Optimization in Medicine (eBook)
X, 195 Seiten
Springer New York (Verlag)
978-0-387-73299-2 (ISBN)
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.
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.
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
Erscheint lt. Verlag | 20.12.2007 |
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Reihe/Serie | Springer Optimization and Its Applications | Springer Optimization and Its Applications |
Zusatzinfo | X, 195 p. 60 illus. |
Verlagsort | New York |
Sprache | englisch |
Themenwelt | Mathematik / Informatik ► Mathematik ► Angewandte Mathematik |
Mathematik / Informatik ► Mathematik ► Finanz- / Wirtschaftsmathematik | |
Medizin / Pharmazie ► Allgemeines / Lexika | |
Medizin / Pharmazie ► Medizinische Fachgebiete ► Radiologie / Bildgebende Verfahren | |
Studium ► 1. Studienabschnitt (Vorklinik) ► Biochemie / Molekularbiologie | |
Technik | |
Schlagworte | algorithms • classification • Global Optimization • Optimization • SOIA • therapy • Ultrasound |
ISBN-10 | 0-387-73299-3 / 0387732993 |
ISBN-13 | 978-0-387-73299-2 / 9780387732992 |
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