diff --git a/PySONIC/core/bls.py b/PySONIC/core/bls.py index d05d911..e06c962 100644 --- a/PySONIC/core/bls.py +++ b/PySONIC/core/bls.py @@ -1,798 +1,798 @@ # -*- coding: utf-8 -*- # @Author: Theo Lemaire # @Email: theo.lemaire@epfl.ch # @Date: 2016-09-29 16:16:19 # @Last Modified by: Theo Lemaire -# @Last Modified time: 2019-11-26 15:34:51 +# @Last Modified time: 2019-12-04 15:45:23 from enum import Enum import os import json import numpy as np import pandas as pd import scipy.integrate as integrate from scipy.optimize import brentq, curve_fit from .batches import Batch from .model import Model from .simulators import PeriodicSimulator from ..utils import logger, si_format, debug from ..constants import * class PmCompMethod(Enum): ''' Enum: types of computation method for the intermolecular pressure ''' direct = 1 predict = 2 def LennardJones(x, beta, alpha, C, m, n): ''' Generic expression of a Lennard-Jones function, adapted for the context of symmetric deflection (distance = 2x). :param x: deflection (i.e. half-distance) :param beta: x-shifting factor :param alpha: x-scaling factor :param C: y-scaling factor :param m: exponent of the repulsion term :param n: exponent of the attraction term :return: Lennard-Jones potential at given distance (2x) ''' return C * (np.power((alpha / (2 * x + beta)), m) - np.power((alpha / (2 * x + beta)), n)) def lookup(func): ''' Load parameters from lookup file, or compute them and sotre them in lookup file. ''' lookup_path = os.path.join(os.path.split(__file__)[0], 'bls_lookups.json') def wrapper(obj): # lookup_path = obj.getLookupsPath() akey = '{:.1f}'.format(obj.a * 1e9) Qkey = '{:.2f}'.format(obj.Qm0 * 1e5) # Open lookup files try: with open(lookup_path, 'r') as fh: lookups = json.load(fh) except FileNotFoundError: lookups = {} # If info not in lookups, compute parameters and add them if akey not in lookups or Qkey not in lookups[akey]: func(obj) if akey not in lookups: lookups[akey] = {Qkey: {'LJ_approx': obj.LJ_approx, 'Delta_eq': obj.Delta}} else: lookups[akey][Qkey] = {'LJ_approx': obj.LJ_approx, 'Delta_eq': obj.Delta} logger.debug('Saving BLS derived parameters to lookup file') with open(lookup_path, 'w') as fh: json.dump(lookups, fh, indent=2) # If lookup exists, load parameters from it else: logger.debug('Loading BLS derived parameters from lookup file') obj.LJ_approx = lookups[akey][Qkey]['LJ_approx'] obj.Delta = lookups[akey][Qkey]['Delta_eq'] return wrapper class BilayerSonophore(Model): ''' Definition of the Bilayer Sonophore Model - geometry - pressure terms - cavitation dynamics ''' # BIOMECHANICAL PARAMETERS T = 309.15 # Temperature (K) delta0 = 2.0e-9 # Thickness of the leaflet (m) Delta_ = 1.4e-9 # Initial gap between the two leaflets on a non-charged membrane at equil. (m) pDelta = 1.0e5 # Attraction/repulsion pressure coefficient (Pa) m = 5.0 # Exponent in the repulsion term (dimensionless) n = 3.3 # Exponent in the attraction term (dimensionless) rhoL = 1075.0 # Density of the surrounding fluid (kg/m^3) muL = 7.0e-4 # Dynamic viscosity of the surrounding fluid (Pa.s) muS = 0.035 # Dynamic viscosity of the leaflet (Pa.s) kA = 0.24 # Area compression modulus of the leaflet (N/m) alpha = 7.56 # Tissue shear loss modulus frequency coefficient (Pa.s) C0 = 0.62 # Initial gas molar concentration in the surrounding fluid (mol/m^3) kH = 1.613e5 # Henry's constant (Pa.m^3/mol) P0 = 1.0e5 # Static pressure in the surrounding fluid (Pa) Dgl = 3.68e-9 # Diffusion coefficient of gas in the fluid (m^2/s) xi = 0.5e-9 # Boundary layer thickness for gas transport across leaflet (m) c = 1515.0 # Speed of sound in medium (m/s) # BIOPHYSICAL PARAMETERS epsilon0 = 8.854e-12 # Vacuum permittivity (F/m) epsilonR = 1.0 # Relative permittivity of intramembrane cavity (dimensionless) tscale = 'us' # relevant temporal scale of the model simkey = 'MECH' # keyword used to characterize simulations made with this model def __init__(self, a, Cm0, Qm0, Fdrive=None, embedding_depth=0.0): ''' Constructor of the class. :param a: in-plane radius of the sonophore structure within the membrane (m) :param Cm0: membrane resting capacitance (F/m2) :param Qm0: membrane resting charge density (C/m2) :param Fdrive: frequency of acoustic perturbation (Hz) :param embedding_depth: depth of the embedding tissue around the membrane (m) ''' # Extract resting constants and geometry self.Cm0 = Cm0 self.Qm0 = Qm0 self.a = a self.d = embedding_depth self.S0 = np.pi * self.a**2 # Derive frequency-dependent tissue elastic modulus if Fdrive is not None: G_tissue = self.alpha * Fdrive # G'' (Pa) self.kA_tissue = 2 * G_tissue * self.d # kA of the tissue layer (N/m) else: self.kA_tissue = 0. # Compute Pm params self.computePMparams() # Compute initial volume and gas content self.V0 = np.pi * self.Delta * self.a**2 self.ng0 = self.gasPa2mol(self.P0, self.V0) def __repr__(self): s = '{}({:.1f} nm'.format(self.__class__.__name__, self.a * 1e9) if self.d > 0.: s += ', d={}m'.format(si_format(self.d, precision=1, space=' ')) return s + ')' @staticmethod def inputs(): return { 'a': { 'desc': 'sonophore radius', 'label': 'a', 'unit': 'nm', 'factor': 1e9, 'precision': 0 }, 'Fdrive': { 'desc': 'US frequency', 'label': 'f', 'unit': 'kHz', 'factor': 1e-3, 'precision': 0 }, 'Adrive': { 'desc': 'US pressure amplitude', 'label': 'A', 'unit': 'kPa', 'factor': 1e-3, 'precision': 2 }, 'Qm': { 'desc': 'membrane charge density', 'label': 'Q_m', 'unit': 'nC/cm^2', 'factor': 1e5, 'precision': 1 } } def filecodes(self, Fdrive, Adrive, Qm, PmCompMethod='predict'): return { 'simkey': self.simkey, 'a': '{:.0f}nm'.format(self.a * 1e9), 'Fdrive': '{:.0f}kHz'.format(Fdrive * 1e-3), 'Adrive': '{:.2f}kPa'.format(Adrive * 1e-3), 'Qm': '{:.1f}nCcm2'.format(Qm * 1e5) } @staticmethod def getPltVars(wrapleft='df["', wrapright='"]'): return { 'Pac': { 'desc': 'acoustic pressure', 'label': 'P_{AC}', 'unit': 'kPa', 