def setup(self):
self.mesh = UnitCubeMesh(5, 5, 5)
# Create time
self.time = Constant(0.0)
# Create stimulus
self.stimulus = Expression("2.0*t", t=self.time, degree=1)
# Create ac
self.applied_current = Expression("sin(2*pi*x[0])*t",
t=self.time,
degree=3)
# Create conductivity "tensors"
self.M_i = 1.0
self.M_e = 2.0
self.cell_model = FitzHughNagumoManual()
self.cardiac_model = CardiacModel(self.mesh, self.time, self.M_i,
self.M_e, self.cell_model,
self.stimulus, self.applied_current)
dt = 0.1
self.t0 = 0.0
self.dt = [(0.0, dt), (dt * 2, dt / 2), (dt * 4, dt)]
# Test using variable dt interval but using the same dt.
self.T = self.t0 + 5 * dt
self.ics = self.cell_model.initial_conditions()
def __init__(self):
self.mesh = UnitCubeMesh(5, 5, 5)
# Create time
self.time = Constant(0.0)
# Create stimulus
self.stimulus = Expression("2.0*t", t=self.time, degree=1)
# Create ac
self.applied_current = Expression("sin(2*pi*x[0])*t",
t=self.time,
degree=3)
# Create conductivity "tensors"
self.M_i = 1.0
self.M_e = 2.0
self.cell_model = FitzHughNagumoManual()
self.cardiac_model = CardiacModel(self.mesh, self.time, self.M_i,
self.M_e, self.cell_model,
self.stimulus,
self.applied_current)
dt = 0.1
self.t0 = 0.0
if Solver == SplittingSolver:
# FIXME: Dolfin-adjoint fails with adaptive timestep and SplittingSolver
self.dt = dt
else:
self.dt = [(0.0, dt), (dt * 2, dt / 2), (dt * 4, dt)]
# Test using variable dt interval but using the same dt.
self.T = self.t0 + 5 * dt
# Create solver object
params = Solver.default_parameters()
if Solver == SplittingSolver:
params.enable_adjoint = enable_adjoint
params.BidomainSolver.linear_solver_type = solver_type
params.BidomainSolver.petsc_krylov_solver.relative_tolerance = 1e-12
else:
params.BasicBidomainSolver.linear_variational_solver.linear_solver = \
"gmres" if solver_type == "iterative" else "lu"
params.BasicBidomainSolver.linear_variational_solver.krylov_solver.relative_tolerance = 1e-12
params.BasicBidomainSolver.linear_variational_solver.preconditioner = 'ilu'
self.solver = Solver(self.cardiac_model, params=params)
(vs_, vs, vur) = self.solver.solution_fields()
if ics is None:
self.ics = self.cell_model.initial_conditions()
vs_.assign(self.ics)
else:
vs_.vector()[:] = ics.vector()
def setup_model():
"Set-up cardiac model based on a slightly non-standard set of parameters."
# Define cell parameters
k = 0.00004; Vrest = -85.; Vthreshold = -70.; Vpeak = 40.;
v_amp = Vpeak - Vrest
l = 0.63; b = 0.013;
cell_parameters = {"c_1": k*v_amp**2, "c_2": k*v_amp, "c_3": b/l,
"a": (Vthreshold - Vrest)/v_amp, "b": l,
"v_rest":Vrest, "v_peak": Vpeak}
cell = FitzHughNagumoManual(cell_parameters)
# Define conductivities
chi = 2000.0 # cm^{-1}
s_il = 3.0/chi # mS
s_it = 0.3/chi # mS
s_el = 2.0/chi # mS
s_et = 1.3/chi # mS
M_i = as_tensor(((s_il, 0), (0, s_it)))
M_e = as_tensor(((s_el, 0), (0, s_et)))
# Define mesh
domain = UnitSquareMesh(20, 20)
time = Constant(0.0)
heart = CardiacModel(domain, time, M_i, M_e, cell)
return heart
def test_solver_with_domains():
mesh = UnitCubeMesh(5, 5, 5)
time = Constant(0.0)
stimulus = Expression("2.0*t", t=time, degree=1)
# Create ac
applied_current = Expression("sin(2*pi*x[0])*t", t=time, degree=3)
# Create conductivity "tensors"
M_i = 1.0
M_e = 2.0
cell_model = FitzHughNagumoManual()
cardiac_model = CardiacModel(mesh, time, M_i, M_e, cell_model,
stimulus, applied_current)
dt = 0.1
t0 = 0.0
dt = dt
T = t0 + 5*dt
ics = cell_model.initial_conditions()
# Create basic solver
params = SplittingSolver.default_parameters()
params["ode_solver_choice"] = "BasicCardiacODESolver"
solver = SplittingSolver(cardiac_model, params=params)
(vs_, vs, vur) = solver.solution_fields()
vs_.assign(ics)
# Solve
solutions = solver.solve((t0, T), dt)
for (interval, fields) in solutions:
(vs_, vs, vur) = fields
def setup(self):
self.mesh = UnitCubeMesh(2, 2, 2)
self.cell_model = FitzHughNagumoManual()
self.cardiac_model = CardiacModel(self.mesh, None,
1.0, 2.0,
self.cell_model)
class TestSplittingSolver(object):
"Test functionality for the splitting solvers."
