Quiescence as an explanation of Gompertzian tumor growth revisited

Abstract

Abstract. Gompertz's empirical equation remains the most popular one in describing cancer cell population growth in a wide spectrum of biomedical situations due to its good fit to data and simplicity. Many efforts were documented in the literature aimed at understanding the mechanisms that may support Gompertz's elegant model equation. One of the most convincing efforts was carried out by Gyllenberg and Webb. They divide the cancer cell population into the proliferative cells and the quiescent cells. In their two dimensional model, the dead cells are assumed to be removed from the tumor instantly. In this paper, we modify their model by keeping track of the dead cells remaining in the tumor. We perform mathematical and computational studies on this three dimensional model and compare the model dynamics to that of the model of Gyllenberg and Webb. Our mathematical findings suggest that if an avascular tumor grows according to our three-compartment model, then as the death rate of quiescent cells decreases to zero, the percentage of proliferative cells also approaches to zero. Moreover, a slow dying quiescent population will increase the size of the tumor. On the other hand, while the tumor size does not depend on the dead cell removal rate, its early and intermediate growth stages are very sensitive to it.

Close Encounters of the Cell Kind: The Impact of Contact Inhibition on Tumour Growth and Cancer Models

“…Conger and Zisikin (1983) examined spheroid growth over multiple cell lines, finding that spheroids have an initial exponential growth phase, followed by a quasi-linear phase where limited nutrient diffusion inhibits growth, and finally a plateau phase. Such dynamics are similar to growth curves exhibited by solid tumours in situ (Steel 1977;Conger and Ziskin 1983;Gyllenberg and Webb 1988;Grimes et al 2016). The Gompertzian model captures tumour growth dynamics especially well, but can lead to unrealistically slow growth in initial phrases.…”

“…Historically, tumour growth has been described by sigmoidal functions, including the von Bertalanffy, Gompertzian and logistic family of models (Steel 1977;Wheldon 1988;Vaidya and Alexandro 1982). In these models, growth is initially unrestrained, before becoming limited by depletion of essential nutrients such as oxygen, with approximately sigmoidal functions generally thought of as adequate to describe general avascular growth (Feller 1940;Gyllenberg and Webb 1988;Marušić et al 1994). On the other hand, it has been suggested based on colony evidence that tumour growth is not limited by nutrient availability, but by spatial constraints (Brú et al 2003), such that tumour radius grows linearly with time, and is restricted to the periphery.…”

Correlation Factors Analysis of Breast Cancer Tumor Volume Doubling Time Measured by 3D-Ultrasound

“…(1) It had a small sample size. (2) Clinical and experimental observation show that malignant tumor growth follows an S-shaped or linear Gompertzian curve [26]. Gompertzian model assumes that TVDT varies according to tumor size.…”

Comparison between model‐predicted tumor oxygenation dynamics and vascular‐/flow‐related Doppler indices

“…The dynamics of the active portion features the spontaneous growth, driven by the Gomperztian function, 35 along with the decrease due to irradiation damages, represented by the linear-quadratic (LQ) model, 36 according the following formula:…”