What is Tissue Optics

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TISSUE OPTICS
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Outline

• What is Tissue Optics
• Absorption in Tissue
• Absorption Process and Parameters
• Typical absorbers in Tissue
• Scattering in Tissue
• Scattering Process and Parameters
• Typical scatterers in Tissue

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What is Tissue Optics?

• Definitions from dictionary
• Optics a science that deals with
• genesis and propagation of light
• changes that it undergoes and produces
• Tissue an aggregate of cells
• usually of a particular kind together with their
  intercellular substance that form one of the
  structural materials of a plant or an animal

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What is Tissue Optics?


Tissue Optics
Tissue
Optics
Investigating Principle
Subject of Interest
We are interested in

• Constituents of Tissue
• Optical Properties of Tissue
• Propagation of Light
• Interaction between Light and Tissue
• Diagnostic and Therapeutic Implications

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Is Tissue Optics Special?

• Three Major Components
• Optical Source Sun
• Medium - Atmosphere
• Detector Human Eyes

• Interaction between light and particles in
  atmosphere
• Absorption
• Scattering (Rayleigh Mie)

• Propagation of Light through Atmosphere

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Tissue Optics
Optical Signal
Light Source
Tissue
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Optical Signal from Tissue

• Large number of Biological Molecules
• Functional and Structural information
• Noninvasive
• Near real time

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Objectives of Tissue Optics

• Key Question How many photons per second will
  reach the tissue chromophore and be absorbed?
• Absorption is important because it transfers
  energy to tissue
• 1. To find the light energy per unit area per
  unit time that reaches a target chromophore at
  some position
• 2. To develop methods by the absorption and
  scattering properties of tissue can be measured

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Ultimate Goal of Tissue Optics

• Assess all optical properties noninvasive in
  living tissue (in vivo)
• Difficulties
• Tissue is a complicated heterogeneous system
• Requires noninvasive in vivo information for
  meaningful diagnostic and therapeutic purposes

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Property of Light

• Classical (wave) Description
• Light is a transverse EM wave with wavelength
  100nm lt l lt10mm
• Quantum (particle) Description
• Localized, massless qunata of energy ? photon
• Ephnhn/l, h 6.626 X 10-34 Js

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Electromagnetic Spectrum
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Light-Matter Interaction

• Governed by energy states of the molecules
• Ground state is the lowest energy state
• Excited states are states of higher energy
• Emol EtranEespinEnuc spinErotEvibEelec
• tran motion of molecules center of mass
• e-/nuc spin nuclear and electron spin
• rot rotation of molecules about its center of
  mass
• vib vibration of the constituent atoms
• elec spatial electronic configuration within the
  molecule
• EtranltEespinltEnuc spinltErotltEvibltEelec

0.1 ev/molec
1 -10 ev/molec
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Type of Optical Signal
Electronic Transition
Vibrational Transition
Elastic Scattering
Absorption
Fluorescence
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Optical Processes (Analogy)

• Absorption compatible relationship ?settle down
• Scattering incompatible relationship ?heck with
  this, leaves
• Fluorescence Very comfortable relationship ?
  off-springs

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ABSORPTION in TISSUE
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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 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. pulse-oximetry)
• Therapeutic applications Absorption of energy is
  the primary mechanism that allows light form a
  source (laser) to produce physical effects on
  tissue for treatment purpose
• Lasik (Laser Assisted in situ Keratomileusis) Eye
  Surgery, Tatoo Removal, PDT

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Mechanism of Absorption (resonance principle)

• When a light wave with that same natural
  frequency impinges upon an atom, then the
  electrons of that atom will be set into
  vibrational motion.
• Just like a tune fork!!!!!
• If a light wave of a given frequency strikes a
  material with electrons having the same
  vibrational frequencies, then those electrons
  will absorb the energy of the light wave and
  transform it into vibrational motion.
• During its vibrations, the electrons interacts
  with neighboring atoms in such a manner as to
  convert its vibrational energy into thermal
  energy. Subsequently, the light wave with that
  given frequency is absorbed by the object, never
  again to be released in the form of light.
• Similar to phonon in crystal lattice ?
  conduction of heat in insulators production of
  sound in solid

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Absorption (quantum view)

• Absorption occurs when the photon frequency
  matches the frequency associated with the
  molecules energy transition
• The absorption of a photon results in
• quantized change in charge separation
• quantized excitation of vibrational modes

