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)
9.035950 seconds (16.91 M allocations: 809.302 MiB, 2.38% gc time, 99.61% compilation time)
retcode: Success
Interpolation: 3rd order Hermite
t: 132-element Vector{Float64}:
0.0
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1.0472562928406122
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3.451776641148454
6.733792423912806
12.450117081023194
⋮
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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/github/actions-runner-2/_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)
1.530938 seconds (77.70 k allocations: 20.866 MiB, 2.63% gc time)
retcode: Success
Interpolation: 3rd order Hermite
t: 8777-element Vector{Float64}:
0.0
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⋮
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u: 8777-element Vector{Vector{Float64}}:
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⋮
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[151714.58661457305, 13079.919116838224, -69.41395636003223, 0.1305609361853242, 0.13056116590876451, 0.13056139667782987, 0.13056162855849152, 0.13056186161938868, 0.13056209593196436, 0.13056233157061004 … 0.001306106030111019, 0.0016905667171542998, 0.0026168429500363598, 0.001748550717392031, 0.9996875526279307, 0.9996857544795018, 0.0067356728292023715, 776.4368542673716, 776.1695152502208, 0.001530243417498353]
[151769.9110574128, 13024.762893012594, -69.30016803324258, 0.12993794087191515, 0.1299381567053503, 0.1299383735936188, 0.1299385916001685, 0.12993881079101227, 0.12993903123485892, 0.1299392530032521 … 0.00132931311539201, 0.0017049146722032033, 0.0026390462223068465, 0.0017773021266455887, 0.9996796990226872, 0.9996779499137823, 0.0067879689906618565, 775.3117455048424, 775.0532397755209, 0.0014817072992678612]
[151822.9141042824, 12971.921751189424, -69.18956820618216, 0.12935187566731496, 0.12935207790630415, 0.1293522811960929, 0.12935248559738324, 0.12935269117333117, 0.12935289798967184, 0.12935310611485268 … 0.0013522660713352283, 0.0017189737579327165, 0.002660802162355008, 0.001805688033331627, 0.9996718726729565, 0.999670180065544, 0.006839175882062826, 774.2135603491694, 773.9632407342749, 0.0014366610746977457]
[151883.63079477762, 12911.391236575922, -69.06086870135819, 0.12869374058370234, 0.12869392686652317, 0.1286941141809962, 0.1286943025843191, 0.12869449213600165, 0.1286946828979836, 0.12869487493475998 … 0.0013794740838786843, 0.0017354819924320535, 0.0026863485073335353, 0.001839278953348717, 0.9996625256133287, 0.9996608998069626, 0.006899268679635052, 772.9329322374338, 772.6916600622686, 0.0013867943937433558]
[151900.78675160542, 12894.287998880653, -69.02411194420453, 0.1285103778205528, 0.12851055951696788, 0.1285107422369757, 0.1285109260367176, 0.12851111097460416, 0.12851129711143078, 0.12851148451050093 … 0.0013873483916889376, 0.0017402250309041128, 0.002693687807958495, 0.0018489869713265213, 0.9996598077201612, 0.999658200834317, 0.006916523846325756, 772.566989958823, 772.3282106357881, 0.001373038445043791]
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/github/actions-runner-2/_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)
2.357577 seconds (125.60 k allocations: 34.894 MiB)
retcode: Success
Interpolation: 3rd order Hermite
t: 14156-element Vector{Float64}:
0.0
0.019333123284849308
0.09098129546757994
0.20735582943983855
0.45611910276862533
1.0472562928406122
2.0342667657223696
3.451776641148454
6.733792423912806
12.450117081023194
⋮
395927.70780771674
405613.0804609899
417481.2406113328
429349.40076167573
442244.02411750116
456809.9075399475
474103.3852925388
491396.8630451301
500000.0
u: 14156-element Vector{Vector{Float64}}:
[150952.75035000002, 13838.37602, -68.79268, 0.12113, 0.12113, 0.12113, 0.12113, 0.12113, 0.12113, 0.12113 … 0.26081, 0.00977, 0.00188, 0.09243, 0.22156, 0.966, 0.00702, 830.0, 830.0, 0.0026]
