    In my opinion the first two answers, from Ben Sidaway and
Laura Miller are completely right: the length tension relation
of the gastroc/soleus declines faster with increasing
plantarflexion angle than the decrease of the moment needed to
stand on the toes. The moment arm of these muscles also
decreases a little, but much less (4). I will try to support
their opinions with some experimental data.
    Data on the force length relation f(phi) are in my paper
(2), figure 5. Phi is the ankle plantarflexion angle, with 90
deg for neutral stance. The moment M needed to stand on the
forefoot can be calculated from a simple model explained in
(3), figure 2. Both are given as a function of the ankle angle
in Table I. The level of rectified EMG M0 can now be
calculated as M0 = M/f(phi). The EMG is then expressed in
units equal to the isometric moment that it would give at
angles where f(phi) = 1. It can be seen that, as long as
f(phi) = 1, M0 declines with phi, as does M, but over 90 deg.
is starts to increase, because f(phi) decreases much faster
than the required moment M.

            TABLE I

    phi      f(phi)       M       M0     
    (deg)                 (Nm)      (Nm)
       70.00     1.00   113.72   113.72  
       75.00     1.00   111.53   111.53  
       80.00     1.00   108.51   108.51  
       85.00     0.95   104.65   110.16  
       90.00     0.90   100.00   111.11  
       95.00     0.70    94.59   135.12  
      100.00     0.56    88.45   157.95  
      105.00     0.40    81.65   204.12  
      110.00     0.24    74.22   309.26  
    Table I indeed shows the effect as found, but possibly in a
too strong degree. There in a secondary effect, namely, that
makes the effect of the decrease of f(phi) less drastic. In
series with the muscle fibres is an elastic element -tendon
and aponeurosis- which is less stretched when the moment
decreases. This makes that the contractile fibres are less
shortened than in the above example. The calculation is
slightly more complicated, but I give the results in Table II

    TABLE II: EMG when rising on the toes, elasticity included
    phi     stretchSEC   f(phic)  M0 
    (deg)     phie(deg)
       70.00    38.64     1.00   113.72
       75.00    38.27     1.00   111.53
       80.00    37.75     1.00   108.51
       85.00    37.07     1.00   104.88
       90.00    36.24     0.87   115.26
       95.00    35.24     0.74   127.40
      100.00    34.08     0.62   142.10
      105.00    32.74     0.51   160.72
      110.00    31.22     0.40   185.83

Table 2 
Parameters used: phi1 = 154 deg., phi1-phi2 = 32 deg (as in
Table I). Quadratic series-elasticity, with M = 250*phie^2
(phie in rad.) phic = phi + phie. For M, see Table I

    The latter point may enlighten the sorrows of V.
Baltzopoulos, that triceps surae cannot lift you so high at
all. Surely the triceps surae muscle fibres are short, which
results in a muscle complex with a very high force for the
given volume, but not so short to make then unfunctional.
    Regarding passive structures, a point raised by Jim Patton,
on this point too I have experimental data, in fig. 4 of (2).
In the plantarflexion range, from 90 to 120 deg, the passive
moment is very small. At strong dorsiflexion it becomes
considerable: 30 Nm at 70 deg, that would reduce M0 to 114 -
30 = 84 Nm. This might explain that the EMG seems continually
to increase with phi in the experiment. On extrapolation, this
fig.4 predicts that you can stand on your forefoot in very
extreme dorsiflexion, below 60 deg. without any muscle
activity (EMG). Has anyone ever observed this?
    I hope this contribution may be of help in the discussion.

At Hof


1)   Hof, A.L. and Jw. van den Berg (1981) EMG to force
processing I: An electrical analogue of the Hill muscle model. 
J. Biomechanics 14 :747 - 758

2)   Hof, A.L. and Jw. van den Berg (1981) EMG to force
processing II: Estimation of parameters of the Hill muscle
model for the human triceps surae by means of a calf ergometer 
 J. Biomechanics 14 :759 - 770

3)   Hof, A.L. and Jw. van den Berg (1981) EMG to force
processing III: Estimation of model parameters for the  human
triceps surae muscle and assessment of the accuracy by means
of a torque plate.  J. Biomechanics 14 :771 - 785

4)   Spoor, C.W.; Vanleeuwen, J.L.; Meskers, C.G.M.; Titulaer,
A.F.; Huson (1990)  Estimation of Instantaneous Moment Arms of
Lower-Leg Muscles   J Biomech   23    :1247

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