Hyperthermia classic commentary: ‘Arrhenius relationships from the molecule and cell to the clinic’ by William Dewey, Int. J. Hyperthermia, 10:457–483, 1994

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Erratum

To the editor

The motivation for writing the above referenced article [1] resulted from the need to establish a thermal dose concept that could be used for quantifying hyperthermic effects reported in the literature and in experiments described in the Dewey laboratory [2–5]. These articles include fundamental thermodynamic equations that quantify heat inactivation in several biological systems. Basically, heat inactivation is quantified by relationships of temperature and duration of heating. These relationships involve an activation energy of about 110–150 kcal mole⁻¹ that has been related to protein denaturation, and is about the same for a variety of biological systems and for temperatures varying from 42°C to 90°C [1],[6]. For most systems, to obtain an isoeffect, a one degree increase in temperature requires about a two-fold decrease in duration of heating. For example, for clonogenic survival of Chinese hamster cells, 135 min at 43.5°C causes about the same decrease in survival as 2–3 s at 57°C [5]. This time and temperature relationship was reported as early as 1947 [7]. However, the absolute heat sensitivity varies greatly between different systems, and is related to variations in an entropy term [3].

To develop a thermal dose concept, a brief description of the Arrhenius analysis is presented. The basic Arrhenius plot is described as follows [2]:in which k₁ and k₂ are the inactivation rates at T₁ and T₂, respectively. The Arrhenius plot of ln k versus 1/T is linear, where T is the absolute temperature in degree Kelvin, 2 is the universal gas constant in cal degree⁻¹ mole⁻¹, the slope is ΔH/2, and A determines the absolute values on the y axis. A shift in the plot of as much as 3°C for heat denaturation of a particular protein has been reported to occur by changing only one amino acid [1]. Also, the Arrhenius plot for heat resistant pig kidney cells is parallel to the plot for Chinese hamster cells, but the values for k are 10-fold lower for pig kidney cells. This shift is caused by a change in the value for A, which includes an entropy term that is relatively independent of temperature [3],[6],[8]. ΔH is the activation energy in cal mole⁻¹, and for both pig kidney cells and Chinese hamster cells, the activation energy is ∼140 kcal mole⁻¹. Arrhenius plots have been compared for several different species and for different tissues [9]; in all cases there is a break in the plots around 43–43.5°C, with activation energies of ∼140 kcal mole⁻¹ for temperatures above the break point and ∼270 kcal mole⁻¹ for temperatures below the break point.

For clonogenic survival curves in which log S is plotted versus duration of heating at a certain temperature, the linear portion of the curve, is defined as D_o, i.e., the heating duration that reduces the survival by 37\% of an initial value. Then, the value for k in min⁻¹ is equal to 1/D_o. In this manner, different values for k are obtained for different temperatures. Also, values for k can be obtained by duration of heating at a certain temperature required for an isoeffect, i.e., a certain survival level or a certain growth delay for tumors, for example. For an isoeffect at various temperatures, a decrease of 1°C requires that the hyperthermic exposure be increased by a factor R, where

Using the relationship between temperature and duration of heating stated above, the durations of heating during short intervals at different temperatures during a heating protocol can be converted into equivalent minutes at a reference temperature of 43°C [1],[4]. Then, these equivalent minutes at 43°C for each interval can be added to obtain equivalent minutes at 43°C for the entire heating protocol (EM₄₃). Furthermore, since there are large variations in the temperature in different regions of a tumor, for example, a thermal isoeffect dose (TID-t min at 43°C) can be calculated in terms of the thermal dose in which 90% of the different regions of the tumor is exceeded (t₄₃T90). This can also be done for any percentile of the temperature distribution, such as 50% of the regions of the tumor (t₄₃T50) and for 10% of the regions of the tumor (t₄₃T10). Finally, for several hyperthermia treatments, the thermal doses for each treatment can be added to obtain a cumulative thermal dose (e.g., CEM₄₃ T90, CEM₄₃ T50, and CEM₄₃ T10).1 Possible complications related to thermal tolerance and low pH are discussed, with the conclusion that neither should present a serious problem in applying the thermal dose concept in the clinic. Finally, promising clinical results were presented indicating that a CEM₄₃ T90 of greater than 25 should show significant enhancement of tumor response (demonstrated for brain tumors), but in addition, a CEM₄₃ T50 of ∼400 may be required.

Subsequent to publication of the Arrhenius citation classic in 1994, several publications have appeared which extend the principles and conclusions outlined in the 1994 publication. First, a primary advantage of the CEM₄₃ thermal isoeffect dosimetric unit (TID) is that, thresholds for damage to a particular tissue do not have to be determined for every possible time temperature combination [9]. These principles have been used extensively in establishing standards for ultrasound, microwave exposure and MRI power standards [10–12].