'factor': 1e-3, 'func': 'Pacoustic({0}t{1}, meta["Adrive"] * {0}stimstate{1}, meta["Fdrive"])'.format( wrapleft, wrapright) }, 'Z': { 'desc': 'leaflets deflection', 'label': 'Z', 'unit': 'nm', 'factor': 1e9, 'bounds': (-1.0, 10.0) }, 'ng': { 'desc': 'gas content', 'label': 'n_g', 'unit': '10^{-22}\ mol', 'factor': 1e22, 'bounds': (1.0, 15.0) }, 'Pmavg': { 'desc': 'average intermolecular pressure', 'label': 'P_M', 'unit': 'kPa', 'factor': 1e-3, 'func': 'PMavgpred({0}Z{1})'.format(wrapleft, wrapright) }, 'Telastic': { 'desc': 'leaflet elastic tension', 'label': 'T_E', 'unit': 'mN/m', 'factor': 1e3, 'func': 'TEleaflet({0}Z{1})'.format(wrapleft, wrapright) }, 'Cm': { 'desc': 'membrane capacitance', 'label': 'C_m', 'unit': 'uF/cm^2', 'factor': 1e2, 'bounds': (0.0, 1.5), 'func': 'v_capacitance({0}Z{1})'.format(wrapleft, wrapright) } } @staticmethod def getPltScheme(): return { 'P_{AC}': ['Pac'], 'Z': ['Z'], 'n_g': ['ng'] } def curvrad(self, Z): ''' Leaflet curvature radius (signed variable) :param Z: leaflet apex deflection (m) :return: leaflet curvature radius (m) ''' if Z == 0.0: return np.inf else: return (self.a**2 + Z**2) / (2 * Z) def v_curvrad(self, Z): ''' Vectorized curvrad function ''' return np.array(list(map(self.curvrad, Z))) def surface(self, Z): ''' Surface area of the stretched leaflet (spherical cap formula) :param Z: leaflet apex deflection (m) :return: stretched leaflet surface (m^2) ''' return np.pi * (self.a**2 + Z**2) def volume(self, Z): ''' Volume of the inter-leaflet space (cylinder +/- 2 spherical caps) :param Z: leaflet apex deflection (m) :return: bilayer sonophore inner volume (m^3) ''' return np.pi * self.a**2 * self.Delta\ * (1 + (Z / (3 * self.Delta) * (3 + Z**2 / self.a**2))) def arealStrain(self, Z): ''' Areal strain of the stretched leaflet epsilon = (S - S0)/S0 = (Z/a)^2 :param Z: leaflet apex deflection (m) :return: areal strain (dimensionless) ''' return (Z / self.a)**2 def capacitance(self, Z): ''' Membrane capacitance (parallel-plate capacitor evaluated at average inter-layer distance) :param Z: leaflet apex deflection (m) :return: capacitance per unit area (F/m2) ''' if Z == 0.0: return self.Cm0 else: return ((self.Cm0 * self.Delta / self.a**2) * (Z + (self.a**2 - Z**2 - Z * self.Delta) / (2 * Z) * np.log((2 * Z + self.Delta) / self.Delta))) def v_capacitance(self, Z): ''' Vectorized capacitance function ''' return np.array(list(map(self.capacitance, Z))) def derCapacitance(self, Z, U): ''' Evolution of membrane capacitance :param Z: leaflet apex deflection (m) :param U: leaflet apex deflection velocity (m/s) :return: time derivative of capacitance per unit area (F/m2.s) ''' dCmdZ = ((self.Cm0 * self.Delta / self.a**2) * ((Z**2 + self.a**2) / (Z * (2 * Z + self.Delta)) - ((Z**2 + self.a**2) * np.log((2 * Z + self.Delta) / self.Delta)) / (2 * Z**2))) return dCmdZ * U @staticmethod def localDeflection(r, Z, R): ''' Local leaflet deflection at specific radial distance (signed) :param r: in-plane distance from center of the sonophore (m) :param Z: leaflet apex deflection (m) :param R: leaflet curvature radius (m) :return: local transverse leaflet deviation (m) ''' if np.abs(Z) == 0.0: return 0.0 else: return np.sign(Z) * (np.sqrt(R**2 - r**2) - np.abs(R) + np.abs(Z)) @staticmethod def Pacoustic(t, Adrive, Fdrive, phi=np.pi): ''' Time-varying acoustic pressure :param t: time (s) :param Adrive: acoustic drive amplitude (Pa) :param Fdrive: acoustic drive frequency (Hz) :param phi: acoustic drive phase (rad) ''' return Adrive * np.sin(2 * np.pi * Fdrive * t - phi) def PMlocal(self, r, Z, R): ''' Local intermolecular pressure :param r: in-plane distance from center of the sonophore (m) :param Z: leaflet apex deflection (m) :param R: leaflet curvature radius (m) :return: local intermolecular pressure (Pa) ''' z = self.localDeflection(r, Z, R) relgap = (2 * z + self.Delta) / self.Delta_ return self.pDelta * ((1 / relgap)**self.m - (1 / relgap)**self.n) def PMavg(self, Z, R, S): ''' Average intermolecular pressure across the leaflet (computed by quadratic integration) :param Z: leaflet apex outward deflection value (m) :param R: leaflet curvature radius (m) :param S: surface of the stretched leaflet (m^2) :return: averaged intermolecular resultant pressure (Pa) .. warning:: quadratic integration is computationally expensive. ''' # Integrate intermolecular force over an infinitely thin ring of radius r from 0 to a fTotal, _ = integrate.quad(lambda r, Z, R: 2 * np.pi * r * self.PMlocal(r, Z, R), 0, self.a, args=(Z, R)) return fTotal / S def v_PMavg(self, Z, R, S): ''' Vectorized PMavg function ''' return np.array(list(map(self.PMavg, Z, R, S))) def LJfitPMavg(self): ''' Determine optimal parameters of a Lennard-Jones expression approximating the average intermolecular pressure. These parameters are obtained by a nonlinear fit of the Lennard-Jones function for a range of deflection values between predetermined Zmin and Zmax. :return: 3-tuple with optimized LJ parameters for PmAvg prediction (Map) and the standard and max errors of the prediction in the fitting range (in Pascals) ''' # Determine lower bound of deflection range: when Pm = Pmmax PMmax = LJFIT_PM_MAX # Pa Zminlb = -0.49 * self.Delta Zminub = 0.0 Zmin = brentq(lambda Z, Pmmax: self.PMavg(Z, self.curvrad(Z), self.surface(Z)) - PMmax, Zminlb, Zminub, args=(PMmax), xtol=1e-16) # Create vectors for geometric variables Zmax = 2 * self.a Z = np.arange(Zmin, Zmax, 1e-11) Pmavg = self.v_PMavg(Z, self.v_curvrad(Z), self.surface(Z)) # Compute optimal nonlinear fit of custom LJ function with initial guess x0_guess = self.delta0 C_guess = 0.1 * self.pDelta nrep_guess = self.m nattr_guess = self.n pguess = (x0_guess, C_guess, nrep_guess, nattr_guess) popt, _ = curve_fit(lambda x, x0, C, nrep, nattr: LennardJones(x, self.Delta, x0, C, nrep, nattr), Z, Pmavg, p0=pguess, maxfev=100000) (x0_opt, C_opt, nrep_opt, nattr_opt) = popt