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.

Biological monitoring of occupational exposure to polycyclic aromatic hydrocarbons in prebake smelting

In 1984, the International Agency for Research on Cancer determined that working in the primary aluminium production process was associated with exposure to certain polycyclic aromatic hydrocarbons (PAHs) that are probably carcinogenic to humans. Key sources of PAH exposure within the occupational environment of a prebake aluminium smelter are processes associated with use of coal-tar pitch. Despite the potential for exposure via inhalation, ingestion and dermal adsorption, to date occupational exposure limits exist only for airborne contaminants. This study, based at a prebake aluminium smelter in Queensland, Australia, compares exposures of workers who came in contact with PAHs from coal-tar pitch in the smelter’s anode plant (n = 69) and cell-reconstruction area (n = 28), and a non-production control group (n = 17). Literature relevant to PAH exposures in industry and methods of monitoring and assessing occupational hazards associated with these compounds are reviewed, and methods relevant to PAH exposure are discussed in the context of the study site. The study utilises air monitoring of PAHs to quantify exposure via the inhalation route and biological monitoring of 1-hydroxypyrene (1-OHP) in urine of workers to assess total body burden from all routes of entry. Exposures determined for similar exposure groups, sampled over three years, are compared with published occupational PAH exposure limits and/or guidelines. Results of paired personal air monitoring samples and samples collected for 1-OHP in urine monitoring do not correlate. Predictive ability of the benzene-soluble fraction (BSF) in personal air monitoring in relation to the 1-OHP levels in urine is poor (adjusted R2 < 1%) even after adjustment for potential confounders of smoking status and use of personal protective equipment. For static air BSF levels in the anode plant, the median was 0.023 mg/m3 (range 0.002–0.250), almost twice as high as in the cell-reconstruction area (median = 0.013 mg/m3, range 0.003–0.154). In contrast, median BSF personal exposure in the anode plant was 0.036 mg/m3 (range 0.003–0.563), significantly lower than the median measured in the reconstruction area (0.054 mg/m3, range 0.003–0.371) (p = 0.041). The observation that median 1-OHP levels in urine were significantly higher in the anode plant than in the reconstruction area (6.62 µmol/mol creatinine, range 0.09–33.44 and 0.17 µmol/mol creatinine, range 0.001–2.47, respectively) parallels the static air measurements of BSF rather than the personal air monitoring results (p < 0.001). Results of air measurements and biological monitoring show that tasks associated with paste mixing and anode forming in the forming area of the anode plant resulted in higher PAH exposure than tasks in the non-forming areas; median 1-OHP levels in urine from workers in the forming area (14.20 µmol/mol creatinine, range 2.02–33.44) were almost four times higher than those obtained from workers in the non-forming area (4.11 µmol/mol creatinine, range 0.09–26.99; p < 0.001). Results justify use of biological monitoring as an important adjunct to existing measures of PAH exposure in the aluminium industry. Although monitoring of 1-OHP in urine may not be an accurate measure of biological effect on an individual, it is a better indicator of total PAH exposure than BSF in air. In January 2005, interim study results prompted a plant management decision to modify control measures to reduce skin exposure. Comparison of 1-OHP in urine from workers pre- and post-modifications showed substantial downward trends. Exposure via the dermal route was identified as a contributor to overall dose. Reduction in 1-OHP urine concentrations achieved by reducing skin exposure demonstrate the importance of exposure via this alternative pathway. Finally, control measures are recommended to ameliorate risk associated with PAH exposure in the primary aluminium production process, and suggestions for future research include development of methods capable of more specifically monitoring carcinogenic constituents of PAH mixtures, such as benzo[a]pyrene.

Models of collective cell spreading with variable cell aspect ratio : a motivation for degenerate diffusion models

Continuum diffusion models are often used to represent the collective motion of cell populations. Most previous studies have simply used linear diffusion to represent collective cell spreading, while others found that degenerate nonlinear diffusion provides a better match to experimental cell density profiles. In the cell modeling literature there is no guidance available with regard to which approach is more appropriate for representing the spreading of cell populations. Furthermore, there is no knowledge of particular experimental measurements that can be made to distinguish between situations where these two models are appropriate. Here we provide a link between individual-based and continuum models using a multi-scale approach in which we analyze the collective motion of a population of interacting agents in a generalized lattice-based exclusion process. For round agents that occupy a single lattice site, we find that the relevant continuum description of the system is a linear diffusion equation, whereas for elongated rod-shaped agents that occupy L adjacent lattice sites we find that the relevant continuum description is connected to the porous media equation (pme). The exponent in the nonlinear diffusivity function is related to the aspect ratio of the agents. Our work provides a physical connection between modeling collective cell spreading and the use of either the linear diffusion equation or the pme to represent cell density profiles. Results suggest that when using continuum models to represent cell population spreading, we should take care to account for variations in the cell aspect ratio because different aspect ratios lead to different continuum models.

Lumia : art/light/motion

Lumia: art/light/motion is an exciting new media exhibition presented by State Library of Queensland in partnership with Queensland-based Kuuki collective artists Priscilla Bracks and Gavin Sade. The exhibition explored contemporary life and encourages thought about the future through an extraordinary collection of hand-crafted and interactive electronic creatures and installations. The beautifully crafted new media artworks in Lumia: art/light/motion combine the bespoke with art and technology to create strange but intriguing objects. Lumia invited audiences to play, learn and then ponder the way we live and the environmental and social implications of our choices.

