Research

Cardiac Arrhythmias

Normal heartbeats are initiated by the propagation of a series of regular electrical impulses, generated from the heart's pacemaker cells. When the propagating electrical wave becomes destabilized, abnormal heartbeats arise and sometimes lead to sudden cardiac arrest, which kills hundreds of thousands of North Americans each year.Cardiac alternans, a beat-to-beat alternation in action potential duration (at the cellular level) or in ECG morphology (at the whole heart level), is a marker of ventricular fibrillation. Investigating cardiac alternans may lead to a better understanding of the mechanisms of cardiac arrhythmias and eventually better algorithms for the prediction and prevention of such dreadful diseases. In paced cardiac tissues, alternans develops under increasingly shorter pacing period. Existing experimental and theoretical studies adopt the assumption that alternans in homogeneous cardiac tissue is exclusively determined by the pacing period. Our recent findings show that, when calcium-driven alternans develops in cardiac fibers, there coexist multiple spatiotemporal patterns for a given pacing period. Thus, knowing the pacing period alone, one can not predict the alternans pattern on a fiber since the pattern depends on the pacing history. Using numerical simulation and theoretical analysis, we show that the coexistence of multiple alternans patterns is induced by the interaction between electrotonic coupling and the instability in calcium cycling. Read details in this PRE article.

Prebifurcation Amplification

Cardiac alternans is a period-doubling bifurcation, which can occur through either a classical mechanism or a border-collision mechanism. Identifying the type of bifurcation mechanism mediating cardiac alternans is crucial for detection and control of this instability.We have introduced a novel technique that allows one to unambiguously distinguish between classical and border-collision bifurcations based on prebifurcation amplification analysis. This technique leads to the interesting discovery of hybrid smooth/nonsmooth behaviors of alternans.

Schematic bifurcation diagrams with discrete sampling. The sampled points (solid dots) are identical for the (a) smooth and (b) border-collision bifurcations. (c-f) Alternate pacing: The trend in Gamma vs B is illustrated for (c) smooth and (d) border-collision bifurcations, and the trend in Gamma vs delta is illustrated for (e) smooth and (f ) border-collision bifurcations.

Electroporation

Electroporation has become an important tool for drug delivery such as gene therapy. The technique uses electric pulses to create transient pores in the cell membrane. To ensure proper uptake of targeted molecules, it is essential to create sufficiently large pores, which remain open long enough. We explore evolution of the pores using dynamical analysis and control of electroporation. A detailed bifurcation analysis reveals the existence of a pair of saddle-node bifurcations. Between the bifurcation points, a range of pore radii are unstable and thus cannot be obtained in physical experiments, imposing limitations on the operation of electroporation. We design a feedback control algorithm to eliminate the bifurcations so that one can easily that is able to achieve any desired pore size. Numerical examples demonstrate the control strategy is robust. The control algorithm will improve the operation of electroporation in drug delivery.

Impact Microactuators

Micro or nano distance manipulations are of prime importance in the MEMS industry. Microdevices are ideal for micropositioning systems due to their small size. Microactuators used to produce small displacements would need large actuation forces and a long driving distance. This would require large voltages to produce the desired forces. Actuators based on impulsive forces provide a solution to this problem. Many impact microactuators have been designed and fabricated in the past decade. Impacts are a source of nonlinearity and a careful study of the dynamics is essential in order to ensure consistent performance of the device.

Click here to see the movie of an impact microactuator.

Atomic Force Microscopy

Tapping-mode atomic force microscopy has wide applications for probing the nanoscale surface and subsurface properties of a variety of materials in a variety of environments. Strongly nonlinear effects due to large variations in the force field on the probe tip over very small length scales and the intermittency of contact with the sample, however, result in strong dynamical instabilities. These can result in a sudden loss of stability of low-contact-velocity oscillations of the atomic-force-microscope tip in favor of oscillations with high contact velocity, coexistence of stable oscillatory motions, and destructive, nonrepeatable, and unreliable characterization of the nanostructure. This work employs dynamical systems tools for piecewise-smooth systems to characterize the loss of stability and associated parameter-hysteresis phenomena.