Core objects¶
The Epithelium object¶

class
tyssue.
Epithelium
(identifier, datasets, specs=None, coords=None, maxbackup=5)¶ Base class defining a connective tissue in 2D or 3D.

property
Nc
¶ The number of cells in the epithelium.

property
Ne
¶ The number of edges in the epithelium.

property
Nf
¶ The number of faces in the epithelium.

property
Nv
¶ The number of vertices in the epithelium.

backup
()¶ Creates a copy of self and keeps a reference to it in the self._backups deque.

property
cell_df
¶ The cell
pd.DataFrame
containing cell associated data e.g. the position of their center or their volume

copy
(deep_copy=True)¶ Returns a copy of the epithelium
 deep_copybool, default True
if True, use a copy of the original object’s datasets to create the new object. If False, datasets are not copied

cut_out
(bbox, coords=None)¶ Returns the index of edges with at least one vertex outside of the bounding box
 bboxsequence of shape (dim, 2)
the bounding box as (min, max) pairs for each coordinates.
 coordslist of str of len dim, default None
the coords corresponding to the bbox.

property
edge_df
¶ The edge
pd.DataFrame
containing edge associated data e.g. their length.This dataframe also contains the whole connexion of the epithelium through the “srce”, “trgt”, “face”, “cell” indices. In 2D, a halfedge is associated with a single (face, srce, trgt) positively oriented triangle. In 3D, the (cell, face, srce, trgt) positively oriented terahedron is also unique.

property
face_df
¶ The face
pd.DataFrame
containing face associated data e.g. the position of their center or their area

face_polygons
(coords=None)¶ Returns a pd.Series of arrays with the coordinates the face polygons
Each element of the Series is a (num_sides, num_dims) array of points ordered counterclockwise.
Vertices are assumed to be ordered in a face. If you are not sure it is the case, you can run sheet.reset_index(order=True) before calling this function.

get_invalid
()¶ Returns a mask over self.edge_df for invalid faces.

get_neighborhood
(elem_id, order, elem='cell')¶ Returns elem_id neighborhood up to a degree of order
For example, if order is 2, it wil return the adjacent cells (or faces) and theses cells neighbors.
 neighborspd.DataFrame with two colums, the index
of the neighboring cell (face), and it’s neighboring order

get_neighbors
(elem_id, elem='cell')¶ Returns the indexes of the adjacent elements (cells or faces) of the element of index elem_id.
 elem_idint
the index of the central element (a face or a cell)
element : {‘cell’  ‘face’}, default ‘cell’
 neghborsset
the cells (or faces) sharing an edge with the central cell (face)

get_opposite_faces
()¶ Populates the ‘opposite’ column of self.face_df with the index of the opposite face or 1 if the face has no opposite.

get_orbits
(center, periph)¶ Returns a dataframe with a (center, edge) MultiIndex with periph elements.
 centerstr,
the name of the center element for example ‘face’, ‘srce’
 periphstr,
the name of the periphery elements, for example ‘trgt’, ‘cell’
>>> cell_verts = sheet.get_orbits('face', 'srce') >>> cell_verts.loc[45] edge 218 75 219 78 220 76 221 81 222 90 223 87 Name: srce, dtype: int64

get_valid
()¶ Set the ‘is_valid’ column to true if the faces are all closed polygons, and the cells closed polyhedra.

idx_lookup
(elem_id, element)¶ returns the current index of the element with the “id” column equal to elem_id
 elem_idint
id of the element to retrieve
 element{“vert””edge””face””cell”}
the corresponding dataset.

remove
(edge_out, trim_borders=False, order_edges=False)¶ Remove the edges indexed by edge_out associated with all the cells and faces containing those edges
If trim_borders is True (defaults to False), there will be a single border edge per border face.

reset_index
(order=False)¶ Resets the datasets to have continuous indices
If order is True (the default), sorts the edges such that for each face, vertices are ordered clockwize

reset_topo
()¶ Recomputes the number of sides for the faces and the number of faces for the cells.

restore
()¶ Resets the eptithelium data to its last backed up state
A copy of the current state prior to restoring is kept in the _bad attribute for inspection. Calling this method multiple times (without calling backup) will go back in the epithelium backups.

sanitize
(trim_borders=False, order_edges=False)¶ Removes invalid faces and associated vertices
If trim_borders is True (defaults to False), there will be a single border edge per border face.

set_bbox
(margin=0.0)¶ Sets the attribute bbox with pairs of values bellow and above the min and max of the vert coords, with a margin.

property
settings
¶ Accesses the specs[‘settings’] dictionnary.

sum_cell
(df)¶ Sums the values of the edgeindexed dataframe df grouped by the values of self.edge_df[“cell”]
summed :
pd.DataFrame
the summed data, indexed by the source vertices.

sum_face
(df)¶ Sums the values of the edgeindexed dataframe df grouped by the values of self.edge_df[“face”]
summed :
pd.DataFrame
the summed data, indexed by the source vertices.

sum_srce
(df)¶ Sums the values of the edgeindexed dataframe df grouped by the values of self.edge_df[“srce”]
summed :
pd.DataFrame
the summed data, indexed by the source vertices.

sum_trgt
(df)¶ Sums the values of the edgeindexed dataframe df grouped by the values of self.edge_df[“trgt”]
summed :
pd.DataFrame
the summed data, indexed by the source vertices.

triangular_mesh
(coords=None, return_mask=False)¶ Return a triangulation of an epithelial sheet (2D in a 3D space), with added edges between face barycenters and junction vertices.
 coordslist of str:
pair of coordinates corresponding to column names for self.face_df and self.vert_df
 return_maskbool, optional, default True
if True, returns face_mask
 vertices(self.Nf+self.Nv, 3) ndarray
all the vertices’ coordinates
 triangles(self.Ne, 3) ndarray of ints
triple of the vertices’ indexes forming the triangular elements. For each junction edge, this is simply the index (srce, trgt, face). This is correctly oriented.
 face_mask: (self.Nf + self.Nv,) mask with 1 iff the vertex corresponds
to a face center

upcast_cell
(df)¶ Reindexes input data to self.edge_df.index by repeating the values for each cell entry
 df
pd.DataFrame
,pd.Series
np.ndarray
or string The data to be upcasted. If array like, should have self.Nc elements. If a string is passed it should be a column of self.cell_df
 upcast_df
pd.DataFrame
orpd.Series
The value repeated like the values of self.edge_df[“cell”]
 df

upcast_cols
(element, columns)¶ Syntactic sugar to upcast from the epithelium datasets.
 element: {‘srce’’trgt’’face’’cell’}
corresponding self.edge_df column over which to index if element is ‘srce’ or ‘trgt’, the upcast data will be taken form self.vert_df
 columns: index
the column(s) to be taken from the input dataset.

upcast_face
(df)¶ Reindexes input data to self.edge_df.index by repeating the values for each face entry
 df
pd.DataFrame
,pd.Series
np.ndarray
or string The data to be upcasted. If array like, should have self.Nf elements. If a string is passed it should be a column of self.face_df
 upcast_df
pd.DataFrame
orpd.Series
The value repeated like the values of self.edge_df[“face”]
 df

upcast_srce
(df)¶ Reindexes input data to self.edge_df.index by repeating the values for each source entry.
 df
pd.DataFrame
,pd.Series
np.ndarray
or string The data to be upcasted. If array like, should have self.Nv elements. If a string is passed it should be a column of self.vert_df
 upcast_df
pd.DataFrame
orpd.Series
The value repeated like the values of self.edge_df[“srce”]
 df

upcast_trgt
(df)¶ Reindexes input data to self.edge_df.index by repeating the values for each target entry
 df
pd.DataFrame
,pd.Series
np.ndarray
or string The data to be upcasted. If array like, should have self.Nv elements. If a string is passed it should be a column of self.vert_df
 upcast_df
pd.DataFrame
orpd.Series
The value repeated like the values of self.edge_df[“trgt”]
 df

update_num_faces
()¶ Updates the number of faces around the cells. The data is registered in the “num_faces” column of self.cell_df.

update_num_sides
()¶ Updates the number of halfedges around the faces. The data is registered in the “num_sides” column of self.face_df.

update_rank
()¶

update_specs
(new, reset=False)¶ Recursively updates the self.specs nested dictionnary, and set the new values to the corresponding columns in the datasets. If reset is True, existing values will be overwritten.

