hhn_network

Complexity

Total Complexity

43

Size/Duplication

Total Lines	396
Duplicated Lines	0 %

9 Methods

Rating	Name	Duplication	Size	Complexity
B	simulate_static()	0	47	6
A	simulate()	0	15	1
B	__init__()	0	38	5
B	_calculate_states()	0	52	4
F	__update_peripheral_neurons()	0	39	11
F	hnn_state()	0	88	9
A	allocate_sync_ensembles()	0	16	1
A	__alfa_function()	0	13	1
B	__update_central_neurons()	0	25	5

"""!


@brief Oscillatory Neural Network based on Hodgkin-Huxley Neuron Model

@details Based on article description:

         - D.Chik, R.Borisyuk, Y.Kazanovich. Selective attention model with spiking elements. 2009.


@authors Andrei Novikov (pyclustering@yandex.ru)

@date 2014-2016

@copyright GNU Public License


@cond GNU_PUBLIC_LICENSE

    PyClustering is free software: you can redistribute it and/or modify

    it under the terms of the GNU General Public License as published by

    the Free Software Foundation, either version 3 of the License, or

    (at your option) any later version.

    

    PyClustering is distributed in the hope that it will be useful,

    but WITHOUT ANY WARRANTY; without even the implied warranty of

    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the

    GNU General Public License for more details.

    

    You should have received a copy of the GNU General Public License

    along with this program.  If not, see <http://www.gnu.org/licenses/>.

@endcond


"""


from pyclustering.nnet import *;

IntEnum was imported with wildcard, but is not used.

initial_type was imported with wildcard, but is not used.

from scipy.integrate import odeint;

The import scipy.integrate could not be resolved.

from pyclustering.utils import allocate_sync_ensembles;


import numpy;

The import numpy could not be resolved.

import random;


class hhn_parameters:

    """!

    @brief Describes parameters of Hodgkin-Huxley Oscillatory Network.

    

    @see hhn_network

    

    """  

    

    ## Intrinsic noise.

    nu      = random.random() * 2.0 - 1.0;

    

    ## Maximal conductivity for sodium current.

    gNa     = 120.0 * (1 + 0.02 * nu);

    

    ## Maximal conductivity for potassium current.

    gK      = 36.0 * (1 + 0.02 * nu);

    

    ## Maximal conductivity for leakage current.

    gL      = 0.3 * (1 + 0.02 * nu);

    

    

    ## Reverse potential of sodium current [mV].

    vNa     = 50.0;

    

    ## Reverse potential of potassium current [mV].

    vK      = -77.0;

    

    ## Reverse potantial of leakage current [mV].

    vL      = -54.4;

    

    ## Rest potential [mV].

    vRest   = -65.0;    

    

    

    ## External current [mV] for central element 1.

    Icn1    = 5.0;

    

    ## External current [mV] for central element 2.

    Icn2    = 30.0;

    

    

    ## Synaptic reversal potential [mV] for inhibitory effects.

    Vsyninh = -80.0;    

    

    ## Synaptic reversal potential [mV] for exciting effects.

    Vsynexc = 0.0;

    

    ## Alfa-parameter for alfa-function for inhibitory effect.

    alfa_inhibitory     = 6.0;

    

    ## Betta-parameter for alfa-function for inhibitory effect.

    betta_inhibitory    = 0.3;

    

    

    ## Alfa-parameter for alfa-function for excitatoty effect.

    alfa_excitatory     = 40.0;

    

    ## Betta-parameter for alfa-function for excitatoty effect.

    betta_excitatory    = 2.0;

    

    

    ## Strength of the synaptic connection from PN to CN1.

    w1 = 0.1;

    

    ## Strength of the synaptic connection from CN1 to PN.

    w2 = 9.0;

    

    ## Strength of the synaptic connection from CN2 to PN.

    w3 = 5.0;

    

    

    ## Period of time [ms] when high strength value of synaptic connection exists from CN2 to PN.

    deltah = 650.0;

    

    ## Threshold of the membrane potential that should exceeded by oscillator to be considered as an active.

    threshold = -10;

    

    ## Affects pulse counter.

    eps = 0.16;



class central_element:

    """!

