Modeling Idiopathic Intracranial Hypertension with a semi- collapsible sinus Scott Stevens Penn State Erie

Idiopathic Intracranial Hypertension (IIH) High pressure (hypertension) In the head (intracranial) Unknown cause (idiopathic) Symptoms: headache, nausea, papilledema (swollen optic nerve), visual obscurations possibly leading to blindness Often concurrent with intracranial venous- sinus stenosis

J N P Higgins, C Cousins, B K Owler, N Sarkies and J D Pickard Idiopathic intracranial hypertension: 12 cases treated by venous sinus stenting Journal of Neurology Neurosurgery and Psychiatry 2003;74: Sinus Stenosis: Blockage or compression? NormalStenosed Sinus

Prevalence IIH prevalence < 1% IIH without papilledema (IIHWOP) ? 6.7% of 724 migraine patients – sinus stenosis. 67.8% of these - IIHWOP. Possibly 1.3 million in United States Nine of ten CDH patients – IIHWOP with Pathological ICP waveforms Bono 2006, Torbey 2004.

B-waves (spikes) Clinically Observed Pathological ICP Waveforms in IIHWOP A-waves (plateaus) Risberg, Lundberg 1969 Torbey 2004

Model Assumptions

Governing Equations: CSF/Brain Compartment

Governing Equations: Cerebral Veins and Saggital Sinus

Downstream Starling Resistor Data: Heil (1997) Model

Keep your eye on “m”: the initial collapsibility parameter.

Governing Differential Equations

Steady-State Equations

Options - Bifurcations

IIH begins Limit Cycles Still healthy As the collapsibility parameter (m) increases, the situation gets worse. Bifurcation Diagram for P F in terms of the collapsibility parameter m

Limit Cycles: Self-excited oscillations – Pathological ICP waveforms

Cerebral Blood Flow Perturbations. Spikes and plateaus together.

Post saddle-node bifurcation: Similar to our previous results. Two stable states: Normal and Elevated Temporary perturbations cause fast, permanent transitions. Cerebral blood flow perturbation - Sleep apnea.

Potential Diagnostic/Validation Method: Bolus CSF withdrawal. Collapsible sinus simulationRigid sinus simulation

Current Endeavors Periodic Forcing Grazing Bifurcations Stochastic influences CBF autoregulation Single DE system Sigmoidal Resistor

Thanks Jesse Stimpson, Senior, Penn State Erie William D. Lakin, Mathematics, University of Vermont Nimish Thakore, Neurology, Case Western Reserve University Paul Penar, Neurosurgery, University of Vermont. NASA - NSF

Extra Slides

A fantastic, web-based direction field / phase portrait utility Rice University

Nullclines in the transformed variables.

Previous Models IIH characteristics 1) Sinus Stenosis 2) intermittent symptoms 3) long term relief 4) fast transitions between states 5) treatment methods Stevens, Previte, Lakin, Thakore, Penar, and Hamschin: "Idiopathic Intracranial Hypertension and Transverse Sinus Stenosis: A Modeling Study". Mathematical Medicine and Biology 2007 Current Model IIHWOP characteristics 1) Retains previous results for IIH 2) Demonstrates Pathological ICP wave-forms in IIHWOP Stevens, Stimpson, Lakin, Thakore, and Penar “A model for idiopathic intracranial hypertension and associated pathological ICP wave-forms. Accepted by IEEE Transaction on Biomedical Engineering.