Buono P.-L.,University of Sfax |
Vinet A.,Institute Of Genie Biomedical |
Belair J.,University of Montréal |
Belair J.,McGill University
AIP Conference Proceedings | Year: 2011
In this paper, we study rings of symmetrically coupled fast/slow systems with a coupling from the fast variables to the slow variable. We focus mainly on the case of coupled Hindmarsh-Rose systems for which we investigate the symmetry-breaking steady-state bifurcations from the homogeneous equilibrium solution. We classify the primary bifurcations of Dn rings (with n even) from an asymptotically stable homogeneous state and obtain formulae for pitchfork and Hopf bifurcation curves. We then investigate the bifurcations from a branch with Dn/2 symmetry and show using numerical simulations that there exists a regime of parameter values for small coupling where the stable equilibria of the system have patterns where neighbouring cells are differentiated. For larger coupling, we observe stable periodic solutions with half-period phase shifts. These findings support the use of this type of coupling as a lateral inhibition mechanism. © 2011 American Institute of Physics.
Belanger S.,Ecole Polytechnique de Montréal |
Belanger S.,Institute Of Genie Biomedical |
Abran M.,Ecole Polytechnique de Montréal |
Abran M.,Institute Of Genie Biomedical |
And 4 more authors.
Journal of Biomedical Optics | Year: 2010
A new optical acquisition scheme based on a pair of digital micromirror devices is developed and applied to three-dimensional tomographic imaging of turbid media. By using pairs of illuminationdetection patterns with a single detector, we were able to perform high-resolution quantitative volumetric imaging of absorption heterogeneities embedded in optically thick samples. Additionally, a tomographic reconstruction algorithm was implemented on a graphical processor unit to provide optical reconstructions at a frame rate of 2 Hz. The structured illumination method proposed in this work has significant cost advantages over camera systems, as only a single detector is required. This configuration also has the potential to increase frame rate. © 2010 Society of Photo-Optical Instrumentation Engineers.
Comtois P.,University of Montréal |
Potse M.,Institute Of Genie Biomedical |
Vinet A.,Institute Of Genie Biomedical
Medecine/Sciences | Year: 2010
Models of cardiac electrical activity cover a wide range of spatial scales, from the genesis of the ionic currents in individual cardiomyocytes to the generation of electrocardiograms on the torso. The level of detail that is appropriate and practicable depends on the problem investigated and the scope of the computations that are required. We briefly present three examples of modelling: the dynamics of the entrainment of a single cell, the impact of fibrosis on electrical propagation in a piece of tissue and the generation of ECG in human. In each case, the methods, results and limitations are discussed.
Bouchard S.,Institute Of Genie Biomedical |
Jacquemet V.,Institute Of Genie Biomedical |
Vinet A.,Institute Of Genie Biomedical
Physical Review E - Statistical, Nonlinear, and Soft Matter Physics | Year: 2011
Acute ischemia (restriction in blood supply to part of the heart as a result of myocardial infarction) induces major changes in the electrophysiological properties of the ventricular tissue. Extracellular potassium concentration ([Ko+]) increases in the ischemic zone, leading to an elevation of the resting membrane potential that creates an "injury current" (I S) between the infarcted and the healthy zone. In addition, the lack of oxygen impairs the metabolic activity of the myocytes and decreases ATP production, thereby affecting ATP-sensitive potassium channels (I Katp). Frequent complications of myocardial infarction are tachycardia, fibrillation, and sudden cardiac death, but the mechanisms underlying their initiation are still debated. One hypothesis is that these arrhythmias may be triggered by abnormal automaticity. We investigated the effect of ischemia on myocyte automaticity by performing a comprehensive bifurcation analysis (fixed points, cycles, and their stability) of a human ventricular myocyte model as a function of three ischemia-relevant parameters [Ko+], I S, and I Katp. In this single-cell model, we found that automatic activity was possible only in the presence of an injury current. Changes in [Ko+] and I Katp significantly altered the bifurcation structure of I S, including the occurrence of early-after depolarization. The results provide a sound basis for studying higher-dimensional tissue structures representing an ischemic heart. © 2011 American Physical Society.