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 PickardIdiopathic intracranial hypertension: 12 cases treated by venous sinus stenting

Journal of Neurology Neurosurgery and Psychiatry 2003;74:1662-1666

Sinus Stenosis: Blockage or compression?

Normal Stenosed 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

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 PF 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 simulation Rigid 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

http://math.rice.edu/~dfield/dfpp.html

Nullclines in the transformed variables.

• Previous Models

IIH characteristics

1) Sinus Stenosis2) intermittent symptoms3) long term relief4) fast transitions between states5) 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 IIH2) 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.