DoG II – the evidence

This is a second post “celebrating” the 60th anniversary of the publication of the determinants of gait. I’d intended to start off with something positive in the first post, that the paper has been subjected to some misinterpretation, but Rodger Kram’s comment has made me reconsider that. Perhaps the notion that energy can be conserved by reducing the vertical excursion of the centre of mass is (CoM)  implicit in parts of the paper if never mentioned explicitly. This has even led me to speculate on how that might have arisen.

Anyway I’d tried to start with a positive because at some time we have to deal with the negatives. These are quite significant because there can be no real doubt that the determinants are wrong!

If we accept that a belief that minimising the vertical component of the centre of mass trajectory will reduce energy cost is implicit in the paper then the determinants are clearly wrong right from the start. There are multiple examples throughout dynamics of systems in which potential and kinetic energy are exchanged without requiring any external energy (the simple pendulum is the most obvious example). There is absolutely no reason why minimising CoM movement should necessarily reduce energy consumption. Even if CoM excursion did lead to increased energy expenditure we now know that most of the determinants don’t actually reduce it. Gard and Childress (1997) started off by showing that pelvic list occurs at the wrong time and a little time later (1999) that the same is true of stance phase knee flexion. A short time later Kerrigan et al. showed that pelvic rotation has little effect on CoM height either.

The stance phase determinants (pelvic list, stance phase knee flexion) become even more bewildering if the aim is to smooth the trajectory of the CoM, because the trajectory is smooth already. Compass gait results in the CoM moving along a circular arc and there can be few trajectories that are smoother than that!

The final nail in the coffin was delivered by both the Chicago (Gard and Childress, 2001) and Boston (Kerrigan et al. 2000) groups establishing that Saunders, Inman and Eberhart had missed the most important determinant of CoM movement  which is movement of the foot and ankle and particularly heel rise in late stance.

We thus have a triple whammy:

  • the axioms on which the determinants are inappropriate (either because the trajectory of the CoM in compass gait is already smooth or because there is no particular reason why reducing its vertical excursion should reduce energy cost)
  • three of the major determinants don’t alter gait in the way the authors claimed
  • the authors missed the most important determinant that does!

I’m not the first to outline this of course. Art Kuo made a similar summary in an article in 2007. The most bizarre commentary, however, is that of Childress and Gard published in the third edition of Human Walking (2006). There’s nothing bizarre about the commentary but there is about its location- immediately after a full reproduction of the chapter as published in previous editions. We thus have a “keynote” chapter in a major text-book followed by a two page summary of why the chapter is wrong. How weird is that?

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Childress, D. S., & Gard, S. A. (2006). Commentary on the six determinants of gait. In J. Rose & J. G. Gamble (Eds.), Human Walking (pp. 19-21). Philadelphia: Lippincott Williams and Wilkins.

Gard, S., & Childress, D. (1997). The effect of pelvic list on the vertical displacement of the trunk during normal walking. Gait and Posture, 5, 233-238.

Gard, S., & Childress, D. (1999). The influence of stance-phase knee flexion on the vertical displacement of the trunk during normal walking. Archives of Physical Medicine and Rehabilitation, 80, 26-32.

Gard, S., & Childress, D. (2001). What determines the vertical displacement of the body during normal walking? Journal of Prosthetics and Orthotics, 13, 64-67.

Kerrigan, D. C., Della Croce, U., Marciello, M., & Riley, P. O. (2000). A refined view of the determinants of gait: significance of heel rise. Archives of Physical Medicine and Rehabilitation, 81(8), 1077-1080.

Kerrigan, D., Riley, P., Lelas, J., & Della Croce, U. (2001). Quantification of pelvic rotation as a determinant of gait. Archives of Physical Medicine and Rehabilitation, 82, 217-220.

Kuo, A. D. (2007). The six determinants of gait and the inverted pendulum analogy: A dynamic walking perspective. Hum Mov Sci, 26(4), 617-656.

