Using NEURON for reaction-diffusion modeling of extracellular dynamics (Newton et al 2018)

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Accession:238892
Development of credible clinically-relevant brain simulations has been slowed due to a focus on electrophysiology in computational neuroscience, neglecting the multiscale whole-tissue modeling approach used for simulation in most other organ systems. We have now begun to extend the NEURON simulation platform in this direction by adding extracellular modeling. NEURON's extracellular reaction-diffusion is supported by an intuitive Python-based where/who/what command sequence, derived from that used for intracellular reaction diffusion, to support coarse-grained macroscopic extracellular models. This simulation specification separates the expression of the conceptual model and parameters from the underlying numerical methods. In the volume-averaging approach used, the macroscopic model of tissue is characterized by free volume fraction—the proportion of space in which species are able to diffuse, and tortuosity—the average increase in path length due to obstacles. These tissue characteristics can be defined within particular spatial regions, enabling the modeler to account for regional differences, due either to intrinsic organization, particularly gray vs. white matter, or to pathology such as edema. We illustrate simulation development using spreading depression, a pathological phenomenon thought to play roles in migraine, epilepsy and stroke.
Reference:
1 . Newton AJH, McDougal RA, Hines ML, Lytton WW (2018) Using NEURON for Reaction-Diffusion Modeling of Extracellular Dynamics. Front Neuroinform 12:41 [PubMed]
Model Information (Click on a link to find other models with that property)
Model Type: Extracellular;
Brain Region(s)/Organism:
Cell Type(s): Hodgkin-Huxley neuron;
Channel(s):
Gap Junctions:
Receptor(s):
Gene(s):
Transmitter(s): Ions;
Simulation Environment: NEURON;
Model Concept(s): Reaction-diffusion;
Implementer(s): Newton, Adam J H [adam.newton at yale.edu]; McDougal, Robert [robert.mcdougal at yale.edu];
Search NeuronDB for information about:  Ions;
"""Simulation of spreading depression"""
from mpi4py import MPI
from neuron import h, crxd as rxd
from neuron.crxd import rxdmath
from matplotlib import pyplot, colors, colorbar
from matplotlib_scalebar import scalebar
from mpl_toolkits.mplot3d import Axes3D
import numpy
import argparse
import os
import sys
import pickle

#when using multiple processes get the relevant id and number of hosts 
pc = h.ParallelContext()
pcid = pc.id()
nhost = pc.nhost()

# set the save directory and if buffering or inhomogeneous tissue
# characteristics are used.
try:
    parser = argparse.ArgumentParser(description = '''Run the spreading
                                     depression simulation''')
    
    parser.add_argument('--edema', dest='edema', action='store_const',
                        const=True, default=False,
                        help='''Use inhomogeneous tortuosity and volume
                        fraction to simulate edema''')
    parser.add_argument('--buffer', dest='buffer', action='store_const',
                        const=True, default=False,
                        help='Use a reaction to model astrocytic buffering')
    parser.add_argument('--tstop', nargs='?', type=float, default=200,
                        help='''duration of the simulation in ms (defaults
                        to 200ms)''')
    parser.add_argument('dir', metavar='dir', type=str,
                        help='a directory to save the figures and data')
    args = parser.parse_args()
except:
    os._exit(1)

outdir = os.path.abspath(args.dir)
if pcid == 0 and not os.path.exists(outdir):
    try:
        os.makedirs(outdir)
    except:
        print("Unable to create the directory %r for the data and figures"
              % outdir)
        os._exit(1)

rxd.nthread(4)  # set the number of rxd threads
rxd.options.enable.extracellular = True # enable extracellular rxd

h.load_file('stdrun.hoc')
h.celsius = 37

numpy.random.seed(6324555+pcid)    # use a difference seed for each process

# simulation parameters
Lx, Ly, Lz = 1000, 1000, 1000      # size of the extracellular space mu m^3
Kceil = 15.0                       # threshold used to determine wave speed
Ncell = int(9e4*(Lx*Ly*Lz*1e-9))   # number of neurons (90'000 per mm^3)
Nrec = 1000

