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Small wireless trunk accelerometers have become a popular approach to unobtrusively quantify human locomotion and provide insights into both gait rehabilitation and sports performance. However, limited evidence exists as to which trunk accelerometry measures are suitable for the purpose of detecting movement compensations while running, and specifically in response to fatigue. The aim of this study was therefore to detect deviations in the dynamic center of mass (CoM) motion due to running-induced fatigue using tri-axial trunk accelerometry. Twenty runners aged 18–25 years completed an indoor treadmill running protocol to volitional exhaustion at speeds equivalent to their 3.2 km time trial performance. The following dependent measures were extracted from tri-axial trunk accelerations of 20 running steps before and after the treadmill fatigue protocol: the tri-axial ratio of acceleration root mean square (RMS) to the resultant vector RMS, step and stride regularity (autocorrelation procedure), and sample entropy. Running-induced fatigue increased mediolateral and anteroposterior ratios of acceleration RMS (p < .05), decreased the anteroposterior step regularity (p < .05), and increased the anteroposterior sample entropy (p < .05) of trunk accelerometry patterns. Our findings indicate that treadmill running-induced fatigue might reveal itself in a greater contribution of variability in horizontal plane trunk accelerations, with anteroposterior trunk accelerations that are less regular from step-to-step and are less predictable. It appears that trunk accelerometry parameters can be used to detect deviations in dynamic CoM motion induced by treadmill running fatigue, yet it is unknown how robust or generalizable these parameters are to outdoor running environments.

Despite frequently declared benefits of using wireless accelerometers to assess running gait in real-world settings, available research is limited. The purpose of this study was to investigate outdoor surface effects on dynamic stability and dynamic loading during running using tri-axial trunk accelerometry. Twenty eight runners (11 highly-trained, 17 recreational) performed outdoor running on three outdoor training surfaces (concrete road, synthetic track and woodchip trail) at self-selected comfortable running speeds. Dynamic postural stability (tri-axial acceleration root mean square (RMS) ratio, step and stride regularity, sample entropy), dynamic loading (impact and breaking peak amplitudes and median frequencies), as well as spatio-temporal running gait measures (step frequency, stance time) were derived from trunk accelerations sampled at 1024Hz. Results from generalized estimating equations (GEE) analysis showed that compared to concrete road, woodchip trail had several significant effects on dynamic stability (higher AP ratio of acceleration RMS, lower ML inter-step and inter-stride regularity), on dynamic loading (downward shift in vertical and AP median frequency), and reduced step frequency (p<0.05). Surface effects were unaffected when both running level and running speed were added as potential confounders. Results suggest that woodchip trails disrupt aspects of dynamic stability and loading that are detectable using a single trunk accelerometer. These results provide further insight into how runners adapt their locomotor biomechanics on outdoor surfaces in situ.

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Research has focused on parameters that are associated with injury risk, e.g. vertical acceleration. These parameters can be influenced by running on different surfaces or at different running speeds, but the relationship between them is not completely clear. Understanding the relationship may result in training guidelines to reduce the injury risk. In this study, thirty-five participants with three different levels of running experience were recruited. Participants ran on three different surfaces (concrete, synthetic running track, and woodchip trail) at two different running speeds: a self-selected comfortable speed and a fixed speed of 3.06 m/s. Vertical acceleration of the lower leg was measured with an accelerometer. The vertical acceleration was significantly lower during running on the woodchip trail in comparison with the synthetic running track and the concrete, and significantly lower during running at lower speed in comparison with during running at higher speed on all surfaces. No significant differences in vertical acceleration were found between the three groups of runners at fixed speed. Higher self-selected speed due to higher performance level also did not result in higher vertical acceleration. These results may show that running on a woodchip trail and slowing down could reduce the injury risk at the tibia.

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In my paper [10] I introduced the syntactical concepts “positive part” and “negative part” of logical formulas in first-order predicate calculus. These concepts make it possible to establish logical systems on inference rules similar to Gentzen's inference rules but without using the concept “sequent” and without needing Gentzen's structural inference rules. Proof-theoretical investigations of several formal systems based on positive and negative parts are published in [11]. In this paper I consider a similar formal system of simple type theory.A syntactical concept of “strict derivability” results from the formal system in [10] by generalization of the axioms and inference rules from first to higher-order predicate calculus and by addition of inference rules for set abstraction by means of a λ-symbol which allows us to form set expressions of arbitrary types from well-formed formulas.