TECHNICAL
XX NOTES
JOURNAL OF APPLIED BIOMECHANICS, 1998, 14, 93-104
Measurement
© 1998 by Humanof
Kinetics
Pressure
Publishers,
and Inc.
Shear
93
A Device for Simultaneous Measurement
of Pressure and Shear Force Distribution
on the Plantar Surface of the Foot
Brian L. Davis, Julie E. Perry, Donald C. Neth,
and Kevin C. Waters
A device has been designed to simultaneously measure the vertical pressure and the
anterior–posterior and medial–lateral distributed shearing forces under the plantar surface of the foot. The device uses strain gauge technology and consists of 16 individual
transducers (each with a surface area measuring 2.5 3 2.5 cm) arranged in a 4 3 4
array. The sampling frequency is 37 Hz and data may be collected for 2 s. The device
was calibrated under both static and dynamic conditions and revealed excellent linearity (±5%), minimal hysteresis (±7.5%), and very good agreement between applied and
measured loads (±5%). Vector addition of the distributed loads gave resultant forces
that were qualitatively very similar to those obtained from a standard force plate. Data
are presented for measurements from the forefoot of 4 diabetic subjects during the
initiation of gait, demonstrating that distributed shear and pressure on the sole of the
foot can be measured simultaneously.
Key Words: diabetic foot, plantar pressure, shear measurement, instrumentation
Ulceration of the plantar tissue of the foot represents a potentially serious problem
for individuals who have sensory neuropathy secondary to diabetes. The principal mechanical factors leading to ulceration are ill-defined. A number of studies (Boulton et al.,
1983; Ctercteko, Dhanendran, Hutton, & LeQuesne, 1981; Stokes, Faris, & Hutton, 1975)
have shown that sites of ulceration correspond to areas of elevated plantar loading, while
others (Pollard & LeQuesne, 1983) have shown that ulceration occurs at sites of maximum shear stress. While high vertical or tangential forces alone could damage skin tissue, there is quite possibly some combination of these forces that is more detrimental
than others. Davis (1993) proposed three scenarios in which the interaction of pressure
and shear forces could cause skin loading conditions that might contribute to ulcer formation.
Although shear is believed to be a significant factor contributing to ulceration
(Bauman, Girling, & Brand, 1963; Brand, 1988; Delbridge, Ctercteko, Fowler, Reeve, &
LaQuesne, 1985), few researchers have investigated frictional forces due to the difficulty
in constructing devices capable of measuring shear (Cavanagh & Ulbrecht, 1991; Masson
The authors are with the Department of Biomedical Engineering, The Lerner Research Institute, The Cleveland Clinic Foundation, 9500 Euclid Ave., Cleveland, OH 44195.
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Davis, Perry, Neth, and Waters
& Boulton, 1991; Thompson 1983). Most devices have been limited to measuring shear
forces in one direction only (Laing et al., 1992; Pollard & LeQuesne, 1983; Pollard,
LeQuesne, & Tappin, 1983; Tappin, Pollard, & Beckett, 1980; Tappin & Robertson, 1991)
and, thus, likely underestimate the maximum shear stresses. A transducer capable of measuring both shear components on the plantar surface of the foot was developed by Lord,
Hosein, and Williams (1992). The transducer measured 16 mm in diameter and 4 mm
thick and was placed in an inlay to permit in-shoe measurement. One limitation of discrete
transducers is that prior knowledge is required about the areas of interest in order to determine placement of individual transducers. As a result, areas experiencing high stresses
may remain undetected if they do not coincide with the areas of interest determined a
priori. The transducer used by Lord and colleagues is also capable of measuring pressure
if an additional component is added. However, all three stresses were not measured simultaneously because the pressure-measuring component made the transducer too large for
in-shoe measurements.
