RADIATIONRESEARCH126, 296-303

(1991)

Oxygen Consumptionand DiffusionEffects in PhotodynamicTherapy THOMAS H. FOSTER,*'t RICHARD S. MURANT,4 ROBERT G. BRYANT,? ROBERT S. KNOX,t SCOTT L. GIBSON,f AND RUSSELL HILFt

Universityof RochesterSchoolof Medicineand Dentistry,Departmentsof *Radiology, Biochemistry,and ?Biophysics,601 ElmwoodAvenue, Rochester,New York14642;and f Universityof Rochester,Departmentof PhysicsandAstronomy,Rochester,New York14627

FOSTER,T. H., MURANT, R. S., BRYANT, R. G., KNOX,R. S., GIBSON,S. L., AND HILF, R. Oxygen Consumption and Diffu-

sion Effects in PhotodynamicTherapy.Radiat. Res. 126, 296303 (1991). Effects of oxygen consumption in photodynamic therapy (PDT) areconsideredtheoreticallyandexperimentally.A mathematical model of the Type II mechanismof photooxidationis used to compute estimates of the rate of therapy-dependentin vivooxygen depletionresultingfrom reactionsof singlet oxygen ('02) with intracellularsubstrate. Calculations indicate that PDT carriedout at incidentlight intensitiesof 50 mW/cm2may consume 302 at rates as high as 6-9 ~Ms-'. An approximate model of oxygen diffusionshows that these consumptionrates are large enough to decrease the radius of oxygenated cells around an isolated capillary. Thus, during photoirradiation, cells sufficientlyremote from the capillarywall may reside at oxygen tensions that are low enough to precludeor minimize '02-mediateddamage.This effectis more pronouncedat higher power densities and accounts for an enhanced therapeuticresponse in tumors treatedwith 360 J/cm2 deliveredat 50 mW/ cm2comparedto the same light dose deliveredat 200 mW/cm2. The analysisfurthersuggeststhat the oxygen depletioncould be partiallyovercomeby fractionatingthe light delivery.In a transplanted mammarytumor model, a regimen of 30-s exposures followed by 30-s darkperiodsproducedsignificantlylonger delays in tumorgrowthwhen comparedto the continuousdelivery of the same total fluence.

c

1991AcademicPress,Inc.

INTRODUCTION The oxygen tension of tumors treated with ionizing radiation has long been recognized as an important factor influencing radiosensitivity and therapeutic response (1-3). A number of treatment strategies that attempt to exploit the increased sensitivity of well-oxygenated tumors have been developed and studied. Fractionation of the X-ray dose (4, 5) and treatment under hyperbaric oxygen conditions (6, 7) are two such methods. It is generally believed that tumor destruction in photodynamic therapy (PDT) is accomplished through the formation of singlet oxygen ('02) and the subsequent reaction 0033-7587/91$3.00 Copyright? 1991by AcademicPress,Inc. All rightsof reproductionin any formreserved.

of 02 with cellular substrates. Considerable attention has been given to the calculation and measurement of the sensitizer and light dose delivered to a tumor undergoing PDT (8-10). Indeed, some recent definitions of dose are based on these criteria (11, 12). While sufficient quantities of light and drug are prerequisites for the photodynamic effect, it is clear that the production of cytotoxic levels of singlet oxygen depends directly upon the presence of ground-state molecular oxygen as well. Although this has generally been recognized (10, 12, 13), much less work has been done in this area, perhaps in part because of the difficulties involved in a direct experimental approach. Two developments over the past year have focused our attention on the critical importance of oxygen in determining tumor response to photodynamic therapy. First, recently completed studies of tumor growth in vivo have shown that tumor response to the same light and drug dose varies significantly with the rate of light delivery to the neoplasm (14). While the enhanced effect produced by light delivered at relatively lower dose rates is compatible with several possible explanations, the results suggest that oxygen depletion at high dose rates may contribute to a diminished tumor cell killing. Second, we have formulated a mathematical description of the interactions among light, sensitizer, oxygen, and substrate that comprise the singlet oxygen model of PDT.1 Solution of the kinetic equations governing these interactions has enabled us to compute estimates of the rate at which oxygen is consumed by the therapy-induced photochemistry in vivo. Results of these calculations, presented in this report, indicate that PDT is capable of consuming oxygen at a rate that is sufficiently high to move a fraction of the treated tumor volume into very low oxygenation, thereby protecting these cells from damage mediated by singlet oxygen. While the predictions of the calculations are necessarily limited by uncertainties in the choice of the various model parameters as well as by the simplifying assumptions of the model itself, they nevertheless provide an approximate theoretical framework within which the effects of the radiation dose rate may be interpreted. More importantly, the calcu' T. H. Foster, PhD thesis, University of Rochester, 1990.

