1932

Abstract

Excitable media are ubiquitous in nature and can be found in physical, chemical, and biological systems that are far from thermodynamic equilibrium. The spatiotemporal self-organization of these systems has long attracted the deep interest of condensed matter physicists and applied mathematicians alike. Spatial inhomogeneity of excitable media leads to nontrivial spatiotemporal dynamics. Here, we report on well-established as well as recent developments in the experimental and theoretical studies of inhomogeneous excitable media.

Loading

Article metrics loading...

/content/journals/10.1146/annurev-conmatphys-033117-054300
2018-03-10
2024-06-24
Loading full text...

Full text loading...

/deliver/fulltext/conmatphys/9/1/annurev-conmatphys-033117-054300.html?itemId=/content/journals/10.1146/annurev-conmatphys-033117-054300&mimeType=html&fmt=ahah

Literature Cited

  1. Winfree AT. 1.  2000. The Geometry of Biological Time Berlin/Heidelberg: Springer [Google Scholar]
  2. Krinsky V, Swinney H. 2.  1991. Wave and Patterns in Biological and Chemical Excitable Media Amsterdam: North-Holland [Google Scholar]
  3. Kapral R, Showalter K. 3.  1995. Chemical Waves and Patterns Dordrecht, Neth.: Springer [Google Scholar]
  4. Zykov VS. 4.  1987. Simulation of Wave Processes in Excitable Media Manchester, UK: Manchester Univ. Press [Google Scholar]
  5. Mikhailov AS. 5.  1990. Foundation of Synergetics New York: Springer [Google Scholar]
  6. Kaplan D, Glass L. 6.  1995. Understanding Nonlinear Dynamics New York: Springer [Google Scholar]
  7. Izhikevich EM. 7.  2007. Dynamical Systems in Neuroscience: The Geometry of Excitability and Bursting Cambridge: MIT Press [Google Scholar]
  8. Sievers AJ, Takeno S. 8.  1998. Phys. Rev. Lett. 61:970 [Google Scholar]
  9. Maimistov AI. 9.  2010. Quantum Electron 40:756–81 [Google Scholar]
  10. Scott AC. 10.  1992. Phys. Rep. 217:1–67 [Google Scholar]
  11. Carmelier E, Vereecke J. 11.  2002. Cardiac Cellular Electrophysiology Dordrecht, Neth.: Kluwer [Google Scholar]
  12. Rosenbaum D, Jalife J. 12.  2001. Optical Mapping of Cardiac Excitation and Arrhythmias New York: Wiley-Blackwell [Google Scholar]
  13. Karma A. 13.  2013. Annu. Rev. Condens. Matter Phys. 4:313–37 [Google Scholar]
  14. Cirak1 F, Cisternas JE, Cuitio AM, Ertl G, Holmes P. 14.  et al. 2003. Science 300:1932–36 [Google Scholar]
  15. Adamatzky AI. 15.  1997. Adv. Mater. Opt. Electron. 7:263–72 [Google Scholar]
  16. Hodgkin AL, Huxley AF. 16.  1952. J. Physiol. 117:500–44 [Google Scholar]
  17. Noble D. 17.  1962. J. Physiol. 160:317–52 [Google Scholar]
  18. Fenton FH, Karma A. 18.  1998. Chaos 8:20–47 [Google Scholar]
  19. Field RJ, Noyes RM. 19.  1974. J. Chem. Phys. 60:1877–84 [Google Scholar]
  20. Martiel JL, Goldbeter A. 20.  1987. Biophys. J. 52:807–28 [Google Scholar]
  21. FitzHugh R. 21.  1961. Biophys. J. 1:445–66 [Google Scholar]
  22. Nagumo J, Arimoto S, Yoshizawa S. 22.  1962. Proc. Inst. Radio Eng. 50:2061–70 [Google Scholar]
  23. Tyson JJ, Fife PC. 23.  1980. J. Chem. Phys. 73:2224–37 [Google Scholar]
  24. Rinzel J, Keller JB. 24.  1973. Biophys. J. 13:1313–37 [Google Scholar]
