  Mitosis in the early syncytial Drosophila embryo is highly correlated in
space and time, as manifested in mitotic wavefronts that propagate across the
embryo. In this paper we investigate the idea that the embryo can be considered
a mechanically-excitable medium, and that mitotic wavefronts can be understood
as nonlinear wavefronts that propagate through this medium. We study the
wavefronts via both image analysis of confocal microscopy videos and
theoretical models. We find that the mitotic waves travel across the embryo at
a well-defined speed that decreases with replication cycle. We find two markers
of the wavefront in each cycle, corresponding to the onsets of metaphase and
anaphase. Each of these onsets is followed by displacements of the nuclei that
obey the same wavefront pattern. To understand the mitotic wavefronts
theoretically we analyze wavefront propagation in excitable media. We study two
classes of models, one with biochemical signaling and one with mechanical
signaling. We find that the dependence of wavefront speed on cycle number is
most naturally explained by mechanical signaling, and that the entire process
suggests a scenario in which biochemical and mechanical signaling are coupled.
