Simulations for propagation of light in bio-medical tissues using Minitab software and Monte Carlo simulations.

1
Simulations for propagation of light in bio-medical tissues
using Minitab software and Monte Carlo simulations.
B00548888
Mr Nathan Mount, University of Ulster Coleraine, Faculty of life and Health Sciences, School
of Biomedical Sciences, BSc (Hons) Biology with DPP
April, 2014

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Content Table:
Abstractand Keywords……………………………………………………………………………………………………………………3
CommonAbbreviations…………………………………………………………………………………………………………………….4
IntroductionandBackground……………………………………………………………………………………………………………5
LightPropagationinTissue……………………………………………………………………………………………………5
Monte CarloSimulations………………………………………………………………………………………………………7
Monte CarloFormulas………………………………………………………………………………………………………….8
PreviousExperiments…………………………………………………………………………………………………………..9
Null Hypotheses…………………………………………………………………………………………………………………10
Methodand Materials…………………………………………………………………………………………………………………….11
Materials……………………………………………………………………………………………………………………………11
Methods …………………………………………………………………………………………………………………………….11
Results…………………………………………………………………………………………………………………………………………….14
3D Surface PlotsforIndividual RBavalues………………………………………………………………………….14
Surface PlotsforDifferentLightSources…………………………………………………………………………….29
Scatter PlotsforDifferentLightSourcesandDifferentPhotonNumbers…………………………..32
Scatter Graphsof DifferentiatingScatteringCoefficientvalues………………………………………….41
Discussion……………………………………………………………………………………………………………………………………….43
Conclusion………………………………………………………………………………………………………………………………………45
Acknowledgements…………………………………………………………………………………………………………………………47
References………………………………………………………………………………………………………………………………………48
Appendix …………………………………………………………………………………………………………………………………………51

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Abstract:
Lightpropagationiscurrentlya popularareafor scientificstudiesasthe informationandknowledge
gainedfromthe measurementof reflected,transmittedorscatteredlightin livingtissue canbe
usedto helpdevelopnon-invasive techniquesfortissue characterization,suchasthe development
of light-sensitive drugsinphotodynamictherapies.Therefore experimentationisimportantto
determine the intensityof lightneededindifferenttypesof tissue toreachthe targetarea and
activate a specificdrug.These techniquescouldthenleadtoearlierdetectionof tumoursinhuman
tissue cells. The study was carriedout usingMonte Carlosimulationsof lightpropagation,
absorbing,scatteringcoefficientsand tissue types usingdifferentdiffuse reflectance values overa
range of lightsources.The study usedstatistical modellingviaMinitabandMonte Carlosimulations
to examine the properties of lightpropagationintissuesastheyallow forgreaterrepetitionof
calculations. Monte Carlosimulations were also the bestforrecreatingthe randommovementsof
lightparticlesintissue astheyreflectoff tissueparticlesandchange theirdirection. The results
obtainedshowedthatScatterandAbsorbance coefficientsalong withdiffusereflectanceall have an
effectonlightpropagationintissues.Theyalsoshowedthatthe type of lightsource usedcanaffect
lightintensityandpenetration.
Key Words:
Scatter,Reflectance,Absorbance,Cancer,Light,Monte Carlo

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Common Abreviations:
 Fsph– Fluence of Spherical LightSource
 Fcyl – Fluence of Cylindrical LightSource
 Fpla– Fluence of PlanarLightSource
 KT - absorptioncoeffienct
 PDT – PhotodynamicTherapy
 QB 64 – Q Basic 64
 RBa - Diffuse reflectance (lightreflectedbytissue surface)
 S - scatteringcoefficency

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Introduction and Background:
Light Propagation in tissue:
There isa greatdeal of interestcurrentlyinstudiesrelatingtolightpropagationinbiomedical
tissues. Twoof the mainreasonsbehindthisisthatit offersnon-invasive optionsintermsof
identifyingphysiological changesthathighlightthe earlystagesof cancers particularlycolon,mouth,
bladderandbreast(Mourant etal.,1995, Ghoshet al.,2001, Kimetal.,2003, Chunget al.,2007,
Antonellietal.,2010). The otheristhat it offersanon-invasive optionfortreatingcancerinthe form
of Photodynamictherapy(PDT) whichusesphotosensitizingdyessuchasa Hematoporphyrin
derivative (HDP) (Bolin etal.,1987, Hea etal.,1998, Lim etal.,2001, Rogerset al.,2013).
The interestinlightpropagationintermsof detectingcancercomesfromthe fact thata single
change in cell structure will affecthowthe lightisreflectedandscattered(Mourantetal.,1998,
Sokolovetal.,1999, Kimet al.,2003). Thismeansthat if a collectionof dataaboutdifferenttissue
compositionswastobe collecteditcouldbe usedtotestfor earlychangesintissue structure due to
cancer (Kimetal.,2003). Over85% of cancersare formedat the epithelial layerof the bodyand
researchintothe changesmade to thislayerby the formationof cancertumourshas enabled
researcherstohighlightearliersignsandlearnmore aboutitsmechanics(Kimetal.,2003). Using a
single lightscatteringonepithelialispreferredasitallow toyou to analysisthe size of theirnucleus
and alsoto analysishowthe cellstendtoreflectthe lightsource (Kimetal.,2003). (Kimetal.,2003)
have shownthat lightpropagationin ratscan be usedtodetectthe onsetof cancers soonerthanby
the use of currentmethods,theyinjectedratswitheitherAOMa carcinogenicsubstance ora saline
placebofortwoweeksandafterwardsreportedthatthere were nonoticeablechangestotheir
colonstructure but whentheircellswhere testedforlightpolarisationthere wassignificant
differencesbetweenthe treatedandcontrol group.A similarstudywascarriedoutby (Giakosetal.,
2011) onlungcancers particularlyAdenocarcinomawhichaccountsforapproximately32% of all lung
cancer cases(Giakosetal.,2011). (Giakosetal.,2011) showedthatdifferentlevelsforscattering
couldbe recordedfor three differentstagesof cancerdevelopmentinthe lungs,theyshowedthat
non-cancerous,precancerousandstage 1cancer tissuesall resultedindifferentlevelsof scattering
whenplacedunderanear infraredlightat785nm. These resultsshow thatlightpropagationin
tissueshasthe potential tobecome anearlywarningsystemforcertaincancers.
For use intreatmentof certaincancers PDT drugssuch as Porfimersodiumandare a developing
interestthatplace dyessuchas HPD dyeson the cancer tumours(Bolinetal.,1987, Tsukagoshi,
1995). The dye isattachedto the tumour butdoesnot activate until itisexposedtoacertain

6
wavelengthof light,thisisdue tothe changingthicknessof humantissuesatdifferentpartsof the
body(Bolinetal.,1987). It has beenstatedthatchangingthe wavelengthof the lightsource effects
howthe lightis able topenetrate the tissue sample(Lee etal.,1998, Wang et al.,2009, Songet al.,
2013). These changesmeanthat to excite aPDT drug at a specificthicknessanda specificlocation
on the humanbodyyou needtohave the lightsource at exactlythe correct angle andwavelength.
Once the a PDT drug like Porfimersodium hasbeenexcitedbythe correctlightsource itreactswith
available oxygentokill the tumourcells(Bolinetal.,1987, Lim etal.,2001). Thisreactionoccurs as in
tissue Oxygenoccursina tripletstate andthe PDT drug isin the singletstate,once the PDTdrug is
excitedbythe lightitisable to react withoxygentoproduce singletoxygen.The singletoxygen
moleculescreatedthenattackthe tumourcellsbeforequicklydyingoff topreventdamage tonon-
cancer cells(Skovsenetal.,2005). One issue thathadarisenwithPDT was thatprolongedexposer
to the lasersbeingusedtoexcite the drugwascausingthe tissue to be heatedbythe energybeing
producedas lightphotons were absorbedbythe tissue (Yoonetal.,1987). Thisheatwas causingthe
tissue tobecome damagedandtookaway the advantage thatPDTs have in that theyare non-
invasive andonlyeffectthe targettissuese.g.tumours.Toovercome thisissuepulsetreatments
became the usedmethodstoppingthe tissuefrombeingdamagedbutensuringthatefficientresults
are still obtained(Limetal.,2001).
Anothernon-invasive techniqueforcancerdiagnosesthathasbecome popularrecentlyisthe use of
Nevoscopyitusesthe scatteringanddiffuse reflectance (RBa) whichisthe lightphotonswhich
reflectstraightof the tissue’ssurface tocreate animage of the tumourinquestion(Patwardhanet
al.,2005). The mostcommoncancer diagnosedandanalysedusingthismethodismelanomawhich
isa formof skincancer,the problemwithinitialproblemwithNevoscopyandmelanomaisthatit
onlyprovidesinformation onone layerat a time (Patwardhanetal.,2005). The aim to overcome
thisproblemistofindthe wavelengths atwhichthe Nevoscope canrunto analyse all layersof the
tissue formedbythe melanomatogive acomplete image (Patwardhanetal.,2005).
These methodshave showntohave advantageswhencomparedtocurrentmethodsfordiagnosing
and treatingcancers;The tissue can be studied In Vivo whicheliminatesthe problemsfacedwith
stainingorfixation;The informationobtainedisquantitativewhichmeansthatdifferencesin
structure will be observedevenif theycannotbe visuallyseen(Hielscher etal.,1997, Kimet al.,
2003).

