The Transition Of Spiral Wave In The Network Induced By Ion Channel Poisoning

Spiral wave is a special class of patterns when the system is far away from equilibriumstate due to the system self-organized, spiral wave was observed in myocardium, cerebral andchemical reaction system. The spiral wave in myocardium can lead to tachycardia, isconsidered to be a mechanism of ventricular loss of flutter which could lead to sudden cardiacdeath. The existence of spiral wave in the cerebral cortex play an active role in informationprocessing and transmission in the biological systems, signals can be propagated in thequiescent domains by generating spiral wave. Therefore, it is important to study how toeliminate the harmful spiral wave and keep the useful. In this paper, the transition of spiralwave (dead, breakup) is discussed in detail due to ion channel poisoning, the formation ofspiral wave is also studied. Some theoretical values of bifurcation parameters such aspoisoning ratio, the size of poisoning area, the poisoning speed are approached. It’s moreprecise to describe the propagation of signals of nervous system by using two-dimensionalnetwork. Confirmed some of the organism’s reaction to the poisoning, for example someorganisms could maintain well under slight poisoning, while deep poisoning makes theneuron system loss part of functions, such as coma and loss of consciousness. The mainpoints are summarized as follows:First, studied the mathematical model of Hodgkin-Huxley neurons both based ontwo-dimensional network and small-world network. The effect of channel block is measuredby the poisoning ratio, which represents the fractions of working, e.g. non-blocked or activeion channels, to the overall number of potassium or sodium ion channels, respectively. Astatistical variable named synchronization factor is defined based on mean-field theory tomeasure the transition of spiral wave, small synchronization factor indicates survival of spiralwave. In regular networks follows are discussed in detail:1) The transition of spiral wave inall networks due to different poisoning ratio;2) The transition of spiral wave in localpoisoning due to different poisoning ratio;3) The transition of spiral wave induced byradiation poisoning. We also observed the transition of spiral wave in small-world networksdue to ion channel block.The study found that when channel noise is not considered the spiral wave dead and thenetwork becomes homogeneous in deep poisoning, the theoretical values of the poisoningratio of potassium and sodium is different when transition of spiral wave occurs; when weakchannel noise is considered indicates that the spiral wave breakup when in deep poisoning,the poisoning ratio of potassium and sodium is different.