AN INTERESTING RESULT FROM an enDAQ 3-AXIS ACCELEROMETER MOUNTED ON THE LOWER BACK of a RUNNER

The runner was me, and the run was the recent Lord Hobo Brewery 6.1K race.

BACKGROUND

Prior to the race we affixed a Mide product, and enDAQ 3-axis accelerometer & barometer unit, to the lumbar region of my backside with paper tape & took vibration data throughout the race.

The affixation:

This blog will cover:

1. The Data
2. FREQUENCY ANALYSIS of VERTICAL MOTION
3. HARMONIC OVERTONES
4. SPINAL RESONANCE RESEARCH
5. Discussion
6. FUTURE STUDIES

THE DATA

This is a typical snippet from the record. The raw data from all 3 axes has been processed so that “X”, axis in orange color is pretty close to gravitational vertical. This is made possible by additional sensors in the enDAQ unit for gravity and magnetic field.

NOTE: There was pilot error. The “X” axis show ‘minus’ when it should be ‘plus’.   So the big 8 G down spike is really an 8 G upward acceleration that occurs during the foot landing in the stance phase of the stride.

ALSO NOTE: There are a lot of wiggles in the “X” vertical acceleration signal.

For reference, & comparison here is a page from a research paper that did show the major accelerations for the lumbar of a runner . The researcher’s signals are qualitatively similar to ours.

FREQUENCY ANALYSIS of VERTICAL MOTION

We did a frequency analysis of the “X” vertical signal and we got this (apologies for picture quality). Vertical is again in orange color

The big peak at the left end is at about 3 Hz, corresponding to my prevously measured and typical 180 foot landings per minute. This was expected. The remainder of the peaks show an intriguing and puzzling set of overtones.

What is the origin of this set of peaks which are neatly spaced at around 3 Hz apart?

Is my spine essentially a plucked string?

Is this the vertical aspect of some lateral motion, or is it compressional up and down the spine?

Is it just an artifact of the measurement analysis?

HARMONIC OVERTONES

Further literature search reveal the following two things:

Thing 1.

A guitar string (or other stretched string) has a fundamental (i.e. lowest) resonant frequency, and a set of harmonic overtones (i.e. higher frequency tones). When the string is carefully stroked at it’s center the result is a pure tone at the fundamental frequency . When the string is just strongly struck hard or plucked at an arbitrary point the sound that results is a mix of the fundamental and many of the harmonic overtones.

Both theory and experiment show the overtone frequencies to be spaced evenly apart, and to be integer multiples of the fundamental frequency (i.e. harmonic).   Here is a measured frequency distribution of the sound from a plucked guitar string:

NOTE: The musical note “E4” is 329.63 Hz , so those peaks are 329.63 Hz apart.

Thing 2.

Similarly a solid rod exhibits a fundamental frequency in compression along it’s long axis, and an associated set of harmonic overtones extending to higher and higher above it.

So both stretched string and solid rod exhibit this ‘picket fence’ of overtones. In principle the spine, being a complex structure as opposed to a uniform cross section perfect string or column, could be exhibiting one, both, or even a mix.   But it seems likely that it’s structure more resembles a column suspended in a bed of flesh than a string stretched tight.  

SPINAL RESONANCE RESEARCH

Some research has been done to measure the fundamental resonant frequency of the spine. The motivation for most of it has been to understand spinal resonance in order to assist design of vehicles, vehicle suspension systems, seats, etc that avoid exciting the fundamental spine resonance, inducing high stress and thereby contributing to lower back pain.

Here are two papers on spinal resonance determination.

The first one used Finite Element Modeling & came up with a figure of 3.5 Hz:

The second one actually measured the mechanical resonance of the spine for several subjects who were seated on a vibrating platform which could be sinusoidally driven:

DISCUSSION

Perhaps surprisingly both these studies came up with fundamental spine resonances close to 3 Hz. But what about the overtones of the spine?  

The spine of course bears only a remote resemblance to a column having a uniform cross section. Starting at the bottom, it is a stack of elastic vertebrae of decreasing cross section separated by elastic layers all of which are impregnated with fluid. Nevertheless, it will have overtones. The question is whether those overtones end up being evenly spaced. If it turns out to be the case that they actually are evenly spaced, that would be quite remarkable and unlikely to be accidental. That is to say, there would be some biological performance advantage to maintaining that condition.

To date I have not been able to find any prior studies of the spine’s harmonic resonances “in the wild”, i.e. during walking or running as opposed to laboratory conditions. The enDAQ permits an easily done non-invasive diagnostic that might turn out to be useful medically for gait study, posture study, spinal study, or perhaps even for running studies. Medical market!

FUTURE STUDIES

Not many conclusions can be drawn in an experiment where there is only one subject.

Hopefully we can get a few different runner volunteers to take a few miles of enDAQ data and see whether a similar feature shows up for anybody else.