Does tumor growth follow a “universal law”?

Abstract

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...

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