The Application of Chaos Theory and Fractal Mathematics to the Study of Cancer Evolution: Placing Metabolism and Immunity Centre Stage

Abstract

Despite the undoubted triumphs that have occurred in the treatment of some cancers, overall, the outcomes for disseminated disease remain poor. A change in perspective is therefore required to develop more effective treatment strategies. This review provides an overview of the potential contribution of chaos theory and fractal mathematics to the study of cancer evolution. The atavistic model of cancer proposes that cancer represents a reversion to an evolutionarily ancient proliferative phenotype, and suggests that cellular metabolism and the immune system are targets to which cancer may be susceptible. The approaches of chaos theory and fractal mathematics point to the same targets, and the synergy of these two perspectives will be explored. The emerging unifying concept which emerges is that the cellular machinery of the differentiated cell resists entropy in favour of stable structure. Each evolutionary development from multicellular organisms upwards, diverts more energy away from entropy. When malignant transformation occurs, the cell succumbs to the draw of the thermodynamic laws, maximizing fractal entropy, reverting to its ancient proliferative phenotype and moving, in its increased dynamic state, into greater chaos. Changes in the chaotic dynamics of cellular function evolve in parallel with changes in the fractal geometry of cellular structure. If the dynamics of the cancer cell can be worked out mathematically, it may be possible to use these dynamics to plan treatment strategies in the way that chaos theory is currently used to, for example, guide satellites. Although the responses of the tumour to the suggested targets may be weaker, they may also be more sustainable, and produce fewer side effects, than the current modalities and the emerging molecularly targeted therapies.