  Left-right symmetry breaking is critical to vertebrate embryonic development;
in many species this process begins with cilia-driven flow in a structure
termed the `node'. Primary `whirling' cilia, tilted towards the posterior,
transport morphogen-containing vesicles towards the left, initiating left-right
asymmetric development. We review recent theoretical models based on the
point-force stokeslet and point-torque rotlet singularities, explaining how
rotation and surface-tilt produce directional flow. Analysis of image
singularity systems enforcing the no-slip condition shows how tilted rotation
produces a far-field `stresslet' directional flow, and how time-dependent
point-force and time-independent point-torque models are in this respect
equivalent. Associated slender body theory analysis is reviewed; this approach
enables efficient and accurate simulation of three-dimensional time-dependent
flow, time-dependence being essential in predicting features of the flow such
as chaotic advection, which have subsequently been determined experimentally. A
new model for the nodal flow utilising the regularized stokeslet method is
developed, to model the effect of the overlying Reichert's membrane. Velocity
fields and particle paths within the enclosed domain are computed and compared
with the flow profiles predicted by previous `membrane-less' models.
Computations confirm that the presence of the membrane produces flow-reversal
in the upper region, but no continuous region of reverse flow close to the
epithelium. The stresslet far-field is no longer evident in the membrane model,
due to the depth of the cavity being of similar magnitude to the cilium length.
Simulations predict that vesicles released within one cilium length of the
epithelium are generally transported to the left via a `loopy drift' motion,
sometimes involving highly unpredictable detours around leftward cilia
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