July 26, 2014


July 7- August 1, 2014
Focus Program on

Organizing Committee:

Tim David, Martin Frasch, Huaxiong Huang, Chun Liu, Robert Miura
Local Coordinator
Qiming Wang

Registration for Program Activities on site
Workshop fees: $100, Students and PDF: $50,
Waived for invited speakers
Confirmed Participants Information for speakers
Accommodation in Toronto Information for funded participants

Background and Rational
The brain consists of only two percent of the entire body weight but due to its high metabolic rate, it requires a fifth of the total cardiac output. The cerebral vasculature has a number of mechanisms that allow for a constant supply of blood with nutrients and oxygen to the cerebral tissue under varying conditions. These are mainly divided into two groups. In the first group is the myogenic mechanism whereby the larger arterioles contract under increasing systemic pressure and the second mechanism is termed functional hyperemia, which describes the local vessel dilation and constriction due to neuronal activity. This latter mechanism, also known as neurovascular coupling, has shown to be increasingly important in the investigation of reduced perfusion. There is now growing evidence for the relationship between how the brain regulates its blood supply locally and neurological disorders such as dementia in older brains and cerebral palsy in younger brains.

A disordered functional hyperemia is associated with several pathologies such as hyper- tension, Alzheimers disease, cortical spreading depression, and ischemic stroke. All of these pathologies start with an altered relationship between neural activity and the cerebral blood flow (CBF). These alterations perturb the delivery of substrates to active brain cells and impair the removal of waste products from cerebral metabolism. It is likely that this disruption contributes to brain dysfunction. Increasing understanding of neural interactions highlights the importance of vascular pathology in cerebral diseases.

Significant progress has been made in both experimental and modeling fronts. As with all models, there must be a substantial data set with which validation studies can be implemented. A substantial amount of experiment has been done on animal models, notably mice and rat. However there are clear differences in the makeup of a number of important parameters between rodent and human populations. In the end, human validation is necessary. For this to be accomplished appropriately, the complex cellular model must be scaled up to allow comparisons.

The focused program shall consist of four related workshops in Neurovascular Coupling and Related Phenomena. The topic of the first workshop is cortical spreading depression (CSD), a pathological condition in the cortex. Most of the experimental and theoretical studies to-date have focused on the two major components of brain tissue itself (neurons and glial cells) without taking the effect of cerebral blood flow (CBF) into account. Recent work has suggested that CBF and neurovascular coupling, or more specifically the failure of neurovascular coupling, play essential roles in the instigation and propagation of CSD, which will be the subject of the second workshop. The third workshop is on perinatal brain development and specifically the modeling and detection of inflammation and acidemia in fetal brain, a condition related to hypoxia and the reduction of oxygen supply. It is believed that a more accurate detection algorithm will depend on the mechanisms of fetal neurovascular coupling. Finally, at a more fundamental level, to understand and model brain homeostasis, one needs to have a deep understanding on the mechanisms of ion transport and the functions of ion channels and pumps. The fourth and final workshop of the program is on the mathematical and computational models for transport of ionic particles in a biological environment.

Workshop on Cortical Spreading Depression (CSD) and Related Neurological Phenomena,
July 7-11, 2014

Organizers: K. C. Brennan (Neurology,U Utah), Robert M. Miura (Math. Sci. and Biomedical Eng, NJIT), Huaxiong Huang (Math. & Statistics, York U), Markus Dahlem (Physics, Humboldt U, Berlin)

In this workshop, we will bring together a group of researchers from the areas of mathematical modeling and experimentalists in neuroscience to address some of the fundamental issues related to neurovascular coupling and cortical spreading depression (CSD) and related neurological phenomenon. CSD is a slow propagating wave of pathological elevation of extracellular potassium. It is linked to migraine with aura, stroke, and possibly other neurological disorders. The main objective of the workshop is to discuss and incorporate recent advances in experimental studies into mathematical models that are capable of reproducing observed phenomenon and to make predictions that can be verified by further experimental studies.

Workshop on Cerebral Blood Flow (CBF) and Models of Neurovascular Coupling,
July 14-18, 2014

Organizers: Tim David (Biomedical Engineering, Canterbury, NZ)

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.

Problem Solving Workshop on Neurovascular Coupling and Developing Brain
July 21-25, 2014

Organizers: Martin Frasch (Obstetrics & Gynaecology, U de Montreal) and Huaxiong Huang and Qiming Wang (Math. & Stats., York U)

Brain injury acquired antenatally remains a major cause of postnatal long-term neurodevelopmental sequelae. There is evidence for a combined role of fetal infection and inflammation and hypoxic-acidemia. Concomitant hypoxia and acidemia (umbilical cord blood pH < 7.00) during labour increase the risk for neonatal adverse outcomes and longer-term sequelae including cerebral palsy. The main manifestation of pathologic inflammation in the feto-placental unit, chorioamnionitis, affects 20% of term pregnancies and up to 60% of preterm pregnancies and is often asymptomatic.

The format of the event will be that of a problem-solving workshop, also called a Study Group (SG). The workshop will provide an informal setting for researchers from life sciences and mathematical sciences to identify key research questions related to perinatal brain development from neurovascular coupling viewpoint. On the first day of this week long workshop, specific problems will be presented to the workshop participants. It will be followed by brainstorm sessions in subsequent days and a summary session on the last day of the workshop.

Workshop on Transport of Ionic Particles in Biological Environments
July 28- Aug 1, 2014

Organizer: Chun Liu, Maximilian Metti (Math., Penn Stat)

The workshop will bring researchers from different disciplinaries around the world to share and discuss their current research and ideas. There will also be discussions on relevant mathematical theories and techniques associated with these topics, such as differential variational approaches; nonlocal diffusion, including fractional Laplacian and other nonlocal interactions; different diffusion limits of kinetic descriptions of charged particles; various coarse graining methods, such as Mori-Zwanzig methods, closure methods, normal modes analysis, homogenization and nonlinear Galerkin methods; regularities, stability and singular limits, fast numerical algorithms and solvers.

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