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(CANCER RESEARCH 31, 1279— 1284, September 19711 tumors have been performed on unirradiated tumors. The few results derived from irradiated solid tumors are somewhat conflicting (2, 9, 11, 25). More investigations are obviously needed in this area. The work described below is an investigation of the proliferation kinetics of 4 different types of tumor in rodents after large single doses of radiation. The results are compared with those obtained from unirradiated tumors of the same type. An attempt is made to explain the gross radiation response of these tumors in terms of their kinetic parameters. MATERIALS AND METHODS The 4 tumors used in these experiments were 3 transplantable fibrosarcomas in John's strain Wistar rats (RIBS, 550, and SSB1) and first transplants from spontaneous mammary carcinomas in C3H mice. The tumors and the methods of implantation have been described previously (4). When the tumors became palpable, their volume was estimated 3 to 6 times weekly, with use of Vernier calipers to measure 3 mutually perpendicular diameters. When the mean diameter reached 8 to 10 mm in rats or 6 to 8 mm in mice, the tumors were irradiated with a large single dose of 250-kV X-rays at a dose rate of 330 to 400 rads/min. The apparatus and technique used were as described by Thomlinson and Craddock (23) for rats and by Howes (13) for mice. 550 and SSB1 tumors received 1000 rads, and RIBS and C3H tumors received 1500 rads. At a predetermined time after irradiation, when all the tumors had resumed growth and it was assumed that most of the radiation-damaged cells had died and been removed from the tumor volume, the kinetic analysis was made. The volume-doubling time was measured from the growth curves. The mean cell cycle time was determined from a labeled mitoses curve. To obtain this, we gave the animals injections of tritiated thymidine (specific activity, 360 mCi/mmole), at a dose of 0.5 pCi/g of body weight. Tumors were excised at various intervals ranging from I to 60 hr after injection, bisected, fixed in 5% formol-NaC1, and embedded in paraffin wax. [email protected] were cut at 0.5-mm intervals throughout the tumor block. Slides were dipped in Ilford KS emulsion, exposed for 6 to 12 weeks at 4°,developed in Kodak D19B developer, fixed in Johnsons' Fixsol, and stained with Ehrlich's hematoxylin and eosin. Sections from at least 4 levels were scored at a magnification of X600 or X750 to determine the fraction of cells and the fraction of mitoses which were labeled. From 2000 to 5000 cells were counted to SEPTEMBER 1971 1279 The Cell Proliferation Kinetics of Four Experimental Tumors after Acute X-irradiation Juliana Denekamp and R. H. Thomlinson Cancer Researth Campaign, Research Unit in Radiobiology, Mount Vernon Hospital, Northwood, Middlesex, England fJ. D./ and Medical Research Council, Experimental Radiopathology Unit, Hammersmith Hospital, London, W.12, England [R. H. T./ SUMMARY There is no significant change in the mean cell cycle time and the duration of its phases in four tumors analyzed at least ten cell cycles after a large dose of radiation. There is, however, a slower overall growth rate of the irradiated tumors which cannot be attributed to a reduced growth fraction. The slower growth may be caused partly by a very slow rate of removal of radiation-damaged cells, but in at least one tumor it can be largely attributed to the development of a slowly increasing core of nonproliferating material. The regression after irradiation does not occur for some days in the sarcomas, but it occurs within the first day in the carcinoma. It is postulated that the time at which shrinkage occurs after irradiation is correlated with the â€oecell loss factor―as measured in the unirradiated tumors. INTRODUCTION The cellular proliferation kinetics of a considerable number of experimental tumors has now been analyzed (review, Ref. 4) together with those of a smaller number of human tumors (e.g., Refs. 1 and 8). It is hoped that eventually this type of information might be used to predict more effective timing of the doses of radiation given in clinical radiotherapy. Animal experiments suggest that the effectiveness of a 2nd dose of radiation depends on a number of factors, which may be influenced by the proliferation kinetics of the cells within the treatment area. These include the extent of intracellular recovery (7, 14), the variation in radiosensitivity with the age ofthe cells in the cell cycle (6, 14, 15, 21), the relative rates of repopulation of normal and malignant cells (16), and the rate and extent of reoxygenation of hypoxic tumor cells (1 3 , 22). Hahn (10) has shown that considerable therapeutic advantages could be gained by manipulating the treatment in terms of just the second of these factors. In addition, certain forms of combined chemical and radiation therapy (e.g., the use of 5-bromodeoxyuridine as a radiosensitizer and chemical methods of cell synchronization) will be most effective in situations where the proliferation kinetics of the normal cells differ greatly from those of the malignant cells (3). Several workers (e.g., Refs. 2 and 17) have shown that the mean cell cycle time of nonmalignant cells becomes shorter after acute irradiation, presumably in response to homeostatic control mechanisms. Most of the proliferation studies on Received January 4, 1971; accepted April 30, 1971. on June 28, 2020. © 1971 American Association for Cancer Research. cancerres.aacrjournals.org Downloaded from
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Page 1: The Cell Proliferation Kinetics of Four Experimental ... · recovery (7, 14), the variation in radiosensitivity with the age ofthe cells in the cell cycle (6, 14, 15, 21), the relative

