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 1 2015-04-01 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) 2 2015-04-01 ABSORPTIONINTISSUES Transmittance • Inoptics,transmittance isthefractionofincident lightataspecifiedwavelengththatpassesthrougha sample. Io :incidentlightintensity, I :transmittedlightintensity, c :concentrationofamolecule, :attenuationcoefficient, l :pathlength. 3 2015-04-01 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 4 2015-04-01 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. 5 2015-04-01 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 6 2015-04-01 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) 7 2015-04-01 PenetrationDepth • Itisdefinedasthedepthatwhichtheintensityof theradiationinsidethematerialfallsto1/e(about 37%)ofitsoriginalvalueat(ormoreproperly,just beneath)thesurface. • AccordingtoBeer‐Lambertlaw,theintensityofan electromagneticwaveinsideamaterialfallsoff exponentiallyfromthesurfaceas • Ifδp denotesthepenetrationdepth,wehave 1/ PenetrationDepth 8 2015-04-01 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 9 2015-04-01 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 = Ioa Pin =Ios Pout = Pin‐Pabs Outgoing Beam Incident Beam Area = s ‐ Area = a = Pout = Io(s‐a) area = s ‐ a 10 2015-04-01 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 11 2015-04-01 ConnectionbetweenT/Aandμa • Now,absorbingmediumischaracterizedbya, 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 12 2015-04-01 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 13 2015-04-01 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 14 2015-04-01 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 15 2015-04-01 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 16 2015-04-01 VisibleandNIRAbsorption • MainAbsorbersatvisibleandNIR – Hemoglobin – Lipid • Hemoglobin – Oxygensaturationisanindicatorofoxygendeliveryand utilizationaswellasmetabolicactivity Hemoglobin • • • • 4 polypeptidechains,2α and2β chains Eachhemoglobinhas4heme(Fe2+)sitestobindO2 Responsibleforoxygentransport Oxyanddeoxyhemoglobin 17 2015-04-01 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 18 2015-04-01 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) 19 2015-04-01 InfraredAbsorption • ProteinIRabsorptionpeak sat6.1,6.45,and8.3 md uetoamideexcitation – Absorptiondepth≤10m in mregion • Waterabsorptionpeakat0 .96,1.44,1.95,2.94 and6.1 m – Absorptiondepth~500mm atλ =800nm,<1matλ =2. 94m – ≤20mthroughout ≥6 m InfraredAbsorption • AbsorptionIR • Watervibrationfrequencies Ref: PW Atkins, “Physical Chemistry”, p576 (1978) 20 2015-04-01 Summary‐ Absorber UV • Protein • Aminoacid • FattyAcid • Peptide • DNA • NADH • FAD • Water Visible&NIR • Hemoglobin • Lipid • Cytochromea3 IR • Water • Protein • Glucose “TherapeuticWindow” 600nm~1000nm SCATTERINGINTISSUES 21 2015-04-01 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) 22 2015-04-01 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 23 2015-04-01 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 24 2015-04-01 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,I1/λ4) – Itbreakswhentheparticlesizeislargerthan10%of wavelength • α≈1:Miescattering(particleaboutthesamesizeas wavelengthoflight) – Morelargertheparticlesize,moreforwardscattering • α>>1:Geometricscattering(particlemuchlarger thanwavelengthoflight) 25 2015-04-01 RayleighScattering • Rayleighscatteringreferstothescatteringoflight offofthemoleculesoftheair,andcanbeextendedto scatteringfromparticlesuptoaboutatenthofthe wavelengthofthelight MieScattering • Forparticlesizeslargerthanawavelength,Mie scatteringpredominates.Thisscatteringproducesa patternlikeanantennalobe,withasharperand moreintenseforwardlobeforlargerparticles. http://www.azom.com/article.aspx?ArticleID=6018 26 2015-04-01 Rayleighvs MieScattering RamanScattering • Itispossiblefortheincidentphotonstointeract withthemoleculesinsuchawaythatenergyis eithergainedorlostsothatthescatteredphotons areshiftedinfrequency.This iscalledinelastic scattering includingRamanscattering(~1in107 photons) • Ramanscatteringproducesscatteredphotonswhich differinfrequencyfromtheradiationsourcewhich causesit,andthedifferenceisrelatedtovibrational and/orrotationalpropertiesofthemoleculesfrom whichthescatteringoccurs. 27 2015-04-01 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 28 2015-04-01 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. 29 2015-04-01 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 30 2015-04-01 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 – Periodicfluctuationincollagenultrastructuresourceof RayleighscatteringinUVandVisiblerange • Cells,10~100μm 31 2015-04-01 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 32 2015-04-01 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] 33 2015-04-01 MetricsforOpticalScattering Pin =IoA Outgoing Beam Incident Beam Area = A ‐ Pout = Io(A‐s) Pscatt = Ios Area = s = Pout = Io(A‐s) area = A – s MetricsofOpticalScattering • Scattering Coefficient, μs [1/m] – μs =Nss , • 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) 34 2015-04-01 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 g0 1 totallybackwardscattering(‐1) backwardscattering(‐1~0) isotropicscattering forwardscattering(0~1) totallyforwardscattering(1) BiologicalTissues,0.65<g<0.95 35 2015-04-01 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 36 2015-04-01 ScatteringExample:SoftTissue • Softtissuesaredominatedbylipidcontent • Thelipidconstitutesthecellularmembranes, membranefoldsandmembranousstructures • Thelipid/waterinterfaceofmembranepresentsa strongrefractiveindexmismatchandsoplaysa majorroleinscattering ScatteringExample:SoftTissue • Lipidcontentofsofttissues 37 2015-04-01 ScatteringExample:SoftTissue • Scatteringcoefficient np: R.I. of particle, nmed: R.I. of medium, fv: volume fraction of particles ScatteringExample:SoftTissue • Anisotropicfactor 38 2015-04-01 ScatteringExample:SoftTissue • Reducedscatteringcoefficient ScatteringExample:SoftTissue • SofttissueMiescatteringsummary – Oftentissuescatteringisapproximatedwith: · . ~ ….. – Scatteringslope:sizeofparticles – Magnitude:volumefraction,concentration 39 2015-04-01 LightTransportinTissue • • • • Scatteringandabsorptionoccursimultaneouslyandarewavelengthdependent b Scatteringmonotonicallydecreaseswithwavelength s ' A AbsorptionislargeinUV,nearvisible,andIR s ' ~ 0.5 4 AbsorptionislowinredandNIRTherapeuticwindow 40
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