Cardiac action potential based on Luo-Rudy phase 1 model (Luo and Rudy 1991), (Wu 2004)

 Download zip file 
Help downloading and running models
Accession:64171
A mathematical model of the membrane action potential of the mammalian ventricular cell is introduced. The model is based, whenever possible, on recent single-cell and single-channel data and incorporates the possibility of changing extracellular potassium concentration [K]o. The fast sodium current, INa, is characterized by fast upstroke velocity (Vmax = 400 V/sec) and slow recovery from inactivation. The time-independent potassium current, IK1, includes a negative-slope phase and displays significant crossover phenomenon as [K]o is varied. The time-dependent potassium current, IK, shows only a minimal degree of crossover. A novel potassium current that activates at plateau potentials is included in the model. The simulated action potential duplicates the experimentally observed effects of changes in [K]o on action potential duration and rest potential. See papers for more and details.
References:
1 . Luo CH, Rudy Y (1991) A model of the ventricular cardiac action potential. Depolarization, repolarization, and their interaction. Circ Res 68:1501-26 [PubMed]
2 . Wu SN (2004) Simulations of the cardiac action potential based on the Hodgkin-Huxley kinetics with the use of Microsoft Excel spreadsheets. Chin J Physiol 47:15-22 [PubMed]
Model Information (Click on a link to find other models with that property)
Model Type: Channel/Receptor;
Brain Region(s)/Organism:
Cell Type(s): Heart cell; Cardiac ventricular cell;
Channel(s):
Gap Junctions:
Receptor(s):
Gene(s):
Transmitter(s):
Simulation Environment: XPP;
Model Concept(s): Ion Channel Kinetics; Action Potentials; Pathophysiology; Heart disease;
Implementer(s): Wu, Sheng-Nan [snwu at mail.ncku.edu.tw]; Sung, Ruey J ;
/
LR_test
readme.html
LR_test.JPG
LR1_test.ode
                            
# Luo-Rudy phase 1 kinetics for cardiac action potential
# Ref: Luo CH, Rudy T. Circ Res 1991;68:1501-1526
# Ref: Wu SN, Chinese J Physiol 2004;47:15-22

#Constant:
number R=8314.0, Fara=96484.6, Temp=310.0, C=1.0

# Initial values
initial V=-81.0, m=0.0, h=0.98, j=0.99, d=0.0, f=1.0, X=0.0, Cai=0.0002

# Value sof the model parameters
param  Nao=140.0, Nai=18.0, Ko=5.4, Ki=145.0, Cao=1.8
param  g_Na=23.0, g_Kmax=0.282, g_Kp=0.0183, g_bl=0.03921, g_b=0.03921
param E_Na=54.4, E_b=-59.87, E_b1=-59.87, PR_NaK=0.01833
param period=500, iStim_mag=8.0, iStim_beg=20.0,  iStim_dur=5.0