Pmavg_fit = LennardJones(Z, self.Delta, x0_opt, C_opt, nrep_opt, nattr_opt) # Compute prediction error residuals = Pmavg - Pmavg_fit ss_res = np.sum(residuals**2) N = residuals.size std_err = np.sqrt(ss_res / N) max_err = max(np.abs(residuals)) logger.debug('LJ approx: x0 = %.2f nm, C = %.2f kPa, m = %.2f, n = %.2f', x0_opt * 1e9, C_opt * 1e-3, nrep_opt, nattr_opt) LJ_approx = {"x0": x0_opt, "C": C_opt, "nrep": nrep_opt, "nattr": nattr_opt} return (LJ_approx, std_err, max_err) @lookup def computePMparams(self): # Find Delta that cancels out Pm + Pec at Z = 0 (m) if self.Qm0 == 0.0: D_eq = self.Delta_ else: (D_eq, Pnet_eq) = self.findDeltaEq(self.Qm0) assert Pnet_eq < PNET_EQ_MAX, 'High Pnet at Z = 0 with ∆ = %.2f nm' % (D_eq * 1e9) self.Delta = D_eq # Find optimal Lennard-Jones parameters to approximate PMavg (self.LJ_approx, std_err, _) = self.LJfitPMavg() assert std_err < PMAVG_STD_ERR_MAX, 'High error in PmAvg nonlinear fit:'\ ' std_err = %.2f Pa' % std_err def PMavgpred(self, Z): ''' Approximated average intermolecular pressure (using nonlinearly fitted Lennard-Jones function) :param Z: leaflet apex deflection (m) :return: predicted average intermolecular pressure (Pa) ''' return LennardJones(Z, self.Delta, self.LJ_approx['x0'], self.LJ_approx['C'], self.LJ_approx['nrep'], self.LJ_approx['nattr']) def Pelec(self, Z, Qm): ''' Electrical pressure term :param Z: leaflet apex deflection (m) :param Qm: membrane charge density (C/m2) :return: electrical pressure (Pa) ''' relS = self.S0 / self.surface(Z) abs_perm = self.epsilon0 * self.epsilonR # F/m return - relS * Qm**2 / (2 * abs_perm) # Pa def findDeltaEq(self, Qm): ''' Compute the Delta that cancels out the (Pm + Pec) equation at Z = 0 for a given membrane charge density, using the Brent method to refine the pressure root iteratively. :param Qm: membrane charge density (C/m2) :return: equilibrium value (m) and associated pressure (Pa) ''' def dualPressure(Delta): x = (self.Delta_ / Delta) return (self.pDelta * (x**self.m - x**self.n) + self.Pelec(0.0, Qm)) Delta_eq = brentq(dualPressure, 0.1 * self.Delta_, 2.0 * self.Delta_, xtol=1e-16) logger.debug('∆eq = %.2f nm', Delta_eq * 1e9) return (Delta_eq, dualPressure(Delta_eq)) def gasFlux(self, Z, P): ''' Gas molar flux through the sonophore boundary layers :param Z: leaflet apex deflection (m) :param P: internal gas pressure (Pa) :return: gas molar flux (mol/s) ''' dC = self.C0 - P / self.kH return 2 * self.surface(Z) * self.Dgl * dC / self.xi @classmethod def gasmol2Pa(cls, ng, V): ''' Internal gas pressure for a given molar content :param ng: internal molar content (mol) :param V: sonophore inner volume (m^3) :return: internal gas pressure (Pa) ''' return ng * Rg * cls.T / V @classmethod def gasPa2mol(cls, P, V): ''' Internal gas molar content for a given pressure :param P: internal gas pressure (Pa) :param V: sonophore inner volume (m^3) :return: internal gas molar content (mol) ''' return P * V / (Rg * cls.T) def PtotQS(self, Z, ng, Qm, Pac, Pm_comp_method): ''' Net quasi-steady pressure for a given acoustic pressure (Ptot = Pm + Pg + Pec - P0 - Pac) :param Z: leaflet apex deflection (m) :param ng: internal molar content (mol) :param Qm: membrane charge density (C/m2) :param Pac: acoustic pressure (Pa) :param Pm_comp_method: computation method for average intermolecular pressure :return: total balance pressure (Pa) ''' if Pm_comp_method is PmCompMethod.direct: Pm = self.PMavg(Z, self.curvrad(Z), self.surface(Z)) elif Pm_comp_method is PmCompMethod.predict: Pm = self.PMavgpred(Z) return Pm + self.gasmol2Pa(ng, self.volume(Z)) - self.P0 - Pac + self.Pelec(Z, Qm) def balancedefQS(self, ng, Qm, Pac=0.0, Pm_comp_method=PmCompMethod.predict): ''' Quasi-steady equilibrium deflection for a given acoustic pressure (computed by approximating the root of quasi-steady pressure) :param ng: internal molar content (mol) :param Qm: membrane charge density (C/m2) :param Pac: external acoustic perturbation (Pa) :param Pm_comp_method: computation method for average intermolecular pressure :return: leaflet deflection canceling quasi-steady pressure (m) ''' lb, ub = -0.49 * self.Delta, self.a Plb, Pub = [self.PtotQS(x, ng, Qm, Pac, Pm_comp_method) for x in [lb, ub]] assert (Plb > 0 > Pub), '[{}, {}] is not a sign changing interval for PtotQS'.format(lb, ub) return brentq(self.PtotQS, lb, ub, args=(ng, Qm, Pac, Pm_comp_method), xtol=1e-16) def TEleaflet(self, Z): ''' Elastic tension in leaflet :param Z: leaflet apex deflection (m) :return: circumferential elastic tension (N/m) ''' return self.kA * self.arealStrain(Z) def TEtissue(self, Z): ''' Elastic tension in surrounding viscoelastic layer :param Z: leaflet apex deflection (m) :return: circumferential elastic tension (N/m) ''' return self.kA_tissue * self.arealStrain(Z) def TEtot(self, Z): ''' Total elastic tension (leaflet + surrounding viscoelastic layer) :param Z: leaflet apex deflection (m) :return: circumferential elastic tension (N/m) ''' return self.TEleaflet(Z) + self.TEtissue(Z) def PEtot(self, Z, R): ''' Total elastic tension pressure (leaflet + surrounding viscoelastic layer) :param Z: leaflet apex deflection (m) :param R: leaflet curvature radius (m) :return: elastic tension pressure (Pa) ''' return - self.TEtot(Z) / R @classmethod def PVleaflet(cls, U, R): ''' Viscous stress pressure in leaflet :param U: leaflet apex deflection velocity (m/s) :param R: leaflet curvature radius (m) :return: leaflet viscous stress pressure (Pa) ''' return - 12 * U * cls.delta0 * cls.muS / R**2 @classmethod def PVfluid(cls, U, R): ''' Viscous stress pressure in surrounding medium :param U: leaflet apex deflection velocity (m/s) :param R: leaflet curvature radius (m) :return: fluid viscous stress pressure (Pa) ''' return - 4 * U * cls.muL / np.abs(R) @classmethod def accP(cls, Ptot, R): ''' Leaflet transverse acceleration resulting