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Optimization in Medicine

:	Carlos J. S. Alves, Panos M. Pardalos, Luis Nunes Vicente
:	Carlos J. S. Alves, Panos M. Pardalos, Luis Nunes Vicente
:	Optimization in Medicine
:	Springer-Verlag
:	9780387732992
:	1
:	CHF 85.30
:

:	Allgemeines
:	English

:	195
:	Wasserzeichen/DRM
:	PC/MAC/eReader/Tablet
:	PDF

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.

	Preface	6
	Contents	8
	List of Contributors	9
	The influence of dose grid resolution on beam selection strategies in radiotherapy treatment design	11
	1 Introduction	12
	2 The beam selection problem	14
	3 The beam selection methods	17
	4 Numerical comparisons	20
	5 Conclusions	31
	References	32
	Decomposition of matrices and static multileaf collimators: a survey	34
	1 Introduction	34
	2 Algorithms for the decomposition time problem	37
	3 Algorithms for the decomposition cardinality problem	43
	4 Combined objective functions	45
	5 Numerical results	48
	Acknowledgements	51
	References	51
	Appendix: The instances	53
	Neuro-dynamic programming for fractionated radiotherapy planning	56
	1 Introduction	56
	2 Model formulation	59
	3 Neuro-dynamic programming	61
	4 Computational experimentation	66
	5 Conclusion	77
	References	78
	Randomized algorithms for mixed matching and covering in hypergraphs in 3D seed reconstruction in brachytherapy	80
	1 Introduction	80
	2 Hypergraph matching model of 3D seed reconstruction	83
	3 Simultaneous matching and covering algorithms	91
	4 Main results and proofs	94
	5 Experimental results	101
	6 Open problems	109
	References	109
	Global optimization and spatial synchronization changes prior to epileptic seizures	112
	1 Introduction	113
	2 Synchronization changes prior to epileptic seizures	114
	3 Optimization of spatial synchronization	122
	4 Estimation of seizure predictability time	125
	5 Results	126
	6 Conclusion	130
	Acknowledgement	131
	References	131
	Optimization-based predictive models in medicine and biology	135
	1 Introduction	136
	2 Background	137
	3 Discrete support vector machine predictive models	139
	4 Classification results on real-world applications	146
	5 Summary and conclusion	154
	Acknowledgement	155
	References	155
	Optimal reconstruction kernels in medical imaging	160
	1 Introduction	160
	2 Approximate inverse as a tool for deriving inversion algorithms	161
	3 Inversion of the Radon transform	163
	4 Optimality criteria	165
	5 The filtered backprojection for the Radon transform in 2 and 3 dimensions	167
	6 Inversion formula for the 3D cone beam transform	170
	Acknowledgement	174
	References	174
	Optimal control in high intensity focused ultrasound surgery	176
	1 Introduction	176
	2 Mathematical models	179
	3 Control and optimization algorithms for ultrasound surgery	181
	4 Conclusions	198
	References	199