QSS.py
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Created: Fri, Nov 15, 15:25

QSS.py
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	import inspect
	import pandas as pd
	import numpy as np
	import matplotlib.pyplot as plt
	from matplotlib import cm, colors

	from ..postpro import getFixedPoints
	from ..core import NeuronalBilayerSonophore
	from .pltutils import *
	from ..utils import logger
	from ..batches import runBatch


	def plotVarQSSDynamics(neuron, a, Fdrive, Adrive, charges, varname, varrange, fs=12):
	''' Plot the QSS-approximated derivative of a specific variable as function of
	the variable itself, as well as equilibrium values, for various membrane
	charge densities at a given acoustic amplitude.

	:param neuron: neuron object
	:param a: sonophore radius (m)
	:param Fdrive: US frequency (Hz)
	:param Adrive: US amplitude (Pa)
	:param charges: charge density vector (C/m2)
	:param varname: name of variable to plot
	:param varrange: range over which to compute the derivative
	:return: figure handle
	'''

	# Extract information about variable to plot
	pltvar = neuron.getPltVars()[varname]

	# Get methods to compute derivative and steady-state of variable of interest
	derX_func = getattr(neuron, 'der{}{}'.format(varname[0].upper(), varname[1:]))
	Xinf_func = getattr(neuron, '{}inf'.format(varname))
	derX_args = inspect.getargspec(derX_func)[0][1:]
	Xinf_args = inspect.getargspec(Xinf_func)[0][1:]

	# Get dictionary of charge and amplitude dependent QSS variables
	nbls = NeuronalBilayerSonophore(a, neuron, Fdrive)
	_, Qref, lookups, QSS = nbls.quasiSteadyStates(
	Fdrive, amps=Adrive, charges=charges, squeeze_output=True)
	df = QSS
	df['Vm'] = lookups['V']

	# Create figure
	fig, ax = plt.subplots(figsize=(6, 4))
	ax.set_title('{} neuron - QSS {} dynamics @ {:.2f} kPa'.format(
	neuron.name, pltvar['desc'], Adrive * 1e-3), fontsize=fs)
	ax.set_xscale('log')
	for key in ['top', 'right']:
	ax.spines[key].set_visible(False)
	ax.set_xlabel('$\\rm {}\ ({})$'.format(pltvar['label'], pltvar.get('unit', '')),
	fontsize=fs)
	ax.set_ylabel('$\\rm QSS\ d{}/dt\ ({}/s)$'.format(pltvar['label'], pltvar.get('unit', '1')),
	fontsize=fs)
	ax.set_ylim(-40, 40)
	ax.axhline(0, c='k', linewidth=0.5)

	y0_str = '{}0'.format(varname)
	if hasattr(neuron, y0_str):
	ax.axvline(getattr(neuron, y0_str) * pltvar.get('factor', 1),
	label=y0_str, c='k', linewidth=0.5)

	# For each charge value
	icolor = 0
	for j, Qm in enumerate(charges):
	lbl = 'Q = {:.0f} nC/cm2'.format(Qm * 1e5)

	# Compute variable derivative as a function of its value, as well as equilibrium value,
	# keeping other variables at quasi steady-state
	derX_inputs = [varrange if arg == varname else df[arg][j] for arg in derX_args]
	Xinf_inputs = [df[arg][j] for arg in Xinf_args]
	dX_QSS = neuron.derCai(*derX_inputs)
	Xeq_QSS = neuron.Caiinf(*Xinf_inputs)

	# Plot variable derivative and its root as a function of the variable itself
	c = 'C{}'.format(icolor)
	ax.plot(varrange * pltvar.get('factor', 1), dX_QSS * pltvar.get('factor', 1), c=c, label=lbl)
	ax.axvline(Xeq_QSS * pltvar.get('factor', 1), linestyle='--', c=c)
	icolor += 1

	ax.legend(frameon=False, fontsize=fs - 3)
	for item in ax.get_xticklabels() + ax.get_yticklabels():
	item.set_fontsize(fs)
	fig.tight_layout()

	fig.canvas.set_window_title('{}_QSS_{}_dynamics_{:.2f}kPa'.format(
	neuron.name, varname, Adrive * 1e-3))

	return fig


	def plotQSSvars(neuron, a, Fdrive, Adrive, fs=12):
	''' Plot effective membrane potential, quasi-steady states and resulting membrane currents
	as a function of membrane charge density, for a given acoustic amplitude.

