This project was developed during Professor Z. M. Kadas' [Department of Mathematics, St. Michael's College] recent Sabbatical Year, which was spent in residence at the University of Vermont. The Vermont Space Grant Consortium has previously provided two Research Minigrants to aid in initiating this research. This project will involve the consistent introduction of autoregulation into compartmental models of the human intracranial system. A highly refined, seven-compartment biomathematical model for this system is described elsewhere [see W.D. Lakin]. In the context of a simplified four-compartment model [1], it has been shown that a resistance which varies linearly with the pressure difference between the arterial and capillary compartments is capable of maintaining a constant blood flow between these two compartments. While constant flow to the capillary bed provides an excellent first approximation, it is known that the physical flow in vivo contains small amplitude pulses superimposed on this constant flow. The proposed work will use perturbation theory to derive the higher-order model equations which govern these small amplitude pulses and determine the appropriate non-linear correction for the resistance element in the model which induces cerebrovascular autoregulation at this level. It appears that this perturbation analysis may also have implications for consistently introducing low-frequency respiratory effects in models of this type. After gaining insight using the simplified four-compartment model, results will be extended to the more robust seven-compartment model, and modifications to intracranial pressure dynamics due to low gravity environments will be considered.
[1] Kadas, Z.M., Lakin, W.D., Yu, J & Penar P.L. A mathematical model of the intracranial system including autoregulation (submitted for publication).