Simulation of Central Airway Gas Flow Dynamics During Conventional and Multifrequency Ventilation

Abstract

Patients with acute respiratory failure often require supportive mechanical ventilation to maintain adequate gas exchange. Recent studies have shown that multifrequency ventilation (MFV), the technique of presenting multiple simultaneous frequencies in flow or pressure at the airway opening, may provide more uniform ventilation distribution and parenchymal strain throughout the mechanically heterogeneous lung. In this study, we simulated gas flow within a porcine central airway tree, from the trachea to the fifth generation, with dynamic boundary conditions (BCs) during volume-controlled conventional mechanical ventilation (CMV) cycled at 0.27 Hz (16.2 min⁻¹), as well as MFV waveforms comprised of two fast sinusoidal components (i.e., 3.5 Hz and 7.0 Hz) superimposed on the 0.27 Hz CMV waveform. By using forced gas flows at the airway opening of the computational lung model, dynamic pressures at various airway segments were predicted, based on the interactions of internal flow with the downstream elastances and peripheral resistances. Internal airflows were simulated and analyzed in both time- and frequency-domains. The results indicate that MFV resulted in stronger asymmetric flow (i.e., “pendelluft”) at end-inspiration and end-expiration. MFV also appeared to augment inlet–outlet phase differences for both pressure and flow compared with CMV, suggesting that MFV may enhance gas mixing, thus facilitating more efficient ventilation.

Introduction

When the lungs are unable to adequately perform their primary function (i.e., oxygenation and removal of carbon dioxide) due to pathophysiologic conditions resulting in acute respiratory failure, mechanical ventilation is necessary to support proper gas exchange. Such therapy may be crucial for patients whose lung function is severely impaired and unable to meet metabolic demands [1]. However, mechanical ventilation does not always guarantee the preservation of normal lung function, due to its inherent limitations. These include the risk of overdistention and volutrauma in patients with mechanically heterogeneous lungs, due to fixed frequency and tidal volume settings that limit adaptability to dynamic respiratory requirements, maldistribution of regional ventilation, and impaired gas exchange [2]. Multifrequency ventilation (MFV) originated from the principle that the superposition of fast and shallow cycling of multiple frequencies components may result in more efficient gas exchange, along with enhanced lung recruitment at lower distending pressure [3]. MFV involves the application of two or more distinct frequency components in flow or pressure simultaneously at the airway opening, which may improve gas transport and more evenly distribute mechanical stresses and strains across the parenchyma [4,5]. Accordingly, MFV has been postulated to reduce the risk for ventilator-induced lung injury [1] and thus may have clinical utility in the treatment of patients with acute respiratory distress syndrome (ARDS) or other forms of heterogeneous lung injury [3–5].

Previous studies have simulated ventilation distribution and parenchymal strain using computer lung models based on empiric flow paradigms and binary tree data structures [4–7]. However, the intricate three-dimensional (3D) internal flow dynamics within the airway tree were inaccessible using these approaches. Computational fluid dynamics (CFD) provides an effective means to model and simulate gas flow behavior comprehensively during MFV, using numerical approaches for solving the governing equations of fluid flow. Thus, CFD has emerged as a powerful tool for studying and understanding the complex airflow patterns, particle deposition, and gas exchange mechanisms within the human respiratory system [8–13]. In the medical field specifically, CFD has been employed to investigate respiratory disorders such as asthma [14,15], chronic obstructive pulmonary disease [16,17], and obstructive sleep apnea [18–20]. These studies have provided insights into the underlying mechanisms, assisting in the development of targeted treatment strategies, and optimization of inhaled drug delivery [21].

