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Dynamics of Glial Cell Defense Mechanisms in Response to Ischemic Hypoxia in the Brain

Three models are introduced that explore the dual role of glial cells in the formation of scar tissue and in the neural repair following hypoxia ischemia in the brain. Scar tissue helps protect the brain during the acute phase of injury by limiting the spread of secondary damage, but limits recovery by inhibiting the repair of damaged neurons. Scar formation is not ideal, however repaired neurons are still susceptible to damage and do nothing to halt the spread of ischemic injury. A stochastic, spatially explicit Cellular Automaton (CA) model is used to capture the dynamics of neural tissue repair and the containment of damage by scar tissue. In addition, two deterministic models are developed to approximate the stochastic process namely, Mean Field (MFA) and Pair Approximation (OPA) models. We show that the MFA neglects all spatial dependence among state variables. The OPA models the dynamics of state variables evolving as pairs, where spatial adjacency matters. Our results compare how the trade-offs between scar tissue formation and neural repair impacts future brain health.

Article Number:
MTBI-11-05M

Year:
2014

Authors:
Matthew Buhr – University of South Dakota
Oscar Garcia – Universidad de Costa Roca
Tiffany Reyes – Whittier College
Hasan Sumdani – University of Texas at Arlington
Kamal Barley – Arizona State University
Adrian Smith – Arizona State University
Benjamin Morin – Arizona State University
Anuj Mubayi – Arizona State University

dynamics_of_glial_cell_defense_mechanisms_in_response_to_ischemic_hypoxia_in_the_brain.pdf