Three-dimensional Monte Carlo model of pulsed-laser treatment of cutaneous vascular lesions

13 Pages·2012·1.24 MB·English

Three-dimensional Monte Carlo model of
pulsed-laser treatment of cutaneous
vascular lesions
Matija Milanicˇ
Boris Majaron
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JournalofBiomedicalOptics16(12),128002(December2011)
Three-dimensional Monte Carlo model of pulsed-laser
treatment of cutaneous vascular lesions
MatijaMilanicˇa andBorisMajarona,b
aJozˇefStefanInstitute,Jamova39,SI-1000Ljubljana,Slovenia
bUniversityofLjubljana,FacultyofMathematicsandPhysics,Jadranska19,SI-1000Ljubljana,Slovenia
Abstract.Wepresentathree-dimensionalMonteCarlomodelofopticaltransportinskinwithanovelapproachto
treatmentofsideboundariesofthevolumeofinterest.Thisrepresentsaneffectivewaytoovercometheinherent
limitationsof“escape”and“mirror”boundaryconditionsandenableshigh-resolutionmodelingofskininclusions
with complex geometries and arbitrary irradiation patterns. The optical model correctly reproduces measured
valuesofdiffusereflectancefornormalskin.Whencoupledwithasophisticatedmodelofthermaltransportand
tissuecoagulationkinetics,italsoreproducesrealisticvaluesofradiantexposurethresholdsforepidermalinjury
andforphotocoagulationofportwinestainbloodvesselsinvariousskinphototypes,withorwithoutapplication
ofcryogenspraycooling.(cid:2)C2011SocietyofPhoto-OpticalInstrumentationEngineers(SPIE).[DOI:10.1117/1.3659205]
Keywords:MonteCarlo;opticalmodel;threedimensions;boundarycondition;diffusereflectance;lasersurgery;vascularlesion;port
winestain;epidermalinjury;cryogenspraycooling.
Paper11390RreceivedJul.21,2011;revisedmanuscriptreceivedSep.23,2011;acceptedforpublicationOct.19,2011;published
onlineNov.23,2011.
1 Introduction relevantexampleisportwinestain(PWS)lesions,withblood
vesseldiametersrangingfrom20to300μm,whichareroutinely
The Monte Carlo (MC) technique is a powerful approach for
treatedwithlasersbeamswithadiameterof5mmormore.
modeling of light transport in strongly scattering biological
Toovercomethisproblem,wehavedevelopedanalternative
tissues. The resulting energy deposition maps can be used in
approach, called “extended layers.” Outside of the voxelized
numericalsimulationsofheattransportandconsequentphysio-
VOI, model photons are propagated in laterally infinite tissue
logicaleffectsinvarioustissuesandorgans.Inordertoobtain
layers,butwithoutrecordingthelocalenergydeposition.This
realisticresultsandtrustablepredictions,however,onemustap-
idea was introduced in the 3D MC optical model by Barton
ply appropriate optical parameters and a representative model
et al.,4 but only at the VOI bottom boundary, thus extending
ofthelesiongeometry.
the optical properties of dermis to the semi-infinite column of
Several earlier studies have extended the multilayer MC
modeldevelopedbyWangetal.1 tothreedimensions.2–4 This tissuebelowtheVOI.Aswedemonstrateinthefollowing,ex-
tendingthesameprincipletothelateraldimensionsoffersgreat
hasenabledtreatmentofskininclusionswitharbitraryshapesir-
advantages in terms of modeling flexibility, accuracy, and/or
radiatedwithspatiallyconfinedlaserbeams.Herein,wepresent
computationaldemands,dependingonwhichoftheformerap-
andtestanaugmentedMCmodeloflaser-irradiatedhumanskin,
proachesisusedforthepurposeofcomparison.
withspecialattentiondevotedtotreatmentofsideboundariesof
Afterdiscussingthemodelgeometryandselectionoftissue
thespatiallydiscretizedvolumeofinterest(VOI).
opticalproperties,wepresentfirstourpredictionsofdiffusere-
In earlier documented three-dimensional (3D) MC models,
flectanceofskinatwavelengthsof532,585,and595nm,which
eitheraperfectlyreflecting(mirror)orescapeboundarycondi-
are most commonly used for treatment of cutaneous vascular
tion (BC) was applied at the VOI’s side surfaces. Rigorously
lesions. Three epidermal melanin concentrations are consid-
speaking,however,thefirstapproachimpliesaninfinitelywide
ered, representing Caucasian, Asian, and African skin. Next,
irradiation beam and periodically distributed skin structures,
weanalyzethedifferencesbetweentheMCsimulationresults
whilethesecondissuitableonlyfortreatmentofentireorgans
as obtained by using the two boundary conditions mentioned
surroundedbyair.
aboveandourextendedlayersapproach,forirradiationofone
For all other cases, a common solution to prevent edge-
ortwobloodvesselsinhumanskinwitha1-mmdiameterlaser
related artifacts from affecting the results is to move the VOI
beam.