    @brief Central element consist of two central neurons that are described by a little bit different dynamic than peripheral.

    

    @see hhn_network

    

    """

    

    ## Membrane potential of cenral neuron (V).

    membrane_potential      = 0.0;

    

    ## Activation conductance of the sodium channel (m).

    active_cond_sodium      = 0.0;

    

    ## Inactivaton conductance of the sodium channel (h).

    inactive_cond_sodium    = 0.0;

    

    ## Inactivaton conductance of the sodium channel (h)

    active_cond_potassium   = 0.0;

    

    ## Times of pulse generation by central neuron.

    pulse_generation_time = None;

    

    ## Spike generation of central neuron.

    pulse_generation = False;

    

    def __init__(self):

        """!

        @brief Constructor of central element.

        

        """

        

        self.pulse_generation_time = [];

    

    def __repr__(self):

        """!

        @brief Returns string that represents central element.

        

        """

        return "%s, %s" % (self.membrane_potential, self.pulse_generation_time);



class hhn_network(network):

    """!

    @brief Oscillatory Neural Network with central element based on Hodgkin-Huxley neuron model. Interaction between oscillators is performed via

           central element (no connection between oscillators that are called as peripheral). Peripheral oscillators receive external stimulus.

           Central element consist of two oscillators: the first is used for synchronization some ensemble of oscillators and the second controls

           synchronization of the first cental oscillator with verious ensembles.

    

    Example:

    @code

        # change period of time when high strength value of synaptic connection exists from CN2 to PN.

        params = hhn_parameters();

        params.deltah = 400;

        

        # create oscillatory network with stimulus

        net = hhn_network(6, [0, 0, 25, 25, 47, 47], params);

        

        # simulate network

        (t, dyn) = net.simulate(1200, 600);

        

        # draw network output during simulation

        draw_dynamics(t, dyn, x_title = "Time", y_title = "V", separate = True);

    @endcode

    

    """

    

    _name = "Oscillatory Neural Network based on Hodgkin-Huxley Neuron Model"

    

    # States of peripheral oscillators

    _membrane_potential     = None;          # membrane potential of neuron (V)

    _active_cond_sodium     = None;          # activation conductance of the sodium channel (m)

    _inactive_cond_sodium   = None;          # inactivaton conductance of the sodium channel (h)

    _active_cond_potassium  = None;          # activation conductance of the potassium channel (n)

    _link_activation_time   = None;          # time of set w3 - connection from CN2 to PN for each oscillator.

    _link_weight3           = None;          # connection strength for each oscillator from CN2 to PN.

    

    _pulse_generation_time  = None;          # time of spike generation for each oscillator.

    _pulse_generation       = None;          # spike generation for each oscillator.

    

    _stimulus = None;               # stimulus of each oscillator

    _noise = None;                  # Noise for each oscillator

    

    _central_element = None;        # Central element description

    

    _params = None;                 # parameters of the network

    

    _membrane_dynamic_pointer = None;        # final result is stored here.

    

    def __init__(self, num_osc, stimulus = None, parameters = None, type_conn = None, type_conn_represent = conn_represent.MATRIX):

        """!

        @brief Constructor of oscillatory network based on Hodgkin-Huxley meuron model.

        

        @param[in] num_osc (uint): Number of peripheral oscillators in the network.

        @param[in] stimulus (list): List of stimulus for oscillators, number of stimulus should be equal to number of peripheral oscillators.

        @param[in] parameters (hhn_parameters): Parameters of the network.

        @param[in] type_conn (conn_type): Type of connections between oscillators in the network (ignored for this type of network).