60 years of the determinants of gait: a misconception

The month of July 2013 marks the 60th anniversary of the publication of The Major Determinants of Normal and Pathological Gait by J B dec M Saunders, Verne Inman and Howard Eberhart.  This is a seminal paper in the history of gait analysis which was revered for many years and is the foundation of the description of normal walking in many text books.  More recently, however, it has come in for substantial criticism.

three determinants

The first named author, John Bertrand deCusance Morant Saunders, was a medically trained Professor of Anatomy at the University of California who was born in South Africa of Scottish descent. The story is that he needed his name on a paper to justify a trip to the Joint Meeting of the Orthopaedic Associations in London in 1952 and Inman and Eberhart obliged. There is little doubt that the ideas were those of Inman, a pioneering Orthopaedic Surgeon, and Eberhart,  an engineer. (Inman first met Eberhart when amputating his leg after a wartime accident at the time when he had been asked to establish the National Research Council Advisory Committee on Artificial Limbs. He invited Eberhart, originally a civil engineer, to join him and the partnership continued for the next thirty years).

Over the month I intend to write a series of posts celebrating this anniversary by looking at different aspects of the paper.  In this post I’d like to dispel one of the myths about the paper which is that it states that the aim of walking is to minimise the excursion of the centre of mass. In a significant review article, for example, Art Kuo (2007) writes “The six determinants of gait theory proposes that a set of kinematic features help to reduce the displacement of the centre of mass. It is based on the premise that the horizontal and vertical displacements are energetically costly”. 

An earlier paper by Ortega and Farley (2005) starts with an almost identical quote which drove the authors to train participants to walk with a nearly flat trajectory of the centre of mass. They then showed that it took nearly twice as much energy (oxygen) to walk a given distance with the flattened trajectory than with the normal trajectory. Gordon, Ferris and Kuo (2009 – who I think did the work earlier but published it considerably later than Ortega and Farley) conducted a very similar study and came up with essentially the same results. The introduction of that paper is interesting in describing how “at least a dozen text books have interpreted [Inman’s] work as meaning it is desirable to minimise or reduce COM movement during walking” and giving an overview of how the ideas have developed through these.

What is interesting though is that nowhere in the original paper (nor in the extended versions that have appeared in the three editions of the book Human Walking) can I find any statement by the  authors that minimisation of the COM movement is the aim of walking. What thy actually said was this:

Translation of a body in straight line with the least expenditure of energy may be achieved mechanically by the use of a wheel, but it is quite impossible by means of bipedal gait. The next most economical method would be the translation of the body through a sinusoidal pathway of low amplitude in which the deflections are gradual. Since force is equal to mass times acceleration and acceleration is a function of time, abrupt changes in the direction of the centre of motion compel a high expenditure of energy. In translating the centre of gravity through a smooth undulating pathway of low amplitude the human body conserves energy; and, as we shall see in considering pathological gait, the body will make every attempt to continue to conserve energy.

What they are proposing is that the body acts to ensure a smooth trajectory not necessarily one of minimal vertical displacement. They start off by describing compass gait, moving with fixed knee with no foot and the problem that they identify with this is that “at the point of intersection with the arcs, the abrupt change in the direction of the forward acceleration [I think they actually mean vertical component of velocity – RB] would require the application of a force of considerable magnitude”. This is actually extremely close to the hypothesis of the Dynamic Walking Group that one of the principal energy costs of walking is the requirement to redirect the centre of mass velocity during step to step transitions (Kuo et al. 2005) despite a contention that  their approach is the antithesis of Inman and Eberhart’s (see Kuo  2007). The six determinants proposed in the original paper are then strategies to smooth the trajectory of the COM but not necessarily to reduce it.

So where did the original and perfectly sensible views of Inman and Eberhart get distorted? Gordon et al. (2009) quote Perry (1992) as saying “minimising the amount that the centre of gravity is displaced from the line of progression is the major mechanism for reducing the muscular effort of walking, and consequently, saving energy”. Perry, of course, trained under Inman, and it may be that like so many pupils it is she that has misrepresented the ideas of her teacher. As an engineer myself, however, I’d take the personal side out. I’d see the original and valid ideas as indicative of the potential for progress when clinicians and engineers come together to address the challenges of clinical biomechanics. The misrepresented and invalid ideas appear when clinicians think they can go it alone!

