In1 J. Rndumon Oncology Bml Phys., Vol. 19, pp 389-399 Printed in the U.S.A. All rights reserved.

0360.3016/90 $3.00 + .I0 Copyright 8 1990 Pergamon Press plc

??Original Contribution

TIME-TEMPER4TURE ANALYSIS OF CELL KILLING OF BHK CELLS HEATED AT TEMPERATURES IN THE RANGE OF 43S”C TO 57.O”C M. J. BORRELLI, C. A. CAIN,

PH.D.,‘,~

PH.D.*

L. L. THOMPSON,

AND W. C. DEWEY,

M.S.,’

PH.D.’

‘Radiation Oncology Research Laboratory, University of California, San Francisco, CED-200, San Francisco, CA 94143; ‘Bioacoustics Research Laboratory, Department of Electrical and Computer Engineering, University of Illinois, 1406 West Green St., Urbana, IL 6 180 1; and ‘Dept. of Radiation Oncology/Physics, Research Laboratory, William Beaumont Hospital, 3601 W. 13 Mile Rd., Royal Oak, MI 48073

Baby hamster kidney (BHK) cells were heated at temperatures in the range of 43.5’C to 57.O”C to determine the time-temperature relationship of cell killing. The cells were grown on 0.025 mm thick pieces of mylar to minimize warm-up times. After heating, the cells were plated for the colony formation assay. The endpoints of I%, lo%, or 90% isosurvival, or the Da values of the survival curves were used to construct plots of the logarithm of the reciprocal of the exposure time versus the reciprocal of the absolute temperature. The data for each endpoint resulted in a straight line plot, indicating that the time-temperature relationship for cell killing remained constant from 43S”C to 57.O”C, namely, a I.&fold increase in exposure time was required for a 1°C decrease in temperature in order to obtain isosurvlival. Heated BHK cells were also examined using electron microscopy. The threshold level of altered morphology was the dissociation of polyribosomal structure and the formation of electron-dense granules within the mitochondria. The time-temperature relationship for the induction of this altered morphology was identical to that for the 90% isosurvival endpoint. Hence, the appearance of altered morphology appears to be related to cell killing. Hyperthermia,

Time-temperature

relationship, Activation energy, Cancer, Cell survival, Morphology.

INTELODUCTION

as high as 60°C (J. Roemer, oral communication April, 1988). It then becomes important to know if the timetemperature relationship of cell killing remains constant at these higher temperatures, or if other breaks and/or more subtle changes in the slope of the time-temperature curve occur. Landry and Marceau (20) analyzed survival data for hyperthermic cell killing at temperatures between 4 1“C and 55°C and reported that the slope of the time-temperature relationship became less steep with increasing temperature. This was most evident for temperatures in excess of 50°C. The experiments performed in this study were designed to determine the time-temperature relationship of cell killing of baby hamster kidney (BHK) cells exposed to temperatures in the range of 43.5”C to 57.O”C. The choice of 43.5”C as the lowest temperature was made to avoid complications that might arise from the development of chronic thermotolerance.

Hyperthermia is being Iused frequently in the treatment of cancer (8,25). Traditionally, treatments have been per-

formed within the temperature range of 42°C to 45°C. The survival response of mammalian cells to these temperatures has been well established, and an activation energy, that has been attrilbuted to cell killing, has been determined using Arrhenius analysis ( 1, 30). Most plots depicting the time-temperature relationship for heat killing (the logarithm of the rate of killing vs the reciprocal of absolute temperature) are broken near 42.5”C to 43.O”C into two linear segments (6, 7). However, the break point has been observed to occur both below (24) and above (14, 26) this range in s,ome systems. This break in the time-temperature curve has been attributed to the development of chronic thermotolerance (2 1, 22). There has been recent clinical interest in using very short exposures at temperatures greater than 45°C and Reprint requests to: M. ;I. Borrelli, Ph.D., Department of Radiation Oncology/Physics, Research Laboratory, William Beaumont Hospital, 3601 West 13 Mile Rd., Royal Oak, MI 480732793. Acknowledgements-The authors would like to thank Mr. Jeffiy Azzalina and Ms. Francine Palmer for their technical assistance,

Dr. Gloria Li for the use of her water baths and incubators, and Dr. Peter Carry for reading the manuscript. This research was supported by NC1 grants CA 24930, CA 3 1808, CA 092 15, and CA 497 15. Accepted for publication 22 February 1990.

