Modeling Idiopathic Intracranial Hypertension with a semicollapsible 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 venoussinus stenosis
Sinus Stenosis: Blockage or compression? Normal Stenosed Sinus 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: 1662 -1666
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.
Clinically Observed Pathological ICP Waveforms in IIHWOP A-waves (plateaus) B-waves (spikes) 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
Bifurcation Diagram for PF in terms of the collapsibility parameter m IIH begins Still healthy Limit Cycles As the collapsibility parameter (m) increases, the situation gets worse.
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 • Current Model IIH characteristics IIHWOP characteristics 1) Sinus Stenosis 2) intermittent symptoms 3) long term relief 4) fast transitions between states 5) treatment methods 1) Retains previous results for IIH 2) Demonstrates Pathological ICP wave-forms in IIHWOP Stevens, Previte, Lakin, Thakore, Penar, and Hamschin: "Idiopathic Intracranial Hypertension and Transverse Sinus Stenosis: A Modeling Study". Mathematical Medicine and Biology 2007 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.
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