validate
()¶ returns True if the mesh is validated
e.g. has only closed polygons and polyhedra

validate_closed_cells
()¶ Returns True if all cells of the epithelium are closed.

property
vert_df
¶ The face
pd.DataFrame
containing vertex associated data e.g. the position of each vertex.

vertex_mesh
(coords, vertex_normals=True)¶ Returns the vertex coordinates and a list of vertex indices for each face of the tissue. If vertex_normals is True, also returns the normals of each vertex (set as the average of the vertex’ edges), suitable for .OBJ export
Vertices are assumed to be ordered in a face. If you are not sure it is the case, you can run sheet.reset_index() before calling this function.

property
Sheet object¶

class
tyssue.
Sheet
(identifier, datasets, specs=None, coords=None)¶ An epithelial sheet, i.e a 2D mesh in a 2D or 3D space, akin to a HalfEdge data structure in CGAL.
The geometric properties are defined in tyssue.geometry.sheet_geometry A dynamical model derived from Fahradifar et al. 2007 is provided in tyssue.dynamics.sheet_vertex_model

extract
(face_mask, coords=['x', 'y', 'z'])¶ Extract a new sheet from the sheet that correspond to a key word that define a face.
face_mask : column name in face composed by boolean value coords :
 sheet_fold_patch_extract :
subsheet corresponding to the fold patch area.

extract_bounding_box
(x_boundary=None, y_boundary=None, z_boundary=None, coords=['x', 'y', 'z'])¶ Extracts a new sheet from the embryo sheet
that correspond to boundary coordinate define by the user.
x_boundary : pair of floats y_boundary : pair of floats z_boundary : pair of floats coords : list of strings, default [‘x’, ‘y’, ‘z’]
coordinates over which to crop the sheet
subsheet : a new
Sheet
object

get_extra_indices
()¶ Computes extra indices:
self.free_edges: halfedges at the epithelium boundary
self.dble_edges: halfedges inside the epithelium, with an opposite
self.east_edges: half of the dble_edges, pointing east (figuratively)
 self.west_edges: half of the dble_edges, pointing west
(the order of the east and west edges is conserved, so that the ith west halfedge is the opposite of the ith east halfedge)
 self.sgle_edges: joint index over free and east edges, spanning
the entire graph without double edges
 self.wrpd_edges: joint index over free edges followed by the
 east edges twice, such that a vector over the whole halfedge
dataframe is wrapped over the single edges
 self.srtd_edges: index over the whole halfedge sorted such that
the free edges come first, then the east, then the west
Also computes:  self.Ni: the number of inside full edges
(i.e. len(self.east_edges))
self.No: the number of outside full edges (i.e. len(self.free_edges))
self.Nd: the number of double half edges (i.e. len(self.dble_edges))
self.anti_sym: pd.Series with shape (self.Ne,) with 1 at the free and east halfedges and 1 at the opposite halfedges.
East and west is resepctive to some orientation at the moment the indices are computed the partition stays valid as long as there are no changes in the topology, so due to vertex displacement, ‘east’ and ‘west’ might not stay valid. This is just a practical naming convention.
As the name suggest, this method is not working for edges in 3D pointing exactly north or south, ie iff edge[‘dx’] == edge[‘dy’] == 0. Until we need or find a better solution, we’ll just assert it worked.

get_force_inference
(coords=None, column=None, free_border_edges=False)¶ Measure force based on Brodland method.
g_gamma_matrix*tension_vector = 0 Equation is homogenous and to avoid tension_vectors = 0, Construction and solve the constrained leastsquares equation system [[g_gamma_matrix.T g_gamma_matrix, C^T_1],
[C_1, 0]] où C1 = {1….1}
shape of g_gamma_matrix = (Ne/2, Nv*len(coords))
Note
Results might not be consistens for highly curved epithelium
coords: coordinates column: None, specify a column name in edge_df to put tension value free_border_edges: bool, default False, take into account edges in the border of the tissue if True
edges_tensions: tension values array if column not define

get_neighborhood
(face, order, elem='face')¶ Returns face neighborhood up to a degree of order.
For example, if order is 2, it wil return the adjacent, faces and theses faces neighbors.
 neighborspd.DataFrame with two colums, the index
of the neighboring face, and it’s neighboring order

get_neighbors
(face, elem='face')¶ Returns the faces adjacent to face.

get_opposite
()¶

classmethod
planar_sheet_2d
(identifier, nx, ny, distx, disty, noise=None)¶ Creates a planar sheet from an hexagonal grid of cells.
identifier : string nx, ny : int
number of cells in the x and y axes
 distx, distyfloat,
the distances in x and y between the cells
 noisefloat, default None
position noise on the hexagonal grid
 planar_sheet: a 2D
Sheet
instance in the (x, y) plane

classmethod
planar_sheet_3d
(identifier, nx, ny, distx, disty, noise=None)¶ Creates a planar sheet from an hexagonal grid of cells.
identifier : string nx, ny : int
number of cells in the x and y axes
 distx, distyfloat,
the distances in x and y between the cells
 noisefloat, default None
position noise on the hexagonal grid
flat_sheet: a 2.5D
Sheet
instance

reset_topo
()¶ Recomputes the number of sides for the faces and the number of faces for the cells.

sort_edges_eastwest
()¶ reorder edges such the free edges are first, then the first half of the double edges, then the other half of the double edges, this way, each subset of the edges dataframe are contiguous.

Monolayer object¶

class
tyssue.
Monolayer
(name, datasets, specs=None, coords=None)¶ 3D monolayer epithelium

property
apical_edges
¶

property
apical_faces
¶

property
apical_verts
¶

property
basal_edges
¶

property
basal_faces
¶

property
basal_verts
¶

classmethod
from_flat_sheet
(name, apical_sheet, specs, thickness=1)¶

get_sub_sheet
(segment)¶ Returns a
Sheet
object of the corresponding segmentsegment: str, the corresponding segment, wether ‘apical’ or ‘basal’

guess_face_segment
(face)¶ Infers the face segment.

guess_vert_segment
(vert)¶ Infers the vertex segment from its surrounding edges.

property
lateral_edges
¶

property
lateral_faces
¶

property
lateral_verts
¶

segment_index
(segment, element)¶

property
Drawing functions¶
Matplotlib based¶
Matplotlib based plotting

tyssue.draw.plt_draw.
create_gif
(history, output, num_frames=None, interval=None, draw_func=None, margin=5, **draw_kwds)¶ Creates an animated gif of the recorded history.
You need imagemagick on your system for this function to work.
history : a
tyssue.History
object output : path to the output gif file num_frames : int, the number of frames in the gif interval : tuples, define begin and end frame of the gif draw_func : a drawing functionthis function must take a sheet object as first argument and return a fig, ax pair. Defaults to quick_edge_draw (aka sheet_view with quick mode)
 marginint, the graph margins in percents, default 5
if margin is 1, let the draw function decide
**draw_kwds are passed to the drawing function

tyssue.draw.plt_draw.
curved_view
(sheet, radius_cutoff=1000.0)¶

tyssue.draw.plt_draw.
draw_edge
(sheet, coords, ax, **draw_spec_kw)¶

tyssue.draw.plt_draw.
draw_face
(sheet, coords, ax, **draw_spec_kw)¶ Draws epithelial sheet polygonal faces in matplotlib Keyword values can be specified at the element level as columns of the sheet.face_df

tyssue.draw.plt_draw.
draw_vert
(sheet, coords, ax, **draw_spec_kw)¶ Draw junction vertices in matplotlib.

tyssue.draw.plt_draw.
get_arc_data
(sheet)¶

tyssue.draw.plt_draw.
parse_face_specs
(face_draw_specs, sheet)¶

tyssue.draw.plt_draw.
plot_forces
(sheet, geom, model, coords, scaling, ax=None, approx_grad=None, **draw_specs_kw)¶ Plot the net forces at each vertex, with their amplitudes multiplied by scaling. To be clear, this is the oposite of the gradient  grad E.

tyssue.draw.plt_draw.
plot_junction
(eptm, edge_index, coords=['x', 'y'])¶ Plots local graph around a junction, for debugging purposes.

