Detecting the breakup of spiral waves in small-world networks of neurons due to channel block

• Published in: Chinese science bulletin Vol. 57; no. 17; pp. 2094 - 2101
• Main Authors: Ma, Jun, Huang, Long, Ying, HePing, Pu, ZhongSheng
• Format: Journal Article
• Language: English
• Published: Heidelberg Springer-Verlag 01.06.2012; SP Science China Press
• Subjects: brain; Chemistry/Food Science; Earth Sciences; Engineering; Humanities and Social Sciences; Life Sciences; multidisciplinary; neurons; Physics; potassium channels; Science; Science (multidisciplinary); sodium channels; 小世界网络; 检测; 河豚毒素; 测量通道; 神经元; 螺旋波; 钠离子通道; 钾离子通道; factor of synchronization; small-world networks; Hodgkin-Huxley neurons; spiral wave; channel block
• ISSN: 1001-6538; 1861-9541
• DOI: 10.1007/s11434-012-5114-2

The breakup of a spiral wave by blockade of sodium and potassium channels in a small-world network of Hodgkin-Huxley neu- rons is investigated in detail. The influence of ion channel block in poisoned excitable membrane patches of a certain size is measured, by varying channel noise and channel densities resulting from the change in conductance. For example, tetrae- thylammonium is known to cause a block （poisoning） of potassium channels, while tetrodotoxin blocks sodium channels. We observed the occurrence of spiral waves, which are ordered waves believed to play an important role in facilitating the propaga- tion of electric signals across quiescent regions of the brain. In this paper, the effect of channel block was measured by the factors xK and xN~, which represent the ratios of unblocked, or active, ion channels, to the overall number of potassium or sodium ion channels, respectively. To quantify these observations, we use a simple but robust synchronization measure, which succinctly captures the transition from spiral waves to other collective states, such as broken segments resulting from the breakup of the spiral wave. The critical thresholds of channel block can be inferred from the abrupt changes occurring in plots of the synchronization measure against different values of xK and xNa. Notably, small synchronization factors can be tightly associated with states where the formation of spiral waves is robust to mild channel block.