Fluid dynamic assessment of positive end-expiratory pressure in a tracheostomy tube connector during respiration

Abstract

High-flow oxygen therapy using a tracheostomy tube is a promising clinical approach to reduce the work of breathing in tracheostomized patients. Positive end-expiratory pressure (PEEP) is usually applied during oxygen inflow to improve oxygenation by preventing end-expiratory lung collapse. However, much is still unknown about the geometrical effects of PEEP, especially regarding tracheostomy tube connectors (or adapters). Quantifying the degree of end-expiratory pressure (EEP) that takes patient-specific spirometry into account would be useful in this regard, but no such framework has been established yet. Thus, a platform to assess PEEP under respiration was developed, wherein three-dimensional simulation of airflow in a tracheostomy tube connector is coupled with a lumped lung model. The numerical model successfully reflected the magnitude of EEP measured experimentally using a lung phantom. Numerical simulations were further performed to quantify the effects of geometrical parameters on PEEP, such as inlet angles and rate of stenosis in the connector. Although sharp inlet angles increased the magnitude of EEP, they cannot be expected to achieve clinically reasonable PEEP. On the other hand, geometrical constriction in the connector can potentially result in PEEP as obtained with conventional nasal cannulae.

Keywords: Computational biomechanics; Computational fluid dynamics; Lumped lung model; Positive end-expiratory pressure (PEEP); Tracheostomy tube connector.

Fig. 1

a Computational domain for 3D CFD involving a modeled connector and schematics of a lumped lung model. b 3D CFD computational model with 50% stenosis, and c generated meshes where adaptive mesh refinement and prismatic layers lining the walls are considered in addition to a polyhedral mesh. The boundary conditions of the lumped lung model were set as inlet velocity U_in, outlet pressures P_out1 and P_out2, and outlet velocity U_out3 (= U_tr (t, P_e, P_al, P_pl)). The standard inlet angle was set as θ = 60°. The inlet and outlet diameters in connectors were commonly set as D_in = 11 mm and D_out = 15.4 mm. The rate of stenosis was defined using the minimum connector diameter D_min as (1—D_min/D_in). The length of the constricted portion of each connector was set as 1 mm

Fig. 2

Flow chart for updating the Dirichlet boundary condition U_out3 in 3D CFD, where α is the coefficient for the temporal updating of U_out3 (0 ≤ α ≤ 1), ε and t_∞ are set as ε = 0.01 and t_∞ = 3 T, respectively. The simulation ends at t = t_∞ = 3 T

Fig. 3

a Snapshot of entire experimental setup and b schematic of experiment. c Time history of tracheal pressure P_tr in a normal connector (i.e., inlet angle θ = 60° without stenosis) at Q_in = 30 L/min. d A comparison of EEP obtained with experimental measurements (blank triangles) versus numerical simulations (solid triangles) as a function of inlet flow rate Q_in in a normal connector, where the errors in experimental data represent temporal fluctuations during the end-expiratory phase

Fig. 4

a Time history of the pleural pressure P_pl, calculated alveoli pressure P_al, and tracheal pressure P_tr (= P_out3), where data are shown after P_al and P_tr have reached the stable periodic phase. Snapshots of b pressure and c velocity fields in a normal connector in each respiratory phase: (left) inspiration, (middle) expiration, and (right) the end of expiration defined with U_tr = 0. Snapshots of streamlines in each phase are also displayed in c, where the color represents the velocity magnitude. The results were obtained with Q_tr = 30 L/min

Fig. 5

a Time history of the tracheal velocity U_tr and lung volume V during a period T (= 5 s) at Q_in = 30 L/min. b The tidal volume ΔV_tidal as a function of Q_in. Data were obtained after reaching stable periodic behavior

Fig. 6

EEP as a function of inlet flow rate Q_in in a normal connector for different inlet angles θ

Fig. 7

a Time histories of P_pl, P_al, and P_tr. Snapshots of b pressure and c velocity fields in each respiratory phase in a connector with 50% stenosis: (left) inspiration, (middle) expiration, and (right) end of expiration. The results were obtained with Q_tr = 30 L/min

Fig. 8

a Normalized EEP (left axis) and normalized tidal volume (right axis) by those obtained with a normal connector (0% stenosis) at Q_in = 30 L/min as a function of the degree of stenosis. b Tidal volume ΔV_tidal obtained with the connector with 50% stenosis as a function of Q_in. The results of ΔV_tidal in a normal connector, as shown in Fig. 5, is also displayed

Fig. 9

EEP for different degrees of stenosis as a function of inlet flow rate Q_in. EEP obtained with a normal connector, as shown in Fig. 6, is also displayed