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Monte Carlo Simulations:
Monte Carlosimulationswere firstsuggestedby(MetropolisandUlam, 1949) theywere chosento
analyse ourRBa, Scatteringcoefficient(S) whichisthe probabilitythata photonwill be scattered
duringit’spathlength,Absorbance coefficient(KT) whichisthe likelihoodthatthe photonwill be
absorbedduringit’spathlengthandfluence profiles/intensityvaluesasitisable to use and
calculate multiplevariantsinthe same run(Flocketal.,1989). Pathlengthsare describedintissues
because of the lightscatteringthatoccurs before aphotonreachesitsdistination(Wangetal.,
2009). Monte Carlohas beenshowntobe more accurate than otherlightpropagationmodelssuch
as diffusiontheory(Flocketal.,1989). (Flocketal.,1989) showedthatMonte Carlosimulations
producedmore accurate resultsforpenetrationdepth,RBaandfluence levelswhencomparedto
diffusiontheorymodelsathigherscatteringangles.Thereare multiple Monte Carlosimulation
programseach designedforspecificconditionstoachieve more accurate results(Banerjee and
Sharma,2010). (Wanget al.,1995) produceda program calledMCML whichsimulatedthe
propagationof unpolarisedlightintissue whereas(Ramella-Romanetal.,2005) produceda program
calledPOLMCfor polarisedlight.
Monte Carlosimulationsworkbyrecordingthe absorbance andscatteringof photonsindifferent
conditions(Prahl etal.,1989). It usesa numberof formulastorandomlycalculate for each
movementof the photonwhetheritwill be absorbed,scatteredorreflected,theserandom
movementsare repeateduntil the photoniseitherabsorbedbythe tissue oritleavesthe tissue at
whichpointitis recorded(Prahl etal.,1989).
The lengthof the photonsmovementsare knownasstepsizes,theyare aconstantlength
throughoutthe simulationandmustbe relevanttothe size of the tissue beingtestedastoosmall a
stepsize andtoofewinteractswill occurtofor anyresultsto be reacted,and if the sizestepwastoo
large thenit wouldn’tgive anaccurate accountof the distance of an individualphotoninthe tissue
(Prahl etal.,1989).

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Monte Carlo Formulas:
 The formulausedforgenerate the stepsizesinMonte Carlosimulationsisasfollows:
∆𝑠 <<
1
𝜇 𝑡
=
1
𝜇 𝑠 + 𝜇 𝑎
Were s and a representthe scatteringandabsorptioncoefficients(Prahl etal.,1989).
 The formulausedto calculate the likelihoodthataphotonwill be reflectedinside the tissue
is:
𝑅( 𝜃𝑖) =
1
2
[
𝑠𝑖𝑛2( 𝜃𝑖 − 𝜃𝑡)
𝑠𝑖𝑛2( 𝜃𝑖 + 𝜃𝑡)
+
𝑡𝑎𝑛2( 𝜃𝑖 − 𝜃𝑡 )
𝑡𝑎𝑛2( 𝜃𝑖 + 𝜃𝑡 )
]
Were R representsthe Fresnelreflectioncoefficient(Prahl etal.,1989).
 The formulausedto calculate the likelihoodthataphotonwill be absorbedbythe tissue is:
𝑓𝑟𝑎𝑐𝑡𝑖𝑜𝑛𝑎𝑏𝑠𝑜𝑟𝑏𝑒𝑑 =
𝜇 𝑎
𝜇 𝑎 + 𝜇 𝑠
= 1 −
𝜇 𝑠
𝜇 𝑎 + 𝜇 𝑠
= 1 − 𝑎
(Prahl etal.,1989).
 The final formulathatis relevanttothisprojectisforcalculatingthe chancesof the photon
beingscatteredinsidethe tissue:
𝑐𝑜𝑠𝜃 =
1
2𝑔
{1 + 𝑔2 − [
1 − 𝑔2
1 − 𝑔 + 2𝑔𝜀
]2}
Were the formulaisusedto represent the Henyey-Greensteinphase function(Prahl etal.,1989).

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Previous Experiments:
PreviousexperimentscarriedoutusingMonte Carloto simulate lightpropagationhave foundthat
between600-1300nm lightislessabsorbedbyhumantissue andisable to penetrate furthered
because of itscompositionof bloodandwater(Lee etal.,1998, Patwardhanet al.,2005, Wang et al,
2009, Songet al.,2013). These findingsalongwiththoseprovidedintable 1andfigure 1were used
to helpcalculate ourranges.(Lee etal.,1998) alsostatedhow lightpenetrationisaffectedbytissue
pigmentationwithlightpenetratingfurtherintopalerskinthandarkerskin.
Table 1 showssome typical valuesof Diffuse reflectance (RBa) andAbsorptioncoefficientvalues(KT)
whichwere usedtosetup the rangesfor our calculations.
Laser Type Wavelength (nm) RBa (Tissue
Reflectance/Thrombus)
KT Values/cm-1
Argon (blue) 488 0.23 0.1-50
Argon (green) 514 0.25 0.1-50
Helium neon (green) 543 0.27 0.1-50
Helium neon (red) 633 0.58 0.1-50
Rhodamine 6G dye (tunable) 570-650 0.45 0.1-50
Ruby (CrAlO3) (red) 694 0.25 0.1-50
Nd:Yag (NIR) 1064 0.5 0.1-50

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Figure 1 showsthe wavelengthandAbsorptioncoefficient(KT) forcommontissue andcellstypes
that are usinginlightpropagationexperiments.Asseenthe some Ultravioletlightandvisiblelight
part of the spectrumare betweenKT0.5-50 thenalongside table 1helptosupportour choice forKT
values
(McShane et al.,2000) alsoshowedhowMonte Carlo simulationsare ideal forcalculatinghow
photosensitivesensorsshouldbe produceddependingonthe tissue type anddepthbyshowingthe
changesinlightdensitydue totissue thicknessorsensordepth.
Null Hypothesis:
Usingthe relevantliterature andpreviousexperimentsthe null hypothesisthatIhope tochallenge
withthisprojectisthat: “A change inthe diffuse reflectance,scatteringcoefficientorabsorption
coefficientwillhave noeffectonthe overall Reflectance of lightbyHumantissue.”

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Method and Materials
Materials:
The followingprogramswere requiredtocarry out thisproject:
 Q basic 64 (V0.954) developedbyGalleon
 MicrosoftExcel 2007 developedby MicrosoftCorporation
 Minitab(V17.1.0) developedbyMinitabIncorporated
 Code::Blocks(V13.12) developedbyCode::Blocks
An Acer5920G laptopwithIntel CoreTM
Duo processors,2.0 Gigahertz(GHz) and 250 Gigabyte (GB)
Hard DiskDrive (HDD) wasusedto carry out the project.
Method:
The firststage of the projectwas to show that changingvaluesof Sand R have an effectonhow
much lightisabsorbedbytissue andhow far thislightpenetratesintothe tissue.UsingaMacro for
Excel producedbyDr. Hagan whichcarriesout the equations 𝑑𝑖a
(x)=-[Ka
B+Ka
T(x)+S]𝑖a
(x)𝑑𝑥+𝑗a
(x)S𝑑𝑥
and 𝑑𝑗a
(x)=[Ka
B+Ka
T(x)+S]𝑗a
(x)𝑑𝑥-𝑖a
(x)S𝑑𝑥(Kessleretal.,1983) the value forS was changedinsteps
rangingfrom1 to 100 inboth formulas.The valuesforKa
B,Ka
T, 𝑖a
and 𝑗a
remainedconstant
throughoutthe processat 0.0833333, 0.1, 5 and 0 respectivelyandthe macrowasset to give 500
resultsrangingbetween0and 20mm. The macro whenrunproducedcolumnsforthe valuesof
depth(mm) andR. The depthatwhichthe valuesforR level outateachvalue of S and the actual
value at whichR levelsoutwere recordedandplacedintoatable which wasconvertedintographs
showingthe changesindepthandReflectance.
The nextstage of the projectwasto show that a statistical programwrittenbyDr.Hagan for Q Basic
64 (QB 64) basedon the equationby(Linand Kan,1970) for calculatingvaluesof Ra gave the same
valuesaswhenthe equationwascalculatedmanually.
Ra
=Ra
B
(1+
𝛾
𝛿
𝜇+
( 𝛾+1)
( 𝛿+1)
𝜇2
2!
+⋯)
1+
𝛾+1
𝛿
𝜇+
(𝛾+1)(𝛾+2)
𝛿(𝛿+1)
𝜇2
2!
+⋯)
Equationwrittenby(LinandKan, 1970).

