Mathematical modelling of the dynamics of multi-layered biological tissues. The project intends to develop a mathematical model of the basic mechanisms that determine the self-organisation of cells into complex tissues during the development of the embryo. Tissue function requires a non-trivial tissue architecture often composed of multiple cell layers which exhibit a remarkable capacity for renewal and defect correction. A cardinal part of embryonic development involves robust shaping of multi- ....Mathematical modelling of the dynamics of multi-layered biological tissues. The project intends to develop a mathematical model of the basic mechanisms that determine the self-organisation of cells into complex tissues during the development of the embryo. Tissue function requires a non-trivial tissue architecture often composed of multiple cell layers which exhibit a remarkable capacity for renewal and defect correction. A cardinal part of embryonic development involves robust shaping of multi-layered tissue morphologies. The project plans to use mathematical models to determine how complex, three-dimensional structures arise from adaptive multicellular biomechanical interactions. It plans to develop a novel computational modelling framework to represent and analyse such systems, which may be applicable to a wide range of problems where tissue mechanics is a key factor such as bone remodelling and wound healing.Read moreRead less
How motor proteins contract the cell cortex and form a cell division ring. This project aims to develop a detailed physical model for motor proteins and filaments and, based on it, derive a fluid-type mean-field mathematical model, which will facilitate numerical simulations and lead to testable predictions. This study will also provide detailed quantitative information on how these processes can be controlled by modifying concentration and properties of structural and motor proteins. This has p ....How motor proteins contract the cell cortex and form a cell division ring. This project aims to develop a detailed physical model for motor proteins and filaments and, based on it, derive a fluid-type mean-field mathematical model, which will facilitate numerical simulations and lead to testable predictions. This study will also provide detailed quantitative information on how these processes can be controlled by modifying concentration and properties of structural and motor proteins. This has potential applications in tumour therapy, developmental biology and in the bioengineering of nanomaterials.Read moreRead less
Bodies in space. By investigating how a change in shape of the human body can produce a change in spatial orientation, the project will bring a fundamental advance of knowledge in the intersection of applied mathematics, sports science and mechanical engineering. These knowledge advances will lead to a novel theory regarding the control of the aerial dynamics of athletes, specifically springboard and platform divers. When applied in collaboration with world class Australian athletes, this theory ....Bodies in space. By investigating how a change in shape of the human body can produce a change in spatial orientation, the project will bring a fundamental advance of knowledge in the intersection of applied mathematics, sports science and mechanical engineering. These knowledge advances will lead to a novel theory regarding the control of the aerial dynamics of athletes, specifically springboard and platform divers. When applied in collaboration with world class Australian athletes, this theory will result in innovative platform and springboard diving techniques and improved performance. The reach of new insights generated by this work extends to many other fields, including robotics, spacecraft dynamics and nano technology.Read moreRead less
Discovery Early Career Researcher Award - Grant ID: DE140101268
Funder
Australian Research Council
Funding Amount
$386,820.00
Summary
Stochastic mathematical modelling of the Wnt signalling pathway. The Wnt signalling pathway is pivotal in multicellular organisms, regulating cellular processes such as proliferation, apoptosis and migration. Faulty Wnt signalling is associated with degenerative diseases, developmental disorders and cancers and is therefore a potential target for therapeutic drugs. This project will perform a stochastic spatial simulation of the Wnt signalling pathway which will be matched to experimental data. ....Stochastic mathematical modelling of the Wnt signalling pathway. The Wnt signalling pathway is pivotal in multicellular organisms, regulating cellular processes such as proliferation, apoptosis and migration. Faulty Wnt signalling is associated with degenerative diseases, developmental disorders and cancers and is therefore a potential target for therapeutic drugs. This project will perform a stochastic spatial simulation of the Wnt signalling pathway which will be matched to experimental data. The model will be extended to integrate with the cell cycle. Increased proliferation in tumours has been linked to mutations in Wnt components. Using the extended model, the effect of Wnt-targeting therapeutic cancer drugs on cancer cell proliferation rates will be predicted and compared to experiments.Read moreRead less
The Systems Biochemistry of Adaptation in Cellular Protein Networks. A living cell must process and interpret a host of diverse signals using a complex network of interacting proteins inside the cell. The detailed molecular mechanisms by which cells exhibit adaptation to these signals remains a fundamental question in biology. This project aims to develop a novel mathematical framework for analysing the capacity of intracellular protein interactions to contribute to cellular adaptation, along ....The Systems Biochemistry of Adaptation in Cellular Protein Networks. A living cell must process and interpret a host of diverse signals using a complex network of interacting proteins inside the cell. The detailed molecular mechanisms by which cells exhibit adaptation to these signals remains a fundamental question in biology. This project aims to develop a novel mathematical framework for analysing the capacity of intracellular protein interactions to contribute to cellular adaptation, along with a novel methodology for validating mathematical models against experimental data. These innovations offer a completely fresh approach to identifying and modulating the adaptive capacities of living cells, which may contribute to overcoming the problem of drug resistance in future therapeutic development.
