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}, Rational{Int64}}(1//100, 10, 1//5, 1//5, false, true, 0//1), 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)
6.995700 seconds (20.22 M allocations: 983.873 MiB, 2.55% gc time, 99.67% 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/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)
2.532713 seconds (134.32 k allocations: 455.922 MiB, 19.84% gc time)
retcode: Success
Interpolation: 3rd order Hermite
t: 8928-element Vector{Float64}:
0.0
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3.451776641148454
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⋮
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u: 8928-element Vector{Vector{Float64}}:
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⋮
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[0.0015306122736882593, 776.1777778843183, 776.4451840785243, 0.0067352862192918165, 0.9996858116842524, 0.9996876101843762, 0.0017483390578107688, 0.002616678863411223, 0.001690460683928338, 0.00130593533335512 … 0.13056703431605654, 0.1305667985753129, 0.13056656416059598, 0.13056633099749437, 0.13056609901454588, 0.13056586814309296, 0.13056563831714654, -69.41480081459319, 13080.331564596181, 151714.17187739676]
[0.001482050729065109, 775.0613455882905, 775.3199137734706, 0.006787588903356454, 0.9996780071094088, 0.9996797565978023, 0.001777092313124226, 0.002638884798087709, 0.0017048103584188727, 0.0013291436146088099 … 0.12994369201081712, 0.12994347014126684, 0.12994324959632853, 0.12994303030443666, 0.1299428121968614, 0.12994259520756962, 0.12994237927309396, -69.30099188927717, 13025.159389549226, 151769.51231374257]
[0.0014369811358487916, 773.9711768711533, 774.2215546069662, 0.006838802266502706, 0.9996702372156249, 0.9996719302296266, 0.001805480134161506, 0.0026606433864831552, 0.001718871154455714, 0.0013520978330364647 … 0.12935729849169433, 0.1293570902665786, 0.12935688335046155, 0.12935667767487222, 0.12935647317405294, 0.12935626978482598, 0.1293560674464684, -69.19037200428639, 12972.30307870616, 151822.53057122976]
[0.001387088933893308, 772.6993808014341, 772.9407063683639, 0.006898902681073527, 0.9996609568705977, 0.9996625831123114, 0.001839073383801483, 0.0026861928533385353, 0.0017353814050314002, 0.0013793074026723236 … 0.12869879303093165, 0.12869860089602234, 0.12869841003616123, 0.12869822038682832, 0.12869803188605983, 0.1286978444743228, 0.12869765809439737, -69.06164930516148, 12911.75541446288, 151883.2644599872]
[0.0013732615225980056, 772.3341498101198, 772.572969551145, 0.00691624163192476, 0.9996582450741126, 0.9996598523053611, 0.0018488280488432878, 0.002693567762134606, 0.0017401474544429024, 0.0013872194629617315 … 0.12851446525724164, 0.12851427778236324, 0.1285140915699366, 0.1285139065566388, 0.12851372268165548, 0.12851353988655806, 0.12851335811518783, -69.02471233893885, 12894.56677968612, 151900.5060763273]
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)
3.674435 seconds (215.14 k allocations: 762.191 MiB, 2.37% 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}}:
[0.0026, 830.0, 830.0, 0.00702, 0.966, 0.22156, 0.09243, 0.00188, 0.00977, 0.26081 … 0.12113, 0.12113, 0.12113, 0.12113, 0.12113, 0.12113, 0.12113, -68.79268, 13838.37602, 150952.75035000002]
[0.0025985659590295374, 829.9994975880693, 829.9999654017583, 0.007020208561323646, 0.9660018276402699, 0.2215639938807744, 0.09242766669618695, 0.001879826176081169, 0.009769882842069916, 0.2608055799112056 … 0.12113000000000405, 0.12113000000038378, 0.12113000001389383, 0.12113000037367234, 0.12113000811850358, 0.1211301421535992, 0.1211319185255175, -68.79732946186226, 13838.375711519551, 150952.7504077194]