	:param neuron: neuron object
	:param a: sonophore radius (m)
	:param Fdrive: US frequency (Hz)
	:param Adrive: US amplitude (Pa)
	:return: figure handle
	'''

	# Get neuron-specific pltvars
	pltvars = neuron.getPltVars()

	# Compute neuron-specific charge and amplitude dependent QS states at this amplitude
	nbls = NeuronalBilayerSonophore(a, neuron, Fdrive)
	_, Qref, lookups, QSS = nbls.quasiSteadyStates(Fdrive, amps=Adrive, squeeze_output=True)
	Vmeff = lookups['V']

	# Compute QSS currents
	currents = neuron.currents(Vmeff, np.array([QSS[k] for k in neuron.states]))
	iNet = sum(currents.values())

	# Compute fixed points in dQdt profile
	dQdt = -iNet
	Q_SFPs = getFixedPoints(Qref, dQdt, filter='stable')
	Q_UFPs = getFixedPoints(Qref, dQdt, filter='unstable')

	# Extract dimensionless states
	norm_QSS = {}
	for x in neuron.states:
	if 'unit' not in pltvars[x]:
	norm_QSS[x] = QSS[x]

	# Create figure
	fig, axes = plt.subplots(3, 1, figsize=(7, 9))
	axes[-1].set_xlabel('$\\rm Q_m\ (nC/cm^2)$', fontsize=fs)
	for ax in axes:
	for skey in ['top', 'right']:
	ax.spines[skey].set_visible(False)
	for item in ax.get_xticklabels() + ax.get_yticklabels():
	item.set_fontsize(fs)
	for item in ax.get_xticklabels(minor=True):
	item.set_visible(False)
	figname = '{} neuron - QSS dynamics @ {:.2f} kPa'.format(neuron.name, Adrive * 1e-3)
	fig.suptitle(figname, fontsize=fs)

	# Subplot: Vmeff
	ax = axes[0]
	ax.set_ylabel('$V_m^*$ (mV)', fontsize=fs)
	ax.plot(Qref * 1e5, Vmeff, color='k')
	ax.axhline(neuron.Vm0, linewidth=0.5, color='k')

	# Subplot: dimensionless quasi-steady states
	cset = plt.get_cmap('Dark2').colors + plt.get_cmap('tab10').colors
	ax = axes[1]
	ax.set_ylabel('QSS gating variables (-)', fontsize=fs)
	ax.set_yticks([0, 0.5, 1])
	ax.set_ylim([-0.05, 1.05])
	for i, (label, QS_state) in enumerate(norm_QSS.items()):
	ax.plot(Qref * 1e5, QS_state, label=label, c=cset[i])

	# Subplot: currents
	ax = axes[2]
	cset = plt.get_cmap('tab10').colors
	ax.set_ylabel('QSS currents ($\\rm A/m^2$)', fontsize=fs)
	for i, (k, I) in enumerate(currents.items()):
	ax.plot(Qref * 1e5, -I * 1e-3, '--', c=cset[i],
	label='$\\rm -{}$'.format(neuron.getPltVars()[k]['label']))
	ax.plot(Qref * 1e5, -iNet * 1e-3, color='k', label='$\\rm -I_{Net}$')
	ax.axhline(0, color='k', linewidth=0.5)
	if Q_SFPs.size > 0:
	ax.plot(Q_SFPs * 1e5, np.zeros(Q_SFPs.size), 'o', c='k', markersize=5, zorder=2)
	if Q_SFPs.size > 0:
	ax.plot(Q_UFPs * 1e5, np.zeros(Q_UFPs.size), 'o', c='k', markersize=5, mfc='none', zorder=2)

	fig.tight_layout()
	fig.subplots_adjust(right=0.8)
	for ax in axes[1:]:
	ax.legend(loc='center right', fontsize=fs, frameon=False, bbox_to_anchor=(1.3, 0.5))
	for ax in axes[:-1]:
	ax.set_xticklabels([])

	fig.canvas.set_window_title(
	'{}_QSS_states_vs_Qm_{:.2f}kPa'.format(neuron.name, Adrive * 1e-3))

	return fig


	def plotQSSVarVsAmp(neuron, a, Fdrive, varname, amps=None, DC=1.,
	fs=12, cmap='viridis', yscale='lin', zscale='lin'):
	''' Plot a specific QSS variable (state or current) as a function of
	membrane charge density, for various acoustic amplitudes.