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1. J. Radiation Oncology 0 Biology 0 Physics

390

There are two concerns that must be considered in determining the time-temperature relationship of cell killing. Firstly, how rapidly cells attain thermal equilibrium, particularly at the higher temperatures. Secondly, how well the temperature is known in the vicinity of the heated cells. If the time required to reach thermal equilibrium is a significant fraction of the heating time, the total heating time required to achieve a given level of cell killing will appear longer. An inaccurate measurement of the temperature to which the cells were exposed will also lead to an erroneous determination of the time-temperature relationship. Artifacts resulting from warm-up delays were minimized by growing cells on 0.025 mm thick pieces of mylar. These were transferred quickly from medium at 37.O”C to culture dishes in an enclosed water bath. The medium in the dishes was pre-warmed to the desired hyperthermic temperature (+O.O5”C), and there was no spatial variation of the temperature within the culture dish. Survival data for each temperature were obtained in 1 day using the same water bath system to heat the cells. Three sets of data were collected in this manner. These data were then used to construct the time-temperature curves for cell killing. The Eyring hypothesis was applied to this data to calculate an activation energy ( 16). Some of the heated cells were also prepared for electron microscopy. This was done to determine: (a) if the nature of the heat-induced altered morphology was the same following isosurvival exposures at the different temperatures, (b) if the induction of altered morphology correlated with the induction of reproductive cell death, and (c) if the time temperature relationship for cell killing and for inducing altered morphology were similar. METHODS

AND

MATERIALS

Survival experiments Baby hamster kidney (BHK) cells were grown as monolayers on 3.5 mm X 35 mm squares of 0.025 mm thick mylar in modified McCoy’s 5A culture medium at pH 7.4. The mylar squares were cleaned and then sterilized with 70% ethanol, rinsed four times with sterile phosphate buffered saline (PBS), and then placed into 60 mm culture dishes containing 5 ml of McCoy’s 5A medium supplemented with: 10% fetal bovine serum (FBS), streptomycin sulphate (0.1 g/l), and penicillin G potassium (0.07 g/l). The mylar squares remained for 30 min in the culture dishes at 37.O”C in a moisture-saturated incubator containing 5% COZ. Cleaning the mylar squares and pre-incubating them in medium promoted cell attachment. Each dish was then seeded with 1.5 X 1O5 BHK cells and returned to the incubator for 48 hr, or until the monolayers were at approximately 80% of confluency. Cells were heated at either 43.5”C, 46.O”C, 5O.O”C, 54.O”C, or 57.O”C. The same water bath was used for each different temperature. The water bath was used first to heat cells at 43.5”C. While these heated cells were being

August 1990. Volume 19. Number 2

plated for the colony formation reset and equilibrated to 46.O”C. for each successive temperature see below). Data for determining temperature were collected in procedure was repeated a total

assay, the water bath was This process was repeated used (except for 54.O”C; a survival curve at each 1 day. This experimental of three times. Heating cells at 43.5”C, 46.O”C or SO.O”C. Sixty mm culture dishes without cells and containing 10 ml of culture medium were placed into an enclosed water bath equipped with a CO* regulating system to maintain the medium pH at 7.4. The frame for holding the culture dishes was designed such that the water level of the bath rose above the level of the medium in the dish, and the dish cover was lifted slightly off the bottom. This latter feature provided for better circulation of CO2 into the dish and prevented water from entering the dish by capillary action through the space between the dish cover and bottom. The water bath was maintained to within 0.05”C of the set temperature. A thermistor calibrated to a NBS-calibrated glass thermometer was used to confirm that the medium in the culture dishes had attained the desired temperature. The culture dishes containing the cells were removed from the nearby 37.O”C incubator one at a time. Each mylar square was removed quickly from the dish using a sterile pair of jeweler’s forceps and transferred to one of the dishes in the water bath. This manuver required less than 2 sec. For heating times shorter than 5 min, only one mylar square was heated at a time. When more than one square was to be heated for longer than 5 min, additional squares were placed sequentially into different dishes in the water bath. The lag time between adding sequential squares to the heated medium was recorded and accounted for in the total heating time for each square. After heating, the mylar squares were removed from the heated medium and placed in dishes containing medium at 37.O”C and pH 7.4. These were returned to the 37.O”C incubator for 5 min. The squares were then removed from the dishes, rinsed in medium containing no FBS, and treated with trypsin (0.25% trypsin in culture medium containing 10% calf serum) to remove the cells. Trypsinized cells were transferred to fresh culture medium, diluted to the required concentration, and then plated into six replicate 25 cm2 culture flasks for the colony formation assay. The innoculated flasks were incubated at 37.O”C for l-2 weeks, depending on the heat treatment used, to allow for colony formation. The BHK cells adhered firmly to the mylar squares. During the initial experiment, the medium in which the cells were heated was examined to detect cell detachment from the mylar. No cell detachment was observed during hyperthermia or when the cells were transferred to another culture dish for trypsinization. The flasks used for the colony formation assay were plated 24 hr earlier with enough lethally irradiated feeder cells (BHK cells irradiated with 25 Gy) such that the final cell density was 4,000 cells/cm2 (3, 15). The use of feeders

