Biomedical Applications

Mathematical optimization for the inverse problem of intensity modulated radiation therapy

  • Yair Censor
    • Categories Biomedical Applications, Global Optimization Applications Tags , , , , ,

    In this tutorial we discuss modeling issues in intensity modulated radiation therapy, contrasting the continuous model with the fully-discretized one and considering feasibility formulations versus optimization setups. We review briefly some mathematical optimization techniques for IMRT. These include global optimization, multi-objective optimization, linear and mixed integer programming and projection methods. Citationin: J.R. Palta and T.R. … Read more

    The global optimization of Morse clusters by potential energy transformations

  • Jon P. K. Doye
  • Marco Locatelli
  • Robert H. Leary
  • Fabio Schoen
    • Categories Basic Sciences Applications, Biomedical Applications, Stochastic Approaches

    The Morse potential is a simple model pair potential that has a single parameter $\rho$ which determines the width of the potential well and allows a wide variety of materials to be modelled. Morse clusters provide a particularly tough test system for global optimization algorithms, and one that is highly relevant to methods that are … Read more

    A randomized global optimization method for protein-protein docking

  • Bernardetta Addis
  • Fabio Schoen
    • Categories Biomedical Applications, Global Optimization Applications, Stochastic Approaches Tags , ,

    In this paper we report results on the problem of docking two large proteins by means of a two-phase monotonic basin hopping method. Given an appropriate force field which is used to measure the interaction energy between two biomolecules which are considered as rigid bodies, we used a randomized global optimization methods based upon the … Read more

    The least-intensity feasible solution for aperture-based inverse planning in radiation therapy.

  • Yair Censor
  • James M. Galvin
  • Darek Michalski
  • Ying Xiao
    • Categories Biomedical Applications, Convex Optimization, Nonlinear Systems and Least-Squares Tags , , , , ,

    Aperture-based inverse planning (ABIP) for intensity modulated radiation therapy (IMRT) treatment planning starts with external radiation fields (beams) that fully conform to the target(s) and then superimposes sub-fields called segments to achieve complex shaping of 3D dose distributions. The segments’ intensities are determined by solving a feasibility problem. The least-intensity feasible (LIF) solution, proposed and … Read more