Which bump does what?

There was some discussion at the CMAS meeting in Glasgow last week about what causes the characteristic bumps in the vertical component of the ground reaction. Before you read on it might be worth just stopping to think this through for yourself. Working from the premise that Newton declared that if there is a net force acting on an object then it must be accelerating – which acceleration does the first bump represent and which bump does the second represent?

Several of us admitted to believing that the prevailing wisdom (“what the textbooks say”) is that the first bump represents a deceleration of the centre of mass as it’s downwards movement is arrested and that the second bump is the upwards acceleration as we push off. This is not the correct explanation as Barry Meadows made clear in his presentation.

I’ve plotted some idealised data below to illustrate what is actually happening. The ground reaction under the left limb is represented in red and that under the right limb in right. One thing we  should do more often is to plot the sum of these which of course is the total force acting on the body (Chris Kirtley does do this in his book, 2006). The first interesting thing to note is that the peak total ground reaction actually occurs just before the middle of double support where two relatively modest forces from the different limbs superimpose.

GR and COM

I’ve also plotted the trajectory of the centre of mass (calculated from a double integration of the total ground reaction). It is at its highest in middle single support and lowest in early double support. The dotted black line shows its minimum value. Before this point the COM is travelling downwards and being decelerated and afterwards it is travelling upwards and being accelerated. Thus the first bump of the ground reaction is acting to accelerate the body upwards and the second bump is acting to decelerate as it falls from its peak height during middle single support. This is the opposite to “what the text books say”.

Or are we being unfair to the text books? I’ve gone back to see.

Whittle (2012) and Kaufman and Davis (writing in Rose and Gamble, 2006) get the explanation spot on.

Gage(2009, p54), on the other hand, states that the “body has been accelerating by gravity as it fell from its zenith at mid-stance to its nadir at loading response. As  a result the total force on the limb as it impacts the floor is about 120% of body weight“. This is a bit vague but essentially wrong. The body has actually been decelerating for half of its fall from zenith to nadir such that the vertical component of its speed is virtually zero at foot contact. The first peak of the ground reaction occurs well after the limb impacts the floor and is a result of the centre of mass being accelerated upwards.

Perry (2010, p459) writes that “the first peak (F1) … is increased above bodyweight by the acceleration of the rapid drop of the body mass”. This is also wrong-  the deceleration of the body mass is almost complete by initial contact and has occurred as a consequence of the GR under the trailing limb. The description of the second peak is even more confused – “the second peak (F3) … is modified by the push of the ankle plantar flexor muscles against the floor in addition to the downward acceleration of the COG as the bodyweight falls forwards over the forefoot rocker“.

So there we have it on a random sample of four books that happen to be on my shelf this afternoon two have the explanation correct and two have it essentially wrong.

There is some additional confusion because the fore-aft component of the ground reaction actually has the opposite effect.  In the first half of stance the GR is acting to decelerate the body in a horizontal direction (at the same time as accelerating it in an upwards direction). In the second half of stance the opposite is occurring as the GR is accelerating the body forwards (at the same time as it is decelerating it as it falls vertically).

.

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

Levine, D., Richards, J., & Whittle, M. W. (2012). Whittle’s Gait Analysis (5th ed.): Churchill Livingstone.

Rose, J., & Gamble, J. (Eds.). (2006). Human Walking (3rd ed.). Philadelphia: Lippincott Williams and Wilkins.

Perry, J., & Burnfield, J. M. (2010). Gait analysis: normal and pathological function (2nd ed.). Pomona, California: Slack.

Gage, J. R., Schwartz, M. H., Koop, S. E., & Novacheck, T. F. (2009). The identification and treatment of gait problems in cerebral palsy (1st ed.). London: Mac Keith Press.

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2 comments

  1. Hi Richard,

    I hope you are doing well. I haven’t seen you for a few years, but I look forward to sharing another pint with you sometime in the future. I am responding to your post on interpretation of the vertical ground reaction force due to a rather unpleasant experience that resulted from this information.

    The idea that you present about the lack of shock absorption during the loading response phase of gait is an interesting notion, but completely contrary to practically everything published in peer-reviewed literature about gait. I have no problem with the free expression of ideas, particularly those that question conventional wisdom, but unfortunately I recently had a manuscript about shock absorption during gait rejected by the journal Human Movement Science (HMS) because the reviewer claimed it was flawed on the basis of the information presented in your blog posting. I wanted to share my experience with you (and your readers) with the hope of creating awareness about how public opinion can influence/hinder the progress of science.

    Our manuscript is based on the fundamental premise that the first peak of the vertical ground reaction force is indicative of the shock absorption that occurs during the loading response phase of walking, a premise that is well-documented in the literature (Berge, Czerniecki, & Klute, 2005; Gard & Konz, 2003; Graham et al., 2007; Lass et al., 2013; Lehmann et al., 1993; Lehmann et al., 1993; Miller & Childress, 1997; Perry & Shanfield, 1993; Wagner et al., 1987). The reviewer of our manuscript for HMS claimed that our understanding of the vertical ground reaction force data was incorrect based upon your blog (i.e., https://wwrichard.net/tag/ground-reaction/). I generally regard blogs to merely be someone’s opinion that is not subject to the rigors of scientific scrutiny like that of a published scientific article. Needless to say, I was deeply offended and disappointed that our manuscript was deemed to be flawed on the basis of your blog posting.

