[CANCERRESEARCH38,3006-3011, September1978]0008-5472/78/0038-0000$02.00

An in Situ Method for Estimating Cell Survival in a Solid Tumor1

Alan A. AIfieri2 and Eric W. Hahn3

RadiationTherapyResearch,MemorialSloan-KetteringCancerCenter,NewYork,NewYork10021

ABSTRACT

The response of the murine Meth-A fibrosarcoma(amethylcholanthrene-inducedtumor) to single and fractionateddosesof X-irradiatlon,actinomycinD chemotherapy, and/or concomitantlocal tumor hyperthermiawasassayedwith the use of an In situ methodfor estimatingcell kill within a solidtumor.The cell survivalassay wasbased on a standardcurve plottingnumberof inoculatedviable cells (101 to 1O@)with and without radiation (10kilorads)-inactivatedhomologoustumor cells (heavily irradiated)versusthe time requiredfor i.m. tumorsto growto 1.0 cu cm. The time for post-treatmenttumorsto growto 1.0 cu cm was cross-referencedto the standardcurve,and the number of survivingcells contributingto tumorregrowth was estimated. The resulting surviving fractioncurvesclosely resemblethose obtainedwithin vitro systems. The advantages and limitationsof this techniqueare discussedas a methodforevaluatingtreatmenteffectlveness.

INTRODUCTION

Severalassaysthat are currently in use for evaluation oftumor response in situ after a particular treatment arebased primarily on post-treatment changes in tumor dimensions. The data are plotted as delay in tumor growth; thegreater the delay, the greater is the treatment response.Other end points are also available in which it is notnecesssaryto measure tumor size; these include survivaltime and some desired level of long-term local tumorcontrol. For a comprehensive review of the experimentalassaysof tumor response,see the paper of Kaliman (7).

There is no question that these assays have and willcontinue to provide the cancer researcher with valuableinformation, but one is continually facedwith the limitationsof these methods. Depending on the technique, some ofthese limitations are: (a) the large number of animalsrequired; (b) the range of initial tumor size at treatmenttime must be quite narrow; (C) the results may be relativeand not absolute; (d) no quantitative estimates may bemade on cell killing; and (e) it is difficult to delineateindividual treatment effects when 2 or more different agentshave been used. Several techniques are being used toovercomesome of these shortcomings. Onesuch approachto measurementof surviving cell fractions soon after treatment is to excise the tumor, obtain single-cell suspensions,and reinoculale known numbers of cells into recipient

I Supported in part by Grants CA 08748 and CA 17410 from the National

Cancer Institute.2 Submitted in partial fulfillment of requirements for an MS. degree in the

Department of Biology, Greduate School, New York University, WashingtonSquare, N. Y.

S To whom requests for reprints should be addressed.

Received September 12, 1977; accepted June 16, 1978.

hosts,as in the dilution assaytechnique (6, 10),or measurement of surviving cell fractions can be made throughincubation of the single-cell suspensions in vitro (1, 5). Theresulting number of tumor takes or colonies formed after aperiod of incubation is then correlated to the number oftumor cells surviving treatment. In addition to being cumbersome,these techniques suffer from technical difficultiessuch as perturbation of the treated tumor cells, inconsistentand low yields of single cell suspensions, and low, oftenerratic, plating efficiencies. However, in spite of manyshortcomings, these in vivo and in vitro assay techniqueshaveshown clearly that reliance on tumor measurementstoestimate the efficacy of an antilumor agent(s), particularlyduring the early stages after treatment, can be misleading(1, 5). Another approach to quantitative assayof treatmenteffectiveness on solid tumors utilizes observations takenfrom the nadir of regressing tumors. These estimates canlead to under- and overestimates of cell kill, as in the“Wilcoxphenomenon―described by Skipper (13). Techniques based on back extrapolation of tumor regrowthcurvesalso havebeen usedto obtain estimatesof survivingtumor cells but can be misleading, particularly when theextrapolation is made to regions below the palpable size.To partially overcome these objections, earlier experimentsby this laboratory used the back extrapolation method andlimited the comparison to control tumor sizeand the treatedtumor size in the palpable region (4). The procedure allowed us to make estimates on relative surviving tumorvolumes following individual and combined modality treatments. The resultant curves closely resembled survivalcurves derived from in vitro studies but were relative tocontrols and yielded no estimate of cell survival.

