# Walking in the groove

While I surfing the web doing a bit of background reading for last week’s post I came across this graph.

Ralston HJ (1958) Energy-speed relation and optimal speed during level walking. Int Z angew. Physiol. einschl. Arbeitsphysiol. 17 (8): 273-288.

It’s another of the classic outputs of Verne Inman’s group, from Henry Ralston, and shows data for a healthy subject to support his hypothesis that we select our walking speed to minimise the energy cost of walking (the energy used to travel a certain distance). The hypothesis is so plausible that it has been almost universally accepted.

What interests me is that despite being so widely accepted I’ve never seen any suggestion of the mechanism through which we might achieve this. It’s a fairly basic principle of control theory that if we want to minimise any particular variable (such as distance walked for a given amount of energy) we need some way of measuring it. Thus it is very difficult to drive a car fuel efficiently if you just have a speedometer and a standard fuel gauge. If you add a readout to the dashboard telling you how much fuel you are using per kilometre travelled and the task becomes trivial. They should be compulsory in a fuel challenged world!

I’m not aware of any proprioceptive mechanism that would allow the brain to “know” how much energy it is using per unit distance walked. I can see that there are complex mechanisms regulating cardiac and pulmonary rate based primarily on carbon dioxide concentration in the blood which might allow us to sense how much energy we are using per unit time, but how can we possible sense how much energy we are using per unit distance. I’m not saying it’s impossible – the brain is a marvellous organ and it is possible that it integrates such a measure of energy rate (per unit time) with information about cadence and proprioception of joint angle and in order to derive a measure of energy cost (per unit distance). This is a complex mechanism however and certainly suggests that, as with so much in biology, whilst the basic hypothesis is extremely simple the mechanisms required to achieve this is far more complex than we might have imagined. As Ralston himself put it, “one of the most interesting problems in physiology is to elucidate the built in mechanism by which a person tends to adopt an optimum walking velocity such that energy expenditure per unit distance is a minimum”.

But this also makes me want to question the underlying hypothesis. Going back to the original paper (which you can read here), Ralston only produces data from one healthy subject and one amputee to support his hypothesis. I’m not aware of many others having explored the hypothesis on an individual level (the conclusion that the self-selected walking speed is close to speed of minimum energy cost for a sample does not mean that the relationship holds for individuals within that sample). I’d be interested to hear from readers of papers that have investigated this relationship in more detail.

The other point that Ralston made which is almost always overlooked is that the curve is “almost flat”. The curve only looks so steep because it has been plotted over such a wide range of values (from 0 through to 150m/s). Just looking at the data plotted I’d suggest that the speed can range from about  56 to 84 m/min whilst the energy cost remains within 5% of the minimum energy cost value. This is almost certainly within the range of measurement error for a variable such as energy cost. In other words the really remarkable thing about the energy curve is that it allows us to walk over quite a range of speeds without having a measureable effect on our energy cost. It is interesting that Ralston managed to make this point and suggest that we select walking speed to minimise energy cost in the same paper!

# Shockingly wrong?

Hi, sorry I’ve been away for so long. How very Australian of me to take all of January off!

We’ve started a new semester on the MSc programme its called “Healthy walking” and for this two weeks the students are working through my video series “Why we walk the way we do“. I’ve also been preparing some study material to support this. In doing this I’ve become even more convinced than ever that the conventional understanding of first double support as a phase of shock absorption is wrong.

Of course one of the old chestnuts that follow from that theory is that stance phase knee flexion is a mechanism to absorb the shock of impact. I’ve been thinking about this for sometime but it wasn’t until I was preparing this material last week that it struck me that it would be useful to look at the knee power graph. Why? – because if there is one thing that shock absorbers do it is absorb energy. You can make an argument that this is all they do. So if the knee is a shock absorber and we look at the knee power graph immediately after foot contact we should expect to see power absorption.If you look at the graph you’ll see quite the reverse. Immediately after foot contact the knee is generating power – this is not the action of a shock absorber.

In case anyone thinks this is just my data we can go to David Winter’s book (1991, figure 4.34b):

This is interesting because the early power generation peak is definitely there but Winter seems to ignore it. He starts numbering at the power absorption peak in late double support that extends into early single support (K1). Its almost as if he can’t bring himself to admit that it’s there – perhaps he was a shock absorption theorist and this didn’t fit in with his world view?

