Lo que Pericles no imaginó: la peste en Atenas y los problemas de vivir asediado

To permit the development of a loading profile based normal walking gait motion capture data was converted to position and velocity data for input to the device controller. Elderly gait was chosen for the purpose of this study, as this represented the less extreme condition, and thus permitted testing on both young and elderly individuals using a single profile, without the risk of damage to the tissue due to compression outside of the normal range.

A.4.4.1. Motion Capture Data

The data used to derive the gait simulation profile was provided from a study conducted at the University of Padova. The data included mean vertical marker velocity profiles from 10 healthy older people (3 female/7 male, mean age 61.2 (SD 5.27) mean height 1.71m (SD 0.81), mean weight 73.8kg (SD 11.73), mean BMI 24.98 (SD 2.3)). The study used a 6 camera stereophotogrammetric system (BTS S.r.l, Padova - 60 Hz). Subjects were asked to walk at a self-selected speed over a Bertec force platform (FP4060–10, Bertec Corporation,

USA – 960 Hz) while an Imago system (410x410 x 0.5 mm, 0.64 cm2 resolution, 150 Hz,

Imagortesi, Piacenza) was used to collect plantar pressure data. Vertical co-ordinate data for the calcaneus were taken from -10% stance to stance +10% to encompass total heel contact. The first derivative of the vertical co-ordinate data was calculated for each trial. Trials which had a correlation coefficient of >0.75 to the average profile were used to calculate a mean and standard deviation of the vertical marker velocity.

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A.4.4.2. Data Processing and Device Drive Profile Generation

The vertical velocity marker data were loaded into python for further processing. Data were re-sampled and converted from percentage stance to milliseconds based on the average total stance of 0.779s (Figure A.4.8.a); this was orientated such that positive velocity is movement away from the ground and negative velocity is movement toward the ground. The velocity profile was then integrated via the trapezoid rule using Python (scipy.integrate.cumtrapz) to give the vertical displacement of the region marker (Figure A.4.8.b) with the same marker orientation. To allow the actuator to drive the device platen, the orientation of the displacement profile was inverted giving positive displacement as displacement of the device platen toward the fixed foot (Figure A.4.8.c). The vertical displacement was then converted to horizontal displacement using the equation for the gradient of the coupling ramp and displacement offset:

3 + 12.576 (EQ 4.1)

The start and end of the horizontal profile was then padded with zeros and a spline fit was applied using the univariate spline function in Python (scipy.interpolate.univariatespline, k=3, s=0.005). The spline function was used because it forced the curve through all of the data points of the original profile and produced a smoothed transition to the zero padded regions (Figure A.4.8.d). This allowed zero values to be achieved for displacement, velocity and acceleration at both the start and end of the profile, permitting profiles to be run consecutively as compression cycles.

A.4.4.3. Gait Simulation Profile Generation

As with the standard profiles, a peak vertical displacement of 15mm was set to prevent over compression of the subject’s tissue. The subject’s foot was braced such that a tissue strain of 0.4 was achieved when the platen of the device was at its peak vertical position. The gait simulation profile takes the form of an impact and rapid offloading trajectory (Figure A.4.9). Each compressive cycle starts with the platen at rest in the home position (mid-point of coupling ramp). The platen is then displaced vertically with velocity increasing to a peak of ~0.3m/s. Tissue compression occurs rapidly, with the platen reaching a peak vertical displacement of 15mm in ~0.1s.

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Figure A.4.8: Device Drive Profile Development

(a) Vertical Velocity of Marker, (b) Vertical Displacement of Marker, (c) Vertical Displacement of Device Platen, (d) Smoothed Vertical Displacement of Device Platen.

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A large negative acceleration (-75m/s2) is then applied which brings the platen to a stop and

initiates decompression of the tissue. The initial decompression is also rapid simulating the transfer of load from the rear foot to the forefoot in gait. The remaining decompression occurs over ~0.3s at a steadily decreasing negative velocity. This returns the platen to zero displacement allowing 10 compressive cycles to be run consecutively.

A.4.4.4 Limitations of Gait simulation Profiles

Limitations exist within both the data used to derive the profiles and the methods of application.

The derived gait simulation profiles for each region are based on individual surface markers. Although markers which provided both stability and proximity to the region of interest were selected, an individual marker cannot truly represent the motion of an internal structure such as the Calcaneus. The small range over which the tissue compression occurs (10 – 20mm) makes the influence of errors generated by marker movement a potential problem. Surface markers are susceptible to vibration and skin movement, which introduces error within the motion capture data. Detection errors are also present due to the accuracy of the camera system used, although this can be minimised by using a close arrangement of motion capture cameras it cannot be completely removed without smoothing. The short duration of the compression and decompression phases (~0.1s) may result in smoothing and sampling techniques having an influence on the derived trajectories due to the attenuation of some high frequency components which are not pure noise (Winter, 1987). The device and profiles

Figure A.4.9: Gait Simulation Profile for the Rear Foot

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developed allow for the application of load and compression of tissue at rates which aim to replicate gait; however the profiles are limited to only the vertical plane of motion and therefore represent a greatly simplified version of the overall gait dynamics. The restriction of the loading profiles to displacement only control also limits the gait-like nature of compression. Due to compliance within the subject bracing the foot is not rigidly fixed during testing, thus without feedback or control based on the load applied to the tissue the displacement driven compression may not be capable of maximally compressing the tissue in a repeatable manner. Controlled compression capable of encompassing both low and high rate trials in-vivo has not previously been attempted and thus the use of displacement only control provides a new benchmark for future studies, which should aim to control both the displacement and load conditions during dynamic testing in-vivo.

A.4.6 Conclusion

Standard profiles were developed in two forms, a triangle wave with low constant velocity and a sinusoidal wave with low variable velocity. These profiles aim to provide data to assess the effect of loading rate on tissue mechanics, whilst also providing a means to compare the derived properties to the data reported within the literature. Gait simulation profiles were developed based on the measured vertical velocity of a marker at the heel during normal gait of healthy elderly subjects. These profiles aim to provide data to characterise the functional response of the tissue during gait, whilst also providing a means to compare to the derived properties to those of the previous in-gait studies. The capacity to assess the response of the tissue at a single anatomical location under both standard and complex conditions provides a unique opportunity to compare the two approaches. This method also allows for models derived based on one condition to be tested under dynamically different conditions, thus permitting the development of robust modelling methods.

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