API documentation

cli

calculus

cardiac_geometries.calculus.estimate_focal_point(mesh, axis=0)

Copmute the focal point based on approximating the endocardial surfaces as a ellipsoidal cap.

\[focal = \sqrt{ l^2 - s^2}\]

Parameters:

mesh (dolfin.mesh) – The mesh

Returns:

focal_point – The focal point

Return type:

float

cardiac_geometries.calculus.get_strain_regions(nsectors=(6, 6, 4, 1))

Mark the cells in the mesh.

For instance if you want to mark this mesh accoring to the AHA 17-segment model, then nsector = [6,6,4,1], i.e 6 basal, 6 mid, 4 apical and one apex

cardiac_geometries.calculus.strain_region_number(T, regions)

For a given point in prolate coordinates, return the region it belongs to.

Parameters:

• regions (numpy.array) – Array of all coordinates for the strain regions taken from the strain mesh.

• T (numpy.array) – Some value i prolate coordinates

Resturn the region number that T belongs to

gmsh

cardiac_geometries.gmsh.lv_ellipsoid(mesh_name: str | Path = '', r_short_endo=0.025, r_short_epi=0.035, r_long_endo=0.09, r_long_epi=0.097, psize_ref=0.005, mu_apex_endo=-3.141592653589793, mu_base_endo=-1.2722641256100204, mu_apex_epi=-3.141592653589793, mu_base_epi=-1.318116071652818) → Path

Create general LV ellipsoid

Parameters:

• mesh_name (str, optional) – Name of the mesh, by default “”

• r_short_endo (float, optional) – Shortest radius on the endocardium layer, by default 0.025

• r_short_epi (float, optional) – Shortest radius on the epicardium layer, by default 0.035

• r_long_endo (float, optional) – Longest radius on the endocardium layer, by default 0.09

• r_long_epi (float, optional) – Longest radius on the epicardium layer, by default 0.097

• psize_ref (float, optional) – The reference point size (smaller values yield as finer mesh, by default 0.005

• mu_apex_endo (float, optional) – Angle for the endocardial apex, by default -math.pi

• mu_base_endo (float, optional) – Angle for the endocardial base, by default -math.acos(5 / 17)

• mu_apex_epi (float, optional) – Angle for the epicardial apex, by default -math.pi

• mu_base_epi (float, optional) – Angle for the epicardial apex, by default -math.acos(5 / 20)

Returns:

Path to the generated gmsh file

Return type:

Path

cardiac_geometries.gmsh.lv_ellipsoid_2D(mesh_name: str | Path = '', r_short_endo: float = 7.0, r_short_epi: float = 10.0, r_long_endo: float = 17.0, r_long_epi: float = 20.0, psize_ref=3.0, mu_apex_endo=-3.141592653589793, mu_base_endo=-1.2722641256100204, mu_apex_epi=-3.141592653589793, mu_base_epi=-1.318116071652818) → Path

Create general LV ellipsoid

Parameters:

• mesh_name (str, optional) – Name of the mesh, by default “”

• r_short_endo (float, optional) – Shortest radius on the endocardium layer, by default 0.025

• r_short_epi (float, optional) – Shortest radius on the epicardium layer, by default 0.035

• r_long_endo (float, optional) – Longest radius on the endocardium layer, by default 0.09

• r_long_epi (float, optional) – Longest radius on the epicardium layer, by default 0.097

• psize_ref (float, optional) – The reference point size (smaller values yield as finer mesh, by default 0.005

• mu_apex_endo (float, optional) – Angle for the endocardial apex, by default -math.pi

• mu_base_endo (float, optional) – Angle for the endocardial base, by default -math.acos(5 / 17)

• mu_apex_epi (float, optional) – Angle for the epicardial apex, by default -math.pi

• mu_base_epi (float, optional) – Angle for the epicardial apex, by default -math.acos(5 / 20)

Returns:

Path to the generated gmsh file

Return type:

Path

cardiac_geometries.gmsh.lv_ellipsoid_flat_base(mesh_name: str | Path = '', r_short_endo: float = 7.0, r_short_epi: float = 10.0, r_long_endo: float = 17.0, r_long_epi: float = 20.0, quota_base: float = -5.0, psize: float = 3.0, ndiv: float = 1.0) → Path

Create an LV ellipsoids with a flat base

Parameters:

• mesh_name (str, optional) – Name of the mesh by default “”

• r_short_endo (float, optional) – Shortest radius on the endocardium layer, by default 7.0