One of the challenges of CFD simulation is the application of realistic physiological boundary condition (BC) for the specific study objective [22]. Simplified boundary conditions for exits have been adopted to compute the internal flows within airway trees that include uniform pressure [23], piston motion [24], and uniform velocity [25]. A major drawback of simplified outlet boundary conditions is that they often fail to produce physiologically consistent results. Another commonly used boundary condition for CFD is patient-specific imaging data that enables personalized simulations, facilitating the analysis of individualized respiratory conditions and treatment planning [26–30]. Computational models prescribed by a 3D airway tree coupled to 3D parenchymal structures can provide a precise flow distribution and tissue deformation [31], but the modeling and computing processes are considered expensive and time-consuming. Coupling a 3D airway tree with lumped-parameter models (i.e., zero-dimensional models)—commonly referred to as the 3D–0D approach—integrates detailed spatial resolution of airflow in the central airways, with the computational efficiency and physiological relevance of simplified peripheral lung modeling. Such coupling enables accurate, yet efficient, simulation of respiratory mechanics [32].

In this study, we hypothesized that the addition of high frequency oscillations to a conventional mechanical ventilation (CMV) waveform would be beneficial for comprehensive gas mixing, given the enhanced resistive force and inertial force in primary airway segments during the fast oscillations in MFV. The CFD simulations were conducted for CMV and MFV scenarios, with physiologically realistic boundary conditions set at the outlets of the central airways. The dynamic outlet boundary conditions in our model utilize distinct lobar volume differences based on anatomic size, with outlet pressures induced by downstream elastic and resistive elements. This approach provides an effective and efficient way to build up realistic exit boundary conditions for investigating flow phenomena within upper or central lung airways of the mammalian respiratory system. Flow phenomena within the airway tree were assessed and compared in both time- and frequency-domains. We found that nonlinear interactions between lower and higher frequency components may indicate more efficient gas mixing during MFV. The numerical scheme adopted in this study may offer an alternative approach for investigating flow phenomena within the central lung airways of the lung, with reasonable computational expense. Portions of this work were presented as a poster at the 2024 Summer Biomechanics, Bioengineering, and Biotransport Conference in Lake Geneva, WI, Abstract No. P102 [33].

Methods

Experimental Protocol.

A 3D airway tree was obtained from the segmentation of a thoracic image of an intubated, healthy porcine subject (56 kg), following induction of general anesthesia with neuromuscular blockade, as part of another ongoing study. The experiment was approved by the University of Iowa Animal Care and Use Committee to ensure humane treatment of animals (Protocol 1022371, approved May 17, 2021) and conformed to the ARRIVE guidelines. Mechanical ventilation was maintained in the animal using our previously reported hybrid oscillatory ventilator [34], using both the CMV and MFV modalities. The CMV waveform consisted of a constant flow rate of about 0.4 L s⁻¹ during inspiration with passive exhalation, with a tidal volume of 0.47 L cycled at 16.2 min⁻¹ (Fig. 1(a)). The MFV waveform combined the base CMV waveform with two sinusoidal components at frequencies of 3.5 Hz and 7 Hz (Fig. 1(b)). Airway flow was measured with a screen pneumotachograph (Hans Rudolph 3700 A, Kansas City, MO), coupled to a differential pressure transducer (Honeywell SSCDRRN002NDAA5, Golden Valley, MN). An esophageal balloon catheter (CooperSurgical, Inc., Trumbull, CT) was placed in the lower third of the esophagus. Airway and esophageal pressures were measured with separate differential pressure transducers (Honeywell SSCDRNN160MDAA5, Golden Valley, MN), and transpulmonary pressure was approximated as their difference. Airway flow, airway pressure, and esophageal pressure during CMV and MFV were low-pass filtered at 40 Hz (Frequency Devices, 8-pole Butterworth 858L8B-2, Ottawa, IL) and simultaneously sampled at 800 Hz by an A/D converter (National Instruments, USB-6003, Austin, TX). The measured airflow waveforms were later adjusted and imposed on the airway inlet as boundary condition for the simulations.

Fig. 1.

The two flow waveforms applied at the trachea (inlet) for CMV (a) and MFV (b) simulations

Model Development.

An X-ray computed tