finitewave-model-courtemanche 0.2.0

Courtemanche model.

Courtemanche finitewave model

This model describes the ionic currents and action potential dynamics of human atrial myocytes. It includes detailed formulations for major ionic currents (fast sodium current, L-type calcium current, inward rectifier potassium current, transient outward potassium current, rapid and slow delayed rectifier potassium currents, and Na⁺/Ca²⁺ exchanger), as well as calcium handling mechanisms.

The Courtemanche model is widely used as a reference atrial electrophysiology model. It has served as the basis for many subsequent atrial modeling studies, including investigations of atrial fibrillation and drug effects.

Reference

Courtemanche M, Ramirez RJ, Nattel S. Ionic mechanisms underlying human atrial action potential properties: insights from a mathematical model. Am J Physiol. 1998 Jul;275(1):H301-21.

DOI: 10.1152/ajpheart.1998.275.1.H301

How to use (quickstart)

python -m examples.courtemanche_example

How to test

python -m pytest -q

Repository structure

.
├── courtemanche/                    # equations package (ops.py)
│   ├── __init__.py
│   └── ops.py                       # model equations (pure functions)
├── implementation/                  # 0D model implementation
│   ├── __init__.py
│   └── courtemanche_0d.py
├── example/
│   └── courtemanche_example.py      # minimal script to run a short trace
├── tests/
│   └── test.py                      # smoke test; reproducibility checks
├── .gitignore
├── LICENSE                          # MIT
├── pyproject.toml                   # configuration file
└── README.md                        # this file

Variables

• u = -84.5 - Membrane potential (mV)
• nai = 11.2 - intracellular Na⁺ concentration (mM)
• ki = 139 - intracellular K⁺ concentration (mM)
• cai = 0.000102 - intracellular Ca²⁺ concentration (mM)
• caup = 1.6 - Ca²⁺ concentration in uptake compartment (mM)
• carel = 1.1 - Ca²⁺ concentration in release compartment (mM)
• m = 0.00291 - activation gate of fast Na⁺ current
• h = 0.965 - fast inactivation gate of I_Na
• j = 0.978 - slow inactivation gate of I_Na
• d = 0.000137 - activation gate of L-type Ca²⁺ current
• f = 0.999837 - inactivation gate of I_CaL
• oa = 0.000592 - activation gate of transient outward K⁺ current
• oi = 0.9992 - inactivation gate of I_to
• ua = 0.003519 - activation gate of ultra-rapid K⁺ current
• ui = 0.9987 - inactivation gate of I_Kur
• xs = 0.0187 - activation gate of slow delayed rectifier K⁺ current
• xr = 0.0000329 - activation gate of rapid delayed rectifier K⁺ current
• fca = 0.775 - Ca²⁺-dependent inactivation gate of I_CaL
• irel = 0 - Ca²⁺ release current from SR
• vrel = 1 - SR release flux variable (voltage-dependent)
• urel = 0 - SR release gate variable
• wrel = 0.9 - SR recovery variable

Parameters

• gna = 7.8 - maximum conductance of fast sodium current (mS/cm²)
• gnab = 0.000674 - maximum conductance of background sodium current (mS/cm²)
• gk1 = 0.09 - maximum conductance of inward rectifier potassium current (mS/cm²)
• gkr = 0.0294 - maximum conductance of rapid delayed rectifier potassium current (mS/cm²)
• gks = 0.129 - maximum conductance of slow delayed rectifier potassium current (mS/cm²)
• gto = 0.1652 - maximum conductance of transient outward potassium current (mS/cm²)
• gcal = 0.1238 - maximum conductance of L-type calcium current (mS/cm²)
• gcab = 0.00113 - maximum conductance of background calcium current (mS/cm²)
• Vc = 20100 - cell volume (µL)
• Vj = Vc * 0.68 - junction volume (µL)
• Vup = Vj * 0.06 * 0.92 - uptake compartment volume (µL)
• Vrel = Vj * 0.06 * 0.08 - release compartment volume (µL)
• ibk = 0.0 - background current (µA/cm²)
• cao = 1.8 - extracellular Ca²⁺ concentration (mM)
• nao = 140 - extracellular Na⁺ concentration (mM)
• ko = 5.4 - extracellular K⁺ concentration (mM)
• caupmax = 15 - maximum Ca²⁺ uptake rate (mM/ms)
• kup = 0.00092 - uptake rate constant (mM)
• kmnai = 10 - Michaelis-Menten constant for Na⁺ (mM)
• kmko = 1.5 - Michaelis-Menten constant for K⁺ (mM)
• kmnancx = 87.5 - Michaelis-Menten constant for Na⁺/Ca²⁺ exchanger (mM)
• kmcancx = 1.38 - Michaelis-Menten constant for Ca²⁺/Na⁺ exchanger (mM)
• ksatncx = 0.1 - saturation constant for Na⁺/Ca²⁺ exchanger
• kmcmdn = 0.00238 - Michaelis-Menten constant for calmodulin (mM)
• kmtrpn = 0.0005 - Michaelis-Menten constant for troponin (mM)
• kmcsqn = 0.8 - Michaelis-Menten constant for calsequestrin (mM)
• trpnmax = 0.07 - maximum troponin concentration (mM)
• cmdnmax = 0.05 - maximum calmodulin concentration (mM)
• csqnmax = 10.0 - maximum calsequestrin concentration (mM)
• inacamax = 1600 - maximum Na⁺ current (µA/cm²)
• inakmax = 0.6 - maximum Na⁺/K⁺ pump current (µA/cm²)
• ipcamax = 0.275 - maximum Ca²⁺ pump current (µA/cm²)
• krel = 30 - release rate constant
• iupmax = 0.005 - maximum uptake current (µA/cm²)
• kq10 = 3 - temperature sensitivity coefficient