Mathematical models for pressure controlled ventilation of oleic acid-injured pigs

Medical practices display power law behaviors similar to spoken languages

Background

Medical care commonly involves the apprehension of complex patterns of patient derangements to which the practitioner responds with patterns of interventions, as opposed to single therapeutic maneuvers. This complexity renders the objective assessment of practice patterns using conventional statistical approaches difficult.

Methods

Combinatorial approaches drawn from symbolic dynamics are used to encode the observed patterns of patient derangement and associated practitioner response patterns as sequences of symbols. Concatenating each patient derangement symbol with the contemporaneous practitioner response symbol creates “words” encoding the simultaneous patient derangement and provider response patterns and yields an observed vocabulary with quantifiable statistical characteristics.

Results

A fundamental observation in many natural languages is the existence of a power law relationship between the rank order of word usage and the absolute frequency with which particular words are uttered. We show that population level patterns of patient derangement: practitioner intervention word usage in two entirely unrelated domains of medical care display power law relationships similar to those of natural languages, and that–in one of these domains–power law behavior at the population level reflects power law behavior at the level of individual practitioners.

Conclusions

Our results suggest that patterns of medical care can be approached using quantitative linguistic techniques, a finding that has implications for the assessment of expertise, machine learning identification of optimal practices, and construction of bedside decision support tools.

A NEW LOOK AT THE STRESS INDEX FOR LUNG INJURY

Ranieri and colleagues1,2 have proposed a simple mathematical equation (Paw(t) ≈ atb+c) where a, b, and c are constants that relates airway pressure, Paw(t), over inspiration (0 ≤ t ≤ ti) in constant flow mechanical ventilation to ventilator-induced lung injury. They have correlated b with low-volume stress (b ≤ 0.9), high-volume stress (b ≥ 1.1), and minimal stress (0.9 ≤ b ≤ 1.1) in the lungs. In this paper we examine the theoretical underpinnings of this empirical equation and show that it has a relationship to the upper and lower inflection points of the Pelastic - V curve during inspiration. An alternative equation [Formula: see text] that comes from the theoretical analysis of this type of mechanical ventilation is presented. Both equations are compared using experimental data.