(CANCER RESEARCH 27 Part 1, 1122-1131,June 1967]
Kinetics
of Cell Proliferation
EMILIA FRINDEL, EDMOND
Institut
Gustave-Roussy,
Villejuif,
P. MALAISE,
of an Experimental
EDWARD
ALPEN', AND MAURICE TUBIANA
Seine, France
SUMMARY
The cellular proliferation kinetics of an exjxrimental fibro
sarcoma in C3H mice have been studied in vitro and in vivo at
various stages in tumor growth.
The duration of the cell cycle measured in vitro is the same as
that measured in vivo and does not change when the increase in
cell number, at first exponential, slows progressively. The slow
ing down of the growth rate and the plateau in vitro are explained
mainly by a reduction in the proportion of cells engaged in the
cell cycle and by increasing cell death.
In vivo, the growth rate is at first rapid and then slows pro
gressively. The duration of the cell cycle is similar in all phases
of tumor growth. A diminution both of the number of labeled
cells after multiple injections of tritiated thymidine and of the
growth fraction is seen as the growth rate slows. It is probable
that in this case also increasing cell death contributes to the
slowing of tumor growth. Autoradiographs in large tumors
after multiple injections show considerable heterogeneity in
labeling from one region of the tumor to another.
INTRODUCTION
The jattern of growth of experimental tumors has been the
object of recent general reviews (5, 6, 10) in which it is indicated
that, in solid tumor as well in neoplastic ascites tumors, the in
crease in the cell number, which is at first quite rapid, progres
sively decreases.
Several paj)ers recently reviewed by Baserga (1) and
Mendelsohn (12) have been devoted to the kinetics of cell pro
liferation in s|x>ntaneous and induced tumors. However, to our
knowledge, no authors have studied the kinetics of cellular
growth in the same type of solid tumors at different stages of
their growth in order to analyze the causes of the decrease in
growth rate which has been observed. It is possible to envisage
several reasons for the observed decrease in growth rate, for
example, either a decrease in the growth fraction or an increase
in the length of the cellular cycle.
We have been studying for several years a fibrosarcoma of the
C3H mouse in which the growth rate is extremely reproducible
from one animal to the next when one injects into a recipient the
same number of cells coming from the same lot of cells cultivated
in vitro (8, 9). During the course of the first 20 days or so after
implantation, the pattern of growth is at first rapid and then
slows considerably without any significant change in the histo
1Present address: U. S. Naval Research Laboratory, San Fran
cisco, California.
Received September 19, 1966; accepted February 16, 1967.
1122
Tumor
logie character of the tumor. For this reason, it seemed to us that
this tumor would lend itself ]>articularly well to studies of evalua
tions of the kinetics of proliferation of individual cells during
tumoral growth. In addition, this cell can be cultivated in vitro,
and under these conditions, one also sees that the growth rate
or to be more explicit, the rate of change of the cell number has
an evolution analogous to those of the solid tumor. The number
of cells at first increases very rapidly, there is then a progressive
slowing in rate, and finally a plateau in cell number is reached. It
ap]>eared to us that a comparative study of the kinetics of pro
liferation in vitro would be very interesting and might provide
further insight into the in vivo process.
MATERIALS AND METHODS
In Vi vo
Cells. NCTC clone 2472 is cultivated in Medium 109 (7, 13)
with 10% added horse serum. The cells injected into the mice
are obtained from a culture in exponential growth. The medium
is renewed the day before. The cells are put into suspension
using trypsin (1:300) solution ata concentration of 0.05f'.¿.
After
centrifuging, they are resusjiended in Medium 109. The final
cell concentration is 7,500,000 cells i>er ml. Into the flanks of
C3H male mice aged 2 to 3 months, 750,000 cells (0.1 ml) are
injected subcutaneously. The pre|iaration and injection of the
cells is completed within half an hour.
Estimation of Tumor Volume. Two hundred mice aged
2 to 3 months were used to study the growth curve of the tumor.
