run_CBG_Model_Frequency_Modulation_Controller.py

# -*- coding: utf-8 -*-
"""
Created on Wed April 03 14:27:26 2019

Description: Cortico-Basal Ganglia Network Model implemented in PyNN using the simulator Neuron.
			This version of the model loads the model steady state and implements DBS frequency 
			modulation controllers where the beta ARV from the STN LFP is calculated at each 
			controller call and used to update the frequency of the DBS waveform that is applied 
			to the network. Full documentation of the model and controllers used is given in:
			
			https://www.frontiersin.org/articles/10.3389/fnins.2020.00166/
			 
@author: John Fleming, john.fleming@ucdconnect.ie
"""

import neuron
h = neuron.h

from pyNN.neuron import setup, run, reset, run_until, run_to_steady_state, run_from_steady_state, end, simulator, Population, SpikeSourcePoisson, SpikeSourceArray, Projection, OneToOneConnector, AllToAllConnector, FromFileConnector, FixedNumberPreConnector, StaticSynapse, NativeCellType, SpikeSourcePoisson, SpikeSourceArray, NoisyCurrentSource, StepCurrentSource
from pyNN.random import RandomDistribution, NumpyRNG
from pyNN import space
from Cortical_Basal_Ganglia_Cell_Classes import Cortical_Neuron_Type, Interneuron_Type, STN_Neuron_Type, GP_Neuron_Type, Thalamic_Neuron_Type
from Electrode_Distances import distances_to_electrode, collateral_distances_to_electrode
from pyNN.parameters import Sequence
from Controllers import standard_PID_Controller
import random
import neo.io
import quantities as pq
import numpy as np
import math
from scipy import signal
import os
import sys

# Import global variables for GPe DBS
import Global_Variables as GV
	
def generate_poisson_spike_times(pop_size, start_time, duration, fr, timestep, random_seed):
    """ generate_population_spike_times generates (N = pop_size) poisson distributed spiketrains
        with firing rate fr.
    
	Example inputs:
		pop_size = 10			
		start_time = 0.0		# ms
		end_time = 6000.0		# ms
		timestep = 1  			# ms
		fr = 1					# Hz
	"""
	
    # Convert to sec for calculating the spikes matrix
    dt = float(timestep)/1000.0                         # sec
    tSim = float(((start_time+duration) - start_time)/1000.0)         # sec
    nBins = int(np.floor(tSim/dt))

    spikeMat = np.where(np.random.uniform(0,1,(pop_size, nBins)) < fr*dt)

    # Create time vector - ms
    tVec = np.arange(start_time, start_time+duration, timestep)

    # Make array of spike times
    for neuron_index in np.arange(pop_size):
        neuron_spike_times = tVec[spikeMat[1][np.where(spikeMat[0][:]==neuron_index)]]
        if neuron_index == 0:
            spike_times = Sequence(neuron_spike_times)
        else:
            spike_times = np.vstack((spike_times, Sequence(neuron_spike_times)))

    return spike_times
	
def generate_DBS_Signal(start_time, stop_time, last_pulse_time_prior, dt, amplitude, frequency, pulse_width, offset):
	"""Generate monophasic square-wave DBS signal
	
	Example inputs:
		start_time = 0				# ms
		stop_time = 12000			# ms
		last_pulse_time_prior 		# ms - time the last DBS pulse occurred at - need to track since stimulation frequency is modulating
		dt = 0.01					# ms 
		amplitude = -1.0			# mA - (amplitude<0 = cathodic stimulation, amplitude>0 = anodic stimulation)
		frequency = 130.0			# Hz
		pulse_width	= 0.06			# ms
		offset = 0					# mA
	"""
	times = np.round(np.arange(start_time, stop_time, dt), 2)
	tmp = np.arange(0, stop_time - start_time, dt)/1000.0
	
	# Check if DBS is switched off
	if frequency == 0:
		DBS_Signal = np.zeros(len(tmp))
		last_pulse_time = last_pulse_time_prior
		next_pulse_time = 1e9
	else:
		# Calculate the duty cycle of the DBS signal
		T = (1.0/frequency)*1000.0	# time is in ms, so *1000 is conversion to ms
		duty_cycle = ((pulse_width)/T)
		# Need to initially set amplitude value > 0 to find last spike time, then can scale by amplitude
		DBS_Signal = offset + 1.0 * (1.0+signal.square(2.0 * np.pi * frequency * tmp, duty=duty_cycle))/2.0
		DBS_Signal[-1] = 0.0
		
		# Calculate the time for the first pulse of the next segment
		try:
			last_pulse_index = np.where(np.diff(DBS_Signal)<0)[0][-1]
			next_pulse_time = times[last_pulse_index] + T - pulse_width
			
			# Track when the last pulse was 
			last_pulse_time = times[last_pulse_index]
			
		except:
			last_pulse_index = len(DBS_Signal)-1 # Catch times when signal may be flat
			next_pulse_time = times[last_pulse_index] + T - pulse_width
			
			# Track when the last pulse was 
			last_pulse_time = times[last_pulse_index]

		# Rescale amplitude
		DBS_Signal *= amplitude
		
	return DBS_Signal, times, next_pulse_time, last_pulse_time

def make_beta_cheby1_filter(Fs, N, rp, low, high):
	"""Calculate bandpass filter coefficients (1st Order Chebyshev Filter)"""
	nyq = 0.5*Fs
	lowcut = low/nyq
	highcut = high/nyq

	b, a = signal.cheby1(N, rp, [lowcut, highcut], 'band')
	
	return b, a
	
def calculate_avg_beta_power(lfp_signal, tail_length, beta_b, beta_a):
	"""Calculate the average power in the beta-band for the current LFP signal window, i.e. beta Average Rectified Value (ARV)
	
