Quantitative Biomedical Optics

Transcription

1 Quantitative Biomedical Optics Theory, Methods, and Applications Irving J. Bigio Boston University Sergio Fantini Tufts University -^ CAMBRIDGE UNIVERSITY PRESS

2 Contents Preface pag 1 Nomenclature l. I Describing the optical radiation field and its interactions with tissue l.2 Quantities describing the optical radiation field l.3 Quantities describing the optical properties of tissue and the interactions between the radiation field and tissue 2 Overview of tissue optical properties 2.1 Absorption and scattering coefficients 2.2 Survey of the primary chromophores in tissue 2.3 Non-chromophore absorbers Lipids Water, water, everywhere - and vibrational modes 2.4 The scattering properties of tissue Sources of scattering in tissue The scattering cross section and its relation to the scattering coefficient The anisotropy factor in tissue The reduced scattering coefficient in tissue 2.5 The Beer-Lambert law to describe absorption and weak scattering Appendix 2. A: Tabulated near-infrared spectra of HbO. Hb, cytochrome c oxidase, water and lipids 3 Introduction to biomedical statistics for diagnostic applications 3.1 The importance of proper statistics 3.2 Assessing the efficacy of dichotomous diagnostic tests Sensitivity, specificity, positive and negative predictive values 3.3 Test accuracy

3 3.4 Dichotomous decisions based on a continuous variable The ROC curve Required sample size and reliability of a test Example 1: testing sensitivity and specificity with pre-diagnosed sets Example 2: determining Se and Sp for a population sample with an expected prevalence Example 3: measuring the prevalence of a disease in a population Prospective vs. retrospective studies 78 General concepts of tissue spectroscopy and instrumentation Atomic spectroscopy Molecular spectroscopy: from diatomic molecules to biological molecules Electronic transitions - the issue of electron spin Fluorescence and phosphorescence Vibrational transitions: IR absorption spectroscopy and Raman spectroscopy Scattering by particles: elastic-scattering spectroscopy Relative merits of different types of tissue spectroscopy Fluorescence measurements and spectroscopy Infrared-absorption spectroscopy Raman spectroscopy Elastic-scattering spectroscopy and diffuse reflectance spectroscopy Introduction to general principles of spectroscopic measurements and instrumentation What is light? Anatomy of a spectrometer Dispersive element: prisms Dispersive element: diffraction gratings Exemplary configuration of a grating spectrometer Basics of optical fibers Numerical aperture of a fiber Basic fiber types Single-mode vs. multimode fibers Graded-index fibers Imaging fiber bundles Photonic-crystal fibers (PCF) 114

4 5 Autofluorescence spectroscopy and reporter fluorescence Fluorescence emission relevant to measurements in biological systems I Quantum yield Excitation-emission matrix Fluorescence intensity vs. fluorophore concentration Fluorescence lifetime Endogenous fluorescent molecules Exogenous "reporter" fluorophores Exogenous fluorophores in common clinical use: fluorescein and indocyanine green Drugs that are fluorescent Fluorescent biomolecular probes Nanoparticles as fluorescent biomarkers: quantum dots Molecular beacon probes based on oligonucleotide hybridization Instrumentation for fluorescence sensing and imaging Instrumentation for point measurements Instrumentation for fluorescence imaging Fluorescence lifetime spectroscopy Measurement of multiple fluorophores Example applications of fluorescence lifetime measurements Polarization and anisotropy of fluorescence emission Combining polarization and time-dependent fluorescence measurements Sensing molecular dynamics with fluorescent biomarkers: FRET Raman and infrared spectroscopy of vibrational modes Vibrational modes in biological molecules Frequencies of some biomolecular vibrational modes The complexity of biological molecules and feature assignment Semi-classical derivation of Raman scattering Wavelength dependence of the scattered field from molecules A little bit less simplification IR-absorption spectroscopy Is it IR-active, Raman-active or both? Homonuclear diatomic molecules Heteronuclear diatomic molecules Linear triatomic molecules Nonlinear triatomic molecules 172

5 6.5 Isotopic shifts Enhancements of Raman scattering Resonance-Raman scattering (RRS) Surface-enhanced Raman scattering (SERS) Coherent anti-stokes Raman spectroscopy (CARS) Instrumentation for IR-absorption and Raman spectroscopy Fourier-transform IR (FTIR) spectroscopy Basic instrumentation for Raman spectroscopy of biological samples Instrumentation invoking fiberoptic probes Data treatment for Raman spectra of biological media Examples of pre-clinicai and clinical applications of Raman spectroscopy 181 Elastic and quasi-elastic scattering from cells and small structures Sources of light scattering in biological systems Scattering by a single particle: coordinates and formalism I9l Rayleigh scattering Polarized Rayleigh scattering Mie theory Exact and numerical calculations of scattering by single particles of arbitrary shape Single-scattering methods to study cell properties: instrumentation and applications Measuring the scattering phase function: methods and devices Flow cytometry Measurements of single scattering events in tissue in a transmission geometry Measurement of singly scattered photons in a backscattering geometry Scattering from cell monolayers Selection of singly backscattered light from bulk tissue Angle-resolved low-coherence interferometry (alci) Scattering from particles in motion Doppler shifts and laser Doppler velocimetry Dynamic light scattering 222

