def planar_wave(ode, domain, D, S1, threshold, d=5):
'''
Finds the conduction velocity of a planar wave. First paces the 0D ode
model for 50 cycles at a BCL of 1000, then initiates a single planar
wave, measuring the conduction velocity half-way in the domain.
'''
# Load the cell model from file
cellmodel = load_ode(ode)
cellmodel = dolfin_jit(cellmodel, field_states, field_parameters)
# Create the CardiacModel for the given domain and cell model
heart = CardiacModel(domain, Constant(0.0), D, None, cellmodel)
# Create the solver
solver = GOSSplittingSolver(heart, GOSSparams())
dolfin_solver = solver.ode_solver
ode_solver = dolfin_solver._ode_system_solvers[0]
BCL = 1000
try:
sspath = "../data/steadystates/"
steadystate = np.load(sspath+"steadystate_%s_BCL%d.npy" % (ode, BCL))
except:
print "Did not find steadystate for %s at BCL: %g, pacing 0D model" % (ode, BCL)
steadystate = find_steadystate(ODE, BCL, 0.01)
# Load steadystate into 2D model
(u, um) = solver.solution_fields()
for node in range(domain.coordinates().shape[0]):
ode_solver.states(node)[:] = steadystate
u.vector()[node] = steadystate[0]
# Define the planar wave stimulus
V = VectorFunctionSpace(domain, 'CG', 1)
S1 = interpolate(S1, V).vector().array()
# Apply the stimulus
ode_solver.set_field_parameters(S1)
xp = 0; yp = 0;
t0 = 0; t1 = 0;
for timestep, (u, vm) in solver.solve((0, tstop), dt):
#plot(u, **plot_args)
x = u.vector()[N/2-d]
y = u.vector()[N/2+d]
print u.vector().max(), x, y
if x > threshold and (x-threshold)*(xp-threshold) < 0:
# X cell has activated
t0 = timestep[0]
if y > threshold and (y-threshold)*(yp-threshold) < 0 and t0 != 0:
# Y cell has activated
t1 = timestep[0]
# Calculate conduction velocity
print "CV: ", 2*d*h/(t1-t0)*1e3
break
xp = x
yp = y
def __init__(self, ode):
# Create the domain
domain = RectangleMesh(0, 0, L, L, N, N)
# Load the cell model from file
cellmodel = load_ode(ode)
cellmodel = dolfin_jit(cellmodel, field_states, field_parameters)
# Create the CardiacModel for the given domain and cell model
heart = CardiacModel(domain, Constant(0.0), D, None, cellmodel)
# Create the solver
solver = GOSSplittingSolver(heart, self.GOSSparams())
# Get the solution fields and subsolvers
dolfin_solver = solver.ode_solver
ode_solver = dolfin_solver._ode_system_solvers[0]
self.solver = solver
self.ode = ode
self.dolfin_solver = dolfin_solver
self.ode_solver = ode_solver
self.domain = domain
def __init__(self, ode):
# Create the domain
domain = RectangleMesh(0, 0, L, L, N, N)
# Load the cell model from file
cellmodel = load_ode(ode)
cellmodel = dolfin_jit(cellmodel, field_states, field_parameters)
# Create the CardiacModel for the given domain and cell model
heart = CardiacModel(domain, Constant(0.0), D, None, cellmodel)
# Create the solver
solver = GOSSplittingSolver(heart, self.GOSSparams())
# Get the solution fields and subsolvers
dolfin_solver = solver.ode_solver
ode_solver = dolfin_solver._ode_system_solvers[0]
self.solver = solver
self.ode = ode
self.dolfin_solver = dolfin_solver
self.ode_solver = ode_solver
self.domain = domain
def pacing_cv(ode, BCL_range, D, L, h, dt):
"""
Pace a 0D cell model for 50 cycles at given BCL, then
simulate a wave in a 1D strand. 5 beats are initiated
at the left hand side of the strand, after the fifth
beat, the conduction velocity is measured.