(CANCER RESEARCH 31, 1279—1284, September 19711

tumors have been performed on unirradiated tumors. The fewresults derived from irradiated solid tumors are somewhatconflicting (2, 9, 11, 25). More investigations are obviouslyneeded in this area. The work described below is aninvestigation of the proliferation kinetics of 4 different typesof tumor in rodents after large single doses of radiation. Theresults are compared with those obtained from unirradiatedtumors of the same type. An attempt is made to explain thegross radiation response of these tumors in terms of theirkinetic parameters.

MATERIALS AND METHODS

The 4 tumors used in these experiments were 3transplantable fibrosarcomas in John's strain Wistar rats(RIBS, 550, and SSB1) and first transplants from spontaneousmammary carcinomas in C3H mice. The tumors and themethods of implantation have been described previously (4).When the tumors became palpable, their volume was estimated3 to 6 times weekly, with use of Vernier calipers to measure 3mutually perpendicular diameters. When the mean diameterreached 8 to 10 mm in rats or 6 to 8 mm in mice, the tumorswere irradiated with a large single dose of 250-kV X-rays at adose rate of 330 to 400 rads/min. The apparatus andtechnique used were as described by Thomlinson andCraddock (23) for rats and by Howes (13) for mice. 550 andSSB1 tumors received 1000 rads, and RIBS and C3H tumorsreceived 1500 rads. At a predetermined time after irradiation,when all the tumors had resumed growth and it was assumedthat most of the radiation-damaged cells had died and beenremoved from the tumor volume, the kinetic analysis wasmade. The volume-doubling time was measured from thegrowth curves. The mean cell cycle time was determined froma labeled mitoses curve. To obtain this, we gave the animalsinjections of tritiated thymidine (specific activity, 360mCi/mmole), at a dose of 0.5 pCi/g of body weight. Tumorswere excised at various intervals ranging from I to 60 hr afterinjection, bisected, fixed in 5% formol-NaC1, and embedded inparaffin wax. [email protected] were cut at 0.5-mm intervalsthroughout the tumor block. Slides were dipped in Ilford KSemulsion, exposed for 6 to 12 weeks at 4°,developed inKodak D19B developer, fixed in Johnsons' Fixsol, and stainedwith Ehrlich's hematoxylin and eosin. Sections from at least 4levels were scored at a magnification of X600 or X750 todetermine the fraction of cells and the fraction of mitoseswhich were labeled. From 2000 to 5000 cells were counted to

SEPTEMBER 1971 1279

The Cell Proliferation Kinetics of Four Experimental Tumors afterAcute X-irradiation

Juliana Denekamp and R. H. Thomlinson

Cancer Researth Campaign, Research Unit in Radiobiology, Mount Vernon Hospital, Northwood, Middlesex, England fJ. D./ and MedicalResearch Council, Experimental Radiopathology Unit, Hammersmith Hospital, London, W.12, England [R. H. T./

SUMMARY

There is no significant change in the mean cell cycle timeand the duration of its phases in four tumors analyzed at leastten cell cycles after a large dose of radiation. There is,however, a slower overall growth rate of the irradiated tumorswhich cannot be attributed to a reduced growth fraction. Theslower growth may be caused partly by a very slow rate ofremoval of radiation-damaged cells, but in at least one tumor itcan be largely attributed to the development of a slowlyincreasing core of nonproliferating material. The regressionafter irradiation does not occur for some days in the sarcomas,but it occurs within the first day in the carcinoma. It ispostulated that the time at which shrinkage occurs afterirradiation is correlated with the “cellloss factor―as measuredin the unirradiated tumors.

