[Kinematic deterministic chaos of fluids and fractal geometry in the carotid system]

Atherosclerosis is a generalized vascular disorder which tends to be localized to specific arterial territories. At the bifurcation of the carotid artery there is a marked predisposition to form plaques of atheroma on the postero-external wall. This tendency is due to the kinematics of fluids and their particular morphological characteristics which are unique in the vascular system. The carotid tree is a physical, non-lineal or in 'non-equilibrium', dynamic system which depends on the fluctuating contribution of energy from the cardiac cycle. It has fractal geometry which follows the Law of Biology of maximum efficiency with a minimum of effort.

The complexity of the relationship between the haemo-rheological and anatomical factors, and the periodic oscillation of flow does not permit use of simple models and classical determinist equations to describe idealized systems of continuous movement and Newtonian fluids. On the contrary, since we are considering a complex dissipative dynamic system. It has marked intrinsic operational freedom adapting its responses to external disturbances well, thus determining vasculo-cerebral autoregulation. The theories of Determinist Chaos and of the Science of Complexity imply the existence of emerging properties which exceed those of the individual elements in the dynamic systems in non-equilibrium, which tend to function in the 'frontier of chaos' at the critical points of phase transition. The carotid tree has non-linear properties, appearance of order and fractal 'sibisemejanza'. Pseudo-chaotic vortices appear--in regions of phase transition between laminar flow and turbulence--with the emergence of a 'strange attractor' near to the postero-external wall of the bulb.

The anatomical and kinematic complexity of the system, together with the irreversibility of the second Law of Thermodynamics, lead to a long-term tendency towards the appearance of a region of stagnant flow with increased Entropy in the territory of the strange attractor which determines--as an inevitable long-term outcome--the tendency to the appearance of atherosclerosis at this particular point.