MODEL7910499126
type: SBMLModel
parameter: 466556
parameter: 466407
rule: 466364
volume units: metaid_0000217
rule: 466401
parameter: 466485
rule: 466326
parameter: 466462
parameter: 466600
parameter: 466526
parameter: 466546
rule: 466394
rule: 466353
rule: 466278
rule: 466356
rule: 466343
parameter: 466473
parameter: 466631
rule: 466307
parameter: 466627
parameter: 466549
parameter: 466534
rule: 466271
parameter: 466592
rule: 466368
parameter: 466615
rule: 466395
rule: 466398
units def: 968762
parameter: 466450
rule: 466320
units def: 968677
parameter: 466628
parameter: 466609
parameter: 466664
rule: 466272
rule: 466350
parameter: 466661
parameter: 466438
units def: 968896
parameter: 466458
parameter: 466423
units def: 969331
parameter: 466580
parameter: 466577
parameter: 466573
parameter: 466648
rule: 466362
parameter: 466426
parameter: 466446
parameter: 466506
parameter: 466588
rule: 466392
rule: 466286
parameter: 466565
parameter: 466416
parameter: 466561
rule: 466289
parameter: 466494
rule: 466313
parameter: 466597
parameter: 466535
parameter: 466576
units def: 969417
parameter: 466489
rule: 466298
rule: 466400
notes: This a model from the article: Alternans and spiral breakup in a human ventricular tissue model. ten Tusscher KH, Panfilov AV. Am J Physiol Heart Circ Physiol. (2006) 291(3); H1088-100 16565318 , Abstract: Ventricular fibrillation (VF) is one of the main causes of death in the Western world. According to one hypothesis, the chaotic excitation dynamics during VF are the result of dynamical instabilities in action potential duration (APD) the occurrence of which requires that the slope of the APD restitution curve exceeds 1. Other factors such as electrotonic coupling and cardiac memory also determine whether these instabilities can develop. In this paper we study the conditions for alternans and spiral breakup in human cardiac tissue. Therefore, we develop a new version of our human ventricular cell model, which is based on recent experimental measurements of human APD restitution and includes a more extensive description of intracellular calcium dynamics. We apply this model to study the conditions for electrical instability in single cells, for reentrant waves in a ring of cells, and for reentry in two-dimensional sheets of ventricular tissue. We show that an important determinant for the onset of instability is the recovery dynamics of the fast sodium current. Slower sodium current recovery leads to longer periods of spiral wave rotation and more gradual conduction velocity restitution, both of which suppress restitution-mediated instability. As a result, maximum restitution slopes considerably exceeding 1 (up to 1.5) may be necessary for electrical instability to occur. Although slopes necessary for the onset of instabilities found in our study exceed 1, they are within the range of experimentally measured slopes. Therefore, we conclude that steep APD restitution-mediated instability is a potential mechanism for VF in the human heart. This model was taken from the CellML repository and automatically converted to SBML. The original model was: tentusscher, panfilov…
units def: 968713
parameter: 466482
rule: 466338
rule: 466325
parameter: 466467
parameter: 466636
parameter: 466601
parameter: 466523
parameter: 466543
parameter: 466477
rule: 466355

466556
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constant: false
units: 968956
value: NaN
name: i_to

968956
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unit: 968968
name: picoA_per_picoF

968980
type: SBMLUnit
exponent: -1.0
scale: -12
multipler: 1.0
kind: FARAD

968968
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scale: -12
multipler: 1.0
kind: AMPERE

466407
type: Parameter
constant: true
units: 969223
value: 8314.472
name: R

969223
type: SBMLUnitsDef
unit: 969259
unit: 969247
unit: 969235
name: joule_per_mole_kelvin

969259
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scale: 0
multipler: 1.0
kind: KELVIN

969247
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multipler: 1.0
kind: MOLE

969235
type: SBMLUnit
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multipler: 1.0
kind: JOULE

