Teach in #25, Efficiency of Gait: What people said...

Richard Baker and others have shown that the waddling gait of spina bifida kids does not mean that
their Centre of Mass (CoM) is moving more. In fact the trajectory of the CoM is close to normal and
the body is moving more around the CoM. The excessive movement of body parts consumes excessive
energy which is not reflected in the trajectory of the CoM and this questions the usefulness of the
CoM to estimate energy cost (in spina bifida at least).

Dr Gabor Barton (MD)
Senior Lecturer in Biomechanics
The Research Institute for Sport & Exercise Sciences,
Liverpool John Moores University
Room 2.51 Henry Cotton Campus, 15-21 Webster Street, Liverpool, L3 2ET
Tel: +44 (0)151 231 4333/4321   Fax: +44 (0)151 231 4353
E-mail: G.J.Barton@livjm.ac.uk


  Thanks to Dr. Daryl Phillips, I was informed that a "teach-in" has just appeared on Dr. Chris Kirtley's Clinical Gait Analysis webpage on the CoM'nalysis module used in the F-Scan /teach-in/efficiency/

  Maybe some of you more mathematical types can help answer some of Dr. Kirtley's questions at the end of the webpage better than I can.  Norman and Bart, go ahead, give it a shot for the rest of us!

  Norman, I know that you must have something to say about all of this!



  Kevin A. Kirby, DPM
  Adjunct Associate Professor
  Department of Applied Biomechanics
  California School of Podiatric Medicine at Samuel Merritt College

  Private Practice:
  107 Scripps Drive, Suite 200
  Sacramento, CA  95825  USA

  Voice:  (916) 925-8111     Fax:  (916) 925-8136

Kevin and all,

  I am traveling, and will get back on this. This will not be a one e-mail, but several. I need to reflect on presenting the material (most clearly) since I do not have a lecture room situation (white board, Power-Point, with questions & answers). Please bear with me in doing so, since I prefer several short e-mails than a few lengthy ones. There are fundamental and theoretical concepts and principles I need to present in help to clarify and provide an understanding. I do wish the readership to be become more knowledgeable on gait, and with the methods for its analysis.

  I could answer yes to the questions, but this would not do justice to the readership.

  You wrote in your reply:
  Kevin Kirby invited us to...

  Are you really sure... hummm, seems that Kevin was out on the Pacific ocean, fishing salmon, and that he was thinking of you and I when placing bait on his hook...

  I have received several e-mails indicating that the following link in the Bibliography on Dr. Kirtley's web site does not work:
   <http://www.tekscan.com/pdfs/CoM'nalysis.pdf> Murphy N (2002) Behind COM'nalysis. Technical and marketing flyer, TekScan Inc., South Boston MA.

  Specifically, the URL for this reference is: http://www.tekscan.com/pdfs/CoM'nalysis.pdf

  Note that there is an apostrophe ' in the word CoM'nalysis and some operating systems do not recognize this symbol.

  For those who which to access, but are unable, please use:

  http://www.tekscan.com/pdfs/CoMnalysis.pdf  (without the apostrophe)

  Of interest to some, posted on Dr. Kirtley's web site is an analysis before treatment (not wearing prescribed orthotics). If you do access the site http://www.tekscan.com/pdfs/CoMnalysis.pdf, scroll down the pages, and you will also see the results with treatment (wearing the prescribed orthotics) for the subject.


Kevin Kirby invited  us to have a look at the teach-in web site of Cris
  Kirtley about the efficiency of gait, in particular as calculated by the
  CoM analysis module introduced by Tekscan on the F-scan pressure
  measurement system.

  Norman,  I hope you do not feel offended by me dissipating some critical
  notes about this CoM module. After all,  the mailbase is a forum for
  discussion and I am quite interested to know your views on the usefulness
  of the CoM analyis. Despite the podiatric community in Canada and the US
  knowing you as the official promoter of the F-scan system, in this way
  tying your hands and head  to a  commercial company, I always appreciated
  your honest and knowledgeable comments about plantar foot pressure
  measurements. And your last contribution on the mailbase about the use and
  non-use of pressure plates is a good illustration of this.

