Mathematics and Physics of Emerging Biomedical Imaging

Mathematics and Physics of Emerging Biomedical Imaging

  • Publisher: National Academies Press
  • ISBN: 9780309053877
  • eISBN Pdf: 9780309552929
  • eISBN Epub: 9780309175975
  • Place of publication:  United States
  • Year of digital publication: 1996
  • Month: February
  • Pages: 261
  • DDC: 510
  • Language: English

This cross-disciplinary book documents the key research challenges in the mathematical sciences and physics that could enable the economical development of novel biomedical imaging devices. It is hoped that the infusion of new insights from mathematical scientists and physicists will accelerate progress in imaging. Incorporating input from dozens of biomedical researchers who described what they perceived as key open problems of imaging that are amenable to attack by mathematical scientists and physicists, this book introduces the frontiers of biomedical imaging, especially the imaging of dynamic physiological functions, to the educated nonspecialist.

Ten imaging modalities are covered, from the well-established (e.g., CAT scanning, MRI) to the more speculative (e.g., electrical and magnetic source imaging). For each modality, mathematics and physics research challenges are identified and a short list of suggested reading offered. Two additional chapters offer visions of the next generation of surgical and interventional techniques and of image processing. A final chapter provides an overview of mathematical issues that cut across the various modalities.

