Use of a sigmoidal equation to analyze the pressure–volume curve obtained by the low flow method

Introduction

The adjustment of PEEP and tidal volume to the lower inflection point and upper inflection point of the P–V curve, respectively, has been proposed to optimize mechanical ventilation in ARDS. Usually, the P–V curve is analyzed by eye from a graph, with high variability. Venegas and colleagues [1] developed a sigmoidal equation that fits remarkably well to P–V curves obtained by the supersyringe method. Our objective was to determine whether this equation is able to model P–V curves obtained by the low flow method.

Methods

The P–V curve was obtained by the low flow method using a Servo Siemens 300 ventilator [2]. Pressure and flow signals were obtained from the analog port (N81) and converted to digital format through a PCMCIA card (Measurement Computing, PC-CARD DAS 16/12). A program was developed to acquire, display, save, and analyze pressure and volume signals from the ventilator. The sigmoidal equation has four fitting parameters: (a) lower asymptote (volume); (b) distance from lower asymptote to upper asymptote (inspiratory capacity); (c) true inflection point (pressure); and (d) range of pressure from (c) to the point of high compliance. The equation is fitted to the P–V data by the least mean square (LMS) algorithm to minimize the sum of squared residuals. After iteration, the best fit correlation (R²) between real curves and those obtained from the equation was calculated. From the fitted equation, three points of interest were defined: the inflection point (c), where the first derivative has a maximum and the second derivative has a zero; the point of maximal compliance increase (Pmci), where the rate of change of upward slope is maximal or where the second derivative of the function has a maximum (calculated as (c) - 1.317 (d)); and the point of maximal compliance decrease (Pmcd), where rate of change of downward slope is maximal or where the second derivative of the function has a minimum (calculated as (c) + 1.317 (d)).

Results

The inspiratory limb of low flow P–V curves were obtained from six mechanically ventilated ARDS patients. The mean R² value between the ventilator volume signal and the volume predicted by the fitted curves was 0.996 ± 0.002 (standard deviation).

Conclusions

The sigmoidal equation described by Venegas and colleagues fits well to P–V curves obtained by the low flow method. Our system may contribute to improve the evaluation of respiratory mechanics and to adjust mechanical ventilation settings at the bedside in ARDS patients.