  25. Barkley D. 25.  1991. Physica D 49:61–70 [Google Scholar]
  26. Tyson JJ, Keener JP. 26.  1988. Physica D 32:327–61 [Google Scholar]
  27. Zykov VS, Krekhov A, Bodenschatz E. 27.  2017. PNAS 114:1281–86 [Google Scholar]
  28. Janke W, Henze C, Winfree AT. 28.  1988. Nature 336:662–65 [Google Scholar]
  29. Fisher RA. 29.  1937. Ann. Eugen. 7:355–69 [Google Scholar]
  30. Kolmogorov AN, Petrovsky IG, Piskunov NS. 30.  1937. Bull. Moscow Univ., Math. Mech. 1:1–25 [Google Scholar]
  31. Zeldovich YB, Frank-Kaminetskii. 31.  1938. Zh. Fiz. Khim. 12:100–5 [Google Scholar]
  32. Casten R, Cohen H, Lagerstrom P. 32.  1975. Quart. Appl. Math. 32:365–402 [Google Scholar]
  33. Ortoleva P, Ross J. 33.  1975. J. Chem. Phys. 63:3398–408 [Google Scholar]
  34. Keener JP. 34.  1980. SIAM J. Appl. Math. 39:528–48 [Google Scholar]
  35. Dockery JD, Keener JP, Tyson JJ. 35.  1988. Physica D 30:177–91 [Google Scholar]
  36. Kessler DA, Levine H. 36.  1989. Physica D 39:1–14 [Google Scholar]
  37. Lewis TJ, Keener JP. 37.  2000. SIAM J. Appl. Math. 61:293–316 [Google Scholar]
  38. Keener JP, Sneyd J. 38.  2008. Mathematical Physiology New York: Springer [Google Scholar]
  39. Gao X, Zhang H, Zykov V, Bodenschatz E. 39.  2014. New J. Phys. 16:033012 [Google Scholar]
  40. Pauwelussen JP. 40.  1981. Physica D 4:67–88 [Google Scholar]
  41. Mornev OA. 41.  1984. Self-Organ. Autowaves Struct. Equilib. 28:111–18 [Google Scholar]
  42. Zemlin CW, Pertsov AM. 42.  2007. Europace 9:vi59–63 [Google Scholar]
  43. Zemlin CW, Mitera BG, Pertsov AM. 43.  2009. Physica D 238:969–75 [Google Scholar]
  44. Zykov V, Oikawa N, Bodenschatz E. 44.  2011. Phys. Rev. Lett. 107:254101 [Google Scholar]
  45. Zykov V, Bodenschatz E. 45.  2014. Phys. Rev. Lett. 112:054101 [Google Scholar]
  46. Meron E. 46.  1992. Phys. Rep. 218:1–66 [Google Scholar]
  47. Fox JJ, Gilmour RF, Bodenschatz E. 47.  2002. Phys. Rev. Lett. 89:198101 [Google Scholar]
  48. Fast VG, Kleber AG. 48.  1997. Cardiovasc. Res. 33:258–71 [Google Scholar]
  49. Steinbock O, Zykov VS, Müller SC. 49.  1993. Phys. Rev. E 48:3295–98 [Google Scholar]
  50. Kuhnert L, Agladze KI, Krinsky VI. 50.  1989. Nature 337:244–47 [Google Scholar]
  51. Zykov VS, Morozova OI. 51.  1980. Biophysics 24:739–44 [Google Scholar]
  52. Zykov VS. 52.  1980. Biophysics 25:906–11 [Google Scholar]
  53. Keener JP. 53.  1986. SIAM J. Appl. Math. 46:1039–56 [Google Scholar]
  54. Gomatam J, Hodson D. 54.  1991. Physica D 49:82–89 [Google Scholar]
  55. Davydov VA, Zykov VS. 55.  1991. Physica D 49:71–74 [Google Scholar]
  56. Zykov VS, Müller SC. 56.  1996. Physica D 97:322–32 [Google Scholar]
  57. Davydov VA, Manz N, Steinbock O, Zykov VS, Müller SC. 57.  2000. Phys. Rev. Lett. 85:868–71 [Google Scholar]
  58. Forester P, Müller SC, Hess B. 58.  1988. Science 241:685–87 [Google Scholar]
  59. Forester P, Müller SC, Hess B. 59.  1989. PNAS 86:6831–34 [Google Scholar]
  60. Forester P, Müller SC, Hess B. 60.  1990. J. Phys. Chem. 94:8859–61 [Google Scholar]
  61. Forester P, Müller SC, Hess B. 61.  1990. Development 109:11–16 [Google Scholar]
  62. Cabo C, Pertsov AM, Baxter WT, Davidenko JM, Gray RA, Jalife J. 62.  1994. Circ. Res. 75:1014–28 [Google Scholar]
