A meshless method for computer integrated surgery

Ashley Horton

    Research output: ThesisDoctoral Thesis

    482 Downloads (Pure)

    Abstract

    This thesis follows the development of a clinically useful, meshless algorithm for
    simulation of soft tissue. The algorithm is designed to operate in irregular 3D
    geometry and allow for automatic discretising. It employs fully nonlinear geometric
    and material formulations and handles almost incompressible media. It includes
    multiple parts and contacts while being fast and sufficiently accurate on consumer
    hardware.
    Before developing the algorithm, existing commercial software (LS-DYNA) is
    used to perform some simulations of craniotomy-induced brain shift. The results
    suggest that the Element Free Galerkin method will be a useful foundation for
    future simulations.
    New software is written to implement a non-conforming background grid instead
    of a structured element mesh for quadrature. Errors introduced by the use of a
    non-conforming background grid, are an order of magnitude smaller than normal
    surgical precision. Simulations are performed with arbitrarily placed nodes to allow
    for irregular geometries, but this often introduces errors and instability. So efficient
    relationships are developed between node density, shape function support size,
    explicit time step size, and the non-conforming quadrature grid.
    Simple geometric problem domains are used to verify the method against an
    established Finite Element solver. Errors are deemed negligible in the context of
    clinical applications. The increased flexibility in discretisation and the capacity to
    handle extreme deformations, are considered more valuable than the small loss of
    accuracy.
    Indentation of porcine brains is simulated and compared to experimental data.
    The results are accurate enough to pursue the method in a more complete surgical
    simulation. So a complete simulation of craniotomy-induced brain shift involving
    irregular geometry, nonlinear formulations, arbitrary discretisation, multiple parts,
    multiple materials, and a contact algorithm is performed. The results demonstrate
    that realtime simulations are possible on existing consumer hardware.
    In order to improve efficiency, we consider combining the meshless method with
    a suitable Finite Element method. Preliminary tests are performed on cylinders
    and ellipsoids to confirm that the combination functions correctly. In a simulation
    of tumour growth the combined method is found to be more efficient than a pure
    meshless method and more stable than a pure Finite Element method. The union
    of these two methods yields a fast, stable, and efficient simulation.
    It is concluded that the meshless method has potential for clinical use in surgical
    simulation.
    Original languageEnglish
    QualificationDoctor of Philosophy
    Publication statusUnpublished - 2015

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