A mathematical model for cell killing by heat applied to a C3H mammary carcinoma in vivo. 1993

J C Lindegaard, and S M Bentzen
Department of Experimental Clinical Oncology, Radiumstationen, Aarhus, Denmark.

Jung (1986) has proposed a mathematical model for cell killing by hyperthermia which assumes that heat killing involves two steps: the production (p) of non-lethal lesions at random and a subsequent conversion (c) into lethal lesions. The p & c model has been shown to predict the survival of CHO cells heated in vitro even when complicated biological phenomena such as thermotolerance and step-down heating (SDH) are involved (Jung 1986, 1991). In the present study the objective was to test the p & c model's ability to describe the effect of single heating and SDH in an experimental tumour in vivo. The endpoint was tumour growth delay (GD). The doubling times (DT) for untreated and heated tumours were similar, and the surviving fraction (SF) could therefore be estimated using: SF = -in(2).GD/DT. SF was fitted to the model by non-linear regression. The p & c model adequately described the GD obtained by SDH (39-44.5 degrees C) and single heating above 42.5 degrees C. Multiple linear regression showed that the residuals for single heating and SDH were independent of both heating time and temperature. However, the residuals for single heating (41-44.5 degrees C) were significantly correlated to heating time when analysed separately. The GD obtained by the use of extended single heating times at or below 42.5 degrees C was therefore overestimated by the model. Development of chronic thermotolerance during heating may account for the observed divergence. The Arrhenius plots for both p and c were log-linear with activation energies of 678 and 311 kJ/mol, respectively. Jung (1986) has previously reported similar p and c activation energies above 42.5 degrees C for CHO cells in vitro.

UI MeSH Term Description Entries
D006979 Hyperthermia, Induced Abnormally high temperature intentionally induced in living things regionally or whole body. It is most often induced by radiation (heat waves, infra-red), ultrasound, or drugs. Fever Therapy,Hyperthermia, Local,Hyperthermia, Therapeutic,Thermotherapy,Induced Hyperthermia,Therapeutic Hyperthermia,Therapy, Fever,Local Hyperthermia
D008325 Mammary Neoplasms, Experimental Experimentally induced mammary neoplasms in animals to provide a model for studying human BREAST NEOPLASMS. Experimental Mammary Neoplasms,Neoplasms, Experimental Mammary,Experimental Mammary Neoplasm,Mammary Neoplasm, Experimental,Neoplasm, Experimental Mammary
D008433 Mathematics The deductive study of shape, quantity, and dependence. (From McGraw-Hill Dictionary of Scientific and Technical Terms, 6th ed) Mathematic
D008954 Models, Biological Theoretical representations that simulate the behavior or activity of biological processes or diseases. For disease models in living animals, DISEASE MODELS, ANIMAL is available. Biological models include the use of mathematical equations, computers, and other electronic equipment. Biological Model,Biological Models,Model, Biological,Models, Biologic,Biologic Model,Biologic Models,Model, Biologic
D005260 Female Females
D000818 Animals Unicellular or multicellular, heterotrophic organisms, that have sensation and the power of voluntary movement. Under the older five kingdom paradigm, Animalia was one of the kingdoms. Under the modern three domain model, Animalia represents one of the many groups in the domain EUKARYOTA. Animal,Metazoa,Animalia
D016923 Cell Death The termination of the cell's ability to carry out vital functions such as metabolism, growth, reproduction, responsiveness, and adaptability. Death, Cell
D051379 Mice The common name for the genus Mus. Mice, House,Mus,Mus musculus,Mice, Laboratory,Mouse,Mouse, House,Mouse, Laboratory,Mouse, Swiss,Mus domesticus,Mus musculus domesticus,Swiss Mice,House Mice,House Mouse,Laboratory Mice,Laboratory Mouse,Mice, Swiss,Swiss Mouse,domesticus, Mus musculus

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