466485
type: Parameter
constant: true
units: 968713
value: NaN
name: time

968713
type: SBMLUnitsDef
unit: 968725
name: millisecond

968725
type: SBMLUnit
exponent: 1.0
scale: -3
multipler: 1.0
kind: SECOND

466462
type: Parameter
constant: false
units: dimensionless
value: NaN
name: xs_inf

466600
type: Parameter
constant: true
units: 969040
value: 2.0
name: Ca_o

969040
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name: millimolar

969066
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kind: LITRE

969054
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kind: MOLE

466526
type: Parameter
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units: 968713
value: NaN
name: gamma_d

466546
type: Parameter
constant: true
units: 969040
value: NaN
name: Ca_ss

466473
type: Parameter
constant: true
units: 968762
value: NaN
name: V

968762
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name: millivolt

968774
type: SBMLUnit
exponent: 1.0
scale: -3
multipler: 1.0
kind: VOLT

466631
type: Parameter
constant: true
units: 969040
value: 2.5E-4
name: K_up

466627
type: Parameter
constant: false
units: dimensionless
value: NaN
name: kcasr

466549
type: Parameter
constant: true
units: 968713
value: NaN
name: time

466534
type: Parameter
constant: false
units: dimensionless
value: NaN
name: f_inf

466592
type: Parameter
constant: true
units: 968956
value: 0.1238
name: g_pCa

466615
type: Parameter
constant: false
units: 969126
value: NaN
name: k2

969126
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unit: 969150
unit: 969138
name: per_millimolar_per_millisecond

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969138
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466450
type: Parameter
constant: false
units: dimensionless
value: NaN
name: alpha_xr2

968677
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unit: 968689
name: litre_micrometre3

968701
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kind: METRE

968689
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multipler: 1.0
kind: LITRE

466628
type: Parameter
constant: true
units: 968737
value: 0.102
name: V_rel

968737
type: SBMLUnitsDef
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name: per_millisecond

968749
type: SBMLUnit
exponent: -1.0
scale: -3
multipler: 1.0
kind: SECOND

466609
type: Parameter
constant: false
units: 969078
value: NaN
name: i_xfer

969078
type: SBMLUnitsDef
unit: 969114
unit: 969102
unit: 969090
name: millimolar_per_millisecond

969114
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kind: SECOND

969102
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kind: LITRE

969090
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kind: MOLE

466664
type: Parameter
constant: true
units: 968956
value: -52.0
name: IstimAmplitude

466661
type: Parameter
constant: true
units: 968713
value: 10.0
name: IstimStart

466438
type: Parameter
constant: false
units: dimensionless
value: NaN
name: xr1_inf

968896
type: SBMLUnitsDef
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name: picoA

968908
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scale: -12
multipler: 1.0
kind: AMPERE

466458
type: Parameter
constant: false
units: dimensionless
value: 0.0095
name: Xs

466423
type: Parameter
constant: false
units: 968956
value: NaN
name: i_K1

969331
type: SBMLUnitsDef
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unit: 969343
name: microF_per_cm2

969356
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kind: METRE

969343
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kind: FARAD

466580
type: Parameter
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units: 968956
value: NaN
name: i_NaCa

466577
type: Parameter
constant: true
units: 969040
value: 1.0
name: K_mk

466573
type: Parameter
constant: false
units: 968713
value: NaN
name: tau_r

466648
type: Parameter
constant: true
units: 969040
value: 2.5E-4
name: K_buf_ss

466426
type: Parameter
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units: dimensionless
value: NaN
name: xK1_inf

466446
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constant: true
units: 968762
value: NaN
name: V

466506
type: Parameter
constant: false
units: 968956
value: NaN
name: i_CaL

466588
type: Parameter
constant: true
units: 969040
value: 1.38
name: Km_Ca

466565
type: Parameter
constant: false
units: 968713
value: NaN
name: tau_s

466416
type: Parameter
constant: false
units: 968762
value: NaN
name: E_Na

466561
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constant: true
units: 968762
value: NaN
name: V

