The order parameter describes the orientational order of a liquid crystal : \(s = \left \langle \text{cos}(2 \theta)\right \rangle\); \(s = 0\;\) for a random sample and \(s = 1\;\) for an isotropic sample. \(\theta\;\) is the angle between the cell direction and the director. The director is a dimensionless unit vector. It represents the direction of preferred orientation of cells in the neighborhood of any point. Because there is no physical polarity along the director axis, n and -n are fully equivalent. Here the neighborhood is defined as a circle with center com and radius r.
Find the director of the center of mass of a cell.
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| Returns: | director (radians) |
Calculate order parameter for a morphology using the cpm grid data. When the requested radius is larger than the maximum radius of the grid, the global order parameter is calculated with getGlobalOrderParameter(); otherwise the local order parameter is calculated with getLocalOrderParameter().
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Calculate local order parameter.
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| Returns: | local order parameter |
See also
Calculate global order parameter.
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| Returns: | global order parameter |
Calculate field with relative director for each pixel. The relative director is the difference to the angle of the cell at that pixel and the relative director on the pixel. Pixels with high values represent unordered areas, such as branchpoints.
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| Returns: | field with relative director values |
See also
Clusters of aligned cells are automatically detected using the relative director field, with the following steps:
Remove all pixels that have a value in the relative director field higher than a given threshold.
- Detect blobs in remaining image with a labeling algorith:
- an opening operation may be performed before labeling.
- areas smaller than a given size are ignored;
- Map each blob on the CPM grid:
- at least a given fraction of the cell must be on the labeled area.
- Check for cells in multiple clusters:
- remove cell from all but biggest cluster;
- remove cluster if it is empty after (a).
Get clusters for a single morphology.
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| Returns: | dictionary with cluster id as key and Cluster instances |
See also
Container for a cell cluster
| Parameters: | id – cluster id |
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| Variables: | cells – list of ids of the cells in the clusters |
A class that holds properties related to a cell at each measured time step. These properties are:
- cluster id and size at each time step
- long axis at each time step
- center of mass at each time step
| Parameters: | id – cell id |
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The angle of a cell is calculated from the inertia tensor of a cell. From the intertia tensor we calucate the eigenvalues and eigenvectors; the eigenvector that corresponds with the largest eigenvalue represents the direction of the long axis of a cell. The angle between the long axis and the x-axis is the cell angle.
Get inertia tensor for a cell
| Parameters: | pix – cell coordinates ([x1,...,xn],[y1,...,yn]) |
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| Returns: | inertia tensor [[Ixx,Ixy],[Ixy,Iyy]] |
Calculate orientation of a cell. The orientation is the eigenvector corresponding to the largest eigenvalue of the cells’ inertia tensor.
| Parameters: | pix – cell coordinates ([x1,...,xn],[y1,...,yn]) |
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| Returns: | unit vector of the cell orientation |
See also
The mean squared displacement describes the displacement of a cell over time with respect to the initial position : \(MSD = \left \langle (x(t) - x(0))^2 \right \rangle\;\). In a similar manner the mean squared angular displacement can be calculated : \(MSD = \left \langle (\theta(t) - \theta(0))^2 \right \rangle\;\)