6 Contents 8 Diffuse reflectance spectroscopy at small source-detector separations Practical optical geometries Monte Carlo simulations: where have the collected photons been? Representing tissue scattering properties in the partially diffuse regime Importance of the phase function for short source-detector separations - phase functions for multiple scattering Higher moments of the phase function The Henyey-Greenstein phase function The modified Henyey-Greenstein phase function Mie-theory phase function for multiple scattering Representing tissue absorption properties in the partially diffuse regime Correction for the vessel-packing effect Empirical models for the diffuse reflectance A representative empirical model Lookup tables The inverse problem: extracting tissue properties Varying the source-detector separation Measurements at multiple wavelengths Special distances for diffuse reflectance measurements: "isosbestic" points Source-detector distances for which the average photon pathlength is insensitive to the tissue reduced scattering coefficient Source-detector separations for which the reflectance is insensitive to the tissue reduced scattering coefficient Source-detector separation for which the reflectance is insensitive to the phase function parameter Typical instrumentation for diffuse reflectance spectroscopy Common components for DRS Calibration of system response Tissue "phantoms" for validation Examples of clinical and pre-clinical applications of DRS with incoherent light Elastic-scattering spectroscopy for detection of dysplasia Measurement of drug concentrations in tissue Quasi-coherent variants of diffuse reflectance spectroscopy Diffuse correlation spectroscopy in the short source-detector distance regime 265

7 Contents Laser speckle contrast imaging Low-coherence enhanced backscattering Transport theory and the diffusion equation The Boltzmann transport equation Expansion of the Boltzmann transport equation into spherical harmonics The P N approximation The Pi approximation The diffusion equation Boundary conditions Infinite medium Boundary between a scattering medium and a non-scattering medium: mismatched refractive index conditions Boundary between a scattering medium and a non-scattering medium: matched refractive index conditions Boundary between two scattering media The microscopic Beer-Lambert law The fluorescence diffusion equation The correlation diffusion equation 308 Appendix 9. A: Low-order spherical harmonics 309 Appendix 9.B: The dependence of the diffusion coefficient on absorption Continuous-wave methods for tissue spectroscopy The objective of tissue spectroscopy CW tissue spectroscopy with diffusion theory CW solution for an infinite, homogeneous medium Determination of the tissue optical properties with CW diffusion theory The modified Beer-Lambert law Continuous-wave diffuse reflectance Total diffuse reflectance vs. single-distance diffuse reflectance Diffuse reflectance with transport theory Two-flux Kubelka-Munk theory Diffusion theory for single-distance reflectance and total diffuse reflectance Spatially modulated spectroscopy Monte Carlo simulations: limits of validity of continuous-wave diffusion theory 340 Appendix 10.A: The Dirac delta 342

8 11 Time-domain methods for tissue spectroscopy in the diffusion regime 348 l l.l Diffusion theory: time-domain solution for an infinite, homogeneous medium Moments of the photon time-of-flight distribution Time-domain diffuse reflectance Limits of validity of time-domain diffusion theory Frequency-domain methods for tissue spectroscopy in the diffusion regime Basic concepts of frequency-domain tissue spectroscopy Diffusion theory: frequency-domain solution for an infinite, homogeneous medium Absolute measurements of (JL and JL' V with frequency-domain spectroscopy Photon-density waves The wavelength of photon-density waves The phase velocity of photon-density waves The attenuation length of photon-density waves The frequency domain as the Fourier transform of the time domain Frequency-domain diffuse reflectance Limits of validity of frequency-domain diffusion theory 385 Appendix 12. A: Fourier integrals of time-domain Green's functions A. 1 Frequency-domain fluence rate in an infinite medium A.2 Frequency-domain diffuse reflectance from a semi-infinite medium Instrumentation and experimental methods for diffuse tissue spectroscopy Light sources Relevant properties of light sources for diffuse optical spectroscopy Spectral distribution of illumination Pulsed and modulated sources Maximum permissible levels of optical exposure of the skin Methods for delivering and collecting light Optical fibers Direct illumination and light collection Optical detectors General description of optical detectors Spectral sensitivity Linearity and dynamic range 401

