Pathophysiology of Cancer and the Entropy Concept

Abstract

Entropy may be seen both from the point of view of thermodynamics and from the information theory, as an expression of system heterogeneity. Entropy, a system-specific entity, measures the distance between the present and the predictable end-stage of a biological system. It is based upon statistics of internal characteristics of the system. A living organism maintains its low entropy and reduces the entropy level of its environment due to communication between the system and its environment. Carcinogenesis is characterized by accumulating genomic mutations and is related to a loss of internal cellular information. The dynamics of this process can be investigated with the help of information theory. It has been suggested that tumor cells might regress to a state of minimum information during carcinogenesis and that information dynamics are integrally related to tumor development and growth. The great variety of chromosomal aberrations in solid tumors has limited its use as a variable to measure tumor aggressiveness or to predict prognosis. The introduction of Shannon’s entropy to express karyotypic diversity and uncertainty associated to sample distribution has overcome this problem. During carcinogenesis, mutations of the genome and epigenetic alterations (e.g. changes in methylation or protein composition) occur, which reduce the information content by increasing the randomness and raising the spatial entropy inside the nucleus. Therefore, we would expect a raise of entropy of nuclear chromatin in cytological or histological preparations with increasing malignancy of a tumor. In this case, entropy is calculated based on the co-occurrence matrix or the histogram of gray values of digitalized images. Studies from different laboratories based on various types of tumors demonstrated that entropy derived variables describing chromatin texture are independent prognostic features. Increasing entropy values are associated with a shorter survival. In summary, the entropy concept helped us to create in a parsimonious way a theoretical model of carcinogenesis, as well as prognostic models regarding survival.

Supported by FAPESP 2007/52015-0 and CNPq 479074/2008-9.