	:param neuron: neuron object
	:param a: sonophore radius (m)
	:param Fdrive: US frequency (Hz)
	:param amps: US amplitudes (Pa)
	:param DC: duty cycle (-)
	:param varname: extraction key for variable to plot
	:return: figure handle
	'''

	# Determine stimulation modality
	if a is None and Fdrive is None:
	stim_type = 'elec'
	a = 32e-9
	Fdrive = 500e3
	else:
	stim_type = 'US'

	# Extract information about variable to plot
	pltvar = neuron.getPltVars()[varname]
	Qvar = neuron.getPltVars()['Qm']
	Afactor = {'US': 1e-3, 'elec': 1.}[stim_type]
	# Q_SFPs = []
	# Q_UFPs = []

	log = 'plotting {} neuron QSS {} vs. amp for {} stimulation @ {:.0f}% DC'.format(
	neuron.name, varname, stim_type, DC * 1e2)
	logger.info(log)

	nbls = NeuronalBilayerSonophore(a, neuron, Fdrive)

	# Get reference dictionaries for zero amplitude
	_, Qref, lookups0, QSS0 = nbls.quasiSteadyStates(Fdrive, amps=0., squeeze_output=True)
	Vmeff0 = lookups0['V']
	if stim_type == 'elec': # if E-STIM case, compute steady states with constant capacitance
	Vmeff0 = Qref / neuron.Cm0 * 1e3
	QSS0 = neuron.steadyStates(Vmeff0)
	df0 = QSS0
	df0['Vm'] = Vmeff0

	# Create figure
	fig, ax = plt.subplots(figsize=(6, 4))
	title = '{} neuron - {}steady-state {}'.format(
	neuron.name, 'quasi-' if amps is not None else '', pltvar['desc'])
	if amps is not None:
	title += '\nvs. {} amplitude @ {:.0f}% DC'.format(stim_type, DC * 1e2)
	ax.set_title(title, fontsize=fs)
	ax.set_xlabel('$\\rm {}\ ({})$'.format(Qvar['label'], Qvar['unit']), fontsize=fs)
	ax.set_ylabel('$\\rm QSS\ {}\ ({})$'.format(pltvar['label'], pltvar.get('unit', '')),
	fontsize=fs)
	if yscale == 'log':
	ax.set_yscale('log')
	for key in ['top', 'right']:
	ax.spines[key].set_visible(False)

	# Plot y-variable reference line, if any
	y0 = None
	y0_str = '{}0'.format(varname)
	if hasattr(neuron, y0_str):
	y0 = getattr(neuron, y0_str) * pltvar.get('factor', 1)
	elif varname in neuron.getCurrentsNames() + ['iNet', 'dQdt']:
	y0 = 0.
	y0_str = ''
	if y0 is not None:
	ax.axhline(y0, label=y0_str, c='k', linewidth=0.5)

	# Plot reference QSS profile of variable as a function of charge density
	var0 = extractPltVar(
	neuron, pltvar, pd.DataFrame({k: df0[k] for k in df0.keys()}), name=varname)
	ax.plot(Qref * Qvar['factor'], var0, '--', c='k', zorder=1,
	label='$\\rm A_{{{}}}=0$'.format(stim_type))
	# if varname == 'dQdt':
	# Q_SFPs += getFixedPoints(Qref, var0, filter='stable').tolist()
	# Q_UFPs += getFixedPoints(Qref, var0, filter='unstable').tolist()

	# Define color code
	mymap = plt.get_cmap(cmap)
	zref = amps * Afactor
	if zscale == 'lin':
	norm = colors.Normalize(zref.min(), zref.max())
	elif zscale == 'log':
	norm = colors.LogNorm(zref.min(), zref.max())
	sm = cm.ScalarMappable(norm=norm, cmap=mymap)
	sm._A = []

	# Get amplitude-dependent QSS dictionary
	if stim_type == 'US':
	# Get dictionary of charge and amplitude dependent QSS variables
	_, Qref, lookups, QSS = nbls.quasiSteadyStates(
	Fdrive, amps=amps, DCs=DC, squeeze_output=True)
	df = QSS
	df['Vm'] = lookups['V']
	else:
	# Repeat zero-amplitude QSS dictionary for all amplitudes
	df = {k: np.tile(df0[k], (amps.size, 1)) for k in df0}