We developed an in vivo method that is based on tumorvolume response, requires no back extrapolation and,based on what we feel are reasonableassumptions, yieldsquantitative estimates of cell survival and surviving cellfractions. This method also allows us to determine individual treatment effects when combined modalities are usedand, ultimately, to determine whether the effect of 2 modalilies are additive or synergistic. A major limitation of thismethod is that a tumor systemmust be available in a singlecell suspension for derivation of the standard referencecurve. The method is described below, followed by severalapplications.

MATERIALSAND METHODS

The Meth-A tumor, a methylcholanthrene-induced fibrosarcoma, was obtained from Dr. T. Boyse, Sloan-KetteringInstitute, and has been maintained in both the solid andasciles form. The tumor has been shown to be highlyantigenic for its syngeneic hosts (9). isogenic male BALB/cmice, 6 to 8 weeks old (Carworth Farms, New City, N. Y.)were inoculated with a single-cell suspension of Meth-A

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Time toMeansurvivalreach1.0timeNo.

of viableNo. ofcucmpostinoculationcells@'animals%takes(days)(days)1.5x10711100@6.529.8±0@9―1.0x10101008.533.7±0.78.0x1051010010.034.9±1.95.0x1051310011.033.9±1.12.5x1051210012.034.0±0.91.5x1041210016.035.5±1.12.0x1031410020.038.2±1.31.8

x 1021281.725.044.5 ±2.04.0x 10'1080.028.045.5 ±2.76.0x 10°147.1+HR

ceIIs@'8.0x105710010.032.4±1.75.0x10@910012.537.0±1.51.0x1051010015.036.7±1.46.0

x 10@910015.536.4 ±1.31.5x 10@910017.536.0 ±1.11.0x103977.822.044.3±1.97.5

x 1021070.022.046.6 ±3.83.8x 102875.024.046.8 ±2.67.5x 10'1040.026.547.8 ±2.78.0x10°1020.034.5HRalone150

In Situ Ce!! Survival

cells obtained from donor mice in which the tumor wasmaintained in the asciles form. The tumor transfer cellswere harvested by peritoneal aspiration, washed in 0.9%NaCIsolution centrifuged for 5 mm at 500 rpm, and resuspended in minimal essential medium (Eagle's) for inoculalion. Viability of the cells was regularly >99%, as determined by their appearance under phase-contrast microscopy and the ability of intact cells to exclude trypan blue.All suspensions were morphologically homogeneous withslight variation in cell size and consisted exclusively ofsingle cells.

For construction of the standard reference curve, viablecell inocula were routinely counted in triplicate with ahemocytometer and diluted with minimal essential medium(Eagle's) to appropriate cell concentrations of 6 cells to 1.5x 10@cells/0.1 ml. For tumor inoculationcellswere constantly agitated with a magnetic spin bar, aspirated with aHamilton syringe, and inoculated i.m. with a 26-gaugeneedle in the right thigh.

For evaluation of the possible importance of feeder cellstimulation and/or acquired immunological suppression oftumor cell populations that may manifest as tumor growthdelay, the standard reference curve was developed withviable cells alone and also when inoculated with radiationinactivated homologous tumor cells. Cells (10/0.1 ml) wereHR4at room temperature with a ‘37CsAEC Ltd. Gammacellunit, at a dose rate of 125 rads/min and a total dose of 10kilorads.

After i.m. inoculation the Meth-Afibrosarcoma is initiallyconfined within normal thigh perimeters with increasinginvasion into muscle and displacement of normal tissuecomponents.

