Decelerating growth and human breast cancer

Spratt, John A.; Fournier, D. von; Spratt, John S.; Weber, Ernst

doi:10.1002/1097-0142(19930315)71:6<2013::aid-cncr2820710615>3.0.co;2-v

Cited by 159 publications

(150 citation statements)

References 21 publications

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“…with 1 between 0.32 and 0.55 (Table 1). The slopes of the UK (Thomas et al, 1984) and British Columbia (Burhenne et al, 1992) Spratt (1993). are less significant in the clinical size ranges than those predicted by parabolic growth ( Figure 1B).…”

Section: Resultsmentioning

confidence: 88%

“…The Gonpertz law was fitted using a liming size of 3100 ml (Norton, 1988 Swedish two-county (6 years) (Fagerberg et al, 1985) NiTmegen (Peer et al, 1994) (Norton. 1988: Spratt et al 1993). Most of the non-linearity in the two-county Swedish data is due to the density of the lowest size category (1-1.5 cm).…”

Section: Resultsmentioning

confidence: 99%

“…possiblY. not representatixe g roups of patients (Gershon-Cohen et al 1963: Heuser et al 1979: Foumier et al 1980: Peer et al 1993: Spratt et al 1993. Several putative lawxs for tumour growth hasve been proposed.…”

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confidence: 99%

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The growth law of primary breast cancer as inferred from mammography screening trials data

Hart

Shochat²,

Agur³

1998

Br J Cancer

152

111

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Summary Despite considerable progress in understanding tumour development. the law of growth for human tumours is still a matter of some dispute. In this study, we used large-scale mammography screening trial data to deduce the growth law of primary breast cancer. We compared the empirical tumour population size distributions of primary breast cancer inferred from these data to the distributions that correspond to various possible theoretical growth functions. From this. we showed that the data are inconsistent with the exponential, logistic and Gompertz laws, but support power law growth (exponent = 0.5). This law indicates unbounded growth but with slowing mass-specific growth rate and doubling time. In the clinical size ranges, it implies a greater decline in the mass-specific growth rate than would be predicted by the Gompertz law using the accepted parameters. This suggests that large tumours would be less sensitive to cycle-specific therapies. and be better treated first by non-cell cycle-specific agents. We discussed the use of our study to estimate the sensitivity of mammography for the detection of small tumours. For example, we estimated that mammography is about 30% less sensitive in the detection of tumours in the 1 to Flehinger. 1991 and Xu and Prorok. 1997 for theoretical discussions). Nex ertheless. the benefit of screening. especiall in youncer women (< 50 Xyears). still remains somew-hat controv-ersial (Fletcher et al. 1993: Tabar et al. 1995 In the present w-ork. we employed extensive clinical data from large mammogaraphv screening trials that should be representatiVe of the general population. Usinc mathematical tools. we extracted from these data useful information about breast cancer growth.

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Section: Resultsmentioning

confidence: 88%

Section: Resultsmentioning

confidence: 99%

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The growth law of primary breast cancer as inferred from mammography screening trials data

Hart

Shochat²,

Agur³

1998

Br J Cancer

152

111

View full text Add to dashboard Cite

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“…We suspect that these large growth rates may be biased as they represent cell growth in vitro in favorable medium without the constrains that normally exist in the tissue. On the other hand, the in vivo studies in the medical literature report growth rates of r that equal 0.001-0.03 days −1 for breast cancer (Spratt et al, 1993;Shochat et al, 1999). Here we assume that the in vivo rates of bladder cancer growth are an order of magnitude slower than in vitro and approximate r to be in the range r = 0.01-0.045 days −1 for our simulations.…”

Section: Model Parametersmentioning

confidence: 99%

Mathematical Model of BCG Immunotherapy in Superficial Bladder Cancer

Bunimovich‐Mendrazitsky

2007

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Immunotherapy with Bacillus Calmette-Guérin (BCG)-an attenuated strain of Mycobacterium bovis (M. bovis) used for anti tuberculosis immunization-is a clinically established procedure for the treatment of superficial bladder cancer. However, the mode of action has not yet been fully elucidated, despite much extensive biological experience. The purpose of this paper is to develop a first mathematical model that describes tumor-immune interactions in the bladder as a result of BCG therapy. A mathematical analysis of the ODE model identifies multiple equilibrium points, their stability properties, and bifurcation points. Intriguing regimes of bistability are identified in which treatment has potential to result in a tumor-free equilibrium or a full-blown tumor depending only on initial conditions. Attention is given to estimating parameters and validating the model using published data taken from in vitro, mouse and human studies. The model makes clear that intensity of immunotherapy must be kept in limited bounds. While small treatment levels may fail to clear the tumor, a treatment that is too large can lead to an over-stimulated immune system having dangerous side effects for the patient.

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“…This assumption approximates the natural deceleration in the growth as the size of the tumour increases [56]. [60].…”

Section: Model Descriptionmentioning

confidence: 99%

Bifurcations and Chaotic Dynamics in a Tumour-Immune-Virus System

Eftimie

Macnamara

Dushoff

et al. 2016

Math. Model. Nat. Phenom.

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Abstract. Despite mounting evidence that oncolytic viruses can be effective in treating cancer, understanding the details of the interactions between tumour cells, oncolytic viruses and immune cells that could lead to tumour control or tumour escape is still an open problem. Mathematical modelling of cancer oncolytic therapies has been used to investigate the biological mechanisms behind the observed temporal patterns of tumour growth. However, many models exhibit very complex dynamics, which renders them difficult to investigate. In this case, bifurcation diagrams could enable the visualisation of model dynamics by identifying (in the parameter space) the particular transition points between different behaviours. Here, we describe and investigate two simple mathematical models for oncolytic virus cancer therapy, with constant and immunitydependent carrying capacity. While both models can exhibit complex dynamics, namely fixed points, periodic orbits and chaotic behaviours, only the model with immunity-dependent carrying capacity can exhibit them for biologically realistic situations, i.e., before the tumour grows too large and the experiment is terminated. Moreover, with the help of the bifurcation diagrams we uncover two unexpected behaviours in virus-tumour dynamics: (i) for short virus half-life, the tumour size seems to be too small to be detected, while for long virus half-life the tumour grows to larger sizes that can be detected; (ii) some model parameters have opposite effects on the transient and asymptotic dynamics of the tumour.

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Decelerating growth and human breast cancer

Cited by 159 publications

References 21 publications

The growth law of primary breast cancer as inferred from mammography screening trials data

The growth law of primary breast cancer as inferred from mammography screening trials data

Mathematical Model of BCG Immunotherapy in Superficial Bladder Cancer

Bifurcations and Chaotic Dynamics in a Tumour-Immune-Virus System

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