Download Light & Matter: Absorption and Scattering

2015-04-01
LightandMatter
Absorption/Scattering
MD6305Laser‐TissueInteractions
Class3
JaeGwan Kim
[email protected] ,X2220
DepartmentofMedicalSystemEngineering
Gwangju InstituteofSciencesandTechnology
Copyright.Mostfigures/tables/textsinthislecturearefromthetextbook“Laser‐Tissue
InteractionsbyMarkolf H.Niemz 2007”andthismaterialisonlyforthosewhotakethis
classandcannotbedistributedtoanyonewithoutthepermissionfromthelecturer.
LightandBulkMatter(tissue)
• Inopaquemedia,therefractionishardtomeasure
duetoabsorptionandscattering
loss
Iinc
Transmittance(%)=Itrans/Iinc
loss
loss
Itrans
• Inlasersurgery,knowledgeofabsorbingand
scatteringpropertiesofaselectedtissueisessential
forthepurposeofpredictingsuccessfultreatment
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LightandBulkMatter(tissue)
• Typesofinteractions
– Reflection(Fresnel’slaw)
1
– Refraction(Snell’slaw)
sin
sin
– Scattering,Diffraction
– Absorption variationintransmission
– Phaseshift
– Emission
LightandTurbidSample
• Opticalpropertiesofturbidsample
–
–
–
–
–
–
Refractiveindex:n
Absorptioncoeff.:μa
Scatteringcoeff.:μs
Scatteringanisotropyfactor:g
ReducedScatteringcoeff.:μs´= μs(1-g)
Totalattenuationcoeff.:μt= μs+ μa
• Optical mean free path of photons= 1/ μt
– Albedo: a=μs/μt (to ascertain whether absorption or scattering
is dominant in turbid media)
– Transportcoeff.:μtr= μs(1-g) + μa
– Diffusioncoeff.:1/(3μtr)
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ABSORPTIONINTISSUES
Transmittance
• Inoptics,transmittance isthefractionofincident
lightataspecifiedwavelengththatpassesthrougha
sample.
Io :incidentlightintensity,
I :transmittedlightintensity,
c :concentrationofamolecule,
 :attenuationcoefficient,
l :pathlength.
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Absorption
• Inphysics,absorption ofelectromagneticradiation
isthewaybywhichtheenergyofaphotonistaken
upbymatter,typicallytheelectronsofanatom.
• Theabsorbance ofamediumisdefinedastheratio
ofabsorbedandincidentintensities.
• Absorptionisduetoapartialconversionoflight
energyintoheatmotionorcertainvibrationsof
molecules oftheabsorbingmaterial
• Molarabsorptivity,alsocalled"molarextinction
coefficient",whichistheabsorptioncoefficient
dividedbymolarity
AbsorptionOrigin
• Lightasanelectromagneticwave
• Electronhasitsnaturalfrequency
• Whenthelightfrequency
(fp)matcheswiththat
fromelectron(fe)
 electronvibrates(resonance)
• Duringitsvibration,electrons
interactswithother
fp
surroundingatoms
 convertsvibrationalenergyto
thermalenergy absorption
Nucleus
e
fe
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Absorption(QuantumView)

Absorptionoccurswhenthephotonfrequencymatchesthe
‘frequency’associatedwiththemolecule’senergytransition
 Theabsorptionofaphotonresultsin:
• quantizedchangeinchargeseparation(ionizing)
• quantizedexcitationofvibrationalmodes(non‐ionizing)
EMRadiationAbsorption
•
Awhitebeamsource‐‐ emittinglightofmultiplewavelengths‐‐ isfocusedona
sample(thecomplementarycolorpairsareindicatedbytheyellowdottedlines).
Uponstrikingthesample,photonsthatmatchtheenergygapofthemolecules
present(greenlightinthisexample)isabsorbed inordertoexcitethemolecule.
Otherphotonstransmitsunaffectedand,iftheradiationisinthevisibleregion
(400‐700nm),thetransmittedlightappearsasitscomplementarycolor.By
comparingtheattenuationofthetransmittedlightwiththeincident,an
absorptionspectracanbeobtained.