  But let us  start with some few comments of mine (which are based on the
  information presented on Cris Kirtley's web site)

  First,  I am always wary to categorize complex phenomena like human gait by
  one figure, here the Gait Perfection Index. There is always the danger or
  temptation  for many clinicians to base their judgment on this one figure
  without taking the effort to look further to other much more informative
  indicators as the individual pressure curves etcŠ(Norman, in your email
  about pressure plates, you yourself stressed the need to  take account of
  many  other gait variables you deemed useful for a thorough gait
  evaluation). From my own experience, I know that the COP path on a colorful
  maximal pressure  picture of the foot,  is sometimes the sole information
  retrieved by many using pressure mats for gait evaluation, because it is
  presented on  the first flashy screen displayed by most pressure systems I

  Secondly, I am not sure and, by my knowledge, it is not proven yet that the
  vertical Com trajectory for normal gait should be a pure 2Hz sinus curve.
  What is the inter- and intra-  subject variability of this curve ? I can
  agree with the fact that the CoM trajectory in all probability will
  RESEMBLE a 2Hz sinus, but I would like to see the results of a study
  investigating  a large amount of subjects without apparent gait abnormality
  or medical history of the lower extremities. As long we do not have this
  information, it is my conviction that the use of Purity Index, and for the
  same reason also the Symmetry Index,  is quite premature for clinical gait

  Thirdly, the logic behind the Conservation Index, being the inverse of the
  sum of all twelve harmonics, escapes my gray cells as an indicator of gait
  And even in the case the three indices would be found valuable parameters,
  why combining them in one single general index, here the Gait Perfection
  Index. I would rather present the three indices separately as they are, as
  each tells its own story about the gait analyzed.

  And finally, a last comment, at least for tonight (it is about 2 o'clock by
  now).  It is well known and Cris Kirtley iterated this on the teach-in,
  that energy efficiency depends heavily on the phase difference between the
  potential energy and kinetic energy curves. Perfect out-of-phase would
  infer maximal energy recovery, and thus maximal efficiency. Which CoM
  module index does take the latter into account ?

  Well, I quit now and as my gray cells are gradually fading out, I'll go for
  a nice sleep. Norman it is your turn now to grasp your pen and present your
  own teach-in.
  I am looking forward to it.

  Regards to all,

   Bart Van Gheluwe
  Laboratory of Biomechanics
  Vrije Universiteit Brussel -Fac. LK
  Vakgroep BIOM
  Pleinlaan 2, 1050 Brussel, Belgium
  Tel.: 02/629.27.33 (31)
  Fax: 02/629.27.36


  I've been using the COM program linked to my fscan for the past year or so.
  What I like about it is that it provides a sort of reference for pre and
  post op 'sort of quantification' for orthotic treatment.  It may be argued
  that as a true value of efficiency there may be some problems but I think it
  is a good way to measure an effect comparing before and after.  I have done
  a study recently scanning 27 patients with a multitude of conditions.  In
  all but 1 if the COM graph improved so did the symptoms.  The case that did
  not was a patient with a large intermetatarsal neuroma who was using a pain
  avoidance strategy and when I 'improved the efficiency' she got more pain.
  She subsequently had surgery and is doing fine.

