Mathematical Model Investigating the Effects of Neurostimulation Therapies on Neural Functioning: Comparing the Effects of Neuromodulation Techniques on Ion Channel Gating and Ionic Flux Using Finite Element Analysis
Neurostimulation therapies demonstrate success as a medical intervention for individuals with neurodegenerative diseases, such as Parkinson’s and Alzheimer’s disease. Despite promising results from these treatments, the influence of an electric current on ion concentrations and subsequent transmembrane voltage is unclear. This project focuses on developing a unique cellular-level mathematical model of neurostimulation to better understand its e↵ects on neuronal electrodynamics. The mathematical model presented here integrates the Poisson-Nernst-Planck system of PDEs and Hodgkin-Huxley based ODEs to model the e↵ects of this neurotherapy on transmembrane voltage, ion channel gating, and ionic mobility. This system is decoupled using the Gauss-Seidel method and then the equations are solved using the finite element method on a biologically-inspired discretized domain. Results demonstrate the influence of transcranial electrical stimulation on membrane voltage, ion channel gating, and transmembrane flux. Simulations also compare the e↵ects of two di↵erent types of neurostimulation (transcranial electrical stimulation and deep brain stimulation) showcasing cellular-level di↵erences resulting from these distinct forms of electrical therapy. Hopefully this work will ultimately help elucidate the principles by which neurostimulation alleviates disease symptoms.
Lindberg, Kaia, "Mathematical Model Investigating the Effects of Neurostimulation Therapies on Neural Functioning: Comparing the Effects of Neuromodulation Techniques on Ion Channel Gating and Ionic Flux Using Finite Element Analysis" (2019). Mathematics Theses. 6.