	# Plot QSS profiles for various amplitudes
	for i, A in enumerate(amps):
	var = extractPltVar(
	neuron, pltvar, pd.DataFrame({k: df[k][i] for k in df.keys()}), name=varname)
	if varname == 'dQdt' and stim_type == 'elec':
	var += A * DC * pltvar['factor']
	ax.plot(Qref * Qvar['factor'], var, c=sm.to_rgba(A * Afactor), zorder=0)
	# if varname == 'dQdt':
	# # mark eq. point if starting point provided, otherwise mark all FPs
	# Q_SFPs += getFixedPoints(Qref, var, filter='stable').tolist()
	# Q_UFPs += getFixedPoints(Qref, var, filter='unstable').tolist()

	# # Plot fixed-points, if any
	# if len(Q_SFPs) > 0:
	# ax.plot(np.array(Q_SFPs) * Qvar['factor'], np.zeros(len(Q_SFPs)), 'o', c='k',
	# markersize=5, zorder=2)
	# if len(Q_UFPs) > 0:
	# ax.plot(np.array(Q_UFPs) * Qvar['factor'], np.zeros(len(Q_UFPs)), 'x', c='k',
	# markersize=5, zorder=2)

	# Add legend and adjust layout
	ax.legend(frameon=False, fontsize=fs)
	for item in ax.get_xticklabels() + ax.get_yticklabels():
	item.set_fontsize(fs)
	fig.tight_layout()
	fig.subplots_adjust(bottom=0.15, top=0.9, right=0.80, hspace=0.5)

	# Plot amplitude colorbar
	if amps is not None:
	cbarax = fig.add_axes([0.85, 0.15, 0.03, 0.75])
	fig.colorbar(sm, cax=cbarax)
	cbarax.set_ylabel(
	'Amplitude ({})'.format({'US': 'kPa', 'elec': 'mA/m2'}[stim_type]), fontsize=fs)
	for item in cbarax.get_yticklabels():
	item.set_fontsize(fs)

	title = '{}_{}SS_{}'.format(neuron.name, 'Q' if amps is not None else '', varname)
	if amps is not None:
	title += '_vs_{}A_{}_{:.0f}%DC'.format(zscale, stim_type, DC * 1e2)
	fig.canvas.set_window_title(title)

	return fig


	def plotEqChargeVsAmp(neurons, a, Fdrive, amps=None, tstim=250e-3, toffset=50e-3, PRF=100.0,
	DCs=[1.], fs=12, xscale='lin', titrate=False, mpi=False):
	''' Plot the equilibrium membrane charge density as a function of acoustic amplitude,
	given an initial value of membrane charge density.

	:param neurons: neuron objects
	:param a: sonophore radius (m)
	:param Fdrive: US frequency (Hz)
	:param amps: US amplitudes (Pa)
	:return: figure handle
	'''

	# Determine stimulation modality
	if a is None and Fdrive is None:
	stim_type = 'elec'
	a = 32e-9
	Fdrive = 500e3
	else:
	stim_type = 'US'

	logger.info('plotting equilibrium charges for %s stimulation', stim_type)

	# Create figure
	fig, ax = plt.subplots(figsize=(6, 4))
	figname = 'charge stability vs. amplitude'
	ax.set_title(figname)
	ax.set_xlabel('Amplitude ({})'.format({'US': 'kPa', 'elec': 'mA/m2'}[stim_type]),
	fontsize=fs)
	ax.set_ylabel('$\\rm Q_m\ (nC/cm^2)$', fontsize=fs)
	if xscale == 'log':
	ax.set_xscale('log')
	for skey in ['top', 'right']:
	ax.spines[skey].set_visible(False)
	for item in ax.get_xticklabels() + ax.get_yticklabels():
	item.set_fontsize(fs)

	Qrange = (np.inf, -np.inf)

	icolor = 0
	for i, neuron in enumerate(neurons):

	nbls = NeuronalBilayerSonophore(a, neuron, Fdrive)

