In May, Professor Stanislav Mintchev chaired a neuroscience session of contributed presentations as part of SIAM DS25, the SIAM Conference on Applications of Dynamical Systems. DS25 brings together application-oriented material and mathematics that informs, supports, or is driven by dynamical systems theory. More details about this neuroscience session can be found here.

In addition to chairing, he presented on his current collaboration with Lai-Sang Young of NYU Courant and Brian Frost of Rockefeller University.

ABSTRACT

Traumatic brain injuries have been associated with the development of axonal varicosities along some of the neurons in affected brain tissues. Referred to as focal axonal swelling (FAS), these defects have been shown to have significant impact on the conduction of electrical current along the axon length due to complexity arising from cable width variation. Mathematical modeling indicates the possibility of substantial interactions between action potentials traveling across such a deformation in a damaged cell. We give a brief overview of our approaches for getting past the computational challenges involved in simulating the transmission of action potentials along a neural axon with functionality that is compromised in this way, and we provide a look ahead at assessing the effects of such injuries on network dynamics paradigms arising in certain areas of the visual cortex.