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Absorption (quantum view)
Vibrational Energy Level
Electronic Energy Level

• Electronic energy levels vary with inter-nuclear
  distance within a molecular orbital
• Each electronic energy levels is associated with
  a manifold of vibrational energy
• Absorption of UV and visible light promotes
  transition between electronic energy levels
• Absorption of infrared light promotes transitions
  between vibrational energy levels

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Metrics for Absorption

• Absorption Cross-section, s m2
• Consider a chromophore idealized as a sphere with
  a particular geometrical size. Consider that this
  sphere blocks incident light and casts a shadow,
  which constitutes absorption.
• The size of absorption shadow absorption
  cross-section

Qa absorption efficiency
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Metrics for Absorption
Pabs Iosa
Pout Io(A-sa)
Pin IoA
Outgoing Beam
Incident Beam
Area A
Area sa
-

Pout Io(A-sa)
area A - sa
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Metrics for Absorption

• Assumptions
• Cross section is independent of relative
  orientation of the impinging light and absorber
• uniform distribution of identical absorbing
  particles
• Absorption Coefficient, ma 1/m
• Absorption cross-sectional area per unit volume
  of medium
• Absorption mean free path, la m
• Represents the average distance a photon travels
  before being absorbed

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Absorption Fundamentals

• Transmission and Absorbance (macroscopic view)
• Transmission
• Absorbance (attenuation, or optical density)

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Connection between T/A and ma

• Now, absorbing medium is characterized by ma,
  transmission, and absorbance. Are they related?
• Lambert Beer Law the linear relationship
  between absorbance and concentration of an
  absorbing species.

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Lambert-Beer Law

• absorption cross-sectional area
  cm2
• IO The intensity entering the sample at z 0
  w/cm2
• I The intensity of light leaving the sample
• IZ The intensity entering the infinitesimal
  slab at Z
• dI the intensity absorbed in the slab

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Lambert-Beer Law
Total opaque area on the slab due to absorbers
Number of absorbers in the slab volume
Loss of intensity
Fraction of photons absorbed
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Lambert-Beer Law
Since
and
e, Molar Extinction Coefficient cm-1M-1 Measure
of Absorbing Power of species
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Lambert-Beer Law
ma 2.303ec
(1) By measuring Transmission or Absorbance for
given M, we can obtain e ? usually ex
vivo (2) With knowledge of e, if we can measure
ma in vivo, we can quantify concentration of
chromophores
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Absorbers in Tissue

• NIR
• Hemoglobin
• Lipids
• Water

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UV Absorption

• Protein, amino acid, fatty acid and DNA
  absorption dominate UV absorption
• Protein is dominant non-water constituent of
  all soft tissue, 30
• Absorption properties determined by peptide bonds
  and amino acid residues
• Peptide excitation about l 190 nm
• amino acids absorption at l 210 - 220 nm and
  260 280 nm
• DNA absorbs radiation for l 320 nm

Amino Acid
Peptide

• Large water absorption l lt 180 nm

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Infrared Absorption

• Protein IR absorption peaks at 6.1, 6.45, and 8.3
  mm due to amide excitation
• Absorption depth 10 mm in l 6 - 7 mm region
• Water absorption peak at 0.96, 1.44, 1.95, 2.94
  and 6.1mm
• Absorption depth
• 500 mm at l 800 nm, lt1 mm at l2.94 mm
• 20 mm throughout l 6 mm

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Respiratory Enzymes NADH, FAD, Cytochrome a3

• These enzymes play a key role in providing the
  proton-motive force necessary for oxidative
  phosphorylation
• If tissue is oxygen starved, NADH and FADH2
  will be enhanced
• Reduced NADH conc. is indicative of high oxygen
  consumption and is characteristic of tumor tissue

NADH
FAD

• NADH (FAD) strongly fluoresce while NAD (FADH2)
  does not
• Cytochrome a3 has a prominent absorption peak at
  l 840 nm

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Visible and NIR Absorption

• Main Absorbers at visible and NIR
• Hemoglobin
• Lipid

• Hemoglobin
• 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 well as metabolic
  activity

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Hemoglobin

• Deoxyhemoglobin has lower absorption than
  oxyhemoglobin in the blue and green
• Bright red arterial blood (blushing)
• Bluish venous blood (cold pale face)
• 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

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Lipid (Fat)

• Important energy store in the body
• Site-specific measurements of body composition
• Monitoring of physiological changes in female
  breast tissue
• Tissue layer model

