Complexity, fractals, disease time, and cancer

Abstract

Despite many years of research, a method to precisely and quantitatively determine cancer disease state remains elusive. Current practice for characterizing solid tumors involves the use of varying systems of tumor grading and staging and thus leaves diagnosis and clinical staging dependent on the experience and skill of the physicians involved. Although numerous disease markers have been identified, no combination of them has yet been found that produces a quantifiable and reliable measure of disease state. Newly developed genomic markers and other measures based on the developing sciences of complexity offer promise that this situation may soon be changed for the better. In this paper, we examine the potential of two measures of complexity, fractal dimension and percolation, for use as components of a yet to be determined "disease time" vector that more accurately quantifies disease state. The measures are applied to a set of micrographs of progressive rat hepatoma and analyzed in terms of their correlation with cell differentiation, ratio of tumor weight to rat body weight and tumor growth time. The results provide some support for the idea that measures of complexity could be important elements of any future cancer "disease time" vector.

Self-scaling tumor growth

“…In particular, the deviations of spatial correlators from the cosine law at small scales are strongly related to the roughness of the profiles at small scales and as such reflect the malignancy and the potential of the tumor being infiltrative [5].…”

“…Similar results hold for the higher order spatial correlators (see Figure 4(a)). Irrespective of the order (n 1 , n 2 ), spatial correlators c n 1 ,n 2 (t, ∆φ) follow the cosine law (5). In the following we refer to the angle φ 0 (t), that marks the validity of the cosine behaviour (5), as the critical angle.…”

“…There are several works where the fractal dimension of tumors has been measured with the aim to classify and determine their malignant nature [2,5]. The tumor boundary has a fractal nature, and its morphology can be characterized by a fractal dimension.…”

“…In general, the roughness of the interface between the tumor and the non-tumor region is an indicator of whether the tumor is likely to become infiltrative or not. Tumors whose interfaces are very rough are seen to be more aggressive [5].…”

Tumor proliferation and diffusion on percolation clusters

“…Theoretical knowledge of percolation is of immense importance in such diverse fields as biology and physics [50]. Lee et al remodeled a tumor growth in a dynamical evolving blood vessel network by adapting the percolation method; but their study did not include any inhomogeneous surrounding matrix [48].…”