Modeling Idiopathic Intracranial Hypertension with a semi-collapsible sinus

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

2. 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

3. Sinus Stenosis: Blockage or compression? 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 Normal Stenosed Sinus

4. 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.

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

10. Model Assumptions

11. Model Assumptions

12. Governing Equations: CSF/Brain Compartment

13. Governing Equations: Cerebral Veins and Saggital Sinus

14. Downstream Starling Resistor Data: Heil (1997) Model

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

16. Governing Differential Equations

17. Steady-State Equations

18. Options - Bifurcations

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

20. Limit Cycles: Self-excited oscillations – Pathological ICP waveforms

21. Cerebral Blood Flow Perturbations. Spikes and plateaus together.

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

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

24. Current Endeavors Periodic ForcingGrazing BifurcationsStochastic influences CBF autoregulation Single DE system Sigmoidal Resistor

25. 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

26. Extra Slides

27. A fantastic, web-based direction field / phase portrait utilityRice University http://math.rice.edu/~dfield/dfpp.html

28. Nullclines in the transformed variables.

30. Previous ModelsIIH characteristics 1) Sinus Stenosis2) intermittent symptoms3) long term relief4) fast transitions between states5) treatment methodsStevens, Previte, Lakin, Thakore, Penar, and Hamschin: "Idiopathic Intracranial Hypertension and Transverse Sinus Stenosis: A Modeling Study". Mathematical Medicine and Biology 2007 Current ModelIIHWOP characteristics1) Retains previous results for IIH2) Demonstrates Pathological ICP wave-forms in IIHWOPStevens, Stimpson, Lakin, Thakore, and Penar “A model for idiopathic intracranial hypertension and associated pathological ICP wave-forms. Accepted by IEEE Transaction on Biomedical Engineering.