INTRODUCTION

The cellular proliferation kinetics of a considerable numberof experimental tumors has now been analyzed (review, Ref.4) together with those of a smaller number of human tumors(e.g., Refs. 1 and 8). It is hoped that eventually this type ofinformation might be used to predict more effective timing ofthe doses of radiation given in clinical radiotherapy. Animalexperiments suggest that the effectiveness of a 2nd dose ofradiation depends on a number of factors, which may beinfluenced by the proliferation kinetics of the cells within thetreatment area. These include the extent of intracellularrecovery (7, 14), the variation in radiosensitivity with the ageofthe cells in the cell cycle (6, 14, 15, 21), the relative rates ofrepopulation of normal and malignant cells (16), and the rateand extent of reoxygenation of hypoxic tumor cells (1 3 , 22).Hahn (10) has shown that considerable therapeutic advantagescould be gained by manipulating the treatment in terms of justthe second of these factors. In addition, certain forms ofcombined chemical and radiation therapy (e.g., the use of5-bromodeoxyuridine as a radiosensitizer and chemicalmethods of cell synchronization) will be most effective insituations where the proliferation kinetics of the normal cellsdiffer greatly from those of the malignant cells (3).

Several workers (e.g., Refs. 2 and 17) have shown that themean cell cycle time of nonmalignant cells becomes shorterafter acute irradiation, presumably in response to homeostaticcontrol mechanisms. Most of the proliferation studies on

Received January 4, 1971; accepted April 30, 1971.

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Juliana Denekamp and R. H. Thomlinson

E@ II

RdI-

110

‘@2CE

Ld@I-Rd

4 ic0

4Rd

a Control 2CC

15

‘C

5

Rads

RIBS

Rads.

SSB1

t 4 e 1@2 16 @O @4 28@ I R 4 8 12 16 ‘@

b

Rads

ssO

t

1'@

RadsiC

!@ C3H

@4 I@ 4@ 12 16@@ e i@ i@ 2@O 24 @8 32TIME (Days) TIME (Days)

Chart 1. Growth curves of the various tumors. Each point represents the computed mean of 6 to 12 tumors ±S.E. a, RIBS sarcomas, controlsand tumors irradiated with 1500 rads; b, SSO sarcomas, controls and tumors irradiated with 1000 rads; c, SSBI sarcomas, controls and tumorsirradiated with 1000 rads; d, C3H mammary carcinomas, controls and tumors irradiated with 1500 rads. The carcinomas shrink within 1 day ofirradiation in contrast with the 3 sarcomas, which continue to grow for some time.

determine the L.I.' on the tumors sampled 1 hr afterthymidine injection. Between 100 and 200 mitoses werecounted to determine the PLM for each tumor sampled,except in the case of SSB1 tumors in which approximately 50mitoses per point were scored because of the very low M.I.(<0.1%).

RESULTS

Growth curves for the 4 types of tumor, with and withoutirradiation, are shown in Chart 1. RIBS tumors continued toenlarge for at least 24 hr after 1500 rads, then regressed forseveral days, and by the 7th day had resumed growth;subsequently, their growth was rather slower than that ofcontrols (Chart la, Table 2). The animals were given injectionsof thymidine 7 days after 1500 rads.

550 tumors did not regress in these experiments althoughearlier transplants had shown some regression when irradiatedwith 1000 rads. Their growth rate was greatly reduced forseveral days and never fully returned to that of control tumors(Chart lb). Many of these tumors had large cystic centers,making it impossible to interpret volume measurements interms of cell numbers. The animals were given injections ofthymidine 7 and 12 days after 1000 rads.