More recently, Huo and Nicol (1995) reported on the development of a 3-D force
distribution measurement system using strain gauge technology. The device consists of an
array of 336 sensors. Although no pressure or shear data were described, the authors reported that the device was suitable for investigating foot loading conditions during the
takeoff phase of the high jump. In our laboratory a device has been developed, also based
on strain gauge technology, which is capable of simultaneously measuring the distribution
of all three force components (vertical, mediolateral, and anteroposterior) on the plantar
surface of the foot.
Methods
Mechanical Design
The device has an overall surface area measuring 10.5 cm 3 10.5 cm and is composed of
16 individual transducers. Each transducer measures 2.5 cm 3 2.5 cm and has two components (Figure 1). The hollow cylindrical aluminum column has two sets of T–strain gauge
rosettes. Each set is mounted at a different level, and within each set four rosettes are
equidistantly spaced around the column. This configuration permits measurement of both
mediolateral and anteroposterior shear forces even in the presence of superimposed vertical forces. Each rosette consists of a 90° arrangement of two 350V standard constantan
strain gauges (Measurements Group, Inc., Raleigh, NC). Compressive forces are measured with an S-shaped cantilever that fits into the end of each vertical column. The cantilever is instrumented with four rosettes, one centered on each of the four vertical faces
(two interior and two exterior faces).
Since surface material affects the coefficient of friction between the foot and the
contact surface, the device is designed to accommodate different surface materials. Specifically, 2.5 cm squares of material are mounted to thin (3 mm) aluminum base plates
that have two small posts on the inferior surface. The top of each transducer is designed
with two small holes at opposite corners to accommodate the “caps” of surface material.
Sixteen individual transducers are arranged in a 4 3 4 array and anchored in a 2 cm
thick aluminum base plate (Figure 2). Spacing between transducers is 1.5 mm. This provides an overall surface area of approximately 10.5 cm 3 10.5 cm. Although this size is
not large enough to permit force measurements under the entire plantar surface, it is large
enough to examine the forefoot area, which is of primary interest since most diabetic foot
ulcers occur in the regions of the metatarsal heads and toes.
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Figure 1 — Schematic representation of the transducer. The transducer consists of a hollow
column with an S-shaped cantilever, both machined from aluminum (Young’s modulus = 70
GPa). All measurements are in centimeters. An enlarged view of the rosette depicts the
orthogonal arrangement of the strain gauges.
Figure 2 — The fully assembled shear and pressure device consisting of 16 transducers in a 4 3
4 array. The total surface area measures 10.5 3 10.5 cm with a 1.5 mm space between adjacent
transducers.
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Davis, Perry, Neth, and Waters
Electronic Design
The electronic interface board (Figure 3) consists of six Wheatstone bridges per post.
Four bridges detect the shear forces and two detect the vertical forces. To handle the
complexity of sampling from 96 bridges (16 posts 3 6 bridges per post), 32 multiplexors
are used and a straight data acquisition method is employed. A 1 V precision regulator is
Figure 3 — Diagram of the electronic interface board showing the representative arrangement
of the six bridges per post. Bridges A and B measure compression, C and D anterior–posterior
shear, and E and F medial–lateral shear. When pressure is applied to the S element, gauges
on either side of the vertical sections of the S change resistance in opposite ways (the
resistance on the outside gauges increases and the resistance on the inside gauges decreases).
The same happens to the gauges on the vertical tube when shear is applied—the resistance
increases or decreases depending on whether the gauge is on the left or right of the tube.
Therefore, the same Wheatstone bridge configuration is used for both the shear and pressure
channels.
Measurement of Pressure and Shear
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used to maintain a constant excitation voltage to all 96 bridges. The positive and negative
outputs from each bridge are fed to one of six channels of the analog multiplexors that are
used differentially in pairs. Four digital output lines from the computer select the bridge
from which data will be acquired. The acquisition sequence first reads Bridge 1 on each of
the 16 transducers, then Bridge 2, and so on until Bridge 6 is read. This permits data to be
sampled at a frequency of 37 Hz for 2 s. The output from each pair of multiplexors is fed
into an amplifier with a gain of 500. The output from each amplifier is then sent to one of
16 analog-to-digital converters. Each multiplexor is controlled via software that has been
written to ensure reliable acquisition and storage of data.
