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single_neuron_erDynamics.lua
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single_neuron_erDynamics.lua
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--------------------------------------------------------------------------------
-- This script solves the cable equation with HH channels on a pyramidal cell --
-- with an injection electrode at the soma. --
-- It also simulates calcium diffusion and buffering as well as ER / PM --
-- exchange with a simplifying 1d cable symmetry assumption. --
-- --
-- NOT (YET) FUNCTIONAL! --
-- While the membrane transport mechanisms can use the diameter information --
-- attached to the neuronal geometry, this is not the case for ConvDiff and --
-- buffering reactions. This must either be achieved using some kind of --
-- user data (might be slow due to element lookup) or by a specialized --
-- discretization, maybe a specialized FVGeometry would be beneficial. --
-- --
-- Author: Markus Breit --
-- Date: 2019-06-07 --
--------------------------------------------------------------------------------
-- for profiler output
SetOutputProfileStats(false)
ug_load_script("ug_util.lua")
ug_load_script("util/load_balancing_util.lua")
AssertPluginsLoaded({"cable_neuron"})
-- init UG
InitUG(3, AlgebraType("CPU", 1))
---------------------------------
-- read command line arguments --
---------------------------------
-- choice of grid
gridName = util.GetParam("-grid", "cable_neuron_app/grids/rat1.ugx")
-- parameters steering simulation
numRefs = util.GetParamNumber("-numRefs", 0)
dt = util.GetParamNumber("-dt", 1e-5) -- in s
endTime = util.GetParamNumber("-endTime", 0.01)
-- specify "-verbose" to output linear solver convergence
verbose = util.HasParamOption("-verbose")
-- vtk output?
generateVTKoutput = util.HasParamOption("-vtk")
pstep = util.GetParamNumber("-pstep", dt, "plotting interval")
-- file handling
outputPath = util.GetParam("-outName", ".")
outputPath = outputPath.."/"
-------------------------
-- biological settings --
-------------------------
-- settings are according to T. Branco
-- membrane conductances (in units of S/m^2)
g_k_ax = 400.0 -- axon
g_k_so = 200.0 -- soma
g_k_de = 30 -- dendrite
g_na_ax = 3.0e4
g_na_so = 1.5e3
g_na_de = 40.0
g_l_ax = 200.0
g_l_so = 1.0
g_l_de = 1.0
-- specific capacitance (in units of F/m^2)
spec_cap = 1.0e-2
-- resistivity (in units of Ohm m)
spec_res = 1.5
-- reversal potentials (in units of V)
e_k = -0.09
e_na = 0.06
e_ca = 0.14
-- equilibrium concentrations (in units of mM)
-- comment: these concentrations will not yield Nernst potentials
-- as given above; pumps will have to be introduced to achieve this
-- in the case where Nernst potentials are calculated from concentrations!
k_out = 4.0
na_out = 150.0
ca_out = 1.5
k_in = 140.0
na_in = 10.0
ca_in = 5e-5
-- equilibrium potential (in units of V)
v_eq = -0.07
-- diffusion coefficients (in units of m^2/s)
diff_k = 1.0e-9
diff_na = 1.0e-9
diff_ca = 2.2e-10
-- temperature in units of deg Celsius
temp = 37.0
------------------------------------
-- create domain and approx space --
------------------------------------
dom = Domain()
requiredSubsets = {"soma", "dend", "apic"}
dom = util.CreateDomain(gridName, numRefs, requiredSubsets)
approxSpace = ApproximationSpace(dom)
approxSpace:add_fct("v", "Lagrange", 1)
approxSpace:add_fct("k", "Lagrange", 1)
approxSpace:add_fct("na", "Lagrange", 1)
approxSpace:add_fct("ca", "Lagrange", 1)
approxSpace:add_fct("cae", "Lagrange", 1)