	Exaqmple inputs:
		lfp_signal 			- window of LFP signal												# samples
		tail_length 		- tail length which will be discarded due to filtering artifact		# samples
		beta_b, beta_a 		- filter coefficients for filtering the beta-band from the signal	
	"""
	
	lfp_beta_signal = signal.filtfilt(beta_b, beta_a, lfp_signal)
	lfp_beta_signal_rectified = np.absolute(lfp_beta_signal)
	avg_beta_power = np.mean(lfp_beta_signal_rectified[-2*tail_length:-tail_length])
	
	return avg_beta_power
	
if __name__ == '__main__':
	
	# Setup simulation
	setup(timestep=0.01, rngseed=3695)
	steady_state_duration = 6000.0				# Duration of simulation steady state
	simulation_runtime = 32000.0				# Duration of simulation from steady state
	simulation_duration = steady_state_duration+simulation_runtime+simulator.state.dt 	# Total simulation time
	rec_sampling_interval = 0.5					# Signals are sampled every 0.5 ms
	Pop_size = 100
	
	# Make beta band filter centred on 25Hz (cutoff frequencies are 21-29 Hz) for biomarker estimation
	beta_b, beta_a = make_beta_cheby1_filter(Fs=(1.0/rec_sampling_interval)*1000, N=4, rp=0.5, low=21, high=29)
	
	# Use CVode to calculate i_membrane_ for fast LFP calculation
	cvode = h.CVode()
	cvode.active(0)
	
	# Get the second spatial derivative (the segment current) for the collateral
	cvode.use_fast_imem(1)
	
	# Set initial values for cell membrane voltages
	v_init = -68
	
	# Create random distribution for cell membrane noise current
	r_init = RandomDistribution('uniform',(0, Pop_size))
	
	# Create Spaces for STN Population
	STN_Electrode_space=space.Space(axes='xy')
	STN_space = space.RandomStructure(boundary=space.Sphere(2000))				# Sphere with radius 2000um
	
	# Generate Possoin-distributed Striatal Spike trains
	#striatal_spike_times = generate_poisson_spike_times(Pop_size, steady_state_duration, simulation_runtime, 20, 1.0, 3695)
	
	# Save/load Striatal Spike times
	#np.save('Striatal_Spike_Times.npy', striatal_spike_times)		# Save spike times so they can be reloaded 
	striatal_spike_times =  np.load('Striatal_Spike_Times.npy')		# Load spike times from file
	for i in range(0,Pop_size):
		spike_times = striatal_spike_times[i][0].value
		spike_times = spike_times[spike_times>steady_state_duration]
		striatal_spike_times[i][0] = Sequence(spike_times)
	
	# Generate teh neuron populations
	Cortical_Pop = Population(Pop_size, Cortical_Neuron_Type(soma_bias_current_amp=0.245), structure=STN_space, label='Cortical Neurons') # Better than above (ibias=0.2575)
	Interneuron_Pop = Population(Pop_size, Interneuron_Type(bias_current_amp=0.070), initial_values={'v': v_init}, label='Interneurons')
	STN_Pop = Population(Pop_size, STN_Neuron_Type(bias_current=-0.125), structure=STN_space, initial_values={'v': v_init}, label='STN Neurons')
	GPe_Pop = Population(Pop_size, GP_Neuron_Type(bias_current=-0.009), initial_values={'v': v_init}, label='GPe Neurons')					# GPe/i have the same parameters, but different bias currents 
	GPi_Pop = Population(Pop_size, GP_Neuron_Type(bias_current=0.006), initial_values={'v': v_init}, label='GPi Neurons')					# GPe/i have the same parameters, but different bias currents 
	Striatal_Pop = Population(Pop_size, SpikeSourceArray(spike_times=striatal_spike_times[0][0]), label='Striatal Neuron Spike Source')	
	Thalamic_Pop = Population(Pop_size, Thalamic_Neuron_Type(), initial_values={'v': v_init}, label='Thalamic Neurons')
	
	# Update the spike times for the striatal populations
	for i in range(0,Pop_size):
		Striatal_Pop[i].spike_times=striatal_spike_times[i][0]
	
	# Load Cortical Bias currents for beta burst modulation
	burst_times_script = "burst_times_1.txt"
	burst_level_script = "burst_level_1.txt"
	modulation_times = np.loadtxt(burst_times_script, delimiter=',')
	modulation_signal = np.loadtxt(burst_level_script, delimiter=',')
	modulation_signal = 0.02*modulation_signal 								# Scale the modulation signal
	cortical_modulation_current = StepCurrentSource(times=modulation_times, amplitudes=modulation_signal)
	Cortical_Pop.inject(cortical_modulation_current)
	
	# Generate Noisy current sources
	Cortical_Pop_Membrane_Noise = [NoisyCurrentSource(mean=0,stdev=0.005,start=steady_state_duration, stop=simulation_duration, dt=1.0) for count in range(Pop_size)]
	Interneuron_Pop_Membrane_Noise = [NoisyCurrentSource(mean=0,stdev=0.005,start=steady_state_duration, stop=simulation_duration, dt=1.0) for count in range(Pop_size)]
	
