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vietSpine_highFreqInhibition.lua
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--------------------------------------------------------------------------------
-- This script solves the cable equation on a 1d version of Viet's --
-- reconstructed spine (with extensions). --
-- --
-- Author: Markus Breit --
-- Date: 2019-01-17 --
--------------------------------------------------------------------------------
ug_load_script("ug_util.lua")
-- init UG
InitUG(3, AlgebraType("CPU", 1));
AssertPluginsLoaded({"cable_neuron"})
--------------
-- settings --
--------------
-- grid
gridName = util.GetParam("-grid", "nernst_planck_app/grid/spines/vietSpine1d.ugx")
-- refinement
numRefs = util.GetParamNumber("-numRefs", 0)
-- time stepping
dt = util.GetParamNumber("-dt", 1e-5) -- in s
endTime = util.GetParamNumber("-endTime", 0.05) -- in s
nSteps = util.GetParamNumber("-nSteps", endTime/dt)
-- specify "-verbose" to output linear solver convergence
verbose = util.HasParamOption("-verbose")
-- vtk output?
generateVTKoutput = util.HasParamOption("-vtk")
pstep = util.GetParamNumber("-pstep", dt)
-- file handling
outDir = util.GetParam("-outName", "viet_1d")
outDir = outDir .. "/"
--------------------------
-- biological settings --
--------------------------
-- membrane conductances (in units of S/m^2)
g_l_k = 0.5
g_l_na = 0.5
-- resistivity (in units of (V s m) / C)
spec_res = 0.407224494 -- deduced from PNP model
-- membrane specific capacitance (in units of C / (V m^2))
spec_cap = 3.585763867e-3 -- deduced from PNP model
-- reversal potentials (in units of V)
e_k = -0.0940
e_na = 0.0640
e_ca = 0.14
-- equilibrium concentrations (in units of mM)
k_out = 4.0
na_out = 145.0
ca_out = 2.0
cl_out = 123.0
k_in = 155.0
na_in = 12.0
ca_in = 5e-5
cl_in = 5.0
-- equilibrium potential (in units of V)
v_eq = -0.070
-- diffusion coefficients (in units of m^2/s)
diff_k = 1.96e-9
diff_na = 1.33e-9
diff_ca = 2.2e-10
diff_cl = 2.03e-9
-- temperature in units of K
temp = 298.15
--------------------------------
-- create approximation space --
--------------------------------
dom = util.CreateDomain(gridName, numRefs, {"dend"})
approxSpace = ApproximationSpace(dom)
approxSpace:add_fct("v", "Lagrange", 1)
approxSpace:init_levels()
approxSpace:init_top_surface()
approxSpace:print_statistic()
OrderCuthillMcKee(approxSpace, true)
u = GridFunction(approxSpace)
-- cable equation
CE = CableEquation("dend, spine, syn", false)
CE:set_spec_cap(spec_cap)
CE:set_spec_res(spec_res)
CE:set_rev_pot_k(e_k)
CE:set_rev_pot_na(e_na)
CE:set_rev_pot_ca(e_ca)
CE:set_k_out(k_out)
CE:set_na_out(na_out)
CE:set_ca_out(ca_out)
CE:set_diff_coeffs({diff_k, diff_na, diff_ca})
CE:set_temperature(temp)
-- leakage
leakK = ChannelLeak("k", "dend")
leakK:set_cond(g_l_k, "dend")
leakK:set_rev_pot(v_eq, "dend")
CE:add(leakK)
leakNa = ChannelLeak("na", "dend")
leakNa:set_cond(g_l_na, "dend")
leakNa:set_rev_pot(v_eq, "dend")
CE:add(leakNa)
-- synapse
nGABAR = 50
local t_on = 0.0
local tau = 0.008 -- GABAR activation decay constant (in s)
local period = 0.005
function channelOpen(t)
local t_p = t % period
return math.exp(-t_p / tau)
end
FRT = 96485.0 / (8.31451 * 298.15) -- in 1 / V
synArea = Integral(1.0, u, "syn")
areaFactor = 9.275e-14 / (math.pi * 0.5*(2.95945e-07 + 1.78e-07) * synArea)
equiv_channel_area = 2.257e-19 -- cross-sectional area of GABAR channel, in m^2,
-- deduced from GHK equation using conductance g = 24pS
-- and reference concentration c_r = 145mM (inside and outside)
channelAreaPerPSDArea = nGABAR*equiv_channel_area / (math.pi * 0.5*(2.95945e-07 + 1.78e-07) * synArea)
vmAtSyn = v_eq
function currentDensityFunction(x, y, z, t, si)
local exp = math.exp(-FRT*vmAtSyn)
local currentCl = 96485.0 * diff_cl / 1e-8 * FRT * vmAtSyn
* (cl_out - cl_in * exp) / (1.0 - exp)
return - channelOpen(t) * channelAreaPerPSDArea * currentCl * areaFactor
end
CE:set_influx_function("currentDensityFunction", "syn")
-- create domain discretization