approxSpace:add_fct("clb", "Lagrange", 1)
approxSpace:add_fct("ip3", "Lagrange", 1)
approxSpace:add_fct("o2", "Lagrange", 1)
approxSpace:add_fct("c1", "Lagrange", 1)
approxSpace:add_fct("c2", "Lagrange", 1)
approxSpace:init_levels()
approxSpace:init_surfaces()
approxSpace:init_top_surface()
approxSpace:print_statistic()
OrderCuthillMcKee(approxSpace, true)
--------------------
-- discretization --
--------------------
-- cable equation
CE = CableEquation("soma, dend, apic", true)
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_celsius(temp)
dendSubsets = "dend, apic"
-- Hodgkin and Huxley channels
HH = ChannelHHNernst("v", "soma, dend, apic")
HH:set_conductances(g_k_ax, g_na_ax, "axon")
HH:set_conductances(g_k_so, g_na_so, "soma")
HH:set_conductances(g_k_de, g_na_de, dendSubsets)
CE:add(HH)
-- leakage
tmp_fct = math.pow(2.3,(temp-23.0)/10.0)
leak = ChannelLeak("v", "axon, soma, " .. dendSubsets)
leak:set_cond(g_l_ax*tmp_fct, "axon")
leak:set_rev_pot(-0.066210342630746467, "axon")
leak:set_cond(g_l_so*tmp_fct, "soma")
leak:set_rev_pot(-0.022074360525636, "soma")
leak:set_cond(g_l_de*tmp_fct, dendSubsets)
leak:set_rev_pot(-0.056314322586687, dendSubsets)
CE:add(leak)
-- Calcium dynamics
volScaleER = math.pi * erRadius*erRadius
volScaleCyt = math.pi * dendRadius*dendRadius - volScaleER
diffCaER = ConvectionDiffusion("ca_er", erVol, "fv1")
diffCaER:set_mass_scale(volScaleER)
diffCaER:set_diffusion(D_cae*volScaleER)
diffClb = ConvectionDiffusion("clb", cytVol, "fv1")
diffClb:set_mass_scale(volScaleCyt)
diffClb:set_diffusion(D_clb*volScaleCyt)
diffIP3 = ConvectionDiffusion("ip3", cytVol, "fv1")
diffIP3:set_mass_scale(volScaleCyt)
diffIP3:set_diffusion(D_ip3*volScaleCyt)
diffIP3:set_reaction_rate(reactionRateIP3*volScaleCyt)
diffIP3:set_reaction(reactionTermIP3*volScaleCyt)
-- buffering --
discBuffer = BufferFV1(cytVol) -- where buffering occurs
discBuffer:add_reaction(
"clb", -- the buffering substance
"ca_cyt", -- the buffered substance
totalClb, -- total amount of buffer
k_bind_clb*volScaleCyt, -- binding rate constant
k_unbind_clb*volScaleCyt -- unbinding rate constant
)
-- er membrane transport systems
ip3r = IP3R({"ca_cyt", "ca_er", "ip3"})
ip3r:set_scale_inputs({1e3,1e3,1e3})
ip3r:set_scale_fluxes({1e15}) -- from mol/(um^2 s) to (mol um)/(dm^3 s)
ryr = RyRImplicit({"ca_cyt", "ca_er", "o2", "c1", "c2"}, erMemVec)
ryr:set_scale_inputs({1e3, 1e3, 1.0, 1.0, 1.0})
ryr:set_scale_fluxes({1e15}) -- from mol/(um^2 s) to (mol um)/(dm^3 s)
ryrStateDisc = RyRImplicit_1drotsym({"ca_cyt", "ca_er", "o2", "c1", "c2"}, {"dend"})
ryrStateDisc:set_calcium_scale(1e3)
serca = SERCA({"ca_cyt", "ca_er"})
serca:set_scale_inputs({1e3,1e3})
serca:set_scale_fluxes({1e15}) -- from mol/(um^2 s) to (mol um)/(dm^3 s)
leakER = Leak({"ca_er", "ca_cyt"})
leakER:set_scale_inputs({1e3,1e3})
leakER:set_scale_fluxes({1e3}) -- from mol/(m^2 s) to (mol um)/(dm^3 s)
discIP3R = MembraneTransport1d(erMem, ip3r)
discIP3R:set_density_function(IP3Rdensity)
discRyR = MembraneTransport1d(erMem, ryr)
discRyR:set_density_function(RYRdensity)
discSERCA = MembraneTransport1d(erMem, serca)
discSERCA:set_density_function(SERCAdensity)
discERLeak = MembraneTransport1d(erMem, leakER)
discERLeak:set_density_function(1e12*leakERconstant/(1e3)) -- from mol/(um^2 s M) to m/s
-- plasma membrane transport
vdcc = VDCC_BG_cable("ca", "soma, " .. dendSubsets)
ncx = NCX_cable("ca", "soma, " .. dendSubsets)
pmca = PMCA_cable("ca", "soma, " .. dendSubsets)
caLeak = IonLeakage("ca", "soma, " .. dendSubsets)
