Biomedical Engineering Reference
In-Depth Information
cilia occurs even though all cilia have the same beating pattern and start with the
same initial conditions. This indicates that the synchronized state is not stable (at
least for the imposed boundary conditions). One should also be aware that, for ex-
ample, the wave length of the metachronal wave or the time it takes to synchronize
strongly depend on the prescribed microscopic force field driving the ciliar beating.
Figure 8.4.
In the three-dimensional model of Gueron et al. [35], beating cilia
spontaneously form metachronal waves, i.e., they beat with a constant phase lag.
Data is for same parameter values as in Figure 8.2. Figure is reprinted from [39].
Copyright (2001), with permission from The Royal Society.
Metachronal wave formation between two neighboring cilia has also been ob-
served numerically in [40]. There, it was also found that the filaments spontaneously
beat with a constant phase lag independent of the initial phase difference. The phase
lag depends on various parameters such as the persistence length.
8.3.2 A General Approach to Collective Effects in Ciliar Arrays
Although the specific models exhibit synchronization of ciliar beating, there is a
certain arbitrariness in prescribing the beating pattern of a cilium. In particular,