Measurements were done daily after the 6th day following the
injection of tumor cells using a caliper. Two dimensions of the
tumor were noted: the larges and smallest diameter. Usually,
they are at right angles; tumor thickness was not measured.
From these two diameters (D and d) and taking into account
the double thickness of the skin overlying the tumor (2 x 0.5 mm),
the volume of the tumor (in cu mm) is calculated from the fol
lowing formula:
4/3-
(D + d - 1)
The volume which is obtained using this formula is larger than
the true volume. Tumor mass and apparent volume have been
compared in 100 animals sacrificed at variable times during the
evolution of the tumor. The results show that for all tumor sizes
the ratio, apparent volume/tumor mass, varies little and equals,
on average, 1.75.
Cell Cycle. The cell cycle is studied by the method of labeled
mitoses. At 3 days, 7 days, and 20 days after inoculation of the
NCTC cells, 60 mice per group received 50 microcuries of thyiniCANCER RESEARCH VOL. 27
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Kinetics
dine-3H intraperitoneally in a single injection and 4 mice of each
group were sacrificed by cervical dislocation at various times,
from 15 minutes to 40 hours after injection of the DNA precursor.
The tumors were dissected and fixed in Carnoy's fixative. Sections
4 microns thick were prepared and autoradiographs were made
by the dipping method using Ilford emulsion. After 3 weeks of
exposure at 4°Cin a wooden light-tight box, the slides were
developed in Kodak D19 B and fixed. The developed slides were
stained with phloxine-hemalum stains. The number of labeled
mitoses per 100 total mitoses was plotted against time after the
pulse label and the form of the curve was obtained. By this means,
it was possible to determine the duration of the cell cycle which
was measured at 60% values on the ascending curves. The mini
mum duration of GÌ
is determined by the time between the injec
tion and the appearance of the first labeled mitoses. The average
duration of G2 is the time between administration of the thymidine-3H and when 50% of the mitoses were labeled. The duration
of mitoses was determined from the mitotic index multiplied by
the generation time which was in turn derived from the period
between the midpoints of 2 successive waves of labeled mitoses.
The duration of the synthetic period for the in vivo experiment
was determined as the time between the 50% labeled mitoses on
the ascending and descending slopes of the curve. Gì
was calcu
lated as the difference between the total generation time and the
sum of the other phases of the cell cycle.
The labeling index (L.I.) was measured in mice killed 1 hour
and 5 days after pulse labeling. Furthermore, 6 mice were in
jected with 50 microcuries thymidine-3H every 5 hours for 30
hours, and the percentage of labeled cells was determined on the
tumors of mice sacrificed one hour after the 7th injection. In all
experiments, the background in the autoradiographs was ex
tremely low and cells containing 2 grains and more were con
sidered as positive cells.
The growth fraction (11) was determined by 2 independent
methods: (a) Five days after a pulse label of thymidine-3H the
ratio between the percent of labeled cells and the percent of
labeled mitoses gives an estimate of the proportion of dividing
cells in a total tumor population if certain theoretic conditions
set forth by Mendelsohn (11) are satisfied, (fo) Knowing the
duration of the S phase (T¡)and the duration of the cycle (Tc)
we can calculate a theoretic labeling index:
L.I. = T./Tc
If the L.I. observed corresponds to the L.I. calculated, then
one can consider that the whole ¡wpulationis proliferating. The
ratio L.I. observed/L.I. calculated is equal to the growth frac
tion.
In Vitro
Stock cultures of NCTC clone 2472 were plated into 6-cm
Petri dishes with an initial number of 2 X IO5cells per plate. The
usual culture medium was used (Medium 109 with 10% added
horse serum). The Petri dishes were placed in an atmosphere of
sterile air of saturated humidity with 109¿added COi in an air
tight box. The culture medium was renewed every 24 hours to
avoid the influence of an impoverished medium on the slowing
down of the growth rate. It is calculated that under these condi
tions the cellular growth rate remains exponential until the mean
JUNE 1967
of Cell Proliferation
of Experimental
Tumor
io'J
/->
E
10'.
