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.
ACTIVITIES
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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