sideboundaries(usuallyoftheescapetype)sufficientlyfarfrom
Finally,wesimulatelasertreatmentofPWSlesionsbymeans
theinvestigatedstructure.However,thisapproachmaybecome
ofselectivephotothermolysis.5Tothisend,wecomplementour
prohibitively time- and memory consuming when studying
MC optical model by numerical modeling of thermal trans-
the response of small absorbing inclusions, requiring fine dis-
portandtissue-specificcoagulationkinetics.Radiantexposure
cretizationoftheVOI,toirradiationwithsignificantlylarger,yet
thresholds for complete photocoagulation of a typical PWS
still finite and not necessarily homogeneous laser beams. One
bloodvessel,aswellasforonsetofepidermalthermaldamage,
arecomputedfordifferentcombinationsoflaserwavelengthand
skinphototype,withandwithoutapplicationofcryogenspray
Address all correspondence to: Matija Milanic, Jozef Stefan Institute, Com-
plex Matter Department, Jamova 39, SI-1000 Ljubljana, Slovenia; Tel:
0038614773975;Fax:[phone];E-mail:[email protected]. 1083-3668/2011/16(12)/128002/12/$25.00(cid:2)C 2011SPIE
(cid:2)
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(CS) cooling,6 and correlated with values from some clinical layers are inherited from the border VOI elements at the re-
reports. spectivedepths,andthemajorityruleswhenevernotallofthem
Namely, despite the unquestionable enhancement of PWS representthesametissue.Perhapsmostimportantly,energyde-
treatment efficacy and safety offered by CS cooling, the risk positioniscomputedandrecordedonlywithintheVOI,which
of permanent epidermal injury still limits the applicable radi- keepsmemoryrequirementsatamanageablelevelandgreatly
ant exposure to levels inadequate for permanent PWS vessel reducesthecomputationtime.
coagulationinmanypatients,especiallythosewithdarkerskin The same principle is applied also at the bottom boundary
phototypes. Development of sufficiently detailed and realistic of the VOI. Specifically, the entire semi-space below the VOI
numericalmodelsofPWSresponsetolaserirradiationshould bottom boundary inherits the optical properties from the low-
facilitatepreliminarytestingofnoveltreatmentstrategieswith est VOI layer, which is occupied by adipose in all presented
the potential to allow safe and effective treatment for a larger examples.
numberofPWSpatients. TheMCcodeisimplementedinVisualC++ (VisualStudio
2008,Microsoft,Redmond,Washington).Utilizationofmulti-
plethreadshelpsspeedupthecomputation.
2 Methodology
2.1 OpticalTransportModel
2.2 SkinModelGeometryandOpticalParameters
Our simulation of light transport in PWS skin is based on the
Ourbasicskinmodeliscomposedofthreelayers,whichrepre-
well-established weighted-photon MC technique.1 In this ap-
senttheepidermis(thickness:60μm),dermis(1.5mm),anda
proach,alargenumberofenergypackets(“photons”)propagate
semi-infinitelayerofsubcutis.
throughthetissueanddepositafractionoftheirenergyintospe-
Melaninisassumedtobehomogeneouslydistributedwithin
cificvolumeelements,accordingtothelocalabsorptionprop-
theepidermis.Theeffectivefractionalcontentofmelanin(f )
erties.Stochasticrelationsareusedtodetermineeachphoton’s mel
is calculated from absorption coefficient at 694 nm (μ ) as
randomtrajectory,accordingtophysicallawsoflightscattering, a,epi
determinedfromdiffusereflectancemeasurementsbySvaasand
reflection,andrefraction.Specificsoftheserelationsdependon
etal.7Tothisend,weusethewell-knownrelations:8
opticalproperties,i.e.,absorptioncoefficient(μ ),scatteringco-
a
efficient(μs),anisotropy(g),andindexofrefraction(n)ofthe μa,epi = fmelμa,mel+(1− fmel)μa,base, (1a)
involvedtissues.Withanincreasingnumberofsimulatedpho-
tonsandeverfinerspatialdiscretizationofthetreatedvolume, (cid:2) (cid:3)
λ −3.33
tthheecreosrureltcitnsgpaetniearlgdyisdtreibpuotsiiotinonofmthaepaibdseoarlblyedcloingvhetregneesrgtoyw. ard μa,mel =6.6·1010mm−1 nm , (1b)
Extending the multilayer MC model1 to three dimensions (cid:2) (cid:3)
allowstreatmentofskininclusionsofarbitrarycomplexshape λ−154nm
and optical heterogeneity. In the presented examples, the VOI μa,base =0.0244mm−1+8.53mm−1 exp − 66.2nm ,
hasdimensionsof1×1mm2 intheplaneparalleltotheskin (1c)
surface (coordinates x and y) and 1.5 mm in depth (z). The where μ represents the absorption coefficient of
a,mel
spatialdiscretizationstepis2×2μm2 inthe(x,z)planeand melanosomeandμ isthebaselinevalueforskin.
a,base
20 μm in the y direction, resulting in a 3D grid with TheresultingmelaninfractionalcontentsforfairCaucasian,
500×50×750voxels. moderately pigmented Middle Eastern or Asian, and African
A special care is devoted to realistic treatment of the VOI skin are f = 1.3%, 3.5%, and 9%, respectively. The corre-
mel
sideboundaries.Asindicatedabove,neithermirror,norescape spondingepidermalabsorptioncoefficientsat532,585,and595
BCissuitableforhigh-resolutiontreatmentofrelativelysmall nm,obtainedbyusingthewavelengthdependencerelations(1),
volumesinhumanskin,irradiatedwithspatiallyconfinedlaser arecollectedinTable1.
beams. In our approach, named extended layers, photons are Forblood,weassumeahematocritof40%andoxygensat-
launchedaccordingtothelaserbeamintensityprofileandprop- urationof70%.Theabsorptioncoefficientsatthreeconsidered
agated in laterally infinite tissue layers until they deposit all wavelengths are obtained by linear interpolation of the values
their energy or escape into the air. Optical properties of these for oxygenated and deoxygenated whole blood as reported by
Table 1 Epidermalabsorptioncoefficientsatthreecommonlaserwavelengths,representativeofthree
skinphototypes.