466494
type: Parameter
constant: true
units: 968762
value: NaN
name: V

466597
type: Parameter
constant: true
units: 968836
value: 0.0146
name: g_pK

968836
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unit: 968848
name: nanoS_per_picoF

968860
type: SBMLUnit
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scale: -12
multipler: 1.0
kind: FARAD

968848
type: SBMLUnit
exponent: 1.0
scale: -9
multipler: 1.0
kind: SIEMENS

466535
type: Parameter
constant: false
units: 968713
value: NaN
name: tau_f

466576
type: Parameter
constant: true
units: 968956
value: 2.724
name: P_NaK

969417
type: SBMLUnitsDef
unit: 969429
name: time

969429
type: SBMLUnit
exponent: 1.0
scale: -3
multipler: 1.0
kind: SECOND

466489
type: Parameter
constant: false
units: 968737
value: NaN
name: beta_h

466482
type: Parameter
constant: false
units: dimensionless
value: 0.7444
name: h

466467
type: Parameter
constant: false
units: 968713
value: NaN
name: tau_xs

466636
type: Parameter
constant: false
units: dimensionless
value: NaN
name: Ca_i_bufc

466601
type: Parameter
constant: false
units: 969040
value: 3.64
name: Ca_SR

466523
type: Parameter
constant: false
units: dimensionless
value: NaN
name: alpha_d

466543
type: Parameter
constant: false
units: 968713
value: NaN
name: tau_f2

466477
type: Parameter
constant: false
units: dimensionless
value: NaN
name: alpha_m

466540
type: Parameter
constant: true
units: 968713
value: NaN
name: time

968872
type: SBMLUnitsDef
unit: 968884
name: microF

968884
type: SBMLUnit
exponent: 1.0
scale: -6
multipler: 1.0
kind: FARAD

466408
type: Parameter
constant: true
units: kelvin
value: 310.0
name: T

466624
type: Parameter
constant: true
units: dimensionless
value: 2.5
name: max_sr

969174
type: SBMLUnitsDef
unit: 969211
unit: 969199
unit: 969187
name: per_millimolar2_per_millisecond

969211
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scale: -3
multipler: 1.0
kind: SECOND

969199
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kind: LITRE

969187
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scale: -3
multipler: 1.0
kind: MOLE

466419
type: Parameter
constant: false
units: 968762
value: NaN
name: E_Ks

969368
type: SBMLUnitsDef
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unit: 969392
unit: 969380
name: litre_per_farad_second

969404
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scale: 0
multipler: 1.0
kind: SECOND

969392
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kind: FARAD

969380
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scale: 0
multipler: 1.0
kind: LITRE

466618
type: Parameter
constant: true
units: 969126
value: 0.045
name: k2_prime

466538
type: Parameter
constant: true
units: 968762
value: NaN
name: V

466654
type: Parameter
constant: false
units: 969040
value: 8.604
name: Na_i

466432
type: Parameter
constant: true
units: 968836
value: 0.153
name: g_Kr

466606
type: Parameter
constant: false
units: 969078
value: NaN
name: i_up

466645
type: Parameter
constant: true
units: 969040
value: 0.3
name: K_buf_sr

466639
type: Parameter
constant: false
units: dimensionless
value: NaN
name: Ca_ss_bufss

466443
type: Parameter
constant: false
units: 968713
value: NaN
name: tau_xr1

466509
type: Parameter
constant: false
units: dimensionless
value: 3.373E-5
name: d

