Nonlinear Flow Sensor Calibration with an Accurate Syringe

Abstract

Flow sensors are required for monitoring patients on mechanical ventilation and in respiratory research. Proper calibration is important for ensuring accuracy and can be done with a precision syringe. This procedure, however, becomes complex for nonlinear flow sensors, which are commonly used. The objective of the present work was to develop an algorithm to allow the calibration of nonlinear flow sensors using an accurate syringe. We first noticed that a power law equation could properly fit the pressure-flow relationship of nonlinear flow sensors. We then developed a software code to estimate the parameters for this equation using a 3 L syringe (calibration syringe). Finally, we tested the performance of a calibrated flow sensor using a different 3 L syringe (testing syringe) and a commercially available spirometer. After calibration, the sensor had a bias ranging from −1.7% to 3.0% and precision from 0.012 L to 0.039 L for volumes measured with the 3 L testing syringe. Calibrated sensor performance was at least as good as the commercial sensor. This calibration procedure can be done at the bedside for both clinical and research purposes, therefore improving the accuracy of nonlinear flow sensors.

Keywords: calibration; flow sensor; mechanical ventilation; nonlinear.

Figure 1

Known flows versus non-calibrated flow sensor (in volts). The graph represents the non-calibrated recordings provided by the flow sensor at different known flows that were generated by a mechanical ventilator (Evita XL). The ventilator was set to volume control with constant flow and connected to the flow sensor. The flow was progressively increased, and we recorded values (in Volts) provided by the non-calibrated flow sensor. Each point in the graph is the average of 15 measurements at each flow step. Error bars represent standard error of mean but are too small to be viewed in the main graph. A subset of the graph is shown in detail (for the second flow point) to allow the visualization of the size of standard error of mean. Regression lines for linear function (dots), power function (traces), and second order polynomial (line) with their respective equations are shown. Compared to the linear function, the power function improves the fitting and accounts for the nonlinear pressure-flow relationship.

Figure 2

Calibration trials and procedures. The graphs represent recordings of 8 trials with a 3 L syringe (calibration syringe) emptied through the flow sensor at different speeds. Signals recorded by the flow sensor prior to calibration are displayed in (A) and were integrated over time (B). Although all trials were done with the same syringe, the integrals have different final values, underscoring the nonlinearity of the flow sensor. A software algorithm was used to find parameters for a power function minimizing the difference between integrals [Flow = A*(voltage^b)]. (C) Shows flow signals after application of calibration parameters. (D) Shows the integrals of calibrated flow signals. Note that after calibration parameters were used, integrals are equal among each other and equal to the volume of the syringe (compare to B).

Figure 3

Comparison of calibrated nonlinear flow sensor with Cosmed flow sensor (converted to ambient conditions of pressure, temperature, and humidity). (A) Shows the performance of both flow sensors over time in a series of strokes generated with the 3 L calibration syringe. (B) Presents data recorded above displayed in a Bland–Altman plot. Each point represents the difference in flows measured with both sensors versus the average flow between both devices. The solid line represents bias, while the dashed lines represent limits of agreement (1.96 SD of differences from the bias).