        @param[in] type_conn_represent (conn_represent): Internal representation of connection in the network: matrix or list.

        

        """

          

        super().__init__(num_osc, conn_type.NONE, type_conn_represent);

        

        self._membrane_potential        = [0.0] * self._num_osc;

        self._active_cond_sodium        = [0.0] * self._num_osc;

        self._inactive_cond_sodium      = [0.0] * self._num_osc;

        self._active_cond_potassium     = [0.0] * self._num_osc;

        self._link_activation_time      = [0.0] * self._num_osc;

        self._link_pulse_counter        = [0.0] * self._num_osc;

        self._link_deactivation_time    = [0.0] * self._num_osc;

        self._link_weight3              = [0.0] * self._num_osc;

        self._pulse_generation_time     = [ [] for i in range(self._num_osc) ];

        self._pulse_generation          = [False] * self._num_osc;

        

        self._noise = [random.random() * 2.0 - 1.0 for i in range(self._num_osc)];

        

        self._central_element = [central_element(), central_element()];

        

        if (stimulus is None):

            self._stimulus = [0.0] * self._num_osc;

        else:

            self._stimulus = stimulus;

        

        if (parameters is not None):

            self._params = parameters;

        else:

            self._params = hhn_parameters();

    

    

    def simulate(self, steps, time, solution = solve_type.RK4, collect_dynamic = True):

        """!

        @brief Performs static simulation of oscillatory network based on Hodgkin-Huxley neuron model.

        

        @param[in] steps (uint): Number steps of simulations during simulation.

        @param[in] time (double): Time of simulation.

        @param[in] solution (solve_type): Type of solver for differential equations.

        @param[in] collect_dynamic (bool): If True - returns whole dynamic of oscillatory network, otherwise returns only last values of dynamics.

        

        @return (list) Dynamic of oscillatory network. If argument 'collect_dynamic' = True, than return dynamic for the whole simulation time,

                otherwise returns only last values (last step of simulation) of dynamic.

        

        """

        

        return self.simulate_static(steps, time, solution, collect_dynamic);

    

    

    def simulate_static(self, steps, time, solution = solve_type.RK4, collect_dynamic = False):

        """!

        @brief Performs static simulation of oscillatory network based on Hodgkin-Huxley neuron model.

        

        @param[in] steps (uint): Number steps of simulations during simulation.

        @param[in] time (double): Time of simulation.

        @param[in] solution (solve_type): Type of solver for differential equations.

        @param[in] collect_dynamic (bool): If True - returns whole dynamic of oscillatory network, otherwise returns only last values of dynamics.

        

        @return (list) Dynamic of oscillatory network. If argument 'collect_dynamic' = True, than return dynamic for the whole simulation time,

                otherwise returns only last values (last step of simulation) of dynamic.

        

        """

        

        self._membrane_dynamic_pointer = None;

        

        # Check solver before simulation

        if (solution == solve_type.FAST):

            raise NameError("Solver FAST is not support due to low accuracy that leads to huge error.");

        elif (solution == solve_type.RKF45):

            raise NameError("Solver RKF45 is not support in python version.");

        

        dyn_memb = None;

        dyn_time = None;

        

        # Store only excitatory of the oscillator

        if (collect_dynamic == True):

            dyn_memb = [];

            dyn_time = [];

            

        step = time / steps;

        int_step = step / 10.0;

        

        for t in numpy.arange(step, time + step, step):

            # update states of oscillators

            memb = self._calculate_states(solution, t, step, int_step);

            

            # update states of oscillators

            if (collect_dynamic == True):

                dyn_memb.append(memb);

                dyn_time.append(t);

            else:

                dyn_memb = memb;

                dyn_time = t;

        

        self._membrane_dynamic_pointer = dyn_memb;

        return (dyn_time, dyn_memb);

    

    

    def _calculate_states(self, solution, t, step, int_step):

The argument solution seems to be unused.

