William D. Lakin

Modeling intracranial pressures in microgravity: the influence of the blood-brain barrier.

INTRODUCTION A majority of astronauts experience symptoms of headache, vomiting, nausea, lethargy, and gastric discomfort during the first few hours or days after entering a microgravity environment. Due to similarities in symptoms and their time evolution, it has been hypothesized that some of these conflicts are related to the development of benign intracranial hypertension in these individuals in microgravity. METHODS This hypothesis was tested using a validated mathematical model that embeds the intracranial system in whole-body physiology. This model was used to predict steady-state intracranial pressures in response to various cardiovascular stimuli associated with microgravity, including changes in arterial pressure, central venous pressure, and blood colloid osmotic pressure. The model also allowed alterations of the blood-brain barrier due to factors such as gravitational unloading and increased exposure to radiation in space to be considered. RESULTS Simulations predicted that intracranial pressure will increase significantly if, combined with a drop in blood colloid osmotic pressure, there is a reduction in the integrity of the blood-brain barrier in microgravity. DISCUSSION These results suggest that in some otherwise healthy individuals microgravity environments may elevate intracranial pressure to levels associated with benign intracranial hypertension, producing symptoms that can adversely affect crew health and performance.

A mathematical model of the intracranial system including autoregulation.

Cerebral autoregulation plays an important role in the dynamic processes of intracranial physiology. This work develops a four-compartment, lumped-parameter model for the interactions of intracranial pressures, volumes, and flows as a test bed for examining the consistent inclusion of explicit autoregulation in mathematical models of the intracranial system. It is hypothesized that autoregulation of the blood supply from the arterioles to the capillary bed can be modeled by allowing the flow resistance at the interface of the artery and capillary compartments in the model to be a function of pressure rather than a constant. The functional dependence on pressure of this resistance parameter is not specified in advance, but emerges naturally from the assumed relationship between pressure differences and flows. Results show that a constant flow from the artery to the capillary compartment can be maintained by a flow resistance which is resistance which is directly proportional to the pressure difference between these two compartments. Oscillatory flow is reestablished in the model at the capillary-cerebrospinal fluid and capillary-venous interfaces.

A Model for Idiopathic Intracranial Hypertension and Associated Pathological ICP Wave-Forms

Idiopathic intracranial hypertension (IIH) is a syndrome of unknown cause characterized by elevated intracranial pressure (ICP). While imaging often reveals a stenosis of the transverse sinuses, the role of this feature in IIH has been in dispute. Many patients with chronic daily headache have been found to actually be suffering from a milder form of IIH without papilledema (IIHWOP). These patients often demonstrate hypertensive B-waves and plateau-like waves upon continuous ICP monitoring. Recently, we presented modeling studies which suggest that the sinus stenosis and hypertension of IIH are physiological manifestations of a stable state of elevated pressures that exists when the transverse sinus is sufficiently collapsible. Many of the features of IIH were explained by this model but the prevalence of pathological ICP wave-forms observed in IIHWOP remained unresolved. The model presented here is a modified version of a previous model with a semi-collapsible sinus represented by a refined downstream Starling-like resistor based on experimental data. The qualitative behavior of this model is presented in terms of the collapsibility of the transverse sinus. For a sufficiently rigid sinus, there is a unique stable state of normal pressures. As the degree of collapsibility increases, there is a Hopf bifurcation, the normal state becomes unstable, low-frequency, high-amplitude ICP waves prevail, and small perturbations can lead to hypertensive ICP spikes. As the collapsibility increases further, so does the duration of the waves, until they are replaced by two stable states: one of normal pressures and one of elevated pressures. In this parameter domain, temporary perturbations can now cause permanent transitions between states. The model presented here retains the capability of our previous model to elucidate many features of IIH and additionally provides insight into the prevalence of the low-frequency, high-amplitude waves observed in IIHWOP.

Normal pressure hydrocephalus: An analysis of aetiology and response to shunting based on mathematical modeling

The dynamics which maintain the state of enlarged cerebral ventricles and normal intracranial pressures (normal pressure hydrocephalus) are not completely understood, making the response to cerebrospinal fluid diversion difficult to predict. Using our previously described mathematical model of intracranial physiology which allows nonlinear relationships of pressure, volume, and flow in 7 distinct compartments, we desired to determine factors which could be responsible for the development and maintenance of the steady state of normal pressure hydrocephalus. Using typical starting values for CSF volume, pressure, and flow, the model indicates that this condition cannot be sustained, in spite of high CSF outflow resistance, unless capillary flow resistance is elevated. This condition can be the result of arterial hypertension. The additional modeling of a CSF diversion device demonstrates predicted time courses for ventricular size reduction which are consistent with clinical observations. We conclude that certain vascular conditions may allow for the maintenance of an enlarged ventricular size, and that mathematical modeling can assist in identifying factors for clinical study that may maintain normal pressure hydrocephalus even after treatment by CSF diversion.

A modeling study of idiopathic intracranial hypertension: etiology and diagnosis.