A number of clinical reports were published in the 1980s and 1990s demonstrating a relationship between delivered thermal dose and outcome in patients treated with thermoradiotherapy [13–17]. Although there was variation in which descriptor of the temperature distribution was best correlated with outcome between these trials, there was invariably a correlation between higher thermal dose and better outcome. Such results strongly suggested that increasing thermal dose prospectively would improve treatment outcome. However, it was not until 2005–2006 that the first phase III trial results emerged, showing that a CEM₄₃ T₉₀ of 20–50 was sufficient to achieve a significant improvement in tumor response [18],[19]. In fact, the Thrall's study that compared the effect of a high thermal dose with the effect of a low thermal dose is the first to demonstrate the value of prospectively controlled thermal dose in achieving local tumor control with thermoradiotherapy [18]. However, more information is needed on the relative importance of CEM₄₃ T90 and CEM₄₃ T50 [20]. These clinical trials utilized a test hyperthermia treatment to eliminate ‘unheatable’ tumors, predicated on reaching a predetermined threshold T₉₀. This set of rules has been challenged since in other phase III trials, the same thermal goals were not met, yet thermoradiotherapy yielded superior results, compared with radiotherapy alone [21]. This is certainly a legitimate question. As with any clinical trial, there were unanswered questions left, such as whether other descriptors of the temperature distribution might have worked better [20] or whether the ‘unheatable’ tumors should have been followed for treatment outcome. Such answers can only be answered once non-invasive thermometry has been established and full 3D temperature distribution data can be acquired.

Second, the thermal isoeffect dose concept can be applied to describe thermal damage obtained during high-temperature thermal ablation procedures [22]. Some examples include lethal thermal dose thresholds of CEM₄₃ > 210 min for 100% necrosis of breast tumors, 180–240 CEM₄₃ for prostate [23–26], 240 CEM₄₃ for liver during RF ablation [27], and 240 CEM₄₃ threshold for general soft tissue destruction and treatment of uterine fibroids with MR guided ultrasound [28],[29]. The thermal isoeffect dose concept has also been extended to describe regions of thermal fixation produced during ablation, as demonstrated for kidney [30] with temperatures of ∼65°C; the thermal isoeffect dose that was dependent on the time of damage assay after treatment was associated with activation energies of 61–95 kcal mole⁻¹. Similarly, results were obtained for shrinkage of bovine chordate tendineae with temperatures of 65–90°C that yielded an activation energy of 109 kcal mole⁻¹ [6]. There are many other applications of thermal ablative therapy for tumors in various sites, as well as for non-oncological uses, and the thermal isoeffect dose should be applicable in these cases. Although thermal dose is useful for predicting direct thermal cell kill, in some tissues the secondary physiological responses (e.g., edema, vascular disruption, release of lytic material) could generate larger zones of necrosis than predicted by thermal dose alone [28]; this necessitates that the accuracy of thermal dose for ablation be established for each specific treatment modality and strategy, as well as tissue type. Thermal dose can also be useful for thermal ablation procedures to establish safety margins and protection of sensitive tissues adjacent to the target region. It should be noted that some attempts to use the thermal isoeffect dose in describing the thermal exposure needed for tissue coagulation (ex vivo liver and muscle) have not been successful [31]. Careful work is needed to determine what the underlying differences are between these studies and others where the concepts seem to work effectively.

Third, MRI is being used for non-invasive temperature measurements and for definition of thermal damage to tumor [32],[33]. Even with full 3D thermal data available, parameters that describe the prognostically important features of the 3D temperature distribution should be identified. Such data are just beginning to emerge and further research is needed to ferret out the most robust method for converging complex 3D thermal data with thermal dosimetric principles and clinical response.

Fourth, the rate of liposomal extravasation from tumor microvessels has been shown to follow the Arrhenius slope for temperatures below those which cause direct thermal damage (40–42°C). This observation provides a thermal dosimetric basis for thermally modulated nanoparticle drug delivery [34].

Finally, teratogenic effects in animals have been correlated with thermal isoeffect dose in animals heated at temperatures in the range of 40–41°C [35].

It should be noted that some investigators have suggested an alternative to using the thermal dose formulation to quantify the delivery of hyperthermia. For example, Lee et al. advocated the use of SAR (Specific absorption rate) [36]. Clearly, SAR is indirectly related to characteristics of the temperature distribution, but use of SAR as opposed to using a method that has biological underpinning may fail unless other important parameters, such as duration of heating and number of heating fractions is controlled. Other investigators have suggested variations in the basic thermal dose calculation method [37]. Examination of alternative dosimetric calculation methods could be tested with existing clinical data to determine whether they are better than the Sapareto and Dewey method [4].

In summary, the hyperthermia field has been progressing well since 1994 when the citation classic was published. Now, with the advent of new technology and biological information on hyperthermic effects, especially in combination with radiation and chemotherapy, the field should continue to move in a positive direction as prospective thermal doses are prescribed for applications of hyperthermia and thermal ablation therapies in treatment of cancer.

Notes

Notes

1. The use of these acronyms was suggested by Paul Stauffer.