Clot Kinetics in the Progression of Cerebral Vasospasm
Hackney, Erin Kathleen
MetadataShow full item record
Cerebral vasospasm following subarachnoid hemorrhage has high morbidity and mortality. Mathematical modeling of the progression of the condition provides insight to improve clinical treatment of patients post subarachnoid hemorrhage. An existing model of the clotting cascade is expanded to include the theoretical conditions of cerebral vasospasm. We consider clotting factor XIIIa, which has been implicated as a primary cause of the entrenchment of the smaller diameter. Solutions for clotting are used as boundary conditions to solve the concentration of diffusible clotting factors in the vessel wall and cerebrospinal fluid (CSF). Each domain (clot, vessel wall, CSF) is described by a separate initial-boundary value problem, requiring unique conditions, reaction-diffusion equations, and diffusion coefficients. Additionally, the results from the first domain (the clot) provide a subset of the boundary conditions for the second and third domains (arterial wall and CSF, respectively). Although this approach captures many detailed components of the clotting process, a simpler method for investigating the formation and dissolution of a clot post subarachnoid hemorrhage is to neglect the bulk of the clot cascade to focus on the most salient features, namely, the formation of cross-linked fibrin and the degradation of fibrin by plasmin. By assuming first order kinetics in the initial hours following hemorrhage, we find a simplified expression with kinetic rates that may be adjusted depending on experimental conditions.