»I
o
m o
10 _
] 1
O
5
10
15
DAYS
CHART 1. Growth curve of the NCTC clone 2472 in vivo (C3H
mouse).
cell surface area is more than 350 sq ß(circle of diameter, 21 n).
When the surface area is less than 350 sq /u,growth slows and the
plateau is reached when the mean cell surface area is 140 sq fj.
(circle of diameter, 13 p). The cell in sus]>ension is a sphere of 14
/z diameter.
In order to have cells which are growing in the exponential
phase, in the slowing phase and in the plateau at the same time,
it was necessary to stagger the time at which the cultures were
started. For the exponential phase cells, cultures were started 48
hours before the time of the experiment while for the slowing
cells and plateau cells, the cultures were started at 72 hours and
96 hours, respectively, before the time of experiment. The num
ber of cells per culture at the start and in the course of the study
are shown in Chart 3.
Thymidine-'H (specific activity, 8.5 c/mmole) was added to
each of the culture dishes to a final concentration 2 juc per ml of
medium. The cells were left in radioactive medium for 15 minutes,
the medium was removed, the cells washed, and new iionradioactive medium was added. At each time point at which the label
ing index of mitoses was to be measured, 2 Petri dishes from each
set, i.e., exixmential, slowing, and plateau cells, were trypsinized,
1123
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E. Frindel, E. P. Malaise, E. Alpen, and M. Tubiana
TABLE 1
the colls were collected, horse serum was added to inactivate the
Percent Labeled Mitoses at Various Times after the Injection
trypsin, and the cells were centrifuged. The bulk of supernatant
of Thymidine-'H
medium was removed and smears were made of cells suspended
For
the
3-day
and
7-day
tumors, 4 tumors were used for each
in a few drops of remaining medium. The slides were fixed in
point and a total number of 50-100 labeled mitoses were counted
absolute methanol and dried. Autoradiographs were stained in
randomly in these tumors. For the 20-day tumor, a total number
10% Giemsa stain.
of 100mitoses was counted in 2 to 3 individual tumors. Asterisk (*)
The percentage of labeled mitoses at the various times was indicates labeled mitosis.
determined by examination of 50 random mitoses. However, for
tumorM*3523207471969
tumorM'050100100100102102100100100100
-day
tumorM«01350505050505050505050505050Total
the plateau cells, mitoses are so infrequent that only 25 mitoses
Time after
were examined. Since the background grain count was less than
injection
(te)15
0.1 grain j>ercell, a mitosis was judged |x>sitive if it had 3 or more
M«013407178927230416160426388697
M1003651691211161111352332441781
M10010010010010
M100100109716454691281218284119795773%
grains above it. The labeling index was determined by count
ing the number of labeled nuclei in 200-400 cells. The same grain
min123571013162024283034405060723-day
count criterion was used, i.e., 3 grains per cell and more as ]>ositive.
The mitotic index was determined by counting the number of
mitoses seen in 2000 cells. These estimates were made on autoradiograph |¡répara
tions.
RESULTS
In
Vivo
The Growth Curve (Chart 1). This is measured from the
6th day. It is possible to calculate the volume of cells injected
since the number of cells (750,000) and mean cell volume (1,400
n) are known. The growth curve between the injection and the
6th day is calculated by interpolation.
The tumor-doubling time, which can be calculated for each
]K)int by taking the e.\]>onential tangent to the growth curve,
increases exponentially with the age of the tumor. The results
are compatible with a growth pattern following a Gompertz
function (5, 6, 10).
The Cell Cycle. The detailed results of the labeled mitosis
count are given in Table 1. Two waves of labeled mitoses were
obtained in all tumors. The peak was reached by 7 hours and was
equal to about 90 to 98%. Chart 2 shows that the cell cycle
varies slightly, if at all, with the age of the tumor. The cell cycle
of the 3-day tumor is about 16.5 hours (Table 2), and about 17.5
hours for the 7-day tumor and the 20-day tumor. The rt |>eriod is
the same for the 3- and 7-day tumor and is equal to about 10
hours. For the 20-day tumor, the S period is about 12.5 hours,
a value not significantly different from the others.