296

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OXYGEN CONSUMPTIONIN PHOTODYNAMICTHERAPY

lated ratesof oxygen consumptionin PDT have led us to explore a promising method of radiation dose fractionation. MATERIALS AND METHODS

d['21 = Sako[302][T]

kd['02]- koa['02][A].

dt

(1)

Here, all bracketedquantitiesare molar concentrations,T denotesthe sensitizertriplets,andka is the rateof chemicalreactionof 02 withacceptor A. As koaand [A]appearonly as a productin this equation,thereis no need to specifyeach separately.Further,the sum

The Basis of the Model The cascadeof eventsthatis believedto leadto potentiallycytotoxic'02 reactionsis well known(15). Photosensitizedproductionof singletoxygen and the subsequentreactionof 02 with an acceptormakeup the TypeII mechanismof oxidation(16). Together,the light-activatedformationof excitedsingletand tripletstatesof the sensitizer,the collisionaltransferof energyto ground-stateoxygen to form 102, and the possibleoxidation reactionmay be expressedas a set of couplednonlineardifferentialequations (see the Appendix).In the model,separateequationsarewrittenfor the concentrationsof excited singletand tripletstatesof the sensitizer, ground-statedioxygen(302),102, andsubstrate.The solutionsof thisset of equationsdescribethe time evolutionof the variousconcentrationsin a photoirradiated sample. Detailsof thesesolutionshavebeen presentedelsewhere'and will form the subjectof a laterreport.For the purposesof this discussion,only the behaviorof the 302 concentrationis considered.Fromthe numericalsolution to the equationgoverningthe concentrationof 302, the rateof oxygen depletionresultingfrom PDT is obtained.This calculatedrate of consumption,along with an assumptionconcerningthe rate of metabolic consumption,may then be used to computethe resultingchangein the spatialdistributionof tissueoxygenin the vicinityof a capillary.

Choiceof Parametersfor Calculationof PDT OxygenConsumption The photophysicalpropertiesof the sensitizerareestimatedon the basis of publishedmeasurementsin vitro.Rateconstantsin the systemof equationshavebeenmeasuredin a varietyof solvents(17) andin environments thatprovidea reasonableapproximationof the situationin vivo(18).Thus the tripletyield(?,) andthe rateof tripletquenchingby molecularoxygen (kot)are chosento be 0.63 and 1.85 x 109M-l s-l, respectively.The fraction of tripletquenchingcollisionswith302 thatyield '02 (SA)is estimated to be approximately 0.5. Measurementsof the oxygendependenceof photodynamiceffectsin vitrosuggesta hematoporphyrin-derivative tripletlifetime (Ttr =/ lkp) of approximately70 us (19). Direct measurementsof triplet lifetimesin severalmodel environmentshave been reportedby Rodgers(18), and, on the basisof thesedata,a Tr,of 800 gs is usedin our calculations. The lifetimeof '02 dependsstronglyupon the solvent(20, 21). In a cell, the two principalenvironmentsencounteredby a sensitizermoleculeare the lipid membranesand the aqueouscytosol. Thereis an approximate 10-folddifferencein the '02 decay rate (kd)betweenthese two milieus. Considerableevidenceis availableto indicatethat the activecomponents of the sensitizerare taken up by and associatedwith lipid membranes withinthe cell (22, 23). However,since the diffusiondistancefor oxygen withinthe lifetimeof a IO2moleculeis on the orderof a cell membrane thickness,thereis no basisto excludeeitherenvironmentfromconsideration.Therefore,calculationsarecarriedout usingboththe aqueousdecay rateof 3.1 x 105s-' (24) and a 10-foldsmallerlipidrate. Almostcertainly,the mostdifficultaspectof the problemto specifywith any confidenceis the effectiveintracellularconcentrationof 02 acceptor and the rate of acceptorreactionwith 102. Nevertheless,the published resultsof severalunsuccessfulattemptsto observethe time-resolvedluminescencefrom singletoxygenin cell suspensions(25, 26) serveto fix an upperlimit for thesequantities. As shownin the Appendix,the 102 equationis written

kd + koa[A]

