{
  "annotation_id": "10ff5c13-4e32-4932-b040-f16ea9f691a1",
  "date_created": "2026-03-02T18:01:03.544000Z",
  "date_modified": "2026-03-02T18:01:03.544000Z",
  "file_hash": "d9cb2ecab1578a083a43d4ca2f8563c83bf6589b52808ab0915dde7621d14b37",
  "private": false,
  "record": {
    "abstract": "Detailed ionic models of cardiac cells are difficult for numerical\nsimulations because they consist of a large number of equations and contain\nsmall parameters. The presence of small parameters, however, may be used for\nasymptotic reduction of the models. Earlier results have shown that the\nasymptotics of cardiac equations are non-standard. Here we apply such a novel\nasymptotic method to an ionic model of human atrial tissue in order to obtain a\nreduced but accurate model for the description of excitation fronts. Numerical\nsimulations of spiral waves in atrial tissue show that wave fronts of\npropagating action potentials break-up and self-terminate. Our model, in\nparticular, yields a simple analytical criterion of propagation block, which is\nsimilar in purpose but completely different in nature to the `Maxwell rule\u0027 in\nthe FitzHugh-Nagumo type models. Our new criterion agrees with direct numerical\nsimulations of break-up of re-entrant waves.",
    "arxiv_id": "physics/0511058",
    "authors": [
      "Radostin D. Simitev",
      "Vadim N. Biktashev"
    ],
    "categories": [
      "physics.bio-ph"
    ],
    "doi": "10.1529/biophysj.105.072637",
    "title": "Conditions for propagation and block of excitation in an asymptotic   model of atrial tissue",
    "url": "https://arxiv.org/abs/physics/0511058"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "5dcd7062-9836-47e1-a158-c77358af3676",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}