    But let’s dig deeper—you claim that your perspective on the vertical ground reaction force was inspired by a conference presentation given by Dr. Barry Meadows, who actually hasn’t published his conflicting viewpoint in a peer-reviewed journal. You point out that the perspective you share with Dr. Meadows goes against “the prevailing wisdom” published in textbooks, which is absolutely correct. Interestingly, you cite Whittle (2012) and Kaufman and Davis (in Chap 4 in Rose and Gamble, 2006) in support of your argument. A careful review of these sources indicates that both texts *omit* any specific reference to shock absorption that occurs during the loading response phase of gait. Therefore, from this evidence it is not possible to convincingly determine that shock absorption is not present during that time in the gait cycle. However, I would like to point out that Whittle has published a couple of papers that specifically address shock absorption in the early stance phase of gait (Collins & Whittle, 1989; Whittle, 1999). Additionally, Kaufman and Sutherland (in Chap 3 of Rose and Gamble, 2006) state explicitly that “The first flexion wave, or stance phase knee flexion, occurs as a shock absorber to aid in weight acceptance…”. Furthermore, Perry & Burnfield (2010) clearly identifies shock absorption as one of four distinct functions of the locomotor unit (i.e., legs and pelvis) during able-bodied gait (in Chap 3). Therefore, it is easy to conclude that there is actually no published scientific evidence to support the assertion of the HMS reviewer (and Dr. Meadows) regarding the first peak of the vertical ground reaction force during walking, an opinion which again is quite contrary to the preponderance of published scientific literature.

    Following are the publications that I cited in previous paragraphs. Please feel free to confirm the validity of my cited information.
    Berge, J. S., Czerniecki, J. M., & Klute, G. K. (2005). Efficacy of shock-absorbing versus rigid pylons for impact reduction in transtibial amputees based on laboratory, field, and outcome metrics. J Rehabil Res Dev, 42(6), 795-808.
    Collins JJ, Whittle MW (1989). Impulsive forces during walking and their clinical implications. Clinical Biomechanics. 8;4(3):179-87.
    Davis RB and Kaufman KR (2006). Chap 4: Kinetics of normal walking. In: Rose J, Gamble JG, editors. Human walking. 3rd ed. Baltimore: Lippincott Williams & Wilkins. p. 53-76.
    Ferris, D. P., Louie, M., & Farley, C. T. (1998). Running in the real world: adjusting leg stiffness for different surfaces. Proc Biol Sci, 265(1400), 989-994.
    Gard, S. A., & Konz, R. J. (2003). The effect of a shock-absorbing pylon on the gait of persons with unilateral transtibial amputation. J Rehabil Res Dev, 40(2), 109-124.
    Graham, L. E., Datta, D., Heller, B., Howitt, J., & Pros, D. (2007). A comparative study of conventional and energy-storing prosthetic feet in high-functioning transfemoral amputees. Arch Phys Med Rehabil, 88(6), 801-806.
    Kaufman KR and Sutherland DH (2006). Chap 3: Kinematics of normal human walking. In: Rose J, Gamble JG, editors. Human walking. 3rd ed. Baltimore: Lippincott Williams & Wilkins. p. 33-51.
    Lass, R., Kickinger, W., Guglia, P., Kubista, B., Kastner, J., Windhager, R., & Holzer, G. (2013). The effect of a flexible pylon system on functional mobility of transtibial amputees. A prospective randomized study. Eur J Phys Rehabil Med, 49(6), 837-847.
    Lehmann, J. F., Price, R., Boswell-Bessette, S., Dralle, A., & Questad, K. (1993). Comprehensive analysis of dynamic elastic response feet: Seattle Ankle/Lite Foot versus SACH foot. Arch Phys Med Rehabil, 74(8), 853-861.
    Lehmann, J. F., Price, R., Boswell-Bessette, S., Dralle, A., Questad, K., & deLateur, B. J. (1993). Comprehensive analysis of energy storing prosthetic feet: Flex Foot and Seattle Foot Versus Standard SACH foot. Arch Phys Med Rehabil, 74(11), 1225-1231.
    Miller, L. A., & Childress, D. S. (1997). Analysis of a vertical compliance prosthetic foot. J Rehabil Res Dev, 34(1), 52-57.
    Perry, J and Burnfield, JM (2010). Gait analysis: Normal and pathological function, 2nd ed. Thorofare, NJ: SLACK Inc.
    Perry, J., & Shanfield, S. (1993). Efficiency of dynamic elastic response prosthetic feet. J Rehabil Res Dev, 30(1), 137-143.
    Wagner, J., Sienko, S., Supan, T., & Barth, D. (1987). Motion analysis of SACH vs. Flex-foot in moderately active below-knee amputees. Clin Prosthet Orthot, 11(1), 55-62.
    Whittle MW. Generation and attenuation of transient impulsive forces beneath the foot: a review. Gait Posture. 1999 10(3):264-75.

    Thank you for the opportunity to express my views on your blog site. I look forward to hearing your and your readers’ responses.

    Sincerely,
    Steven Gard

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