SSB1 tumors responded to 1000 rads as shown in Chart lc.They continued to enlarge for about 6 days and then remainedat a constant size until about 24 days after irradiation. Beyond

I The abbreviations used are: L.l., labeling index; PLM, percentage oflabeled mitoses; M.I., mitotic index; G.F., growth fraction.

this time, the irradiated tumors regrew but at a considerablyslower rate than control tumors of the same volume. SSB1tumors showed no shrinkage even after doses as large as 2000rads (B. Dixon, personal communication). The proliferationkinetics were investigated at 14 days after 1000 rads.

In contrast to the 3 sarcomas, the C3H carcinomasresponded to 1500 rads with a decrease in volume within 24 hr(Chart 14 They continued to shrink for several days, but by12 to 14 days after irradiation they were regrowing at a rateapproaching that of controls. Cell proliferation wasinvestigated at 14 days after 1500 rads.

Chart 2 shows the PLM data obtained from irradiated RIBStumors. Those from unirradiated tumors are included from aprevious publication (4) for comparison. The points canalmost be fitted by the same curve for the first 2 waves,showing that there is no detectable change in the duration ofthe phases of the cell cycle 7 days after irradiation. Theparameters derived from this curve are shown in Table 1. Theduration of mitosis was estimated from the labeling andmitotic indices (Table I ) and the duration of the S phase, withthe relationship

TM (X7'@/log@2) X (M.I./L.I.) (A)

where A is a factor which arises from the exponentialdistribution of ages in a growing population of cells. Its valuelies in the range 0.7 to 1.0 and may be calcula@ed from themeasured cell cycle phases (19).

The PLM data from irradiated 550 tumors are shown inChart 3. The control tumor points are shown for comparison

I280 CANCER RESEARCH VOL. 31

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The volume-doubling time was estimated from growth curves. The otherparameters were estimatedfrom autoradiographs made atvarioustimesafterinjection of tritiatedthymidine.TD

(hr) T@ (hr)Duration

(hi) of:M.I.

(%)L.I. (%)T (hr)G.F. (%)Cellloss

factor(@)aG,SG2MRIBS

7 daysafter1500rads 55 12.82.37.72.40.381.334.019.80.87570.64SSO

‘@“10 daysafterl000rads90 20.59.07.03.80.681.517.832.30.82550.64SSB1

28 daysafter1000rads 240 “39“26“1 1“@‘20.020.0210.677.00.74430.68C3H

14 daysafter1500rads 132 ‘@15“-‘6.8“6 2.1“0.131.314.9“[email protected]“@‘40“@‘0.76

Tumor Cell Kinetics after Irradiation

and are again close to those from the irradiated tumors. Asingle curve can be fitted to both sets of data, indicating nodetectable change in the length of the cell cycle phases (Table1).

Chart 4 shows the PLM data for SSB1 tumors.Unfortunately, some of the irradiated tumors were lost in anattempt to produce autoradiographs from cryostat sections.Attempts to repeat the lost intervals failed, since successivebatches of tumors did not grow at the original control growthrate. However, the 10 points obtained from irradiated tumorsagree well with those from control tumors, suggesting that inthis tumor also there was no significant change in the durationof the cell cycle phases at 28 days after 1000 rads. Theparameters estimated from the curve are shown in Table 1.

The PLM data obtained from irradiated C3H tumors are

Chart 2. Tumor RIBS. The percentage of mitoses that are labeled atvarious times after injection of tritiated thymidine. ., tumors treatedby injection 7 days after 1500 rads; X, unirradiated tumors. The linedrawn is a best fit by eye to the irradiated tumors.

shown in Chart S. They are in agreement with those fromunirradiated tumors and give no indication of a change in theduration of the mean cell cycle time, although no tumors weresampled between 7 and 16 hr.

The longer volume-doubling time of these 4 tumors afterirradiation is not therefore explicable in terms of a change inthe mean cell cycle time. Other factors affecting the rate ofgrowth of a tumor are the fraction of cells that areproliferating (G.F.), changes in the amount of noncellularmaterial present, and the rate at which cells are lost from thetumor volume. The potential doubling time, T, of the totalpopulation of proliferating and nonproliferating cells has beendef'med (19) as the time in which the number of cells in atumor would double in the absence of cell loss. This can becalculated from the duration of DNA synthesis for the

Chart 3. Tumor 550. The percentage of mitoses that are labeled atvarious times after injection of tritiated thymidine. ., tumors treatedby injection 7 and 12 days after 1000 rads; X, unirradiated tumors.