466642
type: Parameter
constant: true
units: 969040
value: 0.001
name: K_buf_c

466420
type: Parameter
constant: false
units: 968762
value: NaN
name: E_Ca

466453
type: Parameter
constant: false
units: 968713
value: NaN
name: tau_xr2

466410
type: Parameter
constant: true
units: 969271
value: 96485.3415
name: F

969271
type: SBMLUnitsDef
unit: 969295
unit: 969283
name: coulomb_per_millimole

969295
type: SBMLUnit
exponent: -1.0
scale: -3
multipler: 1.0
kind: MOLE

969283
type: SBMLUnit
exponent: 1.0
scale: 0
multipler: 1.0
kind: COULOMB

968652
type: SBMLUnitsDef
unit: 968665
name: micrometre3

968665
type: SBMLUnit
exponent: 3.0
scale: -6
multipler: 1.0
kind: METRE

466555
type: Parameter
constant: true
units: 968836
value: 5.92E-4
name: g_bca

466649
type: Parameter
constant: true
units: 968652
value: 0.001094
name: V_sr

466431
type: Parameter
constant: false
units: 968956
value: NaN
name: i_Kr

466447
type: Parameter
constant: true
units: 968713
value: NaN
name: time

466503
type: Parameter
constant: false
units: 968956
value: NaN
name: i_b_Na

466498
type: Parameter
constant: false
units: 968737
value: NaN
name: alpha_j

466562
type: Parameter
constant: true
units: 968713
value: NaN
name: time

466610
type: Parameter
constant: false
units: dimensionless
value: NaN
name: O

466630
type: Parameter
constant: true
units: 968737
value: 0.0038
name: V_xfer

466435
type: Parameter
constant: true
units: 968762
value: NaN
name: V

466492
type: Parameter
constant: false
units: dimensionless
value: 0.7045
name: j

466486
type: Parameter
constant: false
units: dimensionless
value: NaN
name: h_inf

466589
type: Parameter
constant: true
units: 969040
value: 87.5
name: Km_Nai

466591
type: Parameter
constant: false
units: 968956
value: NaN
name: i_p_Ca

466405
type: Parameter
constant: false
units: 968762
value: -85.23
name: V

466550
type: Parameter
constant: false
units: dimensionless
value: NaN
name: fCass_inf

466621
type: Parameter
constant: true
units: 968737
value: 0.005
name: k4

466483
type: Parameter
constant: true
units: 968762
value: NaN
name: V

466480
type: Parameter
constant: false
units: 968713
value: NaN
name: tau_m

466497
type: Parameter
constant: false
units: dimensionless
value: NaN
name: j_inf

466544
type: Parameter
constant: false
units: dimensionless
value: 0.9953
name: fCass

466521
type: Parameter
constant: false
units: dimensionless
value: NaN
name: d_inf

466413
type: Parameter
constant: true
units: 968652
value: 0.016404
name: V_c

466595
type: Parameter
constant: false
units: 968956
value: NaN
name: i_p_K

466558
type: Parameter
constant: true
units: 968836
value: 0.294
name: g_to

466471
type: Parameter
constant: false
units: dimensionless
value: 0.00172
name: m

466491
type: Parameter
constant: false
units: 968713
value: NaN
name: tau_h

466625
type: Parameter
constant: true
units: dimensionless
value: 1.0
name: min_sr

466547
type: Parameter
constant: true
units: 968762
value: NaN
name: V

466512
type: Parameter
constant: true
units: 968713
value: NaN
name: time

466532
type: Parameter
constant: true
units: 968713
value: NaN
name: time

466468
type: Parameter
constant: false
units: 968956
value: NaN
name: i_Na

466528
type: Parameter
constant: false
units: 968713
value: NaN
name: tau_d

466479
type: Parameter
constant: false
units: dimensionless
value: NaN
name: beta_m

466613
type: Parameter
constant: false
units: 969174
value: NaN
name: k1

466594
type: Parameter
constant: true
units: 969040
value: 5.0E-4
name: K_pCa

466266
type: Compartment
constant: true
units: litre
size: 1.0
spatial dimensions: 3.0

