A study of plantar stresses underneath metatarsal heads in the human foot 3

56









CHAPTER 3
EXPERIMENTAL TECHNIQUE




~Because a thing seems difficult for you, do not think it impossible for
anyone to accomplish~
Marcus Aurelius

57
3.1 Instrumented soft tissue indentor
3.1.1 Measurement of soft tissue property under the metatarsal heads
The plantar soft tissue in the pads underneath the metatarsal heads (MTHs) is an
optimal load-bearing structure (Bojsen-Moller and Flagstad, 1976), particularly for
cushioning the highest sub-MTH ground reaction forces (GRF) exerted in the
terminal stance-phase of gait (Cavanagh, 1999). Identification of the mechanical
response of the sub-MTH pad to external loading is essential for clinicians or
users who wish to distinguish between normal and pathological tissue functions.
Both in vivo and in vitro studies have observed stiffening (Gefen et al., 2001,

Klaesner et al., 2002, Pai and Ledoux, 2010), hardening (Piaggesi et al., 1999) or
diminished energy dissipation (Hsu et al., 2007, Hsu et al., 2000) of the sub-MTH
pad in neuropathic diabetic foot. Many believe that such altered tissue properties
that accompany diabetes may severely compromise its cushioning capacity, with
the consequence of elevated peak plantar pressure at the sub-MTH region where
ulcers are most common (Boulton et al., 1983).
Indentation tests offer a convenient way for direct in vivo investigation of
the mechanical responses of the soft tissue, and commonly involves applying a
known deformation (i.e., indentation) directly to the live subject’s tissue, e.g. the
amputee residual tissue covering long bones (Silver-Thorn, 1999, Vannah et al.,
1999) and the heel pad (Rome and Webb, 2000), where the naturally-immobile
skeleton acts as a rigid foundation. However, the intrinsically-small MTH has
great mobility in the plantar-dorsal direction, which often limits the maximum
indenting-force to be directly applied at a desired loading rate, using general-

58
purpose indentors. Previously, for sub-MTH pad indentation, large tissue
deformation, similar to that during actual gait cannot always be achieved (Zheng
et al., 2000, Kwan et al., 2010). Moreover, poor instrument alignment is inherent
to hand-held devices (Kawchuk and Herzog, 1996, Zheng and Mak, 1999) and
limited measurement reliability in trial-and-error procedures (Klaesner et al., 2001,
Wang et al., 1999) often make interpretation of data difficult.
Accurate mechanical characterization of the sub-MTH pad can be further
complicated by metatarsophalangeal (MTP) joint configurations particular to
structurally-specialized tissue frameworks. Early cadaveric-dissection
observations (Bojsen-Moller and Flagstad, 1976) have shown that the initially soft
and pliable tissue pad can become increasingly “tightened” during MTP joint
dorsiflexion. Such tissue “tightening” may significantly restrict skin mobility
against shear forces (Bojsen-Moller and Lamoreux, 1979) and increase the
compressive stiffness of the sub-MTH pad (Garcia et al., 2008). However, this

unique joint-angle-dependent tissue property has not yet been fully elucidated
due to experimental technique limitations.
In this study, a new instrument-driven, in vivo tissue tester, called the sub-
Metatarsal Pad Elasticity Acquisition Instrument (MPEAI), is devised. The tissue
tester enables collection of the localized mechanical response of the plantar soft
tissue pad underneath an individual MTH, in relation to the MTP joint angle. The
intra-tester versus inter-tester variance of the tester was demonstrated when
applied to the 2nd sub-MTH pad. The characteristic force-displacement curves

59
were further utilized for extraction of the hyperelastic material constants to model
the forefoot bulk soft tissue in the finite element model of the foot.

3.1.2 Development of the tissue tester
The MPEAI consists of a special hinged foot-positioning apparatus integrated
together with a portable motorized indentor. This apparatus permits
accommodation of the local sub-MTH pad and reproduction of MTP joint
configurations generated by individuals during actual walking. The integrated
indentor can directly probe the mechanical response of the sub-MTH pad by
inducing rate-controlled tissue deformation, in a way that is similar to that
experienced in gait.