from pressure imbalance :param Ptot: net pressure (Pa) :param R: leaflet curvature radius (m) :return: pressure-driven acceleration (m/s^2) ''' return Ptot / (cls.rhoL * np.abs(R)) @staticmethod def accNL(U, R): ''' Leaflet transverse nonlinear acceleration :param U: leaflet apex deflection velocity (m/s) :param R: leaflet curvature radius (m) :return: nonlinear acceleration term (m/s^2) .. note:: A simplified version of nonlinear acceleration (neglecting dR/dH) is used here. ''' # return - (3/2 - 2*R/H) * U**2 / R return -(3 * U**2) / (2 * R) @staticmethod def checkInputs(Fdrive, Adrive, Qm, Pm_comp_method): ''' Check validity of stimulation parameters :param Fdrive: acoustic drive frequency (Hz) :param Adrive: acoustic drive amplitude (Pa) :param Qm: imposed membrane charge density (C/m2) :param Pm_comp_method: type of method used to compute average intermolecular pressure ''' for k, v in {'Fdrive': Fdrive, 'Adrive': Adrive, 'Qm': Qm}.items(): if not isinstance(v, float): raise TypeError(f'Invalid {k} parameter (must be float typed)') if not isinstance(Pm_comp_method, PmCompMethod): raise TypeError('Invalid Pm computation method (must be "PmCompmethod" type)') if Fdrive <= 0: raise ValueError('Invalid US driving frequency: {} kHz (must be strictly positive)' .format(Fdrive * 1e-3)) if Adrive < 0: raise ValueError('Invalid US pressure amplitude: {} kPa (must be positive or null)' .format(Adrive * 1e-3)) if Qm < CHARGE_RANGE[0] or Qm > CHARGE_RANGE[1]: raise ValueError('Invalid applied charge: {} nC/cm2 (must be within [{}, {}] interval' .format(Qm * 1e5, CHARGE_RANGE[0] * 1e5, CHARGE_RANGE[1] * 1e5)) def derivatives(self, t, y, Fdrive, Adrive, Qm, Pm_comp_method=PmCompMethod.predict): ''' Evolution of the mechanical system :param t: time instant (s) :param y: vector of HH system variables at time t :param Fdrive: acoustic drive frequency (Hz) :param Adrive: acoustic drive amplitude (Pa) :param Qm: membrane charge density (F/m2) :param Pm_comp_method: computation method for average intermolecular pressure :return: vector of mechanical system derivatives at time t ''' # Split input vector explicitly U, Z, ng = y # Correct deflection value is below critical compression if Z < -0.5 * self.Delta: logger.warning('Deflection out of range: Z = %.2f nm', Z * 1e9) Z = -0.49 * self.Delta # Compute curvature radius R = self.curvrad(Z) # Compute total pressure Pg = self.gasmol2Pa(ng, self.volume(Z)) if Pm_comp_method is PmCompMethod.direct: Pm = self.PMavg(Z, self.curvrad(Z), self.surface(Z)) elif Pm_comp_method is PmCompMethod.predict: Pm = self.PMavgpred(Z) Ptot = (Pm + Pg - self.P0 - self.Pacoustic(t, Adrive, Fdrive) + self.PEtot(Z, R) + self.PVleaflet(U, R) + self.PVfluid(U, R) + self.Pelec(Z, Qm)) # Compute derivatives dUdt = self.accP(Ptot, R) + self.accNL(U, R) dZdt = U dngdt = self.gasFlux(Z, Pg) # Return derivatives vector return [dUdt, dZdt, dngdt] def computeInitialDeflection(self, Adrive, Fdrive, Qm, dt, Pm_comp_method=PmCompMethod.predict): ''' Compute non-zero deflection value for a small perturbation (solving quasi-steady equation). ''' Pac = self.Pacoustic(dt, Adrive, Fdrive) return self.balancedefQS(self.ng0, Qm, Pac, Pm_comp_method) @classmethod @Model.checkOutputDir def simQueue(cls, *args, **kwargs): return Batch.createQueue(*args) def simUntilConvergence(self, Fdrive, Adrive, Qm, Pm_comp_method=PmCompMethod.predict): ''' Simulate until periodic stabilization for a specific set of ultrasound parameters, and return output data in a dataframe. :param Fdrive: acoustic drive frequency (Hz) :param Adrive: acoustic drive amplitude (Pa) :param Qm: imposed membrane charge density (C/m2) :param Pm_comp_method: type of method used to compute average intermolecular pressure :return: output dataframe ''' # Determine time step dt = 1 / (NPC_DENSE * Fdrive) # Compute initial non-zero deflection Z = self.computeInitialDeflection(Adrive, Fdrive, Qm, dt, Pm_comp_method=Pm_comp_method) # Set initial conditions y0 = np.array([0., 0., self.ng0]) y1 = np.array([0., Z, self.ng0]) # Initialize simulator and compute solution simulator = PeriodicSimulator( lambda t, y: self.derivatives(t, y, Fdrive, Adrive, Qm, Pm_comp_method), ivars_to_check=[1, 2]) t, y, stim = simulator(y1, dt, 1. / Fdrive) # Prepend initial conditions (prior to stimulation) t, y, stim = simulator.prependSolution(t, y, stim, y0=y0) # Set last stimulation state to zero stim[-1] = 0 # Store output in dataframe and return return pd.DataFrame({ 't': t, 'stimstate': stim, 'Z': y[:, 1], 'ng': y[:, 2] }) @Model.addMeta @Model.logDesc @Model.checkSimParams def simulate(self, Fdrive, Adrive, Qm, Pm_comp_method=PmCompMethod.predict): ''' Wrapper around the simUntilConvergence method, with decorators. ''' return self.simUntilConvergence(Fdrive, Adrive, Qm, Pm_comp_method=Pm_comp_method) def meta(self, Fdrive, Adrive, Qm, Pm_comp_method): return { 'simkey': self.simkey, 'a': self.a, 'd': self.d, 'Cm0': self.Cm0, 'Qm0': self.Qm0, 'Fdrive': Fdrive, 'Adrive': Adrive, 'Qm': Qm, 'Pm_comp_method': Pm_comp_method } def desc(self, meta): return '{}: simulation @ f = {}Hz, A = {}Pa, Q = {}C/cm2'.format( self, *si_format([meta['Fdrive'], meta['Adrive'], meta['Qm'] * 1e-4], 2)) def getCycleProfiles(self, Fdrive, Adrive, Qm): ''' Simulate mechanical system and compute pressures over the last acoustic cycle :param Fdrive: acoustic drive frequency (Hz) :param Adrive: acoustic drive amplitude (Pa) :param Qm: imposed membrane charge density (C/m2) :return: dataframe with the time, kinematic and pressure profiles over the last cycle. ''' # Run default simulation and retrieve last cycle solution logger.info('Running mechanical simulation (a = %sm, f = %sHz, A = %sPa)', si_format(self.a, 1), si_format(Fdrive, 1), si_format(Adrive, 1)) data = self.simulate( Fdrive, Adrive, Qm, Pm_comp_method=PmCompMethod.direct)[0].iloc[-NPC_DENSE:, :] # Extract