Journal of Theoretical Medicine
Volume 1 (1997), Issue 2, Pages 137-151

Mathematical Modelling of the Response of Breast Cancer to Drug Therapy

Directorate of Oncology, Western General Hospital, Edinburgh, Scotland

Received 24 January 1997

Copyright © 1997 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


mathematical modelling of tumour response in breast cancer offers the potential for further understanding of the mechanisms involved in a tumour's imperfect response to chemotherapy. Three different models of assessing response are studied; the simplest consisting of fitting a regression line to the logarithm of the tumour volumes; a study using exponential growth and an S-shaped growth response curve; and one that assumes log cell-kill and the possibilitu of primary tumour resistance to therapy. All thre can explain some facets of tumour biology, but it is the introduction of the possibility of resistance that appears to result in correlations with clinical outcome. The issue of Gompertz growth is discussed, since it is considered, although not without controversy, to best describe not only xenograft but also clinical tumour growth, and yet has not been used in any of the three models discussed. It appears that much of the data used to clinically validate Gompertz growth is before the period of maximum deceleratin, and thus the true relevance of this function to clinical tumour growth remains uncertain.