Genetically engineered cardiac pacemaker: stem cells transfected with HCN2 gene and myocytes - a model

Artificial biological pacemakers were developed and tested in canine ventricles. Next steps will require obtaining oscillations sensitive to external regulations, and robust with respect to long term drifts of expression levels of pacemaker currents and gap junctions. We introduce mathematical models intended to be used in parallel with the experiments. The models describe human mesenchymal stem cells ({\it hMSC}) transfected with HCN2 genes and connected to myocytes. They are intended to mimic experiments with oscillation induction in a cell pair, in cell culture and in the cardiac tissue. We give examples of oscillations in a cell pair, in a 1 dim cell culture, and oscillation dependence on number of pacemaker channels per cell and number of gap junctions. The models permit to mimic experiments with levels of gene expressions not achieved yet, and to predict if the work to achieve this levels will significantly increase the quality of oscillations. This give arguments for selecting the directions of the experimental work

Mechanism of Standing Wave Patterns in Cardiac Muscle

Recent experiments [R. A. Gray et al., Phys. Rev. Lett. 87, 168104 (2001)] have revealed striking standing wave patterns in cardiac muscle. In excitable media, such as cardiac tissue where colliding waves annihilate, standing wave patterns result from a fully nonlinear mechanism. We present a possible physical mechanism explaining these patterns. The phenomenon does not depend on the precise excitable model chosen. Analogies are drawn with weak links in superconductors, and phase-slip solutions in the Ginzburg-Landau equations