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The equationwascalculatedmanuallyusingvaluesof Ra
B=0.9, 𝛾=5, 𝛿=0.1 and 𝜇=1 up to the 5th
factorial andthe valuesobtainedwere comparedtothe valuesproducedbythe QB64 program.
These roughworkingsaren’tattachedbutall valuesagreedwitheachother.
Once the program had beenverifiedvaluesforRwere obtainedatvaryingvaluesof S,KT andRBa.
The valuesforS rangedfrom 1-100 in stepsof 10, thiscoversall possible valuesforHumantissue,
the valuesforKT rangedfrom 0.1 to 50 andthe valuesforRBa rangedfrom0.1 to 0.75 increasingin
stepsof 0.05. 0.1-0.75 where chosenaslimitsforRBavaluesas theycoverlightsource reflectance
for all tissuestypes.DifferentvaluesforRBaand KT were usedeachtime the QB 64 program wasrun
startingat RBa 0.1 and KT 0.1 before increasinginstepstoRBa0.1, KT 50, afterthisthe RBa value
was changedto0.15 and KT returnedto0.1 andthe processwasrepeatedupto RBa 0.75.
Whenthe QB 64 programis run itproducesa setof 10 numberswhichcorrespondtothe 10 values
of S usedforeach KT. MicrosoftExcel wasusedto organise the dataintocolumnsof S, KT and R and
sheetsof RBa values.The valuesproducedbythe QB64 program were placedintothe excel sheets
and the columnswere thentransferred acrosstoa new Minitabproject.
Usingminitabthe total columnsof all KT valuesforeach RBa value were usedtocreate 3D surface
plotsto showthe effectthatchangesinS and KT have on R at each RBa value.
The nextstage was to run a monte carlo simulationinCode::Blockswhere byusingacode createdby
Dr. Hagan changesin lightintensitycouldbe measuredasthe lighttravelsfurtherintothe tissue and
alsoas KT increases.The simulationwassettogive resultsbetween0-3cm, witharesultbeing given
at every0.3mm resultinginastepsize of 0.3mm, itwas alsotoldthat 100,000 photonswere tobe
used.The S value wassetat 50 forall simulationsandthe KTwas changedfrom0.01 to 0.24 insteps
of 0.01. Whenrun,the simulationsproducedresultsforthe changesinlightintensityfromthree
differenttypesof lightsourcesCylinder(Fcyl),Planar(Fpla) andSpherical (Fsph).Eachsimulationran
from0-3cm and useda particularKT value.Aseachsimulationwasrunthe resultsproducedwere
placedback intominitabusingcolumnsforKT,depth(cm),Fsph[1/cm2
],Fcyl[1/cm2
],Fpla[1/cm2
],
once all KT valueshadbeencalculatedthe three lightsource columnsweretransformedtogive their
natural log thisresultsina setof resultswhichismore easilydisplayedandunderstoodvona3D
surface plot,thiscreatedthree newcolumns log(Fsph[1/cm2
]),log(Fcyl[1/cm2
]), log(Fpla[1/cm2
]).
Usingthese newcolumnsandthe valuesfordepthandKT 3D surface plotsforeach lightsource
were producedtocompare the changesin lightintensity.
The last stage of the projectwasto showhow the numberof photonsusedinthe simulationsaffects
the overall qualityof the resultsgiven.Totestthisone KT value of 0.16 waschosen, the monte carlo

13
simulationswererun againforthe three tissue typeshoweverthistime the numberof photonsin
each simulationwaschangedwitheachsimulationusing100,000, 100, 10 photonsrespectively.The
resultsof eachsimulationwere placedintominitabandwere usedtoproduce scattergraphs
showingthe change inqualityateach concentrationof photons.

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Results:
3D Surface Plots for individual RBavalues:
To create graph 1 the followingstepswere taken:Take the Rvaluesacrossall KT valuesforRBa=0.05
producedby the QB64 program fromExcel and place themintoMinitab;In Minitabopenthe graph
tab and thenopen3D surface plots;the surface optionwasselectedandthe variablessetasZ=R,
Y=KT, X=S and thenplotted.
Graph 1 showsthat as scatteringcoefficient (S) valuesfortissueswithavalue of 0.05 for theirability
to reflectlightsources(RBa) increase thereisacoincidingexponential increase of the reflectionof
lightbythat tissue type (R).Italsoshowsthat as the absorptioncoefficient(KT) of the tissue
increasesthe amountof lightreflectedbythe tissue decreasesquicklyasmore isabsorbedbythe
tissue before quicklyincreasingagainafter.Thisisaresultsuggeststhata complex relationship
betweenKTandS exists.
R
0.040
0.045
100
50
S
0.050
0
15
30 KT(cm-1)
45
0
Surface Plot of R vs KT, S at RBa= 0.05

15
producedbythe QB64 program fromexcel andplace themintoMinitab;In Minitabopenthe graph
Graph 2 showsthat as scatteringcoefficient(S) valuesfortissueswithavalue of 0.1 for theirability
to reflectlightsources(RBa) increase thereisacoincidingexponential increase of the reflectionof
lightbythat tissue type (R).Italsoshowsthatas the absorptioncoefficient(KT) of the tissue
increasesthe amountof lightreflectedbythe tissue decreasesasmore isabsorbedintothe tissue
before quicklyincreasingagainafter.Thisisa result suggeststhata complex relationshipbetweenKT
and S exists.The graphalsoshowsan overall increaseinreflectionwhichthe increase of RBafrom
graph 1.
R
0.08
0.09
100
50
S 0
R 0.09
0.10
0
15
30 KT (cm-1)
45
Surface Plot of R vs KT, S at RBa=0.1

16
producedbythe QB64 program fromExcel and place themintoMinitab;In Minitabopenthe graph
to reflectlightsources(RBa) increase thereisanexponential increase of the reflectionof lightby
that tissue type (R).Italsoshowsthatasthe absorptioncoefficient(KT) of the tissue increasesthe
amountof lightreflectedbythe tissue decreasesasmore isabsorbedintothe tissue beforequickly
increasingagainafter.Thisisa resultsuggeststhata complex relationshipbetweenKTandS exists.
The graph alsoshows an overall increase inreflectionwhichthe increase of RBafromgraph 2.
0.12
R
0.13
100
50
S
0.14
0.15
0
15
KT (cm-1)30
45
0

17
to reflectlightsources(RBa) increase thereisanincrease of the reflectionof lightbythattissue type
(R) whichhas become lessexponentialandmore linear.Italsoshowsthatas the absorption
coefficient(KT) of the tissue increasesthe amountof lightreflectedbythe tissue decreasesasmore
isabsorbedintothe tissue onlythistime the reflectiondoesnotincrease assignificantlyafterwards.
Thissuggeststhatas the RBa increasesthe complex relationshipbetweenKTandS becomesover
shadowed.The graphalsoshowsan overall increase inreflectionwhichthe increase of RBafrom
graph 3.
R
0.150
0.165
0.180
100
50
S
R 0.180
0.195
0
15
30 KT (cm-1)
45
0

18
to reflectlightsources(RBa) increase thereisamore linearincrease inthe reflectance of lightby
that tissue type (R.Italsoshowsthat as the absorptioncoefficient(KT) of the tissue increasesthe
amountof lightreflectedbythe tissue decreasesasmore isabsorbedintothe tissue butnow there
isa onlyverysmall increase after,thisresultalsosuggeststhatasthe RBa increasesthe complex
relationshipbetweenKTandS becomesovershadowed.The graphalsoshowsthatas the RBa of the
tissue increasesthe rate atwhichreflectiondropsandlevelsoutdue tothe increase inKTalso
increases,italsoshowsthatagainas the RBa value forthe tissue increasessodoesthe overall
reflectionof lightbythe tissue whencomparedforgraph4.
0.18
0.20
0.22
100
50
S 0
R 0.22
0.24
30
KT (cm-1)45
15
30
0
KT (cm-1)