        """!

        @brief Caclculates new state of each oscillator in the network. Returns only excitatory state of oscillators.

        

        @param[in] solution (solve_type): Type solver of the differential equations.

        @param[in] t (double): Current time of simulation.

        @param[in] step (uint): Step of solution at the end of which states of oscillators should be calculated.

        @param[in] int_step (double): Differentiation step that is used for solving differential equation.

        

        @return (list) New states of membrance potentials for peripheral oscillators and for cental elements as a list where

                the last two values correspond to central element 1 and 2.

                 

        """

        

        next_membrane           = [0.0] * self._num_osc;

        next_active_sodium      = [0.0] * self._num_osc;

        next_inactive_sodium    = [0.0] * self._num_osc;

        next_active_potassium   = [0.0] * self._num_osc;

        

        # Update states of oscillators

        for index in range (0, self._num_osc, 1):

            result = odeint(self.hnn_state, 

                            [ self._membrane_potential[index], self._active_cond_sodium[index], self._inactive_cond_sodium[index], self._active_cond_potassium[index] ], 

                            numpy.arange(t - step, t, int_step), 

                            (index , ));

                            

            [ next_membrane[index], next_active_sodium[index], next_inactive_sodium[index], next_active_potassium[index] ] = result[len(result) - 1][0:4];        

        

        next_cn_membrane            = [0.0, 0.0];

        next_cn_active_sodium       = [0.0, 0.0];

        next_cn_inactive_sodium     = [0.0, 0.0];

        next_cn_active_potassium    = [0.0, 0.0];

        

        # Update states of central elements

        for index in range(0, len(self._central_element)):

            result = odeint(self.hnn_state, 

                            [ self._central_element[index].membrane_potential, self._central_element[index].active_cond_sodium, self._central_element[index].inactive_cond_sodium, self._central_element[index].active_cond_potassium ], 

                            numpy.arange(t - step, t, int_step), 

                            (self._num_osc + index , ));

                            

            [ next_cn_membrane[index], next_cn_active_sodium[index], next_cn_inactive_sodium[index], next_cn_active_potassium[index] ] = result[len(result) - 1][0:4];

        

        # Noise generation

        self._noise = [ 1.0 + 0.01 * (random.random() * 2.0 - 1.0) for i in range(self._num_osc)];

        

        # Updating states of PNs

        self.__update_peripheral_neurons(t, step, next_membrane, next_active_sodium, next_inactive_sodium, next_active_potassium);

        

        # Updation states of CN

        self.__update_central_neurons(t, next_cn_membrane, next_cn_active_sodium, next_cn_inactive_sodium, next_cn_active_potassium);

        

        return next_membrane + next_cn_membrane;

    

    

    def __update_peripheral_neurons(self, t, step, next_membrane, next_active_sodium, next_inactive_sodium, next_active_potassium):

        """!

        @brief Update peripheral neurons in line with new values of current in channels.

        

        @param[in] t (doubles): Current time of simulation.

        @param[in] step (uint): Step (time duration) during simulation when states of oscillators should be calculated.

        @param[in] next_membrane (list): New values of membrane potentials for peripheral neurons.

        @Param[in] next_active_sodium (list): New values of activation conductances of the sodium channels for peripheral neurons.

        @param[in] next_inactive_sodium (list): New values of inactivaton conductances of the sodium channels for peripheral neurons.

        @param[in] next_active_potassium (list): New values of activation conductances of the potassium channel for peripheral neurons.

