ABSTRACT
Spiral waves occur in various types of excitable media and their dynamics determine the spatial excitation patterns. An important type of spiral wave dynamics is drift, as it can control the position of a spiral wave or eliminate a spiral wave by forcing it to the boundary. In theoretical and experimental studies of the Belousov-Zhabotinsky reaction, it was shown that the most direct way to induce the controlled drift of spiral waves is by application of an external electric field. Mathematically such drift occurs due to the onset of additional gradient terms in the Laplacian operator describing excitable media. However, this approach does not work for cardiac excitable tissue, where an external electric field does not result in gradient terms. In this paper, we propose a method of how to induce a directed linear drift of spiral waves in cardiac tissue, which can be realized as an optical feedback control in tissue where photosensitive ion channels are expressed. We illustrate our method by using the FitzHugh-Nagumo model for cardiac tissue and the generic model of photosensitive ion channels. We show that our method works for continuous and discrete light sources and can effectively move spiral waves in cardiac tissue, or eliminate them by collisions with the boundary or with another spiral wave. We finally implement our method by using a biophysically motivated photosensitive ion channel model included to the Luo-Rudy model for cardiac cells and show that the proposed feedback control also induces directed linear drift of spiral waves in a wide range of light intensities.
Subject(s)
Heart , Computer Simulation , FeedbackABSTRACT
The study was aimed to investigate the expression of Toll-like receptor 4 (TLR4) on platelets and to determine whether platelet TLR4 involves in its activation induced by lipopolysaccharide (LPS). Human platelet-rich plasma (PRP) and platelet suspension obtained from 15 healthy individuals pretreated with a concentration of 0.2 microg/ml of LPS in the presence or absence of thrombin (1 U/ml) for 1 hour. The expressions of TLR4, CD62P (P-select) and CD40L on platelets were detected by flow cytometry, and platelet TLR4 expression was further determined by Western blot analysis. The results indicated that the percentage of TLR4-positive platelets induced by thrombin was increased by 32.34% compared with the resting platelets (25.44%, p < 0.05). TLR4 expression on platelets treated with LPS was remarkably elevated in the presence or absence of thrombin. However, the expression level of the former was much higher than that of the latter and thrombin stimulation alone (p < 0.05). Moreover, the similar results were found in Western blot analysis. Synchronously, expressions of CD62P and CD40L on resting platelets were 6.39% and 2.45%, they were also markedly increased when treated with thrombin (42.68% and 14.8%) and LPS respectively, and the increases of expression of CD62P and CD40L were more significant when stimulated with both LPS and thrombin (63.03% and 13.94%). Although anti-TLR4 antibody inhibited significantly the increase of TLR4, CD62P and CD40L on platelets induced by LPS, which did not affect their increase induced by thrombin. In conclusion, the evidence has been shown that functional TLR4 can be expressed on human platelets. It may involve in platelet activation as an important mediator of LPS-induced CD62P and CD40L expressions on platelets.