Epidermalabsorptioncoefficient(mm−1)
Skintype/melaninfractionalcontent 532nm 585nm 595nm
FairCaucasian/f =1.3% 0.770 0.560 0.530
mel
ModeratelypigmentedAsian/f =3.5% 1.984 1.445 1.366
mel
African/f =9.0% 5.020 3.659 3.457
mel
(cid:2)
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Table 2 Absorption coefficient (μa), scattering coefficient (μs),
anisotropycoefficient(g),andrefractiveindex(n)valuesusedinour
MCmodelofopticaltransportinskin.
Tissue λ(nm) μa(mm−1) μs(mm−1) g n
Epidermis 532 a 53.0 0.770 1.45
585 50.0 0.790 1.44
595 50.0 0.790 1.44
Dermis 532 0.248 20.0 0.770 1.37
585 0.211 20.0 0.790 1.37
595 0.100 20.0 0.790 1.37
Subcutis 532 0.075 6.0 0.770 1.34
Fig. 1 Cross-sectional view of our PWS model geometry, including
the epidermal layer (dark gray), six dermal layers with different ab-
585 0.084 5.4 0.770 1.34
sorptionproperties(gray),onehorizontalbloodvessel(white),anda
semi-infiniteadiposelayerunderneath.DashedlinesdelineatetheVOI.
595 0.072 5.4 0.770 1.34
Blood 532 19.55 69.7 0.9638 1.33 Thephotonlaunchingpatternsimulatesanincidentlaserbeam
withatop-hatprofile(diameter:5mm)centeredabovethePWS
585 17.41 72.1 0.9646 1.33 bloodvessel.
595 6.44 82.4 0.9740 1.33
2.3 HeatTransportandThermalDamage
aSeeTable1.
TemperaturefieldevolutioninPWSskiniscomputedusingthe
two-dimensionalheatdiffusionequation
Meinkeetal.9(seeTable2).Theabsorptioncoefficientsofsub-
cutis(adipose)arefromBashkatovetal.10 ∂T (x,z,t)
ρc = k∇2T (x,z,t)+S(x,z,t) (4)
Awiderangeofscatteringparametervaluesforconstituents p ∂t
of human skin can be found in the literature. We have tested
severalcombinationsofthereportedvaluesinMCsimulations wherekisthermalconductivity,ρisdensity,andcpspecificheat.
of both normal (assumed 1% blood in dermis) and PWS skin. Theheat-sourcetermS(x,z,t)assumesthespatialdistribution
Forthisstudy,wehaveselectedthosevaluesofμ andgfrom of energy deposition as obtained from the MC simulation for
s
recent reports, which resulted in good agreement between the thedurationofpulsedlaserexposure(1ms).
predicteddiffusereflectanceandreportedexperimentalvalues. Two-dimensional treatment of heat transport in the central
The value of μ for adipose was calculated from the reduced plane perpendicular to the vessel axis (y = 0.5 mm) will be
s
scattering coefficient (μ(cid:2)) as measured by Baskhatov et al.,10 sufficientbecause—aswewilldemonstratebelow—deposition
s
andtheanisotropycoefficient(g)fromFlocketal.11 of laser energy in the discussed examples is nearly homoge-
Forouranalysisofbloodphotocoagulationinlasertherapy neous along the y direction (i.e., parallel to the vessel axis).
ofPWS,weincludeonebloodvesselwithdiameterd=150μm Consequently,heatflowinthisdirectionisnegligible.
andahorizontalaxis400μmbelowtheskinsurface(Fig.1).
Inordertoaccountforopticalshadingbyother,notexplicitly
modeled PWS vessels,12 the dermis is divided into five 0.2- Table 3 Mean blood vessel radii (ri), fractional blood contents (fi)
mm thick layers and one layer with a thickness of 0.5 mm. (=Re5f3.211n)m, afonrdththeesirxemsuoltdineglPaWbsSorlapytieorns.coefficient values (μa,i) at λ
The corresponding absorption coefficients μ (Table 3) are
a,i
calculated by considering the reported fractional contents of
blood(f)ineachlayer:13 i z(μm) ri(μm) fi(%) μa,i(mm−1)
i
μa,i = fiCiμa,bld+(1− fi)μa,der. (2) 1 60to260 25 5.2 0.383
Here, μ is the absorption coefficient of bloodless dermis 2 260to460 37 8.0 0.436
a,der
(0.053 mm−1 at 532 nm),14 and C is the correction factor
i 3 460to660 34 3.8 0.247
accountingforopticalscreeningwithinabloodvesselofradius
r:15,16 4 660to860 27 2.5 0.204
i
(cid:4) (cid:5)
C = 0.03895+ 0.48588 exp −μa,bldri 5 860to1060 24 2.0 0.183
i 0.1928
(cid:4) (cid:5)
+0.46803 exp −μa,bldri . (3) 6 1060to1560 24 1.5 0.151
0.91443
(cid:2)
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Heatexchangeduetotissueperfusioncanbesafelyneglected ing)ataselectedradiantexposure(H)andcompute(cid:5)(4)along
during the short time periods (below 0.2 s) considered in this thelaserbeamaxis,bothwithintheepidermallayerandthrough
study.17Inaddition,duetothelowbloodvelocityintheectatic thebloodvesselaxis.ByincreasingHinincrementsof0.1J/cm2,
PWSvenules18,19andtheirtortuousshape,onlyasmallfraction wethendeterminetheminimalradiantexposure,atwhichthe
of heated blood can leave the VOI within the studied time in- entirelumenofthesimulatedPWSvesseliscoagulated,H .
