This volume of proceedings consists of the papers presented during the 9th International Workshop on Mathematical Methods in Scattering Theory and Biomedical Engineering, held in Patras, Greece, on 9–11 October 2009.The book contains papers on scattering theory and biomedical engineering — two rapidly evolving fields which have a considerable impact on today's research. All the papers are state-of-the-art, have been carefully reviewed before publication and the authors are well-known in the scientific community. In addition, some papers focus more on applied mathematics, which provides a solid ground for development and innovative research in scattering and biomedical engineering.Contents:Mathematical Methods in Scattering and Biomedical Engineering:The Double Analytic Structure that Allows the Introduction of Vector Ellipsoidal Harmonics (G Dassios)The Inverse Scattering Problem in Linear Elasticity via a Pair of Non-Linear Integral Equations (D Gintides & L Midrinos)Biomedical Engineering:Photon Scattering Applications in Tissue Characterisation and Imaging (R Speller)An Automated Method for Atherosclerotic Plaque Characterization and Quantification Using Intravascular Ultrasound Images (L S Athanasiou et al.)Electromagnetic Scattering and Biomedical Applications:Removing Non Uniform Illumination Effects in Infrared Images (M Vlachos & E Dermatas)Estimation of Human RBC Size Using Light Scattering Images at Multiple Wavelengths (G Apostolopoulos et al.)Size Effects and Enhanced Elastic Theories:Acoustic Scattering by Obstacles Invisible in the Backscattered Direction (B D Sleeman)Two-Dimensional Boundary Element Modeling of Wave Dispersion in Bone — Mimicking Plates with Microstructural Effects (M G Vavva et al.)Mathematical Methods in Mechanics and Biomedical Engineering:Novel Integral Representation for Irrotational Stokes' Flow in the Exterior of a Sphere (G Dassios & M Doschoris)Comparing Two Bilinear Equivalent Matrix Pencils (A A Pantelous et al.)Signal Processing and Non Destructive Methods:The Transmission Eigenvalue Problem (F Cakoni et al.)A Fast Wavelet/BEM for Wave Scattering Solutions (D Ntalaperas et al.)and other papersReadership: Graduate students, academics, researchers and industry in biomedical engineering, bioinformatics, mathematical biology, mathematical physics and computer science.