Pacing response#
using ModelingToolkit
using OrdinaryDiffEq, SteadyStateDiffEq, DiffEqCallbacks
using Plots
using CSV
using DataFrames
using CaMKIIModel
using CaMKIIModel: second
Plots.default(lw=1.5)
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)
10.039273 seconds (19.68 M allocations: 946.775 MiB, 2.67% gc time, 98.85% compilation time)
retcode: Success
Interpolation: 3rd order Hermite
t: 132-element Vector{Float64}:
0.0
0.019333123284849308
0.09098129546757994
0.20735582943983855
0.45611910276862533
1.0472562928406122
2.0342667657223696
3.451776641148454
6.733792423912806
12.450117081023194
⋮
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426137.84488456656
478964.15133511706
500000.0
u: 132-element Vector{Vector{Float64}}:
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⋮
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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 (Model)")
savefig("single-cat.pdf")
"/home/runner/work/camkii-cardiomyocyte-model/camkii-cardiomyocyte-model/.cache/docs/single-cat.pdf"
1Hz#
callback = build_stim_callbacks(Istim, stimend; period=1second, starttime=stimstart)
@time sol = solve(prob, alg; callback)
1.787926 seconds (130.42 k allocations: 459.326 MiB, 5.39% gc time)
retcode: Success
Interpolation: 3rd order Hermite
t: 8928-element Vector{Float64}:
0.0
0.019333123284849308
0.09098129546757994
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1.0472562928406122
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3.451776641148454
6.733792423912806
12.450117081023194
⋮
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500000.0
u: 8928-element Vector{Vector{Float64}}:
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⋮
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[0.12995055681703058, 0.12995025581268177, 0.12994996002206602, 0.12994966918727568, 0.12994938306434534, 0.12994910142232258, 0.12994882404241176, 0.1299485507171847, 0.12994828124985194, 0.12994801545358947 … 1.0030729934311355, 0.6341808751566705, 0.0017770923131236998, 0.00678758890335609, 0.9996780071094089, 0.9996797565978024, 0.18622932277450172, 151769.5123137427, 13025.159389549222, -69.30099188927778]
[0.12936377283996045, 0.12936348777704385, 0.1293632077440708, 0.1293629324942863, 0.1293626617942748, 0.12936239542307118, 0.129362133171341, 0.12936187484062608, 0.12936162024264664, 0.12936136919865757 … 1.0031047123649706, 0.6298929371355398, 0.0018054801341620852, 0.006838802266503942, 0.9996702372156248, 0.9996719302296267, 0.1835786274136847, 151822.5305712299, 12972.303078706154, -69.19037200428396]
[0.12870479947257216, 0.1287045338124558, 0.12870427293343822, 0.12870401660302014, 0.12870376460127084, 0.12870351671999006, 0.12870327276193655, 0.12870303254011625, 0.1287027958771256, 0.12870256260454438 … 1.0031402394217914, 0.6248770764984957, 0.001839073383801114, 0.0068989026810732275, 0.9996609568705979, 0.9996625831123114, 0.18053116062530244, 151883.26445998737, 12911.755414462836, -69.06164930516218]
[0.12852033486130648, 0.12852007492760517, 0.12851981969725462, 0.12851956894207872, 0.12851932244623598, 0.12851908000539725, 0.1285188414259883, 0.12851860652449165, 0.12851837512680156, 0.1285181470676287 … 1.0031501666650124, 0.6234327774593323, 0.0018488280488430592, 0.006916241631924938, 0.9996582450741126, 0.999659852305361, 0.17966386830656403, 151900.50607632747, 12894.566779686067, -69.02471233893849]
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=["CaSSR" "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 ./ 1000, zz, colorbar=:none, yguide="sec.", zguide="Conc. (μM)", xticks=false, size=(600, 600))
annotate!(3, 299, 0.65, "SL")
annotate!(41, 299.25, 0.58, "SR")
savefig("3d-surface.pdf")
"/home/runner/work/camkii-cardiomyocyte-model/camkii-cardiomyocyte-model/.cache/docs/3d-surface.pdf"
2Hz#
callback = build_stim_callbacks(Istim, stimend; period=1 / 2 * second, starttime=stimstart)
@time sol2 = solve(prob, alg; callback)
3.394554 seconds (210.25 k allocations: 768.504 MiB, 15.70% gc time)
retcode: Success
Interpolation: 3rd order Hermite
t: 14163-element Vector{Float64}:
0.0
0.019333123284849308
0.09098129546757994
