A Bidomain Model for Lens Microcirculation.

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There exists a large body of research on the lens of the mammalian eye over the past several decades. The objective of this work is to provide a link between the most recent computational models and some of the pioneering work in the 1970s and 80s. We introduce a general nonelectroneutral model to study the microcirculation in the lens of the eye. It describes the steady-state relationships among ion fluxes, between water flow and electric field inside cells, and in the narrow extracellular spaces between cells in the lens. Using asymptotic analysis, we derive a simplified model based on physiological data and compare our results with those in the literature. We show that our simplified model can be reduced further to the first-generation models, whereas our full model is consistent with the most recent computational models. In addition, our simplified model captures in its equations the main features of the full computational models. Our results serve as a useful link intermediate between the computational models and the first-generation analytical models. Simplified models of this sort may be particularly helpful as the roles of similar osmotic pumps of microcirculation are examined in other tissues with narrow extracellular spaces, such as cardiac and skeletal muscle, liver, kidney, epithelia in general, and the narrow extracellular spaces of the central nervous system, the "brain." Simplified models may reveal the general functional plan of these systems before full computational models become feasible and specific.





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Zhu, Yi, Shixin Xu, Robert S Eisenberg and Huaxiong Huang (2019). A Bidomain Model for Lens Microcirculation. Biophysical journal, 116(6). pp. 1171–1184. 10.1016/j.bpj.2019.02.007 Retrieved from https://hdl.handle.net/10161/27449.

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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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