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University of Cyprus Biomedical Imaging and Applied Optics Tissue Optical Properties Introduction • Interaction between Light and Tissue • • • • • Reflection Refraction Absorption Fluorescence Scattering Light Source Optical Signal Tissue • Depends on • Constituents of tissue • Optical properties of tissue • Propagation of light 2 Absorption • Extraction of energy from light by a molecular species • Diagnostic applications: Transitions between two energy levels of a molecule that are well defined at specific p wavelengths could serve as spectral fingerprint of the molecule • Various types of Chromophores (light absorbers) in Tissue • Wavelength-dependent absorption • Tumor detection and other physiological assessments (e.g. pulseo oximetry) et y) • Therapeutic applications: Absorption of energy is the primary mechanism that allows light g form a source (laser) ( ) to produce p physical effects on tissue for treatment purpose • Lasik (Laser Assisted in situ Keratomileusis) Eye Surgery, Tatoo Removal, PDT 3 Absorption • Absorption occurs when the photon frequency matches the frequency associated with the molecule molecule’s s energy transition ‘frequency’ • Electrons absorb the energy of the light and transform it into vibrational motion • The Th absorption b ti off a photon h t results lt in: i • quantized change in charge separation • quantized excitation of vibrational modes • Electrons interact with neighboring atoms Æ convert vibrational energy into thermal energy 4 • Each electronic energy gy levels is associated with many vibrational energy levels • Absorption of UV and visible i ibl light li ht promotes t transition between electronic energy levels Potentia al Energy Absorption Vibrational Energy Level S1 Electronic E Energy Level • Absorption of infrared light promotes transitions between vibrational energy gy levels 5 S0 Absorption • Absorption p Cross-section,, σ [m2] • Consider a chromophore id li d as a sphere idealized h with ith a particular geometrical size. • Consider that this sphere p blocks incident light and casts a shadow, which constitutes absorption. absorption • The size of absorption shadow = absorption cross-section • Qa: absorption efficiency σ a = Qa ⋅ A 6 Absorption Pabs = Ioσa Pin =IoA Pout = Io(A-σa) Outgoing Beam Incident Beam Area =A - Area = σa = Pout = Io(A-σa) area = A - σa Pabs σa = Io 7 Absorption • Assumptions • Cross section is independent of relative orientation of the impinging light and absorber uniform distribution of Na (molecules/cm3) identical absorbing particles • Absorption Coefficient, ma [1/m] μa = N a ⋅ σ a • Absorption p cross-sectional area p per unit volume of medium • Absorption mean free path, la [m] la = 1 μa • Represents the average distance a photon travels before being absorbed 8 Absorption • Transmission and Absorbance ((macroscopic view)) • Transmission I T= Io • Absorbance (attenuation, or optical density) ⎛ Io ⎞ A = − log(T ) = log ⎜ ⎟ ⎝ I ⎠ 9 Absorption • Lambert – Beer Law: • The linear relationship between absorbance and concentration of an absorbing g species. p • Relates μα, transmission, and absorbance I = Ioe − μa ⋅b μa = N a ⋅ σ a Pabs σa = IO σ= absorption cross-sectional area [cm2] IO = The intensity entering the sample at z = 0 [w/cm2] I = The intensity of light leaving the sample [w/cm2] b = pathlength traveled in the sample [cm] 10 Absorption Absorbers in Tissue NIR • NIR • Hemoglobin • Lipids • Water VISIBLE UV • UV-VIS • • • • • • DNA Hemoglobin Lipids Structural protein* protein Electron carriers* Amino acids* * Absorbers that fluoresce when excited in the UV-VIS 11 Absorption UV Absorption • Protein Protein, amino acid, acid fatty acid and DNA absorption dominate UV absorption • Protein • Dominant ‘non-water’ constituent of all soft tissue, ~ 30% • Absorption properties