def main(argv):
i0 = 3.0
iPulseStrength = 1000000
resultsFilenamePattern = 'results/integrationINapIKFig4-26PulseStrength%d.npz'
phaseFigFilename = 'figures/fig4-26PhaseSpace.eps'
voltageFigFilename = 'figures/fig4-26Voltage.eps'
plt.figure()
plotHighThresholdINapIKVectorField(i=i0)
resultsFilename = resultsFilenamePattern % iPulseStrength
results = np.load(resultsFilename)
ys = results["ys"]
plt.plot(ys[0, :], ys[1, :], label="p=%d" % iPulseStrength)
plt.grid()
plt.legend()
plt.xlabel('Voltage (mv)')
plt.ylabel('K activation variable, n')
plt.savefig(phaseFigFilename)
times = results["times"]
plt.figure()
plt.plot(times, ys[0, :], label="p=%d" % iPulseStrength)
results.close()
plt.grid()
plt.legend()
plt.xlabel('Time (secs)')
plt.ylabel('Voltage (mv)')
plt.savefig(voltageFigFilename)
pdb.set_trace()
def main(argv):
i0 = 10
numberOfPhaseMarks = 8
annotationGap = 0.02
resultsFilename = 'results/integrationINapIKFig10_1.npz'
aFigFilename = 'figures/fig10_1b.eps'
results = np.load(resultsFilename)
times = results['times']
ys = results['ys']
spikeIndices = getPeakIndices(v=ys[0, :])
spikeTimes = times[spikeIndices]
times = np.delete(times, np.arange(0, spikeIndices[0]))
times = times - times[0]
ys = np.delete(ys, np.arange(0, spikeIndices[0]), axis=1)
spikeIndices = spikeIndices - spikeIndices[0]
spikeTimes = spikeTimes - spikeTimes[0]
period = spikeTimes[1] - spikeTimes[0]
phases = times % period
phasesToPlot = np.arange(0, period, period / numberOfPhaseMarks)
indicesBtwFirstAndSecondSpike = np.arange(0, spikeIndices[1])
phasesToSearch = phases[indicesBtwFirstAndSecondSpike]
indicesPhasesToPlot = np.empty(len(phasesToPlot), dtype=np.int64)
for i in xrange(len(phasesToPlot)):
phaseToPlot = phasesToPlot[i]
indicesPhasesToPlot[i] = np.argmin(np.abs(phasesToSearch -
phaseToPlot))
plt.figure()
plotHighThresholdINapIKVectorField(i=i0)
plt.plot(ys[0, :], ys[1, :], label="limit cycle attractor")
plt.plot(ys[0, indicesPhasesToPlot], ys[1, indicesPhasesToPlot], 'ro')
plt.annotate("0,T",
xy=ys[:, 0],
xytext=ys[:, indicesPhasesToPlot[0]] + annotationGap,
color="red",
size=14)
for i in xrange(1, len(indicesPhasesToPlot)):
plt.annotate("%d/%dT" % (i, numberOfPhaseMarks),
xy=ys[:, indicesPhasesToPlot[i]],
xytext=ys[:, indicesPhasesToPlot[i]] + annotationGap,
color="red",
size=14)
plt.grid()
plt.legend(loc="upper left")
plt.xlabel('Voltage (mv)')
plt.ylabel('K activation variable, n')
plt.ylim((-0.1, 0.8))
plt.savefig(aFigFilename)
plt.show()
pdb.set_trace()
def main(argv):
integrationFilename = "results/integrationINapIKFig10_10_matching1-1Sync.npz"
figFilename = "figures/fig10_10b_matching1-1Sync.eps"
nPhases = 6
ylim = (-.1, .7)
fontsize = 20
integrationRes = np.load(integrationFilename)
plt.plot(integrationRes["ysDCTrainPulses"][0, :],
integrationRes["ysDCTrainPulses"][1, :],
label="train pulses")