domainDisc = DomainDiscretization(approxSpace)
domainDisc:add(CE)
assTuner = domainDisc:ass_tuner()
-- create time discretization
timeDisc = ThetaTimeStep(domainDisc)
timeDisc:set_theta(1.0)
-- create operator from discretization
linOp = AssembledLinearOperator(timeDisc)
------------------
-- solver setup --
------------------
-- debug writer
dbgWriter = GridFunctionDebugWriter(approxSpace)
dbgWriter:set_vtk_output(true)
-- linear solver --
convCheck = CompositeConvCheck(approxSpace, 1, 2e-26, 1e-08)
convCheck:set_component_check("v", 1e-21, 1e-12)
convCheck:set_verbose(verbose)
ilu = ILU()
solver = LinearSolver()
solver:set_preconditioner(ilu)
solver:set_convergence_check(convCheck)
--solver:set_debug(dbgWriter)
----------------------
-- time stepping --
----------------------
time = 0.0
-- init solution
b = GridFunction(approxSpace)
u:set(0.0)
Interpolate(v_eq, u, "v")
synArea = Integral(1.0, u, "syn")
areaFactor = 9.275e-14 / (math.pi * 0.5*(2.95945e-07 + 1.78e-07) * synArea)
currentOutFile = assert(io.open(outDir.."meas/current.dat", "a"))
-- write start solution
if generateVTKoutput then
out = VTKOutput()
out:print(outDir.."vtk/solution", u, 0, time)
end
measFcts = "v"
take_measurement(u, time, "syn", measFcts, outDir.."meas/sol")
-- store grid function in vector of old solutions
uOld = u:clone()
solTimeSeries = SolutionTimeSeries()
solTimeSeries:push(uOld, time)
curr_dt = dt
dtred = 2
lv = 0
maxLv = 10
cb_counter = {}
cb_counter[lv] = 0
while endTime-time > 0.001*curr_dt do
-- setup time Disc for old solutions and timestep
timeDisc:prepare_step(solTimeSeries, curr_dt)
vmAtSyn = Integral(u, "v", "syn") / synArea
currentOutFile:write(time, "\t", -currentDensityFunction(0,0,0,time,0) * math.pi * 0.5*(2.95945e-07 + 1.78e-07) * synArea, "\n")
-- reduce time step if cfl < curr_dt
-- (this needs to be done AFTER prepare_step as channels are updated there)
dtChanged = false
cfl = CE:estimate_cfl_cond(solTimeSeries:latest())
print("estimated CFL condition: dt < " .. cfl)
while (curr_dt > cfl) do
curr_dt = curr_dt/dtred
if lv+1 > maxLv then
print("Time step too small.")
exit()
end
lv = lv + 1
cb_counter[lv] = 0
print("estimated CFL condition: dt < " .. cfl .. " - reducing time step to " .. curr_dt)
dtChanged = true
end
-- increase time step if cfl > curr_dt / dtred (and if time is aligned with new bigger step size)
while curr_dt*dtred < cfl and lv > 0 and cb_counter[lv] % (dtred) == 0 do
curr_dt = curr_dt*dtred;
lv = lv - 1
cb_counter[lv] = cb_counter[lv] + cb_counter[lv+1]/dtred
cb_counter[lv+1] = 0
print ("estimated CFL condition: dt < " .. cfl .. " - increasing time step to " .. curr_dt)
dtChanged = true
end
print("++++++ POINT IN TIME " .. math.floor((time+curr_dt)/curr_dt+0.5)*curr_dt .. " BEGIN ++++++")
-- prepare again with new time step size
if dtChanged == true then
timeDisc:prepare_step(solTimeSeries, curr_dt)
end
-- assemble linear problem
matrixIsConst = time ~= 0.0 and dtChanged == false
assTuner:set_matrix_is_const(matrixIsConst)
AssembleLinearOperatorRhsAndSolution(linOp, u, b)
-- apply linear solver
ilu:set_disable_preprocessing(matrixIsConst)
if ApplyLinearSolver(linOp, u, b, solver) == false then
print("Could not apply linear solver.")
exit()
end
-- update to new time
time = solTimeSeries:time(0) + curr_dt
-- vtk output
if generateVTKoutput then
if math.abs(time/pstep - math.floor(time/pstep+0.5)) < 1e-5 then
out:print(outDir.."vtk/solution", u, math.floor(time/pstep+0.5), time)
end
end
take_measurement(u, time, "syn", measFcts, outDir.."meas/sol")
-- updte time series (reuse memory)
oldestSol = solTimeSeries:oldest()
VecScaleAssign(oldestSol, 1.0, u)
solTimeSeries:push_discard_oldest(oldestSol, time)
-- increment check-back counter
cb_counter[lv] = cb_counter[lv] + 1
print("++++++ POINT IN TIME " .. math.floor((time)/curr_dt+0.5)*curr_dt .. " END ++++++")
end
-- end timeseries, produce gathering file
if generateVTKoutput then
out:write_time_pvd(outDir.."vtk/solution", u)
end
currentOutFile:close()