0.20735582943983855
0.45611910276862533
1.0472562928406122
2.0342667657223696
3.451776641148454
6.733792423912806
12.450117081023194
⋮
403252.8064076104
412782.91906571155
423257.62396415835
435362.5046771487
447467.38539013907
461423.863562818
478496.3270349015
495568.790506985
500000.0
u: 14163-element Vector{Vector{Float64}}:
[0.12113, 0.12113, 0.12113, 0.12113, 0.12113, 0.12113, 0.12113, 0.12113, 0.12113, 0.12113 … 0.9911, 0.61179, 0.09243, 0.00702, 0.966, 0.22156, 0.07192, 150952.75035000002, 13838.37602, -68.79268]
[0.12112999999999999, 0.12113, 0.12113, 0.12113, 0.12113, 0.12113, 0.12113, 0.12113, 0.12113, 0.12113 … 0.9911240298625772, 0.61179209692054, 0.09242766669618695, 0.007020208561323646, 0.9660018276402699, 0.2215639938807744, 0.07192100954852718, 150952.7504077194, 13838.375711519551, -68.79732946186226]
[0.12113000000531939, 0.12113000000024629, 0.12112999999996936, 0.12112999999998814, 0.12112999999999756, 0.12112999999999959, 0.12112999999999993, 0.12112999999999999, 0.12112999999999999, 0.12113 … 0.9912126672514168, 0.6118012235185329, 0.09241901973901424, 0.00702008986027517, 0.9660085993318799, 0.2215787945110049, 0.0719247622956487, 150952.75062244057, 13838.374513299192, -68.81607005265552]
[0.12113000352486501, 0.12113000071464508, 0.12113000013259279, 0.12113000002221791, 0.12113000000324825, 0.12113000000037327, 0.12113000000001811, 0.12112999999999313, 0.12112999999999685, 0.12112999999999911 … 0.9913552605900093, 0.6118207061207029, 0.09240497563401104, 0.007017234889558555, 0.9660195931792828, 0.22160283236040595, 0.07193089713793946, 150952.7509740238, 13838.372555328333, -68.84681913285226]
[0.12113031246875829, 0.12113011855881943, 0.12113004261415268, 0.1211300145224514, 0.1211300046922744, 0.12113000143526587, 0.12113000041393686, 0.12113000011158663, 0.12113000002760377, 0.12113000000599933 … 0.9916544804172969, 0.6118814305717646, 0.0923749578279845, 0.0070030143052343926, 0.9660430731013478, 0.2216542075240971, 0.07194417536281429, 150952.7517373371, 13838.368384399068, -68.91207316777846]
[0.12113664606535107, 0.12113391404700644, 0.12113223891788369, 0.12113124406405289, 0.12113067160353039, 0.12113035232069681, 0.12113017964115647, 0.12113008904213221, 0.12113004292180056, 0.12113002016884632 … 0.9923360674037417, 0.6121262615921059, 0.09230364339951613, 0.006946470397388757, 0.9660987611411453, 0.22177624785138977, 0.07197662797870664, 150952.75361533565, 13838.358559292059, -69.06429960994137]
[0.12116110329207945, 0.12115245907382813, 0.12114597183088456, 0.12114118504637392, 0.12113771307938385, 0.12113523852752958, 0.12113350680291797, 0.1211323190247843, 0.12113152423329539, 0.1211310117677002 … 0.9933874251519441, 0.6128292434834117, 0.09218462776986637, 0.0068337541728754475, 0.9661914345949096, 0.2219798989175973, 0.07203363801526848, 150952.75694915713, 13838.34240329337, -69.31024285744343]
[0.12120423665656944, 0.12118928168345969, 0.12117695409406527, 0.12116690224321353, 0.12115880345210753, 0.12115236793976296, 0.12114734156698287, 0.12114350756515986, 0.12114068746411359, 0.12113874145120666 … 0.9947260029718878, 0.61441610851668, 0.09201383579531924, 0.006675512062656749, 0.9663239343003682, 0.22227216398019892, 0.0721216517759309, 150952.76215620188, 13838.319723120678, -69.64637448767432]
[0.1212995420290433, 0.12127783468666772, 0.1212589040374779, 0.1212425879351912, 0.12122873583441052, 0.12121721111566237, 0.12120789316717222, 0.12120067917599112, 0.12119548558727024, 0.1211922491964778 … 0.9971828595843288, 0.6201838932607627, 0.09161908329520764, 0.006355039713677859, 0.9666286957812559, 0.22294828828976576, 0.07235305497134359, 150952.77598869594, 13838.2694938995, -70.35063788657428]
[0.1214553971027536, 0.12143259661681072, 0.12141268299068807, 0.12139558631643757, 0.12138124198529929, 0.12136959056512987, 0.12136057763401646, 0.12135415355743052, 0.1213502731984364, 0.12134889555279481 … 0.9999327439121073, 0.6347673874618533, 0.09093422465365385, 0.005926150085676071, 0.9671554512230358, 0.22412560303273427, 0.07284451729172227, 150952.80529264064, 13838.18882346682, -71.35304509818071]
⋮
