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

CHAPTER EXPERIMENTAL TECHNIQUE ~Because a thing seems difficult for you, not think it impossible for anyone to accomplish~ Marcus Aurelius 56 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- 57 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 subMetatarsal 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 58 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. 59 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 60 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 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 61 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 signalconditioning 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 62 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 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 axialdisplacement 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 tr (avg. = 85 ms) at the maximum deflection δmax (Fig. 3.1.2.3). Selection of δ and  was based on a previous study that elicited detailed deformation characteristics of the 2nd subMTH 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 63 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 tr at the tissue deformation δmax 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 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. 64 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/ δmax) Fig. 3.1.3.4. Force relaxation as percentages at δmax for 2nd Sub-MTH pad of two normal subjects, for increasing MTP joint angles. 65 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. 76 3.2.2.1 Mechanical design of the force sensor The force sensor was designed by utilizing the shear-web principle and straingauge 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 cm2. 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-S254R350) 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 77 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 cm2 (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 straingauge 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 78 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 by 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. 79 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 cm2) were fabricated. A by 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 80 amplification and filtering (3 channels for an individual sensor element), an 8channel universal strain gage input module- SCXI-1520 – was utilized. The SCXI – 1520 offers a programmable amplifier and 4-pole Butterworth filter on each of the eight channels, and simultaneous sampling with track-and-hold circuitry. 3.2.2.4 Sensor calibration Each of the three sensor channels of an individual instrumented force sensor was independently calibrated using an Instron machine. As shown in Fig. 3.2.2.4~6, a loading and unloading cycle of Hz and up to 200 N, moreover, 50 N and 50 N were applied along the vertical, AP and ML axes, respectively. These peak forces applied to each of the three axis of the sensor should cover the range of forces that the sensor may experience for human testing during walking. Cross-talk effects within the sensor were checked by sequentially loading the specific channels and recording the outputs from the other channels. Typical calibration results obtained from one of the nine force sensors is plotted in Fig. 3.2.2.4 ~ 6. It shows the individual loading and unloading plots for vertical (Channel A), AP (Channel BC) and ML (Channel DE) force components. A simple linear regression equation was sufficient to determine the respective calibration factors for each channel. The correlation coefficients (R2 value) were greater than 0.999 for all channels. Measurement errors were quantified as the standard deviation of the maximum local force amplitude in the AP, ML, and vertical directions, respectively. Cross-talk effects were found to be less than 1.6% in all cases. The calibration results are summarized in Table 3.2.2.1. 81 Fig. 3.2.2.4. Calibration graphs showing linearity of the vertical channel. Fig. 3.2.2.5. Calibration graphs showing linearity of the AP shear channel. Fig. 3.2.2.6. Calibration graphs showing linearity of the ML shear channel. 