3.1.2.1 Multiple DOF foot-positioning apparatus
A multiple degree-of-freedom (DOF) apparatus was devised for gait-related foot
positioning and orientation. This is achieved by using a kinematic linkage that
consists of three linear translators and one hinge joint for connection to the base
and forefoot plates (Fig. 3.1.2.1). A cylindrical porthole is drilled into the rear-half
of the transparent acrylic (polymethyl methacrylate) forefoot plate. The hole size
was optimized (i.e. 15 mm in diameter) in order to best encircle an individual
MTH adjacent to the tissue pad. The base of the porthole is internally threaded,

so that a portable indentor can be firmly mounted to it.
Placement of a test subject’s foot on the device is shown in Fig. 3.1.2.1,
whereby the built-in hinge axis can be manipulated in bi-axial directions (i.e.

60
antero-posterior and superio-inferior) for approximation of the MTP joint axis,
which is assumed to pass through the medial aspect of the 1st MTH and the
lateral aspect of the 5th MTH. In this way, rotation of the base plate around the
hinge joint would permit control of MTP joint dorsiflexion within a range of 0° ~
90°. This range of motion is sufficient to capture MTP joint configurations for
simulation of a static stance-phase (Leardini et al., 2007). The joint angle Φ is
measured by a digital inclinometer.


Fig. 3.1.2.1. Schematic diagram of the sub-Metatarsal Pad Elasticity Acquisition
Instrument (MPEAI), showing details of probe tip, accommodation of sub-MTH pad and
inside components of actuator to drive probe tip





61
3.1.2.2 Portable motorized indentor
A motorized indentor was developed; it contains a closed-housing linear actuator,
comprising a 500-step per revolution stepper motor (MYCOM) and a 1.25 mm
pitch tangential screw unit to drive a 5 mm diameter hemispherically-tipped probe.


Fig. 3.1.2.2. (A) Identified 2nd MTH pad. (B) Photograph and (C) schematic diagram of

test set-up, showing ‘trapped’ soft tissue pad and initial contact with probe tip


Fig. 3.1.2.3. (A) Displacement-time profile of indentation cycle for probe tip.

The indentor can be completely integrated into the positioning apparatus
by a snap-lock mechanism via the testing port through which the sub-MTH pad is
fully exposed (Fig. 3.1.2.2). Such a design ensures that the probe tip is
consistently perpendicular to the tissue pad, regardless of testing conditions

62
corresponding to different MTP joint configurations. The MPEAI can be mounted
flush with the floor.
A microchip-based controller (MNC-100 Indexer Unit) and driver are used
to prescribe the desired displacement profiles accurately. As is shown in Fig.
3.1.2.3, this facilitates smooth and continuous movement of the probe tip. A
miniature compression load cell (FUTEK), embedded between the actuator and
the lower-end of the probe tip, records the magnitude of the local reaction force
exerted on the tissue (Fig. 3.1.2.1). Load cell outputs were fed into a signal-
conditioning module and a data acquisition board (National Instruments, SCXI
1520/1314). To avoid tissue damage/pain during testing, a closed-loop control
program for overload protection was written in LabVIEW (National Instruments).
The indentation process automatically terminates when the indenting force
magnitude exceeds 19 N. This corresponds to a nominal stress of 435 kPa at
indentor-soft tissue interface, approximating the peak plantar pressure that
occurs at the sub-MTH region during normal walking (Hayafune et al., 1999). A
schematic diagram of the entire MPEAI system is shown in Fig. 3.1.2.1. Force
and displacement data were collected at a sampling rate of 1,000 Hz.

3.1.3 Assessing in-vivo tissue properties under MTHs

3.1.3.1 Repeatability test of the MPEAI
The repeatability test was conducted to determine the precision of the tissue
tester- MPEAI when a single operator uses the device to perform a series of tests
to obtain the mechanical responses of the 2nd sub-MTH pad of two normal

