def boundary_conditions(geometry, **bcs_parameters):
try:
pericardium_spring = bcs_parameters['pericardium_spring']
base_spring = bcs_parameters['base_spring']
base_bc = bcs_parameters['base_bc']
except KeyError:
msg = "Not all boundary conditions have been set. You have provided "\
"{}".format(bcs_parameters.keys())
raise KeyError(msg)
# Neumann BCs
lv_pressure = pulse.NeumannBC(traction=Constant(0.0, name="lv_pressure"),
marker=geometry.get_lv_marker(),
name="lv")
neumann_bc = [lv_pressure]
if geometry.has_rv():
rv_pressure = pulse.NeumannBC(traction=Constant(0.0,
name="rv_pressure"),
marker=geometry.get_rv_marker(),
name="rv")
neumann_bc += [rv_pressure]
# Robin BC
robin_bc = []
if pericardium_spring > 0.0:
robin_bc += [
pulse.RobinBC(value=Constant(pericardium_spring),
marker=geometry.get_epi_marker())
]
if base_spring > 0.0:
robin_bc += [
pulse.RobinBC(value=Constant(base_spring),
marker=geometry.get_base_marker())
]
# Dirichlet BC
if base_bc == "fixed":
dirichlet_bc = [
partial(
dirichlet_fix_base,
ffun=geometry.ffun,
marker=geometry.get_base_marker(),
)
]
elif base_bc == "fix_x":
dirichlet_bc = [
partial(dirichlet_fix_base_directional,
ffun=geometry.ffun,
marker=geometry.get_base_marker())
]
return pulse.BoundaryConditions(dirichlet=dirichlet_bc,
neumann=neumann_bc,
robin=robin_bc)
def mechanics_bcs(geometry):
# LV Pressure
lvp = df.Constant(0.0)
lv_marker = geometry.markers['ENDO'][0]
lv_pressure = pulse.NeumannBC(traction=lvp, marker=lv_marker, name='lv')
neumann_bc = [lv_pressure]
# Add spring term at the base with stiffness 1.0 kPa/cm^2
base_spring = 1.0
robin_bc = [
pulse.RobinBC(value=df.Constant(base_spring),
marker=geometry.markers["BASE"][0])
]
# Fix the basal plane in the longitudinal direction
# 0 in V.sub(0) refers to x-direction, which is the longitudinal direction
def fix_basal_plane(W):
V = W if W.sub(0).num_sub_spaces() == 0 else W.sub(0)
bc = df.DirichletBC(V.sub(0), df.Constant(0.0), geometry.ffun,
geometry.markers["BASE"][0])
return bc
dirichlet_bc = [fix_basal_plane]
bcs = pulse.BoundaryConditions(dirichlet=dirichlet_bc,
neumann=neumann_bc,
robin=robin_bc)
return bcs
def create_mechanics_problem(solver_parameters):
import pulse
# from pulse import (MechanicsProblem, HeartGeometry, BoundaryConditions,
# NeumannBC, RobinBC, MarkerFunctions, Marker, CRLBasis)
from pulse.material import HolzapfelOgden
mfun = pulse.MarkerFunctions(ffun=solver_parameters['facet_function'],
cfun=solver_parameters['mesh_function'])
material = solver_parameters['material']
microstructure = pulse.Microstructure(f0=material.f0,
s0=material.s0,
n0=material.f0)
crl_basis = pulse.CRLBasis(
c0=solver_parameters['crl_basis']['circumferential'],
r0=solver_parameters['crl_basis']['radial'],
l0=solver_parameters['crl_basis']['longitudinal'])
geometry = pulse.HeartGeometry(mesh=solver_parameters['mesh'],
markers=solver_parameters['markers'],
marker_functions=mfun,
microstructure=microstructure,
crl_basis=crl_basis)
neumann = []
names = ['lv', 'rv']
for i, n in enumerate(solver_parameters['bc']['neumann']):
neumann.append(
pulse.NeumannBC(traction=n[0], marker=n[1], name=names[i]))
robin = []
for i, n in enumerate(solver_parameters['bc']['robin']):
robin.append(pulse.RobinBC(value=n[0], marker=n[1]))
if hasattr(solver_parameters['bc']['dirichlet'], '__len__'):
dirichlet = solver_parameters['bc']['dirichlet']
else:
dirichlet = (solver_parameters['bc']['dirichlet'], )