PWS
terval.Moreover,sinceourVOIrepresentsonlyasmallpartof Analogously,weassessthemaximalsaferadiantexposurevalue,
theirradiatedvolume,thisbloodwillbereplacedbybloodwith H ,wherenothermaldamageisgeneratedwithintheepider-
epi
asimilarlyelevatedtemperature.Forthesereasons,weneglect mis(i.e.,(cid:5) ≤1).Thisrepresentsanestimateoftheepidermal
epi
heatlossduetobloodflowinthepresentdemonstrationexample. damagethreshold.
Thermalpropertiesofmostskinconstituentsarethesameas
usedinourrecentreport.20Thisincludesthetemperaturedepen-
3 Results
dentspecificheatofbloodlessskin,21 andthewayweaccount
forthelatentheatofwatervaporization(inagreementwithother 3.1 DiffuseReflectivity
similarstudies).22,23 Inthepresentstudy,weadditionallytake As a first test of our MC optical model, we compute diffuse
intoaccountthetemperaturedependenceoftissuethermalcon- reflectance of healthy skin (with 1 vol.% of blood distributed
ductivity,k(T),whichwasfoundtohaveanobservableeffecton evenly throughout the dermis) at 532, 585, and 595 nm. The
predicted temperature dynamics, and consequently the extent epidermallayerthicknessisvariedfrom60to80and100μm,
of epidermal, blood, and perivascular thermal damage.20 This whicharetypicalvaluesforhumanskin,32,33 inordertoobtain
temperature dependence is estimated by considering the data arealisticrangeofdiffusereflectance(DR)values.
forwater24 andaccountingfortheproteincontentinbloodand Figure2presentstheobtainedDRvaluesforthethreeepi-
otherskinlayers. dermalthicknesses(seethelegend)indifferentskinphototypes.
ForthedurationofCScooling,weapplyaconvectivebound- TheDRspectraasmeasuredonforearmsofhealthyvolunteers
aryconditionattheskinsurface,withaheattransfercoefficient bySvaasandetal.7arepresentedforcomparison(dashedlines).
H = 5000 W/m2K and outer temperature of −50 ◦C.25,26 At For fair Caucasian skin [Fig. 2(a)], our diffuse reflectance
allothertimes,andfortheexampleswithoutactivecooling,we values (open symbols) fall completely within the range of the
applyatypicalnaturalconvectionvalue(H=10W/m2K)and DRspectrameasuredonthevolaranddorsalsideofthefore-
ambient temperature (25◦C). Adiabatic boundary condition is arm,respectively(dashedlines).InAsianskin[Fig.2(b),gray
appliedatthelateralandbottomboundariesoftheVOIandthe symbols],thepredictedrangeofDRvaluesmatchesthereported
initialskintemperatureissetto35◦C. spectrumratherwell.Thepredictedvaluesatλ=532nmare
Equation(3)issolvedusingthefiniteelementmethodwithin alittlehigher,butarematchedwiththeexperimentalreportby
thesoftwarepackageFEMLAB(COMSOL,California). Randebergetal.(R=0.20).34Anexcellentmatchbetweenthe
The laser-induced thermal damage is assessed within the predicted DR values and experimental spectrum in vivo is ob-
customaryArrheniusmodelofproteindenaturationkinetics,by servedforAfricanskin,specificallyforepidermalthicknessof
computingthethermaldamagecoefficient, 80μm(blacksquares).
(cid:6)
τ Our model results illustrate how an increase in epidermal
(cid:5)(x, z, t)= A exp[−E /RT(x,z,t(cid:2))]dt(cid:2), (5) thickness leads to lower diffuse reflectivity of skin, due to in-
a
0 creased melanin absorption. Moreover, this effect is enhanced
whereRistheuniversalgasconstant.Forblood,thefrequency withincreasingmelanincontent(f ).Consequently,wecanob-
m
factor and activation energy are A = 7.6 × 1066 s−1 and E serveasubstantialchangeofDRwiththeepidermalthickness
a
=427kJ/mol,respectively.27,28 Forepidermisanddermis,we inAsianandAfricanskinphototypes.Incontrast,theeffectis
applythevaluesfromGayloretal.29 (A=2.9×1037 s−1,E rather small, and probably often not discernable from experi-
a
=240kJ/mol),whichwererecentlyconfirmedtobemoresuit- mentaldata,infairCaucasianskin.
able than the values used in earlier modeling.30 Indeed, when Atallthreephototypes,however,thelargestinfluenceofepi-
applying,e.g.,thevaluesfromHenriques,31 oursimulationre- dermalthicknessonDRispredictedatthelongestwavelength,
sultsindicateextensiveperivasculardamagealreadyatradiant 595nm.
exposuresthatdonotinducecoagulationofthevessellumen,20
incontradictionwithhistologicalevidenceintheliterature.