Tumor growth was calculated from vernier caliper measurements of the tumor-bearing thighs and included thetumor and normal tissue components. Initially, these measurements were taken at the maximal diameters of length(d1), width (d2), and depth (d3) from the time that tumorsbecame palpable until death or the occurrence of ulceralion. Water displacement studies confirmed that tumorbearing thigh volumes and the normal leg component(muscle, skin, and bone) as derived from contemporarynon-tumor-bearing legs could be best approximated by theproduct of the meanof the 3 dimensions.

Becausemeasurementsassociatedwith tumor infiltrationin the length plane could conceivably give the largestvariation, this measurement was replaced by the mean ofthe other 2 diameters. Comparisons of results obtained inthis manner with those of tumor volumes calculated withthe use of 3-dimensional measurementshave been shownto be in agreementwith each other by ±5%(4).The normalleg volume associated with the increasing tumor dimensions was subtracted from the total volume on a slidingscale. This was done by multiplication of the square of theaveragethigh diameter (0.6 cm for 8 lolO weeks, BALB/c)by the averagediameter of the tumor (d).

RESULTS

Table 1 and a standard growth curve (not shown) are a

4 The abbreviations used are: HR. heavily irradiated; AMD, actinomycin D;LTH. local tumor hyperthermia.

result of the compilation of averagetumor volumes per cellinoculum to the function

t (d13—V((,)' n

in which t corresponds to measurementstaken each day, nis the number of tumors, and d is the average tumordiameter (cm).

A compilation was made of untreated tumor growth dataplotted as the log of the average tumor volume per group(in cu cm) versusdays. A solid line determined by the leastsquares method through the observed data can be bestrepresentedby the Gompertzianfunction (8):

V@) @70e@(1—e°')

where t@ois the averageinitial tumor volume at time 0, A is aconstant related to the initial slope, with a value of 1.21,and a is the retarding constant for this tumor and has avalue of 0.12. All experimental tumor volume data pointswere graphically fit by superimposition to the standardMeth-Agrowth curve.

The reference curve (Chart 1) was constructed based onthe time required for the tumor to reach 1 Cu cm afterinoculations of single-cell suspensions ranging from 6 cellsto 1.5 x 10@viable cells alone or with the addition of 10@HAcells. The averagetime was calculated for each group of 7to 15 mice/inoculation and is graphically represented as asemilog plot. No significant differences were found for rateof tumor growth for comparable dilutions of viable cells

Table1†‘erelationship of cell inoculum size to tumor growth in

syngeneicmale BALB/c mice

a Single-cell suspensions of Meth-A ascites inoculated i.m.b Mean survival time ±S.E. of mice with tumors.C Melh-A cells (10) irradiated with 10 kilorads.

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A. A. A!fieri and E. W. Hahn

with or without HA cells. However,the presenceof HRcellsdid reduce the percentage of takes (Chart 2) and indicates,perhaps, some immunological interplay, as previously suggested by Révész(11).

A logarithmic curve (Chart 1) fit to the function y = a + bIn x and least-squares fit through the data points of thereference curve gave an exponential plot with a slope of—1.823and an interceptof3.50x 10@days.Extrapolationthroughthedatapointstothey axis(0daystogrow to1.0Cu cm) resultedinan estimateof3.0x 10@Meth-Acellsina1.0-cu cm tumor and is in agreement with previous investigations (12)for cell diameters of the order of 15 @m.

Treatment of Tumor Growth Data and QuantitationofCell Survival. Portionsof the resultsof 3 independentexperiments on the Meth-A fibrosarcoma growing in isogeneic male BALB/c mice are summarized in Table 2. Themethodsof X-irradialion and application of LTH(waler bathat 43@for 15 mm) are presented elsewhere (2, 3). Fractionateddoses of X-irradiation were given with 48-hrseparationbetweentreatments and delivered in 4 equal fractions, withthe total dose ranging from 1.8 to 3.6 kilorads. Animalstreated with chemotherapy were given single i.p. injections(150pg/kg) of AMD (Cosmogen;Merck, Sharp and Dohme,West Point, Pa.)alone or immediately following local tumorirradiation of 1.0, 1.5, and 2.0 kilorads. These treatmentswere selected becausethey were noncuralive and could be