tyssue.draw.plt_draw.
plot_scaled_energies
(sheet, geom, model, scales, ax=None)¶ Plot scaled energies
sheet: a:class: Sheet object geom: a
Geometry
class model: a :class:’Model’ scales: np.linspace of floatfig: a :class:matplotlib.figure.Figure instance ax: :class:matplotlib.Axes instance, default None

tyssue.draw.plt_draw.
quick_edge_draw
(sheet, coords=['x', 'y'], ax=None, **draw_spec_kw)¶

tyssue.draw.plt_draw.
sheet_view
(sheet, coords=['x', 'y'], ax=None, **draw_specs_kw)¶ Base view function, parametrizable through draw_secs
The default sheet_spec specification is:
 {‘edge’: {
‘visible’: True, ‘width’: 0.5, ‘head_width’: 0.2, # arrow head width for the edges ‘length_includes_head’: True, # see matplotlib Arrow artist doc ‘shape’: ‘right’, ‘color’: ‘#2b5d0a’, # can be an array ‘alpha’: 0.8, ‘zorder’: 1, ‘colormap’: ‘viridis’},
 ‘vert’: {
‘visible’: True, ‘s’: 100, ‘color’: ‘#000a4b’, ‘alpha’: 0.3, ‘zorder’: 2},
 ‘face’: {
‘visible’: False, ‘color’: ‘#8aa678’, ‘alpha’: 1.0, ‘zorder’: 1} }
Ipyvolume based¶
3D visualisation inside the notebook.

tyssue.draw.ipv_draw.
browse_history
(history, coords=['x', 'y', 'z'], **draw_specs_kw)¶

tyssue.draw.ipv_draw.
edge_mesh
(sheet, coords, **edge_specs)¶ Creates a ipyvolume Mesh of the edge lines to be displayed in Jupyter Notebooks
mesh: a
ipyvolume.widgets.Mesh
mesh widget

tyssue.draw.ipv_draw.
face_mesh
(sheet, coords, **face_draw_specs)¶ Creates a ipyvolume Mesh of the face polygons

tyssue.draw.ipv_draw.
sheet_view
(sheet, coords=['x', 'y', 'z'], **draw_specs_kw)¶ Creates a javascript renderer of the edge lines to be displayed in Jupyter Notebooks
fig: a
ipyvolume.widgets.Figure
widget mesh: aipyvolume.widgets.Mesh
mesh widget

tyssue.draw.ipv_draw.
update_view
(fig, meshes)¶

tyssue.draw.ipv_draw.
view_ipv
(sheet, coords=['x', 'y', 'z'], **edge_specs)¶ Creates a javascript renderer of the edge lines to be displayed in Jupyter Notebooks
fig: a
ipyvolume.widgets.Figure
widget mesh: aipyvolume.widgets.Mesh
mesh widget
Geometry classes¶
Planar¶

class
tyssue.
PlanarGeometry
¶ Geomtetry methods for 2D planar cell arangements

static
face_projected_pos
(sheet, face, psi)¶ returns the sheet vertices position translated to center the face face at (0, 0) and rotated in the (x, y) plane by and angle psi radians

classmethod
get_phis
(sheet)¶

classmethod
update_all
(sheet)¶ Updates the sheet geometry by updating: * the edge vector coordinates * the edge lengths * the face centroids * the normals to each edge associated face * the face areas

static
update_areas
(sheet)¶ Updates the normal coordinate of each (srce, trgt, face) face.

static
update_normals
(sheet)¶

static
Sheet (2D 1/2)¶

class
tyssue.
SheetGeometry
¶ Geometry definitions for 2D sheets in 3D

static
face_projected_pos
(sheet, face, psi=0)¶ Returns the position of a face vertices projected on a plane perpendicular to the face normal, and translated so that the face center is at the center of the coordinate system
sheet: a :class:Sheet object face: int,
the index of the face on which to rotate the sheet
 psi: float,
Optional angle giving the rotation along the z axis
 rot_pos: pd.DataFrame
The rotated, relative positions of the face’s vertices

static
face_rotation
(sheet, face, psi=0)¶ Returns a 3D rotation matrix such that the face normal points in the z axis
sheet: a :class:Sheet object face: int,
the index of the face on which to rotate the sheet
 psi: float,
Optional angle giving the rotation along the new z axis
 rotation: (3, 3) np.ndarray
The rotation matrix

classmethod
face_rotations
(sheet, method='normal', output_as='edge')¶ Returns the (sheet.Ne, 3, 3) array of rotation matrices such that each rotation returns a coordinate system (u, v, w) where the face vertices are mostly in the u, v plane.
If method is ‘normal’, face is oriented with it’s normal along w if method is ‘svd’, the u, v, w is determined through singular value decompostion of the face vertices relative positions.
svd is slower but more effective at reducing face dimensionality.
 output_as: string, default ‘edge’ Return the (sheet.Ne, 3, 3),
else ‘face’ Return the (sheet.Nf, 3, 3)

classmethod
get_phis
(sheet, method='normal')¶ Returns the angle of the vertices in the plane perpendicular to each face normal. For nottoodeformed faces, sorting vertices by this gives clockwize orientation.
I think nottoodeformed means starconvex here.
The ‘method’ argument is passed to face_rotations

static
normal_rotations
(sheet, output_as='edge')¶ Returns the (sheet.Ne, 3, 3) array of rotation matrices such that each rotation aligns the coordinate system along each face normals
 output_as: string, default ‘edge’ Return the (sheet.Ne, 3, 3),
else ‘face’ Return the (sheet.Nf, 3, 3)

classmethod
reset_scafold
(sheet)¶ Recenters and (in the case of a rod sheet) resets the ab parameters and tip masks

static
svd_rotations
(sheet, output_as='edge')¶ Returns the (sheet.Ne, 3, 3) array of rotation matrices such that each rotation aligns the coordinate system according to each face vertex SVD
 output_as: string, default ‘edge’ Return the (sheet.Ne, 3, 3),
else ‘face’ Return the (sheet.Nf, 3, 3)

classmethod
update_all
(sheet)¶ Updates the sheet geometry by updating: * the edge vector coordinates * the edge lengths * the face centroids * the normals to each edge associated face * the face areas * the vertices heights (depends on geometry) * the face volumes (depends on geometry)

static
update_areas
(sheet)¶ Updates the normal coordniate of each (srce, trgt, face) face.

classmethod
update_height
(sheet)¶ Update the height of the sheet vertices, based on the geometry specified in the sheet settings:
sheet.settings[‘geometry’] can be set to
 cylindrical: the vertex height is
measured with respect to the distance to the the axis specified in sheet.settings[‘height_axis’] (e.g z)
 flat: the vertex height is
measured with respect to the position on the axis specified in sheet.settings[‘height_axis’]
 ‘spherical’: the vertex height is measured with respect to its
distance to the coordinate system centers
 ‘rod’: the vertex height is measured with respect to its
distance to the coordinate height axis if between the focii, and from the closest focus otherwise. The focii positions are updated before the height update.
In all the cases, this distance is shifted by an amount of sheet.vert_df[‘basal_shift’]

static
update_normals
(sheet)¶ Updates the face_df coords columns as the face’s vertices center of mass.

static
update_vol
(sheet)¶ Note that this is an approximation of the sheet geometry module.

static

class
tyssue.
ClosedSheetGeometry
¶ Geometry for a closed 2.5D sheet.
Apart from the geometry update from a normal sheet, the enclosed volume is also computed. The value is stored in sheet.settings[“lumen_vol”]

classmethod
update_all
(sheet)¶ Updates the sheet geometry by updating: * the edge vector coordinates * the edge lengths * the face centroids * the normals to each edge associated face * the face areas * the vertices heights (depends on geometry) * the face volumes (depends on geometry)

static
update_lumen_vol
(sheet)¶

classmethod

class
tyssue.geometry.sheet_geometry.
EllipsoidGeometry
¶ 
static
scale
(eptm, scale, coords)¶ Scales the coordinates coords by a factor delta

static
update_height
(eptm)¶ Update the height of the sheet vertices, based on the geometry specified in the sheet settings:
sheet.settings[‘geometry’] can be set to
 cylindrical: the vertex height is
measured with respect to the distance to the the axis specified in sheet.settings[‘height_axis’] (e.g z)
 flat: the vertex height is
measured with respect to the position on the axis specified in sheet.settings[‘height_axis’]
 ‘spherical’: the vertex height is measured with respect to its
distance to the coordinate system centers
 ‘rod’: the vertex height is measured with respect to its
distance to the coordinate height axis if between the focii, and from the closest focus otherwise. The focii positions are updated before the height update.
In all the cases, this distance is shifted by an amount of sheet.vert_df[‘basal_shift’]

static
Bulk (3D)¶

class
tyssue.
BulkGeometry
¶ Geometry functions for 3D cell arangements

classmethod
update_all
(eptm)¶ Updates the eptm geometry by updating: * the edge vector coordinates * the edge lengths * the face centroids * the normals to each edge associated face * the face areas * the cell areas * the vertices heights (depends on geometry) * the face volumes (depends on geometry)

static
update_areas
(eptm)¶ Updates the normal coordniate of each (srce, trgt, face) face.