"""
# Create domain
N = int(L/h) # number of nodes - 1
domain = IntervalMesh(N, 0, L)
# Define functions
V = FunctionSpace(domain, 'Lagrange', 1)
u = TrialFunction(V)
up = Function(V)
v = TestFunction(V)
# Assemble the mass matrix and the stiffness matrix
M = assemble(u*v*dx)
K = assemble(Constant(dt)*inner(D*grad(u), grad(v))*dx)
A = M + K
pde_solver = LUSolver(A)
pde_solver.parameters["reuse_factorization"] = True
# Set up ODESolver
ode = load_ode(ode)
compiled_ode = dolfin_jit(ode, field_states=["V"], field_parameters = [
"stim_period"])
params = DOLFINODESystemSolver.default_parameters()
params["scheme"] = "RL1"
stim_field = interpolate(Expression("near(x[0],0)*sd", sd=1.), V)
#compiled_ode.set_parameter("stim_duration", stim_field)
BCL = 1000
#compiled_ode.set_parameter("stim_period", BCL)
ode_solver = DOLFINODESystemSolver(domain, compiled_ode, params=params)
solver = ode_solver._ode_system_solvers[0]
try:
states = np.load("../data/steadystate_%s_BCL%d.npy" % (ode, BCL))
except:
states = find_steadystate(BCL, 50, dt, ode, plot_results=False)
for i in range(N+1):
solver.states(i)[:] = states
up.vector()[i] = solver.states(i)[0]
#params = np.zeros((N+1)*2)
solver.set_field_parameters(np.array([BCL]+[0]*N, dtype=np.float_))
#stim_field = interpolate(Expression("0"), V)
#compiled_ode.set_parameter("stim_duration", stim_field)
t = 0.
tstop = 1e6
while t < tstop:
# Step ODE solver
ode_solver.step((t, t+dt), up)
# Assemble RHS and solve pde
b = M*up.vector()
pde_solver.solve(up.vector(), b)
# Plot solution
plot(up, range_min=-80.0, range_max=40.0)
t += dt
def pacing_cv(ode, BCL_range, D, dt, threshold=0, stim_amp=0, plot_args=None):
D = Constant(D) # Must be adjusted with temporal and spatial resolution
L = 20
h = 0.5
dt_low = 0.1
# Create dolfin mesh
N = int(L / h)
domain = IntervalMesh(N, 0, L)
# Load the cell model from file
ode = load_ode(ode)
cellmodel = dolfin_jit(ode,
field_states=["V"],
field_parameters=["stim_period", "stim_amplitude"])
# Create the CardiacModel for the given mesh and cell model
heart = CardiacModel(domain, Constant(0.0), D, None, cellmodel)
# Create the solver
solver = GOSSplittingSolver(heart, GOSSparams())
# Get the solution fields and subsolvers
dolfin_solver = solver.ode_solver
ode_solver = dolfin_solver._ode_system_solvers[0]
results = np.zeros((4, len(BCL_range)))
for i, BCL in enumerate(BCL_range):
# Set the stimulus parameter field
stim_field = np.zeros(2 * (N + 1), dtype=np.float_)
stim_field[0] = BCL
stim_field[1] = stim_amp
ode_solver.set_field_parameters(stim_field)
# Pace 0D cell model and find quasi steady state
sspath = "../data/steadystates/"
try:
states = np.load(sspath + "steadystate_%s_BCL%d.npy" % (ode, BCL))
except:
print "Did not find steadystate for %s at BCL: %g, pacing 0D model" % (
ode, BCL)
find_steadystate(ODE, BCL, 0.01)
# Load quasi steady state into 1D model
(u, um) = solver.solution_fields()
for node in range(N + 1):
ode_solver.states(node)[:] = states
u.vector()[node] = states[0]
# Used for measuring cell activation
xp = 0
yp = 0
results[0][i] = BCL
print "BCL: %g" % BCL
# Do 3 pulses
for pulsenr in range(1, 4):
# Solve the pulse in higher temporal resolution
for timestep, (u, vm) in solver.solve((i * BCL, i * BCL + 50), dt):
if plot_args: plot(u, **plot_args)
x = u.vector()[20]
y = u.vector()[35]
if x > threshold and (x - threshold) * (xp - threshold) < 0:
t0 = (threshold - xp) / (x - xp) * dt + tp
if y > threshold and (y - threshold) * (yp - threshold) < 0:
t1 = (threshold - yp) / (y - yp) * dt + tp
# Calculate conduction velocity
Cv = 15 * h / (t1 - t0) * 1e3
print "\tCv: %g" % Cv
results[pulsenr][i] = Cv
t0 = 0
t1 = 0
xp = x
yp = y
tp = timestep[0]
# Wait for next pulse
for timestep, (u, vm) in solver.solve(
(i * BCL + 50, (i + 1) * BCL), dt_low):
if plot_args: plot(u, **plot_args)
np.save("../data/results/cv_%s" % ode, results)
def spiral(ode,
domain,
D,
S1,
S2,
plot_args={},
save_fig=False,