        

        """

        

        self._membrane_potential = next_membrane[:];

        self._active_cond_sodium = next_active_sodium[:];

        self._inactive_cond_sodium = next_inactive_sodium[:];

        self._active_cond_potassium = next_active_potassium[:];

        

        for index in range(0, self._num_osc):

            if (self._pulse_generation[index] is False):

                if (self._membrane_potential[index] > 0.0):

                    self._pulse_generation[index] = True;

                    self._pulse_generation_time[index].append(t);

            else:

                if (self._membrane_potential[index] < 0.0):

                    self._pulse_generation[index] = False;

            

            # Update connection from CN2 to PN

            if (self._link_weight3[index] == 0.0):

                if ( (self._membrane_potential[index] > self._params.threshold) and (self._membrane_potential[index] > self._params.threshold) ):

                    self._link_pulse_counter[index] += step;

                

                    if (self._link_pulse_counter[index] >= 1 / self._params.eps):

                        self._link_weight3[index] = self._params.w3;

                        self._link_activation_time[index] = t;

            else:

                if ( not ((self._link_activation_time[index] < t) and (t < self._link_activation_time[index] + self._params.deltah)) ):

                    self._link_weight3[index] = 0.0;

                    self._link_pulse_counter[index] = 0.0;

    

    

    def __update_central_neurons(self, t, next_cn_membrane, next_cn_active_sodium, next_cn_inactive_sodium, next_cn_active_potassium):

        """!

        @brief Update of central neurons in line with new values of current in channels.

        

        @param[in] t (doubles): Current time of simulation.

        @param[in] next_membrane (list): New values of membrane potentials for central neurons.

        @Param[in] next_active_sodium (list): New values of activation conductances of the sodium channels for central neurons.

        @param[in] next_inactive_sodium (list): New values of inactivaton conductances of the sodium channels for central neurons.

        @param[in] next_active_potassium (list): New values of activation conductances of the potassium channel for central neurons.

        

        """

        

        for index in range(0, len(self._central_element)):

            self._central_element[index].membrane_potential = next_cn_membrane[index];

            self._central_element[index].active_cond_sodium = next_cn_active_sodium[index];

            self._central_element[index].inactive_cond_sodium = next_cn_inactive_sodium[index];

            self._central_element[index].active_cond_potassium = next_cn_active_potassium[index];

            

            if (self._central_element[index].pulse_generation is False):

                if (self._central_element[index].membrane_potential > 0.0):

                    self._central_element[index].pulse_generation = True;

                    self._central_element[index].pulse_generation_time.append(t);

            else:

                if (self._central_element[index].membrane_potential < 0.0):

                    self._central_element[index].pulse_generation = False;

    

    

    def hnn_state(self, inputs, t, argv):

        """!

        @brief Returns new values of excitatory and inhibitory parts of oscillator and potential of oscillator.

        

        @param[in] inputs (list): States of oscillator for integration [v, m, h, n] (see description below).

        @param[in] t (double): Current time of simulation.

        @param[in] argv (tuple): Extra arguments that are not used for integration - index of oscillator.

        

        @return (list) new values of oscillator [v, m, h, n], where:

                v - membrane potantial of oscillator,

                m - activation conductance of the sodium channel,

                h - inactication conductance of the sodium channel,

                n - activation conductance of the potassium channel.

        

        """

        

        index = argv;

        

        v = inputs[0]; # membrane potential (v).

        m = inputs[1]; # activation conductance of the sodium channel (m).

        h = inputs[2]; # inactivaton conductance of the sodium channel (h).

        n = inputs[3]; # activation conductance of the potassium channel (n).

        

        # Calculate ion current

        # gNa * m[i]^3 * h * (v[i] - vNa) + gK * n[i]^4 * (v[i] - vK) + gL  (v[i] - vL)

        active_sodium_part = self._params.gNa * (m ** 3) * h * (v - self._params.vNa);

        inactive_sodium_part = self._params.gK * (n ** 4) * (v - self._params.vK);

        active_potassium_part = self._params.gL * (v - self._params.vL);

        

        Iion = active_sodium_part + inactive_sodium_part + active_potassium_part;

        

        Iext = 0.0;

        Isyn = 0.0;

        if (index < self._num_osc): 