  On a similar note I have just evaluated 1150 orthotic prescriptions
  subjectively, all were written based on sagittal plane theory.  These are
  all musculoskeletal  patients some complex trauma and neurology cases where
  total resolution may be unrealistic.  Orthotics are both foot and limb
  devices and none of the foot ones were casted, all just treated using
  sagittal plane theory with very small amounts of correction.  The results
  show 92% of patients had significant to total resolution of symptoms.  This
  compares to previous studies I have done showing over 95% improvement.  This
  latest study was with more involved cases so this may explain the drop in

  The fscan study is ongoing and I do rely more on the fscan (using similar
  evaluation process to Howard Dananberg and Bruce Williams).  I am now
  starting to link video clips to the COM and they seem fairly reliable in
  what you see visually and what you see on the graphs.  Also the com graphs
  seem sensitive to 2mm of material thickness which enables very fine tuning.
  I think Howard has mentioned this before and it still amazes me how little
  'posting' you need to get a good clinical result.

  I would add that in many of the non fscan studies (see above) I provided
  treatment based on proprioceptive awareness of body weight, this seems
  excellent for post hip and knee replacement patients and post surgical ankle
  fusions and bunion ops to help fine tune sagittal function.  This is great
  for frontal plane FF conditions too and for assessing medially deviated

  I sent the COM info to Chris Kirtley to get a more traditional overview so I
  will be interested to see what comments it produces globally. I guess I was
  just looking for an accurate reference which was sensitive enough to see
  changes in orthotic function and then cross referencing this with subjective



Robert Fleck, Robert.Fleck@NUTH.NORTHY.NHS.UK

Bart, Bob and all

  While I do not dispute your findings Bob, I have my reservations re: the indices produced by CoMnalysis. I compared my "normal" walk with a much exaggerated Quasimodo type gait: much limping- dragging one foot behind me, much vertical displacement of CoM- CoMnalysis told me that this was more efficient and more symmetrical. Never mind.

  Best wishes,


      Maybe you are just a very efficient hunchback???
  Maybe quasimodo could be a "dead ringer" for you???  ; - )
 Bruce Williams <uwalk4me@ATTBI.COM>


  I think you must have been doing something wrong.  I tried this myself and
  the com was much much worse.  Also when I see each patient I repeat the test
  by magnifying the problem if I can to see if the efficiency is worse. For
  example if someone has a leg length discrepancy and I am happy with the set
  up I then put the raise in the other shoe and run a test to see if the com
  is worse.  I'm not sure what you are doing but the only thing that affects
  the com in my experience is if you start deleting or averaging cells in the
  fscan program or the calibration is not correct.

  I'm sure there is lots more work to be done here but all I was looking to do
  was to try and add some form of quantification to my outcomes.  This seems
  to be the best and most practical for me so far.

  If you like mail me the fscan files and I will take a look


Robert Fleck, Robert.Fleck@NUTH.NORTHY.NHS.UK

Dear Chris,
Thanks for a challenging teach-in.
I'd like to echo Gabor's comments: the internal work done by moving body
segments relative to the CoM will always mean that mechanical efficiency
describe by Cavagna will be an overestimate. Donelan et al in a relatively
recent issue of J.Biomechanics accounted for some portion of the internal
work by considering the contributions of leading and trailing limbs
separately. There are a couple of other problems with this sort of analysis.
Firstly, energetic analysis by the vertical excursion of the CoM assumes no
elastic storage and release of energy (i.e there is an assumption of a
motion similar to a pendulum's with a little resistance added to prevent the
system being 100% efficient). It is possible that some elastic storage of
energy takes place as the body descends and loads the leading limb being
returned in raising the CoM during midstance. In other words energy
transfers could take place between successive vertical oscillations of the
CoM - this energy not being converted into forward-going kinetic energy.
This motion is similar to Pogo stick in which at least a part of the energy
stored in the compressed spring is used to lift the body.
Secondly, the total energy consumed by a biological system performing a
mechanical function is not simply the sum of all external and internal
mechanical work. A classic example is the isovolumic contraction performed
by the left ventricle, in which the pressure of the blood inside the
ventricle is raised by the contraction of the myocardium until the pressure
inside the heart exceeds that of the systemic circulation. Clearly no
mechanical work is done by the heart during this phase, yet the heart wall
is doing significant biological work! In crouch gait we have a similar
phenomena, the extensors of the lower limb are working hard to prevent
collapse of the body. Their contributions to movement either vertically or
horizontally may be quite small in comparision. That is, the vertical
excursion of the CoM and its forward velocity of the body in crouch may
signify a rather efficient gait, but we know differently, don't we?