leakCaConst = -3.4836065573770491e-9 + -- single pump PMCA flux density (mol/s/m^2)
-1.0135135135135137e-9 + -- single pump NCX flux (mol/s/m^2)
3.3017662162505882e-11
caLeak:set_perm(leakCaConst, ca_in, ca_out, v_eq, 2)
CE:add(ncx)
CE:add(pmca)
CE:add(vdcc)
CE:add(caLeak)
-- Na-K pump
nak_ax = Na_K_Pump("", "axon")
nak_ax:set_max_flux(2.6481515257588432) -- mol/(m^2*s)
nak_so = Na_K_Pump("", "soma")
nak_so:set_max_flux(6.05974e-7/4.57658e-06) -- mol/(m^2*s)
nak_de = Na_K_Pump("", dendSubsets)
nak_de:set_max_flux(1.61593e-8/4.57658e-06) -- mol/(m^2*s)
CE:add(nak_ax)
CE:add(nak_so)
CE:add(nak_de)
-- ion leakage
kLeak_ax = IonLeakage("k", "axon")
leakKConst_ax = 0.0000040675975261062531 + -- HH (mol/s/m^2)
-0.00000010983795579882983 -- Na/K (mol/s/m^2)
kLeak_ax:set_perm(leakKConst_ax, k_in, k_out, v_eq, 1)
kLeak_so = IonLeakage("k", "soma")
leakKConst_so = 2.0338e-06 + -- HH (mol/s/m^2)
-(2.0/3.0 * 6.05974e-7) -- Na/K (mol/s/m^2)
kLeak_so:set_perm(leakKConst_so, k_in, k_out, v_eq, 1)
kLeak_de = IonLeakage("k", "soma")
leakKConst_de = 3.0507e-7 + -- HH (mol/s/m^2)
-(2.0/3.0 * 1.61593e-8) -- Na/K (mol/s/m^2)
kLeak_de:set_perm(leakKConst_de, k_in, k_out, v_eq, 1)
-- TODO: What about Na!?
CE:add(kLeak_ax)
CE:add(kLeak_so)
CE:add(kLeak_de)
-- synapses
syn_handler = SynapseHandler()
syn_handler:set_ce_object(CE)
syn_handler:set_activation_timing_alpha(
avg_start, -- average onset of synaptical activity in [s]
avg_dur/6.0, -- average tau of activity function in [s]
dev_start, -- deviation of onset in [s]
dev_dur/6.0, -- deviation of tau in [s]
1.2e-9) -- peak conductivity in [S]
CE:set_synapse_handler(syn_handler)
--[[
-- electrode stimulation
-- 5nA seem to enervate the pyramidal cell with uniform diameters of 1um
-- (coords for 13-L3pyr-77.CNG.ugx, current given in C/ms)
CE:set_influx(5e-9, 6.54e-05, 2.665e-05, 3.985e-05, 0.0, 0.04) -- near soma
CE:set_influx(5e-9, 3.955e-06, 1.095e-06, -3.365e-06, 0.001, 0.0025) -- 1st edge soma to dend
CE:set_influx(0.3e-9, 3.955e-06, 1.095e-06, -3.365e-06, 0.0, 0.03) -- 1st 1st edge soma to dend
CE:set_influx(0.095e-9, 0.0, 0.0, 0.0, 0.1, 0.1) -- soma center vertex
CE:set_influx(0.2e-9, 0.0, 0.0, 0.0, 0.005, 0.0005) -- soma center vertex
CE:set_influx(10.0e-9, 0.000139, 0.00020809, -2.037e-05, 0.005, 0.005) -- distal apical dendrite vertex v1
CE:set_influx(10.0e-9, -3.96e-06, 0.0002173, -5.431e-05, 0.005, 0.005) -- distal apical dendrite vertex v2
--]]
-- 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 --
linConvCheck = CompositeConvCheck(approxSpace, 20, 2e-26, 1e-08)
linConvCheck:set_component_check("v", 1e-21, 1e-12)
linConvCheck:set_verbose(verbose)
ilu = ILU()
cgSolver = CG()
cgSolver:set_preconditioner(ilu)
cgSolver:set_convergence_check(linConvCheck)
--cgSolver:set_debug(dbgWriter)
----------------------
-- time stepping --
----------------------
time = 0.0
-- init solution
u = GridFunction(approxSpace)
b = GridFunction(approxSpace)
u:set(0.0)
Interpolate(v_eq, u, "v")
Interpolate(k_in, u, "k");
Interpolate(na_in, u, "na");
Interpolate(ca_in, u, "ca")
-- write start solution
if generateVTKoutput then
out = VTKOutput()
out:print(filename.."vtk/solution", u, 0, time)
end
-- 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)
-- 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)
-- synchronize (for profiling)
PclDebugBarrierAll()
-- apply linear solver
ilu:set_disable_preprocessing(matrixIsConst)
if ApplyLinearSolver(linOp, u, b, cgSolver) == false then
print("Could not apply linear solver.")
