Cytoskeleton Micromechanics: A Continuum-Microscopic Approach Public Deposited

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  • March 20, 2019
  • Young, Jennifer J.
    • Affiliation: College of Arts and Sciences, Department of Mathematics
  • Creating accurate, whole-cell scale models of the cytoskeleton is computationally challenging, due to the material's highly heterogeneous microstructure. Continuum-based models, homogenization methods, and coarse grained models are common modeling approaches. These methods utilize constant-in-time, average mechanical properties, whereas continuum-microscopic (CM) models utilize a microscopic model to periodically update local mechanical parameters for a macroscopic model. CM methods have been used for heterogeneous media with unchanging microstructures. This research focuses on extending a basic CM algorithm to model heterogeneous media with time-varying microstructures. Microscopic data is saved over time in the form of probability distribution functions. These PDFs are then extrapolated forward in time to predict what the microstructure will look like in the future. Keeping track of the microstructure over time allows for the accurate computation of the local mechanical parameters used in the continuum-level equations. The model was tested on a rectangular domain, representative of a cytoskeleton. Results showed that the elastic parameters computed with this algorithm are similar to those computed with a fully-microscopic simulation. Errors for continuum level variables (such as stress) in the $10% range are deemed an acceptable trade-off for the $50-75% savings in computational expense offered by this algorithm.
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  • In Copyright
  • "... in partial fulfillment of the requirements for the degree of Doctor of Philosophy in the Department of Mathematics."
  • Mitran, Sorin
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  • Chapel Hill, NC
  • Open access

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