More years ago than I would care to admit.

More years ago than I would care to admit, a class in thermodynamics was required as part of my undergraduate course of inquiry in electrical engineering. All of us who were the pair engineering and premedicine students that year chose a particular class given according to the chemistry department, since we could satisfy the one and the other an engineering requirement and a prerequisite for medical instruct at the same time, a form of "double-dipping" that was hard to resist. In short order, we realized that learning chemical thermodynamics was not a trivial undertaking, and many of us were fortunate to survive that class with our grade point averages more or les intact. Fast-forward 30-something years, and chaos theory has become the darling of applied mathematics, and a characteristic of chaos called entropy which is dangerously bring to a period to a property taught in that dreaded thermodynamics class, is being used to describe all sorts of physical schemes including biological systems. A case in point is the article appearing in this issue of CHEST (see page 80) by way of Burioka and colleagues reporting onward measurements of the approximate entropy (ApEn) of respiration during wakefulness and sleep

To the layman, chaos means undesired randomness or disorder. In mathematics, chaos theory (also known as dynamical instability) began as the close attention of the evolution in time of methods that are extremely sensitive to initial conditions. The usual example is for what reason the flapping of a butterfly's wings in southward America can change the weather in Kansas. Chaos theory has evolv into the application of mind of the behavior of physical combination of parts to form a wholes that at first seem entirely random further in fact are not entirely thus Physical systems in general are said to inhabit "phase space," a multidimensional universe where each point corresponds to a fixed value for each variable describing the system, and the evolution in time of as it was a system can be described as a path (or trajectory) from single in kind point to another. The physical bodys described by chaos theory are deterministic, meaning that if it were possible to exactly quantify the variables describing single in kind point, the trajectory leading to the nearest point in a time succession could be entirely predicted. The basis of dynamical instability lies in the ordinance that these variables cannot be completely and exactly described; the initial conditions are enslave to minute uncertainties, and thus the trajectory may change in a seemingly random manner. In general, any trajectory in phase space is said to be found in response to an "attractor," which determines the direction of change Trajectories that move toward an equilibrium position accord to a "point attractor"; trajectories that retrace a path in a strictly periodic emotion are responding to "periodic attractors"; and trajectories that describe broad periods of behavior within certain boundaries, if it were not that never exactly retrace the same path, are, according to definition, responding to a "strange attractor." The latter methods are said to be chaotic on the other hand not random. Such a hypothesis is still deterministic but is nonlinear in that its to come state cannot be precisely predicted across the long term. The beginning of chaos theory was apted by the problem of predicting the moves of three interacting astronomical bodies. Examples of other so physical systems abound and include the stock market, traffic run fluid turbulence, population dynamics, and a myriad of biological processes

Where does the investigation of thermodynamics, and the universal of entropy, fit into this field? Originally, entropy was a thermodynamic estate that was used to describe a gas or other body of particles. In any fixed bulk of gas, the particles comprising that gas could take onward a variety of different arrangements within the turn and the value of entropy describes the number of different arrangements that are possible for the hypothesis of particles within the turn (it is actually related to the natural logarithm of that value). Entropy is the make submissive of the second law of thermodynamics, which specifies that a scheme of particles will preferentially instigate toward a state in which entropy (or randomness) is maximal. For instance, a book of gas will never, forward its own and due to random manner of moving of the gas particles, rearrange itself to possess only a corner of the convolution The concept of entropy has been further widened by investigators of chaos theory to describe the predictability or randomness of physical bodys as they change with time: the higher the value of entropy the more random (or chaotic) the process

The beat-to-beat variability of heart rate has probably been the principally well-known medical application of chaos theory thus far. It has been evident for many years that this variability exists, moreover the mechanisms involved were alone uncovered within the last decade or in the same manner as the necessary analytic techniques became available. Heart rate suits to the balance between sympathetic and parasympathetic input to the sinoatrial node, and this balance of tone normally varies with respiration, be motionless state, circadian rhythm, posture, the renin-angiotensin hypothesis behavioral state, and probably many other factors not now identified. (1,2) In fact, there are thus many factors that normally determine heart rate that it has become evident that a tangled skein cardiac rhythm is an indicator of cardiac health. (12) Heart rate variability (HRV) increases with the gestational age of the fetus and during maturation in early infancy, (1) and then begins a gradual decline, starting in childhood, and continues to decline in the healthy somewhat old (3) Of clinical interest, fetal HRV decreases with antepartum distress, (4) infant HRV in non-rapid inspection movement sleep is lower in near-miss cases of unanticipated infant death syndrome than in healthy children, (5) and HRV declines in patients with congestive heart failure (6) and coronary artery disease, and after acute myocardial infarction. In the latter case, HRV has been correlated with consequence in that reduced indexes of complexity keep to predict poorer survival. (7)

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