determined by peptide bonds and amino acid residues • Peptide excitation about λ = 190 nm • Amino acids absorption at λ = 210 - 220 nm and 260 – 280 nm • DNA Amino Acid Peptide • Absorbs radiation for λ ≤ 320 nm • Large water absorption λ< 180 nm 12 Absorption Infrared Absorption • Protein IR absorption peaks at 6.1, 6.45, and 8.3 μm due to amide excitation • Absorption depth ≤ 10 μm in λ = 6-7 μm region • Water absorption peak at 0.96, 1.44, 1.95, 2.94 and 6.1 μm • Absorption depth • ~ 500 mm at λ = 800 nm • <1 μm at λ=2.94 μm • ≤ 20 μm throughout λ ≥ 6 μm 13 Extinction Coe eff (1/cm M) Absorption 10 6 10 5 10 4 Main Absorbers at visible and NIR ¾ Hemoglobin ¾ Lipid p Hb 10 3 10 2 Hemoglobin HbO2 400 500 600 700 800 900 WAVELENGTH (NM) 1000 Each hemoglobin has 4 heme (Fe2+) sites to bind O2 • Responsible for oxygen transport •HbO2 and Hb • oxygen saturation is an indicator of oxygen delivery and utilization as wellll as metabolic b li activity i i • 14 Hemoglobin • Responsible for oxygen transport • HbO2 and Hb • oxygen saturation is an indicator of o gen delivery oxygen deli er and utilization tili ation as well ell as metabolic activity • Deoxyhemoglobin has lower absorption than oxyhemoglobin in the blue and green • Bright red arterial blood • Bluish venous blood Ex xtinction Coe eff (1/cm M) Absorption 10 6 10 5 10 4 Hb 10 3 HbO2 10 2 400 500 600 700 800 900 WAVELENGTH (NM) • Absorption peaks for HbO2 • 418, 542, 577, and 925 nm • Absorption peaks for Hb • 550, 758, 910 nm • Isosbestic points • 547, 569, 586, and 798 nm 15 1000 Absorption Lipid (Fat) • Monitoring of physiological changes in female breast tissue • Tissue layer model HEMOGLO OBIN (1/mm mM M) • Site-specific measurements of body composition 3.0 0.06 Water 25 2.5 0.04 2.0 HB 0.03 1.5 0.02 1.0 0.5 0.05 Lipid HbO2 0.01 0.00 0.0 0 0 600 700 800 900 1000 WAVELENGTH (nm) 16 WATER & FA AT (1/ mm mM) • Important energy store in the body Scattering • Change g of direction of propagation p p g and/or energy gy of light by a molecular species • Diagnostic applications: Scattering depends on the size, morphology, and structure of the components in tissues (e.g. lipid membrane, collagen fibers, nuclei). l i) • Variations in these components due to disease would affect scattering properties properties, thus providing a means for diagnostic purpose • Therapeutic applications: Scattering signals can be used to determine optimal light dosimetry and provide useful feedback during p g therapy py 17 Scattering Purely absorbing With Scattering Photon pathlength = L Photon pathlength >> L L Lambert- Beer Law does not apply here!!! Need to calculate true pathlength of light 18 Scattering • Why is the sky blue, clouds white and sunsets red? white, • Blue skies are produced due to scattering at shorter wavelengths • Visible light (violet & blue) are selectively l ti l scattered tt d b by O2 and d N2 – much smaller than wavelengths of the light • violet and blue light has been g scattered over and over again • When light encounters larger particles (cloud, fog), Mie scattering occurs • Mie scattering is not wavelength dependent – appears white • Cigarette smoke, too • At sunset • The light must travel over a longer path in the atmosphere • Blue/green is scattered away and only red/orange (scattered less) reaches your eyes 19 Scattering • Mechanism for Light g Scattering g • Light scattering arises from the presence of heterogeneities within a bulk medium • Physical inclusions • Fluctuations in dielectric constant from random thermal motion • Heterogeneity/fluctuations Æ non-uniform temporal/spatial distribution of refractive index in the medium • Passage of an incident EM wave sets electric charges into oscillatory motion and can excite vibrational modes • Scattered light is re-radiated by acceleration of these charges and/or relaxation of vibrational transition 