using ModelingToolkit
using OrdinaryDiffEq, SteadyStateDiffEq, DiffEqCallbacks
using Plots
using CSV
using StatsBase: mean
using DataFrames
using CaMKIIModel
using CaMKIIModel: second
Plots.default(lw=1.5)Pacing simulations
Responses of calcium transients and electrophysiology to pacing frequencies.
Setup the ODE system
Electrical stimulation starts at t=100 seconds and ends at t=300 seconds.
sys = build_neonatal_ecc_sys(simplify=true, reduce_iso=true, reduce_camk=true)
tend = 500.0second
prob = ODEProblem(sys, [], tend)
stimstart = 100.0second
stimend = 300.0second
@unpack Istim = sys
alg = KenCarp47()KenCarp47(; linsolve = nothing, nlsolve = OrdinaryDiffEqNonlinearSolve.NLNewton{Rational{Int64}, Rational{Int64}, Rational{Int64}, Nothing}(1//100, 10, 1//5, 1//5, false, true, nothing), precs = DEFAULT_PRECS, smooth_est = true, extrapolant = linear, controller = PI, autodiff = ADTypes.AutoForwardDiff(),)Single pulse
callback = build_stim_callbacks(Istim, stimstart + 1second; period=10second, starttime=stimstart)
@time sol = solve(prob, alg; callback) 10.250276 seconds (23.61 M allocations: 1.090 GiB, 2.58% gc time, 99.75% compilation time)retcode: Success
Interpolation: 3rd order Hermite
t: 133-element Vector{Float64}:
0.0
0.019333125036189135
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0.2073558192440938
0.45611905918185225
1.0472561699066012
2.034266647380669
3.451776427609829
6.733791989961038
12.450116263175316
⋮
225968.185470419
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273090.82323644345
300321.295846388
339559.0539057869
378796.8119651858
424814.2733577976
479743.0271942651
500000.0
u: 133-element Vector{Vector{Float64}}:
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⋮
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[152317.63870284663, 12478.715631223433, -68.07187662777716, 0.12443123344074972, 0.12443129905387883, 0.12443136516660629, 0.1244314318018155, 0.12443149898331383, 0.12443156673588122, 0.1244316350853195 … 0.0016077462098278857, 0.0018676559606920237, 0.0028908687427421933, 0.002118592433502934, 0.9995811352845655, 0.999580305759473, 0.00737880744402946, 763.3131553753694, 763.1265149018922, 0.0010833535637424978]
[152370.7532592129, 12425.75999351687, -67.94147967983385, 0.12396722913472318, 0.12396727998545705, 0.12396733123365258, 0.12396738289724998, 0.12396743499491454, 0.12396748754607355, 0.1239675405709557 … 0.001640567448670273, 0.0018858070162628717, 0.002918952979521359, 0.0021583769601260477, 0.9995690167221079, 0.9995683392133281, 0.007444452681683283, 762.1163037940552, 761.9351713315386, 0.0010524846070922892]
[152387.29094230235, 12409.271428734324, -67.90040663950961, 0.12382559518794825, 0.12382564156422099, 0.12382568830335723, 0.12382573542172153, 0.12382578293634011, 0.12382583086493484, 0.1238258792259588 … 0.001650929999904272, 0.0018915573828061796, 0.002927855266407584, 0.0021710631364190557, 0.9995651356308054, 0.9995644988617285, 0.007465250324224651, 761.7446965774758, 761.5652273681827, 0.001043150697863048]plot(sol, idxs=(sys.t / 1000 - 100, sys.vm), title="Action potential (single pulse)", ylabel="mV", xlabel="Time (s)", label=false, tspan=(100second, 103second))
plot(sol, idxs=(sys.t / 1000 - 100, sys.Cai_mean), tspan=(100second, 103second), title="Calcium transient", ylabel="Conc. (μM)", xlabel="Time (s)", label="Avg Ca")
