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 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
print "done."
# Get the solution fields
(u, um) = solver.solution_fields()
# Load steadystate into 2D model
for i in range(domain.coordinates().shape[0]):
ode_solver.states(i)[:] = steadystate
u.vector()[i] = 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, 10), dt):
fig = plot(u, interactive=False, **plot_args)
if save_fig and cnt % 10 == 0:
padded_index = '%08d' % cnt
fig.write_png('../tmp/atrial_spiral_%s' % ode + padded_index)
cnt += 1
ode_solver.set_field_parameters(S2)
# Stimulate S2 pulse
for timestep, (u, vm) in solver.solve((10, S2_time + 5 * stim_period), dt):
fig = plot(u, interactive=False, **plot_args)
if save_fig and cnt % 10 == 0:
padded_index = '%08d' % cnt
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
"V_amp/2.*(1+tanh(-sqrt(a/(8*D))*2*sqrt(x[0]*x[0]+x[1]*x[1])/r))+V_init",
r=20.,
a=a,
D=Dx,
V_init=V_init,
V_amp=V_amp)
u.interpolate(init_expr)
# Plot solution
if do_plot:
plot(u, scale=1., range_min=-90., range_max=40.)
# Iterate
t = 0.
for timestep, (u, vm) in solver.solve((0, tstop), dt):
# plot solution
if do_plot:
plot(u, scale=1., range_min=-90., range_max=40.)
if MPI.rank(domain.mpi_comm()) == 0:
print timestep[0], "Min:", u.vector().min(), "Max:", u.vector().max()
else:
u.vector().min()
u.vector().max()
if MPI.rank(domain.mpi_comm()) == 0:
list_timings()
interactive()
print "done."
# Get the solution fields
(u, um) = solver.solution_fields()
# Load steadystate into 2D model
for i in range(domain.coordinates().shape[0]):
ode_solver.states(i)[:] = steadystate
u.vector()[i] = 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, 10), dt):
fig = plot(u, interactive=False, **plot_args)
if save_fig and cnt % 10 == 0:
padded_index = '%08d' % cnt
fig.write_png('../tmp/atrial_spiral_%s' % ode + padded_index)
cnt += 1
ode_solver.set_field_parameters(S2)
# Stimulate S2 pulse
for timestep, (u, vm) in solver.solve((10, S2_time+5*stim_period), dt):
fig = plot(u, interactive=False, **plot_args)
if save_fig and cnt % 10 == 0:
padded_index = '%08d' % cnt
