Intratidal analysis of intraoperative respiratory system mechanics: keep it simple.

Dear Editor,

We thank Dr. Spaeth and colleagues for their interest in our study¹, which was conducted in a subpopulation of the PROVHILO trial².

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 (i.e., 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 behaviour during any modality of controlled ventilation, which does not apply to the stress index³.

Dr. Spaeth and colleagues also express concern over non-negligible 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 1^st-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 Eq. 1:

$${\text{P}}_{\text{aw}}(\text{t})={\text{R}}_1\cdot \dot{\text{V}}+{\text{R}}_2\cdot \left|\dot{\text{V}}\right|\cdot \dot{\text{V}}+{\text{E}}_1\cdot \text{V}+{\text{E}}_2\cdot {\text{V}}^2+{\text{P}}_0$$ Eq. 1

where P_aw 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 P_aw at end-expiration. The root-mean square error after model fitting according to Eq. 1 was reduced in NLRM compared to LRM (ΔRMSE = RMSE_NLRM – RMSE_LRM = −0.0174 [−0.038…−0.007] Median[1^st…3^rd quartile]). However, %E₂ calculated as %E₂ = E₂∙V/(E₁ + E₂∙V) with the parameters extracted from Eq. 1 were highly correlated with the results from our publication¹ (Figure 1). Therefore, accounting for the nonlinear component of resistance does not impact on the conclusions of our study.

Figure 1 -.

Relationship between %E₂ calculated from linear resistance model (LRM) and nonlinear resistance model (NLRM).

The authors of the letter recommended the so-called gliding-SLICE method⁴, which is susceptible to minor fluctuations, artefacts, and signal noise in pressures and/or flows. Furthermore, we did not aim to evaluate the extent to which intra-tidal 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 which robustly characterizes the overall degree of elastic pressure-volume nonlinearity by considering the entire inspiratory phase, using a relatively simple regression model.