Table 1

HOURS AFTER TdR—3H INJECTIONHOURS AFTER TdR—3H INJECTION

Kinetic analysis of irradiated tumors

a0@ of doubtful validity in irradiated tumors. See text.

1281SEPTEMBER 1971

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Ixx

x

Juliana Denekamp and R. H. Thomlinson

IW

(nU

0I-

U-JU

4.-J 4C

I-zUU

U0.

1-'

@O 10 20 30 40

HOURS AFTER TdR—3H INJECTION

Chart 4. Tumor SSB 1. The percentage of mitoses that are labeled at various times after injection of tritiated thymidine. ., tumors treated byinjection 28 days after 1000 rads; x , unirradiated tumors.

X

x

x SSBi TUMORS

x

/I

II

‘I

xx

x

I

kx

‘I

(C)

The values of G.F. obtained by this method are marginallyhigher in RIBS and 550 than those for unirradiated tumors,but because of the uncertainties in T@ for SSB1 and C3Htumors, the differences shown are not significant (Table 2).However, it is clear that the slowing in volume growth ratescannot be interpreted in terms of a reduction in G.F. Thepotential doubling time of the total cell population is, in allcases, much shorter than the measured volume-doubling timeofthe tumors.

The discrepancy between the observed rate of volumeincrease and the calculated rate of increase in cell numbersmay be due to loss of cells from the tumor volume. Steel (19)has shown that cell loss can be estimated in this way if (a)there is a constant distribution of cell size; (b) the proportionof tumor volume occupied by parenchymal cells does notchange during the period over which TD is measured; and (c)the values of L.I. and T@are truly representative of the wholepopulation. Under these conditions a cell loss factor, @,can beestimated which is defined as the proportion of new cellsformed at each division that are lost from the tumor volume:

0=1 —(T/TD)

x

(D)

xx

x

x

XxX

X@X

Estimates of 0 for these 4 tumors are shown in Tables 1 and 2,but their validity is discussed later.

DISCUSSION

The large, single doses of radiation used in theseexperiments cause much cell death in each type of tumor,but the pattern of gross radiation response differs markedlyfrom one to another (Chart 1). The 3 sarcomas continue togrow for several days after irradiation in spite of the mitoticdelay. Since the cells progress toward G2 during this mitoticdelay, the average volume of the cells must increase. Inaddition, the tumor volume may increase because of edema.Eventually these processes occur more slowly than the removalof radiation-killed cells, and the tumors may shrink. In RIBS,the tumors begin to shrink after about 48 hr, whereas SSOtumors show no shrinkage but merely grow more slowly thancontrols. In SSB1 tumor throughout which there is a networkof reticulin and collagen, loss of the radiation-damaged cells isnot accompanied by a reduction in volume even after a dose of2000 rads. The rapid shrinkage of the C3H mammarycarcinoma is in sharp contrast with the response of thesarcomas. Within 24 hr, the C3H tumors have shrunk to about75% of the volume at irradiation. The shrinkage is occurringduring the presumed period of mitotic delay. If the death ofcells that have been lethally damaged by radiation occurs onlyat mitosis and is followed by resorption, this reduction involume cannot be caused solely by the killing effects ofradiation. Rather it is suggested that when cell p@roduction ishalted by irradiation, the cell loss that occurs normally in thistumor (Table 2) is unmasked, and the net result is a reductionin volume. If this hypothesis is generally true, tumors with

proliferating cells and the proportion of labeled cells in thetotal population of proliferating and nonproliferating cells,i.e., the initial L.l.:

T= XT8/L. I. (B)

This calculated value of T can then be used to estimate G.F.from the equation (19):

ln(l +G.F.)Tc/TX 1n2

I282 CANCER RESEARCH VOL. 31

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TumorGroupTD (hr)L.l. (%)Ts (hr)Tc (hr)G.F.(%)0RIBSIrradiated