63
subjects. The location of the 2nd MTH of the right foot was first identified by
palpating the underlying metatarsal tuberosity, and was marked by an ink ring,
which defines the bounds of the plantar MTH region. With the help of an
assistant, the soft-tissue pad can be positioned and sited within the testing port,
making it readily visible to a camera aimed at the side of the forefoot plate (Fig.
3.1.2.1). After correction of joint axis misalignment, the foot was secured by
Velcro straps (3M) and an appropriate distance with respect to the contralateral
foot maintained to simulate a balanced stance-phase. The indentor can be
operated in manual mode by moving the tip axially at a speed of approximately 1
mm/s. Such adjustments, coupled with visual guidance and force feedback,
enabled initial contact between the indentor tip and the soft-tissue pad to be
established easily and with confidence (Fig. 3.1.2.2). Generally, subjects can
sense a threshold indenting force of approximately at 0.2 N upon initial contact.
Following the initial set-up, a sequence of pre-defined indentation cycles
was used to induce large deformation to the local sub-MTH pad. One cycle
corresponds to complete loading and unloading, and exhibits a trapezoidal axial-
displacement profile with a maximum probe depth δ (avg. = 5.6 mm), a constant
loading/unloading rate

(avg. = 9.2 mm/s) and a holding time t
r
(avg. = 85 ms) at
the maximum deflection δ
max

(Fig. 3.1.2.3). Selection of δ and

was based on a
previous study that elicited detailed deformation characteristics of the 2nd sub-
MTH pad during walking, via use of an in-floor ultrasound technique (Cavanagh,
1999). A volume reconstruction of the computer tomography scan images of the
subjects’ right feet in non-weight-bearing conditions provided the initial tissue

64
thickness. This facilitated determination of the local tissue indentation strain up to
an approximate value of 46% and a nominal strain rate of 0.76 /s. Imposition of a
short dwell-time t
r
at the tissue deformation δ
max
enables force relaxation
characteristics to be observed within the same testing cycle (Fig. 3.1.3.1.).
Similar indentation cycles on the 2nd sub-MTH pad were conducted, with
the MTP joint configured at six different dorsiflexion angles – 0°, 10°, 20°, 30°,
40°, and 50°. For each configuration, data was collected for three cycles after 3
cycles of pre-conditioning.

Fig. 3.1.3.1. Typical tissue reaction force patterns obtained for 2nd sub-MTH pad for
similar indentation, but with MTP joint (MTPJ) at different dorsiflexion angles. Note that
the sub-MTH pad tissue response is dependent on MTP joint angle, i.e. lower stiffness at
lower joint dorsiflexion angles and increasing stiffness at higher joint angles.

There was qualitative similarity in all sets of curves for given testing
conditions, and this indicated that the experiments were well-controlled. All the
curves possess similar characteristic profiles, such as nonlinear

loading/unloading phases and a substantial force relaxation component.

65

Fig. 3.1.3.2. Calculated initial stiffness (=initial tissue reaction force/ δ, δ1 mm)


Fig. 3.1.3.3. Calculated end-point stiffness (= peak tissue reaction force/ δ
max
)


Fig. 3.1.3.4. Force relaxation as percentages at δ
max
for 2nd Sub-MTH pad of two normal
subjects, for increasing MTP joint angles.

66
Reproducibility of experimental results for two normal subjects is as
illustrated in Fig. 3.1.3.2 ~ 4, standard deviation bars were shown. Absolute
measurement errors for the calculated initial stiffness (= peak tissue reaction
force/ δ, for δ  1 mm), end-point stiffness (= peak tissue reaction force/ δ
max
),
and force relaxation percentage, quantified in terms of standard deviation, were
less than 0.084 N/mm, 0.133 N/mm, and 0.127% respectively across all testing
configurations. On average, the tissue initial stiffness correlated with data from
literature, which relate to a 4.9 mm diameter tip and a cyclic indentation at 10
mm/s on lower limb soft tissue (Silver-Thorn, 1999). An average increase in end-
point stiffness of the 2nd sub-MTH pad by 104.2% for a 50-degree MTP joint

dorsiflexion generally agreed with that of a previous study (129% ±19.8), where
indentation was applied at the plantar MTH region with the MTP joint extended to
its end-range (Garcia et al., 2008). Force relaxation of the in vivo tissue was
found to be significant (avg. = 8.1%), even during a short holding-time.