def setup(self):
self.mesh = UnitCubeMesh(5, 5, 5)
# Create time
self.time = Constant(0.0)
# Create stimulus
self.stimulus = Expression("2.0*t", t=self.time, degree=1)
# Create ac
self.applied_current = Expression("sin(2*pi*x[0])*t",
t=self.time,
degree=3)
# Create conductivity "tensors"
self.M_i = 1.0
self.M_e = 2.0
self.cell_model = FitzHughNagumoManual()
self.cardiac_model = CardiacModel(self.mesh, self.time, self.M_i,
self.M_e, self.cell_model,
self.stimulus, self.applied_current)
dt = 0.1
self.t0 = 0.0
self.dt = [(0.0, dt), (dt * 2, dt / 2), (dt * 4, dt)]
# Test using variable dt interval but using the same dt.
self.T = self.t0 + 5 * dt
self.ics = self.cell_model.initial_conditions()
@medium
@parametrize(("solver_type"), ["direct", "iterative"])
def test_basic_and_optimised_splitting_solver_exact(self, solver_type):
"""Test that basic and optimised splitting solvers yield
very comparative results when configured identically."""
# Create basic solver
params = BasicSplittingSolver.default_parameters()
params["BasicCardiacODESolver"]["S_polynomial_family"] = "CG"
params["BasicCardiacODESolver"]["S_polynomial_degree"] = 1
solver = BasicSplittingSolver(self.cardiac_model, params=params)
(vs_, vs, vur) = solver.solution_fields()
vs_.assign(self.ics)
# Solve
solutions = solver.solve((self.t0, self.T), self.dt)
for (interval, fields) in solutions:
(vs_, vs, vur) = fields
a = vs.vector().norm("l2")
c = vur.vector().norm("l2")
assert_almost_equal(interval[1], self.T, 1e-10)
if dolfin_adjoint:
adj_reset()
# Create optimised solver with direct solution algorithm
params = SplittingSolver.default_parameters()
params["BidomainSolver"]["linear_solver_type"] = solver_type
params["enable_adjoint"] = False
if solver_type == "direct":
params["BidomainSolver"]["use_avg_u_constraint"] = True
solver = SplittingSolver(self.cardiac_model, params=params)
(vs_, vs, vur) = solver.solution_fields()
vs_.assign(self.ics)
# Solve again
solutions = solver.solve((self.t0, self.T), self.dt)
for (interval, fields) in solutions:
(vs_, vs, vur) = fields
assert_almost_equal(interval[1], self.T, 1e-10)
b = vs.vector().norm("l2")
d = vur.vector().norm("l2")
print "a, b = ", a, b
print "c, d = ", c, d
print "a - b = ", (a - b)
print "c - d = ", (c - d)
# Compare results, discrepancy is in difference in ODE
# solves.
assert_almost_equal(a, b, tolerance=1.)
assert_almost_equal(c, d, tolerance=1.)
def test_fitz_hugh_nagumo_modified(self):
k = 0.00004
Vrest = -85.
Vthreshold = -70.
Vpeak = 40.
k = 0.00004
l = 0.63
b = 0.013
class FHN2(CardiacCellModel):
"""ODE model:
parameters(Vrest,Vthreshold,Vpeak,k,l,b,ist)
input(u)
output(g)
default_states(v=-85, w=0)
Vrest = -85;
Vthreshold = -70;
Vpeak = 40;
k = 0.00004;
l = 0.63;
b = 0.013;
ist = 0.0
v = u[0]
w = u[1]
g[0] = -k*(v-Vrest)*(w+(v-Vthreshold)*(v-Vpeak))-ist;
g[1] = l*(v-Vrest) - b*w;
[specified by G. T. Lines Sept 22 2012]
Note the minus sign convention here in the specification of
I (g[0]) !!
