Project 1
Space Adaptation Syndrome (SAS) is a collection of symptoms, including headache, vomiting, nausea, lethargy, and gastric discomfort, which affect roughly two-thirds of crew members during the first few hours or days of space flight. Although some evidence suggests that SAS may be a form of motion sickness associated with the functioning of the vestibular and sensory systems during exposure to microgravity environments, SAS differs in significant ways from terrestrial manifestations of motion sickness (TMS). While TMS is roughly coincident with the initiation of motion, SAS is delayed. SAS also involves active, rather than passive head motions, and does not involve cold sweats, salivation, facial pallor, or bowel urgency. SAS, unlike TMS, is usually associated with headache, and vomiting tends to be sudden without initial retching or nausea.

A recent study [1] suggests that elevated intracranial pressure (ICP) may play a role in the development of SAS, and several of the symptoms of SAS, e.g. headache and sudden vomiting, resemble those associated with increased ICP. Further, the fact that the onset of SAS occurs early in a flight suggests that it may be related to the well-know fluid shift that begins at launch and continues for approximately 10 hours into the flight. During this period, between 1500mL and 2000mL of fluid may shift from the lower to the upper body. While such a fluid shift can be expected to trigger a coincident rise in ICP, the mechanism involved in this rise, and indeed the effect of microgravity environments on the intracranial space within the nearly-rigid skull, are not well understood. A better understanding of the time course of increases in ICP in response to the fluid shifts of microgravity is needed if the etiology of SAS is to be unraveled, effective countermeasures designed, and the early-flight performance of crew members improved during present and planned space missions. Non-invasive methods for measuring ICP, including use of a Pulsed Phase-Lock Loop (PPLL) ultrasound at NASA Ames Research Center, are currently being developed. Such techniques will be extremely useful in providing data on the time course of ICP increases during the initial stages of exposure to microgravity environments and measuring the effectiveness of potential countermeasures. However, a more direct non-invasive approach to understanding the fundamental mechanisms which produce SAS is also desirable.

The present project will develop a mathematical model for the intracranial system which includes the headward shift of fluids in microgravity and simulates the dynamic adjustment of ICP in response to this shift. The starting point for this project will be a robust lumped-parameter compartmental model of the intracranial system which has already been developed by the principal investigator in collaboration with colleagues in Neurosurgery at UVM [2]. Differential equations describe the dynamic evolution of compartmental pressures, while volumes and flows are related to pressure differences through compliance and resistance functions. The model has been validated by comparison with cerebrospinal fluid (CSF) bolus data generated by the neurosurgeons in a rabbit model [3]. It has also been used to determine the etiology and response to shunting of the Alzheimer like disease state Normal Pressure Hydrocephalus [4].

Since the inception of this project in mid-July, significant progress has been made. Dr. Lakin, in close collaboration with Cordell Gross M.D., past Chair of the Division of Neurosurgery at UVM, has developed a physiologically-realistic mathematical model for the intracranial system in microgravity which includes the headward shift of fluids and is capable of determining the dynamic adjustment of ICP in response to this shift. For the first time, this "lumped-parameter" model does not limit the intracranial space to be a closed system, but embeds the brain within "whole-body" physiology. This innovation is essential to model the stagnation and accumulation of blood in the supraclavicular veins, facial and scalp edema, redistribution of CSF between the brain and spinal thecal, and other effects associated with the headward shift of fluid in microgravity. Differential equations describe the dynamic evolution of compartmental pressures, while volumes and flows are related to pressure differences through compliance and resistance functions. An efficient numerical algorithm for solving the complex coupled model equations has been designed by Dr. Igor Najfeld, a former Staff Scientist at the Institute for Computer Applications in Science and Engineering (ICASE) at NASA Langley Research Center and a current Research Associate on this project. Dr. Scott Stevens, who recently joined this project as a Postdoctoral Assistant, has examined issues associated with model calibration and the relationship between local compartmental and global physiological compliances. A separate description of Dr. Stevens' work follows below. To date, this research progress has resulted in the submission of two papers [5,6] to professional journals.