391

Time-temperature relationship 0 M. J. BORRELLI etal.

was imperative for BHK cells as both the plating efficiency and survival of BHK cells were extremely dependent upon cell density (3). Heating cells at 54.O”C or 57.O”C. The heating procedure was modified slightly for the cells exposed to 54.O”C or 57.O”C since exposure times were so short. A sterile glass container was fitted into the holder in the water bath. This was filled with 25 ml of culture medium and covered with a culture dish cover until the medium equilibrated at either 54.O”C or 57.O”C. The container was fitted in the bath such that the water level was above that of the medium. The larger volume of medium was used to ensure that the mylar squares reached temperature equilibrium rapidly and did not cool the medium significantly. One mylar square at a time was completely immersed in the medium for the required exposure time. It was then transferred to a culture dish containing medium at 37.O”C and treated as described above for the colony formation assay. The mylar squares were very thin (0.025 mm thick) and had a low mass (75-90 mg). Therefore, both the mylar and the cells should have reached thermal equilibrium rapidly. To test this, 13 urn diameter chromel-constantan thermocouples were constructed (12) and then calibrated to the NBS-calibrated glalssthermometer. A thermocouple was attached to a mylar square using a thin film of formavar. This assembly was then transferred from 37.O”C to the 57.O”C medium as described above; the assembly attained 57.O”C in less than 0.2 set (data not shown). This represented an upper limit on the time required to reach thermal equilibrium at 57.O”C. A single experiment &as performed at 54.O”C. The cells were heated in the same water bath system used for the other temperatures, but on a different day. Determining the 90%, IO%, and 1% isosurvival points and Do The 90% isosurvival point for each temperature was determined by heating the cells for exposure times that yielded survival levels in the range of 70% to 100%. The survival data were plotted and the exposure time yielding a survival level of 90%, at each temperature, was determined. The shortest exposure time that could be reproduced reliably was 1 sec. 57°C was selected (empirically) as the highest temperature used in these experiments because a 1 set exposure resulted in a survival level of 90%. The 10% and 1% isosurvival points for each temperature were determined from another set of experiments where cells were heated1 such that survival ranged from 90% down to 0.1% or 0.01%. A curve was fitted to this data by repeated, sequential applications of a polynomial and a cubic spline curve fitting program (5). For each temperature, the exposure times where the survival curve intersected the survival levels of 10% and 1% were recorded. The same results were obtained when a curve was fitted to the survival data by eye.

The exponential portion of the survival curves were determined using: (a) a best fit by eye, or (b) a regression fit (see Eq 1 below) to the data points below 10% survival. Both methods yielded similar values of Do. The time-temperature relationship The isosurvival data at each temperature were used to make a plot of the logaritm of the reciprocal of the exposure time (t), versus the reciprocal of the absolute temperature (T). A regression analysis was used to obtain a best fit line to the data. This had the form; ln(l/t) = A + B(l/T),

(1)

where A is the l/t axis intercept and B is the slope of the line. The 95% confidence interval of each slope, b, was calculated as, b = t’i]SSo,t) -

BW’(,,~,,,T))I/KN - 2)ss(I,T,1

(2)

where SS(,,tj is the sum of the squares of the variable l/t, SS(,,tj is the sum of the squares of the variable l/T, and SP(llLI/T) is the sum of the products of the variables l/t and l/T ( 11). B is the slope of the best fit line to the data, and t’is the value of the t-test for N - 2 degrees of freedom, where N is the number of data points. If the limits of the 95% confidence interval of B, namely, B + b and B - b, do not include zero, it can be concluded that a real correlation between ln( l/t) and l/T exists ( 11). This procedure was repeated using l/D0 instead of l/t in Eq. 1. Application of the Eyring hypothesis The slope of each time-temperature plot, namely, 90%, lo%, or 1% isosurvival data or Do values, was used to calculate the activation energy (P) of cell killing ( 16, 30); P = [4.6 ln(t&,)]/[2.303(

l/T, - l/Tz)]

= -2B (in Kcal/mole).