I think the inclusion of internal work, elastic energetics and physiological
work rather upsets the TekScan model.

Adam Shortland PhD, MIPEM, SRCS
One Small Step Gait Laboratory,
Guy's Hospital

Dear all,

Chris alluded to Cavagna's equation and both Gabor and Adam picked up on it. The equation actually separates out "vertical work" from "horizontal
work".  I don't really like this because energy is a scalar quantity (and therefore so is work) and I can't see the justification for separately
calculating "vertical work" and "horizontal work". I think the equations based on this under-estimate the efficiency of walking by not taking
into account the possibilities of energy transfer between potential energy and those changes in kinetic energy that arise as a consequence of changes
in the horizontal component of the velocity of the centre of mass.

Any comments?


Richard Baker PhD CEng
Gait Analysis Service Manager and Director of Research
Hugh Williamson Gait Laboratory, Royal Children's Hospital, Victoria
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 I was Dave Winter's student at Waterloo those many years ago, we spent (not surprisingly) a fair bit of time discussing
                      work-energy-power in gait. Tekscan's innovation has its roots in some early research on gait energetics which used the COM
                      as the single measure representing the body. That early research was flawed because it ignored the interactions within and
                      between segments (so we were told); so I guess Tekscan may be going down a 'deadend'. In theory, there are an infinite
                      number of ways that I could 'improve' my gait purity (and that doesn't even touch on abstinence from alcohol  ) by
                      manipulating how my limb move - assuming I had a built-in gait purity meter, of course.

                      I guess my concern is the oversimplification of the body in these systems. I mean, let's get over the fact that the human body
                      is complicated and stop trying to make analysing human movement a 'simple' thing. That can only result in a dilution of
                      information and understanding. Analysing human movement can be complicated and I'd rather see more effort go into
                      producing better 'movement analysts' (for lack of a better word) than trying to 'dumb down' measurement tools to appease
                      the masses.


                      Department of Sport & Exercise Science
                      Tamaki Campus
                      University of Auckland
                      Private Bag 92019
                      Auckland, New Zealand

                      Yesterday at the ASB meeting in Toledo I happened to talk to Norman Murphy of Tekscan who explained some of this to me.
                      Unfortunately, I had to run to a session before he got to the part about efficiency.

                      The use of the fourier analysis to look at gait symmetry makes perfect sense to me. If left and right leg have the same effect
                      on COM, the COM movement will only have even harmonics, and therefore the first harmonic is an indicator of asymmetry. A
                      similar analysis to quantify asymmetry in horses (but using head motion, not COM motion) was described by Christian Peham
                      in Vienna (J Biomech 1996).

                      But maybe Tekscan is putting the cart before the horse (no pun intended). Horses use asymmetrical vertical motions of the
                      head to reduce the vertical ground reaction force on one painful forelimb, and increase the force on the other limb. Experts in
                      horse lameness have understood this, hundreds, maybe thousands, of years ago and they always look for asymmetry in head
                      movement to (1) find out which limb is painful (the horse can't tell you!) and (2) quantify lameness. These people have also
                      very well understood the 180 degree phase shift that comes from differentiation of a sine wave to get inertial force from

                      So vertical motion is used as an indicator of vertical ground reaction force, and that may be why it is so useful. But.... if you
                      already know bilateral ground reaction force (as in Tekscan's system) why bother? Could you not directly quantify the
                      asymmetry from the ground reaction force, instead of going through this whole process?

