Modeling Idiopathic Intracranial Hypertension with a semi-collapsible sinus

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Modeling Idiopathic Intracranial Hypertension
with a semi-collapsible sinus

• Scott Stevens
• Penn State Erie

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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

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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
  2003741662-1666

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Prevalence

• IIH prevalence lt 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.
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Clinically Observed Pathological ICP Waveforms in
IIHWOP
A-waves (plateaus)
B-waves (spikes)
Risberg, Lundberg 1969
Torbey 2004
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Model Assumptions
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Model Assumptions
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Governing Equations CSF/Brain Compartment
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Governing Equations Cerebral Veins and Saggital
Sinus
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Downstream Starling Resistor
Data Heil (1997)
Model
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Keep your eye on m the initial collapsibility
parameter.
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Governing Differential Equations
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Steady-State Equations
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Options - Bifurcations
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Bifurcation Diagram for PF in terms of the
collapsibility parameter m
As the collapsibility parameter (m) increases,
the situation gets worse.
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Limit Cycles Self-excited oscillations
Pathological ICP waveforms
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Cerebral Blood Flow Perturbations. Spikes and
plateaus together.
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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.
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Potential Diagnostic/Validation Method Bolus
CSF withdrawal.
Collapsible sinus simulation
Rigid sinus simulation
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Current Endeavors Periodic ForcingGrazing
BifurcationsStochastic influences CBF
autoregulation Single DE system Sigmoidal
Resistor
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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

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Extra Slides
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A fantastic, web-based direction field / phase
portrait utilityRice University
http//math.rice.edu/dfield/dfpp.html
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Nullclines in the transformed variables.
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• 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.

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