That’s it for this post. I’ve emphasised one particular aspect in which I think the work has been unfairly criticised. In later posts I’ll look at some aspects where criticism may have been more justified as well as examining the popular appeal of the approach

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Gordon, K. E., Ferris, D. P., & Kuo, A. D. (2009). Metabolic and mechanical energy costs of reducing vertical center of mass movement during gait. Arch Phys Med Rehabil, 90(1), 136-144.

Kuo, A. D., Donelan, J. M., & Ruina, A. (2005). Energetic consequences of walking like an inverted pendulum: step-to-step transitions. Exerc Sport Sci Rev, 33(2), 88-97.

Kuo, A. D. (2007). The six determinants of gait and the inverted pendulum analogy: A dynamic walking perspective. Hum Mov Sci, 26(4), 617-656.

Ortega, J. D., & Farley, C. T. (2005). Minimizing center of mass vertical movement increases metabolic cost in walking. J Appl Physiol, 99(6), 2099-2107.

Perry, J. (1992). Gait Analysis. Thorofare: SLACK.

Saunders, J. D. M., Inman, V. T., & Eberhart, H. D. (1953). The major determinants in normal and pathological gait. Journal of Bone and Joint Surgery, 35A(3), 543-728.

What is normal walking?

In the last post I commented on the recent paper by Dall et al. (2013) and the context of its publication. As commented on by the author in response to that post, some of the results are interesting in their own right. (I was going to paste a couple of figures from the paper into this article but the publishers require a payment of over $300 to do this legally so you’ll have to download a copy of the paper yourself if you want to see the evidence.)

Figure 1 shows the frequency distribution of minute epochs during which walking was recorded at various cadences. The mean cadence was 76 steps per minute with a cadence of less than 100 steps per minute in about 80% of the minutes during which any walking was recorded. When healthy adults walk at “self-selected” speed in the gait lab they tend to walk at cadences of well over 100 steps per minute (A brief review of the previous literature in Winter (1991) suggests values between 100 and 120). We can thus see that cadence in everyday activity is very different to that during walking in the laboratory.

The paper also includes a second graph (Figure 4) showing the same data but for the sub-set of minutes when the participants walked for the full minute. This shows a mean value of 109 (±9) steps per minute which is in much better agreement with the self-selected walking speeds recorded in the laboratory. The most obvious explanation of these two graphs together is that when we walk for short bouts we do so at much slower cadences than we tend to look at in the laboratory but when we walk continuously for a minute or more that we appear to walk at similar speeds (although the graphs tends to suggest that there is more variability in this in real life than I’d expect in the laboratory).

This can be put together with the data from Orendurff et al. (2008) that shows that 90% of bouts of walking are for less than 100 steps and 75% are less than 40 steps to suggest that the walking we investigate in the gait laboratory is quite different to the walking the we use most frequently in our everyday lives. This worries some people but this misses the reason for performing clinical gait analysis as we do. We use level walking at self-selected speed because it is a well-defined stereotypical movement that we understand reasonably well. We hope that analysing it will give clinical insights into impairments of neurological, muscular or skeletal function. The ultimate hope is that if we base treatment on the results of this analysis then we will improve function in “laboratory walking” and in every day walking as well. I hope you can see that this line of reasoning does not necessarily require laboratory walking to be representative of everyday walking.

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Dall, P. M., McCrorie, P. R., Granat, M. H., & Stansfield, B. W. (2013). Step Accumulation per Minute Epoch Is Not the Same as Cadence for Free-Living Adults. Med Sci Sports Exerc.

Orendurff, M. S., Schoen, J. A., Bernatz, G. C., Segal, A. D., & Klute, G. K. (2008). How humans walk: bout duration, steps per bout, and rest duration. J Rehabil Res Dev, 45(7), 1077-1089.

Winter, D. (1991). The biomechanics and motor control of human gait: Normal, Elderly and Pathological (2nd ed.). Waterloo:: Waterloo Biomechanics.