evaluated in terms of the dynamics of the tumor regrowthresponse.The Melh-A tumor, as previously mentioned, hasbeen shown to be highly anligenlc for its syngeneic hosts.Consequently, when posttreatment surviving cell numbersare estimated to be within the range of 10@cells and less,cures may be observed and are probably related to hostimmunocompelence. We have seen in this system thatinoculations such as 102viable + HA cells were required for50% tumor takes compared to 10@viable cells inoculatedalone (Chart 2). When the treatment kill is estimated toreducethe surviving cells to these low levels,2 populationsof treated animals can exist, 1 with transient and 1 withlong-term tumor regression. Measurementsand the graphical representation of tumor regrowth (Charts 3 to 6) havebeen previously described in this text.

Analysis of Cell Killing and Surviving Fraction. Fromcaliper measurements the average initial tumor volumes(ti0) was approximately 0.7 cu cm, with a cell content (N0)per treatment group ranging from 1.6 to 2.9 x 10@ceLls(Table2).Aftertreatment,tumor volumes were calculatedfor each animal, and the individual delay in days neededtogrow to 1 cu cm was converted to the number of viable cellsresponsible for tumor growth (N, Table 2) in that time withthe use of the standard reference curve (Chart 1). Theassumedsurviving cell fraction was computed with the useof N/N0 (Table 2) for each animal. For example, with asingle dose of 1.7 kilorads, the individual (n = 13) growthdelay in days to reach 1.0 cu cm was determined as 8.3 ±0.7 (S.E.)days. The delay for each tumor was read from thestandard curve as the number of cells required to producea 1.0-cu cm tumor for that particular lime. From these

E

E

E

E

E

0E

00

. ,,a@,cpUs.IO@HRM@,h-Acells(lOUods)

(00

Number Meth-A celie/inocuPohon

Chart 1. Reference curve for i .m. Meth-A fibrosarcoma (see Table 1 forcell inoculum size responsible for mean tumor growth to 1 cu cm in 7 to 14animals/inoculation). The line through the observed data represents alogarithmic curve fit to the function y = a + b In x. Krads, kilorads.

0 - Voble cells.- ., .,

.I

II

I/0

//

HR: IOSleOnllyI,rod,OledCells(l0krods)

DayS post treatment

Chart 3. Tumor volume response (t@/t)to single-dose X-irradiation for 8 to13 animals/treatment (see Table 2). krad, kilorad.

4

2

>

E

z

0

102

01

100 I@ :@ ic@@ 20:@nys@lOSt‘reotme''

25 30 3@

100 c c@@0 20 40 60 80

n/nTumorTakes

Chart 2. Relationship between percentage of takes and the number ofviable cells inoculated (see Table 1). The solid and dashed lines through thedata are best fit by the eye. krads, kilorads.

Chart 4. Tumor volume response (@/t) to single-dose X-irradiation andconcomitant LTH for 10 to 12 animals/treatment (see Table 2). krad, kilorad.

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In Situ Ce!! Survival

, ,@o 1.0 2.0 3.0 4.0

/A@ ,@//@

. 2 day sepo,o@ionbetween fraceons

E

E

0

0E

RI

00

l.c

to-ID5 10 5 20

Daysposttreatment

25 30 35

Chart 5. Tumor volume response (tilt) to fractionated X-irradiation for 10to 11 animals/treatment (see Table 2).

Chart6. Tumor volume response(t?/t) to single-doseAMD (150 @cg/kg)and concomitant X-irradiationfor 7 to 8 animals/treatment(seeTable 2).krad, kilorad.

