Topological constraint on scroll wave pinning

Scroll waves in an excitable medium rotate about tubelike filaments, whose ends, when they exist, can lie on the external boundary of the medium or be pinned to an inclusion. We derive a topological rule that governs such pin ning. It implies that some configurations cannot occur although they might otherwise have been expected. Heart tissue provides an application of these concepts. Computational illustrations based on a FitzHugh-Nagumo model are given.