Abstract
AbstractThe membrane current $$I_m$$
I
m
of the Hodgkin-Huxley (HH) cardiac Purkinje fiber (CPF) model is usually calculated as direct current (DC). In this paper, a conventional alternating current (AC) is used, namely $$I_{AC} = \textrm{Asin}(2 \pi ft)$$
I
AC
=
Asin
(
2
π
f
t
)
, as the impressed injection. Dynamic characters of the model with different AC parameters and various initial conditions are observed through phase plane orbits, waveforms, bifurcation diagrams, and Lyapunov exponent spectra, which reveal multiple coexisting membrane action potential patterns, corresponding to the coexisting attractors of the same or different periods in the phase diagram. Meanwhile, the model undergoes period, quasi-period and local forward or inverse period-doubling bifurcations with changes in amplitude A or frequency f, which further proves the complex nonlinear property of the AC-injected model. In addition, by changing the external current $$I_m$$
I
m
, the sodium-ion and potassium-ion equilibrium potentials, i.e. $$E_{Na}$$
E
Na
and $$E_{K}$$
E
K
, respectively, the regularity of the CPF heartbeat frequency is observed. The state transformations of CPF are found between normal, abnormal and sudden cardiac arrest, and the method adjusting from the dangerous state to the normal heartbeat frequency range is investigated. This study may provide a reference for exploring the evolution of nonlinear dynamics in HH CPF model and protecting the health of life and heart.
Funder
National Natural Science Foundation of China
Key Program of Natural Science Foundation of Jiangxi Province
Innovation Fund for Graduate Students in Jiangxi Province
Publisher
Springer Science and Business Media LLC
Subject
General Physics and Astronomy