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Applications of Automatic Mesh Generation and Adaptive Methods in Computational Medicine

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Modeling, Mesh Generation, and Adaptive Numerical Methods for Partial Differential Equations

Part of the book series: The IMA Volumes in Mathematics and its Applications ((IMA,volume 75))

Abstract

Important problems in Computational Medicine exist that can benefit from the implementation of adaptive mesh refinement techniques. Biological systems are so inherently complex that only efficient models running on state of the art hardware can begin to simulate reality. To tackle the complex geometries associated with medical applications we present a general purpose mesh generation scheme based upon the Delaunay tessellation algorithm and an iterative point generator. In addition, automatic, two- and three-dimensional adaptive mesh refinement methods are presented that are derived from local and global estimates of the finite element error. Mesh generation and adaptive refinement techniques are utilized to obtain accurate approximations of bioelectric fields within anatomically correct models of the heart and human thorax. Specifically, we explore the simulation of cardiac defibrillation and the general forward and inverse problems in electrocardiography (ECG). Comparisons between uniform and adaptive refinement techniques are made to highlight the computational efficiency and accuracy of adaptive methods in the solution of field problems in computational medicine.

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Author information

Authors and Affiliations

  1. Department of Computer Science, University of Utah, Salt Lake City, UT, 84112, USA

    J. A. Schmidt

  2. Department of Biomedical Engineering, Duke University, Durham, NC, 27708, USA

    C. R. Johnson & J. C. Eason

  3. Cardiovascular Research and Training Institute, University of Utah, Salt Lake City, UT, 84112, USA

    R. S. Macleod

Authors
  1. J. A. Schmidt
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  2. C. R. Johnson
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  3. J. C. Eason
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  4. R. S. Macleod
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Editor information

Editors and Affiliations

  1. Institute for Physical Science and Technology, University of Maryland, 20742, College park, MD, USA

    Ivo Babuska

  2. CIC-3 MS K987 Los Alamos National Laboratory, 87545, Los Alamos, NM, USA

    William D. Henshaw

  3. Research Institute for Advanced Computer Science, NASA Ames Research Center, Mail Stop T20G-5, 94035, Moffet Field, CA, USA

    Joseph E. Oliger

  4. Department of Science and Scientific Computation Research Ctr, Rensselaer Polytechnic Institute, 110-8th St, 12180, Troy, NY, USA

    Joseph E. Flaherty

  5. College of Engineering, Joseph Silbert Dean of Engineering Cornell University Cornell University, 242 Carpenter Hall, 14853, Ithaca, NY, USA

    John E. Hopcroft

  6. Army High Performance Computing Research Center, 1100 South Washington Ave. Suite 101, 55415, Minneapolis, MN, USA

    Tayfun Tezduyar

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© 1995 Springer-Verlag New York

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Schmidt, J.A., Johnson, C.R., Eason, J.C., Macleod, R.S. (1995). Applications of Automatic Mesh Generation and Adaptive Methods in Computational Medicine. In: Babuska, I., Henshaw, W.D., Oliger, J.E., Flaherty, J.E., Hopcroft, J.E., Tezduyar, T. (eds) Modeling, Mesh Generation, and Adaptive Numerical Methods for Partial Differential Equations. The IMA Volumes in Mathematics and its Applications, vol 75. Springer, New York, NY. https://doi.org/10.1007/978-1-4612-4248-2_18

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  • DOI: https://doi.org/10.1007/978-1-4612-4248-2_18

  • Publisher Name: Springer, New York, NY

  • Print ISBN: 978-1-4612-8707-0

  • Online ISBN: 978-1-4612-4248-2

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