19
to reflectlightsources(RBa) increase thereisaalmostlinearincrease inthe reflectance of lightby
that tissue type (R). Italsoshowsthat as the absorptioncoefficient(KT) of the tissue increasesthe
amountof lightreflectedbythe tissue decreasesasmore isabsorbedintothe tissue onlythistime
there isno increase inreflectionafterwardsasKT continuestoincrease,insteadthe reflectionleverls
simplylevel off.Thisshowsthatasthe RBa increasesthe complex relationshipbetweenKTandS has
become overshadowed.The graphalsoshowsagainthatas the RBa of the tissue increasesthe rate
at whichreflectiondropsandlevelsoutdue tothe increase inKTalso increasesevenmore,italso
showsthat withthe increase of the RBa value forthe tissue the overall reflectionof lightbythe
tissue increasesagainwhencomparedtograph5.
0.20
0.25
100
50
S
0
R
0.25
0.30
0
15
30
KT (cm-1)45

20
to reflectlightsources(RBa) increase thereisanearlylinearincrease inthe reflectance of lightby
that tissue type (R).Italsoshowsthatas the absorptioncoefficient(KT) of the tissue increasesthe
amountof lightreflectedbythe tissue quicklydecreasesasmore isabsorbedintothe tissue before
levellingout.The graphshowsagainthat as the RBa of the tissue increasesthe rate atwhich
reflectiondropsandlevelsoutdue tothe increase inKTalso increasesevenmore,italsoshowsthat
withthe increase of the RBa value forthe tissue the overall reflectionof lightbythe tissue increases
againwhencomparedto graph6.
R
0.20
0.25
100
50
S
R
0.30
0.35
0
15
30 KT (cm-1)
45
0

21
producedbythe QB64 program fromExcel and place theminto Minitab;In Minitabopenthe graph
to reflectlightsources(RBa) increase thereisanincrease inthe reflectance of lightbythattissue
type (R) whichisbecomingmore exponentialsimilartothe lowerRBavalues.Italsoshowsthat as
the absorptioncoefficient(KT) of the tissue increasesthe amountof lightreflectedbythe tissue
quicklydecreasesasmore isabsorbedintothe tissue before levelling.The graphshowsagainthat as
the RBa of the tissue increasesthe rate atwhichreflectiondropsandlevelsoutdue tothe increase
inKT also increasesevenmore,italsoshowsthatwiththe increase of the RBavalue forthe tissue
the overall reflectionof lightbythe tissue increasesagainwhencomparedtograph7.
R
0.2
0.3
100
50
S
R
0.4
0
15
30 KT (cm-1)
45
0

22
to reflectlightsources(RBa) increase thereisanincreasinglymore exponential increase inthe
reflectance of lightbythattissue type (R).Italsoshowsthat as the absorptioncoefficient(KT) of the
tissue increasesthe amountof lightreflectedbythe tissue quicklydecreasesasmore isabsorbed
intothe tissue before levellingout.The graphshowsagainthat as the RBa of the tissue increasesthe
rate at whichreflectiondropsandlevelsoutdue tothe increase inKTalsoincreasesevenfurther
howevernotassignificantlyasinpreviousresults,italsoshowsthatwiththe increase of the RBa
value forthe tissue there isa slightincrease inthe overall reflectionof lightbythe tissue when
comparedto graph 8.
R
0.2
0.3
100
50
S
R
0.4
0
15
30 KT (cm-1)
45
0

23
To create graph 10 the followingstepsweretaken:Take the Rvaluesacrossall KT valuesforRBa=0.5
Graph 10 showsthat as scatteringcoefficient(S) valuesfortissueswithavalue of 0.5 for their ability
to reflectlightsources(RBa) increase thereisanexponential increase inthe reflectance of lightby
that tissue type (R).Italsoshowsthatas the absorptioncoefficient(KT) of the tissue increasesthe
amountof lightreflectedbythe tissue quicklydecreasesasmore isabsorbedintothe tissue before
levellingout.The graphshowsagainthat as the RBa of the tissue increasesthe rate atwhich
reflectiondropsandlevelsoutdue tothe increase inKTalso slightlyincreaseshowevernoas
significantlyasbefore,italsoshowsthatwiththe increase of the RBavalue forthe tissue there isa
slightincrease inthe overall reflectionof lightbythe tissue whencomparedtograph9.
R
0.2
0.3
100
S
50
R
0.4
0.5
0
15
KT (cm-1)
30
450

24
To create graph 11 the followingstepsweretaken:Take the Rvaluesacrossall KT valuesfor
RBa=0.55 producedbythe QB64 program fromExcel and place themintoMinitab;InMinitabopen
the graph tab and thenopen3D surface plots;the surface optionwasselectedandthe variablesset
as Z=R, Y=KT, X=S and thenplotted.
Graph 11 showsthat as scatteringcoefficient(S) valuesfortissueswithavalue of 0.55 fortheir
abilitytoreflectlightsources(RBa) increasethere isaslightlylessexponentialincrease inthe
tissue increasesthe amountof lightreflectedbythe tissue quicklydecreases asmore isabsorbed
intothe tissue before levellingout.The increase of the rate at whichReflectance dropsandlevels
out due to KT increaseshoweverissosmall now thatit cannotbe seenonthe graph. Itshowsthat
againwiththe increase of the RBa value forthe tissue there isaverysmall increase inthe reflection
of lightbythe tissue whencomparedtograph10.
0.2
R
0.3
0.4
100
50
S
0.4
0.5
15
KT (cm-1)30
45
0
0
KT (cm-1)

25
to reflectlightsources(RBa) increase thereisaslightlyless exponential more linearincreaseinthe
tissue increasesthe amountof lightreflectedbythe tissue quicklydecreases asmore isabsorbed
intothe tissue before levellingout.The increase of the rate at whichReflectance dropsandlevels
out due to KT doesincrease whencomparedtopreviousRBaresultshoweverissosmall now that it
cannot be seenonthe graph. It showsthatagain withthe increase of the RBa value forthe tissue
there isa verysmall increase inthe reflectionof lightbythe tissue whencomparedtograph11.
0.2
100
50
S 0
R 0.4
0.6
0
15
30
KT (cm-1)45

26
Graph 13 showsthat as scatteringcoefficient(S) valuesfortissueswithavalue of 0.65 fortheir
abilitytoreflectlightsources(RBa) increasethere isanalmostlinearincrease inthe reflectance of
lightbythat tissue type (R).The increase of the rate at whichReflectance dropsandlevelsoutdue to
the increasesinKT andRBa hasledto it beingvisualisedasanalmostvertical drop.The graph also
showsthat differentiatingfromthe patternsofar the increase of the RBa value forthe tissue leadto
a decrease inthe overall reflectionof lightbythe tissue whencomparedtograph12.
0.2
100
50
S
0
R 0.4
0.6
0
15
30
KT (cm-1)45

27
to reflectlightsources(RBa) increase thereisanalmostlinearincrease inthe reflectance of lightby
that tissue type (R). The increase of the rate at whichReflectance dropsandlevelsoutdue tothe
increasesinKTand RBa has ledto itbeingvisualisedasanalmostvertical drop.The increase of the
rate at whichReflectance dropsandlevelsoutdue toKT doesincrease whencomparedtoprevious
RBa resultshoweverissosmall nowthatit cannotbe seenonthe graph.However,thisgraphalso
showsthat the increase of the RBa value forthe tissue leadtoa decrease inthe overall reflectionof
lightbythe tissue whencomparedtograph 13.
R
0.0
0.2
0.4
100
50
S
R 0.4
0.6
30 KT (cm-1)
45
0
15
30 KT (cm-1)
0
KT (cm-1)

28
Graph 15 showsthat as scatteringcoefficient(S) valuesfortissueswith avalue of 0.75 fortheir
abilitytoreflectlightsources(RBa) increasethere isanalmostlinearincrease inthe reflectance of
lightbythat tissue type (R). The increase of the rate at whichReflectancedropsandlevelsoutdue
to the increasesinKT andRBa hasledto it beingvisualisedasanalmostvertical drop.The graph also
showsthat the increase of the RBa value forthe tissue leadtoa decrease inthe overall reflectionof
lightbythe tissue whencomparedtograph 14.
0.0
0.2
0.4
100
50
S 0
50
R
0.4
0.6
30
KT (cm-1)45
15
30
0
KT (cm-1)