relevant variables and de-offset time vector t, Z, ng = [data[key].values for key in ['t', 'Z', 'ng']] dt = (t[-1] - t[0]) / (NPC_DENSE - 1) t -= t[0] # Compute pressure cyclic profiles logger.info('Computing pressure cyclic profiles') R = self.v_curvrad(Z) U = np.diff(Z) / dt U = np.hstack((U, U[-1])) data = { 't': t, 'Z': Z, 'Cm': self.v_capacitance(Z), 'P_M': self.v_PMavg(Z, R, self.surface(Z)), 'P_Q': self.Pelec(Z, Qm), 'P_{VE}': self.PEtot(Z, R) + self.PVleaflet(U, R), 'P_V': self.PVfluid(U, R), 'P_G': self.gasmol2Pa(ng, self.volume(Z)), 'P_0': - np.ones(Z.size) * self.P0 } return pd.DataFrame(data, columns=data.keys()) diff --git a/PySONIC/core/nbls.py b/PySONIC/core/nbls.py index 84e3d78..60fd0e6 100644 --- a/PySONIC/core/nbls.py +++ b/PySONIC/core/nbls.py @@ -1,649 +1,648 @@ # -*- coding: utf-8 -*- # @Author: Theo Lemaire # @Email: theo.lemaire@epfl.ch # @Date: 2016-09-29 16:16:19 # @Last Modified by: Theo Lemaire -# @Last Modified time: 2019-12-02 18:53:06 +# @Last Modified time: 2019-12-04 15:44:53 import time from copy import deepcopy import logging import numpy as np import pandas as pd from .simulators import PWSimulator, HybridSimulator, PeriodicSimulator from .bls import BilayerSonophore from .pneuron import PointNeuron from .model import Model from .protocols import TimeProtocol, PulsedProtocol, createPulsedProtocols from ..utils import * from ..threshold import threshold from ..constants import * from ..postpro import getFixedPoints from .lookups import SmartLookup, SmartDict, fixLookup NEURONS_LOOKUP_DIR = os.path.abspath(os.path.split(__file__)[0] + "/../neurons/") class NeuronalBilayerSonophore(BilayerSonophore): ''' This class inherits from the BilayerSonophore class and receives an PointNeuron instance at initialization, to define the electro-mechanical NICE model and its SONIC variant. ''' tscale = 'ms' # relevant temporal scale of the model simkey = 'ASTIM' # keyword used to characterize simulations made with this model titration_var = 'Adrive' # name of the titration parameter def __init__(self, a, pneuron, Fdrive=None, embedding_depth=0.0): ''' Constructor of the class. :param a: in-plane radius of the sonophore structure within the membrane (m) :param pneuron: point-neuron model :param Fdrive: frequency of acoustic perturbation (Hz) :param embedding_depth: depth of the embedding tissue around the membrane (m) ''' # Check validity of input parameters if not isinstance(pneuron, PointNeuron): raise ValueError('Invalid neuron type: "{}" (must inherit from PointNeuron class)' .format(pneuron.name)) self.pneuron = pneuron # Initialize BilayerSonophore parent object BilayerSonophore.__init__(self, a, pneuron.Cm0, pneuron.Qm0(), embedding_depth) def __repr__(self): s = '{}({:.1f} nm, {}'.format(self.__class__.__name__, self.a * 1e9, self.pneuron) if self.d > 0.: s += ', d={}m'.format(si_format(self.d, precision=1, space=' ')) return s + ')' def params(self): return {**super().params(), **self.pneuron.params()} def getPltVars(self, wrapleft='df["', wrapright='"]'): return {**super().getPltVars(wrapleft, wrapright), **self.pneuron.getPltVars(wrapleft, wrapright)} def getPltScheme(self): return self.pneuron.getPltScheme() def filecode(self, *args): return Model.filecode(self, *args) @staticmethod def inputs(): # Get parent input vars and supress irrelevant entries bls_vars = BilayerSonophore.inputs() pneuron_vars = PointNeuron.inputs() del bls_vars['Qm'] del pneuron_vars['Astim'] # Fill in current input vars in appropriate order inputvars = bls_vars inputvars.update(pneuron_vars) inputvars['fs'] = { 'desc': 'sonophore membrane coverage fraction', 'label': 'f_s', 'unit': '\%', 'factor': 1e2, 'precision': 0 } inputvars['method'] = None return inputvars def filecodes(self, Fdrive, Adrive, pp, fs, method, qss_vars): # Get parent codes and supress irrelevant entries bls_codes = super().filecodes(Fdrive, Adrive, 0.0) for key in ['simkey', 'Qm']: del bls_codes[key] codes = { 'simkey': self.simkey, 'neuron': self.pneuron.name, 'nature': 'CW' if pp.isCW() else 'PW', } codes.update(bls_codes) codes.update(pp.filecodes()) codes['fs'] = 'fs{:.0f}%'.format(fs * 1e2) if fs < 1 else None codes['method'] = method codes['qss_vars'] = qss_vars return codes @staticmethod def interpOnOffVariable(key, Qm, stim, lkp): ''' Interpolate Q-dependent effective variable along ON and OFF periods of a solution. :param key: lookup variable key :param Qm: charge density solution vector :param stim: stimulation state solution vector :param lkp: dictionary of lookups for ON and OFF states :return: interpolated effective variable vector ''' x = np.zeros(stim.size) x[stim == 0] = lkp['OFF'].interpVar(Qm[stim == 0], 'Q', key) x[stim == 1] = lkp['ON'].interpVar(Qm[stim == 1], 'Q', key) return x @staticmethod def spatialAverage(fs, x, x0): ''' fs-modulated spatial averaging. ''' return fs * x + (1 - fs) * x0 @timer def computeEffVars(self, Fdrive, Adrive, Qm, fs): ''' Compute "effective" coefficients of the HH system for a specific combination of stimulus frequency, stimulus amplitude and charge density. A short mechanical simulation is run while imposing the specific charge density, until periodic stabilization. The HH coefficients are then averaged over the last acoustic cycle to yield "effective" coefficients. :param Fdrive: acoustic drive frequency (Hz) :param Adrive: acoustic drive amplitude (Pa) :param Qm: imposed charge density (C/m2) :param fs: list of sonophore membrane coverage fractions :return: list with computation time and a list of dictionaries of effective variables ''' # Run simulation and retrieve deflection and gas content vectors from last cycle data = BilayerSonophore.simUntilConvergence(self, Fdrive, Adrive, Qm) Z_last = data.loc[-NPC_DENSE:, 'Z'].values # m Cm_last = self.v_capacitance(Z_last) # F/m2 # For each coverage fraction effvars = [] for x in fs: # Compute membrane capacitance