The labeling index varies only slightly, from 26% for the 3-day
tumor to 24% for the 7-day tumor and 20% for the 20-day tumor
when the cells are examined one hour after pulse labeling. Five
clays after pulse labeling, the labeling index is 22%, 12%, and 10%
for the 3-, 7-, and 20-day tumors, respectively. The median
number of grains per cell was 27-28 for the 3-day and 33-34 for
the 7-day tumors. For the 20-day tumors, the median grain
count per cell varied from 10 in fields of low labeling index to 65
in fields where the labeling index was high. The random median
grain count )x?rcell was 36 and equal to the rnidrange (Charts 5,
6). The mitotic indices in the 20-day tumors paralleled the
labeling index. Table 3 shows the relationship after multiple in
jections between the mitotic index and the labeling index in 35
fields.
The Mitotir Index (Table 3). The mitotic index of the 3-day
tumor is 0.84%; at that time, all the tumors are not yet very
well organized as solid, palpable tumors. Four days after injection
of the cells, the mitotic index is 3%. It then falls to 1.7% at 7
1124
CANCER RESEARCH VOL. 27
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Kinetics of Cell Proliferation of Experimental Tumor
3
—
100-
O
10
20
30
40
60
50
DAY TUMOR
20
7 DAY TUMOR
70
HOURS
CHART 2. Cell cycle in vivo of NCTC tumors at various times after implantation.
days and to 1.4% at 20 days. The mitotic index at 21.5 days is
0.8%.
The Growth Fraction. Table 4 gives the results of the growth
fraction of the tumors by 2 different methods. There is little
différencebetween the 3-day and 7-day tumors. By Method 1,
the growth fraction was found to be 40% and 35% for 3- and 7day tumors, respectively, and 24% for the 20-day tumors. By
-Method 2, the growth fraction is 44% for the 3-day tumors, 40%
for the 7-day tumors, and 29% for the 20-day tumors. With both
methods, the growth fraction of the 20-day tumors is lower than
in the younger tumors. This difference is especially emphasized
by the multiple injections method. By this method, the labeling
index is 84% for the 3-day tumor, 83% for the 7-day tumors, and
36% for the 20-day tumors (Table 2).
The photomicrographs of multiple injected tumors demon
strate the extreme heterogeneity of the late tumors in respect to
the labeling and mitotic indices. It can be seen that some fields
have a high labeling index (up to 82% cells labeled) and high
grain counts ]>ercell, whereas other fields are very slightly labeled
(only 3% of the cells showing grains) (Figs. 1,2).
In
Vitro
The data on the in vitro growth curves including exixmential
phase, slowing down phase, plateau, and doubling times are
given in Chart 3. The overall results are comparable to those
obtained for the in vivo growth curves. The labeled mitosis
curves are given in Chart 4, for cells growing exponentially on the
slowing phase and at the plateau of growth. The generation time
parameters derived from these curves (Table 5) are the same
and are comparable to those found in vivo.
JUNE
1967
TABLE 2
Growth Parameters in Various Growth Phases of Tumors in Vivo
(%)1
tumor
(days)3472021.5Doubling
(hours)24
time
(%)0.8431.71.40.8Cycle
(hours)16.517.517.5Labelingindex
hour
afterinjec 7lions848336
tion202420After
(calculated)38
(measured)110
(measured)index
DISCUSSION
Cell Cycle
The comparison of curves of labeled mitoses suggests that the
cycle has essentially identical characteristics,
whether the cells
are growing in an animal host or in the glass system. It also
apireara that the cellular cycle remains unchanged as cellular
proliferation slows either for the in vitro or in vivo growth of the
tumor. The duration of the phases of the cellular cycle seems
also to remain constant for the NCTC 2472 cell line in spite of
variations in conditions of growth which are important. However,
even though the curves apirear to be essentially the same, one
cannot completely exclude a certain small variation in the
duration of some phases. The duration of G2, determined from the
increase in the curve of labeled mitoses, appears to have a
maximum value not exceeding 3 hours since the maximum
plateau approaches nearly 100% at this time. Evaluation of the
1125
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E. FrÃ-ndel,E. P. Malaise, E. Alpen, and M. Tubiana
TIME
-
2< HOURS
10
TIME
IN
DAYS
CHART 3. Growth curve of the XCTC clone 2472 in vitro.