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Absorption
•
•
•
•
Generalabsorption:wavelengthinsensitive
Selectiveabsorption:wavelengthsensitive
Bodycolors:frominsideofamedium
Surfacecolors:fromsurfacereflection
Absorptance,Absorbance
• Absorptance:
• Absorbance(oropticaldensity(O.D.))
– Inliquids
log
,
10
– Ingases
,
• Lambert’slaw
– Relationshipdescribinghowtheintensityofelectromagnetic
radiationdecreasesexponentially(fromIo toI)withdistance,z
orl,asittravelsthroughanabsorbingmedium
–
exp
exp
wherezor l:opticalpathlength, or
:absorptioncoefficient
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Beer‐Lambert’sLaw
• Beer’slaw
–
,
10
10
‐1
‐1
wheretheunitof :Lmol cm ,c:mol/L=M,and zorl:cm,
molarconcentration=molarity
• Beer‐Lambert’sLaw
⁄
10
2.303
10
AbsorptionSpectraExamples
• 600~1200nm,therapeutic
window,lightpenetratesdeepertissuestructures
• Agreen(531nm)andyellow(568nm)ofkryptonionlasers
 coagulatebloodandbloodvessels(duetohighabsorption
byhemoglobin)
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PenetrationDepth
• Itisdefinedasthedepthatwhichtheintensityof
theradiationinsidethematerialfallsto1/e(about
37%)ofitsoriginalvalueat(ormoreproperly,just
beneath)thesurface.
• AccordingtoBeer‐Lambertlaw,theintensityofan
electromagneticwaveinsideamaterialfallsoff
exponentiallyfromthesurfaceas
• Ifδp denotesthepenetrationdepth,wehave
1/
PenetrationDepth
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MeanFreePath
• themeanfreepath(l) istheaveragedistance
coveredbyamovingparticle(suchasanatom,a
molecule,aphoton)betweensuccessiveimpacts
(collisions)whichmodifyitsdirectionorenergyor
otherparticleproperties
1
•
~10
• ~1mm
• Mosttissueabsorptioncoefficientisbetween
0.1~1cm‐1
AbsorptionandMedicalApp.
• Extractionofenergyfromlightbyamolecularspecies
• Diagnosticapplications:Transitionsbetweentwoenergy
levelsofamoleculethatarewelldefinedatspecific
wavelengthscouldserveasspectralfingerprintofthe
molecule
– VarioustypesofChromophores (lightabsorbers)inTissue
– Wavelength‐dependentabsorption
– Tumordetectionandotherphysiologicalassessments(e.g.pulse‐oxim
etry)
• Therapeuticapplications:Absorptionofenergyisthe
primarymechanismthatallowslightformasource(laser)to
producephysicaleffectsontissuefortreatmentpurpose
– Lasik(LaserAssistedinsituKeratomileusis)EyeSurgery,
Tatoo Removal,PDT
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MetricsforAbsorption
• AbsorptionCross‐section,s[m2]
– Considerachromophore idealizedasaspherewitha
particulargeometricalsize.Considerthatthissphere
blocksincidentlightandcastsashadow,which
constitutesabsorption.
– Thesizeofabsorptionshadow=absorptioncross‐
section
 a  Qa  s
Qa: absorption efficiency
s
s
MetricsforAbsorption
Pabs = Ioa
Pin =Ios
Pout = Pin‐Pabs
Outgoing Beam
Incident Beam
Area = s
‐
Area = a
=
Pout = Io(s‐a)
area = s ‐ a
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MetricsforAbsorption

Assumptions



Crosssectionisindependentofrelativeorientationofthe
impinginglightandabsorber
Uniformdistributionofidenticalabsorbingparticles
Absorptioncoefficient,μa [1/cm]
a  N a  a
Na:volumedensity
=absorbersperm3
Absorptioncross‐sectionalareaperunitvolumeof
medium
Absorptionmeanfreepath,la [cm]
1
la 
a



Representstheaveragedistanceaphotontravelsbeforebeing
absorbed
AbsorptionFundamentals
• TransmissionandAbsorbance(macroscopicview)
L
• Transmission
T
I
Io
• Absorbance(attenuation,oropticaldensity)
I 
A   log(T )  log o 
 I 
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ConnectionbetweenT/Aandμa
• Now,absorbingmediumischaracterizedbya,
transmission,andabsorbance.Aretheyrelated?