	# Inject each membrane noise current into each cortical and interneuron in network
	for Cortical_Neuron, Cortical_Neuron_Membrane_Noise in zip(Cortical_Pop, Cortical_Pop_Membrane_Noise):
		Cortical_Neuron.inject(Cortical_Neuron_Membrane_Noise)
	
	for Interneuron, Interneuron_Membrane_Noise in zip(Interneuron_Pop, Interneuron_Pop_Membrane_Noise):
		Interneuron.inject(Interneuron_Membrane_Noise)
	
	# Load cortical positions - Comment/Remove to generate new positions
	Cortical_Neuron_xy_Positions = np.loadtxt('cortical_xy_pos.txt', delimiter=',')
	Cortical_Neuron_x_Positions = Cortical_Neuron_xy_Positions[0,:]
	Cortical_Neuron_y_Positions = Cortical_Neuron_xy_Positions[1,:]
	
	# Set cortical xy positions to those loaded in
	for cell_id, Cortical_cell in enumerate(Cortical_Pop):
		Cortical_cell.position[0] = Cortical_Neuron_x_Positions[cell_id]
		Cortical_cell.position[1] = Cortical_Neuron_y_Positions[cell_id]
	
	# Load STN positions - Comment/Remove to generate new positions
	STN_Neuron_xy_Positions = np.loadtxt('STN_xy_pos.txt', delimiter=',')
	STN_Neuron_x_Positions = STN_Neuron_xy_Positions[0,:]
	STN_Neuron_y_Positions = STN_Neuron_xy_Positions[1,:]
	
	# Set STN xy positions to those loaded in
	for cell_id, STN_cell in enumerate(STN_Pop):
		STN_cell.position[0] = STN_Neuron_x_Positions[cell_id]
		STN_cell.position[1] = STN_Neuron_y_Positions[cell_id]
		STN_cell.position[2] = 500
		
	"""
	# Position Check - 	
	# 1) Make sure cells are bounded in 4mm space in x, y coordinates
	# 2) Make sure no cells are placed inside the stimulating/recording electrode -0.5mm<x<0.5mm, -1.5mm<y<2mm
	for Cortical_cell in Cortical_Pop:
		while(((np.abs(Cortical_cell.position[0])>2000) or ((np.abs(Cortical_cell.position[1])>2000))) or ((np.abs(Cortical_cell.position[0])<500) and (Cortical_cell.position[1]>-1500 and Cortical_cell.position[1]<2000))):
			Cortical_cell.position = STN_space.generate_positions(1).flatten()
	
	#np.savetxt('cortical_xy_pos.txt', Cortical_Axon_Pop.positions, delimiter=',')	# Save the generated cortical xy positions to a textfile
	
	for STN_cell in STN_Pop:
		while(((np.abs(STN_cell.position[0])>2000) or ((np.abs(STN_cell.position[1])>2000))) or ((np.abs(STN_cell.position[0])<500) and (STN_cell.position[1]>-1500 and STN_cell.position[1]<2000))):
			STN_cell.position = STN_space.generate_positions(1).flatten()
	
	#np.savetxt('STN_xy_pos.txt', STN_Pop.positions, delimiter=',')	# Save the generated STN xy positions to a textfile
	"""
	
	# Assign Positions for recording and stimulating electrode point sources
	recording_electrode_1_position = np.array([0,-1500,250])
	recording_electrode_2_position = np.array([0,1500,250])
	stimulating_electrode_position = np.array([0,0,250])
	
	# Calculate STN cell distances to each recording electrode - only using xy coordinates for distance calculations
	STN_recording_electrode_1_distances = distances_to_electrode(recording_electrode_1_position, STN_Pop)
	STN_recording_electrode_2_distances = distances_to_electrode(recording_electrode_2_position, STN_Pop)
	
	# Calculate Cortical Collateral distances from the stimulating electrode - uses xyz coordinates for distance calculation - these distances need to be in um for xtra
	Cortical_Collateral_stimulating_electrode_distances = collateral_distances_to_electrode(stimulating_electrode_position, Cortical_Pop, L=500, nseg=11)
	#np.savetxt('cortical_collateral_electrode_distances.txt', Cortical_Collateral_stimulating_electrode_distances, delimiter=',')	# Save the generated cortical collateral stimulation electrode distances to a textfile
	
	# Synaptic Connections
	# Add variability to Cortical connections - cortical interneuron connection weights are random from uniform distribution
	gCtxInt_max_weight = 2.5e-3									# Ctx -> Int max coupling value
	gIntCtx_max_weight = 6.0e-3									# Int -> Ctx max coupling value
	gCtxInt = RandomDistribution('uniform',(0, gCtxInt_max_weight), rng=NumpyRNG(seed=3695))
	gIntCtx = RandomDistribution('uniform',(0, gIntCtx_max_weight), rng=NumpyRNG(seed=3695))
	
	# Define other synaptic connection weights and delays
	syn_CorticalAxon_Interneuron = StaticSynapse(weight=gCtxInt, delay=2)	
	syn_Interneuron_CorticalSoma = StaticSynapse(weight=gIntCtx, delay=2)
	syn_CorticalSpikeSourceCorticalAxon = StaticSynapse(weight=0.25, delay=0)
	syn_CorticalCollateralSTN = StaticSynapse(weight=0.12, delay=1)
	syn_STNGPe = StaticSynapse(weight=0.111111, delay=4)
	syn_GPeGPe = StaticSynapse(weight=0.015, delay=4)
	syn_GPeSTN = StaticSynapse(weight=0.111111, delay=3)
	syn_StriatalGPe = StaticSynapse(weight=0.01, delay=1)
	syn_STNGPi = StaticSynapse(weight=0.111111, delay=2)
	syn_GPeGPi = StaticSynapse(weight=0.111111, delay=2)
	syn_GPiThalamic = StaticSynapse(weight=3.0, delay=2)
	syn_ThalamicCortical = StaticSynapse(weight=5, delay=2)
	syn_CorticalThalamic = StaticSynapse(weight=0.0, delay=2)
	