and membrane potential vectors Cm = self.spatialAverage(x, Cm_last, self.Cm0) # F/m2 Vm = Qm / Cm * 1e3 # mV # Compute average cycle value for membrane potential and rate constants effvars.append({**{'V': np.mean(Vm)}, **self.pneuron.getEffRates(Vm)}) # Log process log = '{}: lookups @ {}Hz, {}Pa, {:.2f} nC/cm2'.format( self, *si_format([Fdrive, Adrive], precision=1, space=' '), Qm * 1e5) if len(fs) > 1: log += ', fs = {:.0f} - {:.0f}%'.format(fs.min() * 1e2, fs.max() * 1e2) logger.info(log) # Return effective coefficients return effvars def getLookupFileName(self, a=None, Fdrive=None, Adrive=None, fs=False): fname = '{}_lookups'.format(self.pneuron.name) if a is not None: fname += '_{:.0f}nm'.format(a * 1e9) if Fdrive is not None: fname += '_{:.0f}kHz'.format(Fdrive * 1e-3) if Adrive is not None: fname += '_{:.0f}kPa'.format(Adrive * 1e-3) if fs is True: fname += '_fs' return '{}.pkl'.format(fname) def getLookupFilePath(self, *args, **kwargs): return os.path.join(NEURONS_LOOKUP_DIR, self.getLookupFileName(*args, **kwargs)) def getLookup(self, *args, **kwargs): lookup_path = self.getLookupFilePath(*args, **kwargs) if not os.path.isfile(lookup_path): raise FileNotFoundError('Missing lookup file: "{}"'.format(lookup_path)) with open(lookup_path, 'rb') as fh: frame = pickle.load(fh) if 'ng' in frame['lookup']: del frame['lookup']['ng'] refs = frame['input'] # Move fs to last reference dimension keys = list(refs.keys()) if 'fs' in keys and keys.index('fs') < len(keys) - 1: del keys[keys.index('fs')] keys.append('fs') refs = {k: refs[k] for k in keys} lkp = SmartLookup(refs, frame['lookup']) return fixLookup(lkp) def getLookup2D(self, Fdrive, fs): if fs < 1: lkp2d = self.getLookup(a=self.a, Fdrive=Fdrive, fs=True).project('fs', fs) else: lkp2d = self.getLookup().projectN({'a': self.a, 'f': Fdrive}) return lkp2d - def fullDerivatives(self, t, y, Fdrive, Adrive, phi, fs): + def fullDerivatives(self, t, y, Fdrive, Adrive, fs): ''' Compute the full system derivatives. :param t: specific instant in time (s) :param y: vector of state variables :param Fdrive: acoustic drive frequency (Hz) :param Adrive: acoustic drive amplitude (Pa) - :param phi: acoustic drive phase (rad) :param fs: sonophore membrane coevrage fraction (-) :return: vector of derivatives ''' dydt_mech = BilayerSonophore.derivatives( - self, t, y[:3], Fdrive, Adrive, y[3], phi) + self, t, y[:3], Fdrive, Adrive, y[3]) dydt_elec = self.pneuron.derivatives( t, y[3:], Cm=self.spatialAverage(fs, self.capacitance(y[1]), self.Cm0)) return dydt_mech + dydt_elec def effDerivatives(self, t, y, lkp1d, qss_vars): ''' Compute the derivatives of the n-ODE effective system variables, based on 1-dimensional linear interpolation of "effective" coefficients that summarize the system's behaviour over an acoustic cycle. :param t: specific instant in time (s) :param y: vector of HH system variables at time t :param lkp: dictionary of 1D data points of "effective" coefficients over the charge domain, for specific frequency and amplitude values. :param qss_vars: list of QSS variables :return: vector of effective system derivatives at time t ''' # Unpack values and interpolate lookup at current charge density Qm, *states = y lkp0d = lkp1d.interpolate1D('Q', Qm) # Compute states dictionary from differential and QSS variables states_dict = {} i = 0 for k in self.pneuron.statesNames(): if k in qss_vars: states_dict[k] = self.pneuron.quasiSteadyStates()[k](lkp0d) else: states_dict[k] = states[i] i += 1 # Compute charge density derivative dQmdt = - self.pneuron.iNet(lkp0d['V'], states_dict) * 1e-3 # Compute states derivative vector only for differential variable dstates = [] for k in self.pneuron.statesNames(): if k not in qss_vars: dstates.append(self.pneuron.derEffStates()[k](lkp0d, states_dict)) return [dQmdt, *dstates] - def __simFull(self, Fdrive, Adrive, pp, fs, phi=np.pi): + def __simFull(self, Fdrive, Adrive, pp, fs): # Determine time step dt = 1 / (NPC_DENSE * Fdrive) # Compute initial non-zero deflection - Z = self.computeInitialDeflection(Adrive, Fdrive, phi, self.Qm0, dt) + Z = self.computeInitialDeflection(Adrive, Fdrive, self.Qm0, dt) # Set initial conditions ss0 = self.pneuron.getSteadyStates(self.pneuron.Vm0) y0 = np.concatenate(([0., 0., self.ng0, self.Qm0], ss0)) y1 = np.concatenate(([0., Z, self.ng0, self.Qm0], ss0)) # Initialize simulator and compute solution logger.debug('Computing detailed solution') simulator = PWSimulator( - lambda t, y: self.fullDerivatives(t, y, Fdrive, Adrive, phi, fs), - lambda t, y: self.fullDerivatives(t, y, 0., 0., 0., fs)) + lambda t, y: self.fullDerivatives(t, y, Fdrive, Adrive, fs), + lambda t, y: self.fullDerivatives(t, y, 0., 0., fs)) t, y, stim = simulator( y1, dt, pp, target_dt=CLASSIC_TARGET_DT, print_progress=logger.getEffectiveLevel() <= logging.INFO, monitor_func=None) # monitor_func=lambda t, y: f't = {t * 1e3:.5f} ms, Qm = {y[3] * 1e5:.2f} nC/cm2') # Prepend initial conditions (prior to stimulation) t, y, stim = simulator.prependSolution(t, y, stim, y0=y0) # Store output in dataframe and return data = pd.DataFrame({ 't': t, 'stimstate': stim, 'Z': y[:, 1], 'ng': y[:, 2], 'Qm': y[:, 3] }) data['Vm'] = data['Qm'].values / self.spatialAverage( fs, self.v_capacitance(data['Z'].values), self.Cm0) * 1e3 # mV for i in range(len(self.pneuron.states)): data[self.pneuron.statesNames()[i]] = y[:, i + 4] return data - def __simHybrid(self, Fdrive, Adrive, pp, fs, phi=np.pi): + def __simHybrid(self, Fdrive, Adrive, pp, fs): # Determine time steps dt_dense, dt_sparse = [1. / (n * Fdrive) for n in [NPC_DENSE, NPC_SPARSE]] # Compute initial non-zero deflection - Z = self.computeInitialDeflection(Adrive, Fdrive, phi, self.Qm0, dt_dense) + Z = self.computeInitialDeflection(Adrive, Fdrive, self.Qm0, dt_dense) # Set initial conditions ss0 = self.pneuron.getSteadyStates(self.pneuron.Vm0) y0 = np.concatenate(([0., 