  63. Zykov VS, Mikhailov AS, Müller SC. 63.  1998. Phys. Rev. Lett. 81:2811–14 [Google Scholar]
  64. Zykov VS, Müller SC. 64.  1998. Chaos Solitons Fractals 10:777–82 [Google Scholar]
  65. Zeldovich YaB, Barenblat GI, Librovich VB, Makhviladze GM. 65.  1985. Mathematical Theory of Combustion and Explosion New York: Consult. Bur. [Google Scholar]
  66. Horvath D, Showalter K. 66.  1995. J. Chem. Phys. 102:2471–78 [Google Scholar]
  67. Thul R, Falcke M. 67.  2004. Phys. Rev. Lett. 93:188103 [Google Scholar]
  68. Panfilov AV. 68.  2002. Phys. Rev. Lett. 88:118101 [Google Scholar]
  69. Ten Tusscher KHWJ, Panfilov AV. 69.  2003. Phys. Rev. E 68:062902 [Google Scholar]
  70. Ten Tusscher KHWJ, Panfilov AV. 70.  2003. Multiscale Model Simul 3:265–82 [Google Scholar]
  71. Keener J. 71.  2000. Physica D 136:1–17 [Google Scholar]
  72. Xin J. 72.  2000. SIAM Rev 42:161–230 [Google Scholar]
  73. Runborg O, Theodoropoulos C, Kevrekidis IG. 73.  2002. Nonlinearity 15:491–511 [Google Scholar]
  74. Shajahan TK, Borek B, Shrier A, Glass L. 74.  2011. Phys. Rev. E 84:046208 [Google Scholar]
  75. Alonso S, Kapral R, Bär M. 75.  2009. Phys. Rev. Lett. 102:238302 [Google Scholar]
  76. Alonso S, Bär M, Kapral R. 76.  2009. J. Chem. Phys. 131:214102 [Google Scholar]
  77. Alonso S, Löber J, Bär M, Engel H. 77.  2010. Eur. Phys. J. Spec. Top. 187:31–40 [Google Scholar]
  78. Agladze K, Aliev RR, Yamaguchi T, Yoshikawa K. 78.  1996. J. Phys. Chem. 100:13895–97 [Google Scholar]
  79. Sendina-Nadal I, De Castro M, Sagues F, Gomez-Gesteria M. 79.  2002. Phys. Rev. E 66:016215 [Google Scholar]
  80. Toth A, Gaspar V, Showalter K. 80.  1994. J. Phys. Chem. 98:522–31 [Google Scholar]
  81. Toth A, Showalter K. 81.  1995. J. Chem. Phys. 103:2058–66 [Google Scholar]
  82. Goldstein SS, Rall W. 82.  1974. Biophys. J. 14:731–57 [Google Scholar]
  83. Quiao L, Kevrekidis IG, Punckt C, Rotermund HH. 83.  2006. Phys. Rev. E 73:036219 [Google Scholar]
  84. Kogan BY, Karplus WJ, Billett BS, Stevenson WG. 84.  1992. Physica D 59:275–96 [Google Scholar]
  85. Wiener N, Rosenblueth A. 85.  1946. Arch. Inst. Cardiol. Mex. 16:205–65 [Google Scholar]
  86. Pertsov AM, Ermakova EA, Panfilov AV. 86.  1984. Physica D 14:117–24 [Google Scholar]
  87. Zykov VS, Bordyugov G, Lentz H, Engel H. 87.  2010. Physica D 239:797–807 [Google Scholar]
  88. Nakouzi E, Totz JF, Zhang Z, Steinbock O, Engel H. 88.  2016. Phys. Rev. E 93:022203 [Google Scholar]
  89. Biktashev VN, Barkley D, Biktasheva IV. 89.  2010. Phys. Rev. Lett. 104:058302 [Google Scholar]
  90. Löber J, Engel H. 90.  2013. Phys. Rev. E 93:022203 [Google Scholar]
  91. Gulko FB, Petrov AA. 91.  1972. Biophysics 17:261–66 [Google Scholar]
  92. Iyer AN, Gray RA. 92.  2001. Ann. Biomed. Eng. 29:47–59 [Google Scholar]
  93. Fenton FH, Cherry EM, Hastings HM, Evans SJ. 93.  2002. Chaos 12:852–92 [Google Scholar]
  94. Moe GK, Abildskov JA. 94.  1959. Am. Heart J. 58:59–70 [Google Scholar]
  95. Moe GK, Rheinboldt WC, Abildskov JA. 95.  1964. Am. Heart J. 67:200–20 [Google Scholar]
  96. Zykov VS, Petrov AA. 96.  1977. Biophysics 22:307–14 [Google Scholar]
  97. Panfilov AV, Keener JP. 97.  1993. J. Theor. Biol 163:439–48 [Google Scholar]