• Beer‐Lambert’sLaw:thelinearrelationship
betweenabsorbanceandconcentrationofan
absorbingspecies.
Beer‐Lambert’sLawDerivation
Absorbing species of cross‐sectional area Total area s
I0
Iz
z
Iz-dI
I
dz
Path length L
a=absorptioncross‐sectionalarea=
[cm2]
IO=Theintensityenteringthesampleatz=0[w/cm2]
I=Theintensityoflightleavingthesample
IZ =TheintensityenteringtheinfinitesimalslabatZ
dI =theintensityabsorbedintheslab
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Beer‐Lambert’sLaw
Absorbing species of cross‐sectional area Total area s
I0
Iz
Total opaque area on the slab due to absorbers
·
· ·d
I
Iz-dI
Number of absorbers Effective in the slab volume
absorption area of each individual molecules
dz
z
Path length L
Loss of energy due to the slab
· ·
· ·d
d ·s
Loss of intensity
d
·
d
·d
·
·d
ln
·
·
Fraction of photons
absorbed
Beer‐Lambert’sLaw
·
Since ln
·
·
.
·
2.303log
and ln
1
ln
2.303
log
.
.
· ·
1
2.303
· · ,
·
·
1
2.303
·
2.303
Molar Extinction Coefficient [cm‐1M‐1]
Measure of ‘Absorbing Power’ of species
10
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Beer‐Lambert’sLaw
1. BymeasuringTransmissionorAbsorbancefor
givenM,
wecanobtainε  usuallyexvivo
2. Withknowledgeofε,ifwecanmeasureμa invivo,
wecanquantifyconcentrationofchromophores
AbsorbersinTissue
NIR
NIR
•Hemoglobin
•Lipids
•Water
VISIBLE
UV
UV‐VIS
•DNA
•Hemoglobin
•Lipids
•Structuralprotein*
•Electroncarriers*
•Aminoacids*
*AbsorbersthatfluorescewhenexcitedintheUV‐VIS
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UVAbsorption
• Protein,aminoacid,fattyacid
andDNAabsorptiondominate
UVabsorption
– Proteinisdominant‘non‐water’c
onstituentofallsofttissue,~30
%
– Absorptionpropertiesdetermine
dbypeptidebondsandaminoac
idresidues
– Peptideexcitationaboutλ =190
nm
– aminoacidsabsorptionatλ =21
0‐ 220nmand260– 280nm
– DNAabsorbsradiationforλ ≤32
0nm
Amino Acid
Peptide
 Largewaterabsorptionλ <180nm
NADH,FAD
Glycolysis
 NADH:reduced
formof
nicotinamide
adenine
dinucleotide
 FAD:flavin
adenine
dinucleotide
FADH2
FAD
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Cytochromec(complex)
• Cyt cisasmallheme proteinfoundloosely
associatedwiththeinnermembraneofthe
mitochondrion.(1μm insize,membrane:9nm)
NADH,FAD,Cytochrome
 Theseenzymesplayakeyroleinprovidingtheproton‐motiveforc
enecessaryforoxidativephosphorylation
 Iftissueisoxygenstarved,[NADH]and[FADH2]willbeenhanced
 ReducedNADHconc.isindicativeofhighoxygenconsumptionan
discharacteristicoftumortissue
NADH
FAD
NADH(FAD)stronglyfluorescewhileNAD+ (FADH2)doesnot
 Cytochromea3 hasaprominentabsorptionpeakatλ =840nm
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VisibleandNIRAbsorption
• MainAbsorbersatvisibleandNIR
– Hemoglobin
– Lipid
• Hemoglobin
– Oxygensaturationisanindicatorofoxygendeliveryand
utilizationaswellasmetabolicactivity
Hemoglobin
•
•
