Nonlinear diffusion and exclusion processes with contact interactions

Exclusion processes on a regular lattice are used to model many biological and physical systems at a discrete level. The average properties of an exclusion process may be described by a continuum model given by a partial differential equation. We combine a general class of contact interactions with an exclusion process. We determine that many different types of contact interactions at the agent-level always give rise to a nonlinear diffusion equation, with a vast variety of diffusion functions D(C). We find that these functions may be dependent on the chosen lattice and the defined neighborhood of the contact interactions. Mild to moderate contact interaction strength generally results in good agreement between discrete and continuum models, while strong interactions often show discrepancies between the two, particularly when D(C) takes on negative values. We present a measure to predict the goodness of fit between the discrete and continuous model, and thus the validity of the continuum description of a motile, contact-interacting population of agents. This work has implications for modeling cell motility and interpreting cell motility assays, giving the ability to incorporate biologically realistic cell-cell interactions and develop global measures of discrete microscopic data.

Forecasting negative effects of monotony and sensation seeking on performance during a vigilance task

The driving task requires sustained attention during prolonged periods, and can be performed in highly predictable or repetitive environments. Such conditions could create hypovigilance and impair performance towards critical events. Identifying such impairment in monotonous conditions has been a major subject of research, but no research to date has attempted to predict it in real-time. This pilot study aims to show that performance decrements due to monotonous tasks can be predicted through mathematical modelling taking into account sensation seeking levels. A short vigilance task sensitive to short periods of lapses of vigilance called Sustained Attention to Response Task is used to assess participants‟ performance. The framework for prediction developed on this task could be extended to a monotonous driving task. A Hidden Markov Model (HMM) is proposed to predict participants‟ lapses in alertness. Driver‟s vigilance evolution is modelled as a hidden state and is correlated to a surrogate measure: the participant‟s reactions time. This experiment shows that the monotony of the task can lead to an important decline in performance in less than five minutes. This impairment can be predicted four minutes in advance with an 86% accuracy using HMMs. This experiment showed that mathematical models such as HMM can efficiently predict hypovigilance through surrogate measures. The presented model could result in the development of an in-vehicle device that detects driver hypovigilance in advance and warn the driver accordingly, thus offering the potential to enhance road safety and prevent road crashes.

