The change in vessel diameter (vasoreactivity) controls the local cerebral blood flow and thereby the supply of oxygen and glucose. Although investigations of functional hyperaemia started over 200 years ago, the exact cellular and chemical pathways that are involved are still unknown. However, studies over the last decades indicate that neurons, astrocytes, smooth muscle cells and endothelial cells constitute a functional unit, which is collectively known as a neurovascular unit (NVU). When intercellular communication within the NVU functional hyperaemia is achieved, this process is called neurovascular coupling (NVC). A primary purpose is to maintain homeostasis in the cerebral micro-circulation and several mathematical models have been developed to mimic components of certain chemical pathways within the NVC.

Complex mathematical models can now be used to investigate the intricate relationship between neuronal activity and the regulation of the cerebral blood supply. Indeed they can also provide significant insight into the relationship between diabetes mellitus and the onset of dementia and Alzheimers disease. A physiologically relevant and experimentally validated mathematical model is critically needed to better understand the complexity of the underlying mechanisms, and to potentially identify strategies to prevent neuronal death, brain atrophy, and cognitive decline. These complex mathematical models produce extremely complex dynamical phenomena due to their nonlinear forms and the coupling that occurs between different types of cells. Mathematical analysis is required to investigate the crucial pathways in the model and, if possible, to simplify the system to a form whereby analytical tools can be used.

The above descriptions highlights the complexities involved in developing a viable mathematical model of blood perfusion in the cerebral tissue. However it is necessary if we are to advance our understanding of not only "normal" conditions but also pathological ones. Mathematical models can help in this advancement and it will be accelerated by the work of teams comprised of experts in a variety of areas.

This workshop will bring together international experts in the field of physiological modelling, mathematical analysis/modeling and young investigators. It will provide a framework for discussion, new insights and hopefully advancement in this new and exciting field of mathematical neuroscience