•
•
4 polypeptidechains,2α and2β chains
Eachhemoglobinhas4heme(Fe2+)sitestobindO2
Responsibleforoxygentransport
Oxyanddeoxyhemoglobin
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StructureChangeduetoO2
• Thisshapechangecausesthechangeoflight
absorptionspectrum
HemoglobinConcentration
• Molecularweight:68,000g/mol
• Men:13.8to18.0g/dL (138to182g/L,or8.56to
11.3 mmol/L)mean:15g/dL =2200μM
• Women:12.1to15.1g/dL (121to151g/L,or7.51to
9.37 mmol/L)
• Children:11to16g/dL (111to160g/L,or6.83to
9.93 mmol/L)
• Pregnantwomen:11to12g/dL (110to120g/L,or6.83to
7.45 mmol/L),needtocarefultopreventanemia
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HemoglobinAbsorptionSpectra
• Deoxyhemoglobin haslowerabsorptionthanoxyhe
moglobin intheblueandgreen
• AbsorptionpeaksforHbO2
– 418,542,577,and925nm
• AbsorptionpeaksforHb
– 550,758,910nm
• Isosbestic points
– 547,569,586,and798nm
Extinction Coeff (1/cm M)
– Brightredarterialblood(blushing)
– Bluishvenousblood(coldpaleface)
10
6
10
5
10
4
10
3
10
2
Hb
HbO2
400
500
600
700
800
900
1000
WAVELENGTH (NM)
Lipid(Fat)
0.04
2.0
HB
0.03
1.5
0.02
1.0
0.5
Lipid
HbO2
0.01
0.00
0.0
600
700
800
900
WATER & FAT (1/ mm mM)
HEMOGLOBIN (1/mm mM)
• Importantenergystoreinthebody
• Site‐specificmeasurementsofbodycomposition
• Monitoringofphysiologicalchangesinfemalebreast
tissue
0.06
3.0
Water 0.05
2.5
• Tissuelayermodel
1000
WAVELENGTH (nm)
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InfraredAbsorption
• ProteinIRabsorptionpeak
sat6.1,6.45,and8.3 md
uetoamideexcitation
– Absorptiondepth≤10m in
 mregion
• Waterabsorptionpeakat0
.96,1.44,1.95,2.94 and6.1
m
– Absorptiondepth~500mm
atλ =800nm,<1matλ =2.
94m
– ≤20mthroughout ≥6
m
InfraredAbsorption
• AbsorptionIR
• Watervibrationfrequencies
Ref: PW Atkins, “Physical Chemistry”, p576 (1978)
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Summary‐ Absorber
UV
• Protein
• Aminoacid
• FattyAcid
• Peptide
• DNA
• NADH
• FAD
• Water
Visible&NIR
• Hemoglobin
• Lipid
• Cytochromea3
IR
• Water
• Protein
• Glucose
“TherapeuticWindow”
600nm~1000nm
SCATTERINGINTISSUES
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Scattering‐ Example
Purelyabsorbing
WithScattering
Photonpathlength=L
Photonpathlength>>L
L
Beer‐Lambert’sLawdoesnotapplyhere!!!
Needtocalculatetruepathlength oflight
ScatteringinTissues
• Muchmorecomplicatedthanabsorption
• Lightishardlyobservedfromthesource,but
reachesoureyesindirectlythroughscattering
• Inhomogeneitycausesscattering;cloud,raindrop,
etc.
• Elastic(Rayleigh,Mie)or
inelastic(Raman,Ramen)
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Scattering
• Scattering isageneralphysicalprocesswheresome
formsofradiation,suchaslight,sound,ormoving
particles,areforcedtodeviatefromastraight
trajectory byoneormorelocalizednon‐uniformities
inthemediumthroughwhichtheypass.