static
update_centroid
(eptm)¶ Updates the face_df coords columns as the face’s vertices center of mass. Also updates the edge_df fx, fy, fz columns with their upcasted values

static
update_dcoords
(eptm)¶ Update the edge vector coordinates on the coords basis (default_coords by default). Modifies the corresponding columns (i.e [‘dx’, ‘dy’, ‘dz’]) in sheet.edge_df.
Also updates the upcasted coordinates of the source and target vertices

static
update_ucoords
(eptm)¶

static
update_vol
(eptm)¶

static
validate_face_norms
(eptm)¶

classmethod

class
tyssue.
MonolayerGeometry
¶ 
static
basal_apical_axis
(eptm, cell)¶ Returns a unit vector allong the apicalbasal axis of the cell

classmethod
cell_projected_pos
(eptm, cell, psi=0)¶ Returns the positions of the cell vertices transformed such that the cell center sits at the coordinate system’s origin and the basalapical axis is the new z axis.

static

class
tyssue.
ClosedMonolayerGeometry
¶ 
classmethod
update_all
(eptm)¶ Updates the eptm geometry by updating: * the edge vector coordinates * the edge lengths * the face centroids * the normals to each edge associated face * the face areas * the cell areas * the vertices heights (depends on geometry) * the face volumes (depends on geometry)

static
update_lumen_vol
(eptm)¶

classmethod
Topology functions¶
Base¶

tyssue.topology.base_topology.
add_vert
(eptm, edge)¶ Adds a vertex in the middle of the edge,
which is split as is its opposite(s)
eptm : a
Epithelium
instance edge : int the index of one of the halfedges to splitnew_vert : int the index to the new vertex new_edges : int or list of ints index to the new edge(s). For a sheet, returns a single index, for a 3D epithelium, returns the list of all the new parallel edges new_opp_edges : int or list of ints index to the new opposite edge(s). For a sheet, returns a single index, for a 3D epithelium, returns the list of all the new parallel edges
In the simple case whith two halfedge, returns indices to the new edges, with the following convention:
 s e t
——>
<—— *
oe
 s e ne t
—— —–>
 <—– * —— *
oe nv noe
where “e” is the passed edge as argument, “s” its source “t” its target and “oe” its opposite. The returned edges are the ones between the new vertex and the input edge’s original target.

tyssue.topology.base_topology.
close_face
(eptm, face)¶ Closes the face if a single edge is missing.
This function does not close the adjacent and opposite faces.

tyssue.topology.base_topology.
collapse_edge
(sheet, edge, reindex=True, allow_two_sided=False)¶ Collapses edge and merges it’s vertices, creating (or increasing the rank of) a rosette structure.
If reindex is True (the default), resets indexes and topology data. The edge is collapsed on the smaller of the srce, trgt indexes (to minimize reindexing impact)

tyssue.topology.base_topology.
condition_4i
(eptm)¶ Return an index over the faces violating condition 4 i in Okuda et al 2013, that is edges (from the same face) sharing two vertices simultaneously.

tyssue.topology.base_topology.
condition_4ii
(eptm)¶ Return an array of face pairs sharing more than two halfedges, as defined in Okuda et al. 2013 condition 4 ii
An indication way to solve this:
faces = condition_4ii(eptm) pairs = set(frozenset(p) for p in faces) cols = ['srce', 'trgt', 'face', 'cell', 'length', 'sub_area'] edges = eptm.edge_df[eptm.edge_df["face"].isin(faces[0])][cols].sort_values("face") all_edges = eptm.edge_df.loc[eptm.edge_df["face"].isin(set(faces.ravel())), cols].sort_values("face") all_edges['single'] = all_edges[["srce", "trgt"]].apply(frozenset, axis=1) ufaces = set(faces.ravel()) com_vs = set(all_edges.srce) for face in ufaces: com_vs = com_vs.intersection(all_edges.loc[all_edges["face"] == face, "srce"])

tyssue.topology.base_topology.
drop_two_sided_faces
(eptm)¶ Removes all the two (or one?) sided faces from the epithelium
Note that they are not collapsed, but simply eliminated Does not reindex

tyssue.topology.base_topology.
get_neighbour_face_pairs
(eptm)¶ Returns a pandas Series of neighboring face pairs (as forzen sets of 2 indexes)

tyssue.topology.base_topology.
get_num_common_edges
(eptm)¶ Returns the number of common edges between two neighboring faces this number is set to 1 if those faces are opposite and share the same edges.

tyssue.topology.base_topology.
merge_border_edges
(sheet, drop_two_sided=True)¶ Merge edges at the border of a sheet such that no vertex has only one incoming and one outgoing edge.

tyssue.topology.base_topology.
merge_vertices
(sheet, vert0, vert1, reindex=True)¶ Merge the two vertices vert0 and vert1 iff they are linked by an edge
If reindex is True (the default), resets indexes and topology data
It is more efficient to call directly collapse_edge

tyssue.topology.base_topology.
remove_face
(sheet, face)¶ Removes a face from the mesh.

tyssue.topology.base_topology.
split_vert
(sheet, vert, face, to_rewire, epsilon, recenter=False)¶ Creates a new vertex and moves it towards the center of face.
The edges in to_rewire will be connected to the new vertex.
sheet : a
tyssue.Sheet
instance vert : int, the index of the vertex to split face : int, the index of the face where to move the vertex to_rewire :pd.DataFrame
a subset of sheet.edge_dfwhere all the edges pointing to (or from) the old vertex will point to (or from) the new.
This will leave opened faces and cells
Sheet¶

tyssue.topology.sheet_topology.
cell_division
(sheet, mother, geom, angle=None)¶ Causes a cell to divide
sheet : a ‘Sheet’ instance mother : face index of target dividing cell geom : a 2D geometry angle : division angle for newly formed edge
daughter: face index of new cell
Function checks for perodic boundaries if there are, it checks if dividing cell rests on an edge of the periodic boundaries if so, it displaces the boundaries by a half a period and moves the target cell in the bulk of the tissue. It then performs cell division normally and reverts the periodic boundaries to the original configuration

tyssue.topology.sheet_topology.
face_division
(sheet, mother, vert_a, vert_b)¶ Divides the face associated with edges indexed by edge_a and edge_b, splitting it in the middle of those edes.

tyssue.topology.sheet_topology.
get_division_edges
(sheet, mother, geom, angle=None, axis='x')¶

tyssue.topology.sheet_topology.
resolve_t1s
(sheet, geom, model, solver, max_iter=60)¶

tyssue.topology.sheet_topology.
split_vert
(sheet, vert, face=None, multiplier=1.5, reindex=True, recenter=False, epsilon=None)¶ Splits a vertex towards the center of the face.
This operation removes the face face from the neighborhood of the vertex.

