"""Demo of the of a spreading depression simulation with larger extracellular
voxels and fewer larger neurons.
"""
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(10000*(Lx*Ly*Lz*1e-9)) # DEMO LOW NEURON DENSITY:
# (1'000 per mm^3)
Nrec = 500
somaR = 28 # DEMO LARGE NEURONS: soma radius
dendR = 8 # DEMO LARGE NEURONS: dendrite radius
dendL = 150 # DEMO LARGE NEURONS: 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
#DEMO USES LARGER VOXELS
ecs = rxd.Extracellular(-Lx/2.0, -Ly/2.0,
-Lz/2.0, Lx/2.0, Ly/2.0, Lz/2.0, dx=25,
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)