466607
type: Parameter
constant: false
units: 969078
value: NaN
name: i_leak

969307
type: SBMLUnitsDef
unit: 969319
name: cm2

969319
type: SBMLUnit
exponent: 2.0
scale: -2
multipler: 1.0
kind: METRE

466658
type: Parameter
constant: true
units: 969040
value: 5.4
name: K_o

466643
type: Parameter
constant: true
units: 969040
value: 10.0
name: Buf_sr

466500
type: Parameter
constant: false
units: 968737
value: NaN
name: beta_j

466456
type: Parameter
constant: true
units: 968836
value: 0.392
name: g_Ks

466452
type: Parameter
constant: false
units: dimensionless
value: NaN
name: beta_xr2

466571
type: Parameter
constant: false
units: dimensionless
value: NaN
name: r_inf

466646
type: Parameter
constant: true
units: 969040
value: 0.4
name: Buf_ss

466666
type: Parameter
constant: true
units: 968713
value: 1000.0
name: IstimPeriod

466585
type: Parameter
constant: true
units: dimensionless
value: 2.5
name: alpha

466444
type: Parameter
constant: false
units: dimensionless
value: 0.4712
name: Xr2

466440
type: Parameter
constant: false
units: dimensionless
value: NaN
name: alpha_xr1

466504
type: Parameter
constant: true
units: 968836
value: 2.9E-4
name: g_bna

466425
type: Parameter
constant: true
units: 968836
value: 5.405
name: g_K1

466582
type: Parameter
constant: true
units: 968956
value: 1000.0
name: K_NaCa

466657
type: Parameter
constant: false
units: 969040
value: 136.89
name: K_i

466414
type: Parameter
constant: false
units: 968956
value: NaN
name: i_Stim

466559
type: Parameter
constant: false
units: dimensionless
value: 0.999998
name: s

466476
type: Parameter
constant: false
units: dimensionless
value: NaN
name: m_inf

968811
type: SBMLUnitsDef
unit: 968823
name: per_millivolt

968823
type: SBMLUnit
exponent: -1.0
scale: -3
multipler: 1.0
kind: VOLT

968628
type: SBMLUnitsDef
unit: 968640
name: micrometre

968640
type: SBMLUnit
exponent: 1.0
scale: -6
multipler: 1.0
kind: METRE

466579
type: Parameter
constant: true
units: 969040
value: 40.0
name: K_mNa

968992
type: SBMLUnitsDef
unit: 969028
unit: 969016
unit: 969004
name: nanoA_per_millimolar

969028
type: SBMLUnit
exponent: 1.0
scale: 0
multipler: 1.0
kind: LITRE

969016
type: SBMLUnit
exponent: -1.0
scale: -3
multipler: 1.0
kind: MOLE

969004
type: SBMLUnit
exponent: 1.0
scale: -9
multipler: 1.0
kind: AMPERE

466455
type: Parameter
constant: false
units: 968956
value: NaN
name: i_Ks

466428
type: Parameter
constant: false
units: dimensionless
value: NaN
name: alpha_K1

466570
type: Parameter
constant: true
units: 968713
value: NaN
name: time

466464
type: Parameter
constant: false
units: dimensionless
value: NaN
name: alpha_xs

968920
type: SBMLUnitsDef
unit: 968944
unit: 968932
name: mA_pA

968944
type: SBMLUnit
exponent: -1.0
scale: -12
multipler: 1.0
kind: AMPERE

968932
type: SBMLUnit
exponent: 0.0
scale: -3
multipler: 1.0
kind: AMPERE

466567
type: Parameter
constant: false
units: dimensionless
value: 2.42E-8
name: r

466634
type: Parameter
constant: true
units: 969078
value: 0.006375
name: Vmax_up

466459
type: Parameter
constant: true
units: 968762
value: NaN
name: V

466461
type: Parameter
constant: true
units: 968713
value: NaN
name: time

466541
type: Parameter
constant: false
units: dimensionless
value: NaN
name: f2_inf

466537
type: Parameter
constant: false
units: dimensionless
value: 0.9755
name: f2

