Abstract
Tumour growth kinetics has been analysed on the basis of interactions between two compartments comprising the proliferating and non-proliferating cells. Starting from the differential equations of growth of the cell-populations in the two compartments and assuming the process of intercompartmental cell transfers to be linear, an analytic expression on the variation of growth-fraction with the age of the tumour is obtained. The restricted conditions on the cell-cycle time and cell-loss-rate, under which these differential equations lead to a Gompertzian growth of the tumour, are critically analysed. The formalism permits the estimation of some important cell-kinetic parameters, like growth-fraction or cell-loss-factor, from a knowledge of the tumour-growth curve, cell-cycle-time and a single measurement of the cell-loss-rate of the matured tumour, provided the tumour follows a Gompertzian growth. The validity of the model has been verified with the experimental data on 4 different transplantable murine tumour systems. Usefulness of the model has been demonstrated by making some interesting predictions regarding the radiation response of the tumours from the cell-kinetic parameters.
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Abbreviations
- P:
-
Proliferating
- NP:
-
non proliferating
References
Archambeau, J. O. and Shymko, R. M. (1984)Curr. Probl. Cancer,7, 1.
Bhaumik, K., Mukhopadhyay, R., Dwarakanath, B. S. and Jain, V. K. (1984)NIMHANS J.,2, 129.
Frindel, E., Malaise, E. P., Alpen, E. and Tubiana, M. (1967)Cancer Res.,27, 1122.
Gewehr, K. (1977)Strahlensensibilisierung hypoxischer Tumorzellen, Ph.D. dissertation, University of Dusseldorf, Dusseldorf, FRG.
Henrichs, K. (1979)Nicht-invasive Untersuchungen zur Wachstumskinetik eines soliden experimental Tumors (Sarkom-180), Ph.D. dissertation, University of Dusseldorf, Dusseldorf, FRG.
Jain, V. K., Porschen, W. and Feinendegen, L. E. (1977)Indian J. Exp. Biol.,15, 714.
Laird, A. K. (1964)Br. J. Cancer,18, 490.
Lala, P. K. (1971)Methods Cancer Res.,6, 3.
Lala, P. K. (1972)Cancer Res.,32, 628.
Mendelsohn, M. L. (1960)Science,132, 1496.
Mühlensiepen, H. and Porschen, W. (1976)Untersuchungen der zell kinetischen Parameter beim soliden experimental Tumor Sarkom 180, Interner Bericht, IME, Kernforschungsalnage, Jülich.
Porschen, R., Porschen, W., Mühlensiepen, H. and Feinendegen, L. E. (1983)Cell Tissue Kinet.,16, 549.
Rockwell, S. and Kallman, R. F. (1972)Cell Tissue Kinet.,5, 449.
Simpson-Herren, L. and Lloyd, H. H. (1970)Cancer Chemother. Rep.,54, 143.
Sommer, I. (1977)Bestimmung der Zellverlustrate am soliden experimental Tumour Sarkom-180, Ingenieur-Arbeit, Fachhochschule Jülich, KFA Jülich.
Stecher, G., Bloemertz, H. and Pfitzer, P. (1976)Beitr. Pathol.,158, 255.
Steel, G. G. (1968)Cell Tissue Kinet.,1, 193.
Steel, G. G. (1977)Growth kinetics of tumours (Oxford: Clarendon Press).
Tannock, I. F. (1969)Cancer Res.,29, 1527.
Tubiana, M. (1971)Br. J. Radiol:,44, 325.
Watson, J. V. (1976)Cell Tissue Kinet.,9, 147.
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Bhaumik, K., Jain, V.K. Mathematical models for optimizing tumour radiotherapy. I: A simple two compartment cell-kinetic model for the unperturbed growth of transplantable tumours. J. Biosci. 12, 153–164 (1987). https://doi.org/10.1007/BF02702967
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DOI: https://doi.org/10.1007/BF02702967