• r_short_epi (float, optional) – Shortest radius on the epicardium layer, by default 10.0

• r_long_endo (float, optional) – Longest radius on the endocardium layer, by default 17.0

• r_long_epi (float, optional) – Longest radius on the epicardium layer, by default 20.0

• quota_base (float, optional) – Position of the base relative to the x=0 plane, by default -5.0

• psize (float, optional) – Point size, by default 3.0

• ndiv (float, optional) – Number of divisions, by default 1.0

Returns:

Path to file

Return type:

Path

cardiac_geometries.gmsh.prolate_lv_ellipsoid(mesh_name: str | Path = '', a: float = 2.0, nu_epi: float = 0.8, nu_endo: float = 0.5, psize_ref=1.0, mu_apex_endo=-3.141592653589793, mu_base_endo=-1.2722641256100204, mu_apex_epi=-3.141592653589793, mu_base_epi=-1.318116071652818) → Path

Create an LV ellipsoid in prolate spheroidal coordinates

Parameters:

• mesh_name (str, optional) – _description_, by default “”

• a (float, optional) – _description_, by default 2.0

• nu_epi (float, optional) – _description_, by default 0.8

• nu_endo (float, optional) – _description_, by default 0.5

• psize_ref (float, optional) – _description_, by default 1.0

• mu_apex_endo (_type_, optional) – _description_, by default -math.pi

• mu_base_endo (_type_, optional) – _description_, by default -math.acos(5 / 17)

• mu_apex_epi (_type_, optional) – _description_, by default -math.pi

• mu_base_epi (_type_, optional) – _description_, by default -math.acos(5 / 20)

Returns:

Path to the generated gmsh file

Return type:

Path

cardiac_geometries.gmsh.prolate_lv_ellipsoid_flat_base(mesh_name: str | Path = '', a: float = 25.0, nu_epi: float = 0.8, nu_endo: float = 0.5, quota_base: float = -5.0, psize: float = 3.0, ndiv: float = 1.0) → Path

Create an LV ellipsoid with flat base in prolate spheroidal coordinates

Parameters:

• mesh_name (str, optional) – _description_, by default “”

• a (float, optional) – _description_, by default 25.0

• nu_epi (float, optional) – _description_, by default 0.8

• nu_endo (float, optional) – _description_, by default 0.5

• quota_base (float, optional) – _description_, by default -5.0

• psize (float, optional) – _description_, by default 3.0

• ndiv (float, optional) – _description_, by default 1.0

Returns:

Path to the generated gmsh file

Return type:

Path

cardiac_geometries.gmsh.slab_in_bath(mesh_name: str | Path = '', lx=1.0, ly=0.01, lz=0.5, bx=0.0, by=0.0, bz=0.1, dx=0.001)

Create slab inside a bath

Parameters:

• mesh_name (str, optional) – Name of o, by default “”

• lx (float, optional) – _description_, by default 1.0

• ly (float, optional) – _description_, by default 0.01

• lz (float, optional) – _description_, by default 0.5

• bx (float, optional) – _description_, by default 0.0

• by (float, optional) – _description_, by default 0.0

• bz (float, optional) – _description_, by default 0.1

• dx (float, optional) – _description_, by default 0.001

Returns:

_description_

Return type:

_type_

mesh

cardiac_geometries._mesh.create_biv_ellipsoid(outdir: str | Path | None = None, char_length: float = 0.5, center_lv_x: float = 0.0, center_lv_y: float = 0.0, center_lv_z: float = 0.0, a_endo_lv: float = 2.5, b_endo_lv: float = 1.0, c_endo_lv: float = 1.0, a_epi_lv: float = 3.0, b_epi_lv: float = 1.5, c_epi_lv: float = 1.5, center_rv_x: float = 0.0, center_rv_y: float = 0.5, center_rv_z: float = 0.0, a_endo_rv: float = 3.0, b_endo_rv: float = 1.5, c_endo_rv: float = 1.5, a_epi_rv: float = 4.0, b_epi_rv: float = 2.5, c_epi_rv: float = 2.0, create_fibers: bool = False, fiber_angle_endo: float = -60, fiber_angle_epi: float = 60, fiber_space: str = 'P_1') → Geometry | None

Create BiV ellipsoidal geometry

Parameters:

• outdir (Union[str, Path, None], optional) – Directory where to save the results. If not provided a temporary directory will be created, by default None, by default None