.;@@

:! @\)\C

j \h@

I \@\0.001

0.oo0:@ ‘@ ‘ 2.0 ‘ 3.0 ‘ 4@0

TotalDose(krad)

Chart 7. Assumed surviving cell fraction (N/N0). See Table 2 for TreatmentsA through D as noted,with curve fitting as describedin the text. @,fractionated X-ray; •,single-dose X-ray; 0, X-ray + AMD (150 pg/kg); 0, Xray + LTH.krad, kilorad.

ity or synergism. For example, when LTH or AMD is given in

combination with X-irradiation, an increased cell killing isnoted (Chart 7). For determination of whether the LTH orAMD component is additive or synergistic, a modifiedsurvival curve for concomitant hyperthermiaor AMD and Xirradiation can bederived by subtraction of the heal or AMDeffect. This is obtained by normalization of the combinedtreatment surviving fraction(s) to the respective survivingfraction of that agent alone.

Charts 8 and 9 are assumedsurviving fraction curves forcombination, therapy with dashed lines representing theremoval, by normalization, of the heal alone or AMD componenl. If the effect of either agent is less than additive(protection), the normalized curve would fall above thecurve for X-rayalone. If, however, the effect of either agentwere simply additive, the normalized curve would statistically fall within the limits of the curve for X-rayalone. Thus,a normalized curve, the data points of which fall below theenvelopeof additivily, would be suggestiveof a synergistic(potentiation) interaction. Analysisof the interaction of LTH(Chart8) or AMD (Chart9) with radiation shows addilivity atthe lowest dose of radiation used and synergism (polentialion)atthehigherdoses.

DISCUSSION

individual tumor delays, the estimated number of cells thatsurvived treatment (P@)was calculated to be 5.7± 1.7 x 10@cells. With the average initial tumor volume (V0= 0.62 ±0.02 cu cm) known at time of treatment and with theassumption that 3 x 10@cells equals 1 cu cm (by multiplication), the average number of cells initially treated (N0)was determined to be 1.8 ±0.07 x 10g.An estimate of thepercentageof surviving fraction (Sf) of cells after treatmentcan be calculated, where

Sf =@ =@ X 10 cells@@ = 3.1%,N0 1.8x 108cells

with a variation of approximately ±1%. II is thereforeassumed that approximately 3% of the cells survived asingle dose of 1.7 kilorads. Computation of the data on anindividual basis within each treatment provides an estimateof the statistical variation between animals in each treatmenl group. The resulting data for N/N0 are plotted (Chart7) with respect to lolal dose (kilorads). The solid linesrepresenl compuler-generated least-squaresfit to the dalafor the function

Sf = 1 —f(1 —e—DID.)N,

in which fequals the fractional cell component of a mullicellsystem, and N and D0are derived parameters(14).

In addition to estimation of cell survival of noncurativetherapies, the relative effectiveness of multiple singleagents in combination therapy can be evaluatedfor additiv

Several estimates have been made of tumor cell killingafter treatment in situ by means of in vivo and in vitrotechniques. However, no technique has been reported forestimation of the number of surviving cells without disruplion of the treated cell population. Whether survival curves

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Dose/other(kilorads)nN0 (1@)bfN (10)dSt

