Mathematical Modeling in Biomedical Imaging II Optical, Ultrasound,
This volume reports on recent mathematical and computational advances in optical, ultrasound, and opto-acoustic tomographies. It outlines the state-of-the-art and future directions in these fields and provides readers with the most recently developed math
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For further volumes: http://www.springer.com/series/304
2035
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Habib Ammari Editor
Mathematical Modeling in Biomedical Imaging II Optical, Ultrasound, and Opto-Acoustic Tomographies
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Editor Habib Ammari ´ Ecole Normale Sup´erieure Math´ematiques et Applications 45 rue d’Ulm 75005 Paris France [email protected]
ISBN 978-3-642-22989-3 e-ISBN 978-3-642-22990-9 DOI 10.1007/978-3-642-22990-9 Springer Heidelberg Dordrecht London New York Lecture Notes in Mathematics ISSN print edition: 0075-8434 ISSN electronic edition: 1617-9692 Library of Congress Control Number: 2009932673 Mathematics Subject Classification (2011): 35-XX; 65-XX; 92-XX c Springer-Verlag Berlin Heidelberg 2012 This work is subject to copyright. All rights are reserved, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilm or in any other way, and storage in data banks. Duplication of this publication or parts thereof is permitted only under the provisions of the German Copyright Law of September 9, 1965, in its current version, and permission for use must always be obtained from Springer. Violations are liable to prosecution under the German Copyright Law. The use of general descriptive names, registered names, trademarks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. Printed on acid-free paper Springer is part of Springer Science+Business Media (www.springer.com)
Preface
The aim of this volume is to report recent mathematical and computational advances in optical, ultrasound, and photo-acoustic (also called opto-acoustic) tomographies. The volume outlines the state-of-the-art and future directions in optical and ultrasound imaging. It provides some of the most recent mathematical and computational tools in these fields. It is particularly suitable for researchers and graduate students in applied mathematics and in biomedical engineering. Ultrasound imaging is based on the detection of mechanical properties (acoustic impedance) in biological soft tissues. It can provide good spatial resolution because of its millimetric wavelength and weak scattering at MHz frequencies. However, soft-tissue contrast is relatively poor. Optical tomography is a biomedical imaging modality that uses scattered light as a probe of structural variations in the optical properties of tissue. Optical imaging is very sensitive to optical absorption but can only provide a spatial resolution on the order of 1 cm at cm depths. Photo-acoustic imaging is a promising new biomedical imaging modality. It combines both optical and ultrasound approaches to provide images of optical contrasts (based on the optical absorption) with ultrasonic resolution. The objective of the volume is fourfold: (i) to discuss models for light propagation and present fast algorithms for solving the radiative tran
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