Contact Plugin

Contact plugin implements computations of adhesion energy between neighboring cells.

Together with volume constraint contact energy is one of the most commonly used energy terms in the GGH Hamiltonian. In essence it describes how cells “stick” to each other.

The explicit formula for the energy is:

\begin{eqnarray} E_{adhesion} = \sum_{i,j,neighbors} J\left ( \tau_{\sigma(i)},\tau_{\sigma(j)} \right )\left ( 1-\delta_{\sigma(i), \sigma(j)} \right ) \end{eqnarray}

where i and j label two neighboring lattice sites \(\sigma\)’s denote cell Ids, \(\tau\)’s denote cell types .

In the above formula, we need to differentiate between cell types and cell Ids. This formula shows that cell types and cell Ids are not the same. The Contact plugin in the .xml file, defines the energy per unit area of contact between cells of different types (\(J\left ( \tau_{\sigma(i)},\tau_{\sigma(j)} \right )\)) and the interaction range NeighborOrder of the contact:

<Plugin Name="Contact">
    <Energy Type1="Foam" Type2="Foam">3</Energy>
    <Energy Type1="Medium" Type2="Medium">0</Energy>
    <Energy Type1="Medium" Type2="Foam">0</Energy>

In this case, the interaction range is 2, thus only up to second nearest neighbor pixels of a pixel undergoing a change or closer will be used to calculate contact energy change. Foam cells have contact energy per unit area of 3 and Foam and Medium as well as Medium and Medium have contact energy of 0 per unit area. For more information about contact energy calculations see “Introduction to CompuCell3D”