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Optimisation of piezoelectric metamaterials: Towards robotic stress sensors. This project aims to design new piezoelectric material microstructures that can enhance the measurement of complex local stress states within robotic limbs. The project expects to generate new knowledge of the achievable properties of multi-poled piezoelectric materials and develop computational tools for the analysis and structural optimisation of such materials. The designed microstructures may revolutionise piezoelec ....Optimisation of piezoelectric metamaterials: Towards robotic stress sensors. This project aims to design new piezoelectric material microstructures that can enhance the measurement of complex local stress states within robotic limbs. The project expects to generate new knowledge of the achievable properties of multi-poled piezoelectric materials and develop computational tools for the analysis and structural optimisation of such materials. The designed microstructures may revolutionise piezoelectric sensor technology. Expected outcomes include manufactured proof-of-concept sensors that enable measurement of local stress fields. This should provide significant benefits, such as improved future robot capability and reliability, and research training for next-generation Australian computational mathematicians. Read moreRead less
Fractional dynamic models for MRI to probe tissue microstructure. This project aims to develop new mathematical tools for mapping tissue microstructural properties via the use of space-time fractional calculus methods. In magnetic resonance imaging, mathematical models and their parameters play a key role in associating information between images and biology, with the overall aim of producing spatially resolved maps of tissue property variations. However, models which can inform on changes in mi ....Fractional dynamic models for MRI to probe tissue microstructure. This project aims to develop new mathematical tools for mapping tissue microstructural properties via the use of space-time fractional calculus methods. In magnetic resonance imaging, mathematical models and their parameters play a key role in associating information between images and biology, with the overall aim of producing spatially resolved maps of tissue property variations. However, models which can inform on changes in microscale tissue properties are lacking. The tools developed by this project will be used to generate new magnetic resonance image based maps to convey information on tissue microstructure changes in the human brain. Additionally, the mathematical tools developed will be transferable to other applications where diffusion and transport in heterogeneous porous media play a role.Read moreRead less
Discovery Early Career Researcher Award - Grant ID: DE130101191
Funder
Australian Research Council
Funding Amount
$375,000.00
Summary
Formation of the osteocyte network in bone matrix. The formation of new bone, which occurs throughout life for bone renewal and acutely after fractures, entraps a network of cells that can detect micro-damage and direct repair mechanisms. Mathematical and computational methods will be used to understand how this network can lead to a self-detecting and self-repairing biomaterial.
A Novel Geometric Approach to Shocks in Reaction-Nonlinear Diffusion Models. Reaction-nonlinear diffusion models play a vital role in the study of cell migration and population dynamics. However, the presence of aggregation, or backward diffusion, leads to the formation of shock waves - distinct, sharp interfaces between different populations of densities of cells - and the breakdown of the model. This project will develop new geometric methods to explain the formation and temporal evolution of ....A Novel Geometric Approach to Shocks in Reaction-Nonlinear Diffusion Models. Reaction-nonlinear diffusion models play a vital role in the study of cell migration and population dynamics. However, the presence of aggregation, or backward diffusion, leads to the formation of shock waves - distinct, sharp interfaces between different populations of densities of cells - and the breakdown of the model. This project will develop new geometric methods to explain the formation and temporal evolution of these shock waves, while simultaneously unifying existing regularisation techniques under a single, geometric banner. It will devise innovative tools in singular perturbation theory and stability analysis that will identify key parameters in the creation of shock waves, as well as their dynamic behaviour.Read moreRead less
A geometric theory for travelling waves in advection-reaction-diffusion models. Cell migration patterns often develop distinct sharp interfaces between identifiably different cell populations within a tissue. This research will develop new geometric methods for the mathematical analysis of cell migration models, and will design diagnostic tools to identify key parameters that cause and control these patterns and interfaces.