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Summary - Absorber
UV
Visible NIR
IR

• Protein
• Amino acid
• Fatty Acid
• Peptide
• DNA
• NADH
• FAD
• Water

• Water
• Protein
• Glucose

• Hemoglobin
• Lipid
• Cytochrome a3

Therapeutic Window 600 nm 1000 nm
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SCATTERING in TISSUE
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Scattering in Tissue

• Mother of all Confusion in tissue optics !!!
• Much more complicated than absorption
• Light is hardly observed from the source, but
  reaches our eyes indirectly through scattering
• Inhomogeneity causes scattering cloud, raindrop,
  etc
• Elastic (Rayleigh, Mie) or inelastic (raman)

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Scattering in Tissue

• Diagnostic applications Scattering depends on
  the size, morphology, and structure of the
  components in tissues (e.g. lipid membrane,
  collagen fibers, nuclei). Variations in these
  components due to disease would affect scattering
  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 therapy

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Scattering - Example
Purely absorbing
With Scattering
Photon pathlength gtgt L
Photon pathlength L
L
Lambert- Beer Law does not apply here!!! Need to
calculate true pathlength of light
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Lambert-Beer Law
Since
and
e, Molar Extinction Coefficient cm-1M-1 Measure
of Absorbing Power of species
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Scattering Blue sky revisited

• Blue skies are produced due to scattering at
  shorter wavelengths
• Visible light (violet blue) are selectively
  scattered by O2 and N2 much smaller than
  wavelengths of the light
• violet and blue light has been 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

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Mechanism for Light Scattering

• Light scattering arises from the presence of
  heterogeneities within a bulk medium
• Physical inclusions
• Fluctuations in dielectric constant from random
  thermal motion
• Heterogeneity/fluctuations result in 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

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Elastic vs. Inelastic Scattering

• Elastic scattering no energy change
• Frequency of the scattered wave frequency of
  incident wave
• Probes static structure of material
• Rayleigh and Mie scattering
• Inelastic scattering energy change
• Frequency of the scattered wave ? frequency of
  incident wave
• Internal energy levels of atoms and molecules are
  excited
• Probes vibrational bonds of the molecule
• Raman scattering (stokes? and anti-stokes ?)

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Elastic Scattering

• The light scattered by a system has interacted
  with the inhomogeneities of the system
• Photons are mostly scattered by the structure
  whose size matches the wavelength
• Principal parameters that affect scattering
• Wavelength, l
• Relative refractive index
• Particle radius
• Shape and orientation
• Two types of scattering Rayleigh and Mie

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Rayleigh Scattering
Light Source
Detector

• Scattering from very small particles ? l/10
• Rayleigh scattering is inversely related to
  fourth power of the
• wavelength of the incident light

l is the wavelength of the incident light I is
the intensity of the scattered light
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Mie Scattering

• For scattering of particles comparable or larger
  than the wavelength, Mie scattering predominates
• Because of the relative particle size, Mie
  scattering is not strongly wavelength dependent
• Forward directional scattering

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Scattering in Tissue (I)

• Tissue is composed of a mixture of Rayleigh and
  Mie scattering

Hierarchy of ultrastructure
cells
10 mm
nuclei
TiO2 0.2 2 mm
mitochondria
1 mm
lysosomes, vesicles
Mie Scattering
striations in collagen fibrils macromolecular
aggreagates
0.1 mm
Rayleigh Scattering
membranes
0.01 mm
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Source of Scattering in Tissue

• Refractive index mismatch between lipid and
  surrounding aqueous medium
• Soft tissues are dominated by lipid contents
• Celluar membranes, membrane folds, and
  membraneous structure
• Mitochondria, 1mm
• Intracelluar organelle composed of many folded
  membrane, cristae
• Collegan fibers, 2 3mm
• Collegan fibrils, 0.3 mm
• Periodic fluctuation in collegan ultrastructure
  ?source of Rayleigh scattering in UV and Visible
  range
• Cells

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Metrics for Optical Scattering
Pscatt Ioss
Pout Io(A-ss)
Pin IoA
Outgoing Beam
Incident Beam

• Scattering Cross Section, sscatt m2
• area of an index-matched, perfectly absorbing
  disc necessary to produce
• The measured reduction of light
• sscatt QsAs
• 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

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Metrics of Optical Scattering