bcs = pulse.BoundaryConditions(dirichlet=dirichlet,
neumann=neumann,
robin=robin)
problem = pulse.MechanicsProblem(geometry, material, bcs)
return problem
def build_problem(geometry, matparams):
activation = dolfin.Function(dolfin.FunctionSpace(geometry.mesh, "R", 0))
material = pulse.HolzapfelOgden(
activation=activation,
parameters=matparams,
f0=geometry.f0,
s0=geometry.s0,
n0=geometry.n0,
)
# LV Pressure
lvp = dolfin.Constant(0.0)
lv_marker = geometry.markers["ENDO"][0]
lv_pressure = pulse.NeumannBC(traction=lvp, marker=lv_marker, name="lv")
neumann_bc = [lv_pressure]
# Add spring term at the base with stiffness 1.0 kPa/cm^2
base_spring = 1.0
robin_bc = [
pulse.RobinBC(
value=dolfin.Constant(base_spring), marker=geometry.markers["BASE"][0]
)
]
# 0 in V.sub(0) refers to x-direction, which is the longitudinal direction
def fix_basal_plane(W):
V = W if W.sub(0).num_sub_spaces() == 0 else W.sub(0)
bc = dolfin.DirichletBC(
V.sub(0), dolfin.Constant(0.0), geometry.ffun, geometry.markers["BASE"][0]
)
return bc
dirichlet_bc = [fix_basal_plane]
# Collect boundary conditions
bcs = pulse.BoundaryConditions(
dirichlet=dirichlet_bc, neumann=neumann_bc, robin=robin_bc
)
# Create the problem
problem = pulse.MechanicsProblem(geometry, material, bcs)
return problem, activation, lvp
material = pulse.HolzapfelOgden(
activation=activation,
parameters=matparams,
f0=geometry.f0,
)
# LV Pressure
lvp = Constant(0.0)
lv_marker = markers["ENDO"][0]
lv_pressure = pulse.NeumannBC(traction=lvp, marker=lv_marker, name="lv")
neumann_bc = [lv_pressure]
# Add spring term at the base with stiffness 1.0 kPa/cm^2
base_spring = 1.0
robin_bc = [
pulse.RobinBC(value=Constant(base_spring), marker=markers["BASE"][0])
]
# Fix the basal plane in the longitudinal direction
# 0 in V.sub(0) refers to x-direction, which is the longitudinal direction
def fix_basal_plane(W):
V = W if W.sub(0).num_sub_spaces() == 0 else W.sub(0)
bc = DirichletBC(V.sub(0), Constant(0.0), geometry.ffun,
markers["BASE"][0])
return bc
dirichlet_bc = [fix_basal_plane]
# You can also use a built in function for this
# from functools import partial
def create_problem():
geometry = pulse.HeartGeometry.from_file(
pulse.mesh_paths["simple_ellipsoid"])
activation = dolfin_adjoint.Function(dolfin.FunctionSpace(
geometry.mesh, "R", 0),
name="activation")
activation.assign(dolfin_adjoint.Constant(0.0))
matparams = pulse.HolzapfelOgden.default_parameters()
V = dolfin.FunctionSpace(geometry.mesh, "R", 0)
control = dolfin_adjoint.Function(V)
control.assign(dolfin_adjoint.Constant(1.0))
# control = dolfin_adjoint.Constant(1.0, name="matparam control (a)")
matparams["a"] = control
f0 = dolfin_adjoint.Function(geometry.f0.function_space())
f0.assign(geometry.f0)
s0 = dolfin_adjoint.Function(geometry.s0.function_space())
s0.assign(geometry.s0)
n0 = dolfin_adjoint.Function(geometry.n0.function_space())
n0.assign(geometry.n0)
material = pulse.HolzapfelOgden(activation=activation,
parameters=matparams,
f0=f0,
s0=s0,
n0=n0)
# LV Pressure
lvp = dolfin_adjoint.Constant(0.0, name="lvp")
lv_marker = geometry.markers["ENDO"][0]
lv_pressure = pulse.NeumannBC(traction=lvp, marker=lv_marker, name="lv")
neumann_bc = [lv_pressure]
# Add spring term at the base with stiffness 1.0 kPa/cm^2
base_spring = 1.0
robin_bc = [
pulse.RobinBC(
value=dolfin_adjoint.Constant(base_spring, name="base_spring"),
marker=geometry.markers["BASE"][0],
)
]
