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.
| Identifer | oai:union.ndltd.org:tamu.edu/oai:repository.tamu.edu:1969.1/ETD-TAMU-2009-12-542 |
| Date | 2009 December 1900 |
| Creators | Hackney, Erin Kathleen |
| Contributors | Humphrey, Jay D. |
| Source Sets | Texas A and M University |
| Language | en_US |
| Detected Language | English |
| Type | Book, Thesis, Electronic Thesis, text |
| Format | application/pdf |
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