20 Scattering • Elastic scattering: g no energy gy change g • Frequency of the scattered wave = frequency of incident wave • Probes static structure of material • Rayleigh and Mie scattering • Inelastic scattering: energy change • Frequency q y of the scattered wave ≠ frequency q y of incident wave • Internal energy levels of atoms and molecules are excited • Probes vibrational bonds of the molecule • Raman scattering (stokes↓ and anti-stokes ↑) 21 Scattering Elastic Scattering • The light scattered by a system has interacted with the inhomogeneities g of the system y • Photons are mostly scattered by the structure whose size matches the wavelength • Principal parameters that affect scattering • • • • Wavelength, W l th λ Relative refractive index Particle radius Sh Shape and d orientation i t ti • Two types of scattering: y g and Mie Rayleigh 22 Scattering Rayleigh y g Scattering g Light Source Detector • Scattering from very small particles Æ ≤ λ/10 • Rayleigh scattering is inversely related to fourth power of the wavelength of the incident light 1 I∝ 4 λ λ is the wavelength of the incident light I is the intensity of the scattered light 23 Scattering Mie Scattering g • For scattering of particles comparable or larger than the wavelength, Mie scattering predominates • Because of the relative particle size size, Mie scattering is not strongly wavelength dependent • Forward directional scattering 24 Scattering Pin =IoA Pscatt = Ioσs Pout = Io(A-σs) Incident Beam Outgoing Beam • Scattering Cross Section, σscatt [m2] • ‘area’ of an index-matched, perfectly absorbing disc necessary to produce • The measured reduction of light σscatt = Qs*As • Qs: Scattering efficiency (calculated by Mie theory); defined as the ratio of the scattering section to the projected area of the particle on the detector • As: Area of Scatterer [m2] 25 Scattering • Scattering g Coefficient, μs [[1/m]] • μs =Nsσs , • Ns = the number density of scatterers • σs = scattering tt i efficiency ffi i • Cross-sectional area for scattering per unit volume of medium • Scattering Mean Free Path Path, ls • Average distance a photon travels between scattering events 1 ls = μs 26 Scattering • Anisotropy, g dΩ scattered • Imagine that a photon is photon S’ scattered by a particle so hv that its trajectory is Scatterer d fl t d b deflected by an angle, l θ Scattering • Then, component of a new hv Angle (θ) S trajectory aligned forward Incidenet Photon direction is cos(θ) cos (θ) Photon • Anisotropy is a measure of trajectory forward direction retained Scattering after a single scattering event event, < cos(θ)> totally y backward bac a d scattering scatte g ⎧−11 tota ⎪ g = ⎨ 0 isotropic scattering ⎪ 1 totally forward scattering ⎩ Biological Tissues: 0.65 < g <0.95 27 Scattering • Reduced Scattering C ffi i t μs’’ [1/m] Coefficient, [1/ ] • μs’ incorporates the scattering g coefficient,, μ μs and the anisotropy factor, g μ s ' = (1 − g)μ s • μs’ can be regarded as an effective isotropic scattering coefficient that represent the h cumulative l i effect of several forwardscattering events • Special significant with respect to photon diffusion theory θ ≈ 26o g = cos θ = 0.90 μ s ' = (1 − g ) μ s = 0.10 0 10μ s mpf = 1/ μ s mpf ' = 1/ μ s ' = 10mpf = 10 / μ s 28 Scattering • Scattering g in Tissue • Tissue is composed of a ‘mixture’ of Rayleigh and Mie scattering 10 μm cells nuclei 1 μm Mie Scattering 0 1 μm 0.1 mitochondria lysosomes, vesicles striations in collagen fibrils macromolecular aggreagates Rayleigh Scattering 0.01 μm membranes 29 Scattering • Scattering in Tissue • Refractive R f ti index i d mismatch i t h between lipid and surrounding aqueous medium ed u • Soft tissues are dominated by lipid contents • Celluar membranes, membrane folds,, and membraneous structure • Mitochondria, ~ 1μm • Intracelluar organelle composed of many folded