  98. Quail T, Shrier A, Glass L. 98.  2014. Phys. Rev. Lett. 113:158101 [Google Scholar]
  99. Agladze K, Keener JP, Müller SC, Panfilov AV. 99.  1994. Science 264:1746–48 [Google Scholar]
  100. Cabo C, Pertsov AM, Davidenko JM, Baxter WT, Gray RA, Jalife J. 100.  1996. Biophys. J. 70:1105–11 [Google Scholar]
  101. Bär M, Bandia AK, Kevrekidis IG, Haas G, Rotermund H-H, Ertl G. 101.  1996. J. Phys. Chem. 100:19106–17 [Google Scholar]
  102. Majumder R, Pandit R, Panfilov AV. 102.  2014. Am. J. Physiol. Heart Circ. Physiol. 307:H1024–35 [Google Scholar]
  103. Nattel S. 103.  2008. Circ. Res 102:1298–300 [Google Scholar]
  104. Davydov VA, Zykov VS, Mikhailov AS. 104.  1991. Sov. Phys. Usp. 34:665–84 [Google Scholar]
  105. Biktashev VN, Holden A. 105.  1994. J. Theor. Biol. 169:101–12 [Google Scholar]
  106. Hakim V, Karma A. 106.  1999. Phys. Rev. E 60:5073–105 [Google Scholar]
  107. Sandstede B, Scheel A, Wulf C. 107.  1999. J. Nonlin. Sci. 9:439–78 [Google Scholar]
  108. Zykov VS, Engel H. 108.  2007. World Sci. Lect. Notes Complex Syst. 5:243–72 [Google Scholar]
  109. Elkin YE, Biktashev VN. 109.  1999. J. Biol. Phys. 25:129–47 [Google Scholar]
  110. Wellner M, Pertsov AM, Jalife J. 110.  1999. Phys. Rev. E 59:5192–204 [Google Scholar]
  111. Biktasheva IV, Barkley D, Biktashev VN, Foulkers AJ. 111.  2010. Phys. Rev. E 81:066202 [Google Scholar]
  112. Kudryashova NN, Teplenin AS, Orlova YV, Selina LV, Agladze K. 112.  2004. J. Mol. Cell. Cardiol. 76:227–34 [Google Scholar]
  113. Kudryashova NN, Kazbanov IV, Panfilov AV, Agladze KI. 113.  2015. PLOS ONE 10:e0141832 [Google Scholar]
  114. Jimenez ZA, Marts B, Steinbock O. 114.  2009. Phys. Rev. Lett. 102:244101 [Google Scholar]
  115. Pertsov AM, Wellner M, Vinson M, Jalife J. 115.  2000. Phys. Rev. Lett. 84:2738–41 [Google Scholar]
  116. Dutta S, Steinbock O. 116.  2011. Phys. Chem. Lett. 2:945–49 [Google Scholar]
  117. Margerit D, Barkley D. 117.  2002. Chaos 12:636–49 [Google Scholar]
  118. Yakushevich LV. 118.  1984. Stud. Biophys. 100:195–200 [Google Scholar]
  119. Biktashev VN, Holden AV, Zhang H. 119.  1994. Philos. Trans. R. Soc. A 347:611–30 [Google Scholar]
  120. Alonso S, Bär M, Panfilov AV. 120.  2013. Bull. Math. Biol. 75:1351–76 [Google Scholar]
  121. Spreckelsen R, Hornung D, Steinbock O, Parlitz U, Luther S. 121.  2015. Phys. Rev. E 92:042920 [Google Scholar]
  122. Vinson M, Mironov S, Mulvey S, Pertsov A. 122.  1997. Nature 386:477–80 [Google Scholar]
  123. Amemiya T, Kettunen P, Kadar S, Yamaguchi T, Showalter K. 123.  1998. Chaos 8:872–78 [Google Scholar]
  124. Amemiya T, Kadar S, Kettunen P, Showalter K. 124.  1996. Phys. Rev. Lett. 77:3244–47 [Google Scholar]
  125. Adamatzky A, De Lacy Costello B. 125.  2002. Phys. Rev. E 66:046112 [Google Scholar]
/content/journals/10.1146/annurev-conmatphys-033117-054300
Loading
/content/journals/10.1146/annurev-conmatphys-033117-054300
Loading

Data & Media loading...

  • Article Type: Review Article
This is a required field
Please enter a valid email address
Approval was a Success
Invalid data
An Error Occurred
Approval was partially successful, following selected items could not be processed due to error