(2)

definesthe rateof '02 decayin the presenceof a reactivesubstrate.On the basisof the opticalstudiescitedabove,a consensushas emergedthatthe lifetimeof 02 in vivomustbe lessthan 1 us.As kdis known,thislimitcan be used in conjunctionwith Eq. (2) to estimatethe valueof the product koa[A].The kdappropriatefor '02 in aqueous solution yields a value of 6.87 x 105 s-' for koa[A],while the lipid kdproduces a koa[A]of 9.69 x 105s-'. thatthe l-uAs102 lifetimeis onlyan upperlimit,it is useful Acknowledging

to calculatethe effectof a shorterlifetime.Retainingthe kdsuitablefor a membraneenvironment,a 100-nssingletoxygenlifetimeyieldsa koa[A]of 9.97 X 106 s-1.

Finally,estimatesof the photosensitizerand light dose to the tumor must be made. Frompreliminarymeasurementsof tumortissueexcised from animals intraperitoneally injectedwith PhotofrinII (5 mg/kg), it appearsthatthe sensitizerconcentrationin thetumor24 h followinginjection is approximately4-10 tg/ml (S. L. Gibson, personalcommunication).Basedupon in vitromeasurementsof the absorptionof the sensitizer at comparableconcentrations,an optical density of 0.05 at 630 nm is chosen for these calculations.Typical light irradiationin PDT is performedusing the 630-nm output of a continuous-waveargon-ion-laserpumpeddye laser.The fluencesof radiationusedby differentinvestigators vary;however,fluenceratesin the rangeof 50 to 200 mW/cm2arecommon. Anticipatinglaterexperimentalresults,calculationsare carriedout using both of these values.No attemptis made to computethe spatial distributionof absorbedlightthroughoutthe tumor. Calculationof OxygenDiffusionDistances Solutionof the systemof kineticequationsyieldsthe rateat which302 is consumedby the photochemicalreactionsin PDT. In the Kroghcylinder modelof oxygendiffusion(27), an increasedphotochemical302 consumption decreasesthe oxygenconcentrationfora givenradialdistancefroma capillaryin the treatedtissuevolume.To approachthisproblem,thediffusion equationmustbe solved.In cylindricalcoordinates,this is written rd r rdr

dr dC

J

(3)

=r

whereD is the oxygendiffusioncoefficientof the tissueand C is the concentrationof oxygenat the radialdistance,r, fromthe wallof an isolated capillary.The rateof oxygenconsumptionis specifiedas r andis assumed constant.Whilethisassumptionis strictlyvalidonlywhenkot[302] is much greaterthan kp, its adoptiondoes not substantiallyinfluencethe result. Afterimpositionof the boundaryconditionsof the standardKroghcylinder model, the solutionis obtainedreadily.Then, followingBoag(28), a characteristicdiffusiondistance,b, is definedas the radialdistanceat whichthe 302 concentrationfallsto zero.Fora capillaryof radiusa andan oxygenconcentrationat the capillarywallof Co,this diffusiondistanceis determinedby 4CoD

1

Pa2 : 1ra2

b2

-I

b2

b2

+ aln a

(4)

298

FOSTER ET AL.

