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Scientific Interests Science supervisor: Prof. Dr. Alexander Loskutov Current
Position I
have received an INTAS
PhD
fellowship (March 2004 - March 2006), Ref.Nr. 03-55-1920, to investigate
filament dynamics in computational models of re-entry and fibrillation in
the heart. This project is carried out in collaboration with Dr.
Richard Clayton
from the Department of
Computer Science, Research
Background At
first we proposed a
model of the cardiac tissue as a conductive system with two interacting
pacemakers (sources of excitation) and a refractory time, which plays an
important role in normal cardiac functioning. This model can be used to
describe certain types of cardiac arrhythmias, caused by disturbances in
excitation initiation: AV-blocks
and parasystoles.
The interaction of the spontaneously oscillating nonlinear sources was
analyzed on the base of the circle map derived for bidirectional influence
of the pacemakers. In the parametric space of the model the phase locking
areas were investigated in detail. We
observed splitting of the resonance tongues and the superposition of the
synchronization areas. The
obtained
results suggest that the model can be a useful tool for investigating the
dynamical interaction of the cardiac nodes: can be applied to describe
their entrainment and synchronization, and in the more general sence the
results
make possible to predict the behaviour of excitable systems with two
pacemakers, depending on the type and intensity of their interaction and
the initial phase. The
model occurs to be a universal in the sense that its predictions are not
sensitive to the specific form of interactions, i.e. on the phase response
curve (PRC), which determines a change in phase after the action of
stimulus. Our
study clearly indicates that this PRC based model can be applied to
understand the response to an external stimulus of variable intensity and
duration, as was previously observed in experimental investigations. Using
the above results and the fact that excitation generated by the discharge
of one cell (the action potential) induces a subthreshold depolarization
in the adjacent cell, we have extrapolated our approach to study the
bidirectional interaction among an arbitrary large ensemble of the
pacemaker cells. Investigations on the base of the unified model lead to
the development of the theory
of oscillatory
media with a set of interacting pacemakers, coupled by their PRC. This can
be of a great practical importance due to possible application in
controlling cardiac rhythms by external stimuli. In
the second approach the cardiac tissue is considered as a spatio-extended
system, where
action potential propagation is described by nonlinear differential
equations. As is known, one of the more intriguing properties of excitable
media driven by reaction-diffusion equations is the ability to support
vortices. Therefore, this approach is highly useful for description of
re-entrant cardiac arrhythmias, the most life-threatening of which is the
ventricular fibrillation (VF). During
re-entry electrical activity propagates repeatedly along a closed path,
forming a spiral wave of activation in two dimensions (2D) and a scroll
wave in three dimensions (3D). A characteristic feature of a spiral wave
is presence of a wavebreak at the core of the spiral (spiral wave tip). A
spiral wave tip is sometimes referred as a point of phase singularity (PS),
as at this point the phase of the wave is undefined. 3D scroll waves are
characterised by lines of singularities called filaments. When more than
one spiral wave or scroll wave is present, the pattern of spatio-temporal
activity can be very complex. Using filaments enables us to understand
this turbulent pattern of activity. We
have compared all existing methods for PSs detection, since although
choosing an appropriate approach to identify the location of PSs is
extremely important, investigators use different algorithms, and little is
known about the distinction between these methods. We have found that
number and location of PSs detected using different algorithms differ
markedly on each time step, however some methods locate PSs earlier than
others and if time scale is shifted properly (2-3 ms), then discrepancies
between algorithms are caused by transient PSs. Neither
method is ideal since some of them require some parameter values to be
chosen, while for other techniques transmembrane potential has to be
processed before detecting PSs. However, there is clear advantage of using
techniques that are based on topological charge. They immediately give us
knowledge about the sence of spiral wave rotation (chirality), and this is
an additional feature that is extremely useful for PS tracking. We
have observed dynamics of phase singularities using some of the techniques
for PS detection on the base of just one framework three-variable
Fenton-Karma model with different parameters sets to reproduce various
mechanisms of spiral wave breakup which in principle can occur in cardiac
tissue. A difference between constructed PS trajectories and fluctuation
of their number has shown that a type of a breakup mechanism has a strong
influence on the dynamics of singularities. After comparison of the
results for several breakups, we have got some preliminary ideas
concerning which parameters are responsible for the balance of PS creation
and destruction due to positive-negative collision or collision with
boundaries and how the number of singularities of both chiralities can
decrease which leads to VF termination. |