Bifurcation analyses of a mathematical model for human ventricular myocytes with applications to engineering of biological pacemaker systems

Abstract

We investigated the dynamical mechanisms of biological pacemaker (BP) generation in human ventricular myocytes (HVMs) by bifurcation analyses of a mathematical model. Equilibrium points (EPs), periodic orbits, stability of EPs, and bifurcation points were calculated as functions of conductance or amplitude of inward-rectifier K⁺ current (I_K1), L-type Ca²⁺ current (I_Ca,L), delayed-rectifier K⁺ current (I_K), Na⁺-Ca²⁺ exchanger current (I_NaCa) or constant bias current (I_bias) for constructing bifurcation diagrams. Pacemaker activity (stable limit cycle) abruptly appeared around an unstable EP via a saddle-node bifurcation, when I_K1 was suppressed by 84.6%. After the bifurcation, the I_K1-downregulated HVM has an unstable EP only, which is essentially important for stable BP generation. To elucidate how individual sarcolemmal currents contribute to EP instability and BP generation, we further explored the bifurcation structures of the system during decreases in each current. Our results suggest that 1) I_K1 suppression is necessary for creation of the BP cell system, 2) I_Ca,L is, but I_K or I_NaCa is not, responsible for EP instability as a requisite for stable BP generation, 3) I_K is indispensable for robust pacemaking with large amplitude, high upstroke velocity and stable frequency, and 4) I_NaCa is the dominant pacemaker current, but not necessarily required for BP oscillations. [Jpn J Physiol 55 Suppl:S91 (2005)]