Wave propagation and blocking in inhomogeneous media

Discrete and Continuous Dynamical Systems

Volumn 13, Issue 4, 2005, Pages 843-876

  Aronson, D G ^a   Mantzaris, N V ^a,b   Othmer, H G ^a  

^a UNIVERSITY OF MINNESOTA   (United States)

^b Rice University   (United States)

Author keywords

Calcium waves; Discrete systems; Inhomogeneous media; Wave block

Indexed keywords

EID: 28444453655     PISSN: 10780947     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Review

References (21)

1. D. G. ARONSON AND H. F. WEINBERGER, Nonlinear diffusion in population genetics, combustion and nerve propagation, in Lecture Notes in Mathematics, Springer-Verlag, Berlin, 446, (1975), pp. 5-49.
2. _, Multidimensional nonlinear diffusions arising in population genetics, Adv. Math., 29 (1978), pp. 33-76.
3. S. BOITANO, E. R. DIRKSEN, AND M. J. SANDERSON, Intercellular propagation of calcium waves mediated by inositol trisphosphate, Science, 258 (1992), pp. 292-295.
4. A. C. CHARLES, C. C. G. NAUS, D. ZHU, G. M. KIDDER, E. R. DIRKSEN, AND M. J. SANDERSON, Intercellular calcium signalling via gap junctions in glioma cells, J. Cell Biol., 118 (1992), pp. 195-201.
5. M. O. ENKVIST AND K. D. MCCARTHY, Activation of protein kinase C blocks astroglial gap junction communication and inhibits the spread of calcium waves, J. Neurochem., 59 (1992), pp. 519-526.
6. T. D. HASSINGER, P. B. GUTHRIE, P. B. ATKINSON, M. V. L. BENNETT, AND S. B. KATER, An extracellular signaling component in propagation of astrocytic calcium waves, Proc. Nat. Acad. Sci., 93 (1996), pp. 13268-13273.
7. T. J. LEWIS AND J. P. KEENER, Wave-block in excitable media due to regions of depressed excitability, SIAM J. Appld. Math., 61 (2000), pp. 293-316.
8. H. MCKEAN, Nagumo's equation, Adv. Math., 4 (1970), pp. 209-223.
9. H. P. MCKEAN, Stabilization of solutions of a caricature of the Fitzhugh-Nagumo equation (2), Comm. Pure & Appld. Math., 37 (1984), pp. 299-301.
10. H. P. MCKEAN AND V. MOLL, Stabilization to the standing wave in a simple caricature of the nerve equation, Comm. Pure & Appld. Math., 39 (1986), pp. 485-529.
11. H. G. OTHMER, A continuum model for coupled cells, J. Math. Biol., 17 (1983), pp. 351-369.
12. J. P. PAUWELUSSEN, Nerve impulse propagation in a Branching nerve system: A simple model, Physica, 4D (1981), pp. 67-88.
13. J. RINZEL AND J. B. KELLER, Travelling wave solutions of a nerve conduction equation, Biophys. J., 13 (1973), pp. 1313-1337.
14. J. RINZEL AND D. TERMAN, Propagation phenomena in a bistable reaction-diffusion system, SIAM J. Appld. Math., 42 (1982), pp. 1111-1137.
15. J. SNEYD AND J. SHERRATT, On the propagation of calcium waves in an inhomogeneous medium, SIAM J. Appl. Math., 57 (1997), pp. 73-94.
16. J. SNEYD, M. WILKINS, A. STRAHONJA, AND M. J. SANDERSON, Calcium waves and oscillations driven by an intercellular gradient of inositol (1,4,5)-trisphosphate, Biophys. Chem., 72 (1998), pp. 101-109.
17. P. A. SPIRO AND H. G. OTHMER, The effect of heterogeneously-distributed ryR channels on calcium dynamics in cardiac myocytes, Bull. Math. Biol, 61 (1999), pp. 651-681.
18. A. VERKHRATSKY, R. K. ORKAND, AND H. KETTERMANN, Glial calcium: homeostasis and signaling function., Physiol. Rev., 78 (1998), pp. 99-141.
19. S. YAGODIN, L. A. HOLTZCLAW, AND J. T. RUSSELL, Subcellular calcium oscillators and calcium influx support agonist-induced calcium waves in cultured astrocytes, Mol. and Cell. Biochem., 149 (1995), pp. 137-144.
20. S. V. YAGODIN, L. HOLTZCLAW, C. A. SHEPPARD, AND J. T. RUSSELL, Nonlinear propagation of agonist-induced cytoplasmic calcium waves in single astrocytes, J. Neurobiol., 25 (1994), pp. 265-280.
21. J. YANG, S. KALLIADASIS, J. H. MERKIN, AND S. K. SCOTT, Wave propagation in spatially distributed exciable media, SIAM J. Appl. Math, 63 (2002), pp. 485-509.