(10_2)(f@J/fi)0

0.500.951.501 .701.902.1013

1088

1310112.O±O.2@

1.8±0.12.0±0.21.7±0.1@1.8 ±0.11.9 ±0.12.0±0.2i.i

±0.21.9±0.32.5±0.56.5±0.98.3 ±0.7

11.3 ±0.911.9±0.8200

± 2120 ±18

72 ±1716 ± 6

5.7 ± 1 .72.3 ± 20.82± 0.4100

66.6 ±1036.0 ± 9

9.4 ± 43.2 ± 0.91.2 ± 0.40.4 ±0.20+LTH―

0.50+LTH0.95 + LTH1.30 + LTH1.60 + LTH12

101010102.0±0.2

2.2±0.22.4 ±0.22.4 ±0.32.9 ±0.24.1

±1.05.2±1.08.5±1.8

13.9 ±1.522.4±2.569

±2844 ±16

3.8 ± 20.66 ± 0.060.09 ± 0.0635.0

±1420.0 ± 7

1.6 ± 0.80.28 ± 0.20.03 ±0.0020

+ AMD°1.0 + AMD1.5 + AMD2.0+ AMD8

8771

.6±0.11.7±0.12.0 ±0.21.7 ±0.13.9

±0.45.3 ±1.0

11.7 ±2.019.3 ±1.642

±1121 ±101.2 ±0.40.03 ± 0.0226.0

± 712.0 ± 60.6 ± 0.20.018 ±0.0118h

2.43.03.610

10112.8±0.1

2.4±0.22.1 ±0.12.1 ±0.13.7±0.6

5.2±0.911.9±0.917.7±1.374

±3129 ±12

1.1 ± 0.60.08± 0.0426.0

±1112.0 ±50.52 ± 0.30.04 ± 0.02

A. A. A!fieri and E. W. Hahn

Table 2Quantitative assessment of cell kill for the Meth-A fibrosarcoma “in situ

a Tumors (i.m.) in syngeneic male BALB/c mice.b Mean cell content at initiation of treatment (based on initial volumes x 3.0 x 10@

cells/i-cu cm tumor).0' Mean tumor growth delay to reach 1 .0 cu cm (days).

d Mean surviving cell numbers/group (from individual delays extracted off the standardcurve).

ft LTH (water bath) at 43.0 ±0.1°for 15 mm.f Mean ±S.E.a Dose, 150 pg/kg i.p.h Total dose delivered in 4 equal fractions on alternate days.

associated with deriving “assumed―cell survival curvesfrom in situ tumor cell populations. Because the tumorvolume analysis is assayed without perturbation of thetreated cells, the results reflect tumor cell response in anatural environment, complete with the neurovascular, humoral, nutritional, and immunological interactions. Thus,what we call cell survival and surviving fraction, as derivedwith this method, represents the composite response of adynamic system,which also may include treatment-specificand nonspecific factors. For instance when radiation isused, factors such as radiation-induced division delay ofthe tumor cells and the secondary effects on the endothehum of the fine vasculalure may be important. Additionalfactors that are not treatment specific but are related to thecell killing effectivenessof that treatment result in changesin cell kinetics, which are reflectiveof reassortment, recruitment, and repopulation within the tumor. These factors, aswell as hemorrhage, edema, and the rate of removal ofcellular debris, are directly associated with changes intumor volume. When a treatment causes marginal shortlived changes in tumor volumes, the quanlitalion of cellsurvival depicted at the shoulder region may be more inerror than at limes when the treatment reduced tumorVolumes below the palpable region (approximately 0.5 x102 cu cm). In this region the tumor regrowth curves arerepresentative of surviving clonogenic cells, and many ofthe above-mentioned factors have been nullified or equilibrated. However, as previously mentioned, when a treatment effectively reduces tumor cell numbers to the extent

0Izt2

C0

00

C

(I)

Va,E

4

).0 1.5Dose(krod)

Chart8. Relationshipbetweenassumedsurvivingcell fraction P@/Ptioforsingle-dose X-ray and X-ray and concomitant LTH. Dashed line representscombined therapy normalized to LTH alone and is best-fit by eye. krad.kilorad.

constructed from observations on excised tumors can accurately reflect the course of eventsof a tumor left in situ isquestionable.

The advantage of this assay method is the relative ease

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In Situ Cell Survival

and surviving fraction after treatment. The method of analysis results in curves having the characteristics of typicalsurvival curves generated from in vitro studies, i.e. , aninitial shoulder region followed by an exponential decreaseof the surviving cell fraction with increasing levels of treatment.

ACKNOWLEDGMENTS

The authorsgratefullyacknowledgethe adviceof Dr. J. H. Kim, Departmentof RadiationTherapy.Theauthorsalsowish to expresstheir appreciation to Dr. Howard Skipper, Kettering-Meyer Laboratory of the SouthernResearchInstitute, for critically reviewingthis manuscript.The secretariatassistanceof S. Wind in the preparationof this paper and the assistanceprovidedbyS. Feingoldand D. Lehmanarealsogratefullyacknowledged.

REFERENCES

1. Barendsen, G. S., and Broerse, J. J. Experimental Radiotherapy of a RatRhabdomyosarcoma with 15 MeV Neutrons and 300 kV X-rays. I. Effectsof Single Doses. European J. Cancer, 5: 373-391 , 1969.