# Stimulus
i_Stim=  iStim_mag*(heav(mod(t,period)-iStim_beg)*heav((iStim_beg+iStim_dur)-mod(t,period)))

# Expressions
E_K1= (ln((Ko / Ki)) * R * Temp / Fara)
E_Kp= E_K1
E_K= (ln(((Ko + (PR_NaK * Nao)) / (Ki + (PR_NaK * Nai)))) * R * Temp / Fara)
E_si= (7.7 - (13.0287 * ln(Cai)))
alpha_m= (0.32 * (47.13 + V) / (1.0 - exp( - (0.1 * (47.13 + V)))))
alpha_j= heav(-V-40)*(( - (127140.0 * exp((0.2444 * V))) - (3.474E-5 * exp( - (0.04391 * V)))) * (37.78 + V) / (1.0 + exp((0.311 * (79.23 + V)))))
alpha_h=heav(-V-40)*(0.135 * exp( - (0.14705882352941177 * (80.0 + V))))
alpha_K1= (1.02 / (1.0 + exp((0.2385 * (-59.215 + V - E_K1)))))
alpha_f= (0.012 * exp( - (0.0080 * (28.0 + V))) / (1.0 + exp((0.15 * (28.0 + V)))))
alpha_d= (0.095 * exp( - (0.01 * (-5.0 + V))) / (1.0 + exp( - (0.072 * (-5.0 + V)))))
alpha_X= (5.0E-4 * exp((0.083 * (50.0 + V))) / (1.0 + exp((0.057 * (50.0 + V)))))
Xi=heav(V+100)*((2.837 * (-1.0 + exp((0.04 * (77.0 + V)))) / ((77.0 + V) * exp((0.04 * (35.0 + V))))))
beta_m= (0.08 * exp( - (0.09090909090909091 * V)))
beta_j= heav(-V-40)*((0.1212  * exp( - (0.01052 * V)) / (1.0 + exp( - (0.1378 * (40.14 + V)))))) + heav(V+40)*((0.3 * exp( - (2.535E-7 * V)) / (1.0 + exp( - (0.1 * (32.0 + V))))))
beta_h= heav(-V-40)*((((3.56 * exp((0.079 * V))) + (310000.0 * exp((0.35 * V)))))) + heav(V+40)*((1 / (0.13 * (1.0 + exp( - (0.0900900900900901 * (10.66 + V)))))))
beta_f= (0.0065 * exp( - (0.02 * (30.0 + V))) / (1.0 + exp( - (0.2 * (30.0 + V)))))
Kp= (1.0 / (1.0 + exp((0.16722408026755853 * (7.488 - V)))))
beta_d= (0.07 * exp( - (0.017 * (44.0 + V))) / (1.0 + exp((0.05 * (44.0 + V)))))
beta_K1= (((0.49124 * exp((0.08032 * (5.476 - E_K1 + V)))) + exp((0.06175 * (V - (594.31 + E_K1))))) / (1.0 + exp( - (0.5143 * (4.753 + V - E_K1)))))
K1_inf= (alpha_K1 / (alpha_K1 + beta_K1))
beta_X= (0.0013 * exp( - (0.06 * (20.0 + V))) / (1.0 + exp( - (0.04 * (20.0 + V)))))
g_K= (g_Kmax *(0.18518518518518517 * Ko)^0.5)
g_K1= (0.6047 * (0.18518518518518517 * Ko)^0.5)

i_Na= (g_Na * m^3 * h * j * (V - E_Na))
i_si= (0.09 * d * f * (V - E_si))
i_K= (g_K * X * Xi * (V - E_K))
i_K1= (g_K1 * K1_inf * (V - E_K1))
i_Kp= (g_Kp * Kp * (V - E_Kp))
i_b= (g_b * (V - E_b))

# Differential equations
V'= - ((-i_Stim + i_Na + i_si + i_K + i_K1 + i_Kp + i_b) / C)
m'= ((alpha_m * (1.0 - m)) - (beta_m * m))
h'= ((alpha_h * (1.0 - h)) - (beta_h * h))
j'= ((alpha_j * (1.0 - j)) - (beta_j * j))
d'= ((alpha_d * (1.0 - d)) - (beta_d * d))
f'= ((alpha_f * (1.0 - f)) - (beta_f * f))
X'= ((alpha_X * (1.0 - X)) - (beta_X * X))
Cai'= ( - (1.0E-4 * i_si) + (0.07 * (1.0E-4 - Cai)))

aux iapp=i_Stim
aux ina=I_Na
aux isi=i_si
aux ik=i_K
aux ik1=i_K1
aux ikp=i_Kp
aux iktot=i_K+i_K1+i_Kp

# Numerical and plotting parameters for xpp
@ maxstor=1000000, total=1000, bounds=100000, total=2000, xp=t, yp=V, xlo=0, xhi=2000, ylo=-100, yhi=60
@ meth=Euler, dt=0.01     

done

Loading data, please wait...