Models

A so-called model defines the reaction term of the reaction diffusion equation. While Pigreads comes with a variety of pre-defined models, it is also easily possible to define a model.

Defining a model

A model can be defined by adding it to the dictionary of available models:

import pigreads as pig
from pigreads.schema.model import ModelDefinition

pig.Models.available["fitzhugh1961impulses"] = ModelDefinition(
    name="FitzHugh 1961 & Nagumo 1962",
    description="A 2D simplification of the Hodgkin-Huxley model.",
    dois=[
        "https://doi.org/10.1016/S0006-3495(61)86902-6",
        "https://doi.org/10.1109/JRPROC.1962.288235",
    ],
    variables={"u": 1.2, "v": -0.625},
    diffusivity={"u": 1.0},
    parameters={"a": 0.7, "b": 0.8, "c": 3.0, "z": 0.0},
    code="""
        *_new_u = u + dt * (v + u - u*u*u/3 + z + _diffuse_u);
        *_new_v = v + dt * (-(u - a + b*v)/c);
    """,
)

The definition must adhere to the schema in pigreads.schema.model.ModelDefinition.

Pre-defined models

Name	Key	Variables	Parameters
Aliev & Panfilov 1996	aliev1996simple	2	5
Bar & Eiswirth 1993	bar1993turbulence	2	3
Barkley 1991	barkley1991model	2	3
Beeler & Reuter 1977	beeler1977reconstruction	8	5
Bueno-Orovio et al. 2008	bueno2008minimal	4	28
Courtemanche et al. 1998	courtemanche1998ionic	21	43
Fenton & Karma 1998	fenton1998vortex	3	14
Gray & Scott 1982	gray1983autocatalytic	2	2
Hodgkin & Huxley 1952	hodgkin1952quantitative	4	10
Kabus et al. 2024	kabus2024fast	3	12
Luo & Rudy 1991	luo1991model	8	19
Luo & Rudy 1994	luo1994dynamic	12	46
Majumder et al. 2016	majumder2016mathematical	27	61
Maleckar et al. 2008	maleckar2008mathematical	30	47
Marcotte & Grigoriev 2017	marcotte2017dynamical	2	3
Mitchell & Schaeffer 2003	mitchell2003two	2	5
Nygren et al. 1998	nygren1998mathematical	29	46
Paci et al. 2013	paci2013computational	18	54
Ten Tusscher et al. 2006	tentusscher2006alternans	19	56
Tomek et al. 2019	tomek2019development	43	127
Trivial model	trivial	1	0