Does Cancer Growth Depend on Surface Extension?

A general model for the ontogenetic growth of living organisms has been recently proposed. Here we investigate the extension of this model to the growth of solid malignant tumors. A variety of in vitro and in vivo data are analyzed and compared with the prediction of a 'universal' law, relating properly rescaled tumor masses and tumor growth times. The results support the notion that tumor growth follows such a universal law. Several important implications of this finding are...

Most physical and other natural systems are complex entities composed of a large number of interacting individual elements. It is a surprising fact that they often obey the so-called scaling laws relating an observable quantity with a measure of the size of the system. Here we describe the discovery of universal superlinear metabolic scaling laws in human cancers. This dependence underpins increasing tumour aggressiveness, due to evolutionary dynamics, which leads to an explo...

Comparing both, the more conventional Gompertz tumor growth law (GL) and the ``Universal'' law (UL), recently proposed and applied to cancer,we have investigated the growth law's implications on various radiotherapy regimen. According to GL, the surviving tumor cell fraction could be reduced 'ad libidum', independently of the initial tumor mass,simply by increasing the number of treatments. On the contrary, if tumor growth dynamics would indeed follow the Universal scaling ...

We have previously reported that a 'universal' growth law with fixed scaling exponent p, as proposed by West and collaborators for all living organisms, appears to be able to describe also the growth of tumors in vivo. Here, we investigate in more detail the dynamic behaviour of p using data from the literature. We show that p initially decreases before it again increases up to or even beyond 3/4. These results support the notion that p can vary over time and yet its dynamics...

We have previously reported that a universal growth law, as proposed by West and collaborators for all living organisms, appears to be able to describe also the growth of tumors in vivo. In contrast to the assumption of a fixed power exponent p (assumed by West et al. to be equal to 3/4), we show in this paper the dynamic evolution of p from 2/3 to 1, using experimental data from the cancer literature and in analogy with results obtained by applying scaling laws to the study ...

In this article we shall trace the historical development of tumour growth laws, which in a quantitative fashion describe the increase in tumour mass/volume over time. These models are usually formulated in terms of differential equations that relate the growth rate of the tumour to its current state, and range from the simple one-parameter exponential growth model, to more advanced models that contain a large number of parameters. Understanding the assumptions and consequenc...

Using our previously developed model we demonstrate here, that (1) solid tumor growth and cell invasion are linked, not only qualitatively but also quantitatively, that (2) the onset of invasion marks the time point when the tumor cell density exceeds a compaction maximum, and that (3) tumor cell invasion, reduction of mechanical confinement and angiogenesis can act synergistically to increase the actual tumor mass towards the level predicted by West et al. universal growth c...

Assuming that there is feedback between an expanding cancer system and its organ-typical microenvironment, we argue here that such local tumor growth is guided by co-existence rather than competition with the surrounding tissue. We then present a novel concept that understands cancer dissemination as a biological mechanism to evade the specific carrying capacity limit of its host organ. This conceptual framework allows us to relate the tumor system's volumetric growth rate to...

The physics of solid tumor growth can be considered at three distinct size scales: the tumor scale, the cell-extracellular matrix (ECM) scale and the sub-cellular scale. In this paper we consider the tumor scale in the interest of eventually developing a system-level understanding of the progression of cancer. At this scale, cell populations and chemical species are best treated as concentration fields that vary with time and space. The cells have chemo-mechanical interaction...

Cancer cell population dynamics often exhibit remarkably replicable, universal laws despite their underlying heterogeneity. Mechanistic explanations of universal cell population growth remain partly unresolved to this day, whereby population feedback between the microscopic and mesoscopic configurations can lead to macroscopic growth laws. We here present a unification under density-dependent birth events via contact inhibition. We consider five classical tumor growth laws: e...