grewto 10 times the initialvolume.All animalssurvivedthe studywith routinecare. PhotofrinIIat a doseof 5 mg/kgwasadministered 24 h intraperitoneally priorto photoradiation.Immediatelybeforelighttreatment,animalswere 0.12 anesthetizedby intramuscular administration of 75 mg/kgketamineand6 mg/kg Rompun. Hair coveringthe skin above the tumor was removed with clippers. = 0.09 Irradiationwas performedusing the 630-nm output of a continuouszw wave argon-ion-laser-pumped dye laser(Innova90, CoherentInc., Palo (C Alto, CA). Nine separatetumorsweretreatedwith a lightschedulecomx 0.06 of cycles of 30-s exposuresfollowedby darkperiodsof the same -.\^~~~~~ \prised duration.This30/30 photoradiation wasaccomplishedby placinga timercontrolledelectromechanical shutter(Uniblitz,VincentAssociates,Roch0.03 ~ s\ ~ ~\^~\ 3-.~~ ~ester, NY) in the beam path immediatelybeforethe fiberoptic coupler. The lightwasdirectedto a 1-cm-diameter spotat the surfaceof the tumor N. a lensed fiberoptic (Laserguide,SantaBarbara,CA). Lightintensity a^~~~ ~~~\ ~via \~ 0.00 incidentupon the surfaceof the skin was 100 mW/cm2.The total treat10 15 5 20 25 0 menttime forthe fractionatedirradiationwas2 h, resultingin a totallight dose to the tumorof 360 J/cm2.Intratumoral temperaturemeasurements IRRADIATION TIME (s) n significant s h i s tthatno i induced is at reportedp previouslyshowed hyperthermia FIG. 1. Calculatedestimatesof the rate of PDT-dependentoxygen photoradiationpowerdensitiesof 200 mW/cm' (30). consumptionin vivofor threeinitial302 concentrations:120,iM (-); 60 0.15

juM (---); and 30 iM ( --).

Solutions are computed assuming an

aqueousenvironment,a lifetimeof quenched102 of 1 ls, and an incident photoirradiation intensityof 50 mW/cm2.For all threecases,the rateof 302 consumptionis approximately6.0 ,uMs-~. In termsof b, the resultingexpressionforthe radialconcentrationof oxygen is then givenby 2 ln(b/r)- 1 + r2/b2 C(r)= C 2 ln(b/a) - 1 + a2/b2

(5)

Forthe purposesof thesecalculations,a 5.0-m capillaryradiusanda Coof 63 ,uMareassumed(28). Solutionsof Eqs.(4) and(5) arepresentedin subsequentsectionsof this paper.Here,we note only thatthe increasedratesof oxygenconsumption resultingfrom the effectsof PDT reducethe value of the parameterb throughEq. (4). To achievepartialreoxygenationof cellsresidingbeyond the diffusiondistance,darkintervalsmust be incorporatedinto the light treatmentregimen.The durationof these darkintervalsis suggestedby characteristic distancesthatemergenaturallyfromsolutionsof Eq.(5) and fromestimatesof the intercapillary spacingwithinthe tumor.Basedupon theseconsiderationsand calculatedresultspresentedbelow,30-s darkintervalswereusedin designinga fractionatedscheduleof irradiation.

RESULTS

Calculated estimates of the rates of in vivo 302 depletion

resultingfrom photodynamiceffectsare presentedin Figs. 1 and 2. The resultsin an aqueousenvironmentare presented in Fig. 1 for an incidentlight intensityof 50 mW/ cm2 at 630 nm and a lifetimefor 102 of 1 is. A calculated oxygenconsumptionof 6.0 tAMs-1 is observedto be independent of initial 302 concentration over a wide range of

reasonablevalues.

0.15

0.12

E

0.09

z

LUI

TumorGrowthDelay Studies FemaleFischerratsapproximately42 daysold and weighing80-100 g receivedsingle implantsof R3230ACmammaryadenocarcinomatissue usingthe steriletrochartechniquedescribedpreviously(29). Animalcare and handlingwerecarriedout accordingto the guidelinesestablishedby the UniversityCommitteeon AnimalResourcesat theUniversityof Rochester. Directvolumemeasurementsof excisedtumorsshowedthatthe tumor geometryis approximatelycylindrical.Verniercalipermeasurementsof dimensionsof implantedtumorswere made alongtwo orthogonalaxes, and the volume was computedfrom the expressionfor the volume of a cylinder.At 10-13 days followingimplantation,animalswhose tumors had reached0.5-0.7 cm in the longerdimensionwereselectedfor treatment,andtheirinitialtumorvolumeswererecorded.At the time of treatment, the tumor thicknesswas approximately0.5-0.6 cm. After PDT, tumordimensionswererecordedon a nearlydailybasis until the tumor

x 0

0.06

0.03

0.00 0

5

10

15

20

25

IRRADIATION TIME (s)

FIG. 2. Two calculatedestimatesof the rateof PDT-dependentoxygen consumptionin vivo.In both cases,a lipidenvironmentand an incidentphotoirradiation intensityof 50 mW/cm2areassumed.Thefirst(-), computedwitha lifetimefor '02 of 1 is, yieldsan 302 consumptionrateof 8.6 ,M s-1. The second (---), computed with a 100-ns '02 lifetime, results

in a rateof oxygendepletionof 9.2 uMs-'.

