Journal of Mathematical Biology

, Volume 56, Issue 4, pp 435–463 | Cite as

A bidomain threshold model of propagating calcium waves

  • R. Thul
  • G. D. Smith
  • S. Coombes


We present a bidomain fire-diffuse-fire model that facilitates mathematical analysis of propagating waves of elevated intracellular calcium (Ca2+) in living cells. Modeling Ca2+ release as a threshold process allows the explicit construction of traveling wave solutions to probe the dependence of Ca2+ wave speed on physiologically important parameters such as the threshold for Ca2+ release from the endoplasmic reticulum (ER) to the cytosol, the rate of Ca2+ resequestration from the cytosol to the ER, and the total [Ca2+] (cytosolic plus ER). Interestingly, linear stability analysis of the bidomain fire-diffuse-fire model predicts the onset of dynamic wave instabilities leading to the emergence of Ca2+ waves that propagate in a back-and-forth manner. Numerical simulations are used to confirm the presence of these so-called ‘tango waves’ and the dependence of Ca2+ wave speed on the total [Ca2+].


Bidomain models Calcium waves Stability Wave bifurcation 

Mathematics Subject Classification (2000)



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Copyright information

© Springer-Verlag 2007

Authors and Affiliations

  1. 1.Department of Mathematical SciencesUniversity of NottinghamNottinghamUK
  2. 2.Department of Applied ScienceThe College of William and MaryWilliamsburgUSA

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