Medical Imaging Signals and Systems

For courses in medical imaging systems.

With signal processing as its foundation, this text covers the most important imaging modalities in radiology: projection radiography, x-ray computed tomography, nuclear medicine, ultrasound imaging, and magnetic resonance imaging. Organized into parts to emphasize key overall conceptual divisions, Medical Imaging is most appropriate for engineering students who have taken the prerequisite signals and systems courses as well as elementary probability.

Table of Contents

Preface

Part I: Basic Imaging Principles Overview.

Chapter 1Introduction. History of Medical Imaging.  Physical Signals.  Imaging Modalities. Projection Radiography. Computed Tomography. Nuclear Medicine. Ultrasound Imaging. Magnetic Resonance Imaging. Summary and Key Concepts.

Chapter 2: Signals and Systems.Introduction. Signals. Point Impulse. Line Impulse. Comb and Sampling Functions. Rect and Sinc Functions. Exponential and Sinusoidal Signals. Separable Signals. Periodic Signals. Systems. Linear Systems. Impulse Response. Shift Invariance. Connections of LSI Systems. Separable Systems. Stable Systems. The Fourier Transform. Properties of the Fourier Transform. Linearity. Translation. Conjugation and Conjugate Symmetry. Scaling. Rotation. Convolution. Product. Separable Product. Parseval’s Theorem. Separability. Transfer Function. Circular Symmetry and the Hankel Transform. Sampling. Sampling Signal Model. Nyquist Sampling Theorem. Anti-aliasing Filters. Summary and Key Concepts.

Chapter 3: Image Quality.Introduction. Contrast. Modulation. Modulation Transfer Function. Local Contrast. Resolution. Line Spread Function. Full Width at Half Maximum. Resolution and Modulation Transfer Function. Subsystem Cascade. Resolution Tool. Temporal and Spectral Resolution. Noise. Random Variables. Continuous Random Variables. Discrete Random Variables.Independent Random Variables. Signal-to-Noise Ratio. Amplitude SNR. Power SNR. Differential SNR. Nonrandom Effects. Artifacts. Distortion. Accuracy. Quantitative Accuracy. Diagnostic Accuracy. Summary and Key Concepts.

Part II: Radiographic Imaging.Overview. 

Chapter 4: Physics of Radiography.Introduction. Ionization. Atomic Structure. Electron Binding Energy. Ionization and Excitation. Forms of Ionizing Radiation. Particulate Radiation. Electromagnetic Radiation. Nature and Properties of Ionizing Radiation. Primary Energetic Electron Interactions. Primary Electromagnetic Radiation Interactions. Attenuation of Electromagnetic Radiation. Measures of X-ray Beam Strength. Narrow Beam, Monoenergetic Photons. Narrow Beam, Polyenergetic Photons. Broad Beam Case. Radiation Dosimetry. Exposure. Dose and Kerma. Linear Energy Transfer. The f —factor. Dose Equivalent. Effective Dose. Summary and Key Concepts. 

Chapter 5: Projection Radiography.Introduction. Instrumentation. X-ray Tubes. Filtration and Restriction. Compensation Filters and Contrast Agents. Grids, Airgaps, and Scanning Slits. Film-Screen Detectors. X-ray Image Intensifiers. Image Formation. Basic Imaging Equation. Geometric Effects. Blurring Effects. Film Characteristics. Noise and Scattering. Signal-to-Noise Ratio. Quantum Efficiency and Detective Quantum Efficiency. Compton Scattering. Summary and Key Concepts.

Chapter 6: Computed Tomography.Introduction. CT Instrumentation. CT Generations. X-ray Source and Collimation. CT Detectors. Gantry, Slip Ring, and Patient Table. Image Formation. Line Integrals. CT Numbers. Parallel-Ray Reconstruction. Fan-Beam Reconstruction. Helical CT Reconstruction. Cone Beam CT. Image Quality in CT.  Resolution. Noise. Artifacts. Summary and Key Concepts.  

Part III: Nuclear Medicine Imaging.Overview.

Chapter 7: The Physics of Nuclear Medicine.Introduction. Nomenclature. Radioactive Decay. Mass Defect and Binding Energy. Line of Stability. Radioactivity. Radioactive Decay Law. Modes of Decay. Positron Decay and Electron Capture. Isomeric Transition. Statistics of Decay. Radiotracers. Summary and Key Concepts. 

Chapter 8: Planar Scintigraphy.Introduction. Instrumentation. Collimators. Scintillation Crystal. Photomultiplier Tubes. Positioning Logic. Pulse Height Analyzer. Gating Circuit. Image Capture. Image Formation. Event Position Estimation. Acquisition Modes. Anger Camera Imaging Equation. Image Quality. Resolution. Sensitivity. Uniformity. Energy Resolution. Noise. Factors Affecting Count Rate. Summary and Key Concepts. 

Chapter 9: Emission Computed Tomography.Instrumentation. SPECT Instrumentation. PET Instrumentation. Image Formation. SPECT Image Formation. PET Image Formation. Iterative Reconstruction. Image Quality in SPECT and PET. Spatial Resolution. Attenuation and Scatter. Random Coincidences. Contrast. Noise and Signal-to-Noise. Summary and Key Concepts.

Part IV:  Ultrasound Imaging.Overview.

Chapter 10: The Physics of Ultrasound. Introduction. The Wave Equation. Three-Dimensional Acoustic Waves. Plane Waves. Spherical Waves. Wave Propagation. Acoustic Energy and Intensity. Reflection and Refraction at Plane Interfaces. Transmission and Reflection Coefficients at Plane Interfaces. Attenuation. Scattering. Doppler Effect. Beam Pattern Formation and Focusing. Simple Field Pattern Model. Diffraction Formulation. Focusing. Summary and Key Concepts. 

Chapter 11: Ultrasound Imaging Systems.Introduction. Instrumentation. Ultrasound Transducer. Ultrasound Probes. Pulse-Echo Imaging. The Pulse-Echo Equation. Transducer Motion. Ultrasound Imaging Modes. A-Mode Scan. M-Mode Scan. B-Mode Scan. Steering and Focusing. Transmit Steering and Focusing. Beamforming and Dynamic Focusing. Three-Dimensional Ultrasound Imaging. Summary and Key Concepts.

Part V: Magnetic Resonance Imaging.Overview.

Chapter 12: Physics of Magnetic Resonance.Introduction. Microscopic Magnetization. Macroscopic Magnetization. Precession and Larmor Frequency. Transverse and Longitudinal Magnetization. NMR Signals. Rotating Frame. RF Excitation. Relaxation. The Bloch Equations. Spin Echoes. Contrast Mechanisms. Summary and Key Concepts. 

Chapter 13: Magnetic Resonance Imaging.Instrumentation. System Components. Magnet. Gradient Coils. Radio-Frequency Coils. Scanning Console and Computer. MRI Data Acquisition. Encoding Spatial Position. Slice Selection. Frequency Encoding. Polar Scanning. Gradient Echoes. Phase Encoding. Spin Echoes. Pulse Repetition Interval. Realistic Pulse Sequences. Image Reconstruction. Rectilinear Data. Polar Data. Imaging Equations. Image Quality. Sampling. Resolution. Noise. Signal-to-Noise Ratio. Artifacts. Summary and Key Concepts. Index.