This website has moved to:

http://www.solbergweb.com/james/engineer/old_class_files/foot_sensor/foot_sensor.html

Abstract
The time/pressure distribution of a foot in motion has been the study of many scientists over the past twenty years. In this article, a system was built to measure these pressures. Piezoelectric sensors convert foot pressures to a resistance, which is placed in a voltage divider. The ensuing voltage drop is filtered at a high corner frequency of 50 Hz, and recorded in an oscilloscope through HP VEE. The system was used to gather data at 100 Hz from the gait of one female subject, moving at rates of 60 beats per minute, 120 bpm and 180 bpm and using shod and bare feet. Although the pressures experienced by individual sensors differed from results in the literature, an overall trend of greater mid- and fore-foot pressure with increased speeds was observed in the bare foot case. For the shod foot, there were high pressures in the heel region at low speeds, but an uncharacteristically large pressure in the toe was present for all three speeds. By considering the differences between the shod and bare foot data, a virtual transfer function of the shoe was calculated. From this function it can be seen that the shoe attenuates all frequencies equally. Sources of inaccuracy include sensor attachment, measurement synchronization, locomotion difficulties induced by the test, and the low repeatability of the trials.

Introduction
Spear in hand, a bushman ambles through an otherwise empty expanse of the Kalahari. Cradling a mobile telephone, a socialite darts across a crowded Manhattan intersection. For millions of years before and quite possibly for millions after the advent of planes, trains, and automobiles; mankind has depended predominantly on its feet for a vast range of daily activities. Because these primary means of locomotion often fall victim to afflictions both genetic and acquired; both the general public and the scientific community possess a keen interest in the pressures to which they are subjected and in how these pressures vary with factors such as shoe design and walking surface. Gaining such insight enables researchers to develop methods and devices for minimizing the risk of foot ulceration in diabetic patients; for monitoring the effects of degenerative foot diseases such as leprosy; for assessing the effectiveness of pressure relief insoles; for analyzing changes in gait due to injuries and to deformities such as spina bifida; for investigating the efficacy of reconstructive surgery; and for evaluating variations in load distribution as a result of limb length discrepancy (Cobb and Claremont).

The types of sensors deployed to confront these challenges are as diverse as the feet they measure; and since each approach offers a unique set of benefits and limitations, no single technique is appropriate for all possible applications. For example, the preeminent Kistler force plate achieves high specification, good repeatability, and long-term stability, but cannot measure plantar load distributions; pedobarographs render unequaled resolution for barefoot measurements, but are compromised by extremely temperature-dependent sensitivities (Patil and Srinath); the seven discrete sensors of the Electrodynagram allow both barefoot and in-shoe measurement, but also exhibit high nonlinearity, hysteresis, and drift (Cobb and Claremont); and a system consisting of discrete piezoelectric ceramic transducers provides moisture shielding, uniform load distribution, and minimal sensitivity to lateral strain, but requires calibration of individual transducers (Nevill et al.). Even a piezoelectric copolymer film configuration that boasts a measurement range of 0-1 MPa, linearity to within 1.5%, a hysteresis error of less than 1.5%, sensitivity of ±1 kPa within the calibration range and a worst-case reduction of 3%, and a frequency response of 0.008 to 250 Hz is restricted from widespread clinical use by the need to fashion insoles for each individual subject (Cobb and Claremont).
Differences in calibration methods and inconsistent definitions of such terms as “force,” “pressure,” and “load” make it difficult to quantitatively compare results from myriad methodologies, but qualitative trends from past studies generally agree.

The objective of this project is to utilize conductive polymer sensors in qualifying discrete in-shoe plantar pressure measurements for a single, female subject during both barefoot and shod walking and for speeds varying from a slow walk to a jog. These results are then compared to known data.

Results

The effects of velocity on pressure
When comparing the sensor measurements taken at 60 bpm and 120 bpm, there seems to be little variation.

For the trials with the running shoe, the outer heel exerts more pressure over a longer period of time than do the inner heel and third and second metatarsals. The first metatarsal has the same magnitude and longevity of the outer heel. The big toe experiences larger forces than any of the other parts of the foot, and with a longevity equal to that of the inner heel. This data does not agree with the above research, which stated that the metatarsal would receive the greatest force over the longest period of time.