[0.002593310524681686, 829.9976422525165, 829.9998348635061, 0.00702008986027517, 0.9660085993318799, 0.2215787945110049, 0.09241901973901424, 0.0018789042446514422, 0.009769459049732313, 0.26078941009382306 … 0.12113000089551408, 0.12113000693481112, 0.12113004704056851, 0.12113027926811751, 0.12113143375871602, 0.12113624253259858, 0.12115248970210647, -68.81607005265552, 13838.374513299192, 150952.75062244057]
[0.0025849478335103777, 829.9946506157202, 829.9996133960318, 0.007017234889558555, 0.9660195931792828, 0.22160283236040595, 0.09240497563401104, 0.0018766436937193197, 0.009768805322556195, 0.2607638707001999 … 0.12113010483012127, 0.12113038966346883, 0.12113131833063846, 0.12113403405679991, 0.12114109135582982, 0.12115723910142134, 0.12118951551963696, -68.84681913285226, 13838.372555328333, 150952.7509740238]
[0.00256770780104998, 829.9883445519497, 829.9990964774663, 0.0070030143052343926, 0.9660430731013478, 0.2216542075240971, 0.0923749578279845, 0.0018699196262940568, 0.00976754294689657, 0.2607122383588733 … 0.12113292110288301, 0.12113633873395535, 0.12114295934422187, 0.12115494411090462, 0.12117519662647316, 0.12120713813483534, 0.12125418995384041, -68.91207316777846, 13838.368384399068, 150952.7517373371]
[0.0025298083713907005, 829.9738229154025, 829.9976227528975, 0.006946470397388757, 0.9660987611411453, 0.22177624785138977, 0.09230364339951613, 0.001850533769446942, 0.009765228548607825, 0.26060507831375035 … 0.12115849269665879, 0.1211733598588045, 0.12119414515426227, 0.12122229800810434, 0.12125925929399752, 0.1213063255235844, 0.12136450208851983, -69.06429960994137, 13838.358559292059, 150952.75361533565]
[0.0024748079782158975, 829.9509077855928, 829.9944193668179, 0.0068337541728754475, 0.9661914345949096, 0.2219798989175973, 0.09218462776986637, 0.0018178174419014683, 0.009763403076884485, 0.26047114911179464 … 0.12122454121844703, 0.12125242557826561, 0.12128628091507473, 0.12132672249013034, 0.12137426379919634, 0.12142927821043337, 0.12149196513254239, -69.31024285744343, 13838.34240329337, 150952.75694915713]
[0.0024106893964811337, 829.9205247545176, 829.9883533251192, 0.006675512062656749, 0.9663239343003682, 0.22227216398019892, 0.09201383579531924, 0.001773815690753224, 0.009765046552800477, 0.2603648729749554 … 0.12132150441596078, 0.12135855488207913, 0.12140052118634269, 0.12144759471003595, 0.121499889830345, 0.12155743299711905, 0.12162015426876957, -69.64637448767432, 13838.319723120678, 150952.76215620188]
[0.0023106557277343394, 829.8589858006806, 829.9689941817725, 0.006355039713677859, 0.9666286957812559, 0.22294828828976576, 0.09161908329520764, 0.0016855899094922325, 0.009786689200123853, 0.26041507667541997 … 0.12150439833798571, 0.12154722283384205, 0.12159304920072048, 0.1216418099553358, 0.12169340184085986, 0.12174768443532376, 0.12180447948880598, -70.35063788657428, 13838.2694938995, 150952.77598869594]
[0.002228995040224517, 829.7704141396295, 829.923524981244, 0.005926150085676071, 0.9671554512230358, 0.22412560303273427, 0.09093422465365385, 0.0015688568862426045, 0.009873892913308327, 0.26104417804603025 … 0.12171274673876392, 0.1217515266716739, 0.12179171693004434, 0.12183318573340766, 0.12187579038290373, 0.1219193775332836, 0.121963783644082, -71.35304509818071, 13838.18882346682, 150952.80529264064]
⋮