	"""
	# Create new network topology Connections
	prj_CorticalAxon_Interneuron = Projection(Cortical_Pop, Interneuron_Pop,  FixedNumberPreConnector(n=10, allow_self_connections=False), syn_CorticalAxon_Interneuron, source='middle_axon_node', receptor_type='AMPA')
	prj_Interneuron_CorticalSoma = Projection(Interneuron_Pop, Cortical_Pop,  FixedNumberPreConnector(n=10, allow_self_connections=False), syn_Interneuron_CorticalSoma, receptor_type='GABAa')
	prj_CorticalSTN = Projection(Cortical_Pop, STN_Pop, FixedNumberPreConnector(n=5, allow_self_connections=False), syn_CorticalCollateralSTN, source='collateral(0.5)', receptor_type='AMPA')
	prj_STNGPe = Projection(STN_Pop, GPe_Pop, FixedNumberPreConnector(n=1, allow_self_connections=False), syn_STNGPe, source='soma(0.5)', receptor_type='AMPA')
	prj_GPeGPe = Projection(GPe_Pop, GPe_Pop, FixedNumberPreConnector(n=1, allow_self_connections=False), syn_GPeGPe, source='soma(0.5)', receptor_type='GABAa')
	prj_GPeSTN = Projection(GPe_Pop, STN_Pop, FixedNumberPreConnector(n=2, allow_self_connections=False), syn_GPeSTN, source='soma(0.5)', receptor_type='GABAa')	
	prj_StriatalGPe = Projection(Striatal_Pop, GPe_Pop, FixedNumberPreConnector(n=1, allow_self_connections=False), syn_StriatalGPe, source='soma(0.5)', receptor_type='GABAa')	
	prj_STNGPi = Projection(STN_Pop, GPi_Pop, FixedNumberPreConnector(n=1,allow_self_connections=False), syn_STNGPi, source='soma(0.5)', receptor_type='AMPA')
	prj_GPeGPi = Projection(GPe_Pop, GPi_Pop, FixedNumberPreConnector(n=1,allow_self_connections=False), syn_GPeGPi, source='soma(0.5)', receptor_type='GABAa')
	prj_GPiThalamic = Projection(GPi_Pop, Thalamic_Pop, FixedNumberPreConnector(n=1,allow_self_connections=False), syn_GPiThalamic, source='soma(0.5)', receptor_type='GABAa')
	prj_ThalamicCortical = Projection(Thalamic_Pop, Cortical_Pop, FixedNumberPreConnector(n=1,allow_self_connections=False), syn_ThalamicCortical, source='soma(0.5)', receptor_type='AMPA')
	prj_CorticalThalamic = Projection(Cortical_Pop, Thalamic_Pop, FixedNumberPreConnector(n=1,allow_self_connections=False), syn_CorticalThalamic, source='soma(0.5)', receptor_type='AMPA')
	"""
	
	# Load network topology from file
	prj_CorticalAxon_Interneuron = Projection(Cortical_Pop, Interneuron_Pop,  FromFileConnector("CorticalAxonInterneuron_Connections.txt"), syn_CorticalAxon_Interneuron, source='middle_axon_node', receptor_type='AMPA')
	prj_Interneuron_CorticalSoma = Projection(Interneuron_Pop, Cortical_Pop,  FromFileConnector("InterneuronCortical_Connections.txt"), syn_Interneuron_CorticalSoma, receptor_type='GABAa')
	prj_CorticalSTN = Projection(Cortical_Pop, STN_Pop, FromFileConnector("CorticalSTN_Connections.txt"), syn_CorticalCollateralSTN, source='collateral(0.5)', receptor_type='AMPA')
	prj_STNGPe = Projection(STN_Pop, GPe_Pop, FromFileConnector("STNGPe_Connections.txt"), syn_STNGPe, source='soma(0.5)', receptor_type='AMPA')
	prj_GPeGPe = Projection(GPe_Pop, GPe_Pop, FromFileConnector("GPeGPe_Connections.txt"), syn_GPeGPe, source='soma(0.5)', receptor_type='GABAa')
	prj_GPeSTN = Projection(GPe_Pop, STN_Pop, FromFileConnector("GPeSTN_Connections.txt"), syn_GPeSTN, source='soma(0.5)', receptor_type='GABAa')	
	prj_StriatalGPe = Projection(Striatal_Pop, GPe_Pop, FromFileConnector("StriatalGPe_Connections.txt"), syn_StriatalGPe, source='soma(0.5)', receptor_type='GABAa')	
	prj_STNGPi = Projection(STN_Pop, GPi_Pop, FromFileConnector("STNGPi_Connections.txt"), syn_STNGPi, source='soma(0.5)', receptor_type='AMPA')
	prj_GPeGPi = Projection(GPe_Pop, GPi_Pop, FromFileConnector("GPeGPi_Connections.txt"), syn_GPeGPi, source='soma(0.5)', receptor_type='GABAa')
	prj_GPiThalamic = Projection(GPi_Pop, Thalamic_Pop, FromFileConnector("GPiThalamic_Connections.txt"), syn_GPiThalamic, source='soma(0.5)', receptor_type='GABAa')
	prj_ThalamicCortical = Projection(Thalamic_Pop, Cortical_Pop, FromFileConnector("ThalamicCorticalSoma_Connections.txt"), syn_ThalamicCortical, source='soma(0.5)', receptor_type='AMPA')
	prj_CorticalThalamic = Projection(Cortical_Pop, Thalamic_Pop, FromFileConnector("CorticalSomaThalamic_Connections.txt"), syn_CorticalThalamic, source='soma(0.5)', receptor_type='AMPA')
	