exit()
end
-- log time and vm in Soma
if ProcRank() == 0 then
if cell == "12-L3pyr" then
vm_soma = EvaluateAtClosestVertex(MakeVec(0.0, 0.0, 0.0), u, "v", "soma", dom:subset_handler())
vm_axon = EvaluateAtClosestVertex(MakeVec(-3.828e-05, -0.00013166, -2.34e-05), u, "v", "axon", dom:subset_handler())
vm_dend = EvaluateAtClosestVertex(MakeVec(8.304e-05, -1.982e-05, -8.4e-06), u, "v", "dendrite", dom:subset_handler())
vm_aDend = EvaluateAtClosestVertex(MakeVec(-3.84e-06, 0.00018561, -3.947e-05), u, "v", "apical_dendrite", dom:subset_handler())
measOutVm:write(time, "\t", vm_soma, "\t", vm_axon, "\t", vm_dend, "\t", vm_aDend, "\n")
ca_soma = EvaluateAtClosestVertex(MakeVec(0.0, 0.0, 0.0), u, "ca", "soma", dom:subset_handler())
ca_axon = EvaluateAtClosestVertex(MakeVec(-3.828e-05, -0.00013166, -2.34e-05), u, "ca", "axon", dom:subset_handler())
ca_dend = EvaluateAtClosestVertex(MakeVec(8.304e-05, -1.982e-05, -8.4e-06), u, "ca", "dendrite", dom:subset_handler())
ca_aDend = EvaluateAtClosestVertex(MakeVec(-3.84e-06, 0.00018561, -3.947e-05), u, "ca", "apical_dendrite", dom:subset_handler())
measOutCa:write(time, "\t", ca_soma, "\t", ca_axon, "\t", ca_dend, "\t", ca_aDend, "\n")
else
vm_soma = EvaluateAtClosestVertex(MakeVec(6.9e-07, 3.74e-06, -2.86e-06), u, "v", "soma", dom:subset_handler())
vm_axon = EvaluateAtClosestVertex(MakeVec(-4.05e-06, 6.736e-05, -1.341e-05), u, "v", "axon", dom:subset_handler())
vm_dend = EvaluateAtClosestVertex(MakeVec(-4.631e-05, -0.0001252, 4.62e-06), u, "v", "dendrite", dom:subset_handler())
measOutVm:write(time, "\t", vm_soma, "\t", vm_axon, "\t", vm_dend, "\t", -65, "\n")
ca_soma = EvaluateAtClosestVertex(MakeVec(6.9e-07, 3.74e-06, -2.86e-06), u, "ca", "soma", dom:subset_handler())
ca_axon = EvaluateAtClosestVertex(MakeVec(-4.05e-06, 6.736e-05, -1.341e-05), u, "ca", "axon", dom:subset_handler())
ca_dend = EvaluateAtClosestVertex(MakeVec(-4.631e-05, -0.0001252, 4.62e-06), u, "ca", "dendrite", dom:subset_handler())
measOutCa:write(time, "\t", ca_soma, "\t", ca_axon, "\t", ca_dend, "\t", -65, "\n")
end
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(filename.."vtk/solution", u, math.floor(time/pstep+0.5), time)
end
end
-- 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(filename.."vtk/solution", u)
end
-- close measure file
if ProcRank() == 0 then
measOutVm:close()
measOutCa:close()
end