When comparing the 60 bpm and 120 bpm measurements to the 180 bpm measurements, there are obvious differences. The duration of pressure exertion is now larger for the first, second and third metatarsals, and the magnitudes of these pressures are greater than at the slower rates. This confirms the above research, which states that at faster speeds, pressure is transferred farther up in the foot.  The heel shows a marked decrease in duration of pressure from previous trials.

For the barefoot trials, the trends are much different. At 60 bpm and 120 bpm, the maximum pressure and force duration seem to be the same for the inner and outer heel, and the first, second, and third metatarsals. For 60 bpm, there is comparatively no pressure on the toe, which contrasts greatly with the large pressure seen in the shoe trial. At 120 bpm, the toe pressure has increased to rival the other sensors. At 180 bpm, the inner and outer heel and first metatarsal show a lower peak force and smaller pressure window, while the second metatarsal now bears the most pressure, as predicted by Guten. The toe and third metatarsal seem unchanged.

In summary, the shoe seems to lessen the pressures felt by every part of the foot except the big toe, which experiences a vastly larger pressure. As speeds increase, the bulk of the pressure shifts toward the middle and upper foot.

Pressure impulse
Some of the literature discusses the topic of the “pressure integral” or “pressure impulse”.  It is defined as the area under the pressure curve of a time history, and is thus the integration of pressure with respect to time.  An impulse can be defined as the integration of force with respect with time.  Pressure can be interpreted as a normalized force with respect to effective surface area.  Investigation of the nature of an impulse reveals that an impulse is simply a change in momentum.  Likewise, one may interpret the pressure impulse as a change in momentum per unit area.

The pressure impulse was estimated from numerical integration of the data.  A representative portion of data from each data set was used to estimate the pressure impulse to which each sensor was subjected.  Noteworthy is the fact that the pressure impulse actually decreases with increasing speed.  Initially this may seem counterintuitive.  But, as the subject increased her speed, less energy needed to be exhausted to fluctuate her center of mass in the vertical direction.  For the center of mass to increase in elevation its momentum must change.  This change of momentum is represented by the pressure impulse inferred from the time history of the pressure.  As velocities increase, more salience is placed on minimizing non-conservative energy losses.  Almost none of the potential energy lost during a decrease in center of mass is ever regained during human locomotion.

Frequency domain analysis
Frequency domain analysis is an excellent compliment to the time domain analysis.  Plots were constructed that represent a Fourier analysis for each of the test conditions and each of the sensors.  Each graph was averaged over 3 data sets in attempt to minimize the noise inherent to frequency domain analysis.  The analysis utilized Matlab’s fast Fourier transform.  Each graph shows the frequency contribution to the signal.

Most of the results agreed with the literature.  Much of the data follows similar qualitative trends.  Much of the signal’s bandwidth is below 20 Hz, as expected.  This is consistent with mechanical systems of this scale.  The low-pass filter incorporated in the data acquisition process has a corner frequency of 50 Hz.  This frequency was chosen to minimize aliasing and noise while maintaining broad enough bandwidth to capture most of the dynamics.

Another salient characteristic present in the Fourier analysis data is the presence of spikes.  Initially, these spikes were thought to be some sort of resonating due to exiting some natural frequencies.  These spikes could have been picked up anywhere along data acquisition process (caused from shoe dynamics, sensor dynamics, noise, etc.).  Further investigation discredited these sources.  The spikes occurred at constant intervals.  This is most likely due to harmonics of the same phenomenon.

Shoe Dynamics
One of the main objectives of this project is to gain an insight to the dynamics of a running shoe, and how it affects foot/ground reaction forces.  The final three plots address that issue.  These plots represent the attenuation (or amplification) of pressure at each sensor caused by the dynamic properties of the shoe.  In this sense the shoe was treated as a “black box” and empirical input-output data was collected to determine its dynamics.  The input signal was the pressure between the foot and ground.  This was the data taken during the barefoot trials.

The output signal was the pressure between the foot and shoe.  So, the ratio of these signals reveal the dynamics of the shoe.  An approach similar to that of developing an empirical Bode plot was utilized.  The Bode plot, thus, gives insight to the input-output transfer function.  While the ratio of the output to input magnitudes at each frequency give rise to the magnitude dimension of the Bode plot, phase could not be determined.  Phase losses caused by the shoe dynamics could not be estimated because the input-output data was not taken at the same time.  Care was taken to replicate the experiment with and without wearing a shoe, but they could never be close enough to accurately compare phase differences.