duration of S from the length of the plateau of the mitotic curve
leads one to conclude that there may be an appreciable variation
among individual cells for this phase of the cycle since the slope
of the descending portion of the curve is not steep and the curve
does not fall to low values. However, the variability of S as well
as the mean value of S appears to lie analogous for the different
curves. It must be reiterated, however, that with the labeled
mitoses technic used in these experiments, it is difficult to recog
nize the existence of a small proportion of cells having either
long or short S phase. The Gj phase seems to have a variable
duration, since the return of the curve to a second plateau is not
sharp and definitive and the second peak fails to reach a value
approaching
100%. Further, the shape of the second wave of
labeled mitosis is not the same, the slope being slower for the
20-day tumor curve. This may indicate, in these tumors, a larger
fluctuation in the duration of the Gìphase, the mean deviation
of which may be slightly prolonged. To rule out the possibility
that a small proportion of cells has either a very long or a very
short cell cycle, it would be necessary to undertake more com-
100-
80-
60
(O
ot—
i
o
40
EXPONENTIAL
20
SLOWING
GROWTH
GROWTH
PLATEAU
O
2
5
7
10 12
CHART 4. Cell cycle in vitro of NCTC cells during the exponential
1126
16
20
24
HOURS
growth, the slowing growth, and the plateau.
CANCER
RESEARCH
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VOL. 27
Kinetics of Cell Proliferation of Experimental Tumor
7-DAY TUMOR:
MEDIAN GRAIN COUNT i 20
GRAINS
PER
CELL
bJ
U
O
30
OC
Ul
IO
z
ID
z
20
10
H
25
GRAINS
CHART5. Histogram of grain counts in 7-day tumors.
50
PER
plicated experimental designs, for example the application of the
technics of double labeling, but in any case, whether this phe
nomenon exists or not, it does not apirear to have sufficient
importance to explain the slowing of tumoral growth. Men
delsohn (12) found cell cycles of the same duration in 143
tumors of different ages. Baserga and Gold (2) found in an Ehrlich
ascites that the S and GÌ
phases were practically the same in the
various stages of the ascites growth. Our results corroborate
those findings. It seems likely that the duration of the cell cycle
is a characteristic of the type of cell and does not change notice
ably during the evolution of a tumor. This is confirmed by the
in vitro studies.
In Vitro
As in the growth of this tumor cell line in vivo, one cannot
account for the rapidly altering growth rate on the basis of al
tered chronology of events in those cells which are, in fact,
in the process of reduplication and division. The time between
divisions is 17 hours, almost exactly the same as the time found
for the same generative cycle in tumor growth in vivo. This
generation time is also slightly shorter than the doubling time
for the number of cells during e\i>onential growth phase in vitro
(18 hours).
Since the cycle is not significantly altered, it is necessary to
JUNE 1967
75
CELL
examine the proi>ortion of the cells engaged in reduplication and
division. The growth fraction may be examined by several inde
pendent technics for the cells grown in vitro. The first of these
assumes that the time for mitosis remains the same in spite of
variation of the fraction of cells in the growth phase. If this
assumption is valid, the ratio of mitotic indices in various growth
phases is also the ratio of their growth fractions. The calculations
lead to the results shown in Table 6. It is also [x>ssibleby the same
reasoning to estimate the growth fraction by the ratio of the
labeling index to the measured fraction of the generation time
occupied by synthesis (T,/TC). These calculations are also shown
in Table 6.