[0.13520910346443865, 0.13520870827662543, 0.135208318554708, 0.13520793399753014, 0.13520755432021678, 0.13520717925308837, 0.1352068085406615, 0.13520644194072695, 0.1352060792234987, 0.1352057201708279 … 1.0027850726520209, 0.6668055368045499, 0.0015704594566433654, 0.006401536598238053, 0.9997325765508918, 0.9997345986850065, 0.2078640064710195, 151329.73678923372, 13463.639830820675, -70.16237636695847]
[0.13455871887745238, 0.13455833108905726, 0.13455794885528802, 0.13455757187545275, 0.13455719986511536, 0.13455683255501197, 0.13455646969005264, 0.13455611102840107, 0.13455575634062522, 0.134555405408912 … 1.0028210507255573, 0.6632384126710372, 0.00159228679344234, 0.0064434881853994135, 0.9997269806387863, 0.9997289833818177, 0.20536330420928472, 151381.23645949634, 13412.288684613352, -70.06630769034052]
[0.13388491760684523, 0.13388453864610989, 0.1338841652992494, 0.13388379726737504, 0.1338834342677563, 0.13388307603274402, 0.133882722308778, 0.1338823728554722, 0.13388202744477054, 0.1338816858601663 … 1.0028582126494785, 0.6594216978003619, 0.0016158415907307092, 0.006488433583871561, 0.9997208967515306, 0.9997228759655548, 0.20272624598502773, 151435.35010948047, 13358.332495903669, -69.96406963941773]
[0.13315651036010104, 0.13315614228317174, 0.13315577984617422, 0.13315542275373335, 0.13315507072644198, 0.13315472349979643, 0.1331543808232159, 0.13315404245913856, 0.13315370818218705, 0.13315337777839711 … 1.0028982596642004, 0.6551475163691084, 0.0016424692973950078, 0.006538841664684337, 0.9997139634414586, 0.9997159113620446, 0.19981937499529173, 151494.77361021383, 13299.08347056362, -69.85023064464261]
[0.132478010468822, 0.13247765393330854, 0.1324773030232859, 0.13247695744821267, 0.13247661693325422, 0.1324762812182355, 0.13247595005667678, 0.13247562321490425, 0.13247530047122918, 0.13247498161518936 … 1.0029354455798265, 0.6510175788747912, 0.0016684544490965622, 0.006587639980609921, 0.9997071390528249, 0.9997090568751031, 0.1970561709876059, 151551.04143769506, 13242.982305626703, -69.74087130994391]
[0.13175281948023676, 0.13175247680387933, 0.13175213969321783, 0.1317518078646847, 0.13175148105004214, 0.13175115899535997, 0.1317508414600748, 0.1317505282161217, 0.13175021904713352, 0.13174991374769995 … 1.002975067108428, 0.6464335014704247, 0.0016975971965949728, 0.006641908415667089, 0.9996994194699635, 0.999701297436267, 0.19403968785105935, 151612.22778821777, 13181.978662174579, -69.62018325293417]
[0.13094195162730862, 0.13094162636315007, 0.13094130654461666, 0.13094099189813121, 0.13094068216490617, 0.13094037709995754, 0.1309400764711969, 0.13093978005859372, 0.13093948765340294, 0.13093919905745025 … 1.0030192206367587, 0.6410816549716302, 0.0017320283400838168, 0.0067054196825303575, 0.9996902087860936, 0.9996920347051063, 0.1905839144215264, 151682.02374670637, 13112.39281500162, -69.48017476805288]
[0.13020683677794373, 0.13020652918304443, 0.13020622687027097, 0.13020592957731433, 0.1302056370560456, 0.1302053490715708, 0.13020506540136, 0.13020478583444453, 0.1302045101706759, 0.13020423822004107 … 1.0030591150520023, 0.6360050693666195, 0.0017651047130271612, 0.00676582940615563, 0.9996812693521222, 0.9996830392302855, 0.18736939541487657, 151746.66233734842, 13047.95023829306, -69.34821396043317]
[0.13002745466775253, 0.1300271516512794, 0.13002685386966983, 0.13002656106365967, 0.13002627298799999, 0.1300259894105227, 0.1300257101112801, 0.1300254348817513, 0.13002516352410956, 0.13002489585054583 … 1.0030688308068665, 0.6347315244854327, 0.0017734683214284783, 0.006781012883967502, 0.9996789946620137, 0.9996807506215253, 0.18657252397401958, 151762.6446088315, 13032.01662356243, -69.31523435344016]
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/runner/work/camkii-cardiomyocyte-model/camkii-cardiomyocyte-model/.cache/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/runner/work/camkii-cardiomyocyte-model/camkii-cardiomyocyte-model/.cache/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/runner/work/camkii-cardiomyocyte-model/camkii-cardiomyocyte-model/.cache/docs/bcl-camkact.pdf"
This notebook was generated using Literate.jl.