Publishing one paper to point out faults in another

This post is prompted by a discussion we had internally about a paper co-authored by one of my colleagues at the University (Dall et al. 2013). This was written as a response to an earlier paper (Tudor-Locke et al. 2011) based on data from the National Health and Nutrition Examination Survey (NHANES) for 2005-6 showing how many steps people took in each minute epoch as measured by an activity monitor. They assumed this was a measure of cadence and came up with the conclusion that:

Self-selected walking at 100+ steps/min was a rare phenomenon in this large free-living sample of the U.S. population, but study participants did accumulate ≅ 30 min/day at cadences of 60+ steps/min.

This is simply wrong. Whether the number of steps taken during any minute represents cadence or not will depend on whether the patient has been walking for a full minute or not. Take a person who is recorded as taking ten steps in one minute. This could come from someone who has walking difficulties and walked continuously for a minute but took only ten steps at a true cadence of 10 steps per minute. In this case steps per minute epoch is equal to cadence. Equally it could come from someone who had no difficulty walking and who walked ten steps at a cadence of 120 steps per minute but only for five seconds (ten steps) within the minute. In this case, which will be far more common than the first, cadence and steps per minute epoch are quite different. Recordings of 100 steps per whole minute is not rare because people walk with slow cadence but because it is actually very rare that we walk continuously for a whole minute (Orendurff et al. 2008). If you want to define a threshold value for cadence as was the original intention of Tudor-Locke et al. then you actually have to find some way of recording true cadence and not the number of steps per whole minute.

I think the issues are clear cut so far but then what should our response be? Malcolm and his colleagues had access to data collected with their activPAL device that would allow both true cadence and total number of steps per minute (step accumulation as they call it) to be calculated and demonstrated convincingly, but rather unsurprisingly , that the two are quite different. The published paper (Dall et al. 2013) makes a very interesting read – but should we have to go to this effort? Are there more effective ways of just telling people they are wrong!

Writing a letter to a Journal’s editor is one option but it always feels to me as if there is a time window on this – that the letter should really be submitted fairly soon after an article has been published. I’m not very good at keeping up with the current literature but when I’m working on a particular topic I will often read the relevant articles, both recent and not so recent, quite critically. Working like this it is often some time after publication that I read things that concern me.  A combination of my own inertia and the feeling that I am too late prevent me from doing any more about it.

Maybe I’m wrong in this – maybe we should feel free to use this route at any time that a mistake becomes apparent. Certainly this route ensures that the corrective letter is recorded in the same journal and under the same title as the original article and modern databases are becoming better at flagging this. A disadvantage of the approach of Dall et al. is that the new article is in a different journal published under a completely different title. In this case it has been published in a more technical journal (Medicine and Science in Sports and Engineering) which is unlikely to be read (or even searched) by readers of the original article (in the journal Preventive Medicine).

This wouldn’t be a problem if this were an isolated incident but biomechanics is a complex subject and I suspect that there are many more published mistakes and misconceptions than anyone in the field would want to acknowledge. In the worst case (again more common than we’d want to admit) published mistakes and misconceptions are adopted uncritically by other teams and before you know it what started off as an erroneous paper becomes first a series of erroneous papers and then a tried and trusted method (I’d see the use of CMC  (Kadaba et al. 1989) as a useful measure of repeatability of gait data as an example. Buy my book and read the appendix if you want to know more!).

The situation is exacerbated by the number of people who are involved in biomechanics as a secondary discipline. Some readers (and occasionally authors!) are not in a position to judge whether a method is valid or not. Does this increase the onus on those of us within the community who are aware of problems with specific papers to be more proactive in drawing people’s attention to them?

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Dall, P. M., McCrorie, P. R., Granat, M. H., & Stansfield, B. W. (2013). Step Accumulation per Minute Epoch Is Not the Same as Cadence for Free-Living Adults. Med Sci Sports Exerc.

Kadaba, M. P., Ramakrishnan, H. K., Wootten, M. E., Gainey, J., Gorton, G., & Cochran, G. V. (1989). Repeatability of kinematic, kinetic, and electromyographic data in normal adult gait. J Orthop Res, 7(6), 849-860.