            # PN - peripheral neuron - calculation of external current and synaptic current.

            Iext = self._stimulus[index] * self._noise[index];    # probably noise can be pre-defined for reducting compexity            

            

            memory_impact1 = 0.0;

            for i in range(0, len(self._central_element[0].pulse_generation_time)):

                # TODO: alfa function shouldn't be calculated here (long procedure)

                memory_impact1 += self.__alfa_function(t - self._central_element[0].pulse_generation_time[i], self._params.alfa_inhibitory, self._params.betta_inhibitory);

            

            memory_impact2 = 0.0;

            for i in range(0, len(self._central_element[1].pulse_generation_time)):

                # TODO: alfa function shouldn't be calculated here (long procedure)

                memory_impact2 += self.__alfa_function(t - self._central_element[1].pulse_generation_time[i], self._params.alfa_inhibitory, self._params.betta_inhibitory);        

    

            Isyn = self._params.w2 * (v - self._params.Vsyninh) * memory_impact1 + self._link_weight3[index] * (v - self._params.Vsyninh) * memory_impact2;            

        else:

            # CN - central element.

            central_index = index - self._num_osc;

            if (central_index == 0):

                Iext = self._params.Icn1;   # CN1

                

                memory_impact = 0.0;

                for index_oscillator in range(0, self._num_osc):

                    for index_generation in range(0, len(self._pulse_generation_time[index_oscillator])):

                        # TODO: alfa function shouldn't be calculated here (long procedure)

                        memory_impact += self.__alfa_function(t - self._pulse_generation_time[index_oscillator][index_generation], self._params.alfa_excitatory, self._params.betta_excitatory);

                 

                Isyn = self._params.w1 * (v - self._params.Vsynexc) * memory_impact;

                

            elif (central_index == 1):

                Iext = self._params.Icn2;   # CN2

                Isyn = 0.0;

                

            else:

                assert 0;

        

        

        # Membrane potential

        dv = -Iion + Iext - Isyn;

        

        # Calculate variables

        potential = v - self._params.vRest;

        am = (2.5 - 0.1 * potential) / (math.exp(2.5 - 0.1 * potential) - 1.0);

        ah = 0.07 * math.exp(-potential / 20.0);

        an = (0.1 - 0.01 * potential) / (math.exp(1.0 - 0.1 * potential) - 1.0);

        

        bm = 4.0 * math.exp(-potential / 18.0);

        bh = 1.0 / (math.exp(3.0 - 0.1 * potential) + 1.0);

        bn = 0.125 * math.exp(-potential / 80.0);

        

        dm = am * (1.0 - m) - bm * m;

        dh = ah * (1.0 - h) - bh * h;

        dn = an * (1.0 - n) - bn * n;

        

        return [dv, dm, dh, dn];

        

        

    def allocate_sync_ensembles(self, tolerance = 0.1):

        """!

        @brief Allocates clusters in line with ensembles of synchronous oscillators where each. Synchronous ensemble corresponds to only one cluster.

        

        @param[in] tolerance (double): maximum error for allocation of synchronous ensemble oscillators.

        

        @return (list) Grours (lists) of indexes of synchronous oscillators. For example [ [index_osc1, index_osc3], [index_osc2], [index_osc4, index_osc5] ].

        

        """

        

        ignore = set();

        

        ignore.add(self._num_osc);

        ignore.add(self._num_osc + 1);

        

        return allocate_sync_ensembles(self._membrane_dynamic_pointer, tolerance, 20.0, ignore);

    

    

    def __alfa_function(self, time, alfa, betta):

        """!

        @brief Calculates value of alfa-function for difference between spike generation time and current simulation time.

        

        @param[in] time (double): Difference between last spike generation time and current time.

        @param[in] alfa (double): Alfa parameter for alfa-function.

        @param[in] betta (double): Betta parameter for alfa-function.

        

        @return (double) Value of alfa-function.

        

        """

        

        return alfa * time * math.exp(-betta * time);