82 Table 3.2.2.1. Calibration results of 27 channels corresponding to strain-gauged sensors used for construction of the by sensor array. For each channel (AP: anterioposterior; ML: mediolateral; V: vertical) of an individual sensor measurements were performed. Average measurement errors are 3.7%, 3.4%, and 4.2% for directional forces in the vertical, AP and ML axes, respectively. Hysteresis, on average, was less than 6% for all testing conditions. Sensor No. Measurement errors (%) Hysteresis (%) AP ML V AP ML V #1 3.0 2.8 2.2 5.6 7.2 4.3 #2 3.5 6.2 4.9 4.7 3.2 3.5 #3 5.5 3.2 3.5 6.5 4.2 5.7 #4 4.7 3.4 2.8 3.4 3.6 2.6 #5 2.5 4.3 4.9 6.5 8.3 5.5 #6 3.7 3.5 5.7 4.6 3.2 4.7 #7 4.3 2.2 4.7 5.8 4.2 5.5 #8 3.4 1.4 5.6 7.5 2.7 7.8 #9 2.7 3.2 2.9 6.4 3.2 5.4 Avg (±Std) 3.7±0.9 3.4±0.8 4.2±0.7 5.7±1.2 4.4±1.9 5.0±1.0 83 3.2.2.5 Construction of the new gait platform The calibrated by 3sensor array was mounted flush onto a transparent Acrylic (Polymethyl methacrylate) gait plate, which could accommodate the foot of the human subject (Fig. 3.2.2.7A). With this set-up, the gait platform is capable of obtaining local dynamic pressure/shear stress distribution (i.e. vertical, AP and ML force pattern) and contact timing characteristics. Fig. 3.2.2.7. (A) Schematic diagram of the gait platform. (B) Photo of the foot making contact with the gait plate that was embedded in a 7-meter walk way, sensor location in relation to the placement of the foot plantar surface can be monitored from the reflected mirror image by a high speed camera (Fascam) positioned to capture the side view. Beneath the gait plate, a reflective mirror was positioned at 45 degrees to the vertical direction, permitting direct visualization of the plantar aspect of the forefoot using a Photron Fastcam Super 10K (Tokyo) high-speed camera, placed at right angle to the platform. The mirror has a laser cut rectangular opening to accommodate the fixture for sensor array. As shown in Fig. 3.2.3.1, the image captured clearly indicates the sensor location in relation to a particular 84 anatomical landmark (e.g., the 2nd MTH). The high-speed camera was set to record images at 100 frame per second (fps) with a resolution of 512  480 pixels, providing real-time images of the forefoot plantar surface during walking. The assembled platform (load cell and gait platform) was embedded in a straight, 7-meter long, 1-meter wide walkway (Fig. 3.2.2.7B). The entire surface of the walkway was covered with a slip-resistance material. Visual checks ensured that the gait platform and walkway did not alter the normal gait during subject walking. 3.2.3 Assessing sub-MTH loads A 27-year-old male subject has height of 169 cm and body weight of 65.1 Kg with no foot pathology volunteered for the pilot trial using the gait platform. Informed consent was obtained according to the procedures of the National University of Singapore Institutional Review Board. To take measurement at particular MTH site, the location of the subject’s MTH (for instance, the 2nd MTH) was identified with a black ink dot after palpating the underlying metatarsal and its tuberosity. Nevertheless, this marked location would be blocked by the sensor itself whenever the MTH came into contact with the force sensor (See camera’s view in Fig. 3.2.3.1B), making identification of a single MTH difficult. Furthermore, maintaining a consistent placement of the foot in relation to the force sensor was important in order to obtain reproducible results for successive trials. These problems were solved by using a reference image called the “MTH template” as shown in Fig. 3.2.3.1. 85 Fig. 3.2.3.1. Method to create the “MTH template”: Images of the plantar surface of the forefoot (A) without and (B) with sensor during barefoot walking. Bony mark was used to identify the target metatarsal site. (C) R1~R3 represents three non-collinear markers for image registration between A and B. Xi and Yi are errors due to metatarsal site and sensor location discrepancy. Table 3.2.3.1. Typical targeting errors showing the Xi and Yi offset values for each of the five successive trials at the 2nd MTH. Offset Values T1 T2 T3 T4 T5 Avg. (± Std.) Xi (mm) 0.481 0.712 0.165 0.332 0.477 0.433 (±0.203) Yi (mm) 0.191 0.415 0.179 0.806 0.253 0.369 (±0.262) Averages (±Std) of the offset values are indicated in the last column. In order to create image templates for the 2nd MTH, two forefoot plantar images were captured with and without the sensor in position (Fig. 3.2.3.1A and Fig. 3.2.3.1B). As shown in Fig. 3.2.3.1A, the target metatarsal site could be determined within square contact area centered at the black ink dot which marked the 2nd MTH. Whilst in Fig. 3.2.3.1B, the actual sensor array location could be determined. Using a customized Matlab (Mathworks Inc.) code, the two images were matched by translations in the 2-D plane according to the three non-collinear ink dots marked on hallux (R1, R2, R3) as shown in Fig. 3.2.3.1C. “MTH template” represents the registered images with minimal