membrane, cristae • Collegan fibers, 2 ~ 3μm • Collegan fibrils, 0.3 μm • Periodic P i di fl fluctuation t ti iin collegan ll ultrastructure Æsource of Rayleigh scattering in UV and Visible range • Cells 30 Light Transport in Tissue • Scattering and absorption occur simultaneously and are wavelength dependent μt = μ s' + μa • Scattering monotonically decreases with wavelength • Absorption is large in UV, near visible, visible and IR • Absorption is low in red and NIR Æ Therapeutic window (600 ≤λ≤ 1000 nm) μs ' = A ⋅ λ −b μ s ' ~ λ −0.5 − λ −4 31 Light Transport in Tissue • Modeling of light transport in tissues are often governed by the relative magnitudes of optical p absorption p and scattering • μa >> μs’ : Lambert-Beer Law (λ ≤300nm;λ≥2000nm) • μs’ >> μa : Diffusion Approximation (600nm ~ 1000nm) • μs’ ~ μa : Equation of Radiative Transfer, Monte Carlo (300nm ~ 600 nm; 1000nm ~ 2000nm) • Use Monte Carlo, Transport Theory, y, or Diffusion Theory y Physical Pathlength: Optical Pathlength: Lp Lo Biological Tissue Lo/Lp = 4 or ↑ 32 Light Transport in Tissue • Modeling Photon Propagation μa, μs, g, phase function S “Stochastic” Description p 33 Light Transport in Tissue • Radiative Transport p Theory y • The direct application of EM theory is complicated • RTT deals with the transport of light energy • RTT ignores wave phenomena (polarization, interference) of EMT ds y State Radiative Transport p Equation q Steady Loss due to G G ∂L r , Ω scatt and abs = −(μ a + μ s )L( r , s ) ∂s G G + μ s p(s , s ') L( r , s ) d s ' + S( r , s ) ( ) Overall Energy balance at position r and direction s dA S ∫ 4π Source gain due to scattering term from s’ to s at r L = radiance [W/m2 sr], propagation of photon power P(s, s’) = phase (scattering) function s, s’ = directional vectors of photon propagation S’ 34 Light Transport in Tissue • Diffusion Approximation • Simplified S f form f off RTT at “diffusion “ ff limit” • μs’ >> μa • the number of photon undergoing the random walk is large G ∂j( r , t ) / ∂t << c(μ a + μ s ') = cμ t ' G 1 G 3 G G L( r , s , t ) ≈ φ( r , t ) + j( r , t ) ⋅ s 4π 4π • Isotropic source beyond 1/μt’ • ~10/μt’ (~ 1mm in biological tissue) • far f from f sources & boundaries • assume tissue is “macroscopically homogeneous” G 1 ∂φ ( r , t ) G G G G − ∇ ⋅ D(r )∇φ ( r ) − μaφ ( r , t ) = S ( r , t ) c ∂t G G G where D(r ) = 1/ 3[ μa (r ) + μ s (r )] 35 Tissue Optical Properties • Measurement Strategies g “Black Box” Optical Source ‘input’ TISSUE H(μa, (μ μ μs)) Detector ‘output’ p H: System Function • Goal: To find out H(μa, μs) • Requires Non-Static Non Static system Æ Perturbations in either optical source or tissue 36 Tissue Optical Properties Measurement Schemes • CW (Continuous Wave) Measurement • • • • Simplest p form of measurement Static, continuous wave input requires dynamic tissue property changes E.g. pulse oximetery • Time-Resolved Measurements • Temporal changes in optical sources • Time Domain Photon Migration (TDPM) • Frequency Domain Photon Migration (FDPM) • Spatially-Resolved Measurement • Spatial changes in optical path 37 attenuation μt-total Tissue Optical Properties arterial μt-oxy pulsatile venous (Hb-O2) μt-background ti tissue time μt = non-pulsatile ? • CW (continuous wave) • pulse l oximetry i t locks into pulse • healthy adult calibration accounts for tissue scatter (ms’) • typically t i ll att 2 wavelengths (660, 940 nm) μa + μs’ 38 Tissue Optical Properties • Time Domain Photon Migration (TDPM) • Impulse Function, δ Directly measure ma and ms from TPSF using Diffusion Equation • Complicated and expensive detection system • rather low SNR Temporal Point Spread Function (TPSF) 39 Tissue Optical Properties • Frequency Domain Photon Migration (FDPM) SOURCE TISSUE DETECTED stuff happens AMPLIT TUDE φ ACsrc AC SRC ACdet ACDET DCsrc DC SRC DC DCdet DET TIME φ ~ TIME M = AC/DC 40