2. Hahn,E. W., Alfieri, A. A., and Kim,J. H. SingleDoseX-irradiationandConcomitant Hyperthermia on a Radioresistant Fibrosarcoma in theMouse (Abstract). Intern. J. RadiationOncol. Biophys. 102 (Suppl.):1976.

3. Hahn, E. W., Alfieri, A. A., and Kim, J. H. Single Dose X-irradiation andConcomitant Hyperthermia on a Radioresistant Fibrosarcoma in theMouse.Cancer,in press,1978.

4. Hahn, E. W., Canada, T. R., Alfieri, A. A., and McDonald, J. C. TheInteraction of Hyperthermia with Fast Neutrons or X-rays on Local TumorResponse. Radiation Rae., 68: 39-56, 1976.

5. Hermens, A. F., and Barendsen, G. W. Changes of Cell ProlIferationCharacteristics in a Rat Rhabdomyosarcoma before and after X-irradlation. European J. Cancer, 5: 173-189, 1969.

6. Hewitt, H. B., and Wilson, C. W. A Survival Curve for MammalianLeukaemlaCells Irradiatedin Vivo.Brlt. J. Cancer,13:69-75, 1959.

7. Kallman, R. F. Methods for the Study of Radiation Effects on CancerCells.MethodsCancerRes.,4: 309-354,1968.

8. Laird, A. K. Dynamics of Tumor Growth: Comparison of Growth Ratesand Extrapolation of Growth Curve to One Cell. Brit. J. Cancer, 19: 278-291, 1965.

9. Old, L. J., Boyse, E. A., Clarke, D. A., and Carswell, E. A. AntigenicProperties of Chemically Induced Tumors. Ann. N. Y. Acad. Sci., 101:80-106, 1962.

10. Powers, W. E., and Tolmach, L. J. A Multicomponent X-ray SurvivalCurvefor MouseLymphosarcomaCells Irrediatedin Wvo.Nature,197:710-711, 1963.

11. Révész,L. Effect of X-lrrediation on the Growth of the Ehrlich AscitesTumor. J. NatI. Cancer Inst., 15: 1691-1701 , 1955.

12. Schabel, F. M. Concepts for Systemic Treatment of Micrometastases.Cancer,35: 15-24,1975.

13. Skipper, H. E. Kinetic Behavior versus Response to Chemotherapy. J.NatI.CancerInst.,34: 2-14, 1971.

14. Zeitz, L., and McDonald, J. M. Pitfalls in the Use of in Vitro SurvivalCurvesfor the Determinationof Tumor Cell Survivalwith FractionatedDoses.Brit. J. Rediol.,in press,1978.

0)zIz

C0‘a0

1&.

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4

Chart 9. Relationship between assumed surviving cell fraction t@/P'@0forsingle-dose X-ray and X-ray and concomitant AMD. Dashed line representscombined therapy normalizedto AMD alone and is best-fit by eye. krad,kilorad.

where a proportion of animals are cured (approximately 6log killing), the resulting estimatesof cell survival are basedon 2 populations of animals and lead to large group varialions. We therefore feel that this technique is most usefulwhen the treatment range is between the marginal andcurative levels. Although this method requires quantitativedilutions for establishment of a standard curve, it is lesselaborate than the quantitative titration in vivo by the endpoint dilution technique (7). A major disadvantage of thistechnique is that, although it has been found to be reproducible in vivo, an in vitro assayfor the relative accuracy ofassumed surviving cell populations posttrealment has notbeen achieved. We have attempted to grow this tumor cellline without success.

In conclusion, basing our work initially on logical assumptions and knowing that tumors regrow by the proliferalion of surviving cells, we have developed a method thatcan give a reasonablequantitative estimate of cell survival

Dose (krod)

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1978;38:3006-3011. Cancer Res   Alan A. Alfieri and Eric W. Hahn 

Method for Estimating Cell Survival in a Solid Tumorin SituAn

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