	"""
	# Save the network topology so it can be reloaded 
	#prj_CorticalSpikeSourceCorticalSoma.saveConnections(file="CorticalSpikeSourceCorticalSoma_Connections.txt")
	prj_CorticalAxon_Interneuron.saveConnections(file="CorticalAxonInterneuron_Connections.txt")
	prj_Interneuron_CorticalSoma.saveConnections(file="InterneuronCortical_Connections.txt")
	prj_CorticalSTN.saveConnections(file="CorticalSTN_Connections.txt")
	prj_STNGPe.saveConnections(file="STNGPe_Connections.txt")
	prj_GPeGPe.saveConnections(file="GPeGPe_Connections.txt")
	prj_GPeSTN.saveConnections(file="GPeSTN_Connections.txt")
	prj_StriatalGPe.saveConnections(file="StriatalGPe_Connections.txt")
	prj_STNGPi.saveConnections(file="STNGPi_Connections.txt")
	prj_GPeGPi.saveConnections(file="GPeGPi_Connections.txt")
	prj_GPiThalamic.saveConnections(file="GPiThalamic_Connections.txt")
	prj_ThalamicCortical.saveConnections(file="ThalamicCorticalSoma_Connections.txt")
	prj_CorticalThalamic.saveConnections(file="CorticalSomaThalamic_Connections.txt")
	"""
	
	# Define state variables to record from each population
	Cortical_Pop.record('soma(0.5).v', sampling_interval=rec_sampling_interval)
	Cortical_Pop.record('collateral(0.5).v', sampling_interval=rec_sampling_interval)
	Interneuron_Pop.record('soma(0.5).v', sampling_interval=rec_sampling_interval)
	STN_Pop.record('soma(0.5).v', sampling_interval=rec_sampling_interval)
	STN_Pop.record('AMPA.i', sampling_interval=rec_sampling_interval)
	STN_Pop.record('GABAa.i', sampling_interval=rec_sampling_interval)
	Striatal_Pop.record('spikes')
	GPe_Pop.record('soma(0.5).v', sampling_interval=rec_sampling_interval)
	GPi_Pop.record('soma(0.5).v', sampling_interval=rec_sampling_interval)
	Thalamic_Pop.record('soma(0.5).v', sampling_interval=rec_sampling_interval)
	
	# Conductivity and resistivity values for homogenous, isotropic medium
	sigma = 0.27							# Latikka et al. 2001 - Conductivity of Brain tissue S/m
	rho = (1/(sigma*1e-2))					# rho needs units of ohm cm for xtra mechanism (S/m -> S/cm)
	
	# Calculate transfer resistances for each collateral segment for xtra - units are Mohms
	collateral_rx = (rho/(4*math.pi))*(1/Cortical_Collateral_stimulating_electrode_distances)*(0.01)
	
	# Convert ndarray to array of Sequence objects - needed to set cortical collateral transfer resistances
	collateral_rx_seq = np.ndarray(shape=(1, Pop_size), dtype=Sequence).flatten()
	for ii in range(0, Pop_size):
		collateral_rx_seq[ii] = Sequence(collateral_rx[ii,:].flatten())
		
	# Assign transfer resistances values to collaterals
	for ii, cortical_cell in enumerate(Cortical_Pop):
		cortical_cell.collateral_rx = collateral_rx_seq[ii]
			
	# Create times for when the DBS controller will be called
	# Window length for filtering biomarker
	controller_window_length = 2000.0					# ms
	controller_window_length_no_samples = int(controller_window_length/rec_sampling_interval)
	
	# Window Tail length - removed post filtering, prior to biomarker calculation
	controller_window_tail_length = 100.0				# ms	
	controller_window_tail_length_no_samples = int(controller_window_tail_length/rec_sampling_interval)
	
	controller_sampling_time = 20.0						# ms
	controller_call_times = np.arange(steady_state_duration+controller_window_length+controller_sampling_time, simulation_duration, controller_sampling_time)

	# Initialize the Controller being used:
	# P Controller:
	#controller = standard_PID_Controller(SetPoint=1.0414e-04, Kp=416.7, Ti=0.0, Td=0, Ts=0.02, MinValue=0.0, MaxValue=250.0)		# Controller sampling period, Ts, is in sec
	# PI Controller:
	controller = standard_PID_Controller(SetPoint=1.0414e-04, Kp=19.3, Ti=0.2, Td=0, Ts=0.02, MinValue=0.0, MaxValue=250.0)	
	
	# Generate a square wave which represents the DBS signal - Needs to be initialized to zero when unused to prevent open-circuit of cortical collateral extracellular mechanism
	DBS_Signal, DBS_times, next_DBS_pulse_time, last_DBS_pulse_time = generate_DBS_Signal(start_time=steady_state_duration+10+simulator.state.dt, stop_time=simulation_duration, last_pulse_time_prior = steady_state_duration, 
													dt=simulator.state.dt, amplitude=-1.0, frequency=130.0, pulse_width=0.06, offset=0)	
	
