E-Book, Englisch, Band 12, 195 Seiten
Alves / Pardalos / Vicente Optimization in Medicine
1. Auflage 2007
ISBN: 978-0-387-73299-2
Verlag: Springer
Format: PDF
Kopierschutz: 1 - PDF Watermark
E-Book, Englisch, Band 12, 195 Seiten
Reihe: Springer Optimization and Its Applications
ISBN: 978-0-387-73299-2
Verlag: Springer
Format: PDF
Kopierschutz: 1 - PDF Watermark
This volume presents a wide range of medical applications that can utilize mathematical computing. 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.
Weitere Infos & Material
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