tyssue.topology.sheet_topology.
type1_transition
(sheet, edge01, *, remove_tri_faces=True, multiplier=1.5)¶ Performs a type 1 transition around the edge edge01
See ../../doc/illus/t1_transition.png for a sketch of the definition of the vertices and cells letterings See Finegan et al. for a description of the algotithm https://doi.org/10.1101/704932
sheet : a Sheet instance edge_01 : int
index of the edge around which the transition takes place
 epsilonfloat, optional, deprecated
default 0.1, the initial length of the new edge, in case “threshold_length” is not in the sheet.settings
 remove_tri_facesbool, optional
if True (the default), will remove triangular cells after the T1 transition is performed
 multiplierfloat, optional
default 1.5, the multiplier to the threshold length, so that the length of the new edge is set to multiplier * threshold_length
Bulk and Monolayer¶

tyssue.topology.bulk_topology.
HI_transition
(eptm, face)¶ H → I transition as defined in Okuda et al. 2013 (DOI 10.1007/s1023701204307). See tyssue/doc/illus/IH_transition.png for the algorithm

tyssue.topology.bulk_topology.
IH_transition
(eptm, edge)¶ I → H transition as defined in Okuda et al. 2013 (DOI 10.1007/s1023701204307). See tyssue/doc/illus/IH_transition.png for the algorithm

tyssue.topology.bulk_topology.
cell_division
(eptm, mother, geom, vertices=None, mother_verts=None, daughter_verts=None)¶

tyssue.topology.bulk_topology.
close_cell
(eptm, cell)¶ Closes the cell by adding a face. Assumes a single face is missing

tyssue.topology.bulk_topology.
find_HIs
(eptm, shorts=None)¶

tyssue.topology.bulk_topology.
find_IHs
(eptm, shorts=None)¶

tyssue.topology.bulk_topology.
find_rearangements
(eptm)¶ Finds the candidates for IH and HI transitions Returns —— edges_HI: set of indexes of short edges faces_IH: set of indexes of small triangular faces

tyssue.topology.bulk_topology.
fix_pinch
(eptm)¶ Due to rearangements, some faces in an epithelium will have more than one opposite face.
This method fixes the issue so we can have a valid epithelium back.

tyssue.topology.bulk_topology.
get_division_edges
(eptm, mother, plane_normal, plane_center=None, return_verts=False)¶ Returns an index of the mother cell edges crossed by the division plane, ordered clockwize around the division plane normal.

tyssue.topology.bulk_topology.
get_division_vertices
(eptm, division_edges=None, mother=None, plane_normal=None, plane_center=None, return_all=False)¶

tyssue.topology.bulk_topology.
remove_cell
(eptm, cell)¶ Removes a tetrahedral cell from the epithelium.

tyssue.topology.bulk_topology.
split_vert
(eptm, vert, face=None, multiplier=1.5)¶ Splits a vertex towards a face.
eptm : a
tyssue.Epithelium
instance vert : int the vertex to split face : int, optional, the face to splitif face is None, one face will be chosen at random
 multiplier: float, default 1.5
length of the new edge(s) in units of eptm.settings[“threshold_length”]
For a given face, we look for the adjacent cell with the lowest number of faces converging on the vertex. If this number is higher than 4 we raise a ValueError
If it’s 3, we do a OI transition, resulting in a new edge but no new faces If it’s 4, we do a IH transition, resulting in a new face and 2 ne edges.
see ../doc/illus/IH_transition.png

tyssue.topology.monolayer_topology.
cell_division
(monolayer, mother, orientation='vertical', psi=None)¶ Divides the cell mother in the monolayer.
monolayer: a
Monolayer
instancemother: int, the index of the cell to devide
orientation: str, {“vertical”  “horizontal”  “apical”} if “horizontal”, performs a division in the equatorial plane of the cell. If “vertical” (the default), performs a division along the basalapical axis of the cell. If “apical”, performs a division cutting the apical face perpendicularly to its principal axis
psi: float, default 0 extra rotation angle of the division plane around the basalapical plane
daughter: int, the index of the daughter cell

tyssue.topology.monolayer_topology.
find_basal_edge
(monolayer, apical_edge)¶ Returns the basal edge parallel to the apical edge passed in argument.
monolayer: a
Monolayer
instance
Dynamic models definitions¶
Gradients¶

tyssue.dynamics.base_gradients.
length_grad
(sheet)¶ returns (dx/l, dy/l, dz/l), ie grad_i(l_ij))

tyssue.dynamics.planar_gradients.
area_grad
(sheet)¶

tyssue.dynamics.planar_gradients.
lumen_area_grad
(eptm)¶
Base gradients for sheet like geometries

tyssue.dynamics.sheet_gradients.
area_grad
(sheet)¶

tyssue.dynamics.sheet_gradients.
height_grad
(sheet)¶
Base gradients for bulk geometry

tyssue.dynamics.bulk_gradients.
lumen_volume_grad
(eptm)¶ Calculates the gradient for the volume enclosed by the epithelium.
For a monolayer, it will by default compute the volume enclosed by the basal side (edges whose ‘segment’ column is “basal”). If the polarity is reversed and the apical side faces the lumen, this can be changed by setting eptm.settings[“lumen_side”] to ‘apical’

tyssue.dynamics.bulk_gradients.
volume_grad
(eptm)¶
Effectors and Model factory¶

tyssue.dynamics.factory.
model_factory
(effectors, ref_effector=None)¶ Produces a Model class with the provided effectors.
effectors : list of
effectors.AbstractEffectors
classes. ref_effector : optional, default Noneif passed, will be used for normalization, by default, the last effector in the list is used
 NewModela Model derived class with compute_enregy and compute_gradient
methods
Generic forces and energies

class
tyssue.dynamics.effectors.
AbstractEffector
¶ The effector class is used by model factories to construct a model.

dimensions
= None¶

element
= None¶

static
energy
(eptm)¶

static
get_nrj_norm
(specs)¶

static
gradient
(eptm)¶

label
= 'Abstract effector'¶

magnitude
= None¶

spatial_ref
= (None, None)¶

specs
= {'cell': {}, 'edge': {}, 'face': {}, 'vert': {}}¶

temporal_ref
= (None, None)¶


class
tyssue.dynamics.effectors.
BarrierElasticity
¶ Barrier use to maintain the tissue integrity.

dimensions
= array(1.) * fJ/um**2¶

element
= 'vert'¶

static
energy
(eptm)¶

static
gradient
(eptm)¶

label
= 'Barrier elasticity'¶

magnitude
= 'barrier_elasticity'¶

specs
= {'vert': {'barrier_elasticity': 1.0, 'delta_rho': 0.0, 'is_active': 1}}¶


class
tyssue.dynamics.effectors.
BorderElasticity
¶ 
dimensions
= array(1.) * fJ/um**2¶

element
= 'edge'¶

static
energy
(eptm)¶

static
get_nrj_norm
(specs)¶

static
gradient
(eptm)¶

label
= 'Border edges elasticity'¶

magnitude
= 'border_elasticity'¶

spatial_ref
= ('prefered_length', UnitLength('micrometer', 0.001 * mm, 'um'))¶

specs
= {'edge': {'border_elasticity': 1.0, 'is_active': 1, 'is_border': 1.0, 'length': 1.0, 'prefered_length': 1.0}}¶


class
tyssue.dynamics.effectors.
CellAreaElasticity
¶ 
dimensions
= array(1.) * fJ/um**4¶

element
= 'cell'¶

static
energy
(eptm)¶

static
get_nrj_norm
(specs)¶

static
gradient
(eptm)¶

label
= 'Area elasticity'¶

magnitude
= 'area_elasticity'¶

spatial_ref
= ('prefered_area', array(1.) * um**2)¶

specs
= {'cell': {'area': 1.0, 'area_elasticity': 1.0, 'is_alive': 1, 'prefered_area': 1.0}}¶


class
tyssue.dynamics.effectors.
CellVolumeElasticity
¶ 
dimensions
= array(1.) * fJ/um**6¶

element
= 'cell'¶

static
energy
(eptm)¶

static
get_nrj_norm
(specs)¶

static
gradient
(eptm)¶

label
= 'Volume elasticity'¶

magnitude
= 'vol_elasticity'¶

spatial_ref
= ('prefered_vol', array(1.) * um**3)¶

specs
= {'cell': {'is_alive': 1, 'prefered_vol': 1.0, 'vol': 1.0, 'vol_elasticity': 1.0}}¶


class
tyssue.dynamics.effectors.
FaceAreaElasticity
¶ 
dimensionless
= False¶

dimensions
= array(1.) * fJ/um**4¶

element
= 'face'¶

static
energy
(eptm)¶

static
get_nrj_norm
(specs)¶

static
gradient
(eptm)¶

label
= 'Area elasticity'¶

magnitude
= 'area_elasticity'¶

spatial_ref
= ('prefered_area', array(1.) * um**2)¶

specs
= {'edge': {'sub_area': 0.16666666666666666}, 'face': {'area': 1.0, 'area_elasticity': 1.0, 'is_alive': 1, 'prefered_area': 1.0}}¶