0., self.ng0, self.Qm0], ss0)) y1 = np.concatenate(([0., Z, self.ng0, self.Qm0], ss0)) # Initialize simulator and compute solution is_dense_var = np.array([True] * 3 + [False] * (len(self.pneuron.states) + 1)) logger.debug('Computing hybrid solution') simulator = HybridSimulator( - lambda t, y: self.fullDerivatives(t, y, Fdrive, Adrive, phi, fs), - lambda t, y: self.fullDerivatives(t, y, 0., 0., 0., fs), + lambda t, y: self.fullDerivatives(t, y, Fdrive, Adrive, fs), + lambda t, y: self.fullDerivatives(t, y, 0., 0., fs), lambda t, y, Cm: self.pneuron.derivatives( t, y, Cm=self.spatialAverage(fs, Cm, self.Cm0)), lambda yref: self.capacitance(yref[1]), is_dense_var, ivars_to_check=[1, 2]) t, y, stim = simulator(y1, dt_dense, dt_sparse, 1. / Fdrive, pp) # Prepend initial conditions (prior to stimulation) t, y, stim = simulator.prependSolution(t, y, stim, y0=y0) # Store output in dataframe and return data = pd.DataFrame({ 't': t, 'stimstate': stim, 'Z': y[:, 1], 'ng': y[:, 2], 'Qm': y[:, 3] }) data['Vm'] = data['Qm'].values / self.spatialAverage( fs, self.v_capacitance(data['Z'].values), self.Cm0) * 1e3 # mV for i in range(len(self.pneuron.states)): data[self.pneuron.statesNames()[i]] = y[:, i + 4] return data def __simSonic(self, Fdrive, Adrive, pp, fs, qss_vars=None, pavg=False): # Load appropriate 2D lookups lkp2d = self.getLookup2D(Fdrive, fs) # Interpolate 2D lookups at zero and US amplitude logger.debug('Interpolating lookups at A = %.2f kPa and A = 0', Adrive * 1e-3) lkps1d = {'ON': lkp2d.project('A', Adrive), 'OFF': lkp2d.project('A', 0.)} # Adapt lookups and pulsing protocol if pulse-average mode is selected if pavg: lkps1d['ON'] = lkps1d['ON'] * pp.DC + lkps1d['OFF'] * (1 - pp.DC) tstim = (int(pp.tstim * pp.PRF) - 1 + pp.DC) / pp.PRF toffset = pp.tstim + pp.toffset - tstim tp = TimeProtocol(tstim, toffset) # # Determine QSS and differential variables if qss_vars is None: qss_vars = [] diff_vars = [item for item in self.pneuron.statesNames() if item not in qss_vars] # Create 1D lookup of QSS variables with reference charge vector QSS_1D_lkp = { key: SmartLookup( lkps1d['ON'].refs, {k: self.pneuron.quasiSteadyStates()[k](val) for k in qss_vars}) for key, val in lkps1d.items()} # Set initial conditions sstates = [self.pneuron.steadyStates()[k](self.pneuron.Vm0) for k in diff_vars] y0 = np.array([self.Qm0, *sstates]) # Initialize simulator and compute solution logger.debug('Computing effective solution') simulator = PWSimulator( lambda t, y: self.effDerivatives(t, y, lkps1d['ON'], qss_vars), lambda t, y: self.effDerivatives(t, y, lkps1d['OFF'], qss_vars)) t, y, stim = simulator(y0, self.pneuron.chooseTimeStep(), pp) # Prepend initial conditions (prior to stimulation) t, y, stim = simulator.prependSolution(t, y, stim) # Store output vectors in dataframe: time, stim state, charge, potential # and other differential variables data = pd.DataFrame({ 't': t, 'stimstate': stim, 'Qm': y[:, 0] }) data['Vm'] = self.interpOnOffVariable('V', data['Qm'].values, stim, lkps1d) for key in ['Z', 'ng']: data[key] = np.full(t.size, np.nan) for i, k in enumerate(diff_vars): data[k] = y[:, i + 1] # Interpolate QSS variables along charge vector and store them in dataframe for k in qss_vars: data[k] = self.interpOnOffVariable(k, data['Qm'].values, stim, QSS_1D_lkp) return data def intMethods(self): ''' Listing of model integration methods. ''' return { 'full': self.__simFull, 'hybrid': self.__simHybrid, 'sonic': self.__simSonic } @classmethod @Model.checkOutputDir def simQueue(cls, freqs, amps, durations, offsets, PRFs, DCs, fs, methods, qss_vars, **kwargs): ''' Create a serialized 2D array of all parameter combinations for a series of individual parameter sweeps, while avoiding repetition of CW protocols for a given PRF sweep. :param freqs: list (or 1D-array) of US frequencies :param amps: list (or 1D-array) of acoustic amplitudes :param durations: list (or 1D-array) of stimulus durations :param offsets: list (or 1D-array) of stimulus offsets (paired with durations array) :param PRFs: list (or 1D-array) of pulse-repetition frequencies :param DCs: list (or 1D-array) of duty cycle values :param fs: sonophore membrane coverage fractions (-) :params methods: integration methods :param qss_vars: QSS variables :return: list of parameters (list) for each simulation ''' if ('full' in methods or 'hybrid' in methods) and kwargs['outputdir'] is None: logger.warning('Running cumbersome simulation(s) without file saving') if amps is None: amps = [None] ppqueue = createPulsedProtocols(durations, offsets, PRFs, DCs) queue = [] for f in freqs: for A in amps: for item in ppqueue: for cov in fs: for method in methods: queue.append([f, A, item, cov, method, qss_vars]) return queue def checkInputs(self, Fdrive, Adrive, pp, fs, method, qss_vars): for k, v in {'Fdrive': Fdrive, 'Adrive': Adrive, 'fs': fs}.items(): if not isinstance(v, float): raise TypeError(f'Invalid {k} parameter (must be float typed)') if not isinstance(pp, PulsedProtocol): raise TypeError('Invalid pulsed protocol (must be "PulsedProtocol" instance)') if Fdrive <= 0: raise ValueError('Invalid US driving frequency: {} kHz (must be strictly positive)' .format(Fdrive * 1e-3)) if Adrive < 0: raise ValueError('Invalid US pressure amplitude: {} kPa (must be positive or null)' .format(Adrive * 1e-3)) if qss_vars is not None: if not isinstance(qss_vars, list) or not isinstance(qss_vars[0], str): raise ValueError('Invalid QSS variables: must be None or a list of strings') sn = self.pneuron.statesNames() for item in qss_vars: if item not in sn: raise ValueError(f'Invalid QSS variable: {item} (must be in {sn}') if method not in list(self.intMethods().keys()): raise ValueError(f'Invalid integration method: "{method}"') @Model.logNSpikes @Model.checkTitrate @Model.addMeta @Model.logDesc @Model.checkSimParams def