finitewave-model-courtemanche 0.6.0

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 ina
• j = 0.978 - slow inactivation gate of ina
• d = 0.000137 - activation gating variable for ical
• f = 0.999837 - voltage-dependent inactivation gating variable for ical
• oa = 0.000592 - activation gate for ito
• oi = 0.9992 - inactivation gate of ito
• ua = 0.003519 - activation gating variable for ikur
• ui = 0.9987 - inactivation gate of ikur
• xs = 0.0187 - activation gating variable for iks
• xr = 0.0000329 - activation gating variable for ikur
• fca = 0.775 - Ca²⁺-dependent inactivation gate of ical
• irel = 0 - Ca²⁺ release current from SR
• vrel = 1 - Ca²⁺ flux-dependent inactivation gating variable for irel
• urel = 0 - activation gating variable for irel
• wrel = 0.9 - voltage-dependent inactivation gating variable for irel

Parameters

• gna = 7.8 - maximum conductance of fast sodium current (nS/pF)
• gnab = 0.000674 - maximum conductance of background sodium current (nS/pF)
• gk1 = 0.09 - maximum conductance of inward rectifier potassium current (nS/pF)
• gkr = 0.0294 - maximum conductance of rapid delayed rectifier potassium current (nS/pF)
• gks = 0.129 - maximum conductance of slow delayed rectifier potassium current (nS/pF)
• gto = 0.1652 - maximum conductance of transient outward potassium current (nS/pF)
• gcal = 0.1238 - maximum conductance of L-type calcium current (nS/pF)
• gcab = 0.00113 - maximum conductance of background calcium current (nS/pF)
• Vc = 20100 - cell volume (μm3)
• Vj = Vc * 0.68 - intracellular volume (μm3)
• Vup = Vj * 0.06 * 0.92 - uptake compartment volume (μm3)
• Vrel = Vj * 0.06 * 0.08 - release compartment volume (μm3)
• ibk = 0.0 - background current (pA/pF)
• 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 (pA/pF)
• inakmax = 0.6 - maximum Na⁺/K⁺ pump current (pA/pF)
• ipcamax = 0.275 - maximum Ca²⁺ pump current (pA/pF)
• krel = 30 - maximum release rate for irel
• iupmax = 0.005 - maximum uptake current (mM/ms)
• kq10 = 3 - temperature scaling factor for ikur and ito kinetics
• R = 8.3143 - gas constant (K−1 ⋅ mol−1)
• T = 310.0 - temperature (K)
• F = 96.4867 - Faraday constant (C/mmol)