Kirtley (2006) admits the peak is there and even labels it Ko. He claims however that it is an artefact of the filtering. This claim is unreferenced but I think refers to the work of Bisseling and Hof (2006) which was drawn into a discussion on K0 on the old CGA web-site. I’m not convinced. I don’t think anyone doubts that the ground reaction is anterior to the knee in the first half of double support and the knee is clearly flexing at this point. The inevitable consequence of the combination of these two observations is that power (moment . joint velocity) must be generated. The knee is not acting as a shock absorber.

Putting it another way the knee moment graph clearly shows that the knee flexors are the dominant muscle group at the knee for the first half of double support whereas the knee extensors would have to be dominant for knee flexion to have the capacity to absorb shock.

Of course from about half-way through double support power is absorbed at the knee but this is about 50msec after foot contact which is too long after contact for this to be a consequence of a mechanical “shock” at the time of contact.

On the balance of evidence I’m more and more convinced that stance phase knee flexion is not a shock absorbing mechanism. But if it’s not to absorb shock – what is it for?

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Bisseling, R. W., & Hof, A. L. (2006). Handling of impact forces in inverse dynamics. J Biomech, 39(13), 2438-2444.

Kirtley, C. (2006). Clinical gait analysis (1st ed.). Edinburgh: Elsevier.

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

Winter, D. A. (1992). Foot trajectory in human gait: a precise and multifactorial motor control task. Phys Ther, 72(1), 45-53; discussion 54-46.

# What are the hip adductors for?

Various things have made me think about muscles this week and an issue that’s puzzled me for some time. Why do we have such big hip adductors? Edith Arnold’s paper (2010) is probably the most authoritative we have on the relative strengths of muscles based on muscle volume and fibre length measurements from 21 cadavers. I’ve tabulated the data below. It’s got a few surprises. The gluteus maximus is the largest muscle but several others are considerably greater capacity to generate force (because they have more shorter fibres), the soleus, for example, has nearly twice the force generating capacity.

Adapted from data contained in: Arnold, E. M., Ward, S. R., Lieber, R. L., & Delp, S. L. (2010). A model of the lower limb for analysis of human movement. Annals of Biomedical Engineering, 38(2), 269-279.

What I want to focus on today though is the force generating capacity of the adductors. Summing the peak forces we get 2000N for adductors brevis, longus and magnus working together which is considerably greater the gluteus maximus and up there with the other big muscles. Of course the purpose of muscles is to generate moments and we have to take the moment arm into account as well. The adductors have some of the largest moment arms in the lower limb so their moment generating capacity is even larger than the simple peak force might suggest.

But why do they need to be so large? In both walking (Schwartz, 2008, see figure below) and running (Novacheck 1998) at a range of speeds there is a continuous abductor moment at the hip throughout stance. Indeed because the hip joint is so lateral with respect to the centre of mass of the trunk its very difficult to see how there can be anything other than an internal abductor moment at the hip.

Schwartz, M. H., Rozumalski, A., & Trost, J. P. (2008). The effect of walking speed on the gait of typically developing children. J Biomech, 41(8), 1639-1650.

Anderson and Pandy (2001) in their simulation of human walking found low levels of activation in the adductor magnus. This was confined to a short period  around foot contact presumably to supply the small adductor moment immediately after heel contact as seen above. Unsurprisingly in later analysis  (2003) of the same data they concluded that the adductors make a negligible contribution to the vertical component of the ground reaction. Liu et al. (2006) who were tracking real data, found that the adductors don’t make any contribution to the vertical or fore-aft component of the ground reaction either at normal walking speed (2006) or a range of walking speeds  (2008).

So what’s going on? The adductor magnus is the seventh biggest muscle in the human body and yet it doesn’t seem to do anything during walking or running. There is absolutely no doubt of course that it does come into action during a range of 0ther activities, especially in sport, but how much?  Taking the argument above that it is most likely to be needed when the centre of mass of the trunk is lateral to the hip joint then  there will be relatively few occasions when this occurs in most sports (and I’d suspect even fewer in  non-sporting activities). To get to the size they are the hip adductors must have conferred some evolutionary advantage – but what?

Having written this I’ve been out for a 15km run and guess what – it is my groin (adductors) that is aching. Something really doesn’t add up!