The effects of muscle fatigue on knee function during landing

The human knee acts as a sophisticated shock absorber during landing movements. The ability of the knee to perform this function in the real world is remarkable given that the context of the landing movement may vary widely between performances. For this reason, humans must be capable of rapidly adjusting the mechanical properties of the knee under impact load in order to satisfy many competing demands. However, the processes involved in regulating these properties in response to changing constraints remain poorly understood. In particular, the effects of muscle fatigue on knee function during step landing are yet to be fully explored. Fatigue of the knee muscles is significant for 2 reasons. First, it is thought to have detrimental effects on the ability of the knee to act as a shock absorber and is considered a risk factor for knee injury. Second, fatigue of knee muscles provides a unique opportunity to examine the mechanisms by which healthy individuals alter knee function. A review of the literature revealed that the effect of fatigue on knee function during landing has been assessed by comparing pre and postfatigue measurements, with fatigue induced by a voluntary exercise protocol. The information is limited by inconsistent results with key measures, such as knee stiffness, showing varying results following fatigue, including increased stiffness, decreased stiffness or failure to detect any change in some experiments. Further consideration of the literature questions the validity of the models used to induce and measure fatigue, as well as the pre-post study design, which may explain the lack of consensus in the results. These limitations cast doubt on the usefulness of the available information and identify a need to investigate alternative approaches. Based on the results of this review, the aims of this thesis were to: • evaluate the methodological procedures used in validation of a fatigue model • investigate the adaptation and regulation of post-impact knee mechanics during repeated step landings • use this new information to test the effects of fatigue on knee function during a step-landing task. To address the aims of the thesis, 3 related experiments were conducted that collected kinetic, kinematic and electromyographic data from 3 separate samples of healthy male participants. The methodologies involved optoelectronic motion capture (VICON), isokinetic dynamometry (System3 Pro, BIODEX) and wireless surface electromyography (Zerowire, Aurion, Italy). Fatigue indicators and knee function measures used in each experiment were derived from the data. Study 1 compared the validity and reliability of repetitive stepping and isokinetic contractions with respect to fatigue of the quadriceps and hamstrings. Fifteen participants performed 50 repetitions of each exercise twice in randomised order, over 4 sessions. Sessions were separated by a minimum of 1 week’s rest, to ensure full recovery. Validity and reliability depended on a complex interaction between the exercise protocol, the fatigue indicator, the individual and the muscle of interest. Nevertheless, differences between exercise protocols indicated that stepping was less effective in eliciting valid and reliable changes in peak power and spectral compression, compared with isokinetic exercise. A key finding was that fatigue progressed in a biphasic pattern during both exercises. The point separating the 2 phases, known as the transition point, demonstrated superior between-test reliability during the isokinetic protocol, compared with stepping. However, a correction factor should be used to accurately apply this technique to the study of fatigue during landing. Study 2 examined alterations in knee function during repeated landings, with a different sample (N =12) performing 60 consecutive step landing trials. Each landing trial was separated by 1-minute rest periods. The results provided new information in relation to the pre-post study design in the context of detecting adjustments in knee function during landing. First, participants significantly increased or decreased pre-impact muscle activity or post-impact mechanics despite environmental and task constraints remaining unchanged. This is the 1st study to demonstrate this effect in healthy individuals without external feedback on performance. Second, single-subject analysis was more effective in detecting alterations in knee function compared to group-level analysis. Finally, repeated landing trials did not reduce inter-trial variability of knee function in some participants, contrary to assumptions underpinning previous studies. The results of studies 1 and 2 were used to modify the design of Study 3 relative to previous research. These alterations included a modified isokinetic fatigue protocol, multiple pre-fatigue measurements and singlesubject analysis to detect fatigue-related changes in knee function. The study design incorporated new analytical approaches to investigate fatiguerelated alterations in knee function during landing. Participants (N = 16) were measured during multiple pre-fatigue baseline trial blocks prior to the fatigue model. A final block of landing trials was recorded once the participant met the operational fatigue definition that was identified in Study 1. The analysis revealed that the effects of fatigue in this context are heavily dependent on the compensatory response of the individual. A continuum of responses was observed within the sample for each knee function measure. Overall, preimpact preparation and post-impact mechanics of the knee were altered with highly individualised patterns. Moreover, participants used a range of active or passive pre-impact strategies to adapt post-impact mechanics in response to quadriceps fatigue. The unique patterns identified in the data represented an optimisation of knee function based on priorities of the individual. The findings of these studies explain the lack of consensus within the literature regarding the effects of fatigue on knee function during landing. First, functional fatigue protocols lack validity in inducing fatigue-related changes in mechanical output and spectral compression of surface electromyography (sEMG) signals, compared with isokinetic exercise. Second, fatigue-related changes in knee function during landing are confounded by inter-individual variation, which limits the sensitivity of group-level analysis. By addressing these limitations, the 3rd study demonstrated the efficacies of new experimental and analytical approaches to observe fatigue-related alterations in knee function during landing. Consequently, this thesis provides new perspectives into the effects of fatigue in knee function during landing. In conclusion: • The effects of fatigue on knee function during landing depend on the response of the individual, with considerable variation present between study participants, despite similar physical characteristics. • In healthy males, adaptation of pre-impact muscle activity and postimpact knee mechanics is unique to the individual and reflects their own optimisation of demands such as energy expenditure, joint stability, sensory information and loading of knee structures. • The results of these studies should guide future exploration of adaptations in knee function to fatigue. However, research in this area should continue with reduced emphasis on the directional response of the population and a greater focus on individual adaptations of knee function.