Mathematical Modeling of Cerebral Nitric Oxide Dynamics
Open Access
- Author:
- Tamis, Andrew
- Area of Honors:
- Engineering Science
- Degree:
- Bachelor of Science
- Document Type:
- Thesis
- Thesis Supervisors:
- Corina Stefania Drapaca, Thesis Supervisor
Gary L Gray, Thesis Honors Advisor - Keywords:
- Brain
Nitric Oxide
Model
Mechanotransduction
Covid
Mathematical Model
NO
Endothelium - Abstract:
- Nitric Oxide (NO) is a diffusible molecule that is involved in many key signaling processes within the brain, notably the regulation of cerebral blood flow and pressure. NO is produced within neurons, endothelial cells, and red blood cells, but is only activated within the endothelial cells by the shear stress at the blood-endothelium interface. Accurate mathematical models of chemical messengers like NO provide insight into cardiovascular and brain functions in both healthy and diseased conditions, allowing the development of better diagnostics and treatments. Because of the significance of NO to brain functionality, various mathematical models of NO behavior have been proposed in literature. However, most of these models do not thoroughly incorporate the NO production in the endothelium through mechanotransduction. In this thesis, three models for NO behavior in the brain are proposed that expand upon pre-existing models. Production of NO due to viscous dissipation at the endothelial wall is accounted for using shear stress caused by a Pouiselle flow of blood, and in a separate model by axial oscillations due to pulsatile blood flow. In addition, experimental observations have shown a link between NO trapping due to endothelial microparticles (EMP) and the possibility of anomalous diffusion of NO. It is possible that inflammatory diseases that increase the concentration of EMPs might affect NO diffusion, so a link between NO and the SARS-CoV-2 virus will be introduced. The anomalous diffusion is modeled using a generalized Fick's law that incorporates fractional order derivatives in space. Numerical results for each model presented in this thesis will be given and will be related to real-life observations of NO behavior.