A Mathematics for Medicine:The Network Effect - Bruce J West (Frontiers in Physiology, 2014)
The theory of medicine and its compliment systems biology are intendedto explain the workings of the large number of mutually interdependentcomplex physiologic networks in the human body, and to applythat understanding to maintaining the functions for which nature designedthem. Therefore, when what had originally been made as a simplifying assumptionor a working hypothesis becomes foundational to understandingthe operation of physiologic networks, it is in the best interests of scienceto replace or at least update that assumption. The replacement processrequires, among other things, an evaluation of how the new hypothesis affectsmodern day understanding of medical science. This paper identifieslinear dynamics and Normal statistics as being such arcane assumptionsand explores some implications of their retirement. Specifically, we explorereplacing Normal with fractal statistics, and examine how the latter arerelated to nonlinear dynamics and chaos theory. The observed ubiquityof inverse power laws in physiology entails the need for a new calculus,one that describes the dynamics of fractional phenomena and captures thefractal properties of the statistics of physiological time series. We identifythese properties as a necessary consequence of the complexity resultingfrom the network dynamics, and refer to them collectively as The NetworkEffect.