Mathematical modeling of focal axonal swellings arising in traumatic brain injuries and neurodegenerative diseases
Maia, Pedro Doria
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There is a broad need in the neuroscience, neurological and biomedical engineering communities to better classify, quantify and diagnose Focal Axonal Swellings (FAS) and their impact on cognitive deficits and/or neural functionality. FAS is a critical biomarker in several leading neurodegenerative diseases such as Alzheimer's, Parkinson's, Multiple Sclerosis, and others. They are also a hallmark feature of concussions and Traumatic Brain Injuries -- the leading cause of death among youngsters worldwide and a lightning rod issue in contact sports. In this work, we discuss how different shapes of FAS can affect neuronal signaling and degrade the information encoded in spike trains. We adapted theoretical estimates, derived in idealized axonal geometry settings, to real axons with much more challenging structures. Our methods highlight potential trouble spots of axonal morphology and provide a starting point for novel FAS diagnosis. Finally, we discuss the collective effects of FAS in neuronal networks, where stable response patterns are lost, jeopardizing the system's ability to transmit information. A better understanding of the macroscopic effects of FAS pathologies -- that occur at a cellular level-- can shine new light onto the cognitive, behavioral, perceptual and sensory-motor impairments resulting from such disorders.
- Applied mathematics