Device Calibration
Each individual transducer was calibrated under static conditions. For both loading and
unloading conditions, calibration was carried out under compressive loads (0, 31.15, 75.65,
120.15, 164.65 N) and both anteroposterior and mediolateral loads (0, 22.25, 44.50, and
66.75 N). Two trials of loading and unloading were conducted. During compressive tests,
the weights were placed directly on top of the transducer. Shear loads were applied by
hanging weights from a cord attached at one end to the transducer and passed over a
simple pulley system.
More in-depth testing and calibration were then carried out on one representative
transducer in the array. A series of seven different tests was conducted:
1. A compressive load was applied through point loading to the center of the transducer and to each of the corners at separate times. A load of 111.25 N was clamped to a
board through which three nails were driven. The load was then positioned over the transducer such that one nail was positioned on the transducer in the region of interest and the
other two nails rested on a surrounding support surface. The compressive load measured
by the transducer was then recorded under these five different loading conditions (center
and the four corners).
2. Compressive loads from 31.15 to 164.65 N were applied to the transducer, and
the cross-talk present on the shear force channels was measured.
3. Shear loads ranging from 22.25 to 66.75 N were applied to the transducer, and
the cross-talk present on the compression channels was recorded.
4. Shear forces were applied 1 cm off-center to create a torsional force, and the
effect on both compression and shear was examined. Torsional forces ranged from 0 to
77.88 N.
5. Compressive (0–164.65 N) and shear (0–66.75 N) forces were applied simultaneously.
6. A force that was the vector addition of mediolateral and anteroposterior forces
was applied. The load, ranging from 0 to 77.88 N, was applied along an axis midway
between the mediolateral and anteroposterior axes.
7. A load cell (Sensotek, Columbus, OH; Model 13/2443-08, range 0–225 N) capable of measuring pressure dynamically was used to apply cyclical loads to the transducer. The range of loading was 0 to 60 N at a rate of approximately 3 Hz and 0 to 100 N
at approximately 1 Hz. Data were collected simultaneously from the Sensotek load cell
(370 Hz) and the shear and pressure device (37 Hz).
As a secondary check of the quality of the transducer array, the force profiles obtained from the device were compared to those from an AMTI force plate (AMTI Inc.,
Newton, MA) for one individual. These were two separate trials: one stepping off the
force plate and one stepping off the shear and pressure device. The manner of testing was
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the same as for the subjects (see below). Although calibration of the device was the primary means of validation, this comparison with the force plate profile provided a secondary check of the quality of the output from the shear and pressure device under dynamic
conditions.
Preliminary Subject Trials
Data were collected on the right foot of 4 individuals with diabetes. Two of the subjects
had sensory neuropathy (means: age = 73, height = 1.8 m, weight = 69 kg, vibration score
[Vibratron II] = 16.43, could not feel 6.10 Semmes-Weinstein monofilament), and 2 had
protective sensation (means: age = 65, height = 1.6 m, weight = 91 kg, vibration score =
6.20, could feel 5.07 monofilament). The array of transducers was set flush in a 92 cm 3
122 cm platform, and caps of Minorplast (a material commonly used in therapeutic shoes)
were placed on each of the transducers. A 5 mm thick pad of rubber matting was placed on
the wooden platform surrounding the transducer array. The subjects were tested in their
bare feet and stood with their right forefoot on the transducers. Walking was initiated with
the left leg, and the individuals took two to three steps. In this manner the forces under the
right forefoot were recorded during the initiation phase of walking for three trials. The
purpose of these trials was not to make group comparisons but to show the utility of the
shear and pressure device and provide representative subject data in addition to calibration data.
Results
Calibration Trials
For each of the 16 transducers, a regression equation was determined for applied versus
measured loads for compression, anteroposterior shear, and mediolateral shear under static
loading conditions. A 99% confidence interval was determined for the slopes, and the
ranges were as follows: compression (0.981–1.03), anteroposterior (0.996–1.00), and
mediolateral (0.997–1.00). Compressive results had slightly more variation than shear,
but the widths of the confidence intervals were small and in close proximity to the line of
identity (a value of 1.0).