# Fix the basal plane in the longitudinal direction
# 0 in V.sub(0) refers to x-direction, which is the longitudinal direction
def fix_basal_plane(W):
V = W if W.sub(0).num_sub_spaces() == 0 else W.sub(0)
bc = dolfin_adjoint.DirichletBC(
V.sub(0),
dolfin.Constant(0.0, name="fix_base"),
geometry.ffun,
geometry.markers["BASE"][0],
)
return bc
dirichlet_bc = [fix_basal_plane]
# Collect boundary conditions
bcs = pulse.BoundaryConditions(dirichlet=dirichlet_bc,
neumann=neumann_bc,
robin=robin_bc)
# Create the problem
problem = pulse.MechanicsProblem(geometry, material, bcs)
return problem, control
material = pulse.HolzapfelOgden(activation=activation,
parameters=matparams,
f0=geometry.f0,
s0=geometry.s0,
n0=geometry.n0)
# LV Pressure
lvp = dolfin.Constant(1.0)
lv_marker = geometry.markers['ENDO'][0]
lv_pressure = pulse.NeumannBC(traction=lvp,
marker=lv_marker, name='lv')
neumann_bc = [lv_pressure]
# Add spring term at the base with stiffness 1.0 kPa/cm^2
base_spring = 1.0
robin_bc = [pulse.RobinBC(value=dolfin.Constant(base_spring),
marker=geometry.markers["BASE"][0])]
# Fix the basal plane in the longitudinal direction
# 0 in V.sub(0) refers to x-direction, which is the longitudinal direction
def fix_basal_plane(W):
V = W if W.sub(0).num_sub_spaces() == 0 else W.sub(0)
bc = dolfin.DirichletBC(V.sub(0),
dolfin.Constant(0.0),
geometry.ffun, geometry.markers["BASE"][0])
return bc
dirichlet_bc = [fix_basal_plane]
# You can also use a built in function for this
# from functools import partial
activation.assign(dolfin.Constant(0.2))
matparams = pulse.HolzapfelOgden.default_parameters()
material = pulse.HolzapfelOgden(activation=activation,
parameters=matparams,
f0=geometry.f0)
# LV Pressure
lvp = dolfin.Constant(1.0)
lv_marker = markers_dict["ENDO"][0]
lv_pressure = pulse.NeumannBC(traction=lvp, marker=lv_marker, name="lv")
neumann_bc = [lv_pressure]
# Add spring term at the base with stiffness 1.0 kPa/cm^2
base_spring = 1.0
robin_bc = [
pulse.RobinBC(value=dolfin.Constant(base_spring),
marker=markers_dict["BASE"][0])
]
# Fix the basal plane in the longitudinal direction
# 0 in V.sub(0) refers to x-direction, which is the longitudinal direction
def fix_basal_plane(W):
V = W if W.sub(0).num_sub_spaces() == 0 else W.sub(0)
bc = dolfin.DirichletBC(V.sub(0), dolfin.Constant(0.0), geometry.ffun,
markers_dict["BASE"][0])
return bc
dirichlet_bc = [fix_basal_plane]
# You can also use a built in function for this
# from functools import partial
parameters=matparams,
f0=geometry.f0,
s0=geometry.s0,
n0=geometry.n0,
)
# LV Pressure
lvp = Constant(0.0)
lv_marker = geometry.markers["ENDO"][0]
lv_pressure = pulse.NeumannBC(traction=lvp, marker=lv_marker, name="lv")
neumann_bc = [lv_pressure]
# Add spring term at the epicardium of stiffness 1.0 kPa/cm^2 to represent pericardium
base_spring = 1.0
robin_bc = [
pulse.RobinBC(value=Constant(base_spring), marker=geometry.markers["EPI"][0]),
]
# Fix the basal plane in the longitudinal direction
# 0 in V.sub(0) refers to x-direction, which is the longitudinal direction
def fix_basal_plane(W):
V = W if W.sub(0).num_sub_spaces() == 0 else W.sub(0)
bc = DirichletBC(
V.sub(0),
Constant(0.0),
geometry.ffun,
geometry.markers["BASE"][0],
)
return bc
def solve(
geometry,
EDP=1.0,
ESP=15.0,
Ta=60,
material_parameters=None,
):
"""
Arguments
---------
EDP : float
End diastolic pressure
ESP : float
End systolic pressure
Ta : float
Peak active tension (at ES)
material_parameters : dict
A dictionart with parameter in the Guccione model.