simulate(self, Fdrive, Adrive, pp, fs=1., method='sonic', qss_vars=None): ''' Simulate the electro-mechanical model for a specific set of US stimulation parameters, and return output data in a dataframe. :param Fdrive: acoustic drive frequency (Hz) :param Adrive: acoustic drive amplitude (Pa) :param pp: pulse protocol object :param fs: sonophore membrane coverage fraction (-) :param method: selected integration method :return: output dataframe ''' # Call appropriate simulation function and return simfunc = self.intMethods()[method] simargs = [Fdrive, Adrive, pp, fs] if method == 'sonic': simargs.append(qss_vars) return simfunc(*simargs) def meta(self, Fdrive, Adrive, pp, fs, method, qss_vars): return { 'simkey': self.simkey, 'neuron': self.pneuron.name, 'a': self.a, 'd': self.d, 'Fdrive': Fdrive, 'Adrive': Adrive, 'pp': pp, 'fs': fs, 'method': method, 'qss_vars': qss_vars } def desc(self, meta): s = '{}: {} simulation @ f = {}Hz, A = {}Pa, {}'.format( self, meta['method'], *si_format([meta['Fdrive'], meta['Adrive']], 2), meta['pp'].pprint()) if meta['fs'] < 1.0: s += f', fs = {(meta["fs"] * 1e2):.2f}%' if 'qss_vars' in meta and meta['qss_vars'] is not None: s += f" - QSS ({','.join(meta['qss_vars'])})" return s @staticmethod def getNSpikes(data): return PointNeuron.getNSpikes(data) @logCache(os.path.join(os.path.split(__file__)[0], 'astim_titrations.log')) def titrate(self, Fdrive, pp, fs=1., method='sonic', qss_vars=None, xfunc=None, Arange=None): ''' Use a binary search to determine the threshold amplitude needed to obtain neural excitation for a given frequency and pulsed protocol. :param Fdrive: US frequency (Hz) :param pp: pulse protocol object :param fs: sonophore membrane coverage fraction (-) :param method: integration method :param xfunc: function determining whether condition is reached from simulation output :param Arange: search interval for Adrive, iteratively refined :return: determined threshold amplitude (Pa) ''' # Default output function if xfunc is None: xfunc = self.pneuron.titrationFunc # Default amplitude interval if Arange is None: Arange = [0., self.getLookup().refs['A'].max()] return threshold( lambda x: xfunc(self.simulate(Fdrive, x, pp, fs=fs, method=method, qss_vars=qss_vars)[0]), Arange, x0=ASTIM_AMP_INITIAL, eps_thr=ASTIM_ABS_CONV_THR, rel_eps_thr=1e0, precheck=True) def getQuasiSteadyStates(self, Fdrive, amps=None, charges=None, DC=1.0, squeeze_output=False): ''' Compute the quasi-steady state values of the neuron's gating variables for a combination of US amplitudes, charge densities, at a specific US frequency and duty cycle. :param Fdrive: US frequency (Hz) :param amps: US amplitudes (Pa) :param charges: membrane charge densities (C/m2) :param DC: duty cycle :return: 4-tuple with reference values of US amplitude and charge density, as well as interpolated Vmeff and QSS gating variables ''' # Get DC-averaged lookups interpolated at the appropriate amplitudes and charges lkp = self.getLookup().projectDC(amps=amps, DC=DC).projectN({'a': self.a, 'f': Fdrive}) if charges is not None: lkp = lkp.project('Q', charges) # Specify dimensions with A as the first axis A_axis = lkp.getAxisIndex('A') lkp.move('A', 0) nA = lkp.dims()[0] # Compute QSS states using these lookups QSS = SmartLookup( lkp.refs, {k: v(lkp) for k, v in self.pneuron.quasiSteadyStates().items()}) # Compress outputs if needed if squeeze_output: QSS = QSS.squeeze() lkp = lkp.squeeze() return lkp, QSS def iNetQSS(self, Qm, Fdrive, Adrive, DC): ''' Compute quasi-steady state net membrane current for a given combination of US parameters and a given membrane charge density. :param Qm: membrane charge density (C/m2) :param Fdrive: US frequency (Hz) :param Adrive: US amplitude (Pa) :param DC: duty cycle (-) :return: net membrane current (mA/m2) ''' lkp, QSS = self.getQuasiSteadyStates( Fdrive, amps=Adrive, charges=Qm, DC=DC, squeeze_output=True) return self.pneuron.iNet(lkp['V'], QSS) # mA/m2 def fixedPointsQSS(self, Fdrive, Adrive, DC, lkp, dQdt): ''' Compute QSS fixed points along the charge dimension for a given combination of US parameters, and determine their stability. :param Fdrive: US frequency (Hz) :param Adrive: US amplitude (Pa) :param DC: duty cycle (-) :param lkp: lookup dictionary for effective variables along charge dimension :param dQdt: charge derivative profile along charge dimension :return: 2-tuple with values of stable and unstable fixed points ''' pltvars = self.getPltVars() logger.debug('A = {:.2f} kPa, DC = {:.0f}%'.format(Adrive * 1e-3, DC * 1e2)) # Extract fixed points from QSS charge variation profile def dfunc(Qm): return - self.iNetQSS(Qm, Fdrive, Adrive, DC) fixed_points = getFixedPoints( lkp.refs['Q'], dQdt, filter='both', der_func=dfunc).tolist() dfunc = lambda x: np.array(self.effDerivatives(_, x, lkp)) # classified_fixed_points = {'stable': [], 'unstable': [], 'saddle': []} classified_fixed_points = [] np.set_printoptions(precision=2) # For each fixed point for i, Qm in enumerate(fixed_points): # Re-compute QSS at fixed point *_, QSS = self.getQuasiSteadyStates(Fdrive, amps=Adrive, charges=Qm, DC=DC, squeeze_output=True) # Classify fixed point stability by numerically evaluating its Jacobian and # computing its eigenvalues x = np.array([Qm, *QSS.tables.values()]) eigvals, key = classifyFixedPoint(x, dfunc) # classified_fixed_points[key].append(Qm) classified_fixed_points.append((x, eigvals, key)) # eigenvalues.append(eigvals) logger.debug(f'{key} point @ Q = {(Qm * 1e5):.1f} nC/cm2') # eigenvalues = np.array(eigenvalues).T # print(eigenvalues.shape) return classified_fixed_points def isStableQSS(self, Fdrive, Adrive, DC): lookups, QSS = self.getQuasiSteadyStates( Fdrive, amps=Adrive, DCs=DC, squeeze_output=True) dQdt = -self.pneuron.iNet(lookups['V'], QSS.tables) # mA/m2 classified_fixed_points = self.fixedPointsQSS(Fdrive, Adrive, DC, lookups, dQdt) return len(classified_fixed_points['stable']) > 0