somaR = 11.0     # soma radius
dendR = 1.4      # dendrite radius
dendL = 100.0    # dendrite length
doff = dendL + somaR

alpha0, alpha1 = 0.07, 0.2  # anoxic and normoxic volume fractions 
tort0, tort1 = 1.8, 1.6     # anoxic and normoxic tortuosities 
r0 = 100                    # radius for initial elevated K+

class Neuron:
    """ A neuron with soma and dendrite with; fast and persistent sodium
    currents, potassium currents, passive leak and potassium leak and an
    accumulation mechanism. """
    def __init__(self, x, y, z, rec=False):
        self.x = x
        self.y = y
        self.z = z

        self.soma = h.Section(name='soma', cell=self)
        # add 3D points to locate the neuron in the ECS  
        self.soma.pt3dadd(x, y, z + somaR, 2.0*somaR)
        self.soma.pt3dadd(x, y, z - somaR, 2.0*somaR)
    
        self.dend = h.Section(name='dend', cell=self)
        self.dend.pt3dadd(x, y, z - somaR, 2.0*dendR)
        self.dend.pt3dadd(x, y, z - somaR - dendL, 2.0*dendR)
        #self.dend.nseg = 10 # multiple dendrite segments were used in the
                             # paper but are not necessary for spreading
                             # depression
        self.dend.connect(self.soma, 1,0)
        
        # insert the same mechanisms with the same parameters in both the soma 
        # and the dendrite 
        for mechanism in ['tnak', 'tnap', 'taccumulation3', 'kleak']:
            self.soma.insert(mechanism)
            self.dend.insert(mechanism)

        # the sodium/potassium pump is not used in this model
        self.soma(0.5).tnak.imax = 0
        self.dend(0.5).tnak.imax = 0

        if rec: # record membrane potential (shown in figure 1C)
            self.somaV = h.Vector()
            self.somaV.record(self.soma(0.5)._ref_v, rec)
            self.dendV = h.Vector()
            self.dendV.record(self.dend(0.5)._ref_v, rec)

# Randomly distribute 1000 neurons which we record the membrane potential
# every 100ms
rec_neurons = [Neuron(
    (numpy.random.random()*2.0 - 1.0) * (Lx/2.0 - somaR), 
    (numpy.random.random()*2.0 - 1.0) * (Ly/2.0 - somaR), 
    (numpy.random.random()*2.0 - 1.0) * (Lz/2.0 - somaR), 100)
    for i in range(0, int(Nrec/nhost))]

# Randomly distribute the remaining neurons
all_neurons = [Neuron(
    (numpy.random.random()*2.0 - 1.0) * (Lx/2.0 - somaR),
    (numpy.random.random()*2.0 - 1.0) * (Ly/2.0 - somaR),
    (numpy.random.random()*2.0 - 1.0) * (Lz/2.0 - somaR))
    for i in range(int(Nrec/nhost), int(Ncell/nhost))]

if args.edema:
    # to simulate edema use functions for the diffusion characteristics
    def alpha(x, y, z) :
        return (alpha0 if x**2 + y**2 + z**2 < r0**2
                else min(alpha1, alpha0 +(alpha1-alpha0)
                *((x**2+y**2+z**2)**0.5-r0)/(Lx/2)))

    def tort(x, y, z) :
        return (tort0 if x**2 + y**2 + z**2 < r0**2
                else max(tort1, tort0 - (tort0-tort1)
                *((x**2+y**2+z**2)**0.5-r0)/(Lx/2)))
else:
    # otherwise use the normoxic constants for the diffusion characteristics   
    alpha = alpha1
    tort = tort1


# Where? -- define the extracellular space
ecs = rxd.Extracellular(-Lx/2.0, -Ly/2.0,
                        -Lz/2.0, Lx/2.0, Ly/2.0, Lz/2.0, dx=10,
                        volume_fraction=alpha, tortuosity=tort) 