29
Surface Plots for Different Light Sources:
To create Graph 16 the followingstepswere taken:The valuesof Fsphforall KT valuesobtained
throughthe Code::BlocksMonte Carlosimulationprogramusing100,000 photonswere transferred
to a newMinitabprojectalongside the KTvaluesandrespectivedepth;Usingthe calculatorin
Minitabthe natural Log of these valueswascalculatedandplacedintotheirowncolumn;InMinitab
openthe graph tab and thenopen3D surface plots;The wireframe optionwasselectedandthe
variablessetasZ= log(Fsph[1/cm2]),Y=Depth,X=KTandthenplotted.
Graph 16 showsthe effectthatboth penetratingfurtherintothe tissue andincreasingthe
absorptioncoefficient(KT) canhave onthe lightintensityfromaspherical lightsource suchas a light
on the tipof a fibre optic.Asshowninthe graph as the lightpenetratesfurtherintothe tissuethe
intensityof the lightdecreasesasmore lightisscattered,reflectedandabsorbed.Alsoshowninthe
graph isthat the lightintensityfromaspherical source alsodecreasesasthe KTof the tissue
increases.
log(Fsph[1/cm2])
-5
0
0.2
0.1
Kt (cm-1)
0.20.2
log(Fsph[1/cm2])
5
depth [cm]2
3
0.0
1
depth [cm]2
0
depth [cm]
Surface Plot of log(Fsph[1/cm2]) vs depth [cm], Kt

30
To create Graph 17 the followingstepswere taken:The valuesof Fcyl forall KT valuesobtained
variablessetasZ= log(Fcyl[1/cm2]),Y=Depth,X=KTandthenplotted.
absorptioncoefficient(KT) canhave onthe lightintensityfromacylindrical lightsource suchasa
fluorescenttube.Asshowninthe graphasthe lightpenetratesfurtherintothe tissue the intensity
of the lightdecreasesasmore lightisscattered,reflectedandabsorbedhoweverthisdecreaseisnot
as significantasshownbythe lightsource ingraph 16. Alsoshowninthe graphis that lightintensity
fromthissource ismore greatlyeffectbythe increase inKTthan ingraph 16.
log(Fcyl[1/cm2])
-6
-3
0
0.2
0.1
Kt (cm-1)
0
3
2
3
0.0
1
depth [cm]2
0
depth [cm]
Surface Plot of log(Fcyl[1/cm2]) vs depth [cm], Kt

31
To create Graph 18 the followingstepswere taken:The valuesof Fplafor all KT valuesobtained
variablessetasZ= log(Fpla[1/cm2]),Y=Depth,X=KTandthenplotted.
absorptioncoefficient(KT) canhave onthe lightintensityfromaplanarlightsource such as a
computerscreen.Asshowninthe graph as the lightpenetratesfurtherintothe tissue the intensity
of the lightdecreaseshowever,the decrease forthese planarlightsourcesisfarlesssignificantthan
as shownforthe sourcesingraphs16 and17. Alsoshowninthe graph is thatlightintensityfromthis
source exponentiallydecreasesasthe KTof the tissue increasesandthatthisdecrease ismore
significantthaninbothgraphs16 and 17.
log(Fpla[1/cm2])
-4
0
0.2 0.1
Kt (cm-1)
4
3
0.0
1
depth [cm]2
0
depth [cm]
Surface Plot of log(Fpla[1/cm2]) vs depth [cm], Kt

32
Scatterplots of Different Light Sources andDifferentPhotonNumbers:
To create Graph 19 the followingstepswere taken:The valuesof FsphforKT=0.16 obtained through
the Code::BlocksMonte Carlosimulationprogrammeasuringresultsbetween0-3cmand producing
a resultevery0.03cm using100,000 photonswere transferredtoanew Minitabprojectalongside
the absorptiondepth;InMinitabopenthe graphtab and thenopenScatterplot;The simple option
was selectedandthe variablessetasX= depth(cm),andY= Fsph[1/cm2] and thenplotted.
Graph 19 showshowlightintensityfromspherical sourcessuchasa lightonthe tipof a fibre optic
are affectedasthey penetrate deeperintothe tissue sampleshowingthatthe furtherthe light
travelsthe lessintenseitbecomes.The graphalsoshowshow using100,000 photonsinthe Monte
Carlosimulationresultsincleansmoothresults.
depth [cm]
Fsph[1/cm2]
3.02.52.01.51.00.50.0
14
12
10
8
6
4
2
0
Scatterplot of Fsph [1/cm2] vs depth [cm] at 100,000 photons

33
To create Graph 20 the followingstepswere taken:The valuesof Fcyl forKT=0.16 obtainedthrough
a resultevery0.03cm using100,000 photonswere transferredto anew Minitabprojectalongside
was selectedandthe variablessetasX= depth(cm),andY= Fcyl [1/cm2] and thenplotted.
Graph 20 showshowlightintensityfromcylindrical sourcessuchasa fluorescenttube are affected
as theypenetrate deeperintothe tissue sample showingthatthe furtherthe lighttravelsthe less
intense itbecomes.The graphshowsthatthe lightintensityof cylindrical lightsourcesisless
affectedbythe increasingdepthasittravelsintothe tissue thanthe spherical lightsource ingraph
19. The graph alsoshowshowusing100,000 photonsinthe Monte Carlo simulationresultsinclean
smoothresults.
depth [cm]
Fcyl[1/cm2]
3.02.52.01.51.00.50.0
8
7
6
5
4
3
2
1
0
Scatterplot of Fcyl [1/cm2] vs depth [cm] at 100,000 photons

34
To create Graph 21 the followingstepswere taken:The valuesof FplaforKT=0.16 obtainedthrough
a resultevery0.03cm using100,000 photonswere transferredtoanew Minitabprojectalongside
was selectedandthe variablessetasX= depth(m),andY= Fpla[1/cm2] andthenplotted.
Graph 21 showshowlightintensityfromplanarsourcessuchasa computerscreensare affectedas
theypenetrate deeperintothe tissue sample showingthatthe furtherthe lighttravelsthe less
intense itbecomes.The graphshowsthatthe lightintensityof planarlightsourcesislessaffectedby
the increasingdepthasittravelsintothe tissue thanthe spherical andcylindrical lightsourcesin
graphs 19 and20 forboth spherical andcylindrical.The graphalsoshowshow using100,000
photonsinthe Monte Carlosimulationresultsincleansmoothresults.
depth [cm]
Fpla[1/cm2]
3.02.52.01.51.00.50.0
14
12
10
8
6
4
2
0
Scatterplot of Fpla [1/cm2] vs depth [cm] at 100,000 photons

35
To create Graph 22 the followingstepswere taken:The valuesof FsphforKT=0.16 obtainedthrough
a resultevery0.03cm using100 photonswere transferredtoanew Minitabprojectalongside the
absorptiondepth;InMinitabopenthe graphtab and thenopenScatterplot;The simple optionwas
selectedandthe variablessetasX=depth(cm),and Y= Fsph [1/cm2] and thenplotted.
are affectedastheypenetrate deeperintothe tissue sampleshowingthatthe furtherthe light
travelsthe lessintenseitbecomes.The graphalsoshowshow using100 photonsinthe Monte Carlo
simulationresultsinlesssmoothandmore noisyresultsthanthose producedby100,000 photonsin
graph 19.
depth [cm]
Fsph[1/cm2]
3.02.52.01.51.00.50.0
9
8
7
6
5
4
3
2
1
0
Scatterplot of Fsph [1/cm2] vs depth [cm] at 100 photons

36
the Code::BlocksMonte Carlosimulation programmeasuringresultsbetween0-3cmand producing
selected andthe variablessetasX=depth(cm),and Y= Fcyl [1/cm2] and thenplotted.
22. The graph alsoshowshowusing100 photonsinthe Monte Carlo simulationresultsinunsmooth
resultswhencomparedtograph20.
depth [cm]
Fcyl[1/cm2]
3.02.52.01.51.00.50.0
7
6
5
4
3
2
1
0
Scatterplot of Fcyl [1/cm2] vs depth [cm] at 100 photons

37
selectedandthe variablessetasX=depth(cm),and Y= Fpla[1/cm2] and thenplotted.
graphs 22 and23 forboth spherical andcylindrical.The graphalsoshowshow using100 photonsin
the Monte Carlosimulationresultsinlesssmoothresultsthancomparedtograph 21.
depth [cm]
Fpla[1/cm2]
3.02.52.01.51.00.50.0
14
12
10
8
6
4
2
0
Scatterplot of Fpla [1/cm2] vs depth [cm] at 100 photons

38
To create Graph 25 the followingstepswere taken:The valuesof FsphforKT=0.16 obtainedthrough
a resultevery0.03cm using10 photonswere transferredtoa new Minitabprojectalongsidethe
selectedandthe variablessetasX=depth(cm),and Y= Fsph[1/cm2] and thenplotted.
are affectedastheypenetrate deeperintothe tissue sampleshowingthatthe furtherthe light
travelsthe lessintenseitbecomes.The graphalsoshowshow using10 photonsinthe Monte Carlo
simulationresultsinveryunsmoothandverynoisyresultswhencomparedtothose producedby
100,000 photonsingraph19.
depth [cm]
Fsph[1/cm2]
3.02.52.01.51.00.50.0
6
5
4
3
2
1
0
Scatterplot of Fsph [1/cm2] vs depth [cm] at 10 photons