• char_length (float, optional) – Characteristic length of mesh, by default 0.5

• center_lv_y (float, optional) – X-coordinate for the center of the lv, by default 0.0

• center_lv_y – Y-coordinate for the center of the lv, by default 0.0

• center_lv_z (float, optional) – Z-coordinate for the center of the lv, by default 0.0

• a_endo_lv (float, optional) – Dilation of lv endo ellipsoid in the x-direction, by default 2.5

• b_endo_lv (float, optional) – Dilation of lv endo ellipsoid in the y-direction, by default 1.0

• c_endo_lv (float, optional) – Dilation of lv endo ellipsoid in the z-direction, by default 1.0

• a_epi_lv (float, optional) – Dilation of lv epi ellipsoid in the x-direction, by default 3.0

• b_epi_lv (float, optional) – Dilation of lv epi ellipsoid in the y-direction, by default 1.5

• c_epi_lv (float, optional) – Dilation of lv epi ellipsoid in the z-direction, by default 1.5

• center_rv_x (float, optional) – X-coordinate for the center of the rv, by default 0.0

• center_rv_y (float, optional) – Y-coordinate for the center of the rv, by default 0.5

• center_rv_z (float, optional) – Z-coordinate for the center of the rv, by default 0.0

• a_endo_rv (float, optional) – Dilation of rv endo ellipsoid in the x-direction, by default 3.0

• b_endo_rv (float, optional) – Dilation of rv endo ellipsoid in the y-direction, by default 1.5

• c_endo_rv (float, optional) – Dilation of rv endo ellipsoid in the z-direction, by default 1.5

• a_epi_rv (float, optional) – Dilation of rv epi ellipsoid in the x-direction, by default 4.0

• b_epi_rv (float, optional) – Dilation of rv epi ellipsoid in the y-direction, by default 2.5

• c_epi_rv (float, optional) – Dilation of rv epi ellipsoid in the z-direction, by default 2.0

• create_fibers (bool, optional) – If True create analytic fibers, by default False

• fiber_angle_endo (float, optional) – Angle for the endocardium, by default -60

• fiber_angle_epi (float, optional) – Angle for the epicardium, by default +60

• fiber_space (str, optional) – Function space for fibers of the form family_degree, by default “P_1”

Returns:

A Geometry with the mesh, markers, markers functions and fibers. Returns None if dolfin is not installed.

Return type:

Optional[Geometry]

Raises:

ImportError – If gmsh is not installed

cardiac_geometries._mesh.create_biv_ellipsoid_torso(outdir: str | Path | None = None, char_length: float = 0.5, heart_as_surface: bool = False, torso_length: float = 20.0, torso_width: float = 20.0, torso_height: float = 20.0, rotation_angle: float = 0.5235987755982988, center_lv_x: float = 0.0, center_lv_y: float = 0.0, center_lv_z: float = 0.0, a_endo_lv: float = 2.5, b_endo_lv: float = 1.0, c_endo_lv: float = 1.0, a_epi_lv: float = 3.0, b_epi_lv: float = 1.5, c_epi_lv: float = 1.5, center_rv_x: float = 0.0, center_rv_y: float = 0.5, center_rv_z: float = 0.0, a_endo_rv: float = 3.0, b_endo_rv: float = 1.5, c_endo_rv: float = 1.5, a_epi_rv: float = 4.0, b_epi_rv: float = 2.5, c_epi_rv: float = 2.0, create_fibers: bool = False, fiber_angle_endo: float = -60, fiber_angle_epi: float = 60, fiber_space: str = 'P_1') → Geometry | None

Create BiV ellipsoidal geometry

Parameters:

• outdir (Union[str, Path, None], optional) – Directory where to save the results. If not provided a temporary directory will be created, by default None, by default None

• char_length (float, optional) – Characteristic length of mesh, by default 0.5

• heart_as_surface (bool) – If true, create the heart as a a surface inside the torso, otherwise let the heart be a volume, by default True.

