Mathematical Models of Brain and Cerebrospinal Fluid Dynamics: Application to Hydrocephalus
Open Access
- Author:
- Kauffman, Justin A
- Graduate Program:
- Engineering Science and Mechanics
- Degree:
- Master of Science
- Document Type:
- Master Thesis
- Date of Defense:
- March 22, 2013
- Committee Members:
- Corina Stefania Drapaca, Thesis Advisor/Co-Advisor
- Keywords:
- Hydrocephalus
Mathematical Modeling
Brain Biomechanics - Abstract:
- Hydrocephalus is a serious neurological disorder characterized by abnormalities in the circulation of cerebrospinal fluid (CSF). Hydrocephalus results from an excessive accumulation of CSF in the ventricles of the brain, brain compression, and sometimes an increase in the intracranial pressure. It is believed that hydrocephalus is either caused by an increase in CSF production, or by an obstruction of the circulation of CSF or of the venous outflow system. The treatment is therefore based on CSF flow diversion. Given that the response of the patients who have been treated continues to be poor there is an urgent need to design better therapy protocols for hydrocephalus. Mathematical models of CSF dynamics and CSF-brain interactions could play important roles in the design of improved, patient-specific treatments. One of the first predictive mathematical models of CSF pressure-volume interactions was proposed by Marmarou in the 1970’s and provides a theoretical basis for studying hydrocephalus. However, this model fails to fully capture the complexity of the CSF dynamics. In this thesis we will propose a generalization to Marmarou’s model using fractional calculus. We use a modified Adomian decomposition method to solve analytically the proposed fractional order nonlinear differential equation. Our results show temporal multi-scaling behavior of CSF dynamics. In addition, we also propose a novel coupled-field model using Hamilton’s principle to capture some of the dynamics taking place at the macroscopic and microscopic scales during the onset and evolution of hydrocephalus. Our coupled-field model introduces healing (growth) and inflammation (aging) states of the brain which show distinct temporal variations when we use experimentally measured volumetric data for healthy and hydrocephalic mice.