• Scattering Coefficient, ms 1/m
• ms Nsss ,
• Ns the number density of scatterers
• ss scattering efficiency
• Cross-sectional area for scattering per unit
  volume of medium
• Scattering Mean Free Path, ls
• Average distance a photon travels between
  scattering events

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Anisotropy, g

• Imagine that a photon is scattered by a particle
  so that its trajectory is deflected by an angle,
  q
• Then, component of a new trajectory aligned
  forward direction is cos(q)
• Anisotropy is a measure of forward direction
  retained after a single scattering event, lt
  cos(q)gt

dW
scattered photon
S
hv
Scatterer
Scattering Angle (q)
hv
Incidenet Photon
S
cos (q)
Photon trajectory
Scattering event
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Anisotropy factor, g
totally backward scattering
isotropic scattering
totally forward scattering
Biological Tissues, 0.65 lt g lt0.95

• Reduced Scattering Coefficient, ms 1/m
• ms incorporates the scattering coefficient, ms
  and the anisotropy factor, g
• ms can be regarded as an effective isotropic
  scattering coefficient that represent the
  cumulative effect of several forward-scattering
  events
• Special significant with respect to photon
  diffusion theory

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Reduced Scattering Coefficient
Useful for description of photon propagation
in diffuse Regime
1 iso-scatt step 1/(1-g) aniso-scatt. steps
Each step involves isotropic scattering. Such a
description is equivalent to description of
photon movement using many small steps 1/µs that
each involve only a partial deflection angle
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Light Transport in Tissue

• Scattering and absorption occur simultaneously
  and are wavelength dependent
• Scattering monotonically decreases with
  wavelength ?
• Absorption is large in UV, near visible, and IR
• Absorption is low in red and NIR ?Therapeutic
  window (600 ? 1000 nm)

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Light Transport in Tissue

• Modeling of light transport in tissues are often
  governed by the relative magnitudes of optical
  absorption and scattering
• ma gtgt ms Lambert-Beer Law (l 300nml2000nm)
• ms gtgt ma Diffusion Approximation (600nm
  1000nm)
• ms ma Equation of Radiative Transfer, Monte
  Carlo (300nm 600 nm 1000nm 2000nm)

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Propagation of Photons through Tissue
Scattering and absorbing tissue

• Absorption Coefficient ma
• Scattering Coefficient ms
• Physical Pathlength Lp
• Optical Pathlength Lo

Biological Tissue Lo/Lp 4 or ?
Use Monte Carlo, Transport Theory, or Diffusion
Theory !!!!
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Modeling Photon Propagation
ma, ms, g, phase function S Stochastic
Description
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Radiative Transport Theory

• 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
Steady State Radiative Transport Equation
Loss due to scatt and abs
dA
S
Overall Energy balance at position r and
direction s
Source term
gain due to scattering from s to s at r
S
L radiance W/m2 sr, propagation of photon
power P(s, s) phase (scattering) function s,
s directional vectors of photon propagation
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Diffusion Approximation

• Simplified form of RTT at diffusion limit
• ms gtgt ma
• the number of photon undergoing the random walk
  is large
• 
  ( 200 GHz)
• Isotropic source beyond 1/mt
• 10/mt ( 1mm in biological tissue)
• far from sources boundaries
• assume tissue is macroscopically homogeneous

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Measurement Strategies
Black Box
TISSUE H(ma, ms)
Detector output
Optical Source input
H System Function

• Goal To find out H(ma, ms)
• Requires Non-Static system ? Perturbations in
  either optical source or tissue

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Measurement Schemes

• CW (Continuous Wave) Measurement
• Simplest form of measurement
• Static, continuous wave input
• requires dynamic tissue property changes
• 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

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CW (continuous wave)
mt-total
arterial
venous (Hb-O2)
tissue
mt
ms
ma


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CW Example, pulse-oximetry
pulse oximetry locks into pulse
healthy adult calibration accounts for tissue
scatter (ms)
typically at 2 wavelengths (660, 940 nm)
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TDPM (I)
Impulse Function, d
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TDPM (II)

• Directly measure ma and ms from TPSF using
  Diffusion Equation
• Complicated and expensive detection system
• rather low SNR

Temporal Point Spread Function (TPSF)
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FDPM
SOURCE
DETECTED
TISSUE
stuff happens
ACSRC
f TIME M AC/DC
DCSRC
ACDET
AMPLITUDE
DCDET
TIME