3.2 InfluenceofBoundaryCondition
All calculations cover an interval of 100 ms after the laser
pulse,toensurethatthevalueof(cid:5)hasstoppedincreasing. BeforeembarkingonsimulationsofPWStreatment,weanalyze
theinfluenceofBCimplementedatthesidesoftheVOI.Forthis
analysis,weaugmentourmodelofhealthyskin(fairCaucasian;
2.3.1 Simulationstudyprotocol:lasertreatmentof f = 1.3%), as presented above, with one cylindrical blood
m
PWSwithandwithoutcryogencooling vesselinthedermallayer.Thevessel(diameter:120μm)lies
As a demonstration example, we consider laser irradiation of horizontallyunderthelaserbeamaxis,atasubsurfacedepthof
a PWS blood vessel at wavelengths of 532, 585, and 595 nm, 0.25or0.50mm.
withandwithoutapplicationofCScooling.TheCScoolingis In addition, we consider the case where both vessels are
appliedfor50ms,immediatelybeforethe1mslonglaserpulse. presentsimultaneously.Thisenablesquantitativeassessmentof
FortheexampleswithoutCScooling,thiselementisomitted. theinfluenceofonevesselonenergyuptakeinanothervessel
Foreachlaserwavelengthandskinphototype,wesimulate incloseproximity(a.k.a.opticalshading).Thesamegeometry
thelasertherapysequence(bothwithandwithoutCSprecool- was used in one of the first studies of this effect, as well as
(cid:2)
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(a)
(a)
(b)
(b)
(c)
Fig. 2 Diffusereflectancevaluesat532,585,and595nmforhealthy
skinof:(a)fairCaucasian(opensymbols),(b)moderatelypigmented
Asian(gray),andAfricanphototype(black).Theepidermalthicknessis
setto60,80,or100μm(seethelegend).Dashedlinesindicatethe
correspondingdiffusereflectancespectrainvivo(Ref.5).
of optical screening within individual blood vessels, using 3D
MCmodeling.2Forevenclosercorrespondence,wealsosetthe
epidermal thickness to 60 μm, laser beam diameter to 1 mm,
andradiantexposureto1J/cm2.Foreachmodelgeometry,we
calculate energy deposition maps upon irradiation at 585 nm
whenapplyingthemirrororescapeBC,andcomparethemwith
ourextendedlayer(EL)approach.
The resulting energy deposition profiles along the vertical
beam axis (passing through both vessels’ axes) are presented
Fig. 3 Energydepositionprofilesthroughtheaxesoftwohorizontal
in Fig. 3. Clearly, the choice of BC is reflected primarily vesselslocatedatsubsurfacedepthof0.25and0.5mm(solidblack
in the result for the deeper vessel (z0 = 0.50 mm). For this line),comparedwiththeresultforasinglevessellocatedat0.25mm
vessel, using the mirror BC [fig. 3(a)] results in a 73% larger (thinner, blue), or at 0.5 mm (dashed, red). The boundary condition
appliedatthesidesoftheVOIis:(a)mirror,(b)escape,and(c)extended
energy deposition (integrated over the entire vessel lumen) as
layers.
comparedtotheELresult[Fig.3(c);seeTable4].Theescape
BC[Fig.3(b)],ontheotherhand,resultsin16%lowerenergy
depositioninthesamevesselthantheELapproach. see that the influence of the deeper vessel on the laser energy
For the shallower vessel (z = 0.25 mm), the influence of depositionintheshallowerone—albeitnotverylarge—varies
0
BCissomewhatlesspronounced.ApplicationofthemirrorBC strongly with the choice of BC. Specifically, by applying the
resultsinanoverestimationoftheenergyuptakeby32%,while mirror BC at the side boundaries of the VOI, a reduction of
theescapeBCleadstoa7%lowerenergydepositionestimate depositedenergyby6.3%isobtaineduponintroductionofthe
ascomparedtotheELresult. deepervessel.Thisprediction,however,ismorethantwiceas
The energy deposition results in Table 4 also allow quan- largeastheresultobtainedwiththemorerealisticELapproach
titative assessment of optical shading, i.e., the relative change (i.e., −2.7%). Applying the escape BC, in contrast, yields to
of energy uptake by the presence of a nearby vessel. We can underestimationoftheshadingeffectby∼30%.
(cid:2)
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Table 4 Energy deposition per unit length within a single vessel
(z0 = 0.25 or 0.50 mm) and with both vessels present simultane-
ously(seeFig.3).Resultsforthreeboundaryconditionsarepresented
(λ=585nm).
Boundary Depth Onevessel Bothvessels Relative
condition (mm) (mJ/mm) (mJ/mm) change
Mirror 0.25 137 128 −6.3%
0.50 85 61 −28.4%
Escape 0.25 96 95 −1.9%
0.50 41 29 −29.2%
Extendedlayers 0.25 104 101 −2.7%
Fig. 4 Energy deposition profiles through the axis of a single vessel
0.50 49 35 −28.0% withdiameterof120μm(solidlines)or60μm(dashed),irradiatedat
532nm(thickerblackline),585nm(thinner;blue),and595nm(lighter;
red).Allresultswereobtainedusingtheextendedlayerapproach.