3.1.3.2 Force-displacement response of soft tissue under metatarsal heads
It was found that the mechanical responses of this load-bearing soft tissue (i.e.,
sub-MTH pad) depends not only on external loading conditions, such as the
direction and rate of the loading, which generate responses governed by tissue
anisotropy and viscoelasticity (Zheng and Mak, 1999, Klaesner et al., 2001), but
also on the configuration of the joint articulation overlying the tissue (Garcia et al.,
2008). Tests show that the proposed MPEAI technique is able to produce
consistent results. The force-displacement curve produced has the potential to

67
provide insights into the mechanical behavior of forefoot tissues under MTHs,
and to be used for extraction of the hyperelastic material constants of this bulk
soft tissue in the foot.

3.1.4 Derivation of material constants for plantar soft tissue
3.1.4.1 Classical Hertz contact theory
In analyzing the force-displacement behavior obtained from indentation tests, it is
common practice to refer to classical Hertz contact models, with its assumptions
of linear elasticity and infinitesimal strains, in order to obtain materials’ modulus
values. In hemi-spherical indentation, the Hertzian relationship between the
applied indenting force (F) and the resulting indentation (δ) (Johnson, 1985) is:



2

2321
13
4




//
ER
F
3.1
Where E and

 are Young’s modulus and Poisson’s ratio of the indented
material, respectively, and R is the radius of the rigid indenter. The contact radius,
a, varies with displacement δ according to


Ra
3.2
The Hertz equation is valid when applies to hemi-spherical indentation
provided that the following assumptions are satisfied:
 The strains are small and within the elastic limit,
 Each body can be considered an elastic half-space,
 The surfaces are continuous and non-conforming, and
 The surfaces are frictionless.

68
However, for the present sub-MTH pad indentation, nonlinear and large
tissue deformations (nominal strains up to 46%) were present. Consequently,

errors maybe incurred by directly applying the representation of Hertz equation
beyond their validity range (i.e. at the infinitesimal strain range).
It should be noted that, since the Hertz formalization is based on the
theory of linear elasticity, it should be possible to define measures of stress and
strain that satisfy a Hooke's law of elasticity. The concept of an analogy between
uni-axial compression and spherical indentation was first explored by (Tabor,
1948, Tabor, 1951) who proposed (what has now been widely accepted)
definition of indentation stress (or mean pressure, ) and strain ():

2
a
F



*
,
R
a
20.
*


3.3
Where the strain pre-factor of 0.2 was empirically determined by (Tabor, 1951)
and has since been verified by other investigators (Field and Swain, 1995,
Herbert et al., 2001). The defined indentation stress and strain are similar to their
counterparts in uni-axial loading. In fact, indentation is essentially a compressive
process since only the edge of the contact region experiences tension (Johnson
1985). Dividing stress by strain in Eqs. 3.3 and substituting Eqs. 3.1 and 3.2 for

Hertzian indentation, the following linear relationship (i.e., Hooke’s law) is
obtained:



**



2
13
20


E
3.4

69
From the parallels between indentation and uni-axial compression, it stands to
reason that non-Hooke, uni-axial stress–strain relations can be extended to non-
Hertzian contact with some mathematical manipulations.

3.1.4.2 Direct extraction of hyperelastic material constants
Let us list the Ogden strain energy functions for hyperelastic materials we
derived in Chapter 2, and its corresponding uniaxial stress (σ)–stretch (λ)
equations (1st-order):



3

2
321
2





U
3.5
Under uni-axial compression condition, we have




1
,
2
1
32



3.6
And the uniaxial stress (σ)–stretch (λ) equations for 1st-order Ogden model is
obtained as the following:



121

2


)/(





3.7
By substituting the definitions of σ
∗
and ε
∗
given in Eq. 3.3 for stress and strain,
respectively, the uni-axial relations are transformed into contact equations in
terms of force (F) and contact radius (a, in eq. 3.2). In most indentation tests,
however, the contact radius is not a measurable quantity. Instead, the variation of
indentation depth or displacement (δ) with increasing magnitude of the applied
force is monitored directly, an expression such as Eq. 3.2 relating a and δ is
therefore necessary and useful. Assuming material incompressibility and that the

70
contact radius variability with indentation depth according to Eq. 3.2, we can
have
























 112
2
201201



R
a
R
aa
F
/

3.8
Where force (F) contact radius (a) relation corresponding to the Ogden strain
energy function was expressed in terms of two hyperelastic material parameters:
μ and α, which can be determined directly through nonlinear least square (NLS)
curve fitting procedure.