(3)

The value of p was then reported as; p = -2B + 2b Kcal/mole.

(4)

The units of Kcal/mole were used instead of KJ/mole for easier comparison to earlier reports which presented p in Kcal/mole. Conversion from Kcal/mole to KJ/mole is accomplished by multiplying the former by 4.184 J/Cal. Electron microscopy specimens BHK cells were grown on 3 mm X 5 mm mylar strips and heated as described above. The strips were heated such that, at each temperature, heated samples were obtained for each of the exposure times in the exposure range used to determine the 90% isosurvival level (e.g., see Figs 1 a-c for exposure ranges). Immediately after heating,

I. J. Radiation

392 1 .oo

E 0.90

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Oncology

0 Biology 0 Physics

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August

1990, Volume

19, Number

2

(a)

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Fig. 1. The survival data used to determine the 90% isosurvival points for cells heated at 43S”C, 46.O”C, or 5O.O”C are presented in Figures I a, 1b, or 1c, respectively. The different symbols are data points from two of the three different experiments performed. 90% isosurvival was attained at 57.O”C using a 1 set exposure (data not shown). This can be seen graphically in Figure 2d.

C (set)

each strip was immersed in a fixative solution of 2.5% gluteraldehyde and 2.0% paraformaldehyde in 0.1 M cacodylate buffer (pH 7.4) at room temperature. The strips were stored in the fixative for 24 hr at 4°C. The strips (cell side up) were rinsed twice in fresh cacodylate buffer and post-fixed for 20 min with 1% osmium tetroxide in 0.1 M cacodylate buffer. A graded ethanol series was used to dehydrate the specimens starting with 25% ethanol and ending with three rinses of absolute ethanol. This was followed by five rinses with propylene oxide and then infiltration with epoxy resin (55 parts by volume of dodecenylsuccinic anhydride (DDSA), 25 parts Epon 8 12, 15 parts Araldite 502,2.8 parts dibutyl phthalate (DBP), and 1.4 parts of DMP-30 (an accelerator)). The strips were stored for 2 hr in unpolymerized epoxy. They were then held vertically to remove excess epoxy, and epoxy was wiped clean from the side of the strip that did not contain cells. The strips were arranged (cell side up) onto a silicone rubber mat and sufficient epoxy was added to the strips to cover them yet not overflow their borders. The specimens were then polymerized for 7290 hr at 62°C. In one experiment, 3 mm X 5 mm strips were cut from 35 mm X 35 mm mylar squares containing cells that were heated to determine the 90% isosurvival point. A sample strip was cut from a mylar square that was heated to obtain each one of the data points (closed symbols) in Figures 1 a-c. These 3 mm X 5 mm strips were then processed for electron microscopy. Hence, both survival and morphological data were obtained from the same samples.

* JEOL 1OOC or Phillips 300.

1

Time at 46.0 C (min)

dp

0.70

0.80

0

Once polymerized, the epoxy (containing the embedded cells) was separated easily from the mylar. Small squares (0.5 mm to 1 mm) were cut from the epoxy strips and attached (cell side up) to epoxy stubs (molded from Beam’s capsules) using a cyannoacrylimide adhesive. The specimens were sectioned with an ultramicrotome, with the first sections containing cellular material. Sections were stained with uranyl acetate and lead citrate and examined with an electron microscope* at an accelerating voltage of 80 kV. For each specimen, at least 200 cells were examined with the electron microscope. The shortest heat exposure that induced the minimum degree of altered morphology (described below) in at least 10% of the cell population was defined as the threshold exposure for inducing morphological damage for each temperature. RESULTS Figures 1 a-c show the survival data used to determine the 90% isosurvival point for cells heated at 43.5”C, 46.O”C, and 5O.O”C, respectively. A 1 second exposure at 57°C resulted in a mean survival of 90%. Since this was the shortest, reproducible exposure that could be made, a broader range of exposures resulting in survival between 70% and 99% at 57.O”C was not possible. The 90% survival data for 57.O”C is presented in Figure 2d. Figures 2 a-e present the survival data obtained by heating cells at 43.5”C, 46.O”C, 5O.O”C, 57.O”C, and 54.O”C, respectively. Each datum point in Figures 2a-d

Time-temperature relationship 0 M. J. BORRELLIet

393

al.