Abstract Objective: To investigate the relationship between idiopathic intracranial hypertension (IIH) and transverse sinus stenosis through experiments performed on a validated mathematical model. Methods: A mathematical model of intracranial pressure (ICP) dynamics has been extended to accommodate venous sinus compression through the introduction of a Starling-like resistor between the sagittal and transverse sinuses. Results: In the absence of this type of resistor, the sinuses are rigid, and the model has only a unique, stable steady state with normal pressures. With resistance a function of the external pressure on the sinus, a second stable steady state may exist. This state is characterized by elevated ICP concurrent with a compressed transverse sinus. Simulations predict that a temporary perturbation that causes a transient elevation of ICP can induce a permanent transition from the normal to the higher steady state. Comparisons to clinical data from IIH patients provide supporting evidence for the validity of the models predictions. Simulations suggest a possible clinical diagnostic technique to determine if an individual has a compressible transverse sinus and is at risk for developing IIH. Conclusions: Results of the model experiments suggest that the primary cause of IIH may be a compressible, as opposed to rigid, transverse sinus, and that the observed stenosis is a necessary characteristic of the elevated pressure state.

A differentiable, periodic function for pulsatile cardiac output based on heart rate and stroke volume

Many mathematical models of human hemodynamics, particularly those which describe pressure and flow pulses throughout the circulatory system, require as specified input a modeling function which describes cardiac output in terms of volume per unit time. To be realistic, this cardiac output function should capture, to the greatest extent possible, all relevant features observed in measured physical data. For model analysis purposes, it is also highly desirable to have a model function that is continuous, differentiable, and periodic. This paper addresses both classes of needs by developing such a function. Physically, the present function provides an accurate model for flow into the ascending aorta. It is completely specified by a minimal number of standard input parameters associated with left ventricle dynamics, including heart rate, mean cardiac output, and an estimation of the peak-to-mean flow ratio. Analytically, it can be expressed as a product of two continuous, differentiable and periodic factors. Further, the Fourier expansion of this model function is shown to be a finite Fourier series, and explicit closed-form expressions are given for the non-zero coefficients in this series.

A non-linear haemodynamic model for the arterial pulsatile component of the intracranial pulse wave

An indication that pressure pulses in cerebral arteries may play a role in the configuration of intracranial pressure pulsations is given by the observation that vasospasm of cerebral arteries narrows the amplitude of the intracranial pressure wave. The present work develops a mathematical model for the transmission of arterial pressure pulses across the compliant arterial wall to the surrounding intracranial space. Compliance of both the arterial segment and the intracranial space are considered. So as to retain accuracy at higher values of the mean intracranial pressure, a physiological range in which pulse transmission is enhanced due to lower pressure gradients but intracranial compliance is not necessarily decreased, a logistic fit is used to model the intracranial pressure-volume relationship. A sequence of approximations (with error bounds) is obtained for the induced intracranial pressure pulse amplitude as a function of arterial pulse amplitude, mean transmural pressure, and mean intracranial pressure. It is found that at higher mean intracranial pressures, where the usual exponential assumption for the intracranial pressure-volume curve loses validity, the amplitude of the transmitted arterial pressure pulse depends non-linearly on the mean intracranial pressure.

A mathematical model of the systemic circulatory system with logistically defined nervous system regulatory mechanisms

A mathematical model is developed that accurately describes the pressure, volume and flow dynamics of the systemic circulatory system over the full physiological range of human pressures and volumes. At the heart of this model are mathematical representations for the autonomic and central nervous system reflexes which maintain arterial pressure, cardiac output and cerebral blood flow. These representations involve functions in which a maximum effect and a minimum effect are smoothly connected by a logistic transition. A new approach to modelling the pressure – volume relationship in a vessel with smooth muscle contraction is also presented. To test the model, simulations of cardiac arrest and various haemorrhagic situations were conducted, and predicted results were compared with clinical observations. Near-perfect agreement was obtained between predicted and observed values of the mean circulatory filling pressure, cardiac output and arterial pressure decay in the face of significant haemorrhage, and the critical values delineating progressive from non-progressive hypovolaemic shock.

Modelling the Response of Intracranial Pressure to Microgravity Environments

A majority of astronauts experience symptoms of headache, vomiting, nausea, lethargy, and gastric discomfort during the first few hours or days after entering a microgravity environment. It has been hypothesised that some of these symtoms are related to the development of benign intracranial hypertension as a result of the cephalic fluid shifts and relative venous congestion that occur in microgravity. This hypothesis is tested here using a mathematical model of lumped-parameter type that embeds the intracranial system in whole-body physiology. In addition to considering microgravity environments, this model is used to examine the response of intracranial pressures to head-down tilt (HDT), a ground-based experimental procedure often used to simulate the cardiovascular effects of microgravity. Predicted pressures in these simulations include those in the cerebral vasculature, ventricular and extra-ventricular cerebrospinal fluid (CSF), and the brain tissue extracellular fluid. Various cardiovascular stimuli associated with microgravity, including changes in arterial pressure, central venous pressure, and blood colloid osmotic pressure, are considered both individually and in concert. Small alterations of the blood-brain barrier in space due to factors such as gravitational unloading and increased exposure to radiation are also allowed. Simulation results predict that in a healthy individual the upward fluid shifts and changes in central venous pressure in microgravitycannot, by themselves, produce a large elevation in ICP so long as the blood-brain barrier remains intact. Indeed, in this case the simulations suggest that ICP in microgravity is significantly less than that in long-term HDT, and may even be less than that in the supine position on Earth. However, simulations predict that ICP can increase significantly if, combined with a drop in blood colloid osmotic pressure, there is even a slight reduction in the integrity of the blood-brain barrier. These results suggest that in some otherwise healthy individuals, microgravity environments may elevate ICP to levels associated with benign intracranial hypertension, producing symptoms that can adversely affect crew performance.