threshold=0,
BCL=500):
# Load the cell model from file
cellmodel = load_ode(ode)
cellmodel = dolfin_jit(cellmodel, field_states, field_parameters)
# Create the CardiacModel for the given domain and cell model
heart = CardiacModel(domain, Constant(0.0), D, None, cellmodel)
# Create the solver
solver = GOSSplittingSolver(heart, GOSSparams())
dolfin_solver = solver.ode_solver
ode_solver = dolfin_solver._ode_system_solvers[0]
# Calculate parameter fields
V = VectorFunctionSpace(domain, 'CG', 1)
S1 = interpolate(S1, V).vector().array()
S2 = interpolate(S2, V).vector().array()
nostim = np.zeros(S1.shape, dtype=np.float_)
# Read in steady state from file
try:
sspath = "../data/steadystates/"
steadystate = np.load(sspath + "steadystate_%s_BCL%d.npy" % (ode, BCL))
except:
print "Did not find steadystate for %s at BCL: %g, pacing 0D model" % (
ode, BCL)
steadystate = find_steadystate(ODE, BCL, 0.01)
# Load steadystate into 2D model
(u, um) = solver.solution_fields()
for node in range(domain.coordinates().shape[0]):
ode_solver.states(node)[:] = steadystate
u.vector()[node] = steadystate[0]
cnt = 0
# Stimulate S1 pulse
plot(u, interactive=True, **plot_args)
ode_solver.set_field_parameters(S1)
for timestep, (u, vm) in solver.solve((0, S2_time), dt):
fig = plot(u, interactive=False, **plot_args)
if save_fig and cnt % 5 == 0:
padded_index = '%08d' % cnt
fig.write_png('../tmp/randfib2_spiral_%s' % ode + padded_index)
cnt += 1
ode_solver.set_field_parameters(S2)
# Stimulate S2 pulse
for timestep, (u, vm) in solver.solve((S2_time, S2_time + 100), dt):
fig = plot(u, interactive=False, **plot_args)
if save_fig and cnt % 5 == 0:
padded_index = '%08d' % cnt
fig.write_png('../tmp/randfib2_spiral_%s' % ode + padded_index)
cnt += 1
# Turn of all stimulus and iterate until simulation stop
# We monitor the top right corner to find the randfib_spiral period
ode_solver.set_field_parameters(nostim)
trig_time = []
xp = 0
for timestep, (u, vm) in solver.solve((S2_time + 100, tstop), dt):
fig = plot(u, interactive=False, **plot_args)
x = u.vector()[-1]
if x > threshold and (x - threshold) * (xp - threshold) < 0:
trig_time.append(timestep[0])
print "Trigger: %g" % timestep[0]
xp = x
if save_fig and cnt % 5 == 0:
padded_index = '%08d' % cnt
fig.write_png('../tmp/randfib2_spiral_%s' % ode + padded_index)
cnt += 1
save_fig = True
plot_args = {
'range_min': 0.,
'range_max': 1.,
'mode': 'color',
#'window_width': 1366,
#'window_height': 744
}
ode = 'FK_cAF'
domain = Mesh('atrial_mesh.xml')
# Load the cell model from file
cellmodel = load_ode(ode)
cellmodel = dolfin_jit(cellmodel, field_states, field_parameters)
def GOSSparams():
params = GOSSplittingSolver.default_parameters()
params["pde_solver"] = "monodomain"
params["MonodomainSolver"]["linear_solver_type"] = "iterative"
params["MonodomainSolver"]["theta"] = 1.0
params["ode_solver"]["scheme"] = "RL1"
params["apply_stimulus_current_to_pde"] = False
return params
# Create the CardiacModel for the given domain and cell model
heart = CardiacModel(domain, Constant(0.0), D, None, cellmodel)
def pacing_cv(ode, BCL_range, D, dt, threshold=0, stim_amp=0, plot_args=None):
D = Constant(D) # Must be adjusted with temporal and spatial resolution
L = 20
h = 0.5
dt_low = 0.1
# Create dolfin mesh
N = int(L/h)
domain = IntervalMesh(N, 0, L)
# Load the cell model from file
ode = load_ode(ode)
cellmodel = dolfin_jit(ode, field_states=["V"],
field_parameters=["stim_period", "stim_amplitude"])
# Create the CardiacModel for the given mesh and cell model
heart = CardiacModel(domain, Constant(0.0), D, None, cellmodel)
# Create the solver
solver = GOSSplittingSolver(heart, GOSSparams())
# Get the solution fields and subsolvers
dolfin_solver = solver.ode_solver
ode_solver = dolfin_solver._ode_system_solvers[0]
results = np.zeros((4, len(BCL_range)))
for i, BCL in enumerate(BCL_range):
# Set the stimulus parameter field
stim_field = np.zeros(2*(N+1), dtype=np.float_)