	DBS_Signal = np.hstack((np.array([0, 0]), DBS_Signal))
	DBS_times = np.hstack((np.array([0, steady_state_duration+10]), DBS_times))
	
	# Get DBS time indexes which corresponds to controller call times
	controller_DBS_indexs = []
	for controller_call_time in controller_call_times:
		controller_DBS_indexs.extend([np.where(DBS_times==controller_call_time)[0][0]])
	
	# Set first portion of DBS signal (Up to first controller call after steady state) to zero amplitude
	DBS_Signal[0:] = 0
	next_DBS_pulse_time = controller_call_times[0]
	
	DBS_Signal_neuron = h.Vector(DBS_Signal)
	DBS_times_neuron = h.Vector(DBS_times)
	
	# Play DBS signal to global variable is_xtra
	DBS_Signal_neuron.play(h._ref_is_xtra, DBS_times_neuron, 1)
	
	# Get DBS_Signal_neuron as a numpy array for easy updating
	updated_DBS_signal = DBS_Signal_neuron.as_numpy()
	
	# Initialize tracking the frequencies calculated by the controller
	last_freq_calculated = 0
	last_DBS_pulse_time = steady_state_duration
	
	# GPe DBS current stimulations - precalculated for % of collaterals entrained for varying DBS amplitude
	interp_DBS_amplitudes = np.array([0.0, 0.25, 0.5, 0.75, 1.0, 1.25, 1.5, 1.75, 2, 2.25, 2.50, 3, 4, 5])
	interp_collaterals_entrained = np.array([0, 0, 0, 1, 4, 8, 19, 30, 43, 59, 82, 100, 100, 100])
	GPe_stimulation_order = np.loadtxt('GPe_Stimulation_Order.txt', delimiter=',')
	GPe_stimulation_order = [int(index) for index in GPe_stimulation_order]
	
	# Make new GPe DBS vector for each GPe neuron - each GPe neuron needs a pointer to it's own DBS signal
	GPe_DBS_Signal_neuron = []
	GPe_DBS_times_neuron = []
	updated_GPe_DBS_signal = []
	for i in range(0, Pop_size):
	
		GPe_DBS_Signal, GPe_DBS_times, GPe_next_DBS_pulse_time, GPe_last_DBS_pulse_time = generate_DBS_Signal(start_time=steady_state_duration+10+simulator.state.dt, stop_time=simulation_duration, last_pulse_time_prior = steady_state_duration, 
														dt=simulator.state.dt, amplitude=100.0, frequency=130.0, pulse_width=0.06, offset=0)	
		
		GPe_DBS_Signal = np.hstack((np.array([0, 0]), GPe_DBS_Signal))
		GPe_DBS_times = np.hstack((np.array([0, steady_state_duration+10]), GPe_DBS_times))
		
		# Set the GPe DBS signals to zero amplitude
		GPe_DBS_Signal[0:] = 0
		GPe_next_DBS_pulse_time = controller_call_times[0]
		
		# Neuron vector of GPe DBS signals
		GPe_DBS_Signal_neuron.append(h.Vector(GPe_DBS_Signal))
		GPe_DBS_times_neuron.append(h.Vector(GPe_DBS_times))
		
		# Play the stimulation into eacb GPe neuron
		GPe_DBS_Signal_neuron[i].play(GV.GPe_stimulation_iclamps[i]._ref_amp, GPe_DBS_times_neuron[i], 1)
		
		# Hold a reference to the signal as a numpy array, and append to list of GPe stimulation signals
		updated_GPe_DBS_signal.append(GPe_DBS_Signal_neuron[i].as_numpy())
	
	# Initialise STN LFP list
	STN_LFP = []
	STN_LFP_AMPA = []
	STN_LFP_GABAa = []
	
	# Variables for writing simulation data
	last_write_time = steady_state_duration
	
	# Load the steady state
	run_until(steady_state_duration+simulator.state.dt, run_from_steady_state=True)
	
	# Reload striatal spike times after loading the steady state
	for i in range(0,Pop_size):
		Striatal_Pop[i].spike_times=striatal_spike_times[i][0]
	
	# For loop to integrate the model up to each controller call
	for controller_call_index, controller_call_time in enumerate(controller_call_times):
		
		# Integrate model to controller_call_time
		run_until(controller_call_time-simulator.state.dt)
		
		print(("Controller Called at t: %f" % simulator.state.t))
			
		# Calculate the LFP and biomarkers, etc. 
		STN_AMPA_i = np.array(STN_Pop.get_data('AMPA.i').segments[0].analogsignals[0])
		STN_GABAa_i = np.array(STN_Pop.get_data('GABAa.i').segments[0].analogsignals[0])
		STN_Syn_i = STN_AMPA_i + STN_GABAa_i
		
		# STN LFP Calculation - Syn_i is in units of nA -> LFP units are mV
		STN_LFP_1 = (1/(4*math.pi*sigma))*np.sum((1/(STN_recording_electrode_1_distances*1e-6))*STN_Syn_i.transpose(),axis=0)*1e-6 
		STN_LFP_2 = (1/(4*math.pi*sigma))*np.sum((1/(STN_recording_electrode_2_distances*1e-6))*STN_Syn_i.transpose(),axis=0)*1e-6 
		STN_LFP = np.hstack((STN_LFP, STN_LFP_1 - STN_LFP_2))	
			