                      As I said, I did not get an explanation of Tekscan's "Energy Efficiency Index" that is calculated by their software. If it is based
                      on the amplitude of vertical COM motion, I agree with Drew that this is probably not related to energetics. For example, a
                      pendulum has lots of vertical COM motion, but moves without using any energy. In fact, there may be a negative correlation!
                      Tomorrow at ASB there is a presentation with the title "Flattening the Center of Mass Trajectory Increases the Cost of
                      Walking", by Farley and Ortega. Yesterday there was a poster with the title "Reducing vertical center of mass movement
                      during walking doesn't necessarily reduce metabolic cost" (by Gordon, Ferris, and Kuo). The abstracts will probably be posted
                      at http://www.asb-biomech.org/abstracts.html

                      Ton van den Bogert, PhD
                      Department of Biomedical Engineering
                      Cleveland Clinic Foundation

Dear all,

There are several loose ends from the comments so far on gait efficiency, which I'd like to summarize.

1. Is the amount of Centre of Mass (CoM) motion in any way related to efficiency.
Evidence for: Kerrigan et al (1995) found a strong correlation (r2 = 0.91) between the amplitude of the vertical displacement of the CoM and energy consumption.
Evidence against: Richard Baker reports that children with spina bifida walk with large (inefficient) motions of the body segments but little
CoM motion.
                           Justus Ortega & Clare Farley (at the ASB last week) reported that walking in a way which minimised CoM motion actually HALVED efficiency.

2. Is it, perhaps, the recovery rate between potential (PE) and kinetic energy (KE) that is related to efficiency?
If so, can we agree on a definition for this? Giovanni Cavagna calculates the KE (0.5mv2) by just looking at the rise in FORWARD velocity when the CoM falls. Is this valid? Why ignore the other (vertical and lateral) components?

3. A few people have mentioned the phase relation between PE and KE as being critical, and Cavagna's team have shown that this is highly tuned in African women who carry baskets on their heads - see: http://jeb.biologists.org/cgi/content/full/205/21/3413  - and Griffin & Kram have shown that penguins also optimize this timing: http://www.usatoday.com/weather/resources/coldscience/2000/penguins122000.htm

If this is true, and getting back to the determinants of gait, what might be the joint kinematics associated with such timing?

mailto:[n/a] as usual with your comments.


Kerrigan DC, Viramontes BE, Corcoran PJ, LaRaia PJ (1995) Measured
versus predicted vertical displacement of the sacrum during gait as a
tool to measure biomechanical gait performance. Am J Phys. Med Rehabil.
74: 3-8.

Griffin M and Kram R (2000) Biomechanics: Penguin waddling is not
wasteful. Nature 408, 929.

G. A. Cavagna, P. A. Willems, M. A. Legramandi, and N. C. Heglund
Pendular energy transduction within the step in human walking J. Exp.
Biol., January 11, 2002; 205(21): 3413 - 3422.

Heglund NC, Willems PA, Penta M and Cavagna GA (1995). Energy-saving
gait mechanics with head-supported loads. Nature 375, 52-54
Dr. Chris Kirtley MD PhD
Associate Professor
Dept. of Biomedical Engineering
Catholic University of America

Dear Chris,

My colleague Dan Ferris forwarded this message to me. I was the organizer of
the symposium, "Modern Perspectives on the Six Determinants of Gait," at the
recent ASB meeting. I'm not a member of the Clinical Gait Analysis e-mail
list, but if you don't mind I would like to respond to the points that you
summarized, which appear to be at the tail end of a thoughtful discussion.
This is perhaps too long of a reply to post to the list, but I hope you
might find it helpful.  --Art Kuo (University of Michigan)

 1. Is the amount of Centre of Mass (CoM) motion in any way related to

Possibly, but not in the way predicted by the Six Determinants of Gait. In
parallel with the study of Farley & Ortega (2003), we also presented a
poster with similar evidence (Gordon KE et al. 2003). Our student, Keith
Gordon, had healthy normals walk with reduced CoM motion, and showed
markedly higher metabolic cost. This was found using two methods of reducing
CoM motion while maintaining a regular walking speed: (1) walking with very
short but fast steps, and (2) walking to reduce vertical CoM motion using
visual feedback of a sacral marker height. In normal walking, subjects do
not minimize their CoM motion, yet the preferred gait appears to minimize
metabolic cost for given speed. Our methods were slightly different from
those of Farley & Ortega (2003), but we very much agree with their results.