errors induced 86 due to the discrepancy between the target MTH and the actual sensor locations as evaluated by Xi and Yi (Fig. 3.2.3.1C). With the current gait protocol, the system could achieve an average Xi and Yi errors of 0.433 mm and 0.369 mm respectively, indicating that the offset variability was minimal. Subsequently, the subject initiated gait from a stationary posture and landed the right foot on the platform at the first step of walking. The validity of using the “one-step” protocol in collecting gait variables has been reported by (Peters et al., 2002). Data collection began as subjects started to plantar-flex the right foot at the late stance phase and subsequently push-off, further completing a series of to steps to the end of the walkway at a self-selected speed. In order to obtain measurements for a particular MTH (e.g. the 2nd MTH), the “MTH template” displayed on a laptop screen was compared with the real-time image from the FASTCAM system, so as to guide the subject to an appropriate starting point (i.e., heel-strike position). Using this protocol, an average of three walking trials is required to ensure that the MTH would exactly strike the force sensor. Five successive walking trials recording the GRF components at the MTH sites for the subject who provides the foot geometry for the modeling were collected. The repeatability, quantified as the standard deviation of the maximum local force amplitude, was found to be 3.7%, 9.2% and 8.9% in the vertical, AP and ML directions, respectively. The average peak vertical forces of 33.86 % b.w. are within the range of a previous study (=28.3 ± 6.9 % b.w.) conducted by using an commercial EMED (Novel) capacitance sensor system (Jacob, 2001a). 87 Fig. 3.2.3.2. Typical force traces in vertical, AP and ML directions measured under the 1st (A), 2nd (B), 3rd (C) and 4th (D) MTHs during walking trails (5th MTH data not shown). The vertical, AP and ML forces underneath five MTHs were measured. Fig. 3.2.3.2. presented typical force traces measured underneath the 1st, 2nd, 3rd and 4th MTHs during barefoot walking. Each represents an average graph from five overlaid waveforms’ data corresponding to the five walking trials. It can be seen that shear components can be either uni-phasic or bi-phasic in feature. Similar findings have previously been reported by a number of investigators (Tappin, J et al., 1980. Lord, M et al., 1992. Yavuz, M et al., 2008). Based on the current measurement, bi-phasic waveforms seem to be more apparent for AP shear component at the 2nd, 3rd, 4th and 5th MTH than that of the 1st MTH 88 where a sharp positive peak appears to dominate. On the contrary, the ML shear components are all uni-phasic at the 2nd, 3rd 4th and 5th MTH. Peak AP shear was found at 1st MTH, while ML shear peaked at the 3rd MTH. Peak shear stresses were calculated by dividing the measured peak shear forces by sensing surface area. 3.2.4 Calculation of shear traction ratio Traction is a relationship between the horizontal and vertical forces acting between the foot and its supporting surface. With our customized pressure/shear sensor array, these forces are measured locally at sub-MTH region. As already discussed in Chapter 2, based on the measured sub-MTH loads, it is possible to calculate traction coefficients, which reflect the local shear interaction between the foot and the ground, to define the frictional coefficients used in the finite element foot model. The forces acting on the MTH site are three-dimensional in nature. Thus, each individual force sensor can resolve the resultant ground reaction forces as three orthogonal components: medio-lateral (Fx), anteriorposterior or longitudinal (Fy) and vertical (Fz). The resultant horizontal (i.e. shear) force (Fxy) is the resultant of the Fx and Fy components: F xy  F x2  F y2 3.9 and the traction ratio, Cof, is the ratio of the horizontal and vertical forces: Cof  Fxy Fz 3.10 89 Fig. 3.2.4.1. shows the calculated local shear traction ratio at sub-MTH areas for the typical reading from pressure/shear sensor. The ratio is very high in the instant just following ‘metatarsal strike’ and just before ‘metatarsal push-off’. At these times, Fz is close to zero, so any small, non-zero of resultant shear forces Fxy results in a very high value of Cof. However, since the forces acting at these times are extremely small, the risk of slip is very low, i.e. sticky condition. In the middle of the step, when the body’s weight is centered over the foot, the local traction ratio is relatively low (< 0.1). Over the whole step, the local shear traction ratio averaged 0.14 ± 0.28 Std. Ignoring those transient high values and relative low values at mid-range, the traction ratio had peak values of 0.51 during ‘metatarsal strike’ and 0.52, on average, during the ‘metatarsal push-off’. For the finite element foot model (developed in Chapter 2) simulating push-off stance, a coefficient of 0.52 Coulomb friction on the foot supporting interface was studied. Fig. 3.2.4.1. Local traction ratios obtained at sub-MTH area for a sample reading of horizontal (Fx and Fy) and vertical forces (Fz) from our customized pressure/shear sensor array. 