### Excerpt

The authors expressed concern that our linear regression model assumes a “strictly constant resistance,” and compare its limitations to those of the stress index technique. The stress index assumes that during constant inspiratory flow, the pressure-time profile behaves according to a power law, with negligible dynamic contributions of resistance to transient pressure fluctuations. However, our linear regression analysis of the respiratory system assumes that dissipative pressure losses are not constant, but rather proportional to the measured flow. Such a model is therefore able to characterize minor fluctuations during constant-flow inflation, whereas the stress index cannot. Furthermore, our linear regression technique does not fit a quadratic polynomial to total (ie, resistive and elastic) pressure as a function of volume, but rather only to the elastic pressure. In other words, pressure losses due to resistive and elastic phenomena are estimated separately and simultaneously. Thus the model used for our regression technique can be used to assess nonlinear elastic behavior during any modality of controlled ventilation, which does not apply to the stress index.4

Dr Spaeth et al also express concern over nonnegligible effects of nonlinear resistance in the presence of minor deviations from constant inspiratory flow due to nonlinear flow–dependent resistive properties of endotracheal tubes. We assumed that a linear resistance model (LRM) would sufficiently account for first-order effects of minor flow fluctuations during constant-flow inflation, and thus the nonlinear elastic components of the respiratory system model alone account for nonlinearity in the resulting elastic pressure-volume relationship. To test possible differences, we applied an extended nonlinear resistance model (NLRM), incorporating a flow-dependent component of resistance, as shown in Equation 1:

JOURNAL/asag/04.02/00000539-201802000-00063/math_63MM1/v/2018-04-26T070634Z/r/image-tiff

where Paw is the airway pressure determined at the endotracheal tube, t is time, R1 and R2 are the linear and nonlinear components of resistance, respectively, V is volume, E1 and E2 are the linear and nonlinear components of elastance, respectively, with P0 representing Paw at end-expiration. The root-mean-square error after model fitting according to Equation 1 was reduced in NLRM compared to LRM (ΔRMSE = RMSENLRM − RMSELRM = −0.0174 [−0.038…−0.007] median[first…third quartile]). However, %E2 calculated as %E2 = E2·V/(E1 + E2·V) with the parameters extracted from Equation 1 were highly correlated with the results from our publication1 (Figure). Therefore, accounting for the nonlinear component of resistance does not have an impact on the conclusions of our study.

The authors of the letter recommended the so-called gliding- stepwise multiple linear regression (SLICE) method,5 which is susceptible to minor fluctuations, artifacts, and signal noise in pressures and/or flows. Furthermore, we did not aim to evaluate the extent to which intratidal recruitment and/or overdistension occur within a breath, but rather which of these nonlinear phenomena dominates the mechanical characteristics of the breath. Therefore, it is appropriate to use an approach that robustly characterizes the overall degree of elastic pressure-volume nonlinearity by considering the entire inspiratory phase, using a relatively simple regression model.