It is true that Kerrigan et al. (1995) found a correlation between CoM
motion and metabolic cost, but that was because CoM motion increased with
walking speed. That was a nice study, but their results shouldn't be
interpreted as making CoM a predictor, because speed is also correlated.
Keeping speed constant, it appears that metabolic cost goes up for any
increase or decrease in CoM displacement from what normal subjects prefer.

When subjects increase their vertical CoM motion, such as by taking longer
steps (whether or not speed increases), their metabolic cost also goes up
(Donelan et al., 2002; Gordon et al. 2003). However, we do not consider this
to be due to raising the CoM per se. We hypothesize that inverted pendulum
mechanics allow the CoM to go up and down without necessitating much
expenditure of energy. But regardless of the energy needed to act like an
inverted pendulum, there appears to be a substantial mechanical and
metabolic cost associated with the transition between inverted pendulum
phases, which we call step-to-step transition costs. The CoM velocity needs
to be redirected from one inverted pendulum arc to the next, and that
requires negative work by the leading leg. Positive work is needed to offset
this lost, and much (but not all) of this occurs when pushing off with the
trailing leg. See also Kuo (2001).

 2. Is it, perhaps, the recovery rate between potential (PE) and kinetic
 energy (KE) that is related to efficiency?

I am skeptical that % Recovery is a good predictor of efficiency. In two
different experiments where subjects walked with different step widths
(Donelan et al., 2001) and step lengths (Donelan et al., 2002), we found an
increased metabolic energy expenditure despite an increase in % Recovery. Of
course, there are other situations where % Recovery is inversely correlated
with metabolic cost, but overall I would not consider % Recovery a good
predictor. This is partially because % Recovery does not account for
simultaneous positive and negative work by the legs during double support
(Donelan et al., 2001), as well as other reasons. I am a great admirer of
Cavagna's many contributions to the understanding of walking and running,
but I find % Recovery to be of limited use. In any case, I don't believe %
Recovery has been rigorously tested as a predictor of experimentally
measured metabolic cost.

3. A few people have mentioned the phase relation between PE and KE as
 being critical...

There might very well be a relationship between PE and KE phasing and
metabolic cost, but I don't know of any explanation that makes predictions
that have been tested experimentally. There have been many papers that
analyze data post hoc, and speculate on the mechanism. But as with the Six
Determinants of Gait and % Recovery, I would like to see an experimental
test before embracing any hypothesis.

Donelan, J. M., Kram, R., and Kuo, A. D. (2001) Mechanical and metabolic
determinants of the preferred step width in human walking. Proceedings of
the Royal Society of London, Series B, 268: 1985-1992.

Donelan, J. M., Kram, R., and Kuo, A. D. (2002) Mechanical and metabolic
costs of step-to-step transitions in human walking. Journal of Experimental
Biology, 205: 3717-3727.

Donelan, J. M., Kram, R., and Kuo, A. D. (2002) Simultaneous positive and
negative external mechanical work in human walking, Journal of Biomechanics,
35: 117-124.

Gordon KE, Ferris DP, and Kuo AD (2003) Proc. 27th Ann. Mtg. Amer. Soc.
Biomech., Toledo, OH. #53.

Kuo, A. D. (2001) A simple model predicts the step length-speed relationship
in human walking, Journal of Biomechanical Engineering, 123: 264-269.

The poster above and paper reprints can be found at


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