Theopticalshadingeffectinthedeepervessel,whileobvi-
ouslysignificantlylargerinmagnitude(−28%),isaffectedby upon irradiation with a 5-mm diameter hat-top laser beam at
selectionofeithermirrororescapeBCtoasignificantlylesser λ=532nminmoderatelypigmentedMiddleEasternorAsian
degree. skin(fm=3.5%).TheradiantexposureisH=7.6J/cm2,which
Figure4presentsenergydepositionprofilesthroughasingle is just below the epidermal damage threshold (see Secs. 3.5
vessel (z = 0.25 mm) with diameter of 60 or 120 μm, upon and 3.6). In the central plane perpendicular to the vessel axis
0
laserirradiationat532,585,and595nm,whentheELapproach [y=0.5mm;Fig.5(a)],theenergydepositionwithinthevessel
is applied. At the wavelength of 595 nm, with the lowest μ isnonuniform,withthelargestvaluesnearthetopofthevessel
a
valueinblood,thenear-centralpartofthelargervessel(lighter; lumen.Figure5(b)presentstheenergydepositioninthevertical
redsolidline)absorbsslightlymorelaserenergythanat532and planethroughthevesselaxis.
585nm(thicker;blackandthinner;blue,respectively).Thisis Figure6(a)presentsthecorrespondinglateralenergydepo-
notthecaseforthe60μmvessel(dashedlines),whichisalmost sition profile through the vessel axis (y = z = 0.5 mm). The
opticallythin(μ d<1)attheconsideredwavelengths. result indicates a dip in perivascular dermis, caused by reduc-
a
Energydepositionswithinthevessellumenfromtheresult tionoflightfluenceduetostrongabsorptioninthebloodvessel.
in Fig. 4 are compared with predictions obtained when using Figure 6(b) presents the corresponding energy deposition pro-
the mirror and escape BC in Table 5. The largest discrepancy files in the direction parallel to the vessel axis (x = 0.5 mm).
between the mirror BC and EL approach is observed at λ Energy deposition along the vessel axis (solid black line) is
= 595nm. The mirror BC yields 56% and 48%larger energy practicallyconstantthroughouttheVOI,duetoacomparatively
depositionsin60and120μmvessels,respectively,ascompared largerlaserbeamdiameter(dl=5mm).Energydepositionalong
totheELresults.TheescapeBC,incontrast,leadsto11%lower the top of the PWS vessel (lighter, blue line) is significantly
predictions than the EL approach at both vessel diameters. At largerandshowsaslightdecreasetowardtheVOIborders.At
532 and 585 nm, similar trends but somewhat smaller relative theepidermal–dermal(ED)junction,energydepositionisagain
differencescanbeobserved. nearlyconstant,andlargerthaninthevesselcenter(dashedline).
ThelowernoiselevelinFigs.5(a)and6(a),ascomparedto
Figs.5(b)and6(b)resultsprimarilyfromthefactthattheformer
3.3 DepositionofLaserEnergyinaModelPWS
correspondtoa10timesthickertissueslicethanthelatter(i.e.,
BloodVessel (cid:7)y=20μmversus(cid:7)x=2μm).Inaddition,wehaveaveraged
Figure 5 illustrates spatial distribution of deposited energy 5 centrally located slices to further suppress photon noise in
in a model PWS vessel, as obtained by our MC simulation Fig. 5(a) and obtain a smooth heat source term for Eq. (4).
Table5 Totalenergyuptakebyvesselsof60and120μmdiameterlocatedat0.25mmdepth,uponirradiationat532,585,and595nm.Results
forallthreeboundaryconditionsarepresented.
MirrorBC(mJ/mm) EscapeBC(mJ/mm) Extendedlayers(mJ/mm)
Diameter(μm) 532nm 585nm 595nm 532nm 585nm 595nm 532nm 585nm 595nm
60 51 56 36 35 37 21 38 40 23
120 126 137 110 90 96 66 97 104 74
(cid:2)
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(a)
(a)
(b) (b)
Fig. 6 HorizontalenergydepositionprofilesfromtheresultinFig.5:
(a)throughthevesselaxis(y=z=0.5mm)and(b)alongthevessel
Fig. 5 Cross-sectionalmapsoflaserenergydepositedinamodelPWS
blood vessel (d = 150 μm, z0 = 400 μm) upon irradiation with a axis(solidblackline),alongthetopofthevessellumen(thinner,blue
5-mmdiameterhat-toplaserbeam(l=532nm)andradiantexposureH line),andattheepidermal-dermaljunction(z=60μm;dashed).
=7.6J/cm2 inthecentralplanes:(a)perpendiculartothevesselaxis
(y=0.5mm)and(b)throughthevesselaxis(x=0.5mm).