  • Mathematics and Physics of Emerging Biomedical Imaging
  • Copyright
  • PREFACE
  • Contents
  • Chapter 1 Introduction and Summary
    • PLATE CAPTIONS
  • Chapter 2 X-Ray Projection Imaging
    • 2.1 INTRODUCTION
    • 2.2 MAMMOGRAPHY
      • 2.2.1 Scanning Methods
      • 2.2.2 Area Detectors
    • 2.3 CHEST RADIOGRAPHY
      • 2.3.1 Scanning Methods
      • 2.3.2 Area Detectors
    • 2.4 DIGITAL FLUOROSCOPY
    • 2.5 PORTAL IMAGING
    • 2.6 RESEARCH OPPORTUNITIES
    • 2.7 Suggested Reading
  • Chapter 3 X-Ray Computed Tomography
    • 3.1 INTRODUCTION
      • 3.1.1 History
      • 3.1.2 Principle of Operation
    • 3.2 PRESENT STATUS OF CT INSTRUMENTATION AND TECHNOLOGY
      • 3.2.1 X-Ray Tubes
      • 3.2.2 Detector Systems
      • 3.2.3 Image Artifacts
      • 3.2.4 Quantitative CT
      • 3.2.5 Requirements for High-Speed CT
    • 3.3 SPIRAL CT
    • 3.4 ELECTRON BEAM TECHNIQUES
    • 3.5 DATA HANDLING AND DISPLAY TECHNIQUES
    • 3.6 RESEARCH OPPORTUNITIES
    • 3.7 Suggested Reading
  • Chapter 4 Magnetic Resonance Imaging
    • 4.1 PRINCIPLES OF MAGNETIC RESONANCE IMAGING
    • 4.2 HARDWARE
      • 4.2.1 Magnet Systems: Current Status and Opportunities
      • 4.2.2 Pulsed-field MRI Systems
      • 4.2.3 Radio-frequency Coils for MRI
        • Computational Design of RF Coils 
        • Cooled Receiver Coils for MR Imaging 
        • Use of Multiple Receivers 
      • 4.2.4 Magnetic Field Gradients
        • Local versus Whole-Body Gradients 
        • Design Considerations 
        • Applications
        • Bioeffects 
      • 4.2.5 Research Opportunities for MRI Hardware
        • Magnet Systems
        • Pulsed-field MRI
        • RF Coils
        • Gradient Systems
      • 4.2.6 Suggested Reading Related to MRI Hardware
        • Magnet Systems
        • Pulsed-field MRI
        • RF Coils
        • Gradient Systems
    • 4.3 DYNAMIC MR IMAGE RECONSTRUCTION
      • 4.3.1 Partial Fourier Reconstruction
        • Predominantly One-sided Data Collection 
        • Predominantly Every Other Point 
        • Collecting Multiple Echoes 
        • Two- and Three-Dimensional Extensions 
      • 4.3.2 Reduced Gibbs Ringing
        • Iterative Sigma Filtering 
        • Constraint-based Methods 
        • Parametric Estimation 
      • 4.3.3 High-speed K-space Coverage Techniques
      • 4.3.4 Research Opportunities in Dynamic MR Image Reconstruction
      • 4.3.5 Suggested Reading Related to Dynamic MR Image Reconstruction
    • 4.4 APPLICATIONS OF DYNAMIC MRI
      • 4.4.1 Blood Flow
        • Fourier Velocity Encoding 
        • RF Pulses 
        • Measurement of Wave Speed and Distensibility 
        • Postprocessing 
        • Conclusions Related to MR Imaging of Blood Flow  
      • 4.4.2 Diffusion Imaging
        • Measurement of Diffusion Coefficients in vivo 
        • Mapping of Diffusion Tensor 
      • 4.4.3 Other Tissue Parameters
        • Relaxation Times
        • Oxygen
        • Strain
      • 4.4.4 Functional Brain MRI
        • Contrast Mechanism  
        • Imaging Techniques 
        • Hardware Requirements
        • Field Strength Considerations As discussed above, local field gradients
        • Processing of Functional Images 
        • Safety Considerations 
        • Biophysical Modeling 
      • 4.4.5 Multinuclear MRI
        • MR Spectroscopy and Spectroscopic Imaging 
        • Injected Paramagnetic Contrast Agents and Hyperpolarized Noble Gases 
      • 4.4.6 Microscopic Imaging
        • Resolution 
        • Signal-to-Noise Ratios 
        • Gradients 
        • Diffusion 
        • Motion 
        • Future Applications of in vivo MRI Microscopy 
      • 4.4.7 Research Opportunities Related to Applying Dynamic MRI
        • Blood Flow 
        • Diffusion Imaging 
        • Other Tissue Parameters
        • Functional Brain MRI
        • Multinuclear MRI
        • Microscopic Imaging
      • 4.4.8 Suggested Reading on Applications of Dynamic MRI
        • Blood Flow
        • Diffusion Imaging
        • Other Tissue Parameters
        • Functional Brain MRI
        • Multinuclear MRI
        • Microscopic Imaging
  • Chapter 5 Single Photon Emission Computed Tomography
    • 5.1 INTRODUCTION
    • 5.2 PHYSICAL AND INSTRUMENTATION FACTORS THAT AFFECT SPECT IMAGES
    • 5.3 SPECT INSTRUMENTATION
      • 5.3.1 SPECT System Designs
      • 5.3.2 Special Collimators
      • 5.3.3 New Radiation Detector Technologies
    • 5.4 SPECT IMAGE RECONSTRUCTION
      • 5.4.1 The SPECT Reconstruction Problem
      • 5.4.2 SPECT Image Reconstruction Methods
        • Compensation Methods 