class
tyssue.dynamics.effectors.
FaceContractility
¶ 
dimensions
= array(1.) * fJ/um**2¶

element
= 'face'¶

static
energy
(eptm)¶

static
gradient
(eptm)¶

label
= 'Contractility'¶

magnitude
= 'contractility'¶

spatial_ref
= ('mean_perimeter', UnitLength('micrometer', 0.001 * mm, 'um'))¶

specs
= {'face': {'contractility': 1.0, 'is_alive': 1, 'perimeter': 1.0}}¶


class
tyssue.dynamics.effectors.
FaceVolumeElasticity
¶ 
dimensions
= array(1.) * fJ/um**6¶

element
= 'face'¶

static
energy
(eptm)¶

static
get_nrj_norm
(specs)¶

static
gradient
(eptm)¶

label
= 'Volume elasticity'¶

magnitude
= 'vol_elasticity'¶

spatial_ref
= ('prefered_vol', array(1.) * um**3)¶

specs
= {'edge': {'sub_area': 0.16666666666666666}, 'face': {'is_alive': 1, 'prefered_vol': 1.0, 'vol': 1.0, 'vol_elasticity': 1.0}, 'vert': {'height': 1.0}}¶


class
tyssue.dynamics.effectors.
LengthElasticity
¶ Elastic half edge

dimensions
= array(1.) * fJ/um**2¶

element
= 'edge'¶

static
energy
(eptm)¶

static
get_nrj_norm
(specs)¶

static
gradient
(eptm)¶

label
= 'Length elasticity'¶

magnitude
= 'length_elasticity'¶

spatial_ref
= ('prefered_length', UnitLength('micrometer', 0.001 * mm, 'um'))¶

specs
= {'edge': {'is_active': 1, 'length': 1.0, 'length_elasticity': 1.0, 'prefered_length': 1.0, 'ux': 0.5773502691896257, 'uy': 0.5773502691896257, 'uz': 0.5773502691896257}}¶


class
tyssue.dynamics.effectors.
LineTension
¶ 
dimensions
= array(1.) * fJ/um¶

element
= 'edge'¶

static
energy
(eptm)¶

static
gradient
(eptm)¶

label
= 'Line tension'¶

magnitude
= 'line_tension'¶

spatial_ref
= ('mean_length', UnitLength('micrometer', 0.001 * mm, 'um'))¶

specs
= {'edge': {'is_active': 1, 'line_tension': 1.0}}¶


class
tyssue.dynamics.effectors.
LineViscosity
¶ 
dimensions
= array(1.) * s*nN/um¶

element
= 'edge'¶

static
gradient
(eptm)¶

label
= 'Linear viscosity'¶

magnitude
= 'edge_viscosity'¶

spatial_ref
= ('mean_length', UnitLength('micrometer', 0.001 * mm, 'um'))¶

specs
= {'edge': {'edge_viscosity': 1.0, 'is_active': 1}}¶

temporal_ref
= ('dt', UnitTime('second', 's'))¶


class
tyssue.dynamics.effectors.
LumenAreaElasticity
¶ ..math:
rac{K_Y}{2}(A_{mathrm{lumen}}  A_{0,mathrm{lumen}})^2

dimensions
= array(1.) * fJ/um**4¶

element
= 'settings'¶

static
energy
(eptm)¶

static
gradient
(eptm)¶

label
= 'Lumen volume constraint'¶

magnitude
= 'lumen_elasticity'¶

spatial_ref
= ('lumen_prefered_vol', array(1.) * um**2)¶

specs
= {'settings': {'lumen_elasticity': 1.0, 'lumen_prefered_vol': 1.0, 'lumen_vol': 1.0}}¶


class
tyssue.dynamics.effectors.
LumenVolumeElasticity
¶ Global volume elasticity of the object. For example the volume of the yolk in the Drosophila embryo

dimensions
= array(1.) * fJ/um**6¶

element
= 'settings'¶

static
energy
(eptm)¶

static
get_nrj_norm
(specs)¶

static
gradient
(eptm)¶

label
= 'Lumen volume elasticity'¶

magnitude
= 'lumen_vol_elasticity'¶

spatial_ref
= ('lumen_prefered_vol', array(1.) * um**3)¶

specs
= {'settings': {'lumen_prefered_vol': 1.0, 'lumen_vol': 1.0, 'lumen_vol_elasticity': 1.0}}¶


class
tyssue.dynamics.effectors.
PerimeterElasticity
¶ From Mapeng Bi et al. https://doi.org/10.1038/nphys3471

dimensions
= array(1.) * fJ/um**2¶

element
= 'face'¶

static
energy
(eptm)¶

static
gradient
(eptm)¶

label
= 'Perimeter Elasticity'¶

magnitude
= 'perimeter_elasticity'¶

spatial_ref
= ('prefered_perimeter', UnitLength('micrometer', 0.001 * mm, 'um'))¶

specs
= {'face': {'is_alive': 1, 'perimeter': 1.0, 'perimeter_elasticity': 0.1, 'prefered_perimeter': 3.81}}¶


class
tyssue.dynamics.effectors.
RadialTension
¶ Apply a tension perpendicular to a face.

dimensions
= array(1.) * fJ/um¶

element
= 'face'¶

static
energy
(eptm)¶

static
gradient
(eptm)¶

label
= 'Apical basal tension'¶

magnitude
= 'radial_tension'¶

specs
= {'face': {'height': 1.0, 'radial_tension': 1.0}}¶


class
tyssue.dynamics.effectors.
SurfaceTension
¶ 
dimensions
= array(1.) * fJ/um**2¶

element
= 'face'¶

static
energy
(eptm)¶

static
gradient
(eptm)¶

label
= 'Surface tension'¶

magnitude
= 'surface_tension'¶

spatial_ref
= ('prefered_area', array(1.) * um**2)¶

specs
= {'face': {'area': 1.0, 'is_active': 1, 'surface_tension': 1.0}}¶


tyssue.dynamics.effectors.
dimensionalize
(nondim_specs, dim_specs, effector, ref_effector)¶

tyssue.dynamics.effectors.
elastic_energy
(element_df, var, elasticity, prefered)¶

tyssue.dynamics.effectors.
elastic_force
(element_df, var, elasticity, prefered)¶

tyssue.dynamics.effectors.
normalize
(dim_specs, nondim_specs, effector, ref_effector)¶

tyssue.dynamics.effectors.
scaler
(nondim_specs, dim_specs, effector, ref_effector)¶
Predefined models¶
Vertex model for an Epithelial sheet (see definitions).
Depends on the sheet vertex geometry functions.
Specific functions for apoptosis vertex model

class
tyssue.dynamics.apoptosis_model.
ApicoBasalTension
¶ Effector for the apicalbasal tension.
The energy is proportional to the heigth of the cell

dimensions
= array(1.) * fJ/um**2¶

element
= 'vert'¶

static
energy
(sheet)¶

static
gradient
(sheet)¶

label
= 'Apicalbasal tension'¶

magnitude
= 'radial_tension'¶

specs
= {'vert': {'height': 1.0, 'is_active': 1, 'radial_tension': 0.0}}¶

Dynamical models for monlayer and bulk epithelium.

class
tyssue.dynamics.bulk_model.
LaminaModel
¶ Not implemented yet
Quasistatic solver¶
Epithelium generation utilities¶
The generation module provides utilities to easily create Epithelium
objects.

class
tyssue.generation.shapes.
AnnularSheet
(identifier, datasets, specs=None, coords=None)¶ 2D annular model of a cylinderlike monolayer.
Provides syntactic sugar to access the apical, basal and lateral segments of the epithlium

property
apical_edges
¶

property
apical_verts
¶

property
basal_edges
¶

property
basal_verts
¶

property
lateral_edges
¶

reset_topo
()¶ Recomputes the number of sides for the faces and the number of faces for the cells.

segment_index
(segment, element)¶

property

tyssue.generation.shapes.
Lloyd_relaxation
(sheet, geom, steps=10, coords=None, update_method=None)¶ Performs Lloyd relaxation on the sheet.