		# STN LFP AMPA and GABAa Contributions
		STN_LFP_AMPA_1 = (1/(4*math.pi*sigma))*np.sum((1/(STN_recording_electrode_1_distances*1e-6))*STN_AMPA_i.transpose(),axis=0)*1e-6 
		STN_LFP_AMPA_2 = (1/(4*math.pi*sigma))*np.sum((1/(STN_recording_electrode_2_distances*1e-6))*STN_AMPA_i.transpose(),axis=0)*1e-6 
		STN_LFP_AMPA = np.hstack((STN_LFP_AMPA, STN_LFP_AMPA_1 - STN_LFP_AMPA_2))	
		STN_LFP_GABAa_1 = (1/(4*math.pi*sigma))*np.sum((1/(STN_recording_electrode_1_distances*1e-6))*STN_GABAa_i.transpose(),axis=0)*1e-6 
		STN_LFP_GABAa_2 = (1/(4*math.pi*sigma))*np.sum((1/(STN_recording_electrode_2_distances*1e-6))*STN_GABAa_i.transpose(),axis=0)*1e-6 
		STN_LFP_GABAa = np.hstack((STN_LFP_GABAa, STN_LFP_GABAa_1 - STN_LFP_GABAa_2))	
		
		# Biomarker Calculation:
		lfp_beta_average_value = calculate_avg_beta_power(lfp_signal=STN_LFP[-controller_window_length_no_samples:], tail_length=controller_window_tail_length_no_samples, beta_b=beta_b, beta_a=beta_a)
		print("Beta Average: %f" % (lfp_beta_average_value))
		
		# Calculate the updated DBS Frequency
		DBS_amp = 1.5
		DBS_freq = controller.update(state_value=lfp_beta_average_value, current_time=simulator.state.t)
		
		# Update the DBS Signal
		if controller_call_index+1 < len(controller_call_times):
			
			# Check if the frequency needs to change before the last time that was calculated
			if DBS_freq != last_freq_calculated:
				if DBS_freq == 0.0:					# Check if DBS wants to turn off
					next_DBS_pulse_time = 1e9
				else:								# Calculate new next pulse time if DBS is on
					T = (1.0/DBS_freq)*1e3
					next_DBS_pulse_time = last_DBS_pulse_time + T - 0.06
					
					# Need to check for situation when new DBS time is less than the current time
					if next_DBS_pulse_time <= simulator.state.t:
						next_DBS_pulse_time = simulator.state.t
					
			# Calculate new DBS segment from the next DBS pulse time
			if next_DBS_pulse_time < controller_call_times[controller_call_index+1]:
				
				GPe_next_DBS_pulse_time = next_DBS_pulse_time
				
				# DBS Cortical Collateral Stimulation
				new_DBS_Signal_Segment, new_DBS_times_Segment, next_DBS_pulse_time, last_DBS_pulse_time = generate_DBS_Signal(start_time=next_DBS_pulse_time, stop_time=controller_call_times[controller_call_index+1], last_pulse_time_prior = last_DBS_pulse_time, 
													dt=simulator.state.dt, amplitude=-DBS_amp, frequency=DBS_freq, pulse_width=0.06, offset=0)	
					
				# Update DBS segment - replace original DBS array values with updated ones
				window_start_index = np.where(DBS_times==new_DBS_times_Segment[0])[0][0]
				new_window_sample_length = len(new_DBS_Signal_Segment)
				updated_DBS_signal[window_start_index:window_start_index+new_window_sample_length] = new_DBS_Signal_Segment
				
				# DBS GPe neuron stimulation
				num_GPe_Neurons_entrained = int(np.interp(DBS_amp, interp_DBS_amplitudes, interp_collaterals_entrained))
				
				# Make copy of current DBS segment and rescale for GPe neuron stimulation
				GPe_DBS_Signal_Segment = new_DBS_Signal_Segment.copy()
				GPe_DBS_Signal_Segment *= -1
				GPe_DBS_Signal_Segment[GPe_DBS_Signal_Segment>0] = 100
				
				# Stimulate the entrained GPe neurons
				for i in np.arange(0, num_GPe_Neurons_entrained):
					updated_GPe_DBS_signal[GPe_stimulation_order[i]][window_start_index:window_start_index+new_window_sample_length] = GPe_DBS_Signal_Segment
				
				# Remember the last frequency that was calculated
				last_freq_calculated = DBS_freq
				
			else:
				pass
				
		# Write population data to file
		write_index = "{:.0f}_".format(controller_call_index)
		suffix = "_{:.0f}ms-{:.0f}ms".format(last_write_time, simulator.state.t)
		controller_label = controller.get_label()
		
