Non-linear dynamics for clinicians: chaos theory, fractals, and complexity at the bedside

Author: A L Goldberger1
1 Harvard-Thorndike Laboratory, Department of Medicine, Beth Israel Hospital, Boston, MA 02215, USA.
2 Beth Israel Hosp, Boston, MA
Conference/Journal: Lancet
Date published: 1996 May 11
Other: Volume ID: 347 , Issue ID: 9011 , Pages: 1312-4 , Special Notes: doi: 10.1016/s0140-6736(96)90948-4. , Word Count: 226

PMID: 8622511 DOI: 10.1016/s0140-6736(96)90948-4
Clinicians are increasingly aware of the remarkable upsurge of interest in non-linear dynamics, the branch of the sciences widely referred to as chaos theory. Those attempting to evaluate the biomedical relevance of this subject confront a confusing array of terms and concepts, such as non-linearity, fractals, periodic oscillations, bifurcations, and complexity, as well as chaos.1-4 Therefore, I hope to provide an introduction to some key aspects of non-linear dynamics and review selected applications to physiology and medicine.

Linear systems are well behaved. The magnitude of their responses is proportionate to the strength of the stimuli. Further, linear systems can be fully understood and predicted by dissecting out their components. The subunits of a linear system add up--there are no surprises or anomalous behaviours. By contrast, for non-linear systems proportionality does not hold: small changes can have striking and unanticipated effects. Another complication is that non-linear systems cannot be understood by analysing their components individually. This reductionist strategy fails because the components of a non-linear network interact--ie, they are coupled. Examples include the interaction of pacemaker cells in the heart or neurons in the brain. Their non-linear coupling generates behaviours that defy explanation by traditional (linear) models such as self-sustained, periodic waves (eg, ventricular tachycardia); abrupt changes (eg, sudden onset of a seizure); and, possibly, chaos.