tyssue.generation.shapes.
ellipse_rho
(theta, a, b)¶

tyssue.generation.shapes.
ellipsoid_sheet
(a, b, c, n_zs, **kwargs)¶ Creates an ellipsoidal apical mesh.
 a, b, cfloats
Size of the ellipsoid half axes in the x, y, and z directions, respectively
 n_zsint
The (approximate) number of faces along the z axis.
kwargs are passed to get_ellipsoid_centers
eptm : a
Epithelium
objectThe mesh returned is an Epithelium and not a simpler Sheet so that a unique cell data can hold information on the whole volume of the ellipsoid.

tyssue.generation.shapes.
generate_ring
(Nf, R_in, R_out, R_vit=None, apical='in')¶ Generates a 2D tyssue object aranged in a ring of Nf tetragonal cells with inner diameter R_in and outer diameter R_out
 Nfint
The number of cells in the tissue
 R_infloat
The inner ring diameter
 R_outfloat
The outer ring diameter
 R_vitfloat
The vitelline membrane diameter (a non strechable membrane around the annulus)
 apicalstr {‘in’  ‘out’}
The side of the apical surface if “in”, the apical surface is inside the annulus, facing the lumen as in an organoid; if ‘out’: the apical side is facing the exterior of the tissue, as in an embryo
 eptm
AnnularSheet
2D annular tissue. The R_in and R_out parameters are stored in the class settings attribute.

tyssue.generation.shapes.
get_ellipsoid_centers
(a, b, c, n_zs, pos_err=0.0, phase_err=0.0)¶ Creates hexagonaly organized points on the surface of an ellipsoid
 a, b, c: float
ellipsoid radii along the x, y and z axes, respectively i.e the ellipsoid boounding box will be [[a, a], [b, b], [c, c]]
 n_zsfloat
number of cells on the z axis, typical
 pos_errfloat, default 0.
normaly distributed noise of std. dev. pos_err is added to the centers positions
 phase_errfloat, default 0.
normaly distributed noise of std. dev. phase_err is added to the centers angle ϕ

tyssue.generation.shapes.
sheet_from_cell_centers
(points, noise=0, interp_s=0.0001)¶ Returns a Sheet object from the Voronoï tessalation of the cell centers.
The strategy is to project the points on a sphere, get the Voronoï tessalation on this sphere and reproject the vertices on the original (implicit) surface through linear interpolation of the cell centers.
Works for relatively smooth surfaces (at the very minimum star convex).
 pointsnp.ndarray of shape (Nf, 3)
the x, y, z coordinates of the cell centers
 noisefloat, default 0.0
addiditve normal noise stdev
 interp_sfloat, default 1e4
interpolation smoothing factor (might need to set higher)
sheet : a
Sheet
object with Nf faces

tyssue.generation.shapes.
spherical_monolayer
(R_in, R_out, Nc, apical='out', Lloyd_relax=False)¶ Returns a spherical monolayer with the given inner and outer radii, and approximately the gieven number of cells.
The apical argument can be ‘in’ out ‘out’ to specify wether the apical face of the cells faces inward or outward, reespectively.

tyssue.generation.shapes.
spherical_sheet
(radius, Nf, Lloyd_relax=False, **kwargs)¶ Returns a spherical sheet with the given radius and (approximately) the given number of cells

tyssue.generation.shapes.
update_on_sphere
(sheet)¶
This module provides utlities to modify an input tissue through extrusion or subdivision

tyssue.generation.modifiers.
create_anchors
(sheet)¶ Adds an edge linked to every vertices at the boundary and create anchor vertices

tyssue.generation.modifiers.
extrude
(apical_datasets, method='homotecy', scale=0.3, vector=[0, 0,  1])¶ Extrude a sheet to form a monlayer epithelium
apical_datasets: dictionnary of three DataFrames,
‘vert’, ‘edge’, ‘face’ * method: str, optional {‘homotecy’’translation’’normals’} default ‘homotecy’ * scale: float, optional the scale factor for homotetic scaling, default 0.3. * vector: sequence of three floats, optional, used for the translation
default [0, 0, 1]
if method == ‘homotecy’, the basal layer is scaled down from the apical one homoteticaly w/r to the center of the coordinate system, by a factor given by scale
if method == ‘translation’, the basal vertices are translated from the apical ones by the vector vect
if method == ‘normals’, basal vertices are translated from the apical ones along the normal of the surface at each vertex, by a vector whose size is given by scale

tyssue.generation.modifiers.
subdivide_faces
(eptm, faces)¶ Adds a vertex at the center of each face, and returns a new dataset
eptm: a
Epithelium
instance faces: list,indices of the faces to be subdivided
 new_dset: dict
a dataset with the new faces devided
Hexagonal grids¶

tyssue.generation.hexagonal_grids.
circle
(num_t, radius=1.0, phase=0.0)¶ Returns x and y positions of num_t points regularly placed around a circle of radius radius, shifted by phase radians.
 num_tint
the number of points around the circle
 radiusfloat, default 1.
the radius of the circle
 phasefloat, default 0.0
angle shift w/r to the x axis in radians
points : np.Ndarray of shape (num_t, 2), the x, y positions of the points

tyssue.generation.hexagonal_grids.
hexa_cylinder
(num_t, num_z, radius=1.0, capped=False, noise=0, orientation='transverse')¶ Returns an arrays of x, y positions of points evenly spread on a cylinder with num_t points on the periphery and num_z points on its length.
 num_tint,
The number of points on the periphery
 num_zint,
The number of points along the z axis (the length of the cylinder)
 radiusfloat, default 1
The radius of the cylinder
 cappedbool, default False
If True, the tips of the cylinder are capped by a disk of point as generated by the hexa_disk function.
 noisefloat, default 0
normaly distributed position noise around the cell points
 orientation{‘transverse’  ‘longitudinal’}, default ‘transverse’
the orientation of the cells (with the longueur axis perpendicular or along the length of the cylinder)

tyssue.generation.hexagonal_grids.
hexa_disk
(num_t, radius=1)¶ Returns an arrays of x, y positions of points evenly spread on a disk with num_t points on the periphery.
 num_tint
the number of poitns on the disk periphery, the rest of the disk is filled automaticaly
 radiusfloat, default 1.
the radius of the disk

tyssue.generation.hexagonal_grids.
hexa_grid2d
(nx, ny, distx, disty, noise=None)¶ Creates an hexagonal grid of points

tyssue.generation.hexagonal_grids.
hexa_grid3d
(nx, ny, nz, distx=1.0, disty=1.0, distz=1.0, noise=None)¶ Creates an hexagonal grid of points

tyssue.generation.hexagonal_grids.
three_faces_sheet
(zaxis=False)¶ Creates the apical junctions mesh of three packed hexagonal faces. If zaxis is True (defaults to False), adds a z coordinates, with z = 0.
Faces have a side length of 1.0 +/ 1e3.
face_df: the faces DataFrame indexed from 0 to 2 vert_df: the junction vertices DataFrame edge_df: the junction edges DataFrame

tyssue.generation.hexagonal_grids.
three_faces_sheet_array
()¶ Creates the apical junctions mesh of three packed hexagonal faces. If zaxis is True (defaults to False), adds a z coordinates, with z = 0.
Faces have a side length of 1.0 +/ 1e3.
 points: (13, ndim) np.array of floats
the positions, where ndim is 2 or 3 depending on zaxis
 edges: (15, 2) np.array of ints
indices of the edges
 (Nc, Nv, Ne): triple of ints
number of faces, vertices and edges (3, 13, 15)

tyssue.generation.from_voronoi.
from_2d_voronoi
(voro, specs=None)¶ Creates 2D (sheet geometry) datasets from a Voronoï tessalation
voro: a
scipy.spatial.Voronoi
object datasets: dict
datasets suitable for
Epithelium
implementation

tyssue.generation.from_voronoi.
from_3d_voronoi
(voro)¶ Creates 3D (bulk geometry) datasets from a Voronoï tessalation
voro: a
scipy.spatial.Voronoi
object datasets: dict
datasets suitable for
Epithelium
implementation
Input/output¶

tyssue.io.hdf5.
load_datasets
(h5store, data_names=['face', 'vert', 'edge', 'cell', 'settings'])¶

tyssue.io.hdf5.
save_datasets
(h5store, eptm)¶

tyssue.io.csv.
write_storm_csv
(filename, points, coords=['x', 'y', 'z'], split_by=None, **csv_args)¶ Saves a point cloud array in the storm format