03

10 -II

0

30

60

90 120 150180 Time at 46.0 C (min)

Time at 43.5 C (min)

(d)

(c)

0

1

2

10 -L_?_L 0

3Tn

1

2

3

4

5

Time at 57.0 C (set)

Time at 50.0 C (min)

Fig. 2. The survival data for the cells heated at 43S”C, 46.O”C, 5O.O”C, 57.O”C, or 54.O”C are presented in Figures 2a, 2b, 2c, 2d, or 2e, respectively. For Figures 2a-d, the data points are mean values of results obtained from three experiments. The error bars represent the standard error of the mean @EM). The exposure times for 10% and I % isosurvival were not determined from these figures but from survival curves from each of three separate experiments. Figure 2e is plotted with data obtained from a single survival experiment performed at 54.O”C. The dotted lines in Figures 2c, 2d, and 2e represent the best fit by regression analysis (to Eq 1 using survival (s) instead of 1/t and T instead of l/T) of the data points at survival levels below 10%.

10 -‘V

10

15

20

Time at 54.0 C (set)

25

394

I. J. Radiation Oncology 0 Biology 0 Physics

represents the mean value of data from three experiments, and the error bars represent the standard error of the mean (SEM). The exposure times resulting in 10% or 1% isosurvival were not determined from Figures 2 a-d. Rather, they were determined from the survival curves obtained following each separate experiment. When Figures 2 a-d were used to make the time-temperature plot, an identical result was obtained. The former procedure was used for statistical purposes, for example, obtaining the best fit line to the data and determining the standard error of the mean for each datum point on the time temperature curve. The data in Figure 2e are from a single survival experiment that was performed at 54.O”C. Both isosurvival data and Do values were determined directly from this plot. Figure 3a presents the typical ultrastructure observed in the control BHK cells. Note the organized, clustered structure of the free ribosomes (r) and the morphology of the mitochondria (M). This organization of the free ribosomes has been attributed to their association with mRNA and is referred to as polyribosome structure (23). The morphological structures that responded first to the hyperthermic exposures were the polyribosomes and the mitochondria (Figs. 3 b and c). An identical result was observed for heated Chinese hamster ovary (CHO) cells (2) and other cell lines (4, 13, 23). Following exposures that yielded 10% cell killing (90% isosurvival), dissociation of polyribosome structure (2, 4, 13, 23) and the presence of electron-dense particles within the mitochondria (2) were evident in 10% to 15% of the observed cells (mean = 12.3% + 2.2%). Note that the fraction of the heated cells exhibiting altered morphology, and the nature of the altered morphology induced by the threshold exposures (90% isosurvival) at each different temperature, were similar. This is illustrated in Figures 2b (43.5”C for 7.5 min) and 2c (5O.O”C for 28 set). The time-temperature curves determined from the 90%, lo%, and 1% isosurvival data are presented in Figure 4. The plotted points represent the mean value of the data from the three experiments. In all cases, the standard error of the mean was smaller than the data points. The data for the 10% and 1% isosurvival levels resulted in essentially parallel lines. Also plotted were the data for the threshold exposures required to induce altered morphology in 10% (or more) of the heated cells. These data fell on top of those for 90% isosurvival. The parameters for the linear regression fit (Eq 1) to each data set are presented in Table 1. In Figure 4, 1% and 10% isosurvival data, obtained from the single experiment at 54.O”C are plotted (open symbols). The 54.O”C data were not acquired at the same time as data at the other temperatures, however, they did fit the time-temperature relationship determined by the other data. The Eyring analysis yielded activation energies of 120 Kcal/mole * 2 Kcal/mole and 120 Kcal/mole + 6 Kcal/ mole, for the 1% and 10% isosurvival data, respectively. The data for 90% isosurvival and for the induction of

August 1990. Volume 19, Number 2

altered morphology both yielded an activation energy of 99 Kcal/mole +- 6 Kcal/mole. The time-temperature analysis was also performed in the more traditional manner by plotting the logarithm of l/D0 versus l/T (Fig. 5). Do values were determined from the exponential portion of the survival curves from each individual experiment, or from Figures 2 a-d. The open circle in Figure 5 represents datum from one experiment performed at 54.O”C. The slope of the exponential portion of each survival curve was determined either by eye or by fitting the data points for survival levels below 10% to Eq 1 by a regression analysis. Both methods provided similar curves for the exponential portion of the survival curves and, subsequently, similar values for Do. Figure 5 was plotted using Do values determined by the regression analysis. The parameters for the regression analysis of the timetemperature relationship in Figure 5 are presented in Table 1. The slope (-60.9 X lo3 “K), and the activation energy obtained by the Eyring analysis (122 Kcal/mole) were similar to those obtained using either the 1% or 10% isosurvival data. This was not surprising since the 1% and 10% isosurvival points are located in the upper region of the exponential portion of the survival curves. When this analysis was performed using Do values obtained from survival curves fitted by eye, the values for the slope and activation energy were -63 X 1O3 “K and 126 Kcal/mole, respectively. The two results were different by less than 3.5%.