		STN_Pop.write_data("/Simulation_Output_Results/Controller_Simulations/Freq/"+controller_label+"/STN_Pop/"+write_index+"STN_Soma_v"+suffix+".mat", 'soma(0.5).v', clear=True)
		
		last_write_time = simulator.state.t
	
	"""
	# Write population membrane voltage data to file
	Cortical_Pop.write_data("/Simulation_Output_Results/Controller_Simulations/Freq/"+controller_label+"/Cortical_Pop/Cortical_Collateral_v.mat", 'collateral(0.5).v', clear=False)
	Cortical_Pop.write_data("/Simulation_Output_Results/Controller_Simulations/Freq/"+controller_label+"/Cortical_Pop/Cortical_Soma_v.mat", 'soma(0.5).v', clear=True)
	Interneuron_Pop.write_data("/Simulation_Output_Results/Controller_Simulations/Freq/"+controller_label+"/Interneuron_Pop/Interneuron_Soma_v.mat", 'soma(0.5).v', clear=True)
	GPe_Pop.write_data("/Simulation_Output_Results/Controller_Simulations/Freq/"+controller_label+"/GPe_Pop/GPe_Soma_v.mat", 'soma(0.5).v', clear=True)
	GPi_Pop.write_data("/Simulation_Output_Results/Controller_Simulations/Freq/"+controller_label+"/GPi_Pop/GPi_Soma_v.mat", 'soma(0.5).v', clear=True)
	Thalamic_Pop.write_data("/Simulation_Output_Results/Controller_Simulations/Freq/"+controller_label+"/Thalamic_Pop/Thalamic_Soma_v.mat", 'soma(0.5).v', clear=True)
	"""
	
	# Write controller values to csv files
	controller_measured_beta_values = np.asarray(controller.get_state_history())
	controller_measured_error_values = np.asarray(controller.get_error_history()) 
	controller_output_values = np.asarray(controller.get_output_history())
	controller_sample_times = np.asarray(controller.get_sample_times()) 
	np.savetxt("/Simulation_Output_Results/Controller_Simulations/Freq/"+controller_label+"/controller_beta_values.csv", controller_measured_beta_values, delimiter=',')
	np.savetxt("/Simulation_Output_Results/Controller_Simulations/Freq/"+controller_label+"/controller_error_values.csv", controller_measured_error_values, delimiter=',')
	np.savetxt("/Simulation_Output_Results/Controller_Simulations/Freq/"+controller_label+"/controller_frequency_values.csv", controller_output_values, delimiter=',')	
	np.savetxt("/Simulation_Output_Results/Controller_Simulations/Freq/"+controller_label+"/controller_sample_times.csv", controller_sample_times, delimiter=',')
	
	# Write the STN LFP to .mat file
	STN_LFP_Block = neo.Block(name='STN_LFP')
	STN_LFP_seg = neo.Segment(name='segment_0')
	STN_LFP_Block.segments.append(STN_LFP_seg)
	STN_LFP_signal = neo.AnalogSignal(STN_LFP, units='mV', t_start=0*pq.ms, sampling_rate=pq.Quantity(simulator.state.dt, '1/ms'))
	STN_LFP_seg.analogsignals.append(STN_LFP_signal)
	
	w = neo.io.NeoMatlabIO(filename="/Simulation_Output_Results/Controller_Simulations/Freq/"+controller_label+"/STN_LFP.mat") 
	w.write_block(STN_LFP_Block)
	
	"""
	# Write LFP AMPA and GABAa conmponents to file
	STN_LFP_AMPA_Block = neo.Block(name='STN_LFP_AMPA')
	STN_LFP_AMPA_seg = neo.Segment(name='segment_0')
	STN_LFP_AMPA_Block.segments.append(STN_LFP_AMPA_seg)
	STN_LFP_AMPA_signal = neo.AnalogSignal(STN_LFP_AMPA, units='mV', t_start=0*pq.ms, sampling_rate=pq.Quantity(simulator.state.dt, '1/ms'))
	STN_LFP_AMPA_seg.analogsignals.append(STN_LFP_AMPA_signal)
	w = neo.io.NeoMatlabIO(filename="/Simulation_Output_Results/Controller_Simulations/Freq/"+controller_label+"/STN_LFP_AMPA.mat") 
	w.write_block(STN_LFP_AMPA_Block)
	
	STN_LFP_GABAa_Block = neo.Block(name='STN_LFP_GABAa')
	STN_LFP_GABAa_seg = neo.Segment(name='segment_0')
	STN_LFP_GABAa_Block.segments.append(STN_LFP_GABAa_seg)
	STN_LFP_GABAa_signal = neo.AnalogSignal(STN_LFP_GABAa, units='mV', t_start=0*pq.ms, sampling_rate=pq.Quantity(simulator.state.dt, '1/ms'))
	STN_LFP_GABAa_seg.analogsignals.append(STN_LFP_GABAa_signal)
	w = neo.io.NeoMatlabIO(filename="/Simulation_Output_Results/Controller_Simulations/Freq/"+controller_label+"/STN_LFP_GABAa.mat") 
	w.write_block(STN_LFP_GABAa_Block)
	"""
	
	# Write the DBS Signal to .mat file
	# DBS Amplitude
	DBS_Block = neo.Block(name='DBS_Signal')
	DBS_Signal_seg = neo.Segment(name='segment_0')
	DBS_Block.segments.append(DBS_Signal_seg)
	DBS_signal = neo.AnalogSignal(DBS_Signal_neuron, units='mA', t_start=0*pq.ms, sampling_rate=pq.Quantity(1.0/simulator.state.dt, '1/ms'))
	DBS_Signal_seg.analogsignals.append(DBS_signal)
	DBS_times = neo.AnalogSignal(DBS_times_neuron, units='ms', t_start=DBS_times_neuron*pq.ms, sampling_rate=pq.Quantity(1.0/simulator.state.dt, '1/ms'))
	DBS_Signal_seg.analogsignals.append(DBS_times)
	
	w = neo.io.NeoMatlabIO(filename="/Simulation_Output_Results/Controller_Simulations/Freq/"+controller_label+"/DBS_Signal.mat") 
	w.write_block(DBS_Block)

	print("Simulation Done!")
	
	end()