tyssue.io.obj.
save_junction_mesh
(filename, eptm)¶

tyssue.io.obj.
save_splitted_cells
(fname, sheet, epsilon=0.1)¶

tyssue.io.obj.
save_triangulated
(filename, eptm)¶

tyssue.io.obj.
write_splitted_cells
(*args, **kwargs)¶
Predefined datasets¶
Available predefined datasets:small_hexagonal_snaped.hf5 small_ellipsoid.hf5 rod_sheet.hf5 sheet6x5.hf5 with_4sided_cell.hf5 planar_periodic8x8.hf5 __pycache__ __init__.py small_hexagonal.hf5 before_apoptosis.hf5 15_cells_patch.hf5 with_pinch.hf5
Collision detection and correction¶
Detection¶

tyssue.collisions.intersection.
self_intersections
(sheet)¶ Checks for self collisions for the sheet
 sheeta
Sheet
object This object must have a triangular_mesh method returning a valid triangular mesh.
 edge_pairs: np.ndarray of indices
Array of shape (n_intersections, 2) with the indices of the pairs of intersecting edges
 sheeta
Resolution¶

class
tyssue.collisions.solvers.
CollidingBoxes
(sheet, position_buffer, intersecting_edges)¶ Utility class to manage collisions

get_limits
(shyness=1e10)¶ Iterator over the position boundaries avoiding the collisions.
 shynessfloat
the extra distance between two colliding vertices, on each side of the collision plane.
 lower, uppertwo pd.Series
those Series are indexed by the vertices of the colliding faces giving the lower and upper bounds for the vertices

solve_collisions
(shyness=1e10)¶ Solves the collisions by finding the collision plane.
Modifies the sheet vertex positions inplace such that they rest at a distance
shyness
apart on each side of the collision plane. shynessfloat, default 1e10
the extra distance between two colliding vertices, on each side of the collision plane.
Based on Liu, J.D., Ko, M.T., & Chang, R.C. (1998), A simple selfcollision avoidance for cloth animation. Computers & Graphics, 22(1), 117–128. DOI


tyssue.collisions.solvers.
auto_collisions
(fun)¶ Decorator to solve collisions detections after the execution of the decorated function.
It is assumed that the two first arguments of the decorated function are a
Sheet
object and a geometry classThe function is reexecuted with the updated geometry

tyssue.collisions.solvers.
revert_positions
(sheet, position_buffer, intersecting_edges)¶

tyssue.collisions.solvers.
solve_bulk_collisions
(eptm, position_buffer)¶ Corrects the autocollisions for the outer surface(s) of a 3D epithelium.
eptm : a
Epithelium
object position_buffer : np.array of shape (eptm.Nv, eptm.dim):positions of the vertices prior to the collisions
 changedbool
True if the positions of some vertices were changed

tyssue.collisions.solvers.
solve_sheet_collisions
(sheet, position_buffer)¶ Corrects the autocollisions for the outer surface(s) of a 2.5D sheet.
sheet : a
Sheet
object position_buffer : np.array of shape (sheet.Nv, sheet.dim):positions of the vertices prior to the collisions
 changedbool
True if the positions of some vertices were changed
Miscellanous utils¶

tyssue.utils.utils.
ar_calculation
(sheet, coords=['x', 'y'])¶ Calculates the aspect ratio of each face of the sheet
eptm : a
Sheet
object coords : list of str, optional, default [‘x’, ‘y’]the coordinates on which to compute the aspect ratio
AR: pandas series of aspect ratio for all faces.
As is the case in ImageJ, the returned aspect ratio is always higher than 1

tyssue.utils.utils.
cell_centered_patch
(eptm, cell, neighbour_order)¶ Return subsheet centered on cell with a distance of neighbour order around the cell
eptm : a
Epithelium
instance face : int, id of the center face neighbour_order: int, number of neighbour around the center facepatch: an object of the same class as the input object

tyssue.utils.utils.
combine_specs
(*specs)¶

tyssue.utils.utils.
data_at_opposite
(sheet, edge_data, free_value=None)¶ Returns a pd.DataFrame with the values of the input edge_data at the opposite edges. For free edges, optionaly replaces Nan values with free_value
sheet: a
Sheet
instance edge_data: dataframe contain value of edgeopposite: pandas series contain value of opposite edge

tyssue.utils.utils.
elem_centered_patch
(eptm, elem_idx, neighbour_order, elem)¶ Return subeptm centered on the element (cell or face) with index elem_idx with neighbour_order neighbours around it.
eptm : a
Epithelim
instance index : int, id of the center element neighbour_order: int,neighbourhood ‘degree’ around the center element
patch: an object with the same class as eptm

tyssue.utils.utils.
face_centered_patch
(sheet, face, neighbour_order)¶ Return subsheet centered on face with a distance of neighbour order around the face
sheet : a
Sheet
object face : int, id of the center face neighbour_order: int, number of neighbour around the center facepatch: an object of the same class as the input object

tyssue.utils.utils.
get_next
(eptm)¶ Returns the indices of the next edge for each edge

tyssue.utils.utils.
get_sub_eptm
(eptm, edges, copy=False)¶ Define subepithelium corresponding to the edges.
eptm: a
Epithelium
instance edges: list of edges includes in the subepitheliumsub_eptm: a
Epithelium
instance

tyssue.utils.utils.
modify_segments
(eptm, modifiers)¶ Modifies the datasets of a segmented epithelium according to the passed modifiers.
eptm :
tyssue.Epithelium
modifiers : nested dictionnaryThis functions assumes that the epithelium has a segment_index method as implemented in the
tyssue.Monolayer
.>>> modifiers = { >>> 'apical' : { >>> 'edge': {'line_tension': 1.}, >>> 'face': {'prefered_area': 0.2}, >>> }, >>> 'basal' : { >>> 'edge': {'line_tension': 3.}, >>> 'face': {'prefered_area': 0.1}, >>> } >>> modify_segments(monolayer, modifiers) >>> monolayer.ver_df.loc[monolayer.apical_edges, >>> 'line_tension'].unique()[0] == 1. True

tyssue.utils.utils.
scaled_unscaled
(func, scale, eptm, geom, args=(), kwargs={}, coords=None)¶ Scales the epithelium by an homotetic factor scale, applies the function func, and scales back to original size.
func: the function to apply to the scaled epithelium scale: float, the scale to apply eptm: a
Epithelium
instance geom: aGeometry
class args: sequence, the arguments to pass to func kwargs: dictionary, the keywords argumentsto pass to func
coords: the coordinates on which the scaling applies
If the execution of function fails, the scaling is still reverted
res: the result of the function func

tyssue.utils.utils.
set_data_columns
(datasets, specs, reset=False)¶ Sets the columns of the dataframes in the datasets dictionnary to the uniform values in the specs subdictionnaries.
datasets : dict of dataframes specs : dict of dicts reset : bool, default False
For each key in specs, the value is a dictionnary whose keys are column names for the corresponding dataframe in datasets. If there is no such column in the dataframe, it is created. If the columns allready exists and reset is True, the new value is used.

tyssue.utils.utils.
single_cell
(eptm, cell, copy=False)¶ Define epithelium instance for all element to a define cell.
eptm : a
Epithelium
instance cell : identifier of a cell copy : bool, default Falsesub_etpm: class:’Epithelium’ instance corresponding to the cell

tyssue.utils.utils.
spec_updater
(specs, new)¶ Add element to the new dictionary to the specs dictionary. Update value if the key already exist.
specs: specification that will be modified new: dictionary of new specification

tyssue.utils.utils.
swap_apico_basal
(organo)¶ Swap apical and basal segments of an organoid.

tyssue.utils.utils.
to_nd
(df, ndim)¶ Give a new shape to an input data by duplicating its column.
df : input data that will be reshape ndim : dimension of the new reshape data.
df_nd : return array reshaped in ndim.
Decorators¶

tyssue.utils.decorators.
cell_lookup
(func)¶

tyssue.utils.decorators.
do_undo
(func)¶ Decorator that creates a copy of the first argument (usually an epithelium object) and restores it if the function fails.
The first argument in *args should have backup() and restore() methods.

tyssue.utils.decorators.
face_lookup
(func)¶

tyssue.utils.decorators.
time_exe
(func)¶

tyssue.utils.decorators.
validate
(func)¶ Decorator that validate the epithelium after the decorated function was applied. the first argument of func should be an epithelium instance, and is at least assumed to have a validate method.