It is apparent from the data in Table 6 that, except for the
exponential phase of growth, an increasingly smaller fraction of
the cells are engaged in synthesis or division. However, even
more important, a large discrepancy exists between the relative
birth rates of cells as estimated from the kinetic parameters and
the relative birth rates as measured by increase in cell numbers
as in Chart 3. Even in the exponentially growing system, there is
a deficit between the number of cells actually produced and the
number estimated. In the more slowly growing cultures, a great
percentage of the calculated production does not contribute to
the increase in cell numbers and are lost. Since all the kinetic
parameters are internally consistent and the ratio of labeling
1127
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E. Frindel, E. P. Malaise, E. Alpen, and M. Tubiana
5020 DAY TUMOR : FIELD OF LOW
LABELING INDEX
MEDIAN GRAIN COUNT 10 GRAINS
PER
CELL
20 DAY TUMOR
FIELD OF HIGH
LABELING INDEX
MEDIAN GRAIN COUNT: 65
GRAINS
PER CELL
3
d0LOou.0erUJ£
—r"TT-1
20D
Z10^—l
r--|—
I
fi
1
J-1,
i
1
1
i
i
1
1
i
1
1 l
>---1
'
1
hl : i : ; :
25
1
1—-\
1
.
l
50
s
i
"
'
1
'
H
75
i.r'
100
GRAINS PER CELL
CHART6. Histogram of grain counts in 20-day tumors.
index to mitotic index remains essentially constant, the results of
this calculation seem to be valid. For the plateau culture, the
calculation indicates that roughly 1.6% of the cells are disappear
ing per hour from the culture.
It is interesting to note that if the medium is renewed fre
quently, the plateau is reached when each cell fixed to the glass
takes up a surface area corresponding to a circle of 12 judiameter.
This is almost the same as the diameter of the cell in sus]>ension
(14 fj.).One can therefore understand how under these conditions
the number of cells attached to the wall cannot increase, espe
cially as this cell type only grows as a monolayer in vitro.
In Vivo
We have also found in vivo that in the course of tumor growth,
there is a decrease in growth fraction. The decrease in the number
of labeled cells after multiple injections is especially noticeable.
However, this decrease does not seem to be quite sufficient to
account for the slowing of tumoral growth, with any of the
models of growth pattern (exponential or Gom]>ertzian) used for
the calculations. We have indicated in Table 3 the theoretic
values of the growth fraction which are calculated assuming a
simple 2-compartment model in which the cell population is com
posed of cells at rest or engaged in a 17-hour cycle. It is further
assumed that all mitoses give birth to two viable cells. Thus
1128
TABLE 3
Relationship
after Multiple Injections between Mitotic Index and
Labeling Index in W-day-old Tumors
No. of
fields236321No.
ofmitoses01234%
Labeled
cells2039536364
knowing the doubling time (taken as the exponential tangent of
the growth curve) and hence the observed increment of the num
ber of cells it is easy to calculate the proportion of cells which
must be engaged in the cell cycle to give rise to the requisite num
ber of cells. The ratio of the number of the cells in these 2 com
partments is equal to a theoretic growth fraction. In order to
account for the change in doubling time from 27 to 110 hours in
the course of tumoral growth, one must accept a variation in this
theoretic growth fraction which is as much as a factor of 6. On the
basis of the simple model put forward above, the growth fraction
must, for instance, vary during the interval from the 7th to the
2()th day between 35% and 10%. The variations in growth fracCANCER RESEARCH VOL. 27
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Kinetics of Cell Proliferation of Experimental Tumor
TABLE 4
Growth Fraction and Kinetic Parameters for KCTC Tumor in Vivo
Growth Fraction
TABLE 6
Calculations for NCTC
Cells Grown in Vitro
calculatedGrowth
Parameter
tumor4044002.102.557
-day
tumor3540351.801.8020-day
tumor242910l.GOO.GO
fractionMethod Growth
fractionL.I.T./Te(Irowth
1:L.
I.(M*/M)
100Method X
fractionM.I./M.I.
exp.Birth
rateL.I./F,Birth
2:L.I.Tt/TcTheoretic
rateM.I./TMRatio
/hour220.3%/hoiirPlateau27%26%1.6%/hour1.6%
2%
(2compartments:
growth fraction
17hours)Birth
L.I./M.I.Increment
cell cycle,
thecell
of
number(measured)Exponential86%5%/hour6.4%/hour194%/hourSlowing31%34%2%/hour2.