[0.0019114696198611972, 783.2335456223052, 783.5706100263843, 0.006401536598237259, 0.9997325765508921, 0.9997345986850066, 0.001570459456642526, 0.002475332119040147, 0.0015991246689222279, 0.001163249554719103 … 0.13519968902409513, 0.13519936944519553, 0.13519905079105815, 0.13519873297812576, 0.1351984159261524, 0.13519809955804118, 0.1351977837996914, -70.16237636696027, 13463.639830820615, 151329.73678923372]
[0.0018559861797092312, 782.365278560974, 782.6921656330983, 0.0064434881853989235, 0.9997269806387865, 0.9997289833818177, 0.0015922867934419298, 0.0024930649558120507, 0.0016105830832262831, 0.001180675844218517 … 0.13454953638665704, 0.13454922671372732, 0.13454891806128647, 0.13454861034590704, 0.13454830348746807, 0.1345479974089928, 0.13454769203649625, -70.06630769034166, 13412.288684613286, 151381.23645949631]
[0.0017991858469362822, 781.4261787177652, 781.7426554921899, 0.006488433583872493, 0.9997208967515303, 0.9997228759655545, 0.0016158415907311235, 0.0025120743241089857, 0.0016228666615525078, 0.001199512890870556 … 0.13387599822890345, 0.13387569941436786, 0.13387540170677176, 0.133875105023189, 0.13387480928398002, 0.13387451441263082, 0.13387422033560087, -69.9640696394158, 13358.332495903607, 151435.35010948044]
[0.0017385786798326307, 780.3640957242352, 780.6694749774717, 0.006538841664683693, 0.9997139634414586, 0.9997159113620446, 0.0016424692973948344, 0.002533408070605609, 0.0016366519512620496, 0.0012208313551399772 … 0.133147901717886, 0.1331476153292442, 0.13314733012645366, 0.13314704602755442, 0.1331467629538344, 0.13314648082967, 0.13314619958237636, -69.85023064464396, 13299.08347056358, 151494.77361021377]
[0.0016828788058223239, 779.3292147839201, 779.6244064031861, 0.00658763998060981, 0.9997071390528249, 0.9997090568751029, 0.0016684544490965006, 0.00255407336765676, 0.0016500054458297602, 0.0012416666191171675 … 0.13246971901744392, 0.13246944493569576, 0.13246917209826714, 0.13246890042454043, 0.1324686298370924, 0.13246836026153794, 0.13246809162638237, -69.74087130994414, 13242.98230562667, 151551.041437695]
[0.0016241674459000098, 778.1728546366958, 778.4573206864395, 0.0066419084156642836, 0.999699419469964, 0.9997012974362671, 0.001697597196593821, 0.002577070821669311, 0.0016648661647931226, 0.0012650759161114639 … 0.13174489658962674, 0.1317446364193481, 0.13174437753877238, 0.1317441198692181, 0.13174386333512175, 0.13174360786388473, 0.13174335338572984, -69.62018325294, 13181.978662174546, 151612.22778821771]
[0.0015595490771158635, 776.8159951664153, 777.0886734374524, 0.006705419682527687, 0.9996902087860945, 0.9996920347051066, 0.0017320283400820537, 0.002604005867641175, 0.0016822714393574306, 0.0012927869694984513 … 0.13093447870972347, 0.1309342350968772, 0.13093399280426757, 0.13093375175598218, 0.13093351187911678, 0.1309332731036278, 0.13093303536219322, -69.48017476805755, 13112.39281500155, 151682.0237467063]
[0.0015019225050621086, 775.5252842341367, 775.7874674618907, 0.0067658294061527504, 0.9996812693521229, 0.9996830392302857, 0.001765104713025721, 0.002629646346348554, 0.0016988403880171758, 0.0013194623376813948 … 0.1301998083420986, 0.1301995806763804, 0.1301993543372558, 0.1301991292519352, 0.13019890535051312, 0.1301986825658268, 0.13019846083332295, -69.3482139604377, 13047.950238293004, 151746.66233734836]
[0.0014880014404263435, 775.201325425073, 775.4609759601377, 0.006781012883964196, 0.999678994662014, 0.9996807506215254, 0.0017734683214271913, 0.002636094008043909, 0.0017030067642045802, 0.0013262160662107492 … 0.13002053995797455, 0.1300203163215105, 0.13002009401020564, 0.1300198729521094, 0.13001965307812136, 0.13001943432185198, 0.13001921661949076, -69.3152343534447, 13032.016623562371, 151762.64460883147]
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.