stim_field[0] = BCL
stim_field[1] = stim_amp
ode_solver.set_field_parameters(stim_field)
# Pace 0D cell model and find quasi steady state
sspath = "../data/steadystates/"
try:
states = np.load(sspath+"steadystate_%s_BCL%d.npy" % (ode, BCL))
except:
print "Did not find steadystate for %s at BCL: %g, pacing 0D model" % (ode, BCL)
find_steadystate(ODE, BCL, 0.01)
# Load quasi steady state into 1D model
(u, um) = solver.solution_fields()
for node in range(N+1):
ode_solver.states(node)[:] = states
u.vector()[node] = states[0]
# Used for measuring cell activation
xp = 0; yp=0
results[0][i] = BCL
print "BCL: %g" % BCL
# Do 3 pulses
for pulsenr in range(1,4):
# Solve the pulse in higher temporal resolution
for timestep, (u, vm) in solver.solve((i*BCL, i*BCL+50), dt):
if plot_args: plot(u, **plot_args)
x = u.vector()[20]
y = u.vector()[35]
if x > threshold and (x-threshold)*(xp-threshold) < 0:
t0 = (threshold - xp)/(x - xp)*dt + tp
if y > threshold and (y-threshold)*(yp-threshold) < 0:
t1 = (threshold - yp)/(y - yp)*dt + tp
# Calculate conduction velocity
Cv = 15*h/(t1-t0)*1e3
print "\tCv: %g" % Cv
results[pulsenr][i] = Cv
t0 = 0; t1 = 0
xp = x
yp = y
tp = timestep[0]
# Wait for next pulse
for timestep, (u, vm) in solver.solve((i*BCL+50, (i+1)*BCL), dt_low):
if plot_args: plot(u, **plot_args)
np.save("../data/results/cv_%s"%ode, results)
def spiral(ode, domain, D, S1, S2, plot_args={}, save_fig=False, threshold=0, BCL=500):
# Load the cell model from file
cellmodel = load_ode(ode)
cellmodel = dolfin_jit(cellmodel, field_states, field_parameters)
# Create the CardiacModel for the given domain and cell model
heart = CardiacModel(domain, Constant(0.0), D, None, cellmodel)
# Create the solver
solver = GOSSplittingSolver(heart, GOSSparams())
dolfin_solver = solver.ode_solver
ode_solver = dolfin_solver._ode_system_solvers[0]
# Calculate parameter fields
V = VectorFunctionSpace(domain, 'CG', 1)
S1 = interpolate(S1, V).vector().array()
S2 = interpolate(S2, V).vector().array()
nostim = np.zeros(S1.shape, dtype=np.float_)
# Read in steady state from file
try:
sspath = "../data/steadystates/"
steadystate = np.load(sspath+"steadystate_%s_BCL%d.npy" % (ode, BCL))
except:
print "Did not find steadystate for %s at BCL: %g, pacing 0D model" % (ode, BCL)
steadystate = find_steadystate(ODE, BCL, 0.01)
# Load steadystate into 2D model
(u, um) = solver.solution_fields()
for node in range(domain.coordinates().shape[0]):
ode_solver.states(node)[:] = steadystate
u.vector()[node] = steadystate[0]
cnt = 0
# Stimulate S1 pulse
plot(u, interactive=True, **plot_args)
ode_solver.set_field_parameters(S1)
for timestep, (u, vm) in solver.solve((0, S2_time), dt):
fig = plot(u, interactive=False, **plot_args)
if save_fig and cnt % 5 == 0:
padded_index = '%08d' % cnt
fig.write_png('../tmp/spiral_%s' % ode + padded_index)
cnt += 1
ode_solver.set_field_parameters(S2)
# Stimulate S2 pulse
for timestep, (u, vm) in solver.solve((S2_time, S2_time+100), dt):
fig = plot(u, interactive=False, **plot_args)
if save_fig and cnt % 5 == 0:
padded_index = '%08d' % cnt
fig.write_png('../tmp/spiral_%s' % ode + padded_index)
cnt += 1
# Turn of all stimulus and iterate until simulation stop
# We monitor the top right corner to find the spiral period
ode_solver.set_field_parameters(nostim)
trig_time = []
xp = 0;
for timestep, (u, vm) in solver.solve((S2_time+100, tstop), dt):
fig = plot(u, interactive=False, **plot_args)
x = u.vector()[-1]
if x > threshold and (x-threshold)*(xp-threshold) < 0:
trig_time.append(timestep[0])
print "Trigger: %g" % timestep[0]
xp = x
if save_fig and cnt % 5 == 0:
padded_index = '%08d' % cnt
fig.write_png('../tmp/spiral_%s' % ode + padded_index)
cnt += 1
def pacing_cv(ode, BCL_range, D, L, h, dt):
"""
Pace a 0D cell model for 50 cycles at given BCL, then
simulate a wave in a 1D strand. 5 beats are initiated
at the left hand side of the strand, after the fifth
beat, the conduction velocity is measured.
