Influence of arousal threshold and depth of sleep on respiratory stability in man: analysis using a mathematical model.

We examined the effect of arousals (shifts from sleep to wakefulness) on breathing during sleep using a mathematical model. The model consisted of a description of the fluid dynamics and mechanical properties of the upper airways and lungs, as well as a controller sensitive to arterial and brain changes in CO(2), changes in arterial oxygen, and a neural input, alertness. The body was divided into multiple gas store compartments connected by the circulation. Cardiac output was constant, and cerebral blood flows were sensitive to changes in O(2) and CO(2) levels. Arousal was considered to occur instantaneously when afferent respiratory chemical and neural stimulation reached a threshold value, while sleep occurred when stimulation fell below that value. In the case of rigid and nearly incompressible upper airways, lowering arousal threshold decreased the stability of breathing and led to the occurrence of repeated apnoeas. In more compressible upper airways, to maintain stability, increasing arousal thresholds and decreasing elasticity were linked approximately linearly, until at low elastances arousal thresholds had no effect on stability. Increased controller gain promoted instability. The architecture of apnoeas during unstable sleep changed with the arousal threshold and decreases in elasticity. With rigid airways, apnoeas were central. With lower elastances, apnoeas were mixed even with higher arousal thresholds. With very low elastances and still higher arousal thresholds, sleep consisted totally of obstructed apnoeas. Cycle lengths shortened as the sleep architecture changed from mixed apnoeas to total obstruction. Deeper sleep also tended to promote instability by increasing plant gain. These instabilities could be countered by arousal threshold increases which were tied to deeper sleep or accumulated aroused time, or by decreased controller gains.

Analysis of the interplay between neurochemical control of respiration and upper airway mechanics producing upper airway obstruction during sleep in humans.

Increased loop gain (a function of both controller gain and plant gain), which results in instability in feedback control, is of major importance in producing recurrent central apnoeas during sleep but its role in causing obstructive apnoeas is not clear. The purpose of this study was to investigate the role of loop gain in producing obstructive sleep apnoeas. Owing to the complexity of factors that may operate to produce obstruction during sleep, we used a mathematical model to sort them out. The model used was based on our previous model of neurochemical control of breathing, which included the effects of chemical stimuli and changes in alertness on respiratory pattern generator activity. To this we added a model of the upper airways that contained a narrowed section which behaved as a compressible elastic tube and was tethered during inspiration by the contraction of the upper airway dilator muscles. These muscles in the model, as in life, responded to changes in hypoxia, hypercapnia and alertness in a manner similar to the action of the chest wall muscles, opposing the compressive action caused by the negative intraluminal pressure generated during inspiration which was magnified by the Bernoulli Effect. As the velocity of inspiratory airflow increased, with sufficiently large increase in airflow velocity, obstruction occurred. Changes in breathing after sleep onset were simulated. The simulations showed that increases in controller gain caused the more rapid onset of obstructive apnoeas. Apnoea episodes were terminated by arousal. With a constant controller gain, as stiffness decreased, obstructed breaths appeared and periods of obstruction recurred longer after sleep onset before disappearing. Decreased controller gain produced, for example, by breathing oxygen eliminated the obstructive apnoeas resulting from moderate reductions in constricted segment stiffness. This became less effective as stiffness was reduced more. Contraction of the upper airway muscles with hypercapnia and hypoxia could prevent obstructed apnoeas with moderate but not with severe reductions in stiffness. Increases in controller gain, as might occur with hypoxia, converted obstructive to central apnoeas. Breathing CO2 eliminated apnoeas when the activity of the upper airway muscles was considered to change as a function of CO2 to some exponent. Low arousal thresholds and increased upper airway resistance are two factors that promoted the occurrence and persistence of obstructive sleep apnoeas.

The architecture of a decision support system.

A Decision Support System (DSS) begun in the middle 1960s is described. A DSS collects data for an institution servicing clients, calculates decisions and generates reports on the status of the clients. This paper was written to provide a historical record of the concepts developed. In Part I, we introduce the Decision Support System (DSS), describe its functions, and indicate a possible architecture for such a system. Part 2 describes the concepts developed in the course of programming an experimental system called the Clinical Decision Support System (CDSS). CDSS, which is designed for a medical environment and has been tested at several sites on an experimental basis. The CDSS implementation of a DSS is described in some detail.