(L.I./21,)Increment
rate
" T,, duration of phase S; Te, duration of cycle; M.I., mitotic
index; M.I. exp., mitotic index during exponential
phase; TÃŒI,
duration of mitosis; L.I., labeling index.
number(measured)3-day
of the cell
(M*/M) X 100, percent of labeled mitoses; T., duration
phase S; Te, duration of cycle; L.I., labeling index; asterisk
indicates labeling.
of
(*)
TABLE 5
Generation Time Parameters, Mitotic Index, and Labeling Index
for NCTC Cells in Various Growth Phases in Vitro
small increase to only 30% after 7 injections every 5 hours in 20day tumors. Even if one accepts that those cells which are not in
the S phase at the time of the first injection never divide, the
increase in the labeling index should be clearly larger than that
observed. Another explanation could be a synchrony of cells in
old tumors, but this explanation seems improbable. This con
flict in our results suggests as in the case of the culture in vitro
that a non-negligible pru)H>rtion of cells disap|x>ar immediately
after mitosis—either dying or migrating from the tumor. Fur
(hours)"To.2.7523T.121312TGI+ÃŒI2.2522Te171717Mitotic
parameters
time
of cell
index(%)612419Doubling
index
(%)3.21.10.83Label-.'"/
number
(hours)1824OCthermore,
phaseExponentialSlowingPlateauCycle
Growth
comparison between calculated relative birth rate and
relative increase in cell number observed on the growth curve
shown in Table 4 ap|x>ars to confirm this latter hypothesis. The
mitotic index for 20-day tumors is 1.4%. While this is certainly
inferior to the maximum value of 3'/¿seen for the young tumors
" T,, duration of phase S; Tc, duration of cycle; To»duration
of phase <?,; To,+ìÃ
duration
,
of phases G, and M.
and for tumor cells in vitro, it does suggest again that a signifi
cant proportion of cells must disappear from the tumor after
their birth. 1'yknotic cells scattered throughout the tumor pro
tion measured by the different methods reported here are in
reality less than that required in order to account for the decrease
in growth rate. This would indicate that the simple 2-eompartment model is insufficient to interpret our results. By making use
of a model in which there is a population of cells with a normal 17hour cycle, another ]x>pulation of cells which are at rest, and a
third population of cells which may have prolonged cell cycles of
greater than 17 hours, one can adequately account for the changes
in tumor growth and labeling indices. Hut these calculations have
not been extended since by their characteristics
they are arbi
trary. We are now in the process of studying cell cycles by the
double isotoix; technic in order to substantiate
this model. In
summary, there is certainly a diminution of the growth fraction
but we cannot exclude the )»ssibility that certain phases of the
cell cycle as Gìand S may be prolonged somewhat.
Another phenomenon may provide an explanation of the ob
served facts and allows at the same time an interpretation
of the
other observations which cannot be explained by a prolongation
of the cell cycle. One must find an explanation for the contract
between the labeling index of 20% after a single injection and the
vide some morphologic evidence of cell death. These cells are not
labeled but exist in fields of high labeling index as well as in
areas in which the labeling index is low.
