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    • University of Missouri-Columbia
    • Graduate School - MU Theses and Dissertations (MU)
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    • 2009 Dissertations (MU)
    • 2009 MU dissertations - Freely available online
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    Mathematical problems from cryobiology

    Benson, James Dale
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    Date
    2009
    Format
    Thesis
    Metadata
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    Abstract
    Cryobiology is the study of life anddeath at low temperatures and provides a fascinating setting for applied mathematics. The interdisciplinary nature of cryobiology mirrors the diversity of applications ranging from animal agriculture to laboratory cell and species preservation to critical human clinical applications for the preservation of life and for the killing of cells during cryosurgery. The work comprising this thesis develops approaches for optimization of cryobiological protocols, and defines a new model for common cryobiological procedures. The first step is to advance an understanding of the optimal control of a classical ODE system describing the mass transport that occurs during cryopreservation. This investigation leads to the description of exact solutions to this 70-year-old nonlinear system, a global stability result for the generalized system with n-solutes, controllability and existence of optimal controls in the n-solute case, and a complete synthesis of optimal controls in the 2- solute case. After defining optimal controls, the question arises whether the predicted continuous optimal control of the extracellular environment affects the hypotheses of the ODE model, namely, perfect stirring inside and outside of the cell/tissue-media boundary. We constructed a new model coupling the ODE mass transport at the cell/tissue boundary of changing radius with convection-diffusion and potential flow models and a numerical integration scheme to explore the effects of advection on the cell-media interface.
    URI
    https://doi.org/10.32469/10355/9873
    https://hdl.handle.net/10355/9873
    Degree
    Ph. D.
    Thesis Department
    Mathematics (MU)
    Rights
    OpenAccess.
    This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivs 3.0 License.
    Collections
    • 2009 MU dissertations - Freely available online
    • Mathematics electronic theses and dissertations (MU)

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