466622
type: Parameter
constant: true
units: 969040
value: 1.5
name: EC

466603
type: Parameter
constant: false
units: 969040
value: 3.6E-4
name: Ca_ss

466525
type: Parameter
constant: false
units: dimensionless
value: NaN
name: beta_d

466510
type: Parameter
constant: true
units: 968762
value: NaN
name: V

466417
type: Parameter
constant: false
units: 968762
value: NaN
name: E_K

466633
type: Parameter
constant: true
units: 968737
value: 3.6E-4
name: V_leak

466616
type: Parameter
constant: true
units: 969174
value: 0.15
name: k1_prime

466495
type: Parameter
constant: true
units: 968713
value: NaN
name: time

466598
type: Parameter
constant: false
units: 969040
value: 1.26E-4
name: Ca_i

466652
type: Parameter
constant: true
units: dimensionless
value: NaN
name: d

968786
type: SBMLUnitsDef
unit: 968799
name: millivolt_square

968799
type: SBMLUnit
exponent: 2.0
scale: -3
multipler: 1.0
kind: VOLT

466529
type: Parameter
constant: false
units: dimensionless
value: 0.7888
name: f

466604
type: Parameter
constant: false
units: 969078
value: NaN
name: i_rel

466663
type: Parameter
constant: true
units: 968713
value: 50000.0
name: IstimEnd

466637
type: Parameter
constant: false
units: dimensionless
value: NaN
name: Ca_sr_bufsr

466507
type: Parameter
constant: true
units: 969368
value: 3.98E-5
name: g_CaL

466640
type: Parameter
constant: true
units: 969040
value: 0.2
name: Buf_c

466434
type: Parameter
constant: false
units: dimensionless
value: 0.00621
name: Xr1

466651
type: Parameter
constant: true
units: 968652
value: 5.468E-5
name: V_ss

466553
type: Parameter
constant: false
units: 968956
value: NaN
name: i_b_Ca

466667
type: Parameter
constant: true
units: 968713
value: 1.0
name: IstimPulseDuration

466586
type: Parameter
constant: true
units: dimensionless
value: 0.35
name: gamma

466441
type: Parameter
constant: false
units: dimensionless
value: NaN
name: beta_xr1

466501
type: Parameter
constant: false
units: 968713
value: NaN
name: tau_j

466422
type: Parameter
constant: true
units: dimensionless
value: 0.03
name: P_kna

466660
type: Parameter
constant: false
units: 968956
value: NaN
name: Istim

466564
type: Parameter
constant: false
units: dimensionless
value: NaN
name: s_inf

466619
type: Parameter
constant: true
units: 968737
value: 0.06
name: k3

466655
type: Parameter
constant: true
units: 969040
value: 140.0
name: Na_o

466574
type: Parameter
constant: false
units: 968956
value: NaN
name: i_NaK

466470
type: Parameter
constant: true
units: 968836
value: 14.838
name: g_Na

466429
type: Parameter
constant: false
units: dimensionless
value: NaN
name: beta_K1

466449
type: Parameter
constant: false
units: dimensionless
value: NaN
name: xr2_inf

466531
type: Parameter
constant: true
units: 968762
value: NaN
name: V

466552
type: Parameter
constant: false
units: 968713
value: NaN
name: tau_fCass

466465
type: Parameter
constant: false
units: dimensionless
value: NaN
name: beta_xs

466583
type: Parameter
constant: true
units: dimensionless
value: 0.1
name: K_sat

466568
type: Parameter
constant: true
units: 968762
value: NaN
name: V

466612
type: Parameter
constant: false
units: dimensionless
value: 0.9073
name: R_prime

466474
type: Parameter
constant: true
units: 968713
value: NaN
name: time

466437
type: Parameter
constant: true
units: 968713
value: NaN
name: time

466488
type: Parameter
constant: false
units: 968737
value: NaN
name: alpha_h

466411
type: Parameter
constant: true
units: 968872
value: 0.185
name: Cm