A Tridomain Model for Potassium Clearance in Optic Nerve of Necturus.

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Complex fluids flow in complex ways in complex structures. Transport of water and various organic and inorganic molecules in the central nervous system are important in a wide range of biological and medical processes [C. Nicholson, and S. Hrabetova, Biophysical Journal, 113(10), 2133(2017)]. However, the exact driving mechanisms are often not known. In this paper, we investigate flows induced by action potentials in an optic nerve as a prototype of the central nervous system (CNS). Different from traditional fluid dynamics problems, flows in biological tissues such as the CNS are coupled with ion transport. It is driven by osmosis created by concentration gradient of ionic solutions, which in term influence the transport of ions. Our mathematical model is based on the known structural and biophysical properties of the experimental system used by the Harvard group Orkand et al [R.K. Orkand, J.G. Nicholls, S.W. Kuffler, Journal of Neurophysiology, 29(4), 788(1966)]. Asymptotic analysis and numerical computation show the significant role of water in convective ion transport. The full model (including water) and the electrodiffusion model (excluding water) are compared in detail to reveal an interesting interplay between water and ion transport. In the full model, convection due to water flow dominates inside the glial domain. This water flow in the glia contributes significantly to the spatial buffering of potassium in the extracellular space. Convection in the extracellular domain does not contribute significantly to spatial buffering. Electrodiffusion is the dominant mechanism for flows confined to the extracellular domain.






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Zhu, Yi, Shixin Xu, Robert S Eisenberg and Huaxiong Huang (2021). A Tridomain Model for Potassium Clearance in Optic Nerve of Necturus. Biophysical journal. 10.1016/j.bpj.2021.06.020 Retrieved from https://hdl.handle.net/10161/23458.

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Shixin Xu

Assistant Professor of Mathematics at Duke Kunshan University

Shixin Xu is an Assistant Professor of Mathematics whose research spans several dynamic and interconnected fields. His primary interests include machine learning and data-driven models for disease prediction, multiscale modeling of complex fluids, neurovascular coupling, homogenization theory, and numerical analysis. His current projects reflect a diverse and impactful portfolio:

  • Developing predictive models based on image data to identify hemorrhagic transformation in acute ischemic stroke.
  • Conducting electrodynamics modeling of saltatory conduction along myelinated axons to understand nerve impulse transmission.
  • Engaging in electrochemical modeling to explore the interactions between electric fields and chemical processes.
  • Investigating fluid-structure interactions with mass transport and reactions, crucial for understanding physiological and engineering systems.

These projects demonstrate his commitment to addressing complex problems through interdisciplinary approaches that bridge mathematics with biological and physical sciences.

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