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.