Figure 8(a) presents temperature distribution in the central
cross-sectionalplaneofthemodelPWSgeometryattheendof
Obviously,thesamecouldnotbedoneinthecaseofFig.5(b), 1mslaserpulseirradiation,precededby50msCScooling.The
leading to rather noisy appearance of the profiles in Fig. 6(b). temperature at the bottom of the vessel lumen is considerably
This is not an issue, however, since the latter serves only as lowerthanatthetop.
an illustration of the model behavior and is not used in the Thecorrespondingtemperaturedepthprofilethroughtheves-
subsequentmodelingsteps. selcenterispresentedinFig.8(b)(solidline)andcomparedwith
Thecentraldepthprofileofenergydepositionisverysimilar theresultobtainedforthecasewithoutCSprecooling(dashed).
tothatshowninFig.4(forλ=532nm,d=120μm),andis Note, however, that these profiles correspond to different ra-
thereforenotpresented. diant exposure values, selected to match the respective epi-
dermal damagethresholds (as determinedfurther below):H
epi
=7.6J/cm2withCScoolingversus4.6J/cm2withoutcooling.
Wecanseethatthetworadiantexposurevaluesindeedresultin
3.4 TemperatureandCoagulationMapsin
comparable maximal temperatures within the epidermal layer
Laser-IrradiatedPWSBloodVessel (T≈80◦C).Atthesametime,CScoolingallowssignificantly
Figure 7(a) presents temperature evolution in the model PWS largertemperaturestobeachievedinthelowerpartofthevessel
bloodvesselfromFig.5,irradiatedwitha1mslaserpulseat532 lumen,ascomparedtoirradiationwithoutprecooling.
nmafter50mslongCScooling,asobtainedusingourthermal Theextentoftissuecoagulation,resultingfromeithertreat-
transport model (3). At radiant exposure of H = 7.6 J/cm2, mentapproach,iscomparedinFig.9bypresentingthecross-
epi
justbelowtheepidermaldamagethreshold,thetemperatureat sectionaldistributionsofthedamageparameter(cid:5)(4).Coagu-
thetopofthevessellumen(thinner,blueline)reaches100◦C, lation of blood and dermis is indicated by darker gray shades
butremainsbelow70◦Catthevesselbottom(dashedline). ((cid:5) ≥ 1), while white and magenta areas indicate healthy and
TemperatureevolutionattheEDjunction,meanwhile,shows partly compromised tissue, respectively. In moderately pig-
aninitialdropto10◦CuponCSprecooling,followedbyajump mented Asian skin (f = 3.5%), used in this model example,
m
tothemaximaltemperatureof68◦C[Fig.7(b)]. the model PWS vessel can be only partly coagulated at the
(cid:2)
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(a)
(a)
(b) (b)
Fig. 7 Temperature evolution in laser irradiated PWS: (a) at the top Fig. 8 (a)Temperaturefieldinthecentralcross-sectionofthemodel
(thinner, blue line), center (black), and bottom (short dashed) of the PWSgeometry(y=0.5mm)immediatelyafterpulsedlaserirradiation
vessellumen;and(b)attheepidermal-dermaljunction.Radiantexpo- preceded by CS cooling. (b) Temperature depth profiles through the
sureisH=7.6J/cm2;seetextforotherdetails. vessel center obtained with (solid line) and without CS precooling
(dashed).TheradiantexposurevaluesforCScooling(7.6J/cm2)andno
cooling(4.6J/cm2)matchtherespectiveepidermaldamagethresholds,
maximalsaferadiantexposureallowedforlasertreatmentwith- Hepi.
outCScooling[Fig.9(a)].TheCScoolingapproach[Fig.9(b)],
incontrast,allowssafeapplicationofsignificantlylargerradi-
antexposure.Thisenablesalmostcompletecoagulationofthe
modelPWSbloodvessel,exceptfortheverybottompartofthe
vessellumen(whiteandmagentaregions).
3.5 RadiantExposureThresholds
Forthreelaserwavelengths(λ=532,585,and595nm),twoskin
phototypes (fair Caucasian and moderately pigmented Asian),
andtwocoolingapproaches(nocoolingandCScooling),wede-
terminetheminimalradiantexposure,atwhichtheentirelumen
ofthemodelPWSvesseliscoagulated(H ),andtheepider-
PWS
maldamagethreshold,H ,asdescribedbefore.Providedthat
epi
H islargerthanH ,theintervalbetweenthetwothresholds
epi PWS
indicatestherangeofsafeandtherapeuticallyeffectiveradiant
exposurevaluesfortheselectedskinandtreatmentconditions.
In Fig. 10(a), we compare the obtained radiant exposure
thresholds for fair Caucasian skin. Clearly, a complete coag- Fig. 9 Cross-sectionalmapsofthecoagulationparameter(cid:5)inPWS
ulation of the modelPWS vessel canbesafely achievedat all model geometry (fm = 3.5%): (a) immediately after irradiation with
1mslaserpulseafternaturalconvectioncooling;(b)afterirradiation
testedconditions(seethelabels).
with1mslaserpulseprecededbyCScooling.Theradiantexposurein
Specifically,thesmallestsafetymarginispredictedforPWS eitherexampleisjustbelowtheepidermaldamagethreshold,i.e.,4.6
treatment at 532 nm without precooling of skin (H – H J/cm2and7.6J/cm2for(a)and(b),respectively.
epi PWS
(cid:2)
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Fromclinicalpractice,itiswellknownthattreatmentofPWS
(a)
lesionsinpatientswithmoderatelyanddarklypigmentedskin
isverychallenging,andoftenimpossible,evenwithup-to-date
PDLlasersequippedwithCScoolingdevices.
