Mathematical Modeling of Movement and Growth in Biological Tissues
These researchers are focusing on three projects that are seemingly different, but have similar modeling approaches.
- The first project aims to understand how craniosynostosis, a condition in infants where skull plates fuse prematurely and lead to abnormal head and brain growth, affects intracranial pressures. The researchers are expanding on this project by conducting a parameter study of how relative brain-to-skull growth rates affect these pressures.
- The second project focuses on using mixture theory to model three components in a vertebrate limb bud: the cellular material, the extracellular matrix, and the extracellular fluid. During 2015, the group will implement the model in two and three dimensions and use it to determine how the components must interact to obtain observed limb shapes.
- In the third project, the goal is to gain a better understanding on how a single cell interacts mechanically with a surface to which it is attached. Work during 2015 will incorporate cellular cytoskeletal structures into the model to gain a better understanding of how these structures affect cell shape in cell-substrate interaction.
All three projects use mathematical modeling concepts from continuum mechanics and require either MATLAB or Comsol for solving the governing equations, and additional software, such as Tecplot, for visualization. The numerical implementation of these models results in large, nonlinear algebraic systems for which the speed and capacity of MSI resources would be beneficial.
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