savefig("single-cat.pdf")"/home/github/actions-runner-1/_work/camkii-cardiomyocyte-model/camkii-cardiomyocyte-model/docs/single-cat.pdf"1Hz pacing
callback = build_stim_callbacks(Istim, stimend; period=1second, starttime=stimstart)
@time sol = solve(prob, alg; callback); 1.455669 seconds (77.70 k allocations: 18.125 MiB)plot(sol, idxs=(sys.t / 1000, sys.vm), title="Action potential", ylabel="mV", xlabel="Time (s)", label=false)
plot(sol, idxs=(sys.t / 1000 - 299, sys.vm), title="Action potential", tspan=(299second, 300second), ylabel="mV", xlabel="Time (s)", label=false)
plot(sol, idxs=(sys.t / 1000 - 299, [sys.IK1, sys.Ito, sys.IKs, sys.IKr, sys.If]), tspan=(299second, 300second), ylabel="μA/μF", xlabel="Time (s)", label=["IK1" "Ito" "IKs" "IKr" "If"])
plot(sol, idxs=(sys.t / 1000 - 299, [sys.ICaL, sys.INaCa, sys.ICaT, sys.ICab]), tspan=(299second, 300second), ylabel="μA/μF", xlabel="Time (s)", label=["ICaL" "INaCa" "ICaT" "ICab"])
plot(sol, idxs=(sys.t / 1000 - 299, [sys.Cai_sub_SR, sys.Cai_sub_SL, sys.Cai_mean]), tspan=(299second, 300second), title="Calcium transient", ylabel="μM", xlabel="Time (s)", label=["CaSR" "CaSL" "CaAvg"])
plot(sol, idxs=(sys.t / 1000, sys.CaMKAct * 100), title="Active CaMKII", ylabel="Active CaMKII (%)", xlabel="Time (s)", label=false)
3D surface plot
xx = 1:44
yy = range(299second, 300second, length=100)
zz = [sol(t, idxs=sys.Cai[u]) for t in yy, u in xx]
surface(xx, (yy .- 299second) ./ 1000, zz, colorbar=:none, yguide="(sec.)", zguide="Ca Conc. (μM)", xticks=false, size=(600, 600))
annotate!(3, 0, 0.65, "Ca (SL)")
annotate!(41, 0.25, 0.58, "Ca (SR)")
savefig("3d-surface.pdf")
savefig("3d-surface.png")"/home/github/actions-runner-1/_work/camkii-cardiomyocyte-model/camkii-cardiomyocyte-model/docs/3d-surface.png"Mean calcium
xx = 1:44
yy = [sol(299.22second, idxs=sys.Cai[u]) for u in xx]
avg = mean(yy)
plot(xx, yy, label="Cai", ylabel="Ca Conc. (μM)", xlabel="Compartment (SL to SR)", legend=:topright)
hline!([avg], linestyle=:dash, label="Avg Cai")
savefig("cai-spatial.pdf")
savefig("cai-spatial.png")"/home/github/actions-runner-1/_work/camkii-cardiomyocyte-model/camkii-cardiomyocyte-model/docs/cai-spatial.png"2Hz pacing
callback = build_stim_callbacks(Istim, stimend; period=1 / 2 * second, starttime=stimstart)
@time sol2 = solve(prob, alg; callback) 2.398355 seconds (125.60 k allocations: 29.454 MiB)retcode: Success
Interpolation: 3rd order Hermite
t: 14157-element Vector{Float64}:
0.0
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1.0472561699066012
2.034266647380669
3.451776427609829
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12.450116263175316
⋮
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500000.0
u: 14157-element Vector{Vector{Float64}}:
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⋮
[151294.433099115, 13498.842703870641, -70.22755618184227, 0.13564853577702168, 0.1356488584555999, 0.13564918167137394, 0.13564950549832364, 0.13564983001342068, 0.13565015529678134, 0.13565048143182876 … 0.0011515916734828986, 0.0015913967379185669, 0.0024633717783801557, 0.0015558172846263853, 0.9997383413078001, 0.9997363080732244, 0.006373228067277308, 784.1583100433876, 783.814116395077, 0.0019503120715763087]