299

OXYGEN CONSUMPTIONIN PHOTODYNAMICTHERAPY m

35 0

28

=L

z

0

0

10

c5 x

S.

zw

0 LLI

**0

z 0

(C X 0

es

zw

21

0

14

Hu, -

CD

0

0

rJ)

o

7

0 I

0.1 0

I

0 100

200

DISTANCEFROMCAPILLARY (1mm)

FIG. 3. The calculatedeffect of PDT on tissue oxygenationin the vicinity of an isolatedcapillary.Estimatesof PDT-dependent302 consumptionat two photoirradiationintensitiesare superimposedupon an assumedrate of metabolicconsumptionof 1.7 j,M s-~. Radial oxygen concentrationscomputedfromEq. (5) correspondto the effectof PDT at 200 mW/cm2(o, 0), PDT at 50 mW/cm2(., 0), and metabolicconsumption alone (A). Forboth photoirradiation intensities,the smallersymbols illustratethe negligibleeffectof a completecessationof metabolicoxygen consumption.

Thecorrespondingresultsin thelipidmembraneenvironment are shownin Fig. 2. Here,underconditionsidentical to those specifiedabove, the diminishedkdgives rise to an oxygen consumption rate of 8.6 ,uM s- . The higher koa[A]

correspondingto a lifetime for 102 of 100 ns has a small effect,increasingthe rateof oxygendepletionto 9.2 /MMs-'. At a lightdose rateof 50 mW/cm2,then, the calculatedrate of 302 consumptionin vivodue to PDT-dependentphotochemistryis 6.0-9.0 ,M s-~. Figure 3 illustratesthe consequencesof combiningthe therapy'soxygenconsumptionwiththat of a representative (1.7 jiM s-l) metabolicrate (31). The curvesin the figure depictsolutionsof the oxygenconcentrationequation(Eq. (5)) for five distinctsituations:(i) metabolic302 consumption alone;(ii) combinedmetabolicand PDT consumption for 50 mW/cm2 incident light; (iii) combined metabolic and PDT consumptionfor 200 mW/cm2incidentlight;(iv) PDT consumption alone for 50 mW/cm2 incident light; and (v) PDT consumptionalone for 200 mW/cm2incident light. Throughout,PDT oxygenconsumptionis computed for the case of a 1-,tslifetime for 102 and a lipid environment. Figure4 presentsthe steady-state'02 concentrations that correspondto the above cases(ii) and (iii). Diffusiondistances,b, are calculatedfrom Eq. (4), with the total rateof oxygen consumption,r, determinedfrom the sum of metabolic and photodynamiccontributions. The 302 consumptionratesand diffusiondistancesfor the

100

0

200

(pim) DISTANCEFROMCAPILLARY

FIG. 4. The calculatedradialconcentrationsof '02 in the vicinityof a capillaryfor two photoirradiationintensities:200 mW/cm2(0) and 50 mW/cm2(0). Plotswereobtainedby solvingthe steady-state'02 equation 302 concentrationsillustratedin (Eq. (A4)) for each of the corresponding Fig. 3. Forbothpowerdensities,'02 wascomputedusingthe 302 concenmetabolicandphotodynamiccontrationthatresultsfromsuperimposing tributionsto the oxygenconsumption.

five cases listed above are presentedin Table I. Oxygen diffusiondistancesare stronglyinfluencedby the therapy, decreasingfrom approximately213 Atmin the presenceof metabolicconsumptionaloneto approximately60 ,m during photoradiationat an intensityof 200 mW/cm2. In Table II, the tumor growthdelaysresultingfrom the fractionatedirradiationscheme are comparedwith results reportedpreviously(14) obtainedthroughcontinuousphotoirradiationat variousincidentlight dose rates.Mean tumor volume doublingtimes for 200 and 50 mW/cm2continuous light deliveryare 6.5 and 16.2 days, respectively. The deliveryof the same 360 J/cm2 in multiple fractions significantlyextends(P < 0.001) the mean tumor volume doublingtime to approximately31 days. TABLE I Distances of Oxygen Diffusion (b) Maximum for Several 302 Consumption Rates Consumption

b (Am)

