Biomedical Applications

Continuous optimization of beamlet intensities for photon and proton radiotherapy

  • M. Alber
  • R. Reemtsen
    • Categories Biomedical Applications Tags , , , , , , , ,

    Inverse approaches and, in particular, intensity modulated radiotherapy (IMRT), in combination with the development of new technologies such as multi-leaf collimators (MLCs), have enabled new potentialities of radiotherapy for cancer treatment. The main mathematical tool needed in this connection is numerical optimization. In this article, the variety of continuous optimization approaches, which have been proposed … Read more

    Inherent smoothness of intensity patterns for intensity modulated radiation therapy generated by simultaneous projection algorithms

  • Yair Censor
  • James M. Galvin
  • Darek Michalski
  • Ying Xiao
    • Categories Biomedical Applications, Convex Optimization Tags , , , ,

    The efficient delivery of intensity modulated radiation therapy (IMRT) depends on finding optimized beam intensity patterns that produce dose distributions, which meet given constraints for the tumor as well as any critical organs to be spared. Many optimization algorithms that are used for beamlet-based inverse planning are susceptible to large variations of neighboring intensities. Accurately … Read more

    A randomized heuristic for scene recognition by graph matching

  • Isabelle Bloch
  • Celso C. Ribeiro
  • Maria Claudia Boeres
    • Categories Biomedical Applications, Graphs and Matroids, Meta Heuristics Tags , , , ,

    We propose a new strategy for solving the non-bijective graph matching problem in model-based pattern recognition. The search for the best correspondence between a model and an over-segmented image is formulated as a combinatorial optimization problem, defined by the relational attributed graphs representing the model and the image where recognition has to be performed, together … Read more

    The dose-volume constraint satisfaction problem for inverse treatment planning with field segments

  • Yair Censor
  • James M. Galvin
  • Darek Michalski
  • Ying Xiao
    • Categories Biomedical Applications Tags , ,

    The prescribed goals of radiation treatment planning are often expressed in terms of dose-volume constraints. We present a novel formulation of a dose-volume constraint satisfaction search for the discretized radiation therapy model. This approach does not rely on any explicit cost function. The inverse treatment planning uses the aperture based approach with predefined, according to … Read more

    Transfer function restoration in 3D electron microscopy via iterative data refinement

  • J.M. Carazo
  • Yair Censor
  • C.O.S. Sorzano
  • Gabor T. Herman
  • R. Marabini
    • Categories Biomedical Applications Tags , ,

    Three-dimensional electron microscopy (3D-EM) is a powerful tool for visualizing complex biological systems. As any other imaging device, the electron microscope introduces a transfer function (called in this field the Contrast Transfer Function, CTF) into the image acquisition process that modulates the various frequencies of the signal. Thus, 3D reconstructions performed with these CTF-affected projections … Read more

    A GRASP/VND heuristic for the phylogeny problem using a new neighborhood structure

  • Celso C. Ribeiro
  • Dalessandro Vianna
    • Categories Biomedical Applications, Meta Heuristics Tags , , ,

    A phylogeny is a tree that relates taxonomic units, based on their similarity over a set of characters. The phylogeny problem consists in finding a phylogeny with the minimum number of evolutionary steps. We propose a new neighborhood structure for the phylogeny problem. A GRASP heuristic based on this neighborhood structure and using VND for … Read more

    Randomized Algorithms for Scene Recognition by Inexact Graph Matching

  • Isabelle Bloch
  • Celso C. Ribeiro
  • Maria Claudia Boeres
    • Categories Biomedical Applications, Graphs and Matroids, Meta Heuristics Tags , , ,

    We propose a new method for non-bijective graph matching for model-based pattern recognition. We formulate the search for the best correspondence between a model and an over-segmented image as a new combinatorial optimization problem, defined by the relational attributed graphs representing the model and the image where recognition has to be performed, together with the … Read more

    Heuristics for the Phylogeny Problem

  • Alexandre Andreatta
  • Celso C. Ribeiro
    • Categories Biomedical Applications, Meta Heuristics Tags , ,

    A phylogeny is a tree that relates taxonomic units, based on their similarity over a set of characters. The problem of finding a phylogeny with the minimum number of evolutionary steps (the so-called parsimony criterion) is one of the main problems in comparative biology. In this work, we study different heuristic approaches to the phylogeny … Read more

    A genetic algorithm for the phylogeny problem using an optimized crossover strategy based on path-relinking

  • Celso C. Ribeiro
  • Dalessandro Vianna
    • Categories Biomedical Applications, Graphs and Matroids, Meta Heuristics Tags , ,

    A phylogenetic tree relates taxonomic units, based on their similarity over a set of characters. We propose a new genetic algorithm for the problem of building a phylogenetic tree under the parsimony criterion. This genetic algorithm makes use of an innovative optimized crossover strategy which is an extension of the path-relinking intensification technique originaly proposed … Read more

    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. Citation in: J.R. Palta and … Read more