"""
# Create domain
N = int(L / h) # number of nodes - 1
domain = IntervalMesh(N, 0, L)
# Define functions
V = FunctionSpace(domain, 'Lagrange', 1)
u = TrialFunction(V)
up = Function(V)
v = TestFunction(V)
# Assemble the mass matrix and the stiffness matrix
M = assemble(u * v * dx)
K = assemble(Constant(dt) * inner(D * grad(u), grad(v)) * dx)
A = M + K
pde_solver = LUSolver(A)
pde_solver.parameters["reuse_factorization"] = True
# Set up ODESolver
ode = load_ode(ode)
compiled_ode = dolfin_jit(ode,
field_states=["V"],
field_parameters=["stim_period"])
params = DOLFINODESystemSolver.default_parameters()
params["scheme"] = "RL1"
stim_field = interpolate(Expression("near(x[0],0)*sd", sd=1.), V)
#compiled_ode.set_parameter("stim_duration", stim_field)
BCL = 1000
#compiled_ode.set_parameter("stim_period", BCL)
ode_solver = DOLFINODESystemSolver(domain, compiled_ode, params=params)
solver = ode_solver._ode_system_solvers[0]
try:
states = np.load("../data/steadystate_%s_BCL%d.npy" % (ode, BCL))
except:
states = find_steadystate(BCL, 50, dt, ode, plot_results=False)
for i in range(N + 1):
solver.states(i)[:] = states
up.vector()[i] = solver.states(i)[0]
#params = np.zeros((N+1)*2)
solver.set_field_parameters(np.array([BCL] + [0] * N, dtype=np.float_))
#stim_field = interpolate(Expression("0"), V)
#compiled_ode.set_parameter("stim_duration", stim_field)
t = 0.
tstop = 1e6
while t < tstop:
# Step ODE solver
ode_solver.step((t, t + dt), up)
# Assemble RHS and solve pde
b = M * up.vector()
pde_solver.solve(up.vector(), b)
# Plot solution
plot(up, range_min=-80.0, range_max=40.0)
t += dt
D = as_tensor([[Dx, 0.], [0, Dy]])
dt = 0.125
tstop = 25.0
a = Constant(1.)
V_init = -85.
V_amp = 85.
t = Constant(0.)
# Domain and solution space
do_plot = False
L = 100.
N = 1024
#N = 128
domain = RectangleMesh(-L, -L, L, L, N, N)
cellmodel = dolfin_jit(load_ode("tentusscher_panfilov_2006_M_cell.ode"),
field_states=["V"])
heart = CardiacModel(domain, t, D, None, cellmodel)
ps = GOSSplittingSolver.default_parameters()
ps["pde_solver"] = "monodomain"
ps["MonodomainSolver"]["linear_solver_type"] = "iterative"
ps["MonodomainSolver"]["theta"] = 1.0
ps["ode_solver"]["solver"] = "RL1"
ps["ode_solver"]["num_threads"] = 8 / MPI.size(domain.mpi_comm())
# If cuda
ps["ode_solver"]["use_cuda"] = True
ps["ode_solver"]["cuda_params"]["float_precision"] = "double"
ps["ode_solver"]["cuda_params"]["solver"] = "rush_larsen"
ps["apply_stimulus_current_to_pde"] = True
axis = [-80., 40.]
save_fig = True
plot_args = {'range_min': 0.,
'range_max': 1.,
'mode': 'color',
#'window_width': 1366,
#'window_height': 744
}
ode = 'FK_cAF'
domain = Mesh('atrial_mesh.xml')
# Load the cell model from file
cellmodel = load_ode(ode)
cellmodel = dolfin_jit(cellmodel, field_states, field_parameters)
def GOSSparams():
params = GOSSplittingSolver.default_parameters()
params["pde_solver"] = "monodomain"
params["MonodomainSolver"]["linear_solver_type"] = "iterative"
params["MonodomainSolver"]["theta"] = 1.0
params["ode_solver"]["scheme"] = "RL1"
params["apply_stimulus_current_to_pde"] = False
return params
# Create the CardiacModel for the given domain and cell model
heart = CardiacModel(domain, Constant(0.0), D, None, cellmodel)
# Create the solver
solver = GOSSplittingSolver(heart, GOSSparams())