In Year 2, model calibration will be completed and numerical techniques for efficient solution of the "stiff" system of model equations will be refined. Computer simulations will then be run to simulate entry to microgravity and return to the terrestrial environment. Our hypothesis that many of the debilitating effects of SAS are due to benign intracranial hypertension that is secondary to the edema caused by upward fluid shifts will be tested.

To give confidence in a model's results and predictions, the model must be validated by comparison with measured physiological data. For this purpose, ties have been established with Dr. Alan Hargens in the Gravitational Research Branch at NASA Ames Research Center. Plans also exist to tap the database residing at the Johnson Space Center during the coming year, and Dr. Lakin will be attending the Johnson EPSCoR conference in May.

Dr. William D. Lakin, the principal investigator for this project, is Professor of Mathematics, Statistics, and Biomedical Engineering at the University of Vermont. His areas of expertise include mathematical modeling, differential equations, computational mathematics, and asymptotic methods with applications to biomedicine, fluid mechanics, and aeroelasticity.

[1] Jennings, T. (1990) Space adaptation syndrome is caused by elevated intracranial pressure. Medical Hypothesis 32, 289-291.

[2] Lakin,W.D. (1998) Mathematical modeling of pressure dynamics in the intracranial system.^Ô In G. Oyibo (Ed.), Applied Mathematics: Methods and Techniques, 2nd Ed. Commack, NY: Nova Science Publishers.

[3] Lakin,W.D., Penar, P.L. and Yu,J. (1999) Analysis and validation of a mathematical model of intracranial dynamics in the rabbit. Math. Modelling of Systems 3, 1-19.

[4] Penar, P.L., Lakin, W.D., and Yu, J. (1995) Normal Pressure Hydrocephalus: An analysis of etiology and response to shunting based on mathematical modeling. Neurological Research 17, 83-88.

[5] Steven, S.A. and Lakin, W.D. Recovering the global physiological compliance of the intracranial system using local compliances in a mathematical model. Mathematical and Computer Modelling of Dynamical Systems (submitted).

[6] Stevens, S.A. Mean pressures andflows in the human intracranial system determined by mathematical simulations of a steady-state infusion test. J. Neurosurgery (submitted).

Progress Report: Dr. Scott A. Stevens, Postdoctoral Fellow

I have been working in collaboration with members of the Mathematics and Neurosurgery Departments at UVM on the development of a mathematical model of intracranial fluid dynamics. We are designing a whole-body model in order to study the fluid redistributions associated with the prolonged exposure to microgravity experienced by astronauts.

My role in this project has been the calibration of problem parameters such as mean fluid flows and pressures within the intracranial region of the healthy adult human, specifically in the base state on earth. These intracranial calibrations may then be introduced into the whole-body model. In this way, the effects of microgravity may be modeled as deviations from this base state which may lead to a common disorder in astronauts known as Space Adaptation Syndrome. With the aid of this model, possible intervention techniques may be tested without costly experimentation in microgravity.

My first result this year was pertaining to the small fluid flow into and out of the interstitial brain tissue across the blood-brain and CSF-brain barriers. Due to the magnitude of these flows, it is difficult to measure them experimentally. However, in order to fully understand the effects of microgravity on fluid redistributions within the extracellular tissue, it is necessary to quantify these small flows within a reasonable accuracy level. Through simulated steady-state infusion tests, I was able to compare results with clinical data and obtain estimations of these small flows in the base state.

Presently, I have developed a smaller model of the intracranial region in order to study the pressure-volume relationship of the Cerebrospinal Fluid (CSF) space. This model incorporates some of the aspects of the whole-body model but maintains simplicity by lumping the intracranial region into three compartments: artery, vein, and CSF. Despite the simplicity of this model, the global pressure-volume relationship within the CSF space is realized throughout a complete CSF pressure domain. This is done through the introduction and calibration of three, local, pressure-difference dependent compliances.

In the future I plan to incorporate the results above into the whole-body model, finish calibrating the problem parameters in the base state and begin microgravity simulations.