Fig. 3.1.4.1. Values of material constants (

;

α) obtained through nonlinear least squares
(NLS) minimization using the deduced contact equations for of the 1
st
-order Ogden
hyperelastic model in MATLAB. The calculated root-mean-square-error (RMSE) was as
small as 0.512 N with a R
2
value of 0.9821.

To best represent the forefoot soft tissue material behavior for push-off
finite element simulation, the force-displacement curve corresponding to
metatarsophalangeal joint angle at 30° was chosen to deduce material constants

71
using MATLAB (Math Works, Natick, MA). This yielded μ = 3.75 ｘ10
-2
MPa and
α = 5.5. The results of optimal curve fitting were presented in Fig. 3.1.4.1.

Table 3.1.4.3. The material properties used in the current finite element foot model in
comparison with those existing models for heel pad.
Models Tissues μ (MPa) α D
Current model Sub-MTH pad
3.75 ｘ10
-2

5.50 NA
Erdemir (2006) Heel Pad
1.64ｘ10
-2

6.82 NA
Skin
6.4ｘ10
-1

6.80 NA
Spears (2007)
Heel fat pad
2.9ｘ10
-4

8.80 NA



Fig. 3.1.4.2. Comparison of the stress–strain curves for the current sub-MTH pad and
those previously models: heel pad by Erdemir (2005), heel fat pad and skin model by
Spears (2009).

The material properties of the sub-MTH soft tissue determined presently
were in between those recently published results of the skin and fat tissue of
human heel pad (Erdemir et al., 2006, Spears et al., 2007). This could be
explained by the fact that the current foot soft tissue was modeled as a

72
homogeneous lumped tissue volume and that material difference between the
skin and fat pad had been weighted (Fig. 3.1.4.2.).

3.1.4.3 Use of material constants in plane-strain FEM
The accuracy of the derived material constants were further evaluated in a plane-
strain FE model. The indentation was simulated as frictionless contact between a
rigid hemi-sphere (R = 2.5 mm) and an elastic slab that representative of a sub-
MTH geometry in an axi-symmetric model using ABAQUS.
Although no viscoelastic effects were assumed, this displacement rate
was chosen to be comparable to that from the experiments. The mesh size was
graded to be more refined in the vicinity of the sphere and coarse at the model
extremes. The bottom and side of the slab were fixed in space, and both the rigid
sphere and axis of symmetry for the slab were only permitted to move in the
vertical direction. Contact between the sphere and slab was assumed to be
frictionless. The Ogden material model with the determined constants (μ = 3.75
ｘ 10
-2
MPa and α = 5.5) was used. From the simulations, the agreement
between simulation results and indentation data was extremely good (Figure
3.3.4.3.), suggesting that the material constants determined from this experiment
is valid and accurate to model the forefoot plantar soft tissue during heel rise.

73

Figure 3.3.4.3. Application of the calculated material constants in a plane-strain finite
element model. (A) The MTH geometry was simplified as a sphere with a diameter of r.
(B) The r values was determined through optimal surface fitting of the 3-D contour lines
which defines the actually shape of the 2
nd
MTH. The sub-MTH soft tissue thickness t
was defined as the shortest line distance between the MTH and the plantar surface. (C)
Compressive stress distributions in the sub-MTH tissue during indentation process. (D)
Simulation results correlate well with experimental observation.


Altogether, an integrative MPEAI tissue tester was developed to fulfill the
requirements imposed for in vivo mechanical characterization of localized plantar
soft tissue pads underneath an individual MTH. Tests on the 2nd Sub-MTH pad
show that the proposed MPEAI technique is able to produce consistent and
repeatable results. A key advantage of the proposed device is the integration of a
portable indentor with a special foot-positioning apparatus; this facilitates

