Main Data
Author: Carlos J. S. Alves, Panos M. Pardalos, Luis Nunes Vicente
Editor: Carlos J. S. Alves, Panos M. Pardalos, Luis Nunes Vicente
Title: Optimization in Medicine
Publisher: Springer-Verlag
ISBN/ISSN: 9780387732992
Edition: 1
Price: CHF 160.10
Publication date: 01/01/2007
Category: Mathematics
Language: English
Technical Data
Pages: 195
Kopierschutz: DRM
Geräte: PC/MAC/eReader/Tablet
Formate: PDF
Table of contents

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.

Table of contents
List of Contributors9
The influence of dose grid resolution on beam selection strategies in radiotherapy treatment design11
1 Introduction12
2 The beam selection problem14
3 The beam selection methods17
4 Numerical comparisons20
5 Conclusions31
Decomposition of matrices and static multileaf collimators: a survey34
1 Introduction34
2 Algorithms for the decomposition time problem37
3 Algorithms for the decomposition cardinality problem43
4 Combined objective functions45
5 Numerical results48
Appendix: The instances53
Neuro-dynamic programming for fractionated radiotherapy planning56
1 Introduction56
2 Model formulation59
3 Neuro-dynamic programming61
4 Computational experimentation66
5 Conclusion77
Randomized algorithms for mixed matching and covering in hypergraphs in 3D seed reconstruction in brachytherapy80
1 Introduction80
2 Hypergraph matching model of 3D seed reconstruction83
3 Simultaneous matching and covering algorithms91
4 Main results and proofs94
5 Experimental results101
6 Open problems109
Global optimization and spatial synchronization changes prior to epileptic seizures112
1 Introduction113
2 Synchronization changes prior to epileptic seizures114
3 Optimization of spatial synchronization122
4 Estimation of seizure predictability time125
5 Results126
6 Conclusion130
Optimization-based predictive models in medicine and biology135
1 Introduction136
2 Background137
3 Discrete support vector machine predictive models139
4 Classification results on real-world applications146
5 Summary and conclusion154
Optimal reconstruction kernels in medical imaging160
1 Introduction160
2 Approximate inverse as a tool for deriving inversion algorithms161
3 Inversion of the Radon transform163
4 Optimality criteria165
5 The filtered backprojection for the Radon transform in 2 and 3 dimensions167
6 Inversion formula for the 3D cone beam transform170
Optimal control in high intensity focused ultrasound surgery176
1 Introduction176
2 Mathematical models179
3 Control and optimization algorithms for ultrasound surgery181
4 Conclusions198