DISCUSSION The data presented herein demonstrate that the timetemperature relationship for heat killing of BHK cells remained constant from 43.5”C to 57.O”C. The time-temperature relationship in Eq 1 can also be expressed as, tl =

t2ew(WTI - T~/TITA

(5)

where t, and t: represent the exposure times at two different temperatures T, and T2 (in “K), respectively. B is the slope of the regression fit to the data. This is approximately -60 X lo3 “K for the 1% and 10% isosurvival or Do endpoints, and -50 X lo3 “K for the 90% isosurvival endpoint. Equation 5 can be used to select the exposure time at any temperature in the range of 43.5”C to 57.O”C needed to obtain an isosurvival level that was obtained at another temperature in this range. For example, using B = -60 X 103, the equation says that both a 120 min exposure at 43.5”C and a 3.1 set exposure at 57.O”C should result in isosurvival. An examination of Figures 2a and 2d confirms this. A general rule of thumb that can be derived from this equation is that a decrease in temperature of 1°C requires a 1.8-fold increase in heating time to achieve isosurvival.

Time-temperature relationship 0 M. J. BORRELLI etal.

395

(W Fig. 3. Morphology of control BHK cells is shown in Figure 3a. The ribosomes (r) are seen in clusters characteristic of polyri-

bosomes. The normal morphology of the mitochondria (M) is also evident. Note the relatively homogeneous staining density within the mitochondrial matrix. A portion of the nucleus (Nu) is also visible. The threshold degree of altered morphology for BHK cells heated at either 43S”C (7.5 min), or 50°C (28 set) is depicted in Figures 3b and 3c, respectively. Both exposures resulted in 90% cell survival. The nature of the altered morphology was similar following these treatments and all treatments resulting in 90% cell survival. Electron dense granules (Dg) were observed within the mitochondria, and the organized clusters of ribosomes were less apparent or totally absent. (All figures shown 70% of original size.)

Sapareto and Dewey (28) expressed Eq 5 in a modified form, t, = tzR(r1-rz) ,

(6)

by making the assumption that the difference between T, and Tz was proportionately small, in the denominator of the exponential, when temperature was expressed in “K. The value of R is calculated as; R = eW(T(T+O) 2

(7)

where T is the absolute temperature at which the heating occurred. Using B = -60 X 103, R = 0.564 (calculated

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August 1990, Volume 19, Number 2

1. HeLa cell survival was determined between temperatures of 4 1.O”C and 45.O”C by using heating times of 30 to 300 min (19). For temperatures between 45.O”C and 55.O”C, survival at each temperature was determined by a single 2 min exposure ( 19). The survival data were used to calculate an inactivation constant for cell killing, K, assuming an exponential relationship between survival and both exposure time and temperature, namely, S(T, t) = emK(T)t(20) where S is survival, T is the temperature, and t is the’exposure time. The logarithm of K was then plotted versus l/T (in “K) to define the timetemperature relationship. The assumption that one heating time could be used to determine K (or l/Do) is based on the observation that hyperthermic survival curves for HeLa cells exhibited little or no shoulder (10, 19,20). If a shoulder existed, the value of K derived from one survival point would be too low. Data from other investigators ( 18, 27) show a small, but distinct, shoulder on HeLa survival curves. The shoulder appears to become more prominent as the temperature increases from 44.O”C to 48.O”C (27). If this trend continued up to 55.O”C (no data exist for HeLa cells), using the single survival point would have provided an increasingly lower estimate of K (l/Do) with increasing temperature. This could account for the report that the slope for the time-temperature relationship became less steep with temperature (20). The data presented herein do not suffer from this problem. The isosurvival data and Do values were determined from full survival curves. Unlike isoexposure, isosurvival is an endpoint that can be used to establish time-temperature relationships. The inverse of the exposure time required to achieve isosurviva1 is the mean rate of cell killing to that isosurvival level, at each temperature. Isoexposure data provide mean killing rates to survival levels that decrease with temperature. Hence, the same biological endpoint is not being compared. Another concern with the data of Landry et al. (19) is the manner in which the cells were heated. After removing medium from a culture flask, the sealed flask was plunged into hot water. Both the flask itself and the air contained within had to come to temperature equilibrium. A profile of the temperature rise measured in one flask immersed at 55.O”C illustrated that thermal equilibrium was either

