Arrhenius relationships from the molecule and cell to the clinic

Figures & data

Figure 1. A schematic to illustrate the failure of ΔT × duration of heating (expressed in °-min) to predict thermal damage.

Figure 2. Data were taken from Henriques [12]. Pig skin was exposed to hot water, and the threshold durations of exposure at different temperatures required for complete transepidermal necrosis were determined and tabulated. These values are plotted for the different temperatures, and the activation energy and R were calculated for temperatures between 44 and 52°C. The abscissa at the bottom is the inverse of the absolute temperature in degrees Kelvin. The data for points with question marks were uncertain because of the very short durations of exposure relative to the time required for the temperature of the skin to reach the specified temperature. R = 2.1. ΔH = 150 kcal/mol.

Figure 3. Survival curves for asynchronous Chinese hamster ovary (CHO) cells heated at different temperatures for varying lengths of time. Except for 42.5°C, the individual data points and standard errors of means have been deleted for reasons of clarity. Survival curves for cells heated in the G₁ phase were very similar to those for asynchronous cells, an example of which is indicated for cells heated in the G₁ phase at 42.0°C. To illustrate the wide variation in thermal sensitivity of various cell lines, the dashed line is drawn to show the relative thermal resistance of a pig kidney cell line. The parent line of pig kidney cells was slightly more sensitive, with the 46°C curve similar to that for the 43.5°C curve shown for CHO cells. Data taken from Dewey et al. [8].

Figure 4. Dose-survival response for asynchronous CHO cells at various temperatures plotted as a function of equiv-min at 43°C. The data at 41.5, 42.0 and 42.5 deviate from a single line. as shown by the dashed lines, due to the development of thermotolerance. Survival curves at the different temperatures are shown in Figure 3. Data are taken from Sapareto et al. [3]. ◯, 41.5; ▾, 42.0: ▵, 42.5; ♦, 43.0; □, 43.5; ▿, 44.0; ◊, 44.5; ˆ, 45.5; and ▴, 46.5°C.

Figure 5. Survival versus radiation dose for non-tolerant (left) and thermal tolerant (right) CHO cells. For the non-tolerant cells, synchronous cells in G₁ were either irradiated at 37°C or were heated (▵) for 10–21 min at 45.5°C and then incubated for 10 min at 37°C before they were irradiated at 37°C. For the thermal tolerant cells, synchronous cells in G₁ were heated at 45.5°C for 15 min and then incubated at 37°C for 18 h before they were either irradiated at 37°C or were heated (▵) for 15–40 min at 45.4°C and then incubated for 10 min at 37°C before they were irradiated at 37°C. During the 18-h period, heat-induced delay in G₁ prevented the cells from progressing into S phase. Left, ΔX; right 45.5°C-15 min − (18 h) ΔX.

Figure 6. TER for heat radiosensitization was determined from data in Figure 5 plus additional data (not shown) when the second heat treatment was delivered 18 h after an initial treatment of 15 min at 45.5°C. To obtain the TER, radiation survival curves were first normalized to 1.0 to eliminate the effect of heat killing. Then, when radiation reduced survival 100-fold, TER was calculated as the dose for radiation treatment alone divided by the radiation dose required for a 100-fold reduction in survival when it was delivered 10 min after heating. X/ΔX (closed symbols) is the TER for non-tolerant cells and X/Δ–ΔX (open symbols) is the TER for thermal tolerant cells. The time on the abscissa is the duration of the second heat dose in the case of the thermal tolerant cells and the duration of the single heat dose for the non-tolerant cells.

Figure 7. Data from Oleson et al. [52] and M. Dewhirst, (personal communication) for probability of complete response of 57 superficial non-adenocarcinomas and probability of necrosis (≥80% necrotic) of 44 soft tissue sarcomas as a function of cumulative equiv min at 43°C for the T₉₀ of 5–10 1-h hyperthermic treatments delivered once or twice per week 30–60 min after the radiation doses were delivered 5 days per week for a total dose of 50 Gy. For 5–10 hyperthermia treatments (Mean of 7), the median cumulative equiv in 43°C T₉₀ (CEM₄₃ T₉₀) was 5.4 for soft tissue sarcomas and 2.1 min for superficial tumours. The curves were derived from empirical equations obtained from the clinical data base.

Table 1.  Time–temperature thresholds for chronic damage in various tissues^a

Tissue	Species	Temperature damage threshold	Lesion
Muscle and fat	Pig	(240 min) 46.0°C, 30 min	Necrosis, fibrosis
Skin	Man, rat, mouse	(210 min) 46.5°C, 45 min	Epidermal necrosis
Skin	Man, rat, mouse	(120 min) 44°C, 60 min	Epilation
Oesophagus	Pig	(120 min) 45°C, 30 min	Fibrosis
Cartilage	Rat, mouse	(120 min) 44°C, 60 min	Necrosis
Bladder	Dog, rabbit	(80 min) 46.5°C, 8 min	Mucosal necrosis
Small intestine	Rat, mouse	43°C, 40 min	Crypt loss
Colon	Pig, rabbit	43°C, 30 min	Fibrosis
Liver	Dog	43°C, 30 min	Hepatocyte loss, fibrosis
Brain	Cat, dog	(25 min) 42.5°C, 50 min	Neuronal pyknosis
Kidney	Mouse	43°C, 20 min	Necrosis of glomeruli and tubules

Notes: ^aTemperatures and times that were observed as the thresholds required for the induction of the thermal damage were compiled by Dr Luis Fajardo (personal communication, 1989) from data that he published (see text). When the temperatures were not at 43°C, they were converted to an equivalent time at 43°C by using the TID equation (1) in the text; these values for equiv min 43 (EM₄₃) are in parenthesis.

Figure 8. Actuarial survival following brain implant with interstitial hyperthermia (calculated by the product limit method of Kaplan and Meier) for patients with recurrent anaplastic astrocytoma (AA) and recurrent glioblastoma multiforme (GM). Separate curves are shown for eight patients with AA and T₉₀ ≥ 41.2°C, eight patients with AA and T₉₀ < 41.2°C, 14 patients with GM and T₉₀ ≥ 41.2°C, and 11 patients with GM and T₉₀ < 41.2°C. Note the significantlyimproved survival (p = 0.008) for patients with GM who achieved a T₉₀ of at least 41.2°C. This study was carried out as described by Penny Sneed, Phil Gutin and Paul Stauffer at UCSF [58].

Figure 9. A schematic to illustrate that a region of a tumour that received a low thermal dose (low TID) should contain many viable non-thermotolerant cells after the first heat dose and that these viable cells should be inactivated if they could be heated with a second high heat dose (high TID). In contrast, a few viable thermotolerant cells might remain in the region of the tuniour that received a first high thermal dose, but the thermal resistance of these few cells to a second heat treatment should be of little consequence to the overall survival due to the relatively high thermal sensitivity of the many viable non-thermotolerant cells remaining in the region that received a low thermal dose during the first treatment.

Figure 10. A schematic of results [73] illustrating that the centrosome is a critical target for the killing of CHO cells heated (EM₄₃ of 52) in G₁ to result in survival levels >10%. The lack of staining of centrosomes with antisera is observed in all G₁ cells immediately after heating, but recovery occurs in some of the cells which then undergo a normal bipolar division and form macroscopic colonies. The cells which do not recover a normal centrosome, but instead have a fragmented centrosome, undergo an aberrant multipolar division that results in non-clonogenic multinucleated cells.

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