plt.plot(integrationRes["ysDC"][0, :],
integrationRes["ysDC"][1, :],
label="DC")
plotHighThresholdINapIKVectorField(i=integrationRes["i0"])
plt.xlabel("Membrane Potential (V)")
plt.ylabel("K activation variable, n")
plt.ylim(ylim)
spikeIndices = getPeakIndices(v=integrationRes["ysDCTrainPulses"][0, :])
spikeTimes = integrationRes["timesDCTrainPulses"][spikeIndices]
pulseTimes = np.arange(start=integrationRes["tPulse"],
stop=spikeTimes[-1],
step=integrationRes["Ts"])
pulseIndices = np.empty(pulseTimes.shape)
for i in range(len(pulseIndices)):
pulseIndices[i] = np.argmin(
np.abs(pulseTimes[i] - integrationRes["timesDCTrainPulses"]))
for i in range(len(pulseIndices)):
annotation = r"$\theta_{%d}$" % (i + 1)
plt.annotate(annotation,
xy=(integrationRes["ysDCTrainPulses"][0, pulseIndices[i]],
integrationRes["ysDCTrainPulses"][1,
pulseIndices[i]]),
fontsize=fontsize)
plt.savefig(figFilename)
plt.show()
pdb.set_trace()
def main(argv):
if len(argv) != 3:
sys.exit("Usage: %s tauV i0" % argv[0])
aTauV = float(argv[1])
i0 = float(argv[2])
tauV = lambda v: aTauV
resultsFilename = 'results/integrationINapIKFig6-07TauV%.02fI%.02f.npz' % (
aTauV, i0)
phaseFigFilename = 'figures/fig6-07PhaseSpaceTauV%.02fI%.02f.eps' % (aTauV,
i0)
voltageFigFilename = 'figures/fig6-07VoltageTauV%.02fI%.02f.eps' % (aTauV,
i0)
results = np.load(resultsFilename)
plt.figure()
plotHighThresholdINapIKVectorField(i=results['i0'])
plt.plot(results['ys'][0, :], results['ys'][1, :], label="trayectory")
axes = plt.gca()
ylim = axes.get_ylim()
axes.set_ylim((-0.1, ylim[1]))
plt.grid()
plt.legend()
plt.xlabel('Voltage (mv)')
plt.ylabel('K activation variable, n')
plt.savefig(phaseFigFilename)
plt.figure()
plt.plot(results['times'], results['ys'][0, :])
results.close()
plt.grid()
plt.ylim((-90, -30))
plt.xlim((0, 100))
plt.axhline(y=-60.9325 - 11.0, color="black")
plt.axhline(y=-60.9325 + 11.0, color="black")
plt.xlabel('Time (msec)')
plt.ylabel('Voltage (mv)')
plt.savefig(voltageFigFilename)
pdb.set_trace()
def main(argv):
iPulseStrength = 1000000
resultsFilenamePattern = 'results/integrationINapIKFig4-23PulseStrength%d.npz'
phaseFigFilename = 'figures/fig4-23PhaseSpace.eps'
voltageFigFilename = 'figures/fig4-23Voltage.eps'
plt.figure()
plotHighThresholdINapIKVectorField()
'''
plotINapIKVectorField(I=3.0, c=1.0, eL=-80, gL=8, gNa=20, gK=10,
mVOneHalf=-20, mK=15,
nVOneHalf=-25, nK=5, tauV=0.152, eNa=60,
eK=-90, nDotScaleFactor=200,
vMin=-90.0, vMax=20.0, nVs=19, nVsDense=100,
nMin=0.0, nMax=0.7, nNs=18,
vNullclineLabel="v nullcline",
nNullclineLabel="n nullcline")
'''
resultsFilename = resultsFilenamePattern % iPulseStrength
results = np.load(resultsFilename)
plt.plot(results['ys'][0, :], results['ys'][1, :],
label="p=%d"%iPulseStrength)
plt.grid()
plt.legend()
plt.xlabel('Voltage (mv)')
plt.ylabel('K activation variable, n')
ylim = plt.gca().get_ylim()
