FOCUS PROGRAM
Multi-scale Modelling of Wave
Structures in Tissues
From August 28 to October 6, 2017, theoretical
and experimental researchers in the areas of
mathematical modelling, neuroscience, and
biophysics gathered at the Fields Institute to
develop new ideas and perspectives that can
radically push forward the understanding of wave
structures in the brain.
The program included three one-week long workshops,
namely Wave Transport of Ionic Species, Waves in Neural
Media, and Uncertainty Quantification (UQ) and Parameter
estimation: High Dimensional Manifolds, which included
a mixture of interesting seminars and lively discussions.
The first workshop contained very valuable interactions
between mathematicians and engineers with substantial
cross-fertilisation of ideas. The second workshop benefitted
substantially from the participation of K.C. Brennan, a
clinician specialising in brain phenomena associated with
migraines, and a number of extremely promising discussions
arose from his talk. The third workshop contained a set of
lectures from Pierre Gremauld along with seminars and
research discussions.
There was also a Lecture Series on Mathematical and
Computational Techniques for Life Sciences whose aim was
to train graduate students and young researchers in the
relevant modelling skills. The series was given by Tim David
who provided the participating students and postdocs with a
comprehensive background in the mathematical modelling of
biological systems.
directions arose as a direct result of this program, including
understanding how uncertainty quantification can be applied
to models related to calcium propagation, consistently
homogenising the equations for neural ion transport,
developing a theory for ionic transport within a cell that
is subjected to ion transport across its membrane, and
developing a theory to explain calcium oscillations that have
been observed in the experiments of one of the participants.
We believe that the program was particularly useful for students
and young researchers. They all participated very actively
in the Lecture Series on Mathematical and Computational
Techniques for Life Sciences and gained valuable experience
in both modelling and computational techniques. In summary,
the program was very successful and we hope to run a short
follow-up meeting in approximately two years time.
— Tim David, Sivabal Sivaloganathan, Jonathan Wylie
The program attracted a diverse mix of participants from
a wide range of backgrounds including mathematicians,
clinicians, experimentalists, physicists and engineers. Of the
43 participants, eight were graduate students, seven were
postdoctoral researchers, and 11 identified as female. In
addition participants were based in ten different countries
including two students of Maori heritage all the way from
New Zealand.
A number of promising new collaborations and research
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