74
convenient investigation of the dependence of the local sub-MTH pad and tissue
responses on MTP joint angle. This could prove preferable to studies that focus
on measurement of tissue property in isolation (Wang et al., 1999, Hsu et al.,
2007, Kwan et al., 2010), because the sub-MTH pad may vary its elasticity under
physiologic gait conditions (Bojsen-Moller and Flagstad, 1976, Bojsen-Moller and
Lamoreux, 1979, Garcia et al., 2008), as it adapts to drastically changing
mechanical demands at the sub-MTH region in the terminal stance-phase (Chen
et al., 2010c), where MTP joint dorsiflexion occurs.
It was also demonstrated that the validity of the hyperelastic force
indentation equations introduced herein for describing the large-deformation

sub-MTH tests that obey rubber elastic behavior as exemplified by the plantar
soft tissue. The extracted material constants could serve as useful inputs for
modeling the foot soft tissue in the finite element model, with emphasis on sub-
MTH pad stress responses. An important finding is that the sub-MTH soft tissue
may possess unique joint-angle-dependent tissue property, which has not yet
been elucidated previously due to experimental technique limitations. Thus, with
the present tissue tester, the obtained localized mechanical response of the
plantar soft tissue pad underneath an individual MTH can be considered to be
more accurate than previous investigations.





75
3.2 Gait platform for measuring plantar stresses
3.2.1 3-D plantar stress measurement
The ball of the forefoot supports a significant portion of the body’s weight during
human locomotion. The highest ground reaction force (GRF) has been estimated
to be beneath the foot’s plantar metatarsal sites, including five metatarsal heads
(MTHs) and the underlying protective fat pads, serving as pivot points during
push-off (Hicks, 1955). These localized loadings produce high pressures on
MTHs, which could cause problems to the pathological foot. Excessive pressure
and shear stresses at MTHs have been shown to be associated with
metatarsalgia in rheumatoid arthritis (Roy, 1988), and have been implicated in
the development of ulcers in the insensate foot (Cavanagh et al., 1993a) and
other forefoot structural abnormalities (Sanders et al., 1992). It is therefore
important to be able to accurately determine the localized forces acting on MTHs,
in order to prevent tissue damage in the pathological foot.
There is still a lack of suitable systems capable of measuring the three-

dimensional forces acting on localized anatomical sites such as the plantar MTHs.
Force sensor technology is still far from miniaturization to the point where it could
accurately relate force distribution data to specific anatomical sites (e.g., the 2nd
MTH). (Davis et al., 1998a) presented a method whereby strain-gauged force
sensors were arranged in an array to measure the plantar force distribution.
Recently, (Mackey and Davis, 2006a) developed a similar optical based force
sensor array. Gross plantar force pattern obtained, however, can only be
“mapped” onto a portion of the foot (Yavuz et al., 2009). Subtle variations within

76
individual MTH often cannot be distinguished. Today, many researchers have
theoretically estimated the local GRF acting at foot areas of concern based on
the local plantar pressure distribution and the global GRF (Abuzzahab Jr et al.,
1997, Uccioli et al., 2001, Giacomozzi et al., 2008). However, its accuracy can be
significantly compromised due to the fact that the vertical and the shear force
components may not have a simple linear relationship at the foot-ground
interface (Yavuz et al., 2007).
This study describes the construction of a gait platform-type apparatus,
and a pilot study to demonstrate its repeatability when used to obtain the vertical,
anterior-posterior (AP), and medial-lateral (ML) GRF components acting at the
individual MTHs during walking. The measured plantar shear data could be
potentially useful for the verification of the predicted results obtained from the
foot FE model during contact interactions between the foot and its supporting
interface.

3.2.2 Design, fabrication and calibration of pressure/shear sensor array
A mini tactile force sensor capable of detecting the forces at three orthogonal
directions at the foot-ground interface was developed. The sensor was
incorporated into a gait platform, which enabled direct visual observation of the
forefoot’s plantar surface using a high speed camera. This set-up ensured easy

identification of a single anatomical landmark (e.g., 2nd MTH) at the forefoot’s
plantar surface in contact with the force sensor.


77
3.2.2.1 Mechanical design of the force sensor
The force sensor was designed by utilizing the shear-web principle and strain-
gauge based techniques (Fig. 3.2.2.1). It was fabricated using a single piece of
aluminum bar (2024T351), with a flat top sensing surface that measured a
square contact area of 1.9

1.9 cm
2
.


Fig. 3.2.2.1. (A) Schematic diagram of sensor showing the positions of the strain gauges
and (B) photograph showing the attachment of strain gauges to the front surfaces of the
sensor body. Gauges (not shown) are also bonded to the rear surfaces. The positions of
the vertical and shear channels are also shown.