[150952.7504077194, 13838.375711519551, -68.79732946186226, 0.1211319185255175, 0.1211301421535992, 0.12113000811850358, 0.12113000037367234, 0.12113000001389383, 0.12113000000038378, 0.12113000000000405 … 0.2608055799112056, 0.009769882842069916, 0.001879826176081169, 0.09242766669618695, 0.2215639938807744, 0.9660018276402699, 0.007020208561323646, 829.9999654017583, 829.9994975880693, 0.0025985659590295374]
[150952.75062244057, 13838.374513299192, -68.81607005265552, 0.12115248970210647, 0.12113624253259858, 0.12113143375871602, 0.12113027926811751, 0.12113004704056851, 0.12113000693481112, 0.12113000089551408 … 0.26078941009382306, 0.009769459049732313, 0.0018789042446514422, 0.09241901973901424, 0.2215787945110049, 0.9660085993318799, 0.00702008986027517, 829.9998348635061, 829.9976422525165, 0.002593310524681686]
[150952.7509740238, 13838.372555328333, -68.84681913285226, 0.12118951551963696, 0.12115723910142134, 0.12114109135582982, 0.12113403405679991, 0.12113131833063846, 0.12113038966346883, 0.12113010483012127 … 0.2607638707001999, 0.009768805322556195, 0.0018766436937193197, 0.09240497563401104, 0.22160283236040595, 0.9660195931792828, 0.007017234889558555, 829.9996133960318, 829.9946506157202, 0.0025849478335103777]
[150952.7517373371, 13838.368384399068, -68.91207316777846, 0.12125418995384041, 0.12120713813483534, 0.12117519662647316, 0.12115494411090462, 0.12114295934422187, 0.12113633873395535, 0.12113292110288301 … 0.2607122383588733, 0.00976754294689657, 0.0018699196262940568, 0.0923749578279845, 0.2216542075240971, 0.9660430731013478, 0.0070030143052343926, 829.9990964774663, 829.9883445519497, 0.00256770780104998]
[150952.75361533565, 13838.358559292059, -69.06429960994137, 0.12136450208851983, 0.1213063255235844, 0.12125925929399752, 0.12122229800810434, 0.12119414515426227, 0.1211733598588045, 0.12115849269665879 … 0.26060507831375035, 0.009765228548607825, 0.001850533769446942, 0.09230364339951613, 0.22177624785138977, 0.9660987611411453, 0.006946470397388757, 829.9976227528975, 829.9738229154025, 0.0025298083713907005]
[150952.75694915713, 13838.34240329337, -69.31024285744343, 0.1214919651325424, 0.12142927821043338, 0.12137426379919636, 0.12132672249013034, 0.12128628091507473, 0.12125242557826561, 0.12122454121844703 … 0.26047114911179464, 0.009763403076884485, 0.0018178174419014683, 0.09218462776986637, 0.2219798989175973, 0.9661914345949096, 0.0068337541728754475, 829.9944193668179, 829.9509077855928, 0.0024748079782158957]
[150952.76215620188, 13838.319723120678, -69.64637448767432, 0.12162015426876954, 0.12155743299711902, 0.12149988983034497, 0.1214475947100359, 0.12140052118634262, 0.12135855488207907, 0.12132150441596071 … 0.2603648729749554, 0.009765046552800477, 0.001773815690753224, 0.09201383579531924, 0.22227216398019892, 0.9663239343003682, 0.006675512062656749, 829.9883533251192, 829.9205247545176, 0.0024106893964811324]
[150952.77598869594, 13838.2694938995, -70.35063788657428, 0.12180447948880582, 0.12174768443532359, 0.1216934018408597, 0.12164180995533562, 0.1215930492007203, 0.12154722283384187, 0.12150439833798554 … 0.26041507667541997, 0.009786689200123853, 0.0016855899094922325, 0.09161908329520764, 0.22294828828976576, 0.9666286957812559, 0.006355039713677859, 829.9689941817725, 829.8589858006806, 0.00231065572773434]
[150952.80529264064, 13838.18882346682, -71.35304509818071, 0.12196378364408145, 0.12191937753328307, 0.12187579038290325, 0.1218331857334072, 0.12179171693004393, 0.12175152667167352, 0.12171274673876355 … 0.26104417804603025, 0.009873892913308327, 0.0015688568862426042, 0.09093422465365385, 0.22412560303273427, 0.9671554512230358, 0.005926150085676071, 829.923524981244, 829.7704141396295, 0.00222899504022452]
⋮