• Inconventionaluse,thisalsoincludesdeviationof
reflectedradiationfromtheanglepredictedbythe
lawofreflection.
• Reflectionsthatundergoscatteringareoftencalled
diffusereflections andunscattered reflectionsare
calledspecular (mirror‐like)reflections.
MechanismforLightScattering
• Lightscatteringarisesfromthepresenceofheterogeneities
withinabulkmedium
– Physicalinclusions
– Fluctuationsindielectricconstantfromrandomthermalmotion
• Heterogeneity/fluctuationsresultinnon‐uniformtemporal/
spatialdistributionofrefractiveindexinthemedium
• PassageofanincidentEMwavesetselectricchargesinto
oscillatorymotionandcanexcitevibrationalmodes
• Scatteredlightisre‐radiatedbyaccelerationofthesecharges
and/orrelaxationofvibrationaltransition
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ScatteringOrigin
• Whenthelightfrequency(fp)
≠electronnaturalfreq.(fe)
forcedvibrationoccurswithsamefreq.asfp,but
withmuchsmalleramplitudethaninthecaseof
resonance
 alsothephasediffersfromtheincidentwave
 causephotonsslowdownwhenpenetratinginto
adensermedium
 basicoriginofdispersion
ScatteringOrigin
• AsEMwaveinteractswiththediscreteparticle,theelectron
orbitswithintheparticle’sconstituentmoleculesare
perturbedperiodicallywiththesamefrequency(vo)asthe
electricfieldoftheincidentwave
• Theoscillationorperturbationofelectronclouds a
periodicseparationofchargewithinthemolecule(induced
dipolemoment)
• This oscillatinginduceddipole
moment sourceofEM
wave scatteredlight
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Elasticvs.InelasticScattering
• Elasticscattering:noenergychange
– Frequencyofthescatteredwave=frequencyofincident
wave
– Probesstaticstructureofmaterial
– RayleighandMiescattering
• Inelasticscattering:energychange
– Frequencyofthescatteredwave≠frequencyofincident
wave
– Internalenergylevelsofatomsandmoleculesareexcited
– Probesvibrationalorrotationalbondsofthemolecule
– Ramanscattering
ModelsofLightScattering
whereπDp isthecircumferenceofa particle
andλisthewavelengthofincidentradiation
• α<<1:Rayleighscattering(smallparticlecompared
towavelengthoflight,I1/λ4)
– Itbreakswhentheparticlesizeislargerthan10%of
wavelength
• α≈1:Miescattering(particleaboutthesamesizeas
wavelengthoflight)
– Morelargertheparticlesize,moreforwardscattering
• α>>1:Geometricscattering(particlemuchlarger
thanwavelengthoflight)
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RayleighScattering
• Rayleighscatteringreferstothescatteringoflight
offofthemoleculesoftheair,andcanbeextendedto
scatteringfromparticlesuptoaboutatenthofthe
wavelengthofthelight
MieScattering
• Forparticlesizeslargerthanawavelength,Mie
scatteringpredominates.Thisscatteringproducesa
patternlikeanantennalobe,withasharperand
moreintenseforwardlobeforlargerparticles.
http://www.azom.com/article.aspx?ArticleID=6018
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Rayleighvs MieScattering
RamanScattering
• Itispossiblefortheincidentphotonstointeract
withthemoleculesinsuchawaythatenergyis
eithergainedorlostsothatthescatteredphotons
areshiftedinfrequency.This iscalledinelastic
scattering includingRamanscattering(~1in107
photons)
• Ramanscatteringproducesscatteredphotonswhich
differinfrequencyfromtheradiationsourcewhich
causesit,andthedifferenceisrelatedtovibrational
and/orrotationalpropertiesofthemoleculesfrom
whichthescatteringoccurs.