During operation, load applied at the sensing surface produced a nearly
uniform strain field at each shear web structure located at the sensor body, onto
which a set of miniature 90° Tee strain gauge rosettes (Vishay J2A-13-S254R-
350) were bonded. The sensor was instrumented with a total of five sets of
gauge rosettes, positioned accordingly to capture the three orthogonal forces
independently. The first set (A1/A2) sensed the vertical force component. The
subsequent second and third sets (B1/B2, C1/C2) measured the AP force
component, and finally the fourth and fifth sets (D1/D2, E1/E2) measured the ML

78
force component. This arrangement provided three sensor channels measuring
the normal force, the AP and ML shear forces at the foot’s plantar surface.

3.2.2.2 High-resolution sensor array
Based on similar design principles and the strain-gauge based technique, a
multi-component force sensor with higher special resolution was developed (a
refinement of the original design). It has a smaller sensing-surface area of 0.9 ｘ
0.9 cm
2
(sensing area is only a quarter of its original size). This sensor was
considered to be superior over the original design, as it has higher spatial
resolution to faithfully measure the three-dimensional interfacial stresses at the
regional plantar surface (e.g. areas under MTHs).
Signals from each strain gauge set will be fed into a Wheatstone bridge
circuit. The full-bridge circuit configured for a single channel is as shown in Fig.
3.2.2.2. R1 is an active strain-gauge element (i.e., Tee strain-gauge grid 1)
measuring compressive strain (–ε). R2 is an active strain-gauge element (i.e.,
Tee strain-gauge grid 2) measuring tensile strain (+ε). R3 is an active strain-
gauge element (i.e., Tee strain-gauge grid 3) measuring compressive strain (–ε).
R4 is an active strain-gauge element (i.e., Tee strain-gauge grid 4) measuring
tensile strain (+ε). DC is the excitation source. V is the measured voltage due to
deformation of the beam element. The Wheatstone bridge converts the gauge's
strain-induced resistance changes (as transformed from non-electrical variety i.e.,
force) into a differential and measurable voltage signal V. Force directions can be

79
indicated by negative/positive signs of the signal. Self-temperature compensation
will also be achieved within circuit due to full-bridge configuration.

Fig. 3.2.2.2. Nine strain-gauged force sensors (A) were assembled into a 3 by 3 sensor
array (B), for a single strain-gauge channel, the electronic interface of a full-bridge circuit
configuration was shown (C)



Fig. 3.2.2.3. A screen shot of the dynamic data acquisition (DAQ) system for real-time
strain measurements of the force sensor array using LabVIEW (National Instrument).
The block diagram of the program is not shown.


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With concurrent multi-channel data acquisition system, it is possible to
integrate a single sensor into array with real-time detection capacity for force
distribution. In this study, nine instrumented miniature tactile force sensors (with
sensing area of 0.9 ｘ 0.9 cm
2
) were fabricated. A 3 by 3 sensor matrix by
expanding the individual sensor design thus was assembled (Fig. 3.2.2.2). It
covers a sensing area of 29 by 29 mm, thus can effectively capture the regional
sub-MTH area. For real-time data processing, the National Instrument SCXI data
acquisition platform will be used (Fig. 3.2.2.3.). The maximum sampling rate was
2.27kS/s (i.e., 2,270 Hz) which is more than enough in gait application where
contact stresses may endure for approximately 0.3~0.5s (Mackey and Davis,
2006).

3.2.2.3 Design of force sensor electronics
For real-time dynamic data acquisition, this study uses the SCXI (National
Instruments) signal conditioning system for PC-based instrumentation

applications, with all data set being processed in LabVIEW (Fig. 3.2.2.3). In
general, the SCXI system operates as a front-end signal conditioning system for
PC plug-in Data Acquisition (DAQ) devices through PXI DAQ modules. An SCXI
system consists of a shielded chassis that houses a combination of signal
conditioning input and output modules, which perform a variety of signal
conditioning functions including amplification and filtering for dynamic stain
gauge measurement. An individual force sensor can be directly connected to
SCXI modules for real-time data acquisition. For multiple-channel signal