	# Compute reference charge variation array for zero amplitude
	_, Qref, lookups0, QSS0 = nbls.quasiSteadyStates(Fdrive, amps=0., squeeze_output=True)
	Qrange = (min(Qrange[0], Qref.min()), max(Qrange[1], Qref.max()))
	Vmeff0 = lookups0['V']
	if stim_type == 'elec': # if E-STIM case, compute steady states with constant capacitance
	Vmeff0 = Qref / neuron.Cm0 * 1e3
	QSS0 = neuron.steadyStates(Vmeff0)
	dQdt0 = -neuron.iNet(Vmeff0, np.array([QSS0[k] for k in neuron.states])) # mA/m2

	# Compute 3D QSS charge variation array
	if stim_type == 'US':
	_, _, lookups, QSS = nbls.quasiSteadyStates(Fdrive, amps=amps, DCs=DCs)
	dQdt = -neuron.iNet(lookups['V'], np.array([QSS[k] for k in neuron.states])) # mA/m2
	Afactor = 1e-3
	else:
	Afactor = 1.
	dQdt = np.empty((amps.size, Qref.size, DCs.size))
	for iA, A in enumerate(amps):
	for iDC, DC in enumerate(DCs):
	dQdt[iA, :, iDC] = dQdt0 + A * DC

	# For each duty cycle
	for iDC, DC in enumerate(DCs):
	color = 'k' if len(neurons) * len(DCs) == 1 else 'C{}'.format(icolor)

	# Initialize containers for stable and unstable fixed points
	SFPs = []
	UFPs = []

	stab_points = []

	# Generate QSS batch queue
	QSS_queue = []
	for iA, Adrive in enumerate(amps):
	lookups1D = {k: v[iA, :, iDC] for k, v in lookups.items()}
	lookups1D['Q'] = Qref
	QSS_queue.append([Fdrive, Adrive, DC, lookups1D, dQdt[iA, :, iDC]])

	# Run batch to find stable and unstable fixed points at each amplitude
	QSS_output = runBatch(nbls, 'quasiSteadyStateFixedPoints', QSS_queue, mpi=mpi)

	# Generate simulations batch queue
	sim_queue = nbls.createQueue([Fdrive], amps, [tstim], [toffset], [PRF], [DC], method)

	# Run batch to find stabilization points at each amplitude
	sim_output = runBatch(nbls, 'runIfNone', sim_queue, extra_params=[outdir], mpi=mpi)

	# Retrieve batch output
	for i, Adrive in enumerate(amps):
	SFPs += [(Adrive, Qm) for Qm in QSS_output[i][0]]
	UFPs += [(Adrive, Qm) for Qm in QSS_output[i][1]]

	# TODO: get stabilization point from simulation, if any


	# Plot charge SFPs and UFPs for each acoustic amplitude
	lbl = '{} neuron - {{}}stable fixed points @ {:.0f} % DC'.format(
	neuron.name, DC * 1e2)
	if len(SFPs) > 0:
	A_SFPs, Q_SFPs = np.array(SFPs).T
	ax.plot(np.array(A_SFPs) * Afactor, np.array(Q_SFPs) * 1e5, 'o', c=color,
	markersize=3, label=lbl.format(''))
	if len(UFPs) > 0:
	A_UFPs, Q_UFPs = np.array(UFPs).T
	ax.plot(np.array(A_UFPs) * Afactor, np.array(Q_UFPs) * 1e5, 'x', c=color,
	markersize=3, label=lbl.format('un'))

	# If specified, compute and plot the threshold excitation amplitude
	if titrate:
	if stim_type == 'US':
	Athr = nbls.titrate(Fdrive, tstim, toffset, PRF=PRF, DC=DC)
	ax.axvline(Athr * Afactor, c=color, linestyle='--')
	else:
	for Arange, ls in zip([(0., amps.max(amps.min(), 0.)), ()], ['--', '-.']):
	Athr = neuron.titrate(tstim, toffset, PRF=PRF, DC=DC, Arange=Arange)
	ax.axvline(Athr * Afactor, c=color, linestyle=ls)
	icolor += 1

	# Post-process figure
	ax.set_ylim(np.array([Qrange[0], 0]) * 1e5)
	ax.legend(frameon=False, fontsize=fs)
	fig.tight_layout()

	fig.canvas.set_window_title('QSS_Qstab_vs_{}A_{}_{}_{}%DC{}'.format(
	xscale,
	'_'.join([n.name for n in neurons]),
	stim_type,
	'_'.join(['{:.0f}'.format(DC * 1e2) for DC in DCs]),
	'_with_thresholds' if titrate else ''
	))

	return fig

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