A Mathematical Model of Idiopathic Intracranial Hypertension Thakore, Nimish J 1 ; Stevens, Scott A 2 ; Lakin, William D Department of Neurology, MetroHealth Medical Center and Case Western Reserve University, Cleveland, OH, USA. 2. School of Science, Penn State Erie, The Behrend College, Erie, PA, USA. 3. Department of Mathematics and Statistics, University of Vermont, Burlington, VT, USA. Reproduced with permission from Higgins JNP and Pickard JD (Neurology 62:1907, 2004) High venous pressure elevates ICP High ICP blocks the transverse sinus Starling Resistor Parameters of the downstream Starling resistor Base-Value Steady State Elevated Steady State INTRODUCTION Pathophysiology of IIH - Hypotheses: (A) Cerebral edema; (B) Too much CSF made (C) Too little CSF absorbed: (1) Defective absorption into venous sinus or (2) Venous hypertension Evidence of Venous Hypertension/Obstruction: Venous sinus thrombosis may cause intracranial hypertension Hydrodynamic data Gradient on manometry of venous sinuses - King et al (1995) Evidence of stenosis/tapering of distal transverse sinuses on TOF and ATECO MRI Motivation for this study: King et al (Neurology 58:26-30, 2002) - Disappearance of venous gradient after CSF drainage “The Chicken or the Egg” editorial (Corbett J and Digre K, 2002) Anecdotal reports of benefit from transverse sinus stenting The role of apparent venous stenosis in the pathogenesis of IIH is unknown. It may be the cause of elevated ICP, the effect of elevated ICP, or an exacerbating factor. OBJECTIVES To develop a multi-compartment mathematical model of ICP that includes a collapsible transverse sinus to explain the physiology of IIH METHODS Existing model of ICP: Stevens SA et al (ASEM 76:329, 2005) – Assumptions Constant CSF production rate and cerebral blood flow Flow = Pressure gradient X Fluidity (fluidity = 1/resistance) Deformation = Compliance X Pressure Difference Fluids incompressible. Conservation of mass imposed in 6 compartments Modification: Additional Assumption for IIH: STARLING RESISTOR IN THE DISTAL VENOUS SYSTEM, sensitive to downstream transmural pressure The model involves a system of 6 differential equations, one for each compartment, each of the form Sum (Compliance x Rate of Pressure Difference Change) = Rate of Volume Change = Flow in – Flow out = Sum (Fluidity x Pressure Gradient) In matrix form, this translates into finding solutions of: Where: Basins of Attraction “Collapsible” Sinus “Rigid” Sinus elevated normal Two stable steady states in terms of parameter p Data from three IIH patients (King et al, 2002) before and after ml CSF withdrawal (columns 1 – 6) and the resulting parameter assignments to the model. Pressures are in mmHg. Simulated CSF pressure response to a temporary ICP spike due to apnea. (one minute 50% increase in cerebral blood flow) Simulated CSF pressure response to a temporary CSF drainage blockage. (50 minute 90% decrease in drainage fluidities) RESULTS The original model predicts a single asymptotically stable steady state, corresponding to normal physiology. Inclusion of a Starling resistor in the venous system leads to 2 asymptotically stable steady states: (1) Base-value and (2) Elevated. A third (unstable) steady state corresponds to an saddle point between the two stable states. Appropriate transient perturbations can lead to long-lasting transitions from one steady state to another. Starting with the base-value steady state, a transient increase in ICP (eg from apnea, temporary CSF absorption block) causes a permanent transition to the elevated steady state. Starting with the elevated steady state, transient lowering of ICP (eg from CSF drainage) causes a permanent transition to the base-value steady state. These transitions are abrupt (~ seconds) Parameter p determines the elevation of pressure in the elevated steady state. Parameter m determines the likelihood of achieving the elevated state, and the magnitude of perturbation needed to effect a transition. Shunting, and to a lesser extent, Acetazolamide (1) Eliminate the existence of the elevated steady state for certain parameter values (less area above the bifurcation curve) or (2) Reduce the degree of ICP elevation characteristic of the elevated steady state. A stent in the transverse sinus presumably eliminates the Starling resistor. Weight loss may reduce apneic spells in sleep, a possible precipitating factor for IIH. CONCLUSIONS: According to this model: The primary cause of IIH is a collapsible transverse sinus A precipitating factor that causes transient elevation of ICP is needed to realize the elevated steady state of IIH A compressible transverse sinus and a precipitating factor are sufficient to explain IIH. No additional etiology need be invoked The observed stenosis of the transverse sinuses is a necessary characteristic of the elevated steady state. Abrupt pressure transitions are common in IIH This model explains several aspects of IIH: Observed transverse sinus obstruction and its resolution with CSF drainage, possible link to obesity (sleep apnea), and long-term response to LP Effects of CSF infusion, withdrawal and hypercapnia on continuous ICP recordings and venous sinus flow may be employed to validate this model Simulated CSF pressure response to CSF withdrawal. In the rigid case, the single steady state is elevated because of impaired CSF absorption into venous sinus Bifurcation Line, p-m plane A simulation of King’s experiment (2002) – CSF withdrawal causing a drop in ICP and saggital sinus pressure in a case with a collapsible sinus Rigid sinus Collapsible sinus Rigid sinus Collapsible sinus Rigid sinus Venous sinus pressure ICP Effects of Acetazolamide (ACTZ) and shunts (high and low resistance) on bifurcation curve in p-m plane (left) and ICP of elevated steady state (right) ACTZ Shunt Low High Shunt Low High ACTZ