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

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

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

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

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

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

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

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

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

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

968737
unit: 968749
name: per_millisecond
type: SBMLUnitsDef

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

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

969380
exponent: 1.0
scale: 0
multipler: 1.0
kind: LITRE
type: SBMLUnit

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

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

968872
unit: 968884
name: microF
type: SBMLUnitsDef

969356
exponent: -2.0
scale: -2
multipler: 1.0
kind: METRE
type: SBMLUnit

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

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

968786
unit: 968799
name: millivolt_square
type: SBMLUnitsDef

969138
exponent: -1.0
scale: -3
multipler: 1.0
kind: MOLE
type: SBMLUnit

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

969090
exponent: 1.0
scale: -3
multipler: 1.0
kind: MOLE
type: SBMLUnit

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

968689
exponent: 1.0
scale: 0
multipler: 1.0
kind: LITRE
type: SBMLUnit

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

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

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

969392
exponent: -1.0
scale: 0
multipler: 1.0
kind: FARAD
type: SBMLUnit

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

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

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

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

969368
unit: 969404
unit: 969392
unit: 969380
name: litre_per_farad_second
type: SBMLUnitsDef

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

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

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

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

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

969162
exponent: -1.0
scale: -3
multipler: 1.0
kind: SECOND
type: SBMLUnit

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

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

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

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

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

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

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

968896
unit: 968908
name: picoA
type: SBMLUnitsDef

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

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

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

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

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

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

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

968713
unit: 968725
name: millisecond
type: SBMLUnitsDef

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

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

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

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

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

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

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

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

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

969187
exponent: -2.0
scale: -3
multipler: 1.0
kind: MOLE
type: SBMLUnit

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

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

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

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

968677
unit: 968701
unit: 968689
name: litre_micrometre3
type: SBMLUnitsDef

969331
unit: 969356
unit: 969343
name: microF_per_cm2
type: SBMLUnitsDef

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

969247
exponent: -1.0
scale: 0
multipler: 1.0
kind: MOLE
type: SBMLUnit

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

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

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

968762
unit: 968774
name: millivolt
type: SBMLUnitsDef

969114
exponent: -1.0
scale: -3
multipler: 1.0
kind: SECOND
type: SBMLUnit

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

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

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

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

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

968836
unit: 968860
unit: 968848
name: nanoS_per_picoF
type: SBMLUnitsDef

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

968811
unit: 968823
name: per_millivolt
type: SBMLUnitsDef

969199
exponent: 2.0
scale: 0
multipler: 1.0
kind: LITRE
type: SBMLUnit

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

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

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

969343
exponent: 1.0
scale: -6
multipler: 1.0
kind: FARAD
type: SBMLUnit

969259
exponent: -1.0
scale: 0
multipler: 1.0
kind: KELVIN
type: SBMLUnit

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

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

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

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

969126
unit: 969162
unit: 969150
unit: 969138
name: per_millimolar_per_millisecond
type: SBMLUnitsDef

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

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

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

968956
unit: 968980
unit: 968968
name: picoA_per_picoF
type: SBMLUnitsDef

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

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

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

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

969040
unit: 969066
unit: 969054
name: millimolar
type: SBMLUnitsDef

968652
unit: 968665
name: micrometre3
type: SBMLUnitsDef

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

969417
unit: 969429
name: time
type: SBMLUnitsDef

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

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

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

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

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

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

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

968968
exponent: 1.0
scale: -12
multipler: 1.0
kind: AMPERE
type: SBMLUnit

969404
exponent: -1.0
scale: 0
multipler: 1.0
kind: SECOND
type: SBMLUnit

969102
exponent: -1.0
scale: 0
multipler: 1.0
kind: LITRE
type: SBMLUnit

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

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

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

969235
exponent: 1.0
scale: 0
multipler: 1.0
kind: JOULE
type: SBMLUnit

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

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

968701
exponent: -3.0
scale: -6
multipler: 1.0
kind: METRE
type: SBMLUnit

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

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

968628
unit: 968640
name: micrometre
type: SBMLUnitsDef

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

969054
exponent: 1.0
scale: -3
multipler: 1.0
kind: MOLE
type: SBMLUnit

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

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

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

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

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

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

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

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

969307
unit: 969319
name: cm2
type: SBMLUnitsDef

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

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

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

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

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

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

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

969211
exponent: -1.0
scale: -3
multipler: 1.0
kind: SECOND
type: SBMLUnit

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

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

968908
exponent: 1.0
scale: -12
multipler: 1.0
kind: AMPERE
type: SBMLUnit

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

969066
exponent: -1.0
scale: 0
multipler: 1.0
kind: LITRE
type: SBMLUnit

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

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

969150
exponent: 1.0
scale: 0
multipler: 1.0
kind: LITRE
type: SBMLUnit

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

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

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

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

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

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

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

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

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

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

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

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

MODEL7910499126
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
type: SBMLModel
parameter: 466597
parameter: 466535
parameter: 466576
units def: 969417
parameter: 466489
rule: 466298
area units: area
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

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

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