• torso_length (float, optional) – Length of torso in the x-direction, by default 20.0

• torso_width (float, optional) – Length of torso in the y-direction, by default 20.0

• torso_height (float, optional) – Length of torso in the z-direction, by default 20.0

• rotation_angle (float, optional) – Angle to rotate the torso in order to object realistic position of the heart in a torso, by default pi / 6

• center_lv_x (float, optional) – X-coordinate for the center of the lv, by default 0.0

• center_lv_y (float, optional) – Y-coordinate for the center of the lv, by default 0.0

• center_lv_z (float, optional) – Z-coordinate for the center of the lv, by default 0.0

• a_endo_lv (float, optional) – Dilation of lv endo ellipsoid in the x-direction, by default 2.5

• b_endo_lv (float, optional) – Dilation of lv endo ellipsoid in the y-direction, by default 1.0

• c_endo_lv (float, optional) – Dilation of lv endo ellipsoid in the z-direction, by default 1.0

• a_epi_lv (float, optional) – Dilation of lv epi ellipsoid in the x-direction, by default 3.0

• b_epi_lv (float, optional) – Dilation of lv epi ellipsoid in the y-direction, by default 1.5

• c_epi_lv (float, optional) – Dilation of lv epi ellipsoid in the z-direction, by default 1.5

• center_rv_x (float, optional) – X-coordinate for the center of the rv, by default 0.0

• center_rv_y (float, optional) – Y-coordinate for the center of the rv, by default 0.5

• center_rv_z (float, optional) – Z-coordinate for the center of the rv, by default 0.0

• a_endo_rv (float, optional) – Dilation of rv endo ellipsoid in the x-direction, by default 3.0

• b_endo_rv (float, optional) – Dilation of rv endo ellipsoid in the y-direction, by default 1.5

• c_endo_rv (float, optional) – Dilation of rv endo ellipsoid in the z-direction, by default 1.5

• a_epi_rv (float, optional) – Dilation of rv epi ellipsoid in the x-direction, by default 4.0

• b_epi_rv (float, optional) – Dilation of rv epi ellipsoid in the y-direction, by default 2.5

• c_epi_rv (float, optional) – Dilation of rv epi ellipsoid in the z-direction, by default 2.0

• create_fibers (bool, optional) – If True create analytic fibers, by default False

• fiber_angle_endo (float, optional) – Angle for the endocardium, by default -60

• fiber_angle_epi (float, optional) – Angle for the epicardium, by default +60

• fiber_space (str, optional) – Function space for fibers of the form family_degree, by default “P_1”

Returns:

A Geometry with the mesh, markers, markers functions and fibers. Returns None if dolfin is not installed.

Return type:

Optional[Geometry]

Raises:

ImportError – If gmsh is not installed

cardiac_geometries._mesh.create_lv_ellipsoid(outdir: str | Path | None = None, r_short_endo: float = 7.0, r_short_epi: float = 10.0, r_long_endo: float = 17.0, r_long_epi: float = 20.0, psize_ref: float = 3, mu_apex_endo: float = -3.141592653589793, mu_base_endo: float = -1.2722641256100204, mu_apex_epi: float = -3.141592653589793, mu_base_epi: float = -1.318116071652818, create_fibers: bool = False, fiber_angle_endo: float = -60, fiber_angle_epi: float = 60, fiber_space: str = 'P_1', aha: bool = False, axisymmetric: bool = False) → Geometry | None

Create an LV ellipsoidal geometry

Parameters:

• outdir (Optional[Path], optional) – Directory where to save the results. If not provided a temporary directory will be created, by default None

• r_short_endo (float, optional) – Shortest radius on the endocardium layer, by default 7.0

• r_short_epi (float, optional) – Shortest radius on the epicardium layer, by default 10.0

• r_long_endo (float, optional) – Longest radius on the endocardium layer, by default 17.0

• r_long_epi (float, optional) – Longest radius on the epicardium layer, by default 20.0

• psize_ref (float, optional) – The reference point size (smaller values yield as finer mesh, by default 3

• mu_apex_endo (float, optional) – Angle for the endocardial apex, by default -math.pi

• mu_base_endo (float, optional) – Angle for the endocardial base, by default -math.acos(5 / 17)

• mu_apex_epi (float, optional) – Angle for the epicardial apex, by default -math.pi

• mu_base_epi (float, optional) – Angle for the epicardial apex, by default -math.acos(5 / 20)

• create_fibers (bool, optional) – If True create analytic fibers, by default False

• fiber_angle_endo (float, optional) – Angle for the endocardium, by default -60

• fiber_angle_epi (float, optional) – Angle for the epicardium, by default +60

• fiber_space (str, optional) – Function space for fibers of the form family_degree, by default “P_1”

• aha (bool, optional) – If True create 17-segment AHA regions

• axisymmetric (bool, optional) – If True create a 2D axisymmetric mesh, by default False

Returns:

A Geometry with the mesh, markers, markers functions and fibers. Returns None if dolfin is not installed.

