{
  "abstract": "Patient-specific aortic-valve models can help assess how tissue properties and geometry influence leaflet deformation and coaptation, with potential to inform intervention planning. Large deformations, near-incompressibility, and evolving contact make these simulations computationally demanding and can challenge nonlinear convergence. Differentiable, GPU-accelerated methods offer efficient derivative evaluation and parallel computation, but their matrix-free application to soft-tissue shells with contact remains less established. We developed a forward solver using tatva's energy-based finite-element framework in JAX. The solver combines finite-strain extensible-director shells, hyperelastic constitutive models, and a finite-range repulsive contact energy. Nonlinear equilibrium is solved using a regularized, matrix-free Newton-Krylov method with two-level preconditioning. Automatic differentiation evaluates tangent-vector products without forming or storing the primary tangent matrix, while GPU execution parallelizes element and quadrature-point computations. Constitutive, shell, contact, and self-contact responses were assessed against analytical, semi-analytical, and published benchmarks. At a contact-free plate equilibrium, implicit sensitivities of the converged apex displacement to constitutive parameters, thickness, and pressure agreed with finite differences from independent nonlinear simulations. Simulations of three patient-specific aortic-valve models (two tricuspid and one bicuspid) achieved final relative equilibrium residuals below 10^-4. Median GPU runtimes were approximately 15-25 minutes, with 5.3-6.5-fold speedups relative to corresponding CPU runs on the tested hardware. These results provide component-level verification and demonstrate GPU-accelerated forward valve simulation in the tested cases, supporting future gradient-based inverse studies.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": "research article",
  "arxiv": "2610.38075",
  "author_total": 4,
  "authors": [
    {
      "name": "Mohsen Nakhaei"
    },
    {
      "name": "Alison M. Pouch"
    },
    {
      "name": "Matthew A. Jolley"
    },
    {
      "name": "Wensi Wu"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/039vf1dp0pv58.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.38075",
  "fulltext_url": "https://pmc.ncbi.nlm.nih.gov/articles/PMC13734150/",
  "id": "039vf1dp0pv58",
  "issns": [
    "2331-8422"
  ],
  "landing_url": "https://arxiv.org/abs/2610.38075",
  "language": "en",
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "physics.comp-ph"
    ],
    [
      "arxiv",
      "q-bio.QM"
    ],
    [
      "heading",
      "Article"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2610.38075",
  "pmcid": "PMC13734150",
  "pmid": "42990433",
  "published": "2026-10-27",
  "publisher": "arXiv",
  "ris": "https://research.draconitic.com/paper/039vf1dp0pv58.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:36:23Z",
      "native_id": "2610.38075",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.38075"
    },
    {
      "first_seen": "2026-11-08T12:23:47Z",
      "native_id": "PMC13734150",
      "source": "pmc",
      "url": null
    }
  ],
  "subjects": [
    {
      "field": "biology",
      "origin": "arxiv:q-bio.QM",
      "subfield": "bioinformatics"
    },
    {
      "field": "physics",
      "origin": "arxiv:physics.comp-ph",
      "subfield": "computational"
    }
  ],
  "title": "A Differentiable, GPU-Accelerated Finite-Element Formulation in JAX for Large-Deformation Shells with Contact: Application to Patient-Specific Aortic Valve Simulation",
  "title_text": "A Differentiable, GPU-Accelerated Finite-Element Formulation in JAX for Large-Deformation Shells with Contact: Application to Patient-Specific Aortic Valve Simulation",
  "type": "preprint",
  "updated_at": "2026-11-08T12:23:47Z",
  "url": "https://research.draconitic.com/paper/039vf1dp0pv58",
  "venue": "arXiv",
  "versions": []
}