A more detailed comparison of our predicted therapeutic
thresholdswithradiantexposuresfromseveralclinicalreports
canbefoundinSec.4.
4 Discussion
Inourexperience,thepresentedELapproachisveryeffectivefor
high-resolutionMCmodelingofsmallinclusionsinhumanskin
irradiatedwithaspatiallyconfinedlaserbeam.Asdemonstrated
in Sec. 3.2, the commonly applied mirror and escape BC can
(b) significantly affect predictions of energy deposition when the
VOIsideboundariesarenotpositionedsufficientlyfarfromthe
investigatedinclusionandtheedgeofthelaserbeam.
Specifically,forthecaseof1mmlaserbeamdiameter,the
mirror BC produces severely overestimated energy deposition
values[compareFigs.3(a)and3(c)],byupto73%inthedeeper
model blood vessel, Table 4). This is a direct consequence of
unrealisticallyslowdecreaseoflightfluencewithdepth,dueto
thefactthatnophotonisallowedtoescapethroughtheperfectly
reflecting VOI side walls. Such a large discrepancy is not so
surprisingifweconsiderthattheresultobtainedwiththemirror
BCcorrespondstothesituationwhereaninfinitenumberof1
mmlaserbeams(separatedby1mminbothxandydirection)
Fig. 10 NumericallypredictedthresholdradiantexposuresHPWSand wouldirradiatetheskinsurface—clearlydeliveringmuchmore
Hepi in (a) fair Caucasian skin (fm = 1.3%); and (b) moderately pig- lightthanasinglebeam.
mentedAsianskin(fm =3.5%)forlaserirradiationat532,585,and Inadditiontotheabove,wehavedeterminedthatapplication
595nm,without(left)andwithapplicationofCScooling(right;note
of the mirror BC emphasizes mutual shading between nearby
thelabels).
bloodvessels.Specifically,therelativereductionofenergyup-
takeinthesuperficialvesselcausedbypresenceofthedeeper
=2.1J/cm2).ByadditionofCScooling,theepidermaldamage vesselisoverestimatedbyafactorof2.3(Table4).
threshold (H ) is markedly increased with almost no effect It is evident that the mirror BC can yield realistic predic-
epi
on H , thus increasing the safety margin to a much more tions of light transport in a small volume near the center of a
PWS
comfortable value of 7.5 J/cm2. These results agree very well sufficientlylargelaserbeam.Thiswasutilizedinmanyearlier
withclinicalexperience.AgoodfractionofPWSlesionsinfair modelsofbloodvesselphotocoagulation.4,28,35,36 Byperform-
skin could be treated with no adverse side effects using early ingadirectcomparisonforourPWSmodelgeometry(Fig.1),
pulsed532nmlaserswithoutCScooling.However,introduction wecanconfirmthatthisapproachpredictspracticallyidentical
ofthelatterhasdramaticallyimprovedthesafetyrecordofPWS energy deposition profiles as obtained with our EL approach
therapy.Moreover,byallowingsafeuseofsignificantlyhigher forthe5-mmdiameterhat-toplaserbeamwiththesameenergy
radiantexposures,ithasenabledtreatmentofmany“resistant” density.Tobeprecise,thebloodvesselenergyuptakeobtained
PWSlesions,featuringdeeperand/orlargerbloodvessels. withthemirrorBCwasactually∼2%lower.Weattributethis
Atthetwolongerlaserwavelengths(585and595nm),with effect to the fact that the reflecting VOI boundaries produce
lowerabsorptioninepidermalmelaninascomparedto532nm, mirror images of not only the laser source but also of the ab-
thedifferenceH –H isconsiderablylarger.Forourmodel sorbingstructuresinsidetheVOI,therebyreducingthefluence
epi PWS
geometry,thepredictedrangeofsafeyettherapeuticallyeffec- atthecorrespondingdepths,whichisnotthecasewithourEL
tiveradiantexposurevaluesthusamountsto∼6J/cm2 without approach.
cooling,andraisesto∼13J/cm2 withapplicationof50msCS However, without the ability to perform a more realistic
cooling. This is also in good agreement with clinical experi- computation, it might be very difficult to determine the beam
ence,whichmadesuchpulseddyelasers(PDLs)thepreferred diameter at which the limit of infinitely wide irradiation, in-
treatmentmodalityforthemajorityofPWSpatients. herently implied by the mirror BC, is achieved for any spe-
Incontrastwiththeabove,ourresultspredictthatcomplete cific combination of tissue optical properties, target structure
coagulationofthemodelPWSvesselinmoderatelypigmented depth, VOI dimensions, etc. The results in Table 5, for exam-
AsianskincannotbeobtainedsafelywithoutapplicationofCS ple, show that discrepancies between the mirror BC and our
cooling, as H < H at all tested wavelengths [Fig. 10(b); EL approach increase with decreasing absorption coefficient
epi PWS
left part]. With CS cooling (right), however, safe treatment of of tissues (from 532 to 595 nm), which can be attributed di-
PWS appears possible at 585 and 595 nm, but with only a rectly to consequently increasing effective free path. In addi-
marginaldifferencebetweenH andH (1.8to2.0J/cm2). tion,ourELapproachalsoenableshigh-resolutionmodelingof
epi PWS
(cid:2)
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