Return type:

Optional[Geometry]

Raises:

ImportError – If gmsh is not installed

cardiac_geometries._mesh.create_slab(outdir: str | Path | None = None, lx: float = 20.0, ly: float = 7.0, lz: float = 3.0, dx: float = 1.0, create_fibers: bool = True, fiber_angle_endo: float = -60, fiber_angle_epi: float = 60, fiber_space: str = 'P_1') → Geometry | None

Create slab geometry

Parameters:

• outdir (Optional[Path], optional) – Directory where to save the results. If not provided a temporary directory will be created, by default None

• lx (float, optional) – Length of slab the x-direction, by default 20.0

• ly (float, optional) – Length of slab the x-direction, by default 7.0

• lz (float, optional) – Length of slab the z-direction, by default 3.0

• dx (float, optional) – Element size, by default 1.0

• create_fibers (bool, optional) – If True create analytic fibers, by default True

• fiber_angle_endo (float, optional) – Angle for the endocardium, by default -60

• fiber_angle_epi (float, optional) – Angle for the epicardium, by default +60

• fiber_space (str, optional) – Function space for fibers of the form family_degree, by default “P_1”

Returns:

A Geometry with the mesh, markers, markers functions and fibers. Returns None if dolfin is not installed.

Return type:

Optional[Geometry]

Raises:

ImportError – If gmsh is not installed

cardiac_geometries._mesh.create_slab_in_bath(outdir: str | Path | None = None, lx: float = 1.0, ly: float = 0.01, lz: float = 0.5, bx: float = 0.0, by: float = 0.0, bz: float = 0.1, dx: float = 0.001) → Geometry | None

Create slab geometry

Parameters:

• outdir (Optional[Path], optional) – Directory where to save the results. If not provided a temporary directory will be created, by default None

• lx (float, optional) – Length of slab the x-direction, by default 1.0

• ly (float, optional) – Length of slab the x-direction, by default 0.5

• lz (float, optional) – Length of slab the z-direction, by default 0.01

• bx (float, optional) – Thickness of bath the x-direction, by default 0.0

• by (float, optional) – Thickness of bath the x-direction, by default 0.0

• bz (float, optional) – Thickness of bath the z-direction, by default 0.1

• dx (float, optional) – Element size, by default 0.001

Returns:

A Geometry with the mesh, markers, markers functions and fibers. Returns None if dolfin is not installed.

Return type:

Optional[Geometry]

Raises:

ImportError – If gmsh is not installed

dolfin_utils

class cardiac_geometries.dolfin_utils.Geometry(mesh, markers, marker_functions)

marker_functions: MarkerFunctions

Alias for field number 2

markers: Dict[str, Tuple[int, int]]

Alias for field number 1

mesh: Mesh

Alias for field number 0

class cardiac_geometries.dolfin_utils.MarkerFunctions(vfun, efun, ffun, cfun)

cfun: MeshFunction

Alias for field number 3

efun: MeshFunction

Alias for field number 1

ffun: MeshFunction

Alias for field number 2

vfun: MeshFunction

Alias for field number 0

cardiac_geometries.dolfin_utils.mark_cell_function(fun, mesh, foc, regions)

Iterates over the mesh and stores the region number in a meshfunction

geometry

class cardiac_geometries.geometry.FileNames(value)

An enumeration.

class cardiac_geometries.geometry.H5Path(h5group, fname, mesh_key, is_dolfin, is_mesh, is_meshfunction, is_function, dim)

dim: int

Alias for field number 7

fname: str

Alias for field number 1

h5group: str

Alias for field number 0

is_dolfin: bool

Alias for field number 3

is_function: bool

Alias for field number 6

is_mesh: bool

Alias for field number 4

is_meshfunction: bool

Alias for field number 5

mesh_key: str

Alias for field number 2

class cardiac_geometries.geometry.H5Paths(value)

An enumeration.

class cardiac_geometries.geometry.MeshTypes(value)

An enumeration.

class cardiac_geometries.geometry.Microstructure(f0, s0, n0)

f0: Function

Alias for field number 0

n0: Function

Alias for field number 2

s0: Function

Alias for field number 1

utils

viz

cardiac_geometries.viz.dolfin_to_hd5(obj: Function, h5name, time='', name=None)

Save object to and HDF file.

Parameters:

• obj (dolfin.Function) – The object you want to save

• name (str) – Name of the object

• h5group (str) – The folder you want to save the object withing the HDF file. Default: ‘’