Trajectory Analysis in Health Care by David W. Hollar

Author:David W. Hollar
Language: eng
Format: epub
Publisher: Springer International Publishing, Cham

9.6 Complexity and Stability

From these brief examples, we see that the complexity of living systems involves a careful balance between periodic trajectories that maintain stability and disturbances that can positively shift the trajectory to a new trajectory (e.g., pregnancy) for a biological purpose, but many disturbances can create instabilities that ultimately compromise health for the short-term (e.g., disease, injury) or long-term (aging ). Biological systems at multiple levels maintain stability for health, whereas deviations from stability represent chaos. The task of the health epidemiologist is to measure chaos and the variables contributing to chaos. The task of the health policy maker is to introduce programs and protocols for controlling these variables. The task of the clinician is to restore the body to stability.

Each system has its own unique features for its level of biological hierarchy, whether the system involves biochemical pathways on a cell membrane, the methylation and acetylation of gene control regions on chromosomes , cell-to-cell communications, or large structural interactions between body systems. There are no consistent, universal models to explain all of these systems. However, we are proposing the use of the Lyapunov exponent as a measure of trajectory divergence in these systems when they are evaluated over time. Similarly, the coherence length, or correlation, measures the consistency between successive iterations of a system when it returns to a similar point on a periodic cycle. Just as the earth follows an elliptical orbit that is at perihelion (nearest the sun’s focus of the ellipse) around June 20 and that is at aphelion (furthest from the sun’s focus of the ellipse) around December 21, we can reliably plot the earth’s position on the ellipse from year to year (ignoring overall solar motion), such that its λ ∼ 0. The solar system has been remarkably stable over millions of years, although long-term resonances between planets potentially could plunge this system into chaos, perhaps with further forcing actions as the solar system oscillates along the galactic plane.

Human physiology and earth ecosystems are much more finite in their duration. Our bodies have positive and negative feedback processes that maintain overall system stability . Nevertheless, perturbations to system trajectories can alter the periodicities of trajectories over time and even plunge some systems into chaos. Chaotic events might be short term, in the case of epileptic seizures or occasional arrhythmias, or they might be chronic and debilitating. The longitudinal collection of multiple variable data at many time points can establish patterns of system behaviors and the events that lead to their deviation (i.e., disruptors or barriers ) as well as events that restore the stability of these systems (i.e., facilitators ). As stated in previous chapters, the current statistical and epidemiological practice is to collect snapshots of data for individuals when the variables associated with these data might vary on an hourly, daily, or weekly cycle . A given snapshot of data collection might occur at a cyclic high or low point, or within the window of a cycle that is normal, when a subsequent cycle might be aberrant.

Download

Copyright Disclaimer:
This site does not store any files on its server. We only index and link to content provided by other sites. Please contact the content providers to delete copyright contents if any and email us, we'll remove relevant links or contents immediately.