  We present a hybrid vertex/cell-centred model for mechanically simulating
planar cellular monolayers undergoing cell reorganisation. Cell centres are
represented by a triangular nodal network, while the cell boundaries are formed
by an associated vertex network. The two networks are coupled through a
kinematic constraint which we allow to relax progressively. Special attention
is paid to the change of cell-cell connectivity due to cell reorganisation or
remodelling events. We handle these situations by using a variable resting
length and applying an Equilibrium-Preserving Mapping (EPM) on the new
connectivity, which computes a new set of resting lengths that preserve nodal
and vertex equilibrium. We illustrate the properties of the model by simulating
monolayers subjected to imposed extension and during a wound healing process.
The evolution of forces and the EPM are analysed during the remodelling events.
As a by-product, the proposed technique enables to recover fully vertex or
fully cell-centred models in a seamlessly manner by modifying a numerical
parameter of the model.
