A simulation model of the natural history of human breast cancer

Abstract

Summary In order to assess the time at which the distant metastases were initiated, a model has been developed to simulate the natural history of human breast cancer. The metastasis appearance curves were fitted to those observed for tumours of various sizes among the 2648 patients treated at the Institut Gustave Roussy from 1954 to 1972. The model assumes that metastases are initiated when the tumour reaches a threshold volume (distribution of this volume was estimated in a previous article). Two With exponential growth, it was necessary to introduce correlations to obtain a satisfactory fit of the metastases appearance curves: between the tumour volume at diagnosis and the doubling time (RI = -0.3), and between the tumour volume at metastasis initiation and the doubling time (R2=0.3). The growth duration of the metastases before their detection was found to equal about 18 metastases doubling times at detection and the mean ratio between the doubling time of a tumour and its metastases equal to 2.2.With Gompertzian growth, it was impossible to adjust satisfactorily the proportions of metastases at diagnosis as a function of the primary tumour volume. However, when we ignore this, the best fit was obtained when the duration of metastases growth before detection was about the same as for exponential growth.With either growth pattern, the model predicts that the proportion of patients with metastases would be reduced by -30% if the primary tumours were treated 12 months earlier. This prediction is consistent with the results of the screening programs for breast cancer.In a previous article we studied the relationship between the size of the primary tumour at initial treatment and the incidence of distant metastases during the course of the disease. The data showed that the primary tumour at the time of metastasis initiation is, on the average, only slightly smaller than at the time of tumour diagnosis (Koscielny et al., 1984).This conclusion conflicts with the predictions of previous models of the natural history of breast cancer. Igot & Legal (1968), and later Breuer (1976) assumed that metastases grow exponentially from the time of origin and they extrapolated metastases growth curves backwards in order to determine when the metastases contained one single cell. Assuming identical growth rates for both primary tumours and metastases, they concluded that metastasis commences very early in the development of the primary.This divergence can be explained by the following hypotheses: (a) the number of cells necessary for Correspondence: S. Koscielny. Received 1 January 1985; and in revised form, 11 June 1985. metastasis initiation is much greater than one. (b) the metastasis growth rate is more rapid than the primary tumour one. (c) tumour growth is not exponential.The model proposed in this paper was developed in order to assess the time at which the distant metastases were initiated, taking into account the clinical data, particularly the relationship between primary tumour size and the metastases appearanc...

The natural history of human breast cancer. The relationship between involvement of axillary lymph nodes and the initiation of distant metastases

“…It was found that the mean tumour volume at which the first distant metastasis is initiated is markedly larger than that which was previously evaluated by a simple backwards extrapolation to one cell of the growth curve of the metastasis. This relatively late metastatic spread is consistent with the effectiveness of mammographic screening of breast cancer; moreover the predictions of the model are in good quantitative agreement with the results of screening programmes (Koscielny et al, 1985).The aim of this paper is to assess the mean volume of breast tumours at the time of the involvement of the first, second, third, etc., axillary nodes, and to compare these volumes with that of the tumour at the time at which the first distant metastasis is initiated. Two main results were obtained.…”

“…However, this correlation has never been quantified. Moreover, the significance of the presence of a given number of involved axillary lymph nodes is probably different in a patient with a large tumour of 5cm in diameter or a small tumour of 0.5cm in diameter (Fisher & Slack, 1970;Tubiana et al, 1986) and this difference deserves further investigation.Recently, clinical interest in these problems has markedly increased since the selection of patients in whom the administration of adjuvant chemotherapy is justified requires a good understanding of the natural history of human breast tumours and a proper use of the relevant prognostic indicators.In previous papers, we have developed a computer method for the analysis of the natural history of breast cancer in order to extract, from a series of over 4,000 patients treated at Villejuif, information which otherwise could not have been obtained (Koscielny et al, 1984(Koscielny et al, , 1985. The study of the relationship between the size of the breast tumour and the dissemination probability was made without any assumption as to the pattern of tumour growth.…”

Cancer metabolism and the dynamics of metastasis

“…The prediction of such a 'critical mass' has been pursued by many researchers (e.g. Koscielny et al [5] for breast cancer, Yorke et al [6] for prostate cancer), based on the assumption that tumor growth follows Gompertz's law and that such a 'critical mass' can be deduced from statistical inference on patient datasets.…”

Analysis and comparison of multimodal cancer treatments

“…However, all of the aforementioned papers consider only the primary tumor, even though metastases is responsible for most cancer mortality. Several researchers have developed stochastic simulation models of breast cancer that incorporate the primary tumor and metastases, and have calibrated their models to clinical data to generate some insights into the efficacy of chemotherapy and the nature of the metastatic spread [23]- [27]. The models of Retsky and co-workers are the most similar in spirit to ours, in that they incorporate the dormancy-followed-by-rapid-growth phenomenon revealed by Folkman's work.…”

“…The models of Retsky and co-workers are the most similar in spirit to ours, in that they incorporate the dormancy-followed-by-rapid-growth phenomenon revealed by Folkman's work. Although the simulation models in [23]- [27] are more complicated than our model, and in some cases are based on a clever statistical analysis of a wealth of data (e.g., [28]), these studies do not compare different multimodal treatments.…”