[151288.62104415678, 13504.638084823886, -70.23823367042856, 0.13572313904377917, 0.13572346284522058, 0.13572378717155006, 0.13572411209672341, 0.13572443769768694, 0.1357247640545305, 0.13572509125064924 … 0.0011496906111967177, 0.0015901343307786573, 0.00246141802694959, 0.0015534313010536903, 0.999738949582253, 0.9997369142782591, 0.006368602803588028, 784.2539488165831, 783.908569522741, 0.0019567703653966483]
[151342.70484164095, 13450.709173214926, -70.13829757647937, 0.13503325081398088, 0.13503356399118546, 0.13503387780351536, 0.13503419232505973, 0.1350345076329035, 0.13503482380728066, 0.1350351409317362 … 0.001167606322847834, 0.0016019893515117033, 0.0024797648942170487, 0.0015759026497015958, 0.999733202269883, 0.9997311850729016, 0.006412025812574796, 783.3517205173213, 783.0172437016106, 0.0018973668171123283]
[151405.82763862537, 13387.769003732496, -70.02001387851226, 0.13424041646088497, 0.13424071674904542, 0.1342410177848571, 0.13424131964214556, 0.1342416223977214, 0.13424192613153246, 0.13424223092682588 … 0.00118917341984684, 0.001616133747727137, 0.0025016546134142546, 0.0016029106137966955, 0.9997262348697125, 0.9997242425479561, 0.006463800412863881, 782.2640065439807, 781.9418862078487, 0.001829984144647414]
[151465.65866015328, 13328.112853326347, -69.90621448874845, 0.13350138071232204, 0.13350166829263255, 0.1335019567112258, 0.1335022460412585, 0.13350253635884515, 0.13350282774320907, 0.13350312027684264 … 0.001210299682207733, 0.001629858328048285, 0.0025228944396657603, 0.001629321472930608, 0.9997193586119162, 0.9997173940466885, 0.006514003394706948, 781.1992099129778, 780.888436942781, 0.0017680431407495745]
[151527.14093053757, 13266.811981849993, -69.78751901572474, 0.13275475940478693, 0.1327550334503447, 0.13275530841035094, 0.13275558435683252, 0.13275586136472886, 0.13275613951204068, 0.13275641887998765 … 0.0012327352774691102, 0.0016442953884569826, 0.002545236612865768, 0.0016573207883583138, 0.9997120004261576, 0.9997100702714233, 0.006566775588702545, 780.0716046980167, 779.7721240663591, 0.0017063348138984533]
[151592.43307441697, 13201.71423171755, -69.65943614166004, 0.1319763542289987, 0.13197661331739421, 0.13197687338383596, 0.1319771344986946, 0.13197739673518644, 0.13197766016951848, 0.13197792488104274 … 0.0012574125167130058, 0.0016600180089672196, 0.0025695683240656033, 0.001688062907777251, 0.9997038433964126, 0.9997019528297642, 0.006624208354699795, 778.8382669012374, 778.5503711878772, 0.0016429494984142987]
[151664.57962851107, 13129.784354459216, -69.51541194084247, 0.13113391542772257, 0.1311341573995749, 0.13113440039723182, 0.13113464448867881, 0.13113488974464985, 0.13113513623876766, 0.13113538404769248 … 0.001285756407378889, 0.0016778719859812602, 0.0025971974575968453, 0.0017232983966568264, 0.9996943910561734, 0.9996925541726791, 0.006689366577848935, 777.4344026251804, 777.1588227002477, 0.0015754658479022426]
[151731.32743016913, 13063.238598283564, -69.37972253619243, 0.13037134029544867, 0.13037156589425433, 0.13037179254231016, 0.13037202030487213, 0.1303722492498338, 0.13037247944786123, 0.13037271097253567 … 0.0013130444821922813, 0.0016948701326679068, 0.0026235026794193023, 0.001757151537022017, 0.9996852088495349, 0.9996834273128746, 0.006751359955192751, 776.0990037351922, 775.8343670414222, 0.0015154026427403316]
[151762.65011433122, 13032.011194869308, -69.3152248543311, 0.13001916088541096, 0.13001937856723725, 0.13001959730332227, 0.13001981715747246, 0.13002003819607347, 0.13002026048822168, 0.13002048410586411 … 0.0013262238101087573, 0.0017030075441871067, 0.00263609461423843, 0.001773474138269699, 0.9996807481101285, 0.9996789938505761, 0.006781014319054366, 775.4608628072868, 775.2012130626564, 0.0014879970177772758]
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-2/_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/github/actions-runner-2/_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/github/actions-runner-2/_work/camkii-cardiomyocyte-model/camkii-cardiomyocyte-model/.cache/docs/bcl-camkact.pdf"
This notebook was generated using Literate.jl.