9 ESI Contents Temporal response Responsivity and sensitivity Shot noise Experimental approaches for time-resolved spectroscopy Time domain Streak camera Time-correlated single-photon counting Time gating Frequency domain Homodyne detection Heterodyne detection Diffuse optical imaging and tomography Collective photon paths in a scattering medium Sensitivity function of a given optical signal to a specific optical property The CW region of sensitivity Infinite geometry Semi-infinite geometry Backprojection methods Diffuse optical imaging with time-gated approaches Spatial frequency-domain imaging Diffuse optical tomography: the forward problem Deterministic forward models: transport theory and diffusion theory Analytical solutions Finite-difference method (FDM) Finite-element method (FEM) Stochastic models and methods: Monte Carlo simulations and random walk theory Diffuse optical tomography: the inverse problem Linear methods based on perturbation theory Linearization for absorption and diffusion perturbations The CW sensitivity function for absorption perturbations in infinite and semi-infinite media Discretization of the problem into a linear system of equations Nonlinear, iterative methods based on calculation of the Jacobian Regularization of the inverse imaging problem Contrast and resolution in diffuse optical imaging 453

10 Contents Optical properties contrast Image contrast Spatial resolution 456 Appendix 14. A: Fluence rate Green's functions for a semi-infinite medium In vivo applications of diffuse optical spectroscopy and imaging Oximetry The oxygen dissociation curve of hemoglobin Pulse oximetry Tissue oximetry Oxygen saturation of hemoglobin in blood-perfused tissue Redox state of cytochrome c oxidase Skeletal muscle studies The oxygen dissociation curve of myoglobin Blood volume, blood flow, and oxygen consumption in skeletal muscle NIRS measurements of muscle metabolism during exercise Confounding factors in optical studies of skeletal muscle Functional brain investigations Effects of brain activation on hemoglobin and oxidized cytochrome concentrations Modeling the hemoglobin concentration dependence on CBV, CBF, and CMR Diffuse correlation spectroscopy (DCS) to measure cerebral blood flow Optical imaging of intrinsic signals (OIS): high-resolution brain mapping Functional near-infrared imaging (fniri): noninvasive brain mapping Optical mammography Small-animal imaging Prospects of diffuse optics for biomedical applications Combining light and ultrasound: acousto-optics and opto-acoustics Basic concepts of ultrasound imaging The nature of ultrasound The source of contrast in ultrasound imaging Ultrasound transducers Spatial resolution in ultrasound imaging 5 17

11 16.2 Acousto-optic spectroscopy and imaging by ultrasonic tagging of light Mechanisms of ultrasonic modulation of light intensity Experimental methods to detect ultrasonically tagged light Applications of ultrasonically tagged light Photoacoustic imaging Generation of ultrasound by pulsed illumination Instrumentation for photoacoustic imaging Photoacoustic tomography and microscopy The range of penetration depths afforded by photoacoustic imaging Photoacoustic tomography (PAT) Photoacoustic microscopy (PAM) Applications of photoacoustic imaging Imaging of tissue vascularization and microvasculature Hemoglobin saturation and blood flow Other applications 538 Modern optical microscopy for biomedical applications Basic elements and theory of a classical microscope Magnification Resolving power and the point spread function The optical transfer function Enhancement of resolution with immersion objective lens Microscopic imaging based on phase contrast (PC) and differential interference contrast (DIC) Phase contrast imaging with spatially coherent illumination Phase contrast imaging with incoherent illumination Applications of phase contrast and DIC microscopy Optical sectioning: confocal microscopy Basic design of a confocal microscope Axial resolution of a confocal microscope Application example of in vivo confocal microscopy Nonlinear optical microscopy Multi-photon excitation fluorescence microscopy Harmonic generation microscopy Phase shifts and radiation patterns Symmetry of the sample and enabled applications Super-resolution microscopy 574

12 lfflijj ffijlüb i* fli Contents Direct super-resolution: near-field scanning optical microscopy (NSOM) Point-source localization techniques for super-resolution Stimulated emission depletion (STED) microscopy Stochastic methods of super-resolution 18 Optical coherence tomography 18.1 The coherence length of light Coherence length of a short laser pulse Coherence length of a long-pulse or continuous light source 18.2 Time-domain optical coherence tomography Sources of contrast and basics of OCT Detection of the TD-OCT signal Scanning of TD-OCT to achieve an image Maximum sectioning depth and transverse resolution 18.3 Frequency-domain optical coherence tomography Spectral-domain OCT Swept-source OCT The SNR advantage of FD-OCT 18.4 Doppler OCT 18.5 Instrumentation for OCT Optical components Light sources and detectors Transverse scanning 18.6 Speckle in OCT images 18.7 A sampling of OCT applications 19 Optical tweezers and laser-tissue interactions 19.1 Optical tweezers Forces resulting from radiation pressure Trapping force for particles larger than the wavelength Trapping of particles much smaller than the wavelength Trapping of particles similar in size to the wavelength Generic instrumentation for optical tweezers Calibration of trapping force 19.2 A sampling of applications of optical tweezers 19.3 Sub-thermal, thermal, and ablative applications of lasers Sub-thermal irradiation Non-ablative thermal effects Laser tissue welding Interstitial laser thermotherapy Tissue ablation and microsurgery

13 Contents Laser-assisted in vitro fertilization Laser refractive surgery Some cosmetic applications in dermatology 637 Answers to selected problems identified by * 645 Table of symbols 649 Table of acronyms 654 Index 659