plt.ylim([-0.1, ylim[1]])
plt.savefig(phaseFigFilename)
plt.figure()
plt.plot(results['times'], results['ys'][0, :],
label="p=%d"%iPulseStrength)
results.close()
plt.grid()
plt.legend()
plt.xlabel('Time (secs)')
plt.ylabel('Voltage (mv)')
plt.savefig(voltageFigFilename)
pdb.set_trace()
def main(argv):
results10_4Filename = 'results/integrationINapIKFig10_4LeftPanel.npz'
results10_10Filename = 'results/integrationINapIKFig10_10.npz'
figFilename = 'figures/fig10_10b.eps'
nPhases = 4
ylim = (-.1, .7)
fontsize = 20
results10_4 = np.load(results10_4Filename)
results10_10 = np.load(results10_10Filename)
plt.plot(results10_10["ys"][0, :],
results10_10["ys"][1, :],
label="limit cycle pulse")
plt.plot(results10_4["ysDC"][0, :],
results10_4["ysDC"][1, :],
label="limit cycle DC")
plotHighThresholdINapIKVectorField(i=results10_10["i0"])
plt.xlabel("Membrane Potential (V)")
plt.ylabel('K activation variable, n')
plt.ylim(ylim)
pulseTimes = results10_10["offset"]+\
np.arange(start=0, stop=nPhases, step=1)*results10_10["Ts"]
pulseIndices = np.empty(pulseTimes.shape)
for i in range(len(pulseIndices)):
pulseIndices[i] = np.argmin(
np.abs(pulseTimes[i] - results10_10["times"]))
for i in range(len(pulseIndices)):
annotation = r"$\theta_%d$" % (i + 1)
plt.annotate(annotation,
xy=(results10_10["ys"][0, pulseIndices[i]],
results10_10["ys"][1, pulseIndices[i]]),
fontsize=fontsize)
plt.savefig(figFilename)
plt.show()
pdb.set_trace()
def main(argv):
def integrateForwardManually(deriv, t0, y0, dt, nTSteps):
ts = np.empty(nTSteps)
ys = np.empty((len(y0), nTSteps))
t = t0
y = y0
ts[0] = t
ys[:, 0] = y
for i in range(1, nTSteps):
t = t + dt
y = y + dt * deriv(y=y, t=t)
print("t=%.02f, V=%.02f, n=%.02f" % (t, y[0], y[1]))
ts[i] = t
ys[:, i] = y
return {"times": ts, "ys": ys}
def integrateBackwardManually(deriv, t0, y0, dt, nTSteps):
ts = np.empty(nTSteps)
ys = np.empty((len(y0), nTSteps))
t = t0
y = y0
ts[0] = t
ys[:, 0] = y
for i in range(1, nTSteps):
t = t - dt
y = y + dt * deriv(y=y, t=t)
if y[1] < 0.0:
y[1] = 0.0
print("t=%.02f, V=%.02f, n=%.02f" % (t, y[0], y[1]))
ts[i] = t
ys[:, i] = y
return {"times": ts, "ys": ys}
epsilon = 1e-6
# v0 = 10.00
v0 = -61.0
n0 = 0.48110
t0 = 0.0
# tf = 1*7.25
tf = 1 * 7.25
dt = 1e-3
nTSteps = int(round((tf - t0) / dt))
i0 = 10
def i(t):
return (i0)
iNapIKModel = INapIKModel.getHighThresholdInstance()
iNapIKModel.setI(i=i)
# n0 = iNapIKModel._nInf(v=v0)
y0 = np.array([v0, n0])
# res = integrateForward(deriv=iNapIKModel.deriv, t0=t0, y0=y0, dt=dt, nTSteps=nTSteps)
res = integrateBackward(deriv=iNapIKModel.deriv,
t0=tf,
y0=y0,
dt=dt,
nTSteps=nTSteps)
# res = integrateForwardManually(deriv=iNapIKModel.deriv, t0=t0, y0=y0, dt=dt, nTSteps=nTSteps)
# res = integrateBackwardManually(deriv=iNapIKModel.deriv, t0=tf, y0=y0, dt=dt, nTSteps=nTSteps)
plt.plot(res["times"], res["ys"][0, :])
plt.xlabel("Time (sec)")