Metabolic(1.7 uMs-') PDT at 50 mW/cm2 PDT at 50 mW/cm2+ metabolic PDT at 200 mW/cm2 PDT at 200 mW/cm2+ metabolic

213 107 99 61 60

Note. Thesecalculatedvaluesof the parameterb areobtainedthrough solutionof Eq. (4) for the five casesdepictedin Fig. 3. Oxygenconsumption associatedwith PDT is computedassuminga 1-,ts'02 lifetimeand a lipid environment.

300

FOSTERET AL.

TABLE II Tumor Volume Doubling Times for Several IrradiationStrategiesin PDT Lightdelivery

Meandoublingtime (days)

Controls(no light) 200 mW/cm2continuous 100 mW/cm2continuous 50 mW/cm2continuous 100 mW/cm230 s on/30 s off

2.8 + 0.5 6.5 + 1.3 8.5 + 1.5 16.2 + 2.8 31.3 + 1.5

Note. In all cases,the total lightdeliveredto the tumorwas 360 J/cm2. Tumorsweretreated24 h afteradministrationof 5.0 mg/kgbody weight PhotofrinII. Data are reportedas the mean time in days(+ the standard errorof the mean)followingPDT for the tumorto doubleits initialvolume. Valuesfor 200, 100, and 50 mW/cm2continuousphotoirradiation are from (14). Meanand standarderrorfor the 30/30 fractionatedtreatment arebasedon data fromnine separatetumors.

DISCUSSION In this rodent tumor, it is clear that for a given dose of Photofrin II, the same total light energy delivered to the tumor is capable of evoking strikingly different therapeutic responses. In studies presented here and previously (14), a total light dose of 360 J/cm2 produced mean tumor volume doubling times that vary from approximately 6 to 31 days. The factors influencing the degree of tumor response are the intensity of the photoradiation and the introduction of dark intervals during the treatment period. Our mathematical analysis suggests that oxygen consumption resulting from the photochemistry is a critical feature of PDT. The calculations indicate that the therapy may be responsible for consuming oxygen at a rate that is substantial with respect to reasonable estimates of metabolic 302 consumption. As illustrated in the plots of Fig. 3, increased oxygen consumption would decrease the radial distance from a capillary at which oxygenation is sufficient to support 102 production. The dependence of 102 formation on 302 concentration may be expressed in terms of the kp/kotratio1 (19). While the details of the radial 102 profiles that correspond to the plots of Fig. 3 are influenced by the specific values chosen for these rate constants, the essential features of the result are not. Thus this model predicts that PDT can cause a significant volume ofphotoirradiated cells to become hypoxic temporarily, a state in which they could be protected from singlet oxygen generation and attack. In Fig. 3, a comparison of the oxygenation resulting from PDT at 50 and 200 mW/cm2 suggests that a largertissue volume is susceptible to cell death as a result of photosensitization involving '02 at the lower incident power. The results of Gibson et al. (14) are consistent with this interpretation. The model goes further, however. Even at the relatively low incident light power of 50 mW/cm2, PDT appears to

