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Bharath www.morganclaypool.com ISBN: 9781598296112 paperback ISBN: 9781598296129 ebook DOI 10.2200/S00165ED1V01Y200811BME026 A Publication in the Morgan & Claypool Publishers series SYNTHESIS LECTURES ON BIOMEDICAL ENGINEERING Lecture #27 Series Editors: John D. Enderle Series ISSN Synthesis Lectures on Biomedical Engineering ISSN Print 1930-0328 Electronic 1930-0336 IntroductoryMedical Imaging A. A. Bharath Imperial College, London SYNTHESIS LECTURES ON BIOMEDICAL ENGINEERING #27 M Morgan &cLaypool publishers &C ABSTRACT This book provides an introduction to the principles of several of the more widely used methods in medical imaging. Intended for engineering students, it provides a final-year undergraduate- or graduate-level introduction to several imaging modalities, including MRI, ultrasound and X-Ray CT. The emphasis of the text is on mathematical models for imaging and image reconstruction physics. Emphasis is also given to sources of imaging artefacts. Such topics are usually not addressed across the different imaging modalities in one book, and this is a notable strength of the treatment given here. KEYWORDS Medical Imaging, Ultrasonic Imaging, X-Ray Imaging, Magnetic Resonance Imag- ing, Computer Aided Tomography (CAT), Mathematical Models for Imaging, Image Formation Physics, Image Reconstruction. ix Contents Synthesis Lectures on Biomedical Engineering . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iii Contents . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ix 1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .1 2 Diagnostic X-Ray Imaging . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 2.1 Basic Principles of X-Ray Imaging . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 2.1.1 Ideal Description of Imaging Process 3 2.2 Relevant Physics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .4 2.2.1 Atomic Structure 4 2.2.2 Nature of X-Rays 4 2.2.3 X-Ray Generation 5 2.2.4 X-Ray Spectra 7 2.2.5 X-Ray Interactions with Matter 8 2.3 Attenuation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13 2.3.1 The Basics 13 2.3.2 Variation of Linear Attenuation Coefficient 15 2.3.3 Beam Hardening 15 2.4 Image Formation Physics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .17 2.4.1 Film 17 2.4.2 Modelling Film Characteristics 18 2.5 X-Ray Image Quality . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19 2.5.1 Broad Image Quality Goals 19 2.6 The Real Imaging Process . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23 2.6.1 Geometrical Considerations 23 2.6.2 Quantum (Photon) Considerations 25 x CONTENTS 2.6.3 Beam Hardening 26 2.6.4 Film Effects 26 2.6.5 Grouping the Effects of Unsharpness 27 2.7 Quantitative Measures of Image Quality . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27 2.7.1 Measures of Spatial Resolution 27 2.7.2 Measures of Contrast 27 2.8 Dosage . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28 2.8.1 Exposure 29 2.8.2 Absorbed Dose 30 2.8.3 KERMA 30 2.8.4 Converting exposure to absorbed dose in air 30 2.8.5 Dose in Air vs Dose in Tissue 30 2.8.6 Genetic & Effective Dose Equivalents 31 2.8.7 Dose and Image Contrast 31 2.8.8 Dose and Signal/Noise Ratio 32 2.9 Practical Issues . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32 2.9.1 The X-ray Source 32 2.9.2 Spatial Distribution of X-Ray Photons 33 2.9.3 Receptors 34 2.9.4 Dosage & Contrast Issues 35 2.9.5 Contrast Agents 35 2.9.6 Safety 36 3 X-Ray CT . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37 3.1 Planar X-Rays:Review . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37 3.1.1 Limitations 37 3.1.2 Solutions to Contrast and Depth Collapse 41 3.2 Slicing Fred . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42 3.2.1 Linear Projections 42 3.2.2 Basic Principle of CT 43 3.3 Algebraic Interpretation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44