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rmiller83
03-29-2010, 12:21 AM
Hello subscribers,

A perspective to add on this discussion:

It is always good to see papers like the recent Lieberman et al. (2010) study, as they help generate discussions such as this one and advance the field by motivating new lines of work, and it is undoubtably positive to have our topics of interest appear in journals like Nature. I don't know if running with or without shoes or with one footstrike pattern or the other is better for warding off injuries, and I will not pretend to know anything about evolution. I do know a thing or two about forces and masses, though (or at least like to think so!).

The term "impact transient" implies that there is a portion of the GRF that is due to impact, and a portion that is not. The "effective mass" used by Lieberman et al. (2010) is defined as the portion of the total mass that is accelerated when a multi-body system experiences an impact event (Ker et al., 1989; Derrick et al., 2000; Derrick, 2004). A key assumption made by Lieberman et al. (2010) in deriving their Eq. 2 is that the entire vertical magnitude of the GRF during the impact phase accelerates an effective mass. The principle of mechanical coupling states that all forces applied to a jointed, multi-segment body act to accelerate all segments of the body (Zajac & Gordon, 1989). The entire vertical GRF, at any time including the impact phase, cannot be assigned to a portion of the body mass, as the force must accelerate the whole body (although it will clearly impart greater accelerations on some segments than on others).

To study the effect of impact forces on the body within the context of effective mass, we should seek to isolate the portion of the GRF due to impact from that which is not due to impact. Is this process as simple as splitting up the force in the time domain at a particular time, say the valley between the peaks? I will argue that it is not. Fourier analysis tells us that the GRF is comprised of a series of sine waves with various amplitudes and frequencies that all overlap in time, and sum to give the total GRF. The relatively high frequencies are associated with impact portion of the movement, and the relatively low ones are associated with the mid-stance "active" portion. Due to the temporal overlap between these waveforms, the impact portion cannot be isolated in the time domain (it actually cannot be isolated in the frequency domain either, although the error here is much smaller than trying to do it in the time domain).

Let's make the assumption that the first 25% or so of the stance phase is the "impact portion", and the remaining 75% is the "active portion". I'll make the further assumption that by mid-stance, the impact transient has dampened out and has no direct influence on the active peak. This assumption seems reasonable given the heavily-damped nature of our soft tissues. Consider the time and frequency domains of the vertical GRF during rearfoot striking (Fig. 1):

Figure 1: (a) Time domain and (b) frequency domain of the vertical GRF component for a 60-kg subject running at 3.4 m/s.

The peak "impact force" is 1264 N, and the peak "active force" is 1539 N. The high-frequency band associated with the impact peak is clearly evident above ~ 8-10 Hz. This is why we get attenuation of the impact peak if the GRF is lowpass filtered at too low of a cutoff frequency, but the active peak is relatively unaffected. Let's try to isolate the active portion by filtering out all the frequency content above 8 Hz (Fig. 2). Similarly, let's try to extract the impact portion by filtering out all the frequency content below 8 Hz (Fig. 3). Here's what we get:

Figure 2: (a) Time domain and (b) frequency domain from Fig. 1 after applying an 8-Hz lowpass filter.

Figure 3: (a) Time domain and (b) frequency domain from Fig. 1 after applying an 8-Hz highpass filter.

Here the impact peak is now 536 N (Fig. 3a), and the active peak is now 1475 N (Fig. 2a). We lost ~ 4% of the active peak with this extraction method, which can be seen in the mid-stance portion of Fig. 3a. This indicates that the frequency bands of the impact and active portions overlap a little, and that we have attributed some of the active portion to the impact portion, and vice-versa. This error is unavoidable and would be present at any cutoff frequency. However, since we only lost 4% of the active peak, it seems that the degree of overlap is relatively small compared to the total bandwidth of either portion.

If the entire GRF during the impact phase in the time domain (in this case, the first 45 ms or so in Fig. 1a) is due to the impact transient, then the peak force during the first 45 ms of Fig. 3a should be about the same as the peak force during the first 45 ms in Fig. 1a. This is clearly not the case; the peak in Fig. 1a is over twice as large as the peak in Fig. 3a. The "impact" peak in Fig. 1a is comprised of contributions from both the impact and active portions of the stance phase.

This result should cause us to re-consider the first assumption regarding a distinct impact portion of stance in the time domain. Since muscles are active throughout stance, it doesn't make sense to me to consider distinct impact and active phases. Figure 2 indicates that the active portion of stance persists throughout the entire stance phase, not just the final 75%, which makes sense in consideration of EMG data and estimates of muscle forces during stance (Neptune et al., 2000). By this same argument, it also does not make sense to attribute any dynamic during the first 25% of stance to the impact event, since the active phase begins immediately, and muscles during late swing are active in preparation for impact (Bobbert et al., 1992). We therefore cannot isolate the magnitude of the impact peak in the context of effective mass by choosing the magnitude of the vertical GRF at a particular point in time.

Tim Derrick presented a method at ISB in Indianapolis on extracting the impact portion using a spline-fitting technique . The extracted impact peaks were highly correlated with the original impact peaks for different conditions of rearfoot striking, although the extracted peaks were about 40% smaller than the original peak for normal running, which would have a large effect on effective mass calculations. It would be interesting to perform this extraction analysis, as well as a frequency domain analysis, on GRF from running with shoes, running barefoot, different footfall patterns, etc.

Ross

References:

Bobbert MF, Yeadon MR, and Nigg BM (1992). Mechanical analysis of the landing phase in heel-toe running. Journal of Biomechanics, 25, 223-234.

Derrick TR (2004). The effects of knee contact angle on impact forces and accelerations. Medicine and Science in Sports and Exercise, 36, 832-837.

Derrick TR, Caldwell GE, and Hamill J (2000). Modeling the stiffness characteristics of the human body while running with various stride lengths. Journal of Applied Biomechanics, 16, 36-51.

Ker RF, Bennett MB, Alexander RM, and Kester RC (1989). Foot strike and the properties of the human heel pad. Proceedings of the Institution of Mechanical Engineers (Part H), 203, 191-196.

Lieberman DE, Venkadesan M, Werbel WA, Daoud AI, D'Andrea S, Davis IS, Mang'eni RO, and Pitsiladis Y (2010). Foot strike patterns and collision forces in habitual barefoot versus shod runners. Nature, 463, 531-535.

Miller RH and Hamill J (2009). Computer simulation of the effect of shoe cushioning on internal and external loading during running impacts. Computer Methods in Biomechanics and BIomedical Engineering, 12, 481-490.

Neptune RR, Wright IC, and van den Bogert AJ (2000). A method for numerical simulation of single limb ground contact events: application to heel-toe running. Computer Methods in Biomechanics and Biomedical Engineering, 3, 321-334.

Scott SH and Winter DA (1990). Internal forces of chronic running injury sites. Medicine and Science in Sports and Exercise, 22, 357-369.

Wright IC, Neptune RR, van den Bogert AJ, and Nigg BM (1998). Passive regulation of impact forces in heel-toe running. Clinical Biomechanics, 13, 521-531.

Zajac FE and Gordon ME (1989). Determining muscle's force and action in multi-articular movement. Exercise and Sport Sciences Reviews, 17, 187-230.

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Ross H. Miller
Doctoral student
Dept. of Kinesiology
University of Massachusetts