A few interesting and a lot of not-so-interesting conclusions were drawn from this analysis.  Probably the most obvious observation is the lack of frequency dependence.  While the shoe transfer function is non-linear, a simple linear model could be fit to the model.  In its simplest form the linear model would be a zeroth order system.  This means no energy storage, and the system can only dissipate nonconservative energy.  But, without an estimate of the behavior of the phase, conclusive analysis could not be performed.

The attenuated magnitudes across all frequencies can be a double-edged sword.  Shoes are designed to absorb shock, which means dissipating energy.  It is apparent that this is in fact true.  This alleviates potentially traumatic forces the body is subjected to.  But, by absorbing shock less force can be transferred from the foot to the ground.  Sprinting shoes are designed to dissipate as little energy as possible.  While this is not recommended for extended duration, discomfort is compromised for performance.

Data analysis

The effects of velocity on pressure
When comparing the sensor measurements taken at 60 bpm and 120 bpm, there seems to be little variation.
For the trials with the running shoe, the outer heel exerts more pressure over a longer period of time than do the inner heel and third and second metatarsals. The first metatarsal has the same magnitude and longevity of the outer heel. The big toe experiences larger forces than any of the other parts of the foot, and with a longevity equal to that of the inner heel. This data does not agree with the above research, which stated that the metatarsal would receive the greatest force over the longest period of time.

When comparing the 60 bpm and 120 bpm measurements to the 180 bpm measurements, there are obvious differences. The duration of pressure exertion is now larger for the first, second and third metatarsals, and the magnitudes of these pressures are greater than at the slower rates. This confirms the above research, which states that at faster speeds, pressure is transferred farther up in the foot.  The heel shows a marked decrease in duration of pressure from previous trials.

For the barefoot trials, the trends are much different. At 60 bpm and 120 bpm, the maximum pressure and force duration seem to be the same for the inner and outer heel, and the first, second, and third metatarsals. For 60 bpm, there is comparatively no pressure on the toe, which contrasts greatly with the large pressure seen in the shoe trial. At 120 bpm, the toe pressure has increased to rival the other sensors. At 180 bpm, the inner and outer heel and first metatarsal show a lower peak force and smaller pressure window, while the second metatarsal now bears the most pressure, as predicted by Guten. The toe and third metatarsal seem unchanged.

Conclusion
The system described in this report was successively used to gather data at 100 Hz from the gait of one female subject, moving at rates of 60 beats per minute, 120 bpm and 180 bpm and using shod and bare feet. Although the pressures experienced by individual sensors differed from results in the literature, an overall trend of greater mid- and fore-foot pressure with increased speeds was observed in the bare foot case. For the shod foot, there were high pressures in the heel region at low speeds, but an uncharacteristically large pressure in the toe was present for all three speeds. By considering the differences between the shod and bare foot data, a virtual transfer function of the shoe was calculated. From this function it can be seen that the shoe attenuates all frequencies equally. Sources of inaccuracy include sensor attachment, measurement synchronization, locomotion difficulties induced by the test, and the low repeatability of the trials. This system could be further applied to analyze the presence of pronation and supination disorders, and the values of different models of running shoe.

References

Cobb, J. and Claremont, D.J. “Transducers for foot pressure measurement: Survey of recent developments.” Medical & Biological Engineering & Computing 33.4 (Jul 1995): 525-532.

Guten, G. “Running injuries.” W.B. Saunders Company. USA, 1997.

Lord, Marilyn et al. “Foot pressure measurement: A review of clinical findings.” Journal of Biomedical Engineering 8 (Oct 1986): 283-293.

Nevill, A.J. et al. “In-shoe foot pressure measurement system utilizing piezoelectric film transducers.” Medical & Biological Engineering & Computing. 33.1 (Jan 1995): 76-81.

Nigg, B. “Biomechanics of running shoes.” Human Kinetics Publishers, Inc. Champaign, IL, 1986.

Patil, K.M. and Srinath, M.S. “New image-processing system for analysis, display and measurement of static and dynamic foot pressures.” Medical & Biological Engineering & Computing 28.5 (Sep 1990): 416-422.

Zhu, Hongsheng et al. “A microprocessor-based data-acquisition system for measuring plantar pressures from ambulatory subjects.” IEEE Transactions on Biomedical Engineering 38.7 (Jul 1991): 710-714.
 

last modified 6 august 2000