Pressure-dependent stress relaxation in acute respiratory distress syndrome and healthy lungs: an investigation based on a viscoelastic model

Abstract

Introduction: Limiting the energy transfer between ventilator and lung is crucial for ventilatory strategy in acute respiratory distress syndrome (ARDS). Part of the energy is transmitted to the viscoelastic tissue components where it is stored or dissipates. In mechanically ventilated patients, viscoelasticity can be investigated by analyzing pulmonary stress relaxation. While stress relaxation processes of the lung have been intensively investigated, non-linear interrelations have not been systematically analyzed, and such analyses have been limited to small volume or pressure ranges. In this study, stress relaxation of mechanically ventilated lungs was investigated, focusing on non-linear dependence on pressure. The range of inspiratory capacity was analyzed up to a plateau pressure of 45 cmH2O.

Methods: Twenty ARDS patients and eleven patients with normal lungs under mechanical ventilation were included. Rapid flow interruptions were repetitively applied using an automated super-syringe maneuver. Viscoelastic resistance, compliance and time constant were determined by multiple regression analysis using a lumped parameter model. This same viscoelastic model was used to investigate the frequency dependence of the respiratory system's impedance.

Results: The viscoelastic time constant was independent of pressure, and it did not differ between normal and ARDS lungs. In contrast, viscoelastic resistance increased non-linearly with pressure (normal: 8.4 (7.4-11.9) [median (lower - upper quartile)] to 35.2 (25.6-39.5) cmH2O.sec/L; ARDS: 11.9 (9.2-22.1) to 73.5 (56.8-98.7)cmH2O.sec/L), and viscoelastic compliance decreased non-linearly with pressure (normal: 130.1(116.9-151.3) to 37.4(34.7-46.3) mL/cmH2O; ARDS: 125.8(80.0-211.0) to 17.1(13.8-24.7)mL/cmH2O). The pulmonary impedance increased with pressure and decreased with respiratory frequency.

Conclusions: Viscoelastic compliance and resistance are highly non-linear with respect to pressure and differ considerably between ARDS and normal lungs. None of these characteristics can be observed for the viscoelastic time constant. From our analysis of viscoelastic properties we cautiously conclude that the energy transfer from the respirator to the lung can be reduced by application of low inspiratory plateau pressures and high respiratory frequencies. This we consider to be potentially lung protective.

Figure 1

Super-syringe maneuver. Representative time-series for standardized super-syringe maneuvers obtained from one acute respiratory distress syndrome (ARDS) and one patient with healthy lungs (control). Volume steps of 100 mL were repetitively applied up to a maximum plateau pressure of 45 cmH₂O. After each volume step, airflow was interrupted for three seconds.

Figure 2

Lumped parameter model. Electrical circuit analog to the spring-and-dashpot model. R denotes the Newtonian airway resistance and C_st the static compliance. R_ve and C_ve are the resistance and the compliance of the viscoelastic component, respectively. The respiratory airflow represents the input and the respiratory pressure P_rs the output of the model.

Figure 3

Flow interruption technique. (a) Respiratory flow and (b) pressure P_rs time-series of one 100 mL volume step including the phases of volume loading ( >0 mL/sec) and stress relaxation ( = 0 mL/sec during occlusion interval). (a) Labeled points indicate: (1) start of valve closure, (2) flow falling below zero due to valve characteristics, (3) estimated end of valve closure. The data between (1) and (3) were excluded from the fitting process [see Additional file 1]. (b) P_rs with maximum pressure (P_{rs, max}) and approximated plateau pressure (P_plat). P_{rs, sim} depicts the model-simulated respiratory pressure by use of the fitted parameter values. (i) denotes the initial resistive pressure drop (P_{rs, max} down to P₁), (ii) denotes the succeeding slow pressure change indicating stress relaxation between level P₁ and P_plat.

Figure 4

Results of parameter estimation. Estimated parameters of viscoelasticity for the acute respiratory distress syndrome (ARDS) group and the control group in terms of lower quartiles, medians and upper quartiles plotted against plateau pressure (P_plat). Values on the right side of the diagrams indicate the overall medians. Statistically significant levels are indicated by * P ≤ 0.05, † P ≤ 0.01 and ‡ P ≤ 0.001. (a) Resistance of viscoelastic model component (R_ve) as well as (b) compliance of viscoelastic model component (C_ve) differ significantly between both groups. For both parameters, a notably non-linear progression with increasing pressure was observed. (c) Time constant of viscoelastic model component (τ_ve) does not differ between the two patient groups, and it does not depend on P_plat.

Figure 5

Frequency analysis. Frequency dependence of the respiratory systems mechanical impedance. The four curves were extracted from the magnitude diagram of a Bode plot, which was obtained from the Laplace transform representing the electrical circuit model. The curves represent the impedance of the model for plateau pressures of 7.5 cmH₂O (low) and 42.5 cmH₂O (high) for both patient groups. Note that the y-axis of the diagram is scaled by 20·log, i.e. dB, while the insert is linearly scaled.