[151354.19420334432, 13439.253002492358, -70.11690426780343, 0.13488795000641443, 0.1348882608790284, 0.13488857240847651, 0.13488888466883386, 0.134889197737171, 0.13488951169370647, 0.13488982662196933 … 0.0011714778997270765, 0.0016045377215039335, 0.0024837087523778213, 0.001580753987214195, 0.9997319551501551, 0.9997299428816093, 0.0064213548378238006, 783.1565113710683, 782.8243130861404, 0.001884946372827718]
[151411.11641793043, 13382.495708785875, -70.01002783151426, 0.13417459889685127, 0.13417489808748193, 0.13417519803424058, 0.13417549881091148, 0.13417580049426212, 0.13417610316419556, 0.13417640690391186 … 0.001191011779363847, 0.001617331895474334, 0.002503508907967861, 0.0016052103056997126, 0.9997256378212201, 0.9997236491534587, 0.0064681800817270345, 782.171205476479, 781.8501024883045, 0.00182443339648492]
[151469.34230083844, 13324.440130226201, -69.89915511388243, 0.13345627716926942, 0.13345656395971753, 0.13345685159327145, 0.13345714014302204, 0.133457429685016, 0.1334577202984064, 0.133458012065613 … 0.0012116220322422333, 0.0016307132902277917, 0.0025242178615493796, 0.0016309728900818178, 0.9997189255677189, 0.9997169642306044, 0.006517130118393648, 781.1325720052721, 780.8224861291436, 0.0017642902257018387]
[151529.77413356834, 13264.186678699503, -69.78239059303546, 0.1327230777615251, 0.13272335119534862, 0.13272362554649686, 0.13272390088692387, 0.13272417729149394, 0.13272445483813003, 0.13272473360797143 … 0.0012337163178489808, 0.0016449227902860534, 0.0025462076826685805, 0.0016585427821168399, 0.9997116770147796, 0.9997097491628607, 0.006569069556773318, 780.0225091795579, 779.7235039026924, 0.0017037351933072578]
[151596.2465111836, 13197.912280276701, -69.65188886803128, 0.13193136645407436, 0.13193162465683825, 0.1319318838409229, 0.13193214407659645, 0.13193240543696824, 0.13193266799813366, 0.13193293183932814 … 0.0012588831314433657, 0.0016609489375790229, 0.0025710088341273163, 0.0016898931285749352, 0.9997033559644787, 0.9997014671136001, 0.006627604685634913, 778.7651805942892, 778.4779485147646, 0.0016393169006806724]
[151658.41189441687, 13135.933597624971, -69.52782341735232, 0.13120519022655952, 0.13120543368778598, 0.13120567817193363, 0.13120592374722498, 0.1312061704846404, 0.13120641845805908, 0.13120666774440828 … 0.0012832895427149263, 0.001676327869710939, 0.0025948080358615157, 0.0017202359276864909, 0.9996952189950367, 0.9996933743294271, 0.006683734466549797, 777.556033880584, 777.2794208596608, 0.0015811308628416237]
[151725.67377341233, 13068.875229527343, -69.39131274589532, 0.13043528892142994, 0.13043551593018796, 0.1304357439862796, 0.13043597315519675, 0.13043620350507815, 0.13043643510684552, 0.13043666803434595 … 0.001310689639367462, 0.0016934110604342656, 0.0026212443894967313, 0.0017542350543941923, 0.9996860060220164, 0.9996842167640255, 0.0067460345133910846, 776.2133640551177, 775.9478173251572, 0.00152040043375649]
[151762.65788403733, 13032.003600768106, -69.31520476340353, 0.13001906573958336, 0.13001928342841831, 0.13001950217152, 0.13001972203268902, 0.13001994307830533, 0.13002016537745975, 0.13002038900209387 … 0.001326220900161864, 0.0017030114450090675, 0.002636101269855324, 0.0017734749949406443, 0.9996807488470206, 0.9996789925962177, 0.006781032725035116, 775.4606948906832, 775.2010464531234, 0.001487990026769612]plot(sol2, idxs=(sys.t / 1000, sys.vm), title="Action potential", ylabel="mV", xlabel="Time (s)", label=false)