Control55 2434.030.07.7 9.012.8 13.257 450.640.00SSOIrradiated

Control90 3417.816.47.0 7.820.5 20.555 480.640.00SSB1Irradiated

Control240 7810.613.1“-1110.7“3939.043 600.680.25C3HIrradiated

Control132 10814.915.9@‘66.5“@‘1S15.0‘@‘4037“@‘0.760.70

@x ,@%. _

**

Tumor Cell Kinetics after Irradiation

less as they cease to divide and are eventually removed fromthe tumor. Lethally injured cells that are not visibly damagedwill influence the estimate of G.F. also, since they will becounted in the initial L.I. Furthermore, when a cell that hasincorporated tritiated thymidine dies, this labeled thymidinemay become available to other cells which are synthesizingDNA (18). Such reutilization of thymidine interferes with thePLM technique, which is only valid if the thymidine isavailable for a very short period of time. These problems canbe avoided by not investigating the cell kinetics of the systemuntil several cycle times after the irradiation, as in the workdescribed here. Of course, if a transient change in the meanduration of the cell cycle had occurred, it would have beenmissed in these experiments.

In all of the tumors, the volume-doubling time wassomewhat longer after irradiation than in the controls, but nosignificant change in the cell cycle time was observed. In someother studies, a change in T@ after irradiation has beenobserved. Brown (2) found a slight elongation of T@ in7,12-dimethylbenz(a)anthracene-induced hamster cheek pouchcarcinomas. Hermens and Barendsen (1 1) have reported aconsiderable reduction of T@ in a rat rhabdomyosarcoma.Similarly, Van Peperzeel (25) found a shortening of T@ in amouse adenocarcinoma. Frindel et al. (9) found no change inT@ in the solid version of fibrosarcoma NCTC in mice,although a change was observed in the ascitic version. These 4studies were all performed within the first 4 days afterirradiation.

There seems to be a slight increase in G.F. of RIBS and 550tumors after irradiation but possibly a slight decrease in SSB1tumors. Because of the problems inherent in the measurementsof G.F., changes of this degree are not likely to be significant.In particular, the estimates depend on the assumption that allradiation-killed cells have been removed and should any dyingcells remain and be counted in the L.I., the values of G.F.obtained will be underestimates.

Vascular failure in tumors leads to the presence ofnonproliferating cells (20) and also to cells which areprotected from radiation injury by hypoxia (13, 23, 24). Theproportion of hypoxic cells has been estimated at 10 to 20% ina number of experimental tumors (12, 13), while the G.F. ofmany tumors is between 40 and 60% (4). Improvements in theavailability of oxygen from the blood supply after irradiationresult in reoxygenation of hypoxic tumor cells, as has beenshown to occur in RIBS (23) and C3H tumors (1 3). Thisimprovement must also lead to the return of some potentiallyclonogenic cells into the proliferating fraction, since the tumorcan regrow from these rescued hypoxic cells. However, if thetime course of increases in G.F. were similar to the time courseof reoxygenation, they would not have been observed in thepresent study. The use of cytotoxic chemicals orradiosensitizers that are incorporated only by cycling cellswould have greater therapeutic possibilities if noncycling cellscame into cycle during treatment.

Since there is no change in the mean cell cycle duration andlittle change in the G.F. at the long time after irradiation atwhich they were measured in these 4 tumors, anotherexplanation must be found for the discrepancy between thepotential doubling time and the observed volume-doubling

C3H TUMORSRnRdRn10I'-

0'LU

Rd

4—J.

X

xx

I'3'

x

Chart 5. C3H mammary carcinoma. The percentage of mitoses thatare labeled at various times after injection of tritiated thymidine. •,tumors treated by injection 14 days after 1500 rads; X, unirradiatedtumo rs.

Table 2A comparison ofthe kinetics ofunirradiated tumors and those

irradiatedwith singledoses of X-raysThe parameters were estimated from autoradiographic analysis of

tumors after injection of tritiated thymidine.

HOURS AFTER TdR—3H INJECTION

large cell loss factors before irradiation should shrink rapidlywhen irradiated and those with small cell loss factors shouldcontinue to grow for some time before shrinking. A review ofthe published kinetic data on tumors (4) suggests that, ingeneral, sarcomas have low values of 0 and carcinomas havehigh values. This relationship and its correlation with radiationresponse is now being tested in other animal tumors (5).

