An Anatomical Model of the Cerebral Vasculature and the Autoregulation of Cerebral Blood Flow

With the advent of detailed brain imaging techniques, considerable information can be gathered about the anatomy and physiology of the human cerebral vasculature. This enables us to move beyond simple lumped parameter models of the vasculature towards more detailed spatial models: this is critical in a number of brain diseases, such as stroke, where the brain's response is strongly dependent upon the local vascular properties. However, this is not yet understood within the context of a whole brain model, since the local response is influenced by both local and global processes. Here we describe a method of determining geometry in a branching cerebral vascular network. We use available pressure and velocity data to optimize the geometry (diameter and length) in order to fulfill the criterion that flow is conserved in a bifurcating network. The geometry depends only on the capillary diameter and the number of generations of vessels. We then use the pressure and flow relationship set out by Boas [1] along with Poiseuille's law to determine flow and pressure at every point in the system. Finally, data for oxygen concentration from Vovenko [3] is used to establish the correct parameter values to use in the mass transport equation in order to calculate the oxygen concentration in the model. The established geometry can be used as a basis for developing an improved model of the cerebral vasculature which incorporates autoregulation. This paper uses Arciero's proposition [4] that a signal is conducted upstream to influence vessels. We will also be able to investigate alternative network sizes and the effect of changing part of the geometry, or changing flow on the rest of the network.