plt.ylabel("Voltage (mV)")
plt.ylim((-100, 20))
plt.figure()
plotHighThresholdINapIKVectorField(i=i0)
plt.plot(res["ys"][0, :], res["ys"][1, :], label="limit cycle attractor")
plt.xlim((-100, 20))
plt.xlabel('Voltage (mv)')
plt.ylabel('K activation variable, n')
plt.show()
pdb.set_trace()
def main(argv):
indexPhaseX0 = 10
numberOfPhasesForX0 = 40
i0 = 10
nSPLUNew = 1000
vMin = -90
vMax = 15
nMin = -0.1
nMax = 0.8
marginStart = "minX"
integrationFilename = "results/integrationINapIKFig10_1.npz"
isochronFilename = \
"results/isochronINapIKFig10_1Phase%02dOver%d.npz"%(indexPhaseX0,
numberOfPhasesForX0)
figFilename = \
"figures/isochronINapIKFig10_1Phase%02dOver%d.eps"%(indexPhaseX0,
numberOfPhasesForX0)
results = np.load(integrationFilename)
times = results["times"]
ys = results["ys"]
spikeIndices = getPeakIndices(v=ys[0,:])
spikeTimes = times[spikeIndices]
times = np.delete(times, np.arange(0,spikeIndices[0]))
times = times-times[0]
ys = np.delete(ys, np.arange(0,spikeIndices[0]), axis=1)
spikeIndices = spikeIndices-spikeIndices[0]
spikeTimes = spikeTimes-spikeTimes[0]
period = spikeTimes[1]-spikeTimes[0]
phases = times%period
phasesForX0 = np.arange(0, period, period/numberOfPhasesForX0)
indicesBtwFirstAndSecondSpike = np.arange(0, spikeIndices[1])
phasesToSearch = phases[indicesBtwFirstAndSecondSpike]
indicesPhasesForX0 = np.empty(len(phasesForX0), dtype=np.int64)
for i in xrange(len(phasesForX0)):
phaseForX0 = phasesForX0[i]
indicesPhasesForX0[i] = np.argmin(np.abs(phasesToSearch-phaseForX0))
x0 = ys[:, indicesPhasesForX0[indexPhaseX0]]
results = np.load(isochronFilename)
isochron = results["isochron"]
validIndices = np.logical_and(np.logical_and(vMin<=isochron[0,:],
isochron[0,:]<=vMax),
np.logical_and(nMin<=isochron[1,:],
isochron[1,:]<=nMax)).nonzero()[0]
isochron = isochron[:,validIndices]
# sortedIsochron = sortIsochron(isochron=isochron, marginStart=marginStart)
# splTck, splU = splprep(sortedIsochron, s=5.0)
# splUNew = np.linspace(splU.min(), splU.max(), nSPLUNew)
# splXInter, splYInter = splev(splUNew, splTck, der=0)
# plt.figure()
plotHighThresholdINapIKVectorField(i=i0)
plt.plot(ys[0, :], ys[1, :], label="limit cycle attractor")
# pdb.set_trace()
plt.annotate("x0", xy=x0, color="red", size=14)
def i(t):
return(i0)
model = INapIKModel.getHighThresholdInstance(i=i)
# plotINapIKNullclines(i=i0, eL=model._eL, gL=model._gL, eNa=model._eNa, gNa=model._gNa, eK=model._eK, gK=model._gK, mVOneHalf=model._mVOneHalf, mK=model._mK, nVOneHalf=model._nVOneHalf, nK=model._nK)
plt.plot(isochron[0,:], isochron[1,:], marker="o", color="lightgray",
linestyle="-")
# plt.plot(splXInter, splYInter, color="gray", linestyle="solid")
plt.legend(loc="upper left")
plt.xlabel("Voltage (mv)")
plt.ylabel("K activation variable, n")
plt.xlim((-90, 15))
plt.ylim((-0.1, 0.8))
plt.savefig(figFilename)
plt.show()
pdb.set_trace()