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Anderson, F. C., & Pandy, M. G. (2001). Dynamic optimization of human walking. J Biomech Eng, 123(5), 381-390.

Anderson, F. C., & Pandy, M. G. (2003). Individual muscle contributions to support in normal walking. Gait Posture, 17(2), 159-169.

Arnold, E. M., Ward, S. R., Lieber, R. L., & Delp, S. L. (2010). A model of the lower limb for analysis of human movement. Annals of Biomedical Engineering, 38(2), 269-279.

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.

Liu, M. Q., Anderson, F. C., Schwartz, M. H., & Delp, S. L. (2008). Muscle contributions to support and progression over a range of walking speeds. J Biomech, 41(15), 3243-3252.

Novacheck, T. F. (1998). The biomechanics of running. Gait Posture, 7(1), 77-95.

Schwartz, M. H., Rozumalski, A., & Trost, J. P. (2008). The effect of walking speed on the gait of typically developing children. J Biomech, 41(8), 1639-1650.

# Taking it slowly

Hi, I’m back, refreshed from a family holiday in France and Spain and invigorated by an excellent ESMAC conference in Glasgow. Thanks to so many people that used the opportunity to say how much they liked the blog – I suppose I better keep going. The view counter passed 10,000 earlier today so let’s see if we can keep it ticking over.

I’ve no doubt that, for clinical gait analysts, the most important paper published over the last decade is Mike Schwartz’ study on the effect of walking speed on gait variables (2008). It’s the only paper that I maintain a link to on my desktop and I rarely interpret any patient data without referring to it. If you haven’t already done so then download it now and do the same (let’s see if we can knock Tom Novacheck’s [1998] review of running biomechanics off the top of the Gait and Posture most downloaded papers table and replace it with a genuine scientific study!).

In the study quite a lot of kids were asked to walk at a range of walking speeds. The resulting gait trials were divided up into five groups by walking speed and the average gait variables for the different groups were calculated. The darker the blue in the figure above the faster the walking with the middle trace representing self-selected walking speed. You can see that the gait traces change quite considerably with walking speed even when there is nothing wrong with the child.

We were looking at data from a patient with a rare genetic disorder today. I think if I’d looked at the same data ten years ago I’d have made all sorts of pronouncement on his gait impairments. Now I just look at Mike’s paper and can say, “Yep, he’s walking slowly”, not only that but, “he’s walking slowly in exactly the same way as anyone else would walk slowly”.  It might be worth trying to work out why he’s walking slowly but there is no evidence in the gait data of any specific impairment that is affecting his walking.

I was chatting about this in the group and talking about how we walk with different gait patterns at different speeds and one of my colleagues asked quite, “Why?”. It’s one of those simple questions that caught me completely unawares and started me thinking.

Kinematically, there is absolutely no reason why anyone shouldn’t walk more slowly by having exactly the same pattern of movement but simply going through that pattern more slowly. You could thus walk slowly in a way that gives exactly the same gait graphs (after time normalisation, see previous post on this). The answer of course is that walking is not primarily driven by the kinematics but the kinetics. The way that energy flows between the segments and the way this is mediated by muscle activity depends very much on how fast the segments move. Kinetic energy is proportional to the square of speed and forces and moments act to produce accelerations.  Walking slowly efficiently requires quite different dynamic mechanisms to walking quickly efficiently.

Although this answers the question at one level it only does so partially. What would be really interesting would to be to look at how the curves change with speed from the context of how we understand the process of normal walking and see if we can explain why the gait pattern varies the way it does. Anyone who can do this easily and comprehensively has a better understanding of normal walking than I do. I’m going to have to go away and think about this.

One thing that I think would be quite instructive would be to try and do this practically. Stick some markers on yourself and record yourself walking normally. Then try and see if you can walk slowly but in the same kinematic pattern (after time normalisation). I wouldn’t mind betting that it’s not possible. Even if it is possible to match the kinematics this will require quite different kinetics and muscle activations. You may even be able to feel which muscles you are having to use differently. I suspect there’s be  a huge amount to learn from such an exercise.

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Novacheck, T. F. (1998). The biomechanics of running. Gait Posture, 7(1), 77-95.

Schwartz, M. H., Rozumalski, A., & Trost, J. P. (2008). The effect of walking speed on the gait of typically developing children. J Biomech, 41(8), 1639-1650.

# 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.