cause pronounced oxygen depletion at distances remote from the capillary wall. For cells metabolizing at the 1.7 ,iM s-1 rate depicted in Fig. 3, photoirradiation at 50 mW/cm2 would reduce the diffusion distance from approximately 213 to 100 ,tm. Reoxygenation of tissue metabolizing at this rate therefore requires diffusion lengths of at least 100 ,um.If the rate of tumor cell metabolic oxygen consumption is lower than 1.7 ,uM s-', still longer diffusion lengths are required in order to accomplish full reoxygenation. In general, a characteristic diffusion time may be defined by the basic scale relationship, Tr L2/D, in which the time, r, is expressed in terms of a length scale, L, and the diffusion constant, D. Taking length scales on the order of 100300 Limand a tissue oxygen diffusion constant of 2.0 X 10-5 cm2 s-1 into this equation results in calculated diffusion times of 5 to 45 s. These times, then, serve as a guide for determining the duration of dark intervals in the delivery of light doses in multiple fractions for photodynamic therapy. Oxygen consumption resulting from PDT and its effect upon the oxygen diffusion distance suggested to us the exploration of a light delivery scheme comprised of short irradiation periods separated by dark intervals whose lengths are governed by the characteristic diffusion times. In calculating these times, an estimate of the rate of metabolic 302 consumption and the average intercapillary spacing in the tumor are required; neither quantity has been determined in the R3230AC tumor line. Nevertheless, the measured 302 consumption of resting muscle (31) and the intercapillary distances of 300 ,m determined histologically in a squamous-cell carcinoma (32) provide useful guides. Thus our choice of 30-s dark periods represents an estimate drawn from these data and our calculated rates of PDT oxygen consumption. The selection of 30-s irradiation intervals and an incident light intensity of 100 mW/cm2 were based in part on a desire to limit the total time for delivery of 360 J/cm2 to 2 h. In this way, the results from the 30/30 treatment scheme could be compared with results obtained from the continuous administration of light at 50 mW/cm2 without the introduction of yet another variable, the total treatment time. Before leaving the plots of Fig. 3, it should be noted that reducing the metabolic 302 consumption to zero in a volume of tissue undergoing PDT has a negligible effect on the tissue oxygenation near a capillary. If this were not the case, it might be supposed that if some fraction of malignant cells is killed by an initial treatment, the resulting decrease in metabolic oxygen consumption would increase the oxygenation of surviving cells, thereby rendering them more susceptible to a subsequent light dose. Arguments like this have been used as the motivation for using fractionation of the X-ray dose in radiation therapy (5). Our calculations suggest that this effect will not be important for PDT. Even assuming a 100% killing of cells, the radial distribution of

301

OXYGEN CONSUMPTION IN PHOTODYNAMIC THERAPY

remains dominated by the photodynamiccontributions duringirradiation. It is possibleto offerinterpretationsof at leastsome of the tumorgrowthdelaydatathatdo not relyupon photochemical oxygen consumption.For example, since the time requiredto delivera fixed amount of total light energyto a tumor is inverselyrelatedto the incidentpowerdensity,it could be arguedthat the longertreatmenttimes associated withthe low dose ratesmay somehowbe responsibleforthe enhancedeffect.Whilethis hypothesiswouldbe consistent with experimentalresultsfor the variouscontinuousphotoirradiationregimens,it could not account for the improved results obtained from the 2-h 30/30 fractionated treatment. The total lightdose deliveredto the tumorwas 360 J/cm2 for each of the continuousand fractionatedprotocolsdiscussedin this report.Therefore,it is not possibleto invoke the photobleachingof PhotofrinII to explainthe resultsof the tumor growth delay experiments.A recent paper by Moan and Anholt (33) has describedthe rapid,reversible bleachingof aluminumphthalocyaninedisulfonatein vivo. However,thereis no evidenceeitherin the publishedliterature (34, 35) or in unpublisheddata from our laboratory (R. S. Murant,personalcommunication)for the transient bleachingof PhotofrinII. Indeed,the reversiblebleaching of Photofrin would render impossible the normal tissue protectionobservedby Boyle and Potter(35). Recently, considerableattention has been given to the effectsof PDT on tumor vasculature(36-40). It is interesting to consider the calculationsand experimentalresults presentedhere in light of these demonstratedvasculareffects. The oxygen concentrationis obviouslyhigherin the capillariesandarteriolesthanit is in the tumorcells.Assuming that the vasculardamagecausedby PDT resultsfrom 102, the likelihood that the therapywill become oxygenlimited is alwaysmore pronouncedin the cells than in the vasculature.At high PDT lightintensities,our analysissuggeststhat the depletionof oxygenmay be sufficientto limit 1O2formationto a small volume of cells in the immediate vicinity of a capillary.Under these conditions,the relative contribution of direct cell killing to tumor destruction would be diminished. As the light intensity decreases,however,the resulting increasein oxygenationincreasesthe volume of cells that may be killedby 0O2.Thus one would predictan increased contributionto tumordestructionfromdirectintracellular effects.The deliveryof light in multiple fractionsextends this volume still furtherby providingdarkintervalsduring which cells remote from the capillariesmay become partiallyreoxygenated.The cyclicoxygendepletionand reoxygenationpredictedby ourmodelwouldappearto be qualitatively supportedby data recentlyreportedby Tromberget al. (41). Of course,as soon as the microvasculatureof the tumor is destroyedby any mechanism,no furtherreoxy302

