Optimization in Medicine (eBook)

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