39
a resultevery0.03cm using10 photonswere transferredtoa new Minitabprojectalongsidethe
selectedandthe variablessetasX=depth(cm),and Y= Fcyl[1/cm2] and thenplotted.
25. The graph alsoshowshowusing10 photonsinthe Monte Carlosimulationresultsin very
unsmooth andverynoisyresultswhencomparedtograph20 whichused100,000 photonsto
produce the resultsinitssimulation.
depth [cm]
Fcyl[1/cm2]
3.02.52.01.51.00.50.0
7
6
5
4
3
2
1
0
Scatterplot of Fcyl [1/cm2] vs depth [cm] at 10 photons

40
a resultevery0.03cm using10 photonswere transferredtoa new Minitab projectalongsidethe
selectedandthe variablessetasX=depth(cm),and Y= Fpla[1/cm2] and thenplotted.
graphs 25 and26 forboth spherical andcylindrical.The graphalsoshowshow using10 photonsin
the Monte Carlosimulationresultsinveryunsmoothandverynoisyresultswhencomparedtograph
21 whichused100,000 photonsto produce the resultsinitssimulation.
depth [cm]
Fpla[1/cm2]
3.02.52.01.51.00.50.0
16
14
12
10
8
6
4
2
0
Scatterplot of Fpla [1/cm2] vs depth [cm] at 10 photons

41
Scatter graphfor Differentiating Scattering Coefficient valuesandtheir effect
on Light PenetrationandReflectance Coefficients:
To create graph 28 the followingstepsweretaken:Usingthe Marco inExcel producedbyDr. Hagan
take the depthvalue at whichthe Reflectance valuesleveloutateach value forS ranging5-100;
Place these depthvaluesinatable againsttheircorrespondingvalue forS;OpenInserttabinExcel;
Chose Scattergraphs; Firstoptionwithmarkersonlywaschosenandplotted.
Graph 28 showshowfar lightcan penetrate intosample tissueseachwithadifferentScattering
coefficient(S) value rangingfrom5-100.The graph showsthatas the S value increases,the depthto
whichlightisable to penetrate decreasessuggestingthatincreasedscatteringaffectslight
penetration.
0
5
10
15
20
25
0 20 40 60 80 100 120
Depthatwhichlightcanbeabsorped
(mm)
S value
Graph showing the maximumdepth at which
light can penetrate to in a sample tissues at
certain values for S

42
To create graph 29 the followingstepsweretaken:Usingthe Marco inExcel producedbyDr. Hagan
take value at whichthe Reflectance valuesleveloutateach value forS ranging5-100; Place these
depthvaluesinatable againsttheircorrespondingvalue forS;OpenInserttabinExcel;Chose
Scatter graphs;Firstoptionwithmarkers onlywaschosenandplotted.
Graph 28 showshowthe Reflectance coefficientisaffectedbydifferentScatteringcoefficient(S)
valuesrangingfrom5-100. The graph showsthat as the S value increases,the reflectancecoefficient
of the tissue increases aswell.Thissuggeststhatthere isarelationshipbetweenthese two
coefficients.
0.82
0.84
0.86
0.88
0.9
0.92
0.94
0.96
0.98
0 20 40 60 80 100 120
Rvalue
S value
A graph showing the effectof increased
Scattering coefficient on the Reflectance
coefficient of sample tissues
R value

43
Discussion:
ThisprojectusedMonte Carlo simulationstotestthe null hypothesisthat“A change in the Diffuse
reflectance,scatteringcoefficientorabsorptioncoefficientwillhave noeffectonthe overall
Reflectance of lightbyHumantissue.”Overthe course of the projecttwoothersmallernull
hypothesiswereformulated,one statingthat“A change in the lightsource usedwill notaffectthe
abilityof the lightphotonstopenetrate intohumantissue samples”and“The numberof photons
usedinMonte Carlosimulationsdoesnotaffectthe overall qualityof the resultsprovided”.
The resultswhichwere obtainedandare showningraphs1-15 show that as the RBa of the tissue
samplesincreasedthe overall reflectance of lightbythe tissue samplechanged.BetweenRBa0.05
and 0.6 itwas shownthatthe overall reflectance (R) of the tissue increasedfrom0.05to 0.53, thisis
because asRBa valuesincrease the greaterthe amountof lightphotonswhichwill simplyreflectof
the tissuessurface (Golnabi,2001).BetweenRBa0.6 and 0.75 howeverthe overall reflectionof light
photonsbythe tissue drops.
AlsoshowninGraphs 1-15 isthat changesinKT resultinchangesof the overall reflectance of the
tissue forexample ingraph13 at KT 0.1 (cm-1
) the reflectance of the tissue is0.56howeverbythe
time that KT hasincreasedto5 (cm-1
) the reflectance of the tissue hasdroppedto0.09. Thisshows
that as KT increasesthe amountof lightphotonsbeingabsorbedbythe tissue insteadof being
reflectedincreasesaswell.
Graphs 1-15 alsoshowthat as the S valuesincrease foreachtissue sample the overallreflectanceof
the tissue increases thisisdue tothe increasedscatteringof the lightphotonswhichmakesitharder
fromthemto penetrate the tissue (Hanrahan,andKrueger,1993). For RBa 0.5 at KT 50 the S values
increasedfrom0.18 to 0.36 whereasforKT 0.1 S valuesincreasedfrom0.46 to 0.50.
Thisraiseda questionwhichhadnotbeenhypothesisedinthat“dothe scatteringcoefficient,
absorbance coefficientanddiffuse reflectance directlyaffecteachother”.
These resultshoweverare able todisprove ourinitial nullhypothesis that“A change inthe Diffuse
reflectance,scatteringcoefficientorabsorptioncoefficientwillhave noeffectonthe overall
Reflectance of lightbyHumantissue.”
The graphs 16-18 were createdwhenone of the smalleradditional null hypotheseswasadded.From
graphs 16-18 youcan see thatthe spherical,cylindricalandplanarlightsourcesare all affectedby
the increase inKT and depthintothe tissue,howeverwhilespherical andcylindricallightsource
intensitiesdecreasedatsimilarrates,graph18 showsthatplanar lightsourceswere able tomaintain

44
theirintensityforlongerbefore beginning todecrease.These resultsare supportedby(Songetal.,
2013) whoshowedthatas the lightsource whenfurtherintothe tissue samplethe lowerthe light
intensitybecame,theyalsoshowedthatasthe distance betweenthe photosensitivesensorandthe
lightsource increasedthe lightintensityagaindropped.Thesegraphshelptodisprove thisnull
hypothesisandhelptoshowthatdifferentlightsourcesdo have aneffectonthe abilityof photons
to penetrationtissuesamples.Despitedisprovingthe null hypothesesthese resultsdidraise another
issue,forall lightsourcesthe graphsshowedthatbythe time the photonshadpenetratedupto2cm
the overall intensityhaddroppedtonearly0.Thiswouldbe an issue intermsof PDT drugs and
gettinga bigenoughexcitementtothe sensortoattack the tumouror evenexcitingthematall
wouldprove difficultatsimilartissuedepths.One possible answertothis isto have small
excitementsof PDTdrugsall overthe tumour(Samiaetal.,2003, Juzenasetal.,2011).
Nanoparticlesrange from2-100µm and are coveredingoldandzinc photodynamicdrugsare a
solutionforPDTdrugs whichiscurrentlybeingresearched (Samiaetal.,2003, Juzenasetal.,2011).
Usinga wavelengthof 488nm theyare able toavoidmuch of the scatterand absorbance that
resultedinthe lightsourcestestedinprojectdyingout(Samiaetal.,2003). Due to the lack or scatter
and absorbance these nanoparticlesare able toreachtumoursthat are deepwithintissue with
recordsshowingtripletstate oxygenbeingconvertedtosingletstate oxygenat1270mm (Samiaet
al.,2003).
The final null hypothesesthatwasaddedwasthat “The numberof photonsusedinMonte Carlo
simulationsdoesnotaffectthe overall qualityof the resultsprovided”. Totestthishypothesesthe
numberof photonswasloweredforeachlightsource at a chosenKT value of 0.16 from 100,000
photonsto 100 to 10. From graphs 19, 22, 25 you can see thatthe FsphMonte Carlo simulationrun
using10 photonsproducedresultsthatwere considerablemore noisythanthose producedby100
and 100,000 photons.
For the Fcyl Monte Carlosimulationsyoucansee thatgraphs 23 and 26 for 10 and 100 photons
producedmessyandnoisyresultswhencomparedto100,000 photonsusedingraph 20. A reason
maybe behindwhyboth100 and10 photongraphswere noisyforFcyl but notfor Fsphis that
Monte Carloisrandom andtherefore 100,000 have a higherchance of gettingthe correct answer
more often,butfor the same reasonsitis possible forasimulationusing100 photonsto obtain
randomresultsthatfollowthe correcttrendneatlywhichiswhatmay have happenedinFsph
simulationshowningraph22.