Because of the extended time period over which cell deathcaused by irradiation is manifested, several problems arise inanalyzing the proliferation kinetics. The PLM techniquecannot be used at short intervals after an acute dose ofradiation because of the mitotic delay. When this delay is overand mitoses reappear in the tissue, a PLM curve can beobtained, but at first this will include cells that have beenlethally injured and are destined to die at a subsequentdivision. These cells influence the measurements progressively

SEPTEMBER 1971 I283

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Juliana Denekamp and R. H. Thomlinson

time. In terms of Steel's model, this discrepancy would beinterpreted as a loss of cells from the tumor volume continuingto occur at least 10 cell cycles after irradiation. However,Steel's model is only applicable under certain well-definedconditions, one of which is that the proportion of the tumorvolume occupied by visually intact cells does not changeduring the period over which TD@ measured (19). In all 3sarcomas, there is an obvious change in the gross structure ofthe tumor after irradiation. To varying degrees, they eachadopt a mode of growth with cell proliferation in the rim andcell death in the center. In RIBS, the dead cells form acoagulated necrotic mass; in SSB 1, a fine network of reticulinand collagen fibers persists in the center though almost all thecells have disappeared; and in SSO, the center becomes liquidand is without cellular structure. This picture is consistentwith the absence of efficient cell removal even afterirradiation. Subsequent growth of these tumors is from cellproliferation at the periphery. In growth of this type, wherethe kinetic parameters can be estimated only from the rim, adiscrepancy between Tand TD will be found, without any cellloss from the tumor volume. Therefore, the large values of 0quoted in Table 2 are overestimates, and the discrepancycannot be interpreted entirely as loss of cells. This problemwill be discussed in detail in another publication (J.Denekamp, J. F. Fowler, A. C. Begg, and E. W. Emery,manuscript in preparation). The irradiated C3H tumors showthe least change in histology after irradiation. This can beattributed to the ability for rapid removal of radiation-killedcells in a tumor which is normally losing cells at aconsiderable rate. In this tumor, the cell loss factor afterirradiation is hardly different from that estimated forunirradiated tumors.

ACKNOWLEDGMENTS

We are grateful to Professor J. F. Fowler for his advice, interest, andstimulation throughout this project, also to Dr. J. M. Brown, Dr. I. F.Tannock, and Dr. E. W. Emery for their helpful criticisms of themanuscript. We thank Mrs. M. M. Ball and Mrs. W. Wilson for theirtechnical assistance.

REFERENCES

1. Bennington, J. L. Cellular Kinetics of Invasive SquamousCarcinoma of the Human Cervix. Cancer Res., 29: 1082—1088,1969.

2. Brown, J. M. The Effect of Acute X-irradiation on the CellProliferation Kinetics of Induced Carcinomas and Their NormalCounterpart. Radiation Res., 43: 627—653, 1970.

3. Brown, J. M., and Ellis, F. The Use of Pyrimidine Analogues inRadiotherapy. Brit. J. Radiol., 43: 155—156,1969.

4. Denekamp, J. The Cellular Proliferation Kinetics of AnimalTumors. Cancer Res., 30: 393—400, 1970.

5. Denekamp, J. Discussion. In: Time and Dose Relationships in

Radiation Biology as Applied to Radiotherapy, NCI-AECConference, Carmel, Calif., 1969, pp. 144—145. BrookhavenNational Laboratory, BNL 50203 (CS?), 1970.

6. Denekamp, J., Ball, M. M., and Fowler, J. F. Recovery andRepopulation in Mouse Skin as a Function of Time afterX-irradiation. Radiation Res., 37: 361—370,1969.

7. Elkind, M. M., and Sutton, H. X-ray Damage and Recovery inMammalianCells in Culture. Nature, 184: 1293, 1959.

8. Frindel, E., Malaise, E., and Tubiana, M. Cell Proliferation Kineticsin Five Human Solid Tumors. Cancer, 22: 61 11—6120, 1968.

9. Frindel, E., Vassort, F., and Tubiana, M. Effects of Irradiation onthe Cell Cycle of an Experimental Ascites Tumor of the Mouse.Intern. J. Radiation Biol., 17: 329—337,1970.

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1971;31:1279-1284. Cancer Res   Juliana Denekamp and R. H. Thomlinson  after Acute X-irradiationThe Cell Proliferation Kinetics of Four Experimental Tumors

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