Optimization in Medicine

1. Auflage 2007
ISBN: 978-0-387-73299-2
Verlag: Springer-Verlag
Format: PDF
Kopierschutz: Adobe DRM (»Systemvoraussetzungen)

E-Book, Englisch, 195 Seiten

Optimization has become an essential tool in addressing the limitation of resources and need for better decision-making in the medical field. Both continuous and discrete mathematical techniques are playing an increasingly important role in understanding several fundamental problems in medicine.

This volume presents a wide range of medical applications that can utilize mathematical computing. Examples include using an algorithm for considering the seed reconstruction problem in brachytherapy and using optimization-classification models to assist in the early prediction, diagnosis and detection of diseases. Discrete optimization techniques and measures derived from the theory of nonlinear dynamics, with analysis of multi-electrode electroencephalographic (EEG) data, assist in predicting impending epileptic seizures. Mathematics in medicine can also be found in recent cancer research. Sophisticated mathematical models and optimization algorithms have been used to generate treatment plans for radionuclide implant and external beam radiation therapy. Optimization techniques have also been used to automate the planning process in Gamma Knife treatment, as well as to address a variety of medical image registration problems.

This work grew out of a workshop on optimization which was held during the 2005 CIM Thematic Term on Optimization in Coimbra, Portugal. It provides an overview of the state-of-the-art in optimization in medicine and will serve as an excellent reference for researchers in the medical computing community and for those working in applied mathematics and optimization.

Autoren/Hrsg.

Inhaltsverzeichnis

1;Preface;6
2;Contents;8
3;List of Contributors;9
4;The influence of dose grid resolution on beam selection strategies in radiotherapy treatment design;11
4.1;1 Introduction;12
4.2;2 The beam selection problem;14
4.3;3 The beam selection methods;17
4.4;4 Numerical comparisons;20
4.5;5 Conclusions;31
4.6;References;32
5;Decomposition of matrices and static multileaf collimators: a survey;34
5.1;1 Introduction;34
5.2;2 Algorithms for the decomposition time problem;37
5.3;3 Algorithms for the decomposition cardinality problem;43
5.4;4 Combined objective functions;45
5.5;5 Numerical results;48
5.6;Acknowledgements;51
5.7;References;51
5.8;Appendix: The instances;53
6;Neuro-dynamic programming for fractionated radiotherapy planning;56
6.1;1 Introduction;56
6.2;2 Model formulation;59
6.3;3 Neuro-dynamic programming;61
6.4;4 Computational experimentation;66
6.5;5 Conclusion;77
6.6;References;78
7;Randomized algorithms for mixed matching and covering in hypergraphs in 3D seed reconstruction in brachytherapy;80
7.1;1 Introduction;80
7.2;2 Hypergraph matching model of 3D seed reconstruction;83
7.3;3 Simultaneous matching and covering algorithms;91
7.4;4 Main results and proofs;94
7.5;5 Experimental results;101
7.6;6 Open problems;109
7.7;References;109
8;Global optimization and spatial synchronization changes prior to epileptic seizures;112
8.1;1 Introduction;113
8.2;2 Synchronization changes prior to epileptic seizures;114
8.3;3 Optimization of spatial synchronization;122
8.4;4 Estimation of seizure predictability time;125
8.5;5 Results;126
8.6;6 Conclusion;130
8.7;Acknowledgement;131
8.8;References;131
9;Optimization-based predictive models in medicine and biology;135
9.1;1 Introduction;136
9.2;2 Background;137
9.3;3 Discrete support vector machine predictive models;139
9.4;4 Classification results on real-world applications;146
9.5;5 Summary and conclusion;154
9.6;Acknowledgement;155
9.7;References;155
10;Optimal reconstruction kernels in medical imaging;160
10.1;1 Introduction;160
10.2;2 Approximate inverse as a tool for deriving inversion algorithms;161
10.3;3 Inversion of the Radon transform;163
10.4;4 Optimality criteria;165
10.5;5 The filtered backprojection for the Radon transform in 2 and 3 dimensions;167
10.6;6 Inversion formula for the 3D cone beam transform;170
10.7;Acknowledgement;174
10.8;References;174
11;Optimal control in high intensity focused ultrasound surgery;176
11.1;1 Introduction;176
11.2;2 Mathematical models;179
11.3;3 Control and optimization algorithms for ultrasound surgery;181
11.4;4 Conclusions;198
11.5;References;199