Calibration plots (Figure 4) are presented for the four conditions that introduced
noise into the system. Even with the possible presence of cross-talk, the data showed very
good linearity and excellent agreement between applied and measured loads. The quality
of the data was not degraded by the introduction of torsion, the combination of mediolateral/
anteroposterior forces, or combined compressive/shear forces. With the present design,
forces in all three directions can be measured with accuracies that are within 5% of the
true value. For each of the plots in Figure 4, linearity values were determined as a percentage of the full-scale measurable output. These values, corresponding to Figure 4a–4d,
respectively, were ±4.5%, ±5.1%, ±2.4%, and ±4.2%. The values for the first three plots
represent the maximum error present, whereas in the fourth condition the value is the
average error. This fourth condition measured the effect of torsion on compression, and
we do not feel that the maximum error calculated as ±12% provides a realistic representation of the limitations of the device. (Torsion was created by applying a shear load at the
extreme corner of the transducer, and it is highly unlikely that loading conditions under
the foot would replicate this unusual loading scenario.)
For the point-loading test, in which vertical point loads were applied at the extreme corners of the sensor, the highest reading was 4.8% (1.3 N) greater than the load
Measurement of Pressure and Shear
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Figure 4— Calibration plots for the conditions that introduce cross-talk into the system: (a)
vector addition of medial–lateral and anterior–posterior forces, (b) effect of compression on
shear measurements, and the effect of torsion on (c) shear and (d) compression. Data correspond
to three trials of loading (solid lines) and unloading (dashed lines). Details of loads are given in
the Device Calibration section of the manuscript.
measured in the center of the sensor. The lowest reading was 14% (3.8 N) lower than
the central reading of 27.2 N. When vertical loads were applied to the transducer, the
average cross-talk on the shear channels was 5.2% (3.2 N) of the applied load; with anteroposterior loading, the average cross-talk on the vertical channels was 13.3% (4.8 N);
and during mediolateral loading, the average cross-talk was 4.3% (2.3 N) of the
applied load.
Dynamic calibration of a single transducer with the Sensotek load cell (Figure 5)
resulted in an average difference of 3 N between the load cell and the pressure transducer. This difference corresponded to 3% and 5% of the maximum applied loads under
1 Hz and 3 Hz nominal loading rates, respectively. From the 3 Hz data, the hysteresis of
the transducer was determined to be ±7.4%. Because technical limitations did not permit dynamic calibration at greater than 3 Hz, a Fourier transform was performed on the
data to determine the frequency content of the applied load. A signal-to-noise ratio of
20:1 was used as the cutoff for meaningful signal content. With this criterion, the maximum frequency contained in the signal was 14 Hz. The secondary check of the device,
as a whole, under dynamic conditions revealed that the force profiles obtained from
the device qualitatively resembled very closely the data from the AMTI force plate
(Figure 6).
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Figure 5 — Dynamic performance of a transducer in the shear and pressure device when
loaded at rates of approximately (a) 1 Hz and (b) 3 Hz using a Sensotek load cell. The average
difference between the load cell and the transducer was 3 N.
Subject Trials
The sites of maximum pressure and shear were the same for some of the subjects; however, for the entire group the sites of maximum shear and pressure did not correspond
(Figure 7). The highest pressure occurred in the region corresponding to the medial metatarsal heads (Area 3, S2), whereas the site of highest shear force was in the lateral metatarsal
heads (Area 3, S3). The greatest difference between shear and pressure values occurred in
Region 3, S2. The average magnitude of the shear forces was approximately 25% of the
compressive loads. In terms of the direction of shear forces at adjacent sites (not shown), the
peak value of the difference between forces directed away from each other was about twofold
greater than the difference between forces directed toward each other, indicating a greater
tendency for the tissue to be stretched than bunched (Perry, Davis, & Hall, 1995).