ISOSURVIVAL

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~/TX

I

I

3.10

3.05

3.00

10s (OK-‘)

Fig. 4. The data in Figures 1 a-c and 2 a-d were used to create these plots of the time-temperature relationship for cells heated at 43.5”C, 46°C 50°C or 57°C (with l/T X lo3 OK-’ values of; 3.158, 3.133, 3.095, and 3.03, respectively). The data points represent the mean of data from three separate experiments. The data symbols are larger than the standard error of the mean. Square symbols represent the 90% isosurvival data, circles represent the 10% isosurvival data, and triangles represent the 1% isosurvival data. The stars correspond to the shortest exposures required to induce the threshold level of altered morphology within at least 10% of the heated cells. The open circle and triangle represent data from one experiment at 54.O”C.

for T = 323.3”K (5O.O”Q midrange of the temperatures used). Using Eq 6 provided similar results to those obtained with Eq 5, for example, 120 min at 435°C is calculated to yield isosurvival with 3.2 set at 57.O”C. Many cell types (including BHK) exhibit similar slopes for their time-temperature relationships for cell killing at temperatures between 43.O”C to just under 5O.O”C (20, 24,26, 28, 30). Hence, the time-temperature relationship for BHK cells should be applicable to other cell lines, within this temperature range. Will this be so for temperatures between 5O.O”Cand 57.O”C? It has been reported that the slope of the time-temperature relationship for HeLa cells became less steep above 50°C (20), that is, the time-temperature relationship was no longer a simple exponential function like that of Eq

Table 1. Parameters Endpoint

A

90% isosurvival 10% isosurvival 1% isosurvival Do

150.2 179.0 180.2 185.3

* To convert

Kcal/mole

to KJ/mole,

multiply

for the regression

analyses of time-temperature

B (“K) -49.6 -59.8 -59.9 -60.9

X X x x

b (“K) lo3 lo3 103 lo3

the former by 4.184 J/Cal.

3.0 3.1 1.2 2.8

x x x x

103 103 103 lo3

data p (Kcal/mole)* 99 f 6 120 f 6 12022 122 k 6

Time-temperature relationship 0 M. J.

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~~~~~

3.10

3.05

3.00

l/T x 103 (OK-‘) Time-temperature relationship plot of the logarithm of l/D0 versus l/T. The data points are larger than the standard error of the mean. The open circle represents datum from one experiment at 54.O”C.

Fig. 5.

never established or established very slowly during the 2 minute exposure time ( 19). As exposure times lengthen, the time required to reach thermal equilibrium becomes a smaller fraction thereof. Hence, errors in determining isosurvival exposure times for points on the shoulder of survival curves will be greater than those for points on the exponential portion. Therefore, a time-temperature relationship determined from D,, is affected least by delays in reaching thermal equilibrium. However, for heat treatments at 54.O”C and 57.O”C, exposure times were in seconds (for BHK cells), even on the exponential portion of the survival curve. Hence, a short delay in reaching thermal equilibrium ( 1 set to 2 set) would affect the shape of the time-temperature relationship substantially, even one established using Do as an endpoint. How underestimating (either K (overestimating Do) or overestimating the exposure time required to attain an isosurvival level can produce an error in the time-temperature relationship is illustrated by our own experience. The initial experiments with these BHK cells indicated that the slope of the timle-temperature relationship (determined from either isosurvival data or Do values) became less steep above 5O.O”C (data not shown). Subsequently, the heating protocol was improved to reach thermal equilibrium more quickly (by enclosing the water bath, heating cells on a smaller, thinner mylar substrate, using a larger volume of heated medium, etc.). The results presented in this report were then obtained. With the initial protocol, the time required to reach thermal equilibrium represented too large a fraction of the total heating time. Hence, the determi:ned values of both the exposure time to reach isosurvival and Do were too large. The error