Orendurff, M. S., Schoen, J. A., Bernatz, G. C., Segal, A. D., & Klute, G. K. (2008). How humans walk: bout duration, steps per bout, and rest duration. J Rehabil Res Dev, 45(7), 1077-1089.

Tudor-Locke C, Camhi SM, Leonardi C, Johnson WD, Katzmarzyk PT, Earnest CP, Church TS. Patterns of adult stepping cadence in the 2005-2006 NHANES. Prev Med 2011;53:178-81.

The last post – on the inverted pendulum

I think this will be my last post focussing on the inverted pendulum. In the first I gave a brief overview and in the second I looked at the vertical component of the ground reaction. The anterior component is also very interesting (well at least I think so).

You’ll remember that the inverted pendulum is a mechanism that allows a mass (body) that has some initial kinetic energy to move in a circular arc over the pivot  (foot). Early on the centre of mass is rising, gaining potential energy and thus, in a conservative system, must be slowing down. If it is decelerating in the horizontal direction then a force must be acting in the horizontal direction to cause this. The only force acting on the mechanism in this direction is the ground reaction so it must be directed posteriorly. As the mass approaches its high point it gains height, and thus loses speed, more slowly so this force must reduce and will be zero when the mass is at its high point. After this it starts to descend, loses potential energy and must speed up. If the mass is accelerating in the horizontal direction then a force must be causing this. During this phase the horizontal component of the ground reaction must be anterior. In qualitative terms, therefore, the horizontal component of the ground reaction under a passive inverted pendulum is predicted to be the same as that under the foot during walking.

Inverted pendulum

Curve in top half is vertical component and lower down is the horizontal components

The graph above shows the results of a quantitative analysis using sensible figures for mass (the dashed line shows the effect of a including a non-zero moment of inertia), leg length and initial velocity. I’ve only plotted this from middle of first double support to the middle of second double support as this is the period of the gait cycle that the inverted pendulum models.

Although (as commented on in the previous post) the vertical component of the ground reaction is quite different from the predictions of the inverted pendulum the horizontal component is nearly identical. We thus reach the conclusion that a completely passive mechanism (a stick with a weight on one end) generates almost exactly the same horizontal forces as we do when we are walking.

This is quite interesting in the context of the argument about whether the foot is “lifted off” or “pushed off” in second double support. On the basis of the horizontal component of the ground reaction it is clearly pushed off, but only to the extent that it would be if the leg was a completely passive mechanism.

It’s also interesting to think about this in the context of induced acceleration analysis. Because the underlying skeleton is unstable any induced acceleration analysis (e.g. Liu et al., 2006) will attribute the majority of the ground reaction to muscle forces. Interpreting what each muscle is doing and what clinical implications this has is quite complex. Thinking about the kinetics of the inverted pendulum, however, leads to the conclusion that the muscles are acting primarily to maintain the length of the limb and enable it to perform as an inverted pendulum would. It may be that this understanding leads to clearer clinical interpretation.

It certainly helps with the interpretation of the rather counter –intuitive finding of Liu et al. that the gluteus medius contributes to forward progression. In order for the body to move as an inverted pendulum it is important that trunk is not allowed to fall in relation to the hip and it is the gluteus medius that contributes that stability. The gluteus medius thus contributes to forwards progression by maintaining stability and allowing the passive dynamics of the inverted pendulum to do its business.

At the ankle and knee during late single support and second double support there is the added complexity of preserving the integrity of the inverted pendulum at the same time as allowing knee flexion to start in preparation for swing. Flexing of the knee alone would allow partial collapse of the pendulum but plantarflexing the ankle (reducing dorsiflexion) at the same time allows the overall length of the limb to be maintained. It is the plantarflexors that are required for this and, as might be expected, the induced acceleration shows these muscles as the primary contributors to the anterior component of the ground reaction through this period.

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Liu, M. Q., Anderson, F. C., Pandy, M. G., & Delp, S. L. (2006). Muscles that support the body also modulate forward progression during walking. J Biomech, 39(14), 2623-2630.