Discussion
Identifying sites of maximum shear and pressure is important in working with diabetic
individuals because ulceration of the foot is most likely to occur at these sites (Boulton et
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Figure 6 — Comparison of force profiles in all three planes for the shear and pressure device
and an AMTI force plate. Qualitatively, the profiles are nearly identical. Data represent one
trial on each device.
al., 1983; Cavanagh & Ulbrecht, 1991). In contrast to shear devices that have been used in
previous investigations, the current device is capable of measuring true shear (the resultant of mediolateral and anteroposterior forces) rather than being limited to measuring
only one component of the shear force. This permits a more accurate and representative
analysis of the frictional forces acting on the plantar surface of the foot. Furthermore, with
the current device, it is now possible to examine the combined effects of distributed vertical and shear forces. As mentioned previously, some authors have shown that ulceration
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Figure 7 — Magnitude of peak pressure and shear results obtained from 4 individuals with
diabetes. The vertical axes refer to force in newtons. The other axes define the array of
transducers. Block (1, S1) represents the hallux; (4, S1) the 1st metatarsal head, and (4, S4) the
fifth metatarsal head. Note that the scales are different for the pressure and shear plots, and
the direction of the shear forces is not depicted.
occurs at sites of maximum shear, while others have shown that it corresponds to sites of
maximum pressure. Since all three force components can be measured simultaneously,
this issue can now be investigated in greater detail.
One major limitation of the current design is the small overall size of the device
combined with the large individual transducer area of 6.25 cm2. The large transducer area
likely results in underestimations of true peak pressures and limits the ability to discriminate between adjacent areas of high stresses. The small overall size of the transducer array
restricts the area of analysis to only a portion of the plantar surface of the foot and limits
the activities under which forces may be investigated. Furthermore, the device is not suitable for in-shoe measurements.
The frequency response of a system is also an important aspect of system design.
Frequency response can be approximated by considering each individual transducer element as a simple cantilever with a mass at one end (i.e., the aluminum column with the Sshaped mass at one end). The resonant frequency of the unloaded device is calculated to
be 350 Hz. This suggests that the device can be loaded under activities similar to those
typically used with force plates (the resonant frequency of the AMTI force plate is about
500 Hz). However, it is necessary to consider that the sampling frequency of the device is
currently limited to 37 H, which limits the loading responses that can be investigated.
Thermal stability of the device is maintained through the Wheatstone bridge arrangement. The four gauges (per bridge) are mounted on the same piece of aluminum so
changes in temperature should affect all gauges similarly. Two gauges are mounted in
parallel with the axis of strain application, while two gauges are mounted orthogonal to
the axis. This orthogonal arrangement compensates for changes in temperature. Additionally, it has been demonstrated that the device behaves very linearly, there is good
agreement between applied and measured loads, and there is minimal hysteresis. These
Measurement of Pressure and Shear
103
characteristics are typical of transducers that are (a) constructed from aluminum or steel,
which behave in a linear manner up to the yield point and (b) strain-gauged according
to the guidelines prescribed by the gauge manufacturer (Measurements Group, Inc.,
Raleigh, NC).
Conclusions
With the development of the current device, we have demonstrated that loading under the
feet can be simultaneously measured in three dimensions (vertical, mediolateral, and anteroposterior) with accuracies to within 5% of the true value. The ability to quantify loading under the foot in this manner has the potential to (a) fill a void in the clinical literature
by allowing researchers to investigate complex loading conditions at the foot/ground interface and (b) address limitations in the biomechanical literature by better defining boundary conditions that are important in finite element models.
References
Bauman, J.H., Girling, J.P., & Brand, P.W. (1963). Plantar pressures and trophic ulceration: An evaluation of footwear. Journal of Bone and Joint Surgery, 45B, 652-673.
Boulton, A.J.M., Hardisty, C.A., Betts, R.P., Franks, C.I., Worth, R.C., Ward, J.D., & Duckworth, T.