A robust structure and motion replacement for bundle adjustment

This paper demonstrates the application of a robust form of pose estimation and scene reconstruction using data from camera images. We demonstrate results that suggest the ability of the algorithm to rival methods of RANSAC based pose estimation polished by bundle adjustment in terms of solution robustness, speed and accuracy, even when given poor initialisations. Our simulated results show the behaviour of the algorithm in a number of novel simulated scenarios reflective of real world cases that show the ability of the algorithm to handle large observation noise and difficult reconstruction scenes. These results have a number of implications for the vision and robotics community, and show that the application of visual motion estimation on robotic platforms in an online fashion is approaching real-world feasibility.

Digital processing of diffusion-tensor images of avascular tissues

Diffusion is the process that leads to the mixing of substances as a result of spontaneous and random thermal motion of individual atoms and molecules. It was first detected by the English botanist Robert Brown in 1827, and the phenomenon became known as ‘Brownian motion’. More specifically, the motion observed by Brown was translational diffusion – thermal motion resulting in random variations of the position of a molecule. This type of motion was given a correct theoretical interpretation in 1905 by Albert Einstein, who derived the relationship between temperature, the viscosity of the medium, the size of the diffusing molecule, and its diffusion coefficient. It is translational diffusion that is indirectly observed in MR diffusion-tensor imaging (DTI). The relationship obtained by Einstein provides the physical basis for using translational diffusion to probe the microscopic environment surrounding the molecule.

Planning and implementing trajectories for autonomous underwater vehicles to track evolving ocean processes based on predictions from a regional ocean model

Path planning and trajectory design for autonomous underwater vehicles (AUVs) is of great importance to the oceanographic research community because automated data collection is becoming more prevalent. Intelligent planning is required to maneuver a vehicle to high-valued locations to perform data collection. In this paper, we present algorithms that determine paths for AUVs to track evolving features of interest in the ocean by considering the output of predictive ocean models. While traversing the computed path, the vehicle provides near-real-time, in situ measurements back to the model, with the intent to increase the skill of future predictions in the local region. The results presented here extend prelim- inary developments of the path planning portion of an end-to-end autonomous prediction and tasking system for aquatic, mobile sensor networks. This extension is the incorporation of multiple vehicles to track the centroid and the boundary of the extent of a feature of interest. Similar algorithms to those presented here are under development to consider additional locations for multiple types of features. The primary focus here is on algorithm development utilizing model predictions to assist in solving the motion planning problem of steering an AUV to high-valued locations, with respect to the data desired. We discuss the design technique to generate the paths, present simulation results and provide experimental data from field deployments for tracking dynamic features by use of an AUV in the Southern California coastal ocean.

A geometrical approach to the motion planning problem for a submerged rigid body

The main focus of this paper is the motion planning problem for a deeply submerged rigid body. The equations of motion are formulated and presented by use of the framework of differential geometry and these equations incorporate external dissipative and restoring forces. We consider a kinematic reduction of the affine connection control system for the rigid body submerged in an ideal fluid, and present an extension of this reduction to the forced affine connection control system for the rigid body submerged in a viscous fluid. The motion planning strategy is based on kinematic motions; the integral curves of rank one kinematic reductions. This method is of particular interest to autonomous underwater vehicles which can not directly control all six degrees of freedom (such as torpedo shaped AUVs) or in case of actuator failure (i.e., under-actuated scenario). A practical example is included to illustrate our technique.

Trajectory design for autonomous underwater vehicles based on ocean model predictions for feature tracking

Trajectory design for Autonomous Underwater Vehicles (AUVs) is of great importance to the oceanographic research community. Intelligent planning is required to maneuver a vehicle to high-valued locations for data collection. We consider the use of ocean model predictions to determine the locations to be visited by an AUV, which then provides near-real time, in situ measurements back to the model to increase the skill of future predictions. The motion planning problem of steering the vehicle between the computed waypoints is not considered here. Our focus is on the algorithm to determine relevant points of interest for a chosen oceanographic feature. This represents a first approach to an end to end autonomous prediction and tasking system for aquatic, mobile sensor networks. We design a sampling plan and present experimental results with AUV retasking in the Southern California Bight (SCB) off the coast of Los Angeles.

Multi-objective four-dimensional vehicle motion planning in large dynamic environments

This paper presents Multi-Step A* (MSA*), a search algorithm based on A* for multi-objective 4D vehicle motion planning (three spatial and one time dimension). The research is principally motivated by the need for offline and online motion planning for autonomous Unmanned Aerial Vehicles (UAVs). For UAVs operating in large, dynamic and uncertain 4D environments, the motion plan consists of a sequence of connected linear tracks (or trajectory segments). The track angle and velocity are important parameters that are often restricted by assumptions and grid geometry in conventional motion planners. Many existing planners also fail to incorporate multiple decision criteria and constraints such as wind, fuel, dynamic obstacles and the rules of the air. It is shown that MSA* finds a cost optimal solution using variable length, angle and velocity trajectory segments. These segments are approximated with a grid based cell sequence that provides an inherent tolerance to uncertainty. Computational efficiency is achieved by using variable successor operators to create a multi-resolution, memory efficient lattice sampling structure. Simulation studies on the UAV flight planning problem show that MSA* meets the time constraints of online replanning and finds paths of equivalent cost but in a quarter of the time (on average) of vector neighbourhood based A*.