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HistoryofRamanSpectroscopy
• Ramaneffect:SirKariamanickam Srinivasa Krishnan
andSirChandrasekhara Venkata Raman
From ‘THE RAMAN EFFECT’ by JADAVPUR, CALCUTTA
RamanScattering
• Stokesvs Anti‐stokesscattering
• TheRamaneffectcantakeplaceforanyfrequencyofthe
incidentlight.Incontrasttothefluorescenceeffect,the
Ramaneffectisthereforenotaresonanteffect
Vibrationalstateofthe
moleculeismoreenergetic
thantheinitialstate
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RamanSystemSet‐up
785nm laser source
Laser power controller
Spectrograph
Thermoelectrically cooled CCD
RamanSystemSet‐up
Laser delivery fiber
Optical fiber‐
based probe
The others are 7 collection fibers.
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RamanScattering
• Ramanshiftsarereportedinunitsofwavenumber
(cm‐1);∆
• Ex)785nmlaser,
500cm‐1  819.67nm,2000cm‐1  934.58nm
50000
300000
Intensity (a.u.)
Intensity (a.u.)
(b)
(c)
(a)
A
150000
30000
x50
x100
x300
x500
2000
1000
(c)(d)
0
(a)
(b)
-1000
1120
1140
1160
1180
-1
Wavenumber (cm )
20000
B
10000
100000
50000
40000
Intensity (a.u.)
250000
200000
3000
raw data
x1
x300
0
600
800 1000 1200 1400 1600 1800 2000
-1
Wavenumber (cm )
600
800
1000
1200
1400
1600
1800
-1
Wavenumber (cm )
ScatteringinTissues
• Diagnosticapplications:Scatteringdependsonthesize,
morphology,andstructureofthecomponentsintissues(e.g.
lipidmembrane,collagenfibers,nuclei).Variationsinthese
componentsduetodiseasewouldaffectscatteringproperties
,thusprovidingameansfordiagnosticpurpose
• Therapeuticapplications:Scatteringsignalscanbeusedto
determineoptimallightdosimetry andprovideuseful
feedbackduringtherapy
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ScatteringinTissue(I)
• Tissueiscomposedofa‘mixture’ofRayleighandMi
escattering
Hierarchyofultrastructure
10μm
cells
nuclei
*TiO2 :0.2~2μm
1μm
MieScattering
0.1μm
mitochondria
lysosomes,vesicles
striationsincollagenfibrils
macromolecularaggregates
RayleighScattering
0.01μm
membranes
SourceofScatteringinTissue
• Refractiveindexmismatchbetweenlipidandsurrounding
aqueousmedium
– Softtissuesaredominatedbylipidcontents
– Cellularmembranes,membranefolds,andmembraneous
structure
• Mitochondria,~1μm
– Intracellularorganellecomposedofmanyfolded
membrane,cristae
• Collagenfibers,2~3μm
– Collagenfibrils,0.3μm
– Periodicfluctuationincollagenultrastructuresourceof
RayleighscatteringinUVandVisiblerange
• Cells,10~100μm
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CellStructure
(1)nucleolus
(2)nucleus
(3)ribosome
(4)vesicle
(5)roughendoplasmicreticulum (ER)
(6)Golgiapparatus
(7)Cytoskeleton
(8)smoothendoplasmicreticulum
(9)mitochondria
(10)vacuole
(11)cytoplasm
(12)lysosome
(13)centrioles withincentrosome
Mitochondria
• 1microninsize,foldedlipidmembranes,
membranes9nmthick
• Refractiveindexmismatchbetweenlipidandwater
causesscattering
• AlsocontainsmetaboliccofactorsNAD,FADusedfor
protonpumpovermembranetogenerateATP
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CollagenFibers,Fibrils
• Fibersare2‐3micronindiameterandcomposedofsmallerfibrils0.3
microninsize(electronmicrograph),strongMiescatteringinIR
• Fibrilscomposedoftropocollagen molecules,havebandedpattern(70nm
period),optical“crystal”2ndharmonicgenerators,periodicstructure
contributestoRayleighscattering(visibleandUVrange)
• CrossLinks,hydroxylysyl pyridinoline andlysyl perydinoline are
fluorescent
Cross links
MetricsforOpticalScattering
• ScatteringCross‐section,
[m2]
– ‘area’ofanindex‐matched,perfectlyabsorbingdisc