(1983). Dynamic foot pressure and other studies as diagnostic and management aids in diabetic neuropathy. Diabetes Care, 6, 26-33.
Brand, P.W. (1988). Repetitive stress in the development of diabetic foot ulcers. In M.E. Levin &
L.W. O’Neal (Eds.), The diabetic foot (4th ed., pp. 83-90). St. Louis, MO: Mosby.
Cavanagh, P.R., & Ulbrecht, J.S. (1991). Biomechanics of the diabetic foot: A quantitative approach
to the assessment of neuropathy, deformity and plantar pressure. In M.H. Jahss (Ed.), Disorders of the foot and ankle (2nd ed., pp. 1864-1907). Philadelphia: Saunders.
Ctercteko, G.C., Dhanendran, M., Hutton, W.C., & LeQuesne, L.P. (1981). Vertical forces acting on
the feet of diabetic patients with neuropathic ulceration. British Journal of Surgery, 68, 608614.
Davis, B.L. (1993). Foot ulceration: Hypotheses concerning shear and vertical forces acting on adjacent regions of skin. Medical Hypotheses, 40, 44-47.
Delbridge, L., Ctercteko, G., Fowler, C., Reeve, T.S., & LeQuesne, L.P. (1985). The aetiology of
diabetic neuropathic ulceration of the foot. British Journal of Surgery, 72, 1-6.
Huo, M., & Nicol, K. (1995). 3-D force distribution measuring system. In K. Hakkinen, K.L. Keskinen,
P.V. Komi, & A. Mero (Eds.), XVth Congress of the International Society of Biomechanics:
Book of Abstracts (pp. 410-411). Jyväskylä, Finland: Gummerus.
Laing, P., Deogan, H., Cogley, D., Crerand, S., Hammond, P., & Klenerman, L. (1992). The development of the low profile Liverpool shear transducer. Clinical Physics and Physiological Measurement, 13, 115-124.
Lord, M., Hosein, R., & Williams, R.B. (1992). Method for in-shoe shear stress measurement. Journal of Biomedical Engineering, 14, 181-186.
Masson, E.A., & Boulton, A.J.M. (1991). Pressure assessment methods in the foot. In R.G. Frykberg
(Ed.), The high risk foot in diabetes mellitus (pp. 139-149). New York: Churchill Livingstone.
Perry, J.E., Davis, B.L., & Hall, J.O. (1995). Profiles of shear loading in the diabetic foot. In K.
Hakkinen, K.L. Keskinen, P.V. Komi, & A. Mero (Eds.), XVth Congress of the International
Society of Biomechanics: Book of Abstracts (pp. 722-723). Jyväskylä, Finland: Gummerus.
Pollard, J.P., & LeQuesne, L.P. (1983). Method of healing diabetic forefoot ulcers. British Medical
Journal, 286, 436-437.
Pollard, J.P., LeQuesne, L.P., & Tappin, J.W. (1983). Forces under the foot. Journal of Biomedical
Engineering, 5, 37-40.
Stokes, I.A.F., Faris, I.B., & Hutton, W.C. (1975). The neuropathic ulcer and loads on the foot in
diabetic patients. Acta Orthopaedica Scandinavica, 46, 839-847.
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Davis, Perry, Neth, and Waters
Tappin, J.W., Pollard, J., & Beckett, E.A. (1980). Method of measuring ‘shearing’ forces on the sole
of the foot. Clinical Physics and Physiological Measurement, 1, 83-85.
Tappin, J.W., & Robertson, K.P. (1991). Study of the relative timing of shear forces on the sole of the
forefoot during walking. Journal of Biomedical Engineering, 13, 39-42.
Thompson, D.E. (1983). Pathomechanics of soft tissue damage. In M.E. Levin & L.W. O’Neal (Eds.),
The diabetic foot (3rd ed., pp. 148-161). St. Louis, MO: Mosby.
Acknowledgments
Construction of the shear and pressure device was financially supported by an NIH-NIAMS39750 Center Grant and by Thor-Lo, Inc., Statesville, NC.