A better understanding of the growth kinetics of malignant tumors is of paramount importance for the development of more successful treatment strategies. Given the lack of clinical data at non-symptomatic stages, it has been conjectured, that in most solid malignant human tumors two or three decades elapse between the first carcinogenic stimulus and the clinical emergence of the neoplasm (Tubiana, 1986). Since a tumor is clinically detectable with conventional diagnostic tools at approximately 1 cm 3 in volume, representing a population of about 1 billion cells, some 30 cell doublings from the progenitory cancer cell must occur in order to reach this 'diagnostic' stage.Assuming typical volume doubling times of about 100 days, this scenario corresponds to a preclinical time of roughly 8 years . In the next 10 volume doublings up to about 10 3 cm 3 in size (which is reportedly lethal in primary breast cancer by Retsky, 1997), the clinical history of the tumor passes through a microscopic, avascular growth phase, followed by angiogenesis, necessary to sustain a macroscopic size (Folkman, 1971).Continuous tumor progression leads then eventually to local tissue invasion and metastasis, depending on the particular cancer type.A recent paper from West et al (2001) shows that, regardless of the different masses and development times, mammals, birds, fish and molluscs all share a common growth pattern.Provided that masses and growth times for the different organisms are properly rescaled, the same universal exponential curve fits their ontogenetic growth data. The authors explain this phenomenon with basic cellular mechanisms (West et al, 2002), assuming a common fractal pattern in the vascularization of the investigated taxa. In our case, m 0 and M are the initial and final masses of the tumor, and a is a parameter expected to be related to the tumor's characteristics (e.g., its ability to metastasize or invade, or its affinity for nutrients uptake). Since the definition of the parameters is non-trivial, a multistep fitting procedure is adopted for their determination. M are allowed to respectively decrease and increase, and y 0 and α reestimated until a best-fit (consistent with the available biological infomation) is obtained.For our analysis, we have used available data from the literature, spanning in vitro experiments (multicellular tumor spheroids (Chignola et al, 2000, Nirmala et al, 2001) as well as in vivo data (both, from animal models (Steel, 1977;Cividalli et al, 2002) and patients (Norton, 1988; Yorke et al, 1993). The results are presented in Figures 1, 2 and 3, respectively, and plotted against equation [2]. The data fit the universal growth curve very well. Table 1 presents an estimate of the relevant parameters and, further supporting our claim, shows very high R 2 correlation coefficients between actual and fitted data.In the following, we will briefly discuss possible implications of our conjecture that tumor growth also follows a universal law. proposed that, upon reaching a certain " critical" vo...

Most organisms grow according to simple laws, which in principle can be derived from energy conservation and scaling arguments, critically dependent on the relation between the metabolic rate B of energy flow and the organism mass m. Although this relation is generally recognized to be of the form B͑m͒ = m p , the specific value of the exponent p is the object of an ongoing debate, with many mechanisms being postulated to support different predictions. We propose that multicellular tumor spheroids provide an ideal experimental model system for testing these allometric growth theories, especially under controlled conditions of malnourishment and applied mechanical It was recently proposed 1 that tumors may follow the general model of ontogenetic growth for all living organisms (from mammals to mollusks to plants) developed by West, Brown and Enquist (WBE). 2 The beauty of the WBE model is that it is entirely based on energy conservation and other general physical arguments, i.e., scaling. The authors start with the assumption that the energy intake, supplied by ingested nutrients, is spent partly to support the metabolic functions of the organism's existing cells and partly for cell replication, i.e., to reproduce new cells. Based on this key assumption, a universal growth curve is derived, which the authors conjectured to be applicable to all living organisms. Their conjecture, based on a fractal-like distribution model, is supported by data encompassing many different species. 2 Although they assumed B ϰ m p with p =3/4, their value of p is not universally accepted. Indeed there is strong evidence that growth may be consistent with a 2 / 3 law in the case of birds and small mammals. 3 Due to its implications for tumor metastasis, cell turnover rates, angiogenesis, and invasion, the proposal of Ref. 1 has immediately contributed to an ongoing debate. 4,5 Many different explanations have been put forward for the scaling laws, ranging from four-dimensional biology. 6 and quantum statistics 7 to long-bone allometry combined with muscular development, 8 but, as yet, the debate is far from being settled. In this letter we suggest that multicellular tumor spheroids (MTS) are excellent experimental model systems to test the validity of the proposed mechanisms. MTS are spherical aggregations of malignant cells, 9,10 which can be grown in vitro under strictly controlled nutritional and mechanical conditions. Although cells appear to preserve the evolutionary self-organization rules governing the growth of the original tumor line, they also evolve according to the environmental conditions of the particular experimental setting. Here we show that MTS indeed grow following a scaling law and obtain their expected properties under conditions of malnourishment and rising mechanical stress-conditions that often apply to tumors in vivo.Following WBE, we assume, for simplicity, that metabolism and growth are the same for all MTS cells. Let B be the resting metabolic energy expenditure. Then, at any time t and for any discrete sho...

Both the lack of nutrient supply and rising mechanical stress exerted by the microenvironment appear to be able to cause discrepancies between the actual, observed tumor mass and that