45
The Fpla Monte Carlo simulationingraph21 using100,000 photonsgave cleanresults,butgraphs24
and 27 at 100 and 10 photonsbothproducednoisyresultswhencompared.A trendalsoshown
throughoutgraphs19-27 isthat Fplamaintainsitslightintensityforthe longestperiodof time,
helpingtosupportthe resultsobtainedinthe surface plotsingraphs16-18. The reasonbehindthe
messyandnoisyresultsforthe majorityof graphsat 100 and 10 photonsisbecause of the
randomisationof Monte Carloandthere simplyaren’tenoughphotonsavailable torepeatthe
experimenttoobtaindesiredresults.
These resultsare supportedby(Limetal.,2001) whoshowedthatas tissue depthincreasedlight
intensitydecreasedexponentially.(Yoonetal.,1987) also supportthese resultswiththeirfindson
flurence ratesandtissue depth.
(Flocketal.,1989) helptosupportour resultsastheyalsofoundthat highernumbersof photons
needtobe usedinMonte Carlo simulationstoobtaincleanprecise results.These resultsdisprove
the null hypothesesthat“The numberof photonsusedinMonte Carlo simulationsdoesnotaffect
the overall qualityof the resultsprovided”.
Graphs 28 and 29 were placedinto supportinformationgatheredanddisplayedinother graphs.
Graph 28 showshowincreasingvaluesof Sresultindecreasingpenetrationbythe lightphotons
supportinggraphs1-15 whichshowthatas S increasessodoesthe valuesforR across all RBa values.
Graph 29 also supportsthese findsasitshowsa directrelationshipbetweenanincrease inSvalues
and an increase inR values.
Conclusion:
Thisstudyhelpedtoshowthat the scatteringcoefficient,absorptioncoefficientanddiffuse
reflectance of individual tissuesamplesall have aneffectonthe abilityof thattissue toreflectlight
froma numberof sourcesnamelyspherical,cylindrical andplanar.Anotherresultobservedthat
wasn’tanticipatedwasthe possibilityof acomplex relationshipinvolvingall three of the factorsthat
theytested. The implicationof the resultsof these testsacrossall valuesof RBaisthat hopefully
theywill enable otherstocalculate the optimumdepthof tissue atwhichtoplace a PDT drug or a
photosensitivesensor.Theywill alsobe able touse these resultstodecide onthe type of light
source to use and the wavelengthatwhichtouse it at.
These resultshave openedupotherroutesof investigationaswell,the reductionof lightintensityin
all lightsourcesto nearly0 at 2cm meanthat alternative optionswill have be sourcedandas
mentionednanoparticlescouldbe asolutionfortumourcellsata depthwhere traditional light

46
sourcescannotexcite the drugenoughto combatthe tumour.The complex relationshipbetween
scatteringandabsorbance coefficientanddiffusereflectancewillalsohave tobe investigatedto
discovertheirindividual andcombinedeffectsonlightpropagationandthemselves.

47
Acknowledgements
I would like to thank Dr. Paul Hagan for his help throughout this project, his guidance
through the programming side of the project and his general engagement throughout made
the whole process more logical and easier to put across.
I would also like to thank both my parents for their continued support throughout my
education both now and in the future, as without their support and reassurance I reckon
there would have been a lot of extensions asked for and many more EC1 forms filled in.
I would also like to thank Google, Youtube and The Buckfast Monks who have never left my
side throughout my time here at university and have pulled me through countless
assignments and kept me sane these last few weeks.
One final acknowledgement I would like to make is to Miss Sarah Curran, without her I very
much doubt I would have progressed to this stage of my degree with so little drama, her
constant nagging and making sure I have my head screwed on about my work has ensured
that I progressed through final year and am now so close to graduating.

48
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51
Appendix:
Appendix A Showsthe Marcoproducedby Dr. Hagan to obtainthe S, R and DepthvaluesforGraphs
28 and 29.

52
Appendix BShowsthe QB64 program usedto obtainthe R valuesforthe differentRBa and KT
valuesused.

53
Appendix CShows one sheetof the Excel Documentineachthe RBa andKT valueswere organised.

54
Appendix DShowsanexample MinitabProjectfora surface plotforone of the RBa value.

55
Appendix Eshowsthe minitab projectinwhichthe surface plotsforthe differentlightsourceswere
generated.

56
Appendix Fshowsthe MintabProjectinwhichthe 100,000 scatter plotsforlightsourceswere
generated.

57
Appendix G shows the code for the Monte Carlo simulation that was carried
out in Code::Blocks.
/********************************************
* Monte Carlo simulation yielding spherical, cylindrical, and planar
* responses to an isotropic point source in an infinite homogeneous
* medium with no boundaries. This program is a minimal Monte Carlo
* program scoring photon distributions in spherical, cylindrical,
* and planar shells.
**********/
#include <math.h>
#include <stdio.h>
#define PI 3.1415926
#define LIGHTSPEED 2.997925E10 /* in vacuo speed of light [cm/s] */
#define ALIVE 1 /* if photon not yet terminated */
#define DEAD 0 /* if photon is to be terminated */
#define THRESHOLD 0.01 /* used in roulette */
#define CHANCE 0.1 /* used in roulette */
#define COS90D 1.0E-6
/* If cos(theta) <= COS90D, theta >= PI/2 - 1e-6 rad. */
#define ONE_MINUS_COSZERO 1.0E-12
/* If 1-cos(theta) <= ONE_MINUS_COSZERO, fabs(theta) <= 1e-6 rad. */
/* If 1+cos(theta) <= ONE_MINUS_COSZERO, fabs(PI-theta) <= 1e-6 rad.
*/
#define SIGN(x) ((x)>=0 ? 1:-1)
#define InitRandomGen (double) RandomGen(0, 1, NULL)
/* Initializes the seed for the random number generator. */
#define RandomNum (double) RandomGen(1, 0, NULL)
/* Calls for a random number from the randum number generator. */
/* DECLARE FUNCTION */
double RandomGen(char Type, long Seed, long *Status);
/* Random number generator */
main() {
/* Propagation parameters */
double x, y, z; /* photon position */
double ux, uy, uz; /* photon trajectory as cosines */
double uxx, uyy, uzz; /* temporary values used during SPIN */
double s; /* step sizes. s = -log(RND)/mus [cm] */
double costheta; /* cos(theta) */
double sintheta; /* sin(theta) */
double cospsi; /* cos(psi) */
double sinpsi; /* sin(psi) */
double psi; /* azimuthal angle */
double i_photon; /* current photon */
double W; /* photon weight */
double absorb; /* weighted deposited in a step due to absorption */
short photon_status; /* flag = ALIVE=1 or DEAD=0 */
/* other variables */
double Csph[101]; /* spherical photon concentration CC[ir=0..100] */
double Ccyl[101]; /* cylindrical photon concentration CC[ir=0..100] */
double Cpla[101]; /* planar photon concentration CC[ir=0..100] */

58
double Fsph; /* fluence in spherical shell */
double Fcyl; /* fluence in cylindrical shell */
double Fpla; /* fluence in planar shell */
double mua; /* absorption coefficient [cm^-1] */
double mus; /* scattering coefficient [cm^-1] */
double g; /* anisotropy [-] */
double albedo; /* albedo of tissue */
double nt; /* tissue index of refraction */
double Nphotons; /* number of photons in simulation */
short NR; /* number of radial positions */
double radial_size; /* maximum radial size */
double r; /* radial position */
double dr; /* radial bin size */
short ir; /* index to radial position */
double shellvolume; /* volume of shell at radial position r */
double CNT; /* total count of photon weight summed over all bins */
/* dummy variables */
double rnd; /* assigned random value 0-1 */
short i, j; /* dummy indices */
double u, temp; /* dummy variables */
FILE* target; /* point to output file */
/**** INPUT
Input the optical properties
Input the bin and array sizes
Input the number of photons
*****/
mua = 1; /* absorption coefficient (KT)/ cm^-1 */
mus = 50; /* scattering coefficient (S)/ cm^-1 */
g = 0.90;
nt = 1.33;
Nphotons = 10000; /* set number of photons in simulation */
radial_size = 3.0; /* cm, total range over which bins extend */
NR = 100; /* set number of bins. */
/* IF NR IS ALTERED, THEN USER MUST ALSO ALTER THE ARRAY DECLARATION TO
A SIZE = NR + 1. */
dr = radial_size/NR; /* cm */
albedo = mus/(mus + mua);
/**** INITIALIZATIONS
*****/
i_photon = 0;
InitRandomGen;
for (ir=0; ir<=NR; ir++) {
Csph[ir] = 0;
Ccyl[ir] = 0;
Cpla[ir] = 0;
}
/**** RUN
Launch N photons, initializing each one before progation.
*****/
do {
/**** LAUNCH
Initialize photon position and trajectory.