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397

was greatest at 57.O”C where exposure times were all less than 6 seconds. How quickly did the BHK cells reach thermal equilibrium at 57.O”C? The thermocouple measurement of 0.2 set is an upper limit. The mechanical and electrical noise generated during the measurement did not allow for a temperature reading prior to this time. If any error was made in determining the exposure times required to attain isosurvival at 5O.O”C to 57.O”C, it would be that they were too long. Hence, the true slope of the time-temperature relationship would become more steep (l/t larger) in this temperature range, not less steep. Neither the timetemperature relationships established with isosurvival endpoints or Do values suggested any change in their slopes for temperatures above 5O.O”C. Thus, it is proposed that the data presented herein best represent the time-temperature relationship for cell killing within the temperature range of 43.5”C to 57.O”C. Landry et al. (19) also heated cells with lasers. The induced temperature rises were calculated, not measured, and the calculated temperatures were all above 70°C. Since our study did not use temperatures exceeding 57.O”C, the time-temperature relationship for killing cells at higher temperatures cannot be addressed. It is possible that some cells will not respond like BHK cells to temperatures above 5O.O”C. However the similar time-temperature relationship exhibited by so many different cell lines at temperatures below 5O.O”C suggests that this is unlikely. It is proposed that if other cell lines are heated using the protocol presented above, time-temperature relationships similar to that of BHK cells will be obtained. Equation 5 has already proven useful in the laboratory. Survival data at one temperature have been used to help design survival experiments at other temperatures by estimating the heating times required to attain isosurvival levels. This has been done for CHO cells, Swiss 3T3 cells, and NG108-15 cells (data not shown). Will this time-temperature relationship prove useful in designing clinical treatments at different temperatures in the range of 43.5”C to 57”C? As mentioned earlier, many cell types (including human (20, 26)) have exhibited a similar slope for their time-temperature relationship at temperatures between 43.5”C to 5O.O”C (1, 20, 24, 26, 28, 30). Hence, on a cellular level, it seems that BHK and human cells have similar time-temperature relationships for hyperthermic killing. A bigger concern is if cells in vivo will have the same time-temperature relationship as cells in vitro. Data for several tissues heated to temperatures below 50°C suggest that this is so (9). Careful experimentation in an in vivo system, at temperatures above 5O”C, will be required to determine if this similarity extends to the higher temperatures. The observation that the time-temperature relationship obtained from either isosurvival endpoints or Do values are similar is relevant to the clinic; that is, Eq 5 or Eq 6

398

I. J. Radiation Oncology 0 Biology0 Physics

may be used to predict exposure times, for temperatures in the range of 43.5”C to 57.O”C, required to achieve an isoeffect located in different regions of the survival curve. This is important because there may be times a physician will want to induce a level of heat killing that is not in the exponential portion of the survival curve. The similar results obtained with either isosurvival data or Do values suggest that isoeffect endpoints occuring on, or near, the exponential portion of the survival curve can be used interchangely to discuss time-temperature relationships, and perhaps other aspects of hyperthermic cell killing (22). For example, the Eyring analysis demonstrated that the activation energies calculated for either the 1% or 10% isosurvival endpoints ( 120 Kcal/mole) or the Do endpoint (122 Kcal/mole), were essentially identical and constant over the temperature range of 43.5”C to 57.O”C. The significance of these activation energies with respect to heat killing is unknown. There are some who have suggested that their similarity to the activation energy for protein denaturation (30) or DNA damage ( 17) may implicate these structures as targets for hyperthermic cell killing. For example, these activation energy values may be relevent to the preferential binding of proteins in the nucleus following hyperthermia (27, 29). Some question the use of the Eyring analysis for irreversible processes such as inducing cell death. However, this analysis has been applied to reversible and irreversible biochemical or biological processes (16). Furthermore, the Eyring hy-

August 1990. Volume 19. Number 2

pothesis states that the activation energy applies to the rate limiting step in a series of reactions. The rate limiting step may be a reversible process, for example, the heatinduced binding of protein to the nucleus (27,29), which in turn induces an irreversible lethal change within the cell. In any event, the interpretation of these results is left to the reader. The incorporation of the Erying analysis into this report in no way detracts from the main intent and conclusions of the study. The time-temperature relationship for 90% isosurvival differed significantly from that of the other endpoints. The obvious the shoulder

difference is that these data were taken from of the survival curve where the rate of cell

killing was changing continuously. The results did demonstrate that time-temperature relationships could be established for isoeffects occurring vival curves.

on the shoulder

of sur-

The similarity in the results of the analysis obtained by using either 90% isosurvival or the endpoint of induced altered morphology in 10% of the cells suggests that the two events are related. A direct relationship between altered morphology and survival has already been established for CHO cells (2). It cannot be determined if altered morphology is a mechanism that causes hyperthermic killing. However the link between altered morphology survival may mean that similar heat-induced cellular function effect both endpoints.

changes

cell and in

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