Modelling of some biological materials using continuum mechanics

Continuum mechanics provides a mathematical framework for modelling the physical stresses experienced by a material. Recent studies show that physical stresses play an important role in a wide variety of biological processes, including dermal wound healing, soft tissue growth and morphogenesis. Thus, continuum mechanics is a useful mathematical tool for modelling a range of biological phenomena. Unfortunately, classical continuum mechanics is of limited use in biomechanical problems. As cells refashion the �bres that make up a soft tissue, they sometimes alter the tissue's fundamental mechanical structure. Advanced mathematical techniques are needed in order to accurately describe this sort of biological `plasticity'. A number of such techniques have been proposed by previous researchers. However, models that incorporate biological plasticity tend to be very complicated. Furthermore, these models are often di�cult to apply and/or interpret, making them of limited practical use. One alternative approach is to ignore biological plasticity and use classical continuum mechanics. For example, most mechanochemical models of dermal wound healing assume that the skin behaves as a linear viscoelastic solid. Our analysis indicates that this assumption leads to physically unrealistic results. In this thesis we present a novel and practical approach to modelling biological plasticity. Our principal aim is to combine the simplicity of classical linear models with the sophistication of plasticity theory. To achieve this, we perform a careful mathematical analysis of the concept of a `zero stress state'. This leads us to a formal de�nition of strain that is appropriate for materials that undergo internal remodelling. Next, we consider the evolution of the zero stress state over time. We develop a novel theory of `morphoelasticity' that can be used to describe how the zero stress state changes in response to growth and remodelling. Importantly, our work yields an intuitive and internally consistent way of modelling anisotropic growth. Furthermore, we are able to use our theory of morphoelasticity to develop evolution equations for elastic strain. We also present some applications of our theory. For example, we show that morphoelasticity can be used to obtain a constitutive law for a Maxwell viscoelastic uid that is valid at large deformation gradients. Similarly, we analyse a morphoelastic model of the stress-dependent growth of a tumour spheroid. This work leads to the prediction that a tumour spheroid will always be in a state of radial compression and circumferential tension. Finally, we conclude by presenting a novel mechanochemical model of dermal wound healing that takes into account the plasticity of the healing skin.

Real-time performance modelling of a sustained attention to response task

Vigilance declines when exposed to highly predictable and uneventful tasks. Monotonous tasks provide little cognitive and motor stimulation and contribute to human errors. This paper aims to model and detect vigilance decline in real time through participant’s reaction times during a monotonous task. A lab-based experiment adapting the Sustained Attention to Response Task (SART) is conducted to quantify the effect of monotony on overall performance. Then relevant parameters are used to build a model detecting hypovigilance throughout the experiment. The accuracy of different mathematical models are compared to detect in real-time – minute by minute - the lapses in vigilance during the task. We show that monotonous tasks can lead to an average decline in performance of 45%. Furthermore, vigilance modelling enables to detect vigilance decline through reaction times with an accuracy of 72% and a 29% false alarm rate. Bayesian models are identified as a better model to detect lapses in vigilance as compared to Neural Networks and Generalised Linear Mixed Models. This modelling could be used as a framework to detect vigilance decline of any human performing monotonous tasks.

Predicting effects of monotony on driver’s vigilance

Monotony has been identified as a contributing factor to road crashes. Drivers’ ability to react to unpredictable events deteriorates when exposed to highly predictable and uneventful driving tasks, such as driving on Australian rural roads, many of which are monotonous by nature. Highway design in particular attempts to reduce the driver’s task to a merely lane-keeping one. Such a task provides little stimulation and is monotonous, thus affecting the driver’s attention which is no longer directed towards the road. Inattention contributes to crashes, especially for professional drivers. Monotony has been studied mainly from the endogenous perspective (for instance through sleep deprivation) without taking into account the influence of the task itself (repetitiveness) or the surrounding environment. The aim and novelty of this thesis is to develop a methodology (mathematical framework) able to predict driver lapses of vigilance under monotonous environments in real time, using endogenous and exogenous data collected from the driver, the vehicle and the environment. Existing approaches have tended to neglect the specificity of task monotony, leaving the question of the existence of a “monotonous state” unanswered. Furthermore the issue of detecting vigilance decrement before it occurs (predictions) has not been investigated in the literature, let alone in real time. A multidisciplinary approach is necessary to explain how vigilance evolves in monotonous conditions. Such an approach needs to draw on psychology, physiology, road safety, computer science and mathematics. The systemic approach proposed in this study is unique with its predictive dimension and allows us to define, in real time, the impacts of monotony on the driver’s ability to drive. Such methodology is based on mathematical models integrating data available in vehicles to the vigilance state of the driver during a monotonous driving task in various environments. The model integrates different data measuring driver’s endogenous and exogenous factors (related to the driver, the vehicle and the surrounding environment). Electroencephalography (EEG) is used to measure driver vigilance since it has been shown to be the most reliable and real time methodology to assess vigilance level. There are a variety of mathematical models suitable to provide a framework for predictions however, to find the most accurate model, a collection of mathematical models were trained in this thesis and the most reliable was found. The methodology developed in this research is first applied to a theoretically sound measure of sustained attention called Sustained Attention Response to Task (SART) as adapted by Michael (2010), Michael and Meuter (2006, 2007). This experiment induced impairments due to monotony during a vigilance task. Analyses performed in this thesis confirm and extend findings from Michael (2010) that monotony leads to an important vigilance impairment independent of fatigue. This thesis is also the first to show that monotony changes the dynamics of vigilance evolution and tends to create a “monotonous state” characterised by reduced vigilance. Personality traits such as being a low sensation seeker can mitigate this vigilance decrement. It is also evident that lapses in vigilance can be predicted accurately with Bayesian modelling and Neural Networks. This framework was then applied to the driving task by designing a simulated monotonous driving task. The design of such task requires multidisciplinary knowledge and involved psychologist Rebecca Michael. Monotony was varied through both the road design and the road environment variables. This experiment demonstrated that road monotony can lead to driving impairment. Particularly monotonous road scenery was shown to have the most impact compared to monotonous road design. Next, this study identified a variety of surrogate measures that are correlated with vigilance levels obtained from the EEG. Such vigilance states can be predicted with these surrogate measures. This means that vigilance decrement can be detected in a car without the use of an EEG device. Amongst the different mathematical models tested in this thesis, only Neural Networks predicted the vigilance levels accurately. The results of both these experiments provide valuable information about the methodology to predict vigilance decrement. Such an issue is quite complex and requires modelling that can adapt to highly inter-individual differences. Only Neural Networks proved accurate in both studies, suggesting that these models are the most likely to be accurate when used on real roads or for further research on vigilance modelling. This research provides a better understanding of the driving task under monotonous conditions. Results demonstrate that mathematical modelling can be used to determine the driver’s vigilance state when driving using surrogate measures identified during this study. This research has opened up avenues for future research and could result in the development of an in-vehicle device predicting driver vigilance decrement. Such a device could contribute to a reduction in crashes and therefore improve road safety.

Performance evaluation of an adaptive travel time prediction model

This paper presents a travel time prediction model and evaluates its performance and transferability. Advanced Travelers Information Systems (ATIS) are gaining more and more importance, increasing the need for accurate, timely and useful information to the travelers. Travel time information quantifies the traffic condition in an easy to understand way for the users. The proposed travel time prediction model is based on an efficient use of nearest neighbor search. The model is calibrated for optimal performance using Genetic Algorithms. Results indicate better performance by using the proposed model than the presently used naïve model.