"""
def __init__(self):
CardiacCellModel.__init__(self)
def default_parameters(self):
parameters = Parameters("FHN2")
parameters.add("Vrest", Vrest)
parameters.add("Vthreshold", Vthreshold)
parameters.add("Vpeak", Vpeak)
parameters.add("k", k)
parameters.add("l", l)
parameters.add("b", b)
parameters.add("ist", 0.0)
return parameters
def I(self, v, w, time=None):
k = self._parameters["k"]
Vrest = self._parameters["Vrest"]
Vthreshold = self._parameters["Vthreshold"]
Vpeak = self._parameters["Vpeak"]
ist = self._parameters["ist"]
i = -k * (v - Vrest) * (w + (v - Vthreshold) *
(v - Vpeak)) - ist
return -i
def F(self, v, w, time=None):
l = self._parameters["l"]
b = self._parameters["b"]
Vrest = self._parameters["Vrest"]
return l * (v - Vrest) - b * w
def num_states(self):
return 1
def __str__(self):
return "Modified FitzHugh-Nagumo cardiac cell model"
def _run(cell):
if dolfin_adjoint:
from dolfin_adjoint import adj_reset
adj_reset()
solver = BasicSingleCellSolver(cell, Constant(0.0))
# Setup initial condition
(vs_, vs) = solver.solution_fields()
vs_.vector()[0] = 30. # Non-resting state
vs_.vector()[1] = 0.
T = 2
solutions = solver.solve((0, T), 0.25)
times = []
v_values = []
s_values = []
for ((t0, t1), vs) in solutions:
times += [0.5 * (t0 + t1)]
v_values.append(vs.vector()[0])
s_values.append(vs.vector()[1])
return (v_values, s_values, times)
# Try the modified one
cell_mod = FHN2()
(v_values_mod, s_values_mod, times_mod) = _run(cell_mod)
# Compare with our standard FitzHugh (reparametrized)
v_amp = Vpeak - Vrest
cell_parameters = {
"c_1": k * v_amp**2,
"c_2": k * v_amp,
"c_3": b / l,
"a": (Vthreshold - Vrest) / v_amp,
"b": l,
"v_rest": Vrest,
"v_peak": Vpeak
}
cell = FitzHughNagumoManual(cell_parameters)
(v_values, s_values, times) = _run(cell)
msg = "Mismatch in %s value comparison, diff = %.16e"
v_diff = abs(v_values[-1] - v_values_mod[-1])
s_diff = abs(s_values[-1] - s_values_mod[-1])
assert (v_diff < 1.e-12), msg % v_diff
assert (s_diff < 1.e-12), msg % s_diff
# Look at some plots
import os
if int(os.environ.get("DOLFIN_NOPLOT", 0)) != 1:
import pylab
pylab.title("Standard FitzHugh-Nagumo")
pylab.plot(times, v_values, 'b*')
pylab.plot(times, s_values, 'r-')
pylab.figure()
pylab.title("Modified FitzHugh-Nagumo")
pylab.plot(times_mod, v_values_mod, 'b*')
pylab.plot(times_mod, s_values_mod, 'r-')
def test_fitzhugh_nagumo_manual(self):
"""Test that the manually written FitzHugh-Nagumo model gives
comparable results to a given reference from Sundnes et al,
2006."""
class Stimulus(Expression):
def __init__(self, **kwargs):
self.t = kwargs["t"]
def eval(self, value, x):
if float(self.t) >= 50 and float(self.t) < 60:
v_amp = 125
value[0] = 0.05 * v_amp
else:
value[0] = 0.0
if dolfin_adjoint:
from dolfin_adjoint import adj_reset
adj_reset()
cell = FitzHughNagumoManual()
time = Constant(0.0)
cell.stimulus = Stimulus(t=time, degree=0)
solver = BasicSingleCellSolver(cell, time)
# Setup initial condition
(vs_, vs) = solver.solution_fields()
ic = cell.initial_conditions()
vs_.assign(ic)
# Initial set-up
interval = (0, 400)
dt = 1.0
times = []
v_values = []
s_values = []
# Solve
solutions = solver.solve(interval, dt=dt)
for (timestep, vs) in solutions:
(t0, t1) = timestep
times += [(t0 + t1) / 2]
v_values += [vs.vector()[0]]
s_values += [vs.vector()[1]]
# Regression test
v_max_reference = 2.6883308148064152e+01
s_max_reference = 6.8660144687023219e+01
tolerance = 1.e-14
print "max(v_values) %.16e" % max(v_values)
print "max(s_values) %.16e" % max(s_values)
msg = "Maximal %s value does not match reference: diff is %.16e"
v_diff = abs(max(v_values) - v_max_reference)
s_diff = abs(max(s_values) - s_max_reference)
assert (v_diff < tolerance), msg % ("v", v_diff)
assert (s_diff < tolerance), msg % ("s", s_diff)
# Correctness test
import os
if int(os.environ.get("DOLFIN_NOPLOT", 0)) != 1:
import pylab
pylab.plot(times, v_values, 'b*')
pylab.plot(times, s_values, 'r-')