90 In summary, the combined load sensor array and gait platform successfully measured the three-dimensional dynamic contact forces underneath the 2nd MTH. The advantage offered by the current system is that a single set of force sensor array is required to accurately measure isolated plantar metatarsal force distributions during walking. Such local variations in the vertical and shear force components, including their magnitude and temporal characteristics, are of significant research and clinical interest (Tappin and Robertson, 1991, Perry et al., 2002, Yavuz et al., 2008). Moreover, the in vivo plantar shear stresses, in terms of magnitudes and directions (i.e., vector addition of anterior–posterior (AP), and medial–lateral (ML) components) and its site-specific variations in temporal interplay, were collected and analyzed. This provided valuable data for verification of the foot FE model. 91 [...]... 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 cm2 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... 3. 2.2. 7A) With this set-up, the gait platform is capable of obtaining local dynamic pressure/shear stress distribution (i.e vertical, AP and ML force pattern) and contact timing characteristics Fig 3. 2.2.7 (A) Schematic diagram of the gait platform (B) Photo of the foot making contact with the gait plate that was embedded in a 7-meter walk way, sensor location in relation to the placement of the foot plantar. .. indicated in the last column In order to create image templates for the 2nd MTH, two forefoot plantar images were captured with and without the sensor in position (Fig 3. 2 .3. 1A and Fig 3. 2 .3. 1B) As shown in Fig 3. 2 .3. 1A, the target metatarsal site could be determined within square contact area centered at the black ink dot which marked the 2nd MTH Whilst in Fig 3. 2 .3. 1B, the actual sensor array location... (Fig 3. 2 .3. 1C) With the current gait protocol, the system could achieve an average Xi and Yi errors of 0. 433 mm and 0 .36 9 mm respectively, indicating that the offset variability was minimal Subsequently, the subject initiated gait from a stationary posture and landed the right foot on the platform at the first step of walking The validity of using the “one-step” protocol in collecting gait variables has... linearity of the vertical channel Fig 3. 2.2.5 Calibration graphs showing linearity of the AP shear channel Fig 3. 2.2.6 Calibration graphs showing linearity of the ML shear channel 82 Table 3. 2.2.1 Calibration results of 27 channels corresponding to 9 strain-gauged sensors used for construction of the 3 by 3 sensor array For each channel (AP: anterioposterior; ML: mediolateral; V: vertical) of an individual... 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 69 contact radius variability with indentation depth according to Eq 3. 2, we can have  a. .. surface during walking The assembled platform (load cell and gait platform) was embedded in a straight, 7-meter long, 1-meter wide walkway (Fig 3. 2.2.7B) The entire surface of the walkway was covered with a slip-resistance material Visual checks ensured that the gait platform and walkway did not alter the normal gait during subject walking 3. 2 .3 Assessing sub-MTH loads A 27-year-old male subject has... 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... 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 72 Figure 3. 3.4 .3 Application of the calculated material constants in a plane-strain finite element model (A) The MTH geometry was... that of the 1st MTH 88 where a sharp positive peak appears to dominate On the contrary, the ML shear components are all uni-phasic at the 2nd, 3rd 4th and 5th MTH Peak AP shear was found at 1st MTH, while ML shear peaked at the 3rd MTH Peak shear stresses were calculated by dividing the measured peak shear forces by sensing surface area 3. 2.4 Calculation of shear traction ratio Traction is a relationship . 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. 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. 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