plot(sol2, idxs=(sys.t / 1000 - 299, sys.vm), title="Action potential", tspan=(299second, 300second), ylabel="mV", xlabel="Time (s)", label=false)
plot(sol2, idxs=(sys.t / 1000 - 299, [sys.Cai_sub_SR, sys.Cai_sub_SL, sys.Cai_mean]), tspan=(299second, 300second), title="Calcium transient", ylabel="Concentration (μM)", xlabel="Time (s)", label=["CaSSR" "CaSL" "CaAvg"])
plot(sol2, idxs=(sys.t / 1000, sys.CaMKAct * 100), title="Active CaMKII", ylabel="Active CaMKII (%)", xlabel="Time (s)", label=false)
Comparing 1 and 2 Hz pacing
idxs = (sys.t / 1000 - 299, sys.vm)
plot(sol, idxs=idxs, title="Action potential", lab="1Hz", tspan=(299second, 300second))
plot!(sol2, idxs=idxs, lab="2Hz", tspan=(299second, 300second), xlabel="Time (s)", ylabel="Voltage (mV)")
savefig("bcl-ap.pdf")"/home/github/actions-runner-1/_work/camkii-cardiomyocyte-model/camkii-cardiomyocyte-model/docs/bcl-ap.pdf"idxs = (sys.t / 1000 - 299, sys.Cai_mean)
plot(sol, idxs=idxs, title="Calcium transient", lab="1Hz", tspan=(299second, 300second))
plot!(sol2, idxs=idxs, lab="2Hz", tspan=(299second, 300second), xlabel="Time (s)", ylabel="Concentration (μM)")
savefig("bcl-cat.pdf")"/home/github/actions-runner-1/_work/camkii-cardiomyocyte-model/camkii-cardiomyocyte-model/docs/bcl-cat.pdf"idxs = (sys.t / 1000, sys.CaMKAct * 100)
plot(sol, idxs=idxs, title="CaMKII", lab="1Hz")
plot!(sol2, idxs=idxs, lab="2Hz", xlabel="Time (s)", ylabel="Active fraction (%)")
savefig("bcl-camkact.pdf")"/home/github/actions-runner-1/_work/camkii-cardiomyocyte-model/camkii-cardiomyocyte-model/docs/bcl-camkact.pdf"Runtime information
using InteractiveUtils
InteractiveUtils.versioninfo()Julia Version 1.12.4
Commit 01a2eadb047 (2026-01-06 16:56 UTC)
Build Info:
Official https://julialang.org release
Platform Info:
OS: Linux (x86_64-linux-gnu)
CPU: 12 × Intel(R) Core(TM) i7-8700 CPU @ 3.20GHz
WORD_SIZE: 64
LLVM: libLLVM-18.1.7 (ORCJIT, skylake)
GC: Built with stock GC
Threads: 2 default, 1 interactive, 2 GC (on 12 virtual cores)
Environment:
JULIA_CI = true
JULIA_CONDAPKG_OFFLINE = true
LD_LIBRARY_PATH = /home/github/actions-runner-1/_work/_tool/Python/3.14.2/x64/lib
JULIA_NUM_THREADS = 2
JULIA_PROJECT = /home/github/actions-runner-1/_work/camkii-cardiomyocyte-model/camkii-cardiomyocyte-model/Project.toml
JULIA_DEPOT_PATH = /home/github/.julia:/home/github/actions-runner-1/_work/_tool/julia/1.12.4/x64/local/share/julia:/home/github/actions-runner-1/_work/_tool/julia/1.12.4/x64/share/julia
JULIA_CONDAPKG_BACKEND = Null
JULIA_LOAD_PATH = @:@v#.#:@stdlibusing Pkg
Pkg.status()Project CaMKIIModel v0.7.0
Status `~/actions-runner-1/_work/camkii-cardiomyocyte-model/camkii-cardiomyocyte-model/Project.toml`
[336ed68f] CSV v0.10.15
[5a033b19] CurveFit v1.4.0
[a93c6f00] DataFrames v1.8.1
[459566f4] DiffEqCallbacks v4.12.0
[f6369f11] ForwardDiff v1.3.2
[23fbe1c1] Latexify v0.16.10
[2fda8390] LsqFit v0.15.1
⌅ [961ee093] ModelingToolkit v10.32.1
[77ba4419] NaNMath v1.1.3
[1dea7af3] OrdinaryDiffEq v6.108.0
[91a5bcdd] Plots v1.41.5
[2913bbd2] StatsBase v0.34.10
[9672c7b4] SteadyStateDiffEq v2.9.0
Info Packages marked with ⌅ have new versions available but compatibility constraints restrict them from upgrading. To see why use `status --outdated`This notebook was generated using Literate.jl.