59
Implements an isotropic point source.
*****/
i_photon += 1; /* increment photon count */
W = 1.0; /* set photon weight to one */
photon_status = ALIVE; /* Launch an ALIVE photon */
x = 0; /* Set photon position to origin. */
y = 0;
z = 0;
/* Randomly set photon trajectory to yield an isotropic source. */
costheta = 2.0*RandomNum - 1.0;
sintheta = sqrt(1.0 - costheta*costheta); /* sintheta is always
positive */
psi = 2.0*PI*RandomNum;
ux = sintheta*cos(psi);
uy = sintheta*sin(psi);
uz = costheta;
/* HOP_DROP_SPIN_CHECK
Propagate one photon until it dies as determined by ROULETTE.
*******/
do {
/**** HOP
Take step to new position
s = stepsize
ux, uy, uz are cosines of current photon trajectory
*****/
while ((rnd = RandomNum) <= 0.0); /* yields 0 < rnd <= 1 */
s = -log(rnd)/(mua + mus); /* Step size. Note: log() is base e
*/
x += s * ux; /* Update positions. */
y += s * uy;
z += s * uz;
/**** DROP
Drop photon weight (W) into local bin.
*****/
absorb = W*(1 - albedo); /* photon weight absorbed at this step */
W -= absorb; /* decrement WEIGHT by amount absorbed */
/* spherical */
r = sqrt(x*x + y*y + z*z); /* current spherical radial position */
ir = (short)(r/dr); /* ir = index to spatial bin */
if (ir >= NR) ir = NR; /* last bin is for overflow */
Csph[ir] += absorb; /* DROP absorbed weight into bin */
/* cylindrical */
r = sqrt(x*x + y*y); /* current cylindrical radial position */
Ccyl[ir] += absorb; /* DROP absorbed weight into bin */
/* planar */
r = fabs(z); /* current planar radial position */

60
Cpla[ir] += absorb; /* DROP absorbed weight into bin */
/**** SPIN
Scatter photon into new trajectory defined by theta and psi.
Theta is specified by cos(theta), which is determined
based on the Henyey-Greenstein scattering function.
Convert theta and psi into cosines ux, uy, uz.
*****/
/* Sample for costheta */
rnd = RandomNum;
if (g == 0.0)
costheta = 2.0*rnd - 1.0;
else {
double temp = (1.0 - g*g)/(1.0 - g + 2*g*rnd);
costheta = (1.0 + g*g - temp*temp)/(2.0*g);
}
sintheta = sqrt(1.0 - costheta*costheta); /* sqrt() is faster than sin().
*/
/* Sample psi. */
psi = 2.0*PI*RandomNum;
cospsi = cos(psi);
if (psi < PI)
sinpsi = sqrt(1.0 - cospsi*cospsi); /* sqrt() is faster than sin().
*/
else
sinpsi = -sqrt(1.0 - cospsi*cospsi);
/* New trajectory. */
if (1 - fabs(uz) <= ONE_MINUS_COSZERO) { /* close to perpendicular.
*/
uxx = sintheta * cospsi;
uyy = sintheta * sinpsi;
uzz = costheta * SIGN(uz); /* SIGN() is faster than division. */
}
else { /* usually use this option */
temp = sqrt(1.0 - uz * uz);
uxx = sintheta * (ux * uz * cospsi - uy * sinpsi) / temp + ux *
costheta;
uyy = sintheta * (uy * uz * cospsi + ux * sinpsi) / temp + uy *
costheta;
uzz = -sintheta * cospsi * temp + uz * costheta;
}
/* Update trajectory */
ux = uxx;
uy = uyy;
uz = uzz;
/**** CHECK ROULETTE
If photon weight below THRESHOLD, then terminate photon using Roulette
technique.
Photon has CHANCE probability of having its weight increased by factor
of 1/CHANCE,
and 1-CHANCE probability of terminating.
*****/
if (W < THRESHOLD) {
if (RandomNum <= CHANCE)
W /= CHANCE;

61
else photon_status = DEAD;
}
} /* end STEP_CHECK_HOP_SPIN */
while (photon_status == ALIVE);
/* If photon dead, then launch new photon. */
} /* end RUN */
while (i_photon < Nphotons);
/**** SAVE
Convert data to relative fluence rate [cm^-2] and save to file called
"mcpdtmin.out".
*****/
target = fopen("montecarlopdt.out", "w");
/* print header */
fprintf(target, "number of photons = %fn", Nphotons);
fprintf(target, "bin size = %5.5f [cm] n", dr);
fprintf(target, "last row is overflow. Ignore.n");
/* print column titles */
fprintf(target, "r [cm] t Fsph [1/cm2] t Fcyl [1/cm2] t Fpla
[1/cm2]n");
/* print data: radial position, fluence rates for 3D, 2D, 1D geometries */
for (ir=0; ir<=NR; ir++) {
/* r = sqrt(1.0/3 - (ir+1) + (ir+1)*(ir+1))*dr; */
r = (ir + 0.5)*dr;
shellvolume = 4.0*PI*r*r*dr; /* per spherical shell */
Fsph = Csph[ir]/Nphotons/shellvolume/mua;
shellvolume = 2.0*PI*r*dr; /* per cm length of cylinder */
Fcyl = Ccyl[ir]/Nphotons/shellvolume/mua;
shellvolume = dr; /* per cm2 area of plane */
Fpla =Cpla[ir]/Nphotons/shellvolume/mua;
fprintf(target, "%5.5f t %4.3e t %4.3e t %4.3e n", r, Fsph, Fcyl,
Fpla);
}
fclose(target);
} /* end of main */
/* SUBROUTINES */
/**************************************************************************
* RandomGen
* A random number generator that generates uniformly
* distributed random numbers between 0 and 1 inclusive.
* The algorithm is based on:
* W.H. Press, S.A. Teukolsky, W.T. Vetterling, and B.P.
* Flannery, "Numerical Recipes in C," Cambridge University
* Press, 2nd edition, (1992).
* and
* D.E. Knuth, "Seminumerical Algorithms," 2nd edition, vol. 2
* of "The Art of Computer Programming", Addison-Wesley, (1981).

62
*
* When Type is 0, sets Seed as the seed. Make sure 0<Seed<32000.
* When Type is 1, returns a random number.
* When Type is 2, gets the status of the generator.
* When Type is 3, restores the status of the generator.
*
* The status of the generator is represented by Status[0..56].
*
* Make sure you initialize the seed before you get random
* numbers.
****/
#define MBIG 1000000000
#define MSEED 161803398
#define MZ 0
#define FAC 1.0E-9
double RandomGen(char Type, long Seed, long *Status){
static long i1, i2, ma[56]; /* ma[0] is not used. */
long mj, mk;
short i, ii;
if (Type == 0) { /* set seed. */
mj = MSEED - (Seed < 0 ? -Seed : Seed);
mj %= MBIG;
ma[55] = mj;
mk = 1;
for (i = 1; i <= 54; i++) {
ii = (21 * i) % 55;
ma[ii] = mk;
mk = mj - mk;
if (mk < MZ)
mk += MBIG;
mj = ma[ii];
}
for (ii = 1; ii <= 4; ii++)
for (i = 1; i <= 55; i++) {
ma[i] -= ma[1 + (i + 30) % 55];
if (ma[i] < MZ)
ma[i] += MBIG;
}
i1 = 0;
i2 = 31;
} else if (Type == 1) { /* get a number. */
if (++i1 == 56)
i1 = 1;
if (++i2 == 56)
i2 = 1;
mj = ma[i1] - ma[i2];
if (mj < MZ)
mj += MBIG;
ma[i1] = mj;
return (mj * FAC);
} else if (Type == 2) { /* get status. */
for (i = 0; i < 55; i++)
Status[i] = ma[i + 1];
Status[55] = i1;
Status[56] = i2;
} else if (Type == 3) { /* restore status. */
for (i = 0; i < 55; i++)
ma[i + 1] = Status[i];
i1 = Status[55];

63
i2 = Status[56];
} else
puts("Wrong parameter to RandomGen().");
return (0);
}
#undef MBIG
#undef MSEED
#undef MZ
#undef FAC

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