The- autoradiographir
studies in the tumors of mice which
have received 7 injections of thyinidine-3H show that in these
large tumors at 20-days, the growth fraction and the proportion
of cells labeled varies considerably from one region to the other
in the tumor. The slowing of growth is thus not a universal
process throughout the whole tissue mass but is very hetero
geneous. It seems that certain regions of the tumor continue to
proliferate rapidly, while in others, nearly all the cells are found
at rest. One may, of course, ask if such a result is not due to an
artifact, the labeled precursor not reaching certain regions of the
tumor. This is an unlikely explanation since the mitotic index
and the labeling index vary in a parallel fashion throughout the
tumor. Analogous observations have been made by certain other
authors on mice (4) or human tumors (3), in which it has been
observed that there exist regions in which there are practically
no cells labeled. These variations have in general been attributed
to variability in conditions of vascularization;
however, we have
JUNE
1967
1129
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E. Frindel, E. P. Malaise, E. Alpen, and M. Tubiana
not observed that the regions which are heavily labeled in the
mouse tumor have a particularly marked increase in blood sup
ply over those regions which are less well labeled. Thus, we can
not confirm a hypothesis of variability in vascularization as a
basis for inhomogeneity of labeling, but our results do not on the
other hand permit us to exclude it. It must be remarked, how
ever, that, as in man, the mean grain count is lower in the region
where labeled cells are infrequent than it is for those regions
where the labeling index is high. The mean number of grains per
cell in a high labeling index region is comparable to that found
for cells of tumors which are growing rapidly while the poorly
labeled regions have mean grain counts of less than ì
of the higher
value. One may interpret the variation in grain count per cell as
either the result of variability in vascularization or by a varia
tion of the synthetic rate for DNA.
The variation in labeling index from one zone to the other in
the tumor without a corresponding variation in histologie aspect
raises a problem of significance relative to the growth fraction.
The cells which do not divide, are they in G0,if so is this state
reversible? Also, may the cells be stimulated to re-enter in divi
sion by appropriate external influences? Baserga and Gold's
data (2) showing that Ehrlich ascites tumor cells at a plateau
stage would promptly re-enter DNA synthesis when transferred
to new mice and our own results on tumor growth after irradiation
(8) suggest that probably a high proportion of cells are in a
reversible state and can be stimulated to re-enter division.
2. Baserga, R., and Gold, R. The Uptake of Tritiated Thymidine
by Newly Transplanted Ehrlich Ascites Tumor Cells. Exptl.
Cell Res., 3/.- 576-585, 1903.
3. Kissel, P., Duprez, A., Schmitt, J., and Dollander, A. Autohistoradiographie
des Cancers Digestifs Humains in Vivo.
Compt. Rend. Soc. Biol. 159: 1400-1403, 1905.
4. Kligerman, M., Heidenreich, W. F., and Greene, S. Distribu
tion of Tritiated Thymidine About a Capillary Sinusoid in a
Transplanted Mouse Tumor. Nature, 196: 282-283, 1962.
5. Laird, A. K. Dynamics of Tumor Growth. Brit. J. Cancer, 18:
490-502, 1964.
6. Laird, A. K. Dynamics of Tumor Growth: Comparison of
Growth Rates and Extrapolation
of Growth Curve to One
Cell. Brit. J. Cancer, 19: 278-291, 1965.
7. MacQuilkin, W. T., Evans, V. J., and Earle, W. R. The Adap
tation of Additional Lines of NCTC Clone 929 (Strain L)
Cells to Chemically Defined Protein Free Medium NCTC 109.
J. Nati. Cancer Inst., 19: 885-908, 1957.
8. Malaise, E., and Tubiana, M. Croissance des Cellules d'un
9.
10.
11.
ACKNOWLEDGMENTS
We are indebted to Mrs. Françoise Vassort for help and dis
cussion and to Dr. R. Gerard Marchant and his staff, for their
work on the pathology of the tumor. We would also like to thank
Miss Ruzica Marianovitch,
Mrs. Gilberte Grange, Mrs. Nicole
Chavaudra, and Mrs. Nicole Moreau for their technical assistance.
REFERENCES
1. Baserga, R. The [Relationship of the Cell Cycle to Tumor
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FIG. 1. Photomicrograph
FIG. 2. Photomicrograph
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of a multiple-injected
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Mendelsohn, M. L. The Kinetics of Tumor Cell Proliferation.
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20-day tumor showing heterogeneity with respect to the labeling index. X 900.
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CANCER
RESEARCH
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Kinetics of Cell Proliferation of an Experimental Tumor
Emilia Frindel, Edmond P. Malaise, Edward Alpen, et al.
Cancer Res 1967;27:1122-1131.
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