necessarytoproduce
– Themeasuredreductionoflight
·
– Qs:Scatteringefficiency(calculatedbyMietheory);
definedastheratioofthescatteringcrosssectiontothe
projectedareaoftheparticleonthedetector
– As:Areaofascatterer [m2]
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MetricsforOpticalScattering
Pin =IoA
Outgoing Beam
Incident Beam
Area = A
‐
Pout = Io(A‐s)
Pscatt = Ios
Area = s
=
Pout = Io(A‐s)
area = A – s
MetricsofOpticalScattering
• Scattering Coefficient, μs [1/m]
– μs =Nss ,
• Ns = the number density of scatterers
• s = 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
–
,
~100cm-1  ~0.1mm
• Most tissues have
– 50cm-1 (prostate) < μs < 1000cm-1 (tooth enamel)
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ScatteringAnisotropy,g
• Imagine that a photon is
scattered by a particle
so that its trajectory is
deflected by an angle, 
• Then, component of a
new trajectory aligned
forward direction is
cos()
• Anisotropy is a measure
of forward direction
retained after a single
scattering event,
<cos()>, a mean value
of cos().
scattered
photon
Scatterer
Incident
Photon
hv
hv
Scattering Angle ()
S
Photon trajectory
d
S’
cos ()
Scattering event
Anisotropyfactor,g
• Anisotropyisameasureofforwarddirection
retainedafterasinglescatteringevent
(=meanvalueofcos())
 1

g0
1

totallybackwardscattering(‐1)
backwardscattering(‐1~0)
isotropicscattering
forwardscattering(0~1)
totallyforwardscattering(1)
BiologicalTissues,0.65<g<0.95
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ReducedScatteringCoefficient
• Lumped property ( ) incorporating the scattering
coefficient ( ) and the anisotropy factor( )
1
g  cos   0.90
1isoscattering step
=1/(1‐g)
anisoscattering
steps
  26o
 s '  (1  g )  s  0.10 s
mfp  1 /  s
mfp'  1 /  s '
ReducedScatteringCoefficient
• Thepurposeofthereducedscatteringcoefficientisto
describethediffusionofphotons(isotropicscattering)ina
randomwalkofstepsizeof1/ whichisthereducedmean
freepath(mfp’)
• Suchadescriptionisequivalenttothedescriptionofphoton
diffusion ( >> )
1bigisotropicsteps
mfp’ = 1/μs’
Eachstepinvolvesisotropic
scattering.
Suchadescriptionisequivalent
todescriptionofphoton
movementusingmanysmall
steps1/µs thateachinvolve
onlyapartialdeflectionangle.
Anisotropicsteps
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ScatteringExample:SoftTissue
• Softtissuesaredominatedbylipidcontent
• Thelipidconstitutesthecellularmembranes,
membranefoldsandmembranousstructures
• Thelipid/waterinterfaceofmembranepresentsa
strongrefractiveindexmismatchandsoplaysa
majorroleinscattering
ScatteringExample:SoftTissue
• Lipidcontentofsofttissues
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ScatteringExample:SoftTissue
• Scatteringcoefficient
np: R.I. of particle, nmed: R.I. of medium, fv: volume fraction of particles
ScatteringExample:SoftTissue
• Anisotropicfactor
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ScatteringExample:SoftTissue
• Reducedscatteringcoefficient
ScatteringExample:SoftTissue
• SofttissueMiescatteringsummary
– Oftentissuescatteringisapproximatedwith:
·
.
~
…..
– Scatteringslope:sizeofparticles
– Magnitude:volumefraction,concentration
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LightTransportinTissue
•
•
•
•
Scatteringandabsorptionoccursimultaneouslyandarewavelengthdependent
b
Scatteringmonotonicallydecreaseswithwavelength  s '  A  
AbsorptionislargeinUV,nearvisible,andIR
 s ' ~ 0.5  4
AbsorptionislowinredandNIRTherapeuticwindow
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