# What? -- define the species
k = rxd.Species(ecs, name='k', d=2.62, charge=1, initial=lambda nd: 40 
                if nd.x3d**2 + nd.y3d**2 + nd.z3d**2 < r0**2 else 3.5,
                ecs_boundary_conditions=3.5)

na = rxd.Species(ecs, name='na', d=1.78, charge=1, initial=133.574,
                 ecs_boundary_conditions=133.574)

if args.buffer:
    # Additional species are used for a phenomenological model of astrocytic
    # buffering 
    kb = 0.0008
    kth = 15.0
    kf = kb / (1.0 + rxdmath.exp(-(k - kth)/1.15))
    Bmax = 10

    A = rxd.Species(ecs,name='buffer', charge=1, d=0,
                    initial = lambda nd: 0 if nd.x3d**2 + nd.y3d**2 + nd.z3d**2
                    < r0**2 else Bmax)
    AK = rxd.Species(ecs,name='bound', charge=1, d=0,
                    initial = lambda nd: Bmax if nd.x3d**2 + nd.y3d**2 + 
                    nd.z3d**2 < r0**2 else 0)

    # What? -- specify the reactions involved
    buffering = rxd.Reaction(k + A, AK, kf, kb)

pc.set_maxstep(100) # required when using multiple processes

# initialize and set the intracellular concentrations
h.finitialize()
for sec in h.allsec():
    sec.nai = 4.297

def progress_bar(tstop, size=40):
    """ report progress of the simulation """
    prog = h.t/float(tstop)
    fill = int(size*prog)
    empt = size - fill
    progress = '#' * fill + '-' * empt
    sys.stdout.write('[%s] %2.1f%% %6.1fms of %6.1fms\r' % (progress, 100*prog, pc.t(0), tstop))
    sys.stdout.flush()

def plot_rec_neurons():
    """ Produces plots of record neurons membrane potential (shown in figure 1C) """
    # load the recorded neuron data
    somaV, dendV, pos = [], [], []
    for i in range(nhost):
        fin = open(os.path.join(outdir,'membrane_potential_%i.pkl' % i),'rb')
        [sV, dV, p] = pickle.load(fin)
        fin.close()
        somaV.extend(sV)
        dendV.extend(dV)
        pos.extend(p)

        for idx in range(somaV[0].size()):  
            # create a plot for each record (100ms)

            fig = pyplot.figure()
            ax = fig.add_subplot(111,projection='3d')
            ax.set_position([0.0,0.05,0.9,0.9])
            ax.set_xlim([-Lx/2.0, Lx/2.0])
            ax.set_ylim([-Ly/2.0, Ly/2.0])
            ax.set_zlim([-Lz/2.0, Lz/2.0])
            ax.set_xticks([int(Lx*i/4.0) for i in range(-2,3)])
            ax.set_yticks([int(Ly*i/4.0) for i in range(-2,3)])
            ax.set_zticks([int(Lz*i/4.0) for i in range(-2,3)])

            cmap = pyplot.get_cmap('jet')
            for i in range(Nrec):
                x = pos[i]
                soma_z = [x[2]-somaR,x[2]+somaR]
                cell_x = [x[0],x[0]]
                cell_y = [x[1],x[1]]
                scolor = cmap((somaV[i].get(idx)+70.0)/70.0)
                # plot the soma
                ax.plot(cell_x, cell_y, soma_z, linewidth=2, color=scolor, 
                        alpha=0.5)
    
                dcolor = cmap((dendV[i].get(idx)+70.0)/70.0)
                dend_z = [x[2]-somaR, x[2]-somaR - dendL]
                # plot the dendrite
                ax.plot(cell_x, cell_y, dend_z, linewidth=0.5, color=dcolor, 
                        alpha=0.5)

            norm = colors.Normalize(vmin=-70,vmax=0)
            pyplot.title('Neuron membrane potentials; t = %gms' % (idx * 100))