        • Three-Dimensional Reconstruction Methods for Special Collimator Designs 
    • 5.5 RESEARCH OPPORTUNITIES
    • 5.6 Suggested Reading
  • Chapter 6 Positron Emission Tomography
    • 6.1 INTRODUCTION
      • 6.1.1 History
      • 6.1.2 Applications
      • 6.1.3 Principle of Operation
    • 6.2 CURRENT STATUS OF PET TECHNOLOGY
      • 6.2.1 γ-Ray Detectors
      • 6.2.2 Limitations of the Spatial Resolution
      • 6.2.3 System Electronics
      • 6.2.4 Data Correction and Reconstruction Algorithms
    • 6.3 THREE-DIMENSIONAL ACQUISITION AND RECONSTRUCTION
      • 6.3.1 Principle of Three-Dimensional Acquisition
      • 6.3.2 Three-Dimensional Reconstruction
      • 6.3.3 Scatter Correction in Three Dimensions
      • 6.3.4 Attenuation Correction in Three Dimensions
    • 6.4 RESEARCH OPPORTUNITIES
    • 6.5 Suggested Reading
  • Chapter 7 Ultrasonics
    • 7.1 INTRODUCTION
    • 7.2 INSTRUMENTATION
      • 7.2.1 Transducers
        • Field Distributions 
        • Acoustics and Vibration 
        • Electromechanical Properties of Ferroelectric Materials 
      • 7.2.2 Ultrasonic Beam Forming
      • 7.2.3 Signal Processing
    • 7.3 SCATTERING
    • 7.4 ULTRASONIC TOMOGRAPHY
    • 7.5 RESEARCH OPPORTUNITIES
    • 7.6 Suggested Reading
  • Chapter 8 Electrical Source Imaging
    • 8.1 INTRODUCTION
    • 8.2 OUTLINE OF ESI RECONSTRUCTION METHODS
      • 8.2.1 Forward Problem
      • 8.2.2 Inverse Problem
      • 8.2.3 Temporal Regularization
    • 8.3 RESEARCH PROBLEMS AND OPPORTUNITIES
    • 8.4 Suggested Reading
  • Chapter 9 Electrical Impedance Tomography
    • 9.1 INTRODUCTION
    • 9.2 COMPARISON TO OTHER MODALITIES
    • 9.3 PRESENT STATUS OF EIT AND LIMITATIONS
    • 9.4 RESEARCH OPPORTUNITIES
    • 9.5 Suggested Reading
  • Chapter 10 Magnetic Source Imaging
    • 10.1 INTRODUCTION
    • 10.2 MATHEMATICAL CONSIDERATIONS
    • 10.3 SOURCE MODELS
    • 10.4 RESOLUTION
    • 10.5 SUMMARY
    • 10.6 RESEARCH OPPORTUNITIES
    • 10.7 Suggested Reading
  • Chapter 11 Medical Optical Imaging
    • 11.1 INTRODUCTION
    • 11.2 DATA ACQUISITION STRATEGIES
    • 11.3 COMPARISONS WITH OTHER IMAGING MODALITIES
    • 11.4 POSSIBLE APPLICATIONS OF OPTICAL TOMOGRAPHY
    • 11.5 RESEARCH OPPORTUNITIES
    • 11.6 Suggested Reading
  • Chapter 12 Image-Guided Minimally Invasive Diagnostic and Therapeutic Interventional Procedures
    • 12.1 THERAPEUTIC INTERVENTION EXPERIENCE WITH DIFFERENT IMAGING MODALITIES
      • 12.1.1 X-Ray Imaging
      • 12.1.2 Computed Tomography
      • 12.1.3 Ultrasound
      • 12.1.4 Endoscopy
      • 12.1.5 Magnetic Resonance Imaging
    • 12.2 THE ROLES OF IMAGING IN THERAPY
      • 12.2.1 Planning
      • 12.2.2 Guidance
      • 12.2.3 Monitoring and Localization
      • 12.2.4 Control
    • 12.3 THERMAL SURGERY
      • 12.3.1 Interstitial Laser Therapy
      • 12.3.2 Cryotherapy
      • 12.3.3 Focused Ultrasound
    • 12.4 RESEARCH AND DEVELOPMENT OPPORTUNITIES
      • Planning
        • Guidance and Localization
          • Monitoring
          • Control
          • Instruments and Systems
    • 12.5 Suggested Reading
  • Chapter 13 Frontiers of Image Processing for Medicine
    • 13.1 IMAGE SEGMENTATION
    • 13.2 COMPUTATIONAL ANATOMY
    • 13.3 REGISTRATION OF MULTIMODALITY IMAGES
    • 13.4 SYNTHESIS OF PARAMETRIC IMAGES
    • 13.5 DATA VISUALIZATION
    • 13.6 TREATMENT PLANNING
    • 13.7 RESEARCH OPPORTUNITIES
    • 13.8 Suggested Reading
  • Chapter 14 A Cross-Cutting Look at the Mathematics of Emerging Biomedical Imaging
    • 14.1 MATHEMATICAL MODELS FOR PARTICULAR IMAGING MODALITIES
      • 14.1.1 Transmission Computed Tomography
      • 14.1.2 Emission Computed Tomography
      • 14.1.3 Ultrasound Computed Tomography
      • 14.1.4 Optical Tomography
      • 14.1.5 Electrical Impedance Tomography
      • 14.1.6 Magnetic Resonance Imaging
      • 14.1.7 Vector Tomography
      • 14.1.8 Tensor Tomography
      • 14.1.9 Magnetic Source Imaging
      • 14.1.10 Electrical Source Imaging
    • 14.2 FORWARD PROBLEMS
    • 14.3 INVERSE PROBLEMS
    • 14.4 ILL-POSEDNESS AND REGULARIZATION
      • 14.4.1 The Tikhonov-Phillips Method
      • 14.4.2 The Truncated Singular Value Decomposition
      • 14.4.3 Iterative Methods
      • 14.4.4 Regularization by Discretization
      • 14.4.5 Maximum Entropy
    • 14.5 SAMPLING
      • 14.5.1 Sampling in Real Space
      • 14.5.2 Sampling in Fourier Space
    • 14.6 PRIORS AND SIDE INFORMATION
    • 14.7 RESEARCH OPPORTUNITIES
    • 14.8 Suggested Reading
  • Index

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