Default: {'C': 2.0, 'bf': 8.0, 'bt': 2.0, 'bfs': 4.0}
filename : str
Filname where to store the results
"""
# Create model
activation = df.Function(df.FunctionSpace(geometry.mesh, "R", 0))
matparams = pulse.Guccione.default_parameters()
if material_parameters is not None:
matparams.update(material_parameters)
material = pulse.Guccione(activation=activation,
parameters=matparams,
active_model="active_stress",
f0=geometry.f0,
s0=geometry.s0,
n0=geometry.n0)
lvp = df.Constant(0.0)
lv_marker = geometry.markers['ENDO'][0]
lv_pressure = pulse.NeumannBC(traction=lvp, marker=lv_marker, name='lv')
neumann_bc = [lv_pressure]
# Add spring term at the base with stiffness 1.0 kPa/cm^2
base_spring = 1.0
robin_bc = [
pulse.RobinBC(value=df.Constant(base_spring),
marker=geometry.markers["BASE"][0])
]
# Fix the basal plane in the longitudinal direction
# 0 in V.sub(0) refers to x-direction, which is the longitudinal direction
def fix_basal_plane(W):
V = W if W.sub(0).num_sub_spaces() == 0 else W.sub(0)
bc = df.DirichletBC(V.sub(0), df.Constant(0.0), geometry.ffun,
geometry.markers["BASE"][0])
return bc
dirichlet_bc = [fix_basal_plane]
# Collect boundary conditions
bcs = pulse.BoundaryConditions(dirichlet=dirichlet_bc,
neumann=neumann_bc,
robin=robin_bc)
# Create the problem
problem = pulse.MechanicsProblem(geometry, material, bcs)
xdmf = df.XDMFFile(df.mpi_comm_world(), 'output.xdmf')
# Solve the problem
print(("Do an initial solve with pressure = 0 kPa "
"and active tension = 0 kPa"))
problem.solve()
u, p = problem.state.split()
xdmf.write(u, 0.0)
print("LV cavity volume = {} ml".format(geometry.cavity_volume(u=u)))
# Solve for ED
print(("Solver for ED with pressure = {} kPa and active tension = 0 kPa"
"".format(EDP)))
pulse.iterate.iterate(problem, lvp, EDP, initial_number_of_steps=20)
u, p = problem.state.split(deepcopy=True)
xdmf.write(u, 1.0)
df.File("ED_displacement.xml") << u
print("LV cavity volume = {} ml".format(geometry.cavity_volume(u=u)))
# Solve for ES
print(("Solver for ES with pressure = {} kPa and active tension = {} kPa"
"".format(ESP, Ta)))
pulse.iterate.iterate(problem, lvp, ESP, initial_number_of_steps=50)
pulse.iterate.iterate(problem,
activation,
Ta,
adapt_step=False,
max_iters=100,
initial_number_of_steps=40)
u, p = problem.state.split(deepcopy=True)
xdmf.write(u, 2.0)
df.File("ES_displacement.xml") << u
print("LV cavity volume = {} ml".format(geometry.cavity_volume(u=u)))