            # add a colorbar 
            ax1 = fig.add_axes([0.88,0.05,0.04,0.9])
            cb1 = colorbar.ColorbarBase(ax1, cmap=cmap, norm=norm,
                                                orientation='vertical')
            cb1.set_label('mV')
            
            # save the plot
            filename = 'neurons_{:05d}.png'.format(idx)
            pyplot.savefig(os.path.join(outdir,filename))
            pyplot.close()

def plot_image_data(data, min_val, max_val, filename, title):
    """Plot a 2d image of the data"""
    sb = scalebar.ScaleBar(1e-6)
    sb.location='lower left'
    pyplot.imshow(data, extent=k[ecs].extent('xy'), vmin=min_val,
                  vmax=max_val, interpolation='nearest', origin='lower')
    pyplot.colorbar()
    sb = scalebar.ScaleBar(1e-6)
    sb.location='lower left'
    ax = pyplot.gca()
    ax.xaxis.set_visible(False)
    ax.yaxis.set_visible(False)
    ax.add_artist(sb)
    pyplot.title(title)
    pyplot.xlim(k[ecs].extent('x'))
    pyplot.ylim(k[ecs].extent('y'))
    pyplot.savefig(os.path.join(outdir,filename))
    pyplot.close()

    
h.dt = 10  # use a large time step as we are not focusing on spiking behaviour
           # but on slower diffusion


def run(tstop):
    """ Run the simulations saving figures every 100ms and recording the wave progression every time step"""
    if pcid == 0:
        # record the wave progress (shown in figure 2)
        name = '' if not args.edema else '_edema'
        name += '' if not args.buffer else '_buffer'
        fout = open(os.path.join(outdir,'wave_progress%s.txt' % name),'a')

    while pc.t(0) < tstop:
        if int(pc.t(0)) % 100 == 0:
            # plot extracellular concentrations averaged over depth every 100ms 
            if pcid == 0:
                plot_image_data(k[ecs].states3d.mean(2), 3.5, 40,
                                'k_mean_%05d' % int(pc.t(0)/100),
                                'Potassium concentration; t = %6.0fms'
                                % pc.t(0))

            if pcid == nhost - 1 and args.buffer:
                plot_image_data(AK[ecs].states3d.mean(2), 0, 10,
                                'buffered_mean_%05d' % int(pc.t(0)/100),
                                'Buffered concentration; t = %6.0fms' % pc.t(0))
        if pcid == 0: progress_bar(tstop)
        pc.psolve(pc.t(0)+h.dt)  # run the simulation for 1 time step
        
        # determine the furthest distance from the origin where
        # extracellular potassium exceeds Kceil (dist)
        # And the shortest distance from the origin where the extracellular
        # extracellular potassium is below Kceil (dist1)
        if pcid == 0:
            dist = 0
            dist1 = 1e9
            for nd in k.nodes:
                r = (nd.x3d**2+nd.y3d**2+nd.z3d**2)**0.5
                if nd.concentration>Kceil and r > dist:
                    dist = r
                if nd.concentration<=Kceil and r < dist1:
                    dist1 = r

            fout.write("%g\t%g\t%g\n" %(pc.t(0), dist, dist1))
            fout.flush()
    if pcid == 0:
        progress_bar(tstop)
        fout.close()
        print("\nSimulation complete. Plotting membrane potentials")

    # save membrane potentials
    soma, dend, pos = [], [], []
    for n in rec_neurons:
        soma.append(n.somaV)
        dend.append(n.dendV)
        pos.append([n.x,n.y,n.z])
    pout = open(os.path.join(outdir,"membrane_potential_%i.pkl" % pcid),'wb')
    pickle.dump([soma,dend,pos],pout)
    pout.close()
    pc.barrier()    # wait for all processes to save

    # plot the membrane potentials (shown in figure 1C)
    if pcid == 0:
        plot_rec_neurons()

#run the simulation
run(args.tstop)

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