Panfilov A V, Keldermann R H, Nash M P
Department of Theoretical Biology, Utrecht University, Padualaan 8, Utrecht 3584 CH, The Netherlands.
Proc Natl Acad Sci U S A. 2007 May 8;104(19):7922-6. doi: 10.1073/pnas.0701895104. Epub 2007 Apr 27.
Rotating spiral waves organize excitation in various biological, physical, and chemical systems. They underpin a variety of important phenomena, such as cardiac arrhythmias, morphogenesis processes, and spatial patterns in chemical reactions. Important insights into spiral wave dynamics have been obtained from theoretical studies of the reaction-diffusion (RD) partial differential equations. However, most of these studies have ignored the fact that spiral wave rotation is often accompanied by substantial deformations of the medium. Here, we show that joint consideration of the RD equations with the equations of continuum mechanics for tissue deformations (RD-mechanics systems), yield important effects on spiral wave dynamics. We show that deformation can induce the breakup of spiral waves into complex spatiotemporal patterns. We also show that mechanics leads to spiral wave drift throughout the medium approaching dynamical attractors, which are determined by the parameters of the model and the size of the medium. We study mechanisms of these effects and discuss their applicability to the theory of cardiac arrhythmias. Overall, we demonstrate the importance of RD-mechanics systems for mathematics applied to life sciences.
旋转螺旋波在各种生物、物理和化学系统中组织激发。它们是多种重要现象的基础，如心律失常、形态发生过程以及化学反应中的空间模式。通过对反应扩散（RD）偏微分方程的理论研究，人们对螺旋波动力学有了重要的认识。然而，这些研究大多忽略了一个事实，即螺旋波旋转通常伴随着介质的显著变形。在这里，我们表明，将RD方程与组织变形的连续介质力学方程（RD-力学系统）联合考虑，会对螺旋波动力学产生重要影响。我们表明，变形可导致螺旋波破裂成复杂的时空模式。我们还表明，力学作用会导致螺旋波在整个介质中漂移，趋向于由模型参数和介质大小决定的动态吸引子。我们研究了这些效应的机制，并讨论了它们在心律失常理论中的适用性。总体而言，我们证明了RD-力学系统在应用于生命科学的数学中的重要性。
