For interested researchers, I am listing (non-exhaustively)
some research projects that I can supervise. These projects can be at
the level of a Ph.D. thesis or Master thesis and are mostly indicated
for highly motivated Engineers, Mathematicians, and Physicists.
1) Data analysis of ECGs: We
have access to a large number of data sets of ECGs. We intend to
extract relevant information from the shape and time evolution of the
heart dynamics that are encoded in the ECGs.
2) Image analysis of left atria of AF patients:
We have a large library of high-resolution voltage maps of the left
atrium of patients suffering from atrial fibrillation. The
high-resolution images are used to extract some useful biomarkers that
could be indicative of the state of the patient. We use spatial
statistics to determine the level of fibrosis affecting the patient.
More work has to be done to extract new and more accurate biomarkers.
3) Modeling and simulation of the heart dynamics:
Thanks to the computational power of today's computers, we are now able
to simulate quite accurately some biophysical problems like the
electrical activity that is taking place inside the heart. In order to
perform such numerical simulations, one has to solve stiff
nonlinear-coupled partial differential equations. These solutions are a
numerical challenge and we are always interested in improving the
numerical schemes that are available. The main practical objective of
the project is to help in the design of the implantation of internal
cardiac devices.
4) Application of control tools for stabilizing unstable dynamics (Fluid and Cardiac systems):
The theory of control is well established and extremely useful in
industrial applications. However, when one considers spatially extended
systems the state variables are hugely increased and some new
techniques are necessary to control the dynamics.
5) Study of synchronization and control properties in complex networks:
The study of complex networks has experienced a large increase in the
last decade. The scientific community has realized that many
complicated common systems can be classified in the family of complex
networks. Despite the huge amount of progress that the field of complex
networks has experienced, there are still some interesting open
questions. In particular, one is interested in studying time-varying
complex networks when the connections between the nodes of the network
are created and destroyed as a function of time. This latter problem
has important applications in Biology (see System Biology).