genationof the cellsis possible.Therefore,interpretationof the data from our tumor growthdelay studieswould indicate that the arteriolesand capillariesmust remainviable duringa significantfractionof the photoirradiation. APPENDIX In the singletoxygenmodel of PDT, the concentrations of excited states of the photosensitizer,ground-stateoxygen, singletoxygen,and the singlet-oxygenacceptoraredescribedby the coupledset of differentialequations, (Al)

di dt = Ia(t)- km[S,]-kisc[S,l] d[T]

d = kis[S -

ko[302][T] - kp[T]

d[02] = -Sakot[302][T]+ kd[102] dt d[d2]

dt

dA dt

= Sakot[302][T] - kd['02]

(A2)

(A3)

- koa[O02][A] (A4)

_-koa[102][A],

(A5)

in whichthe bracketedquantitiesaremolarconcentrations. All termsare definedin the Glossary.Under conditionsof steady-stateirradiationandin the absenceof bleaching,Eq. (Al) for the excited singlet states of the photosensitizeris immediatelysolved,giving (A6)

+ka [SJ =km km + kisc

Then, insertingthis expressioninto Eq. (A2) yields for the triplets d[T]

d[ dt

= k kisc +k km+

kisc

-

kot[302T]-

kp[T]

(A7)

and reducesthe system to four equations.The quantum yield of triplet formation, t, is defined by the new term, kisc(km + kisc).Numerical solutions to these equations are

obtained using the method of Gear (42) as described previously.1 Glossary sensitizerfirstexcitedsingletstate So sensitizergroundstate T sensitizertripletstate 302 groundstate molecularoxygen 102 singletoxygen SI

302

FOSTERET AL.

11. A singletoxygenacceptor rate of formation of sensitizer excited states (M s~) Ia km sum of radiativeand nonradiativedecayratesfromSI 12. to So (s-1) kisc intersystemcrossingrate from S, to T (s-1) kt, rate of sensitizer triplet quenching by 302 (M-1 s-1) kp sum of radiativeand nonradiativedecayratesfromT 13.

W. R. POTTER, T. S. MANG, and T. J. DOUGHERTY, The theoryof photodynamictherapydosimetry:Consequencesof photodestruction of sensitizer.Photochem.Photobiol.46, 97-101 (1987). M. S. PATTERSON,B. C. WILSON, and R. GRAFF,In vivo testsof the conceptof photodynamicthresholddose in normalratliverphotosensitizedby aluminumchlorosulphonated phthalocyanine.Photochem.Photobiol.51, 343-349 (1990). A. E. PROFIO and D. R. DOIRON, Dosimetryconsiderationsin phototherapy.Med.Phys.8, 190-196 (1981).

14.

S. L. GIBSON,K. R. VANDERMEID, R. S. MURANT,R. F. ROUBERTAS,and R. HILF,Effectsof variousphotoradiation regimenson the

to So (s-1) quantum yield of 102 formation Od S, 4d/0t, the fraction of triplet quenching collisions with 302 that result in 102 kd 102 to 302 decay rate (s-1) koa the rateof reactionof 102 with acceptorA (M-' s-') ACKNOWLEDGMENTS

15. 16.

This work was supportedby USPHS GrantsCA49004and CA36856 andby a BiomedicalResearchSupportGrant,PHSS07 RR07069.T.H.F. 17. gratefullyacknowledgessupportfromfundsprovidedby the Department of Radiologyat the Universityof RochesterSchoolof Medicineand Dentistry.He alsothanksDr. AlfredClark,Jr.,formanyhelpfuldiscussionsof oxygentransport,consumption,and diffusionand for his carefulreading 18. of the manuscript.The authorsthank QuadralogicTechnologies,Inc., Vancouver,BC,Canadafor the gift of PhotofrinII. RECEIVED: July 17, 1990; ACCEPTED: January 15, 1991

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