{
  "abstract": "Many reduced and control-oriented respiratory models prescribe a ventilatory waveform. Here we ask a narrower inverse question: once cycle duration and mechanical closure are fixed, what ventilation pattern maximizes a reduced oxygen-transfer criterion? We study a minimal 0D model coupling global lung deformation to alveolar oxygen concentration. Under explicit quantitative and nondegeneracy assumptions, every optimal control is bang-bang with exactly two switchings, producing one inflation phase followed by one deflation phase. Thus optimality selects the internal two phase inspiration-expiration organization. The concentration of oxygen is not impose at the beginning and the end of a cycle. We prove that repetition of a fixed mechanical cycle induces a unique stable periodic concentration regime, where the concentration at the beginning and the end remains the same. Numerical simulations recover the two-switch structure for the nominal parameter set and indicate its persistence in a linear viscoelastic extension.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": null,
  "author_total": 5,
  "authors": [
    {
      "name": "Mabrouk Ben Jaba"
    },
    {
      "name": "Yannick Privat"
    },
    {
      "name": "Jean-François Scheid"
    },
    {
      "name": "Zakaria Belhachmi"
    },
    {
      "name": "Benjamin Mauroy"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/0xxsv9gqxqmfp.bib",
  "cited_by": 0,
  "doi": null,
  "fulltext_url": null,
  "id": "0xxsv9gqxqmfp",
  "issns": [],
  "landing_url": "https://hal.science/hal-05768458v1",
  "language": "en",
  "licence": "CC-BY-NC-ND-4.0",
  "licence_label": "CC BY-NC-ND 4.0",
  "licence_source": "article",
  "licence_url": "https://creativecommons.org/licenses/by-nc-nd/4.0/",
  "metadata_licence": null,
  "native_subjects": [
    [
      "hal",
      "0.info"
    ],
    [
      "hal",
      "0.math"
    ],
    [
      "hal",
      "1.info.info-mo"
    ],
    [
      "hal",
      "1.math.math-oc"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://hal.science/hal-05768458/document",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-29",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/0xxsv9gqxqmfp.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:17:42Z",
      "native_id": "hal-05768458",
      "source": "hal",
      "url": "https://hal.science/hal-05768458v1"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "hal:1.math.math-oc",
      "subfield": "optimisation-control"
    }
  ],
  "title": "Optimal bang-bang ventilation under mechanical cycle closure: a reduced lung gas-exchange model",
  "title_text": "Optimal bang-bang ventilation under mechanical cycle closure: a reduced lung gas-exchange model",
  "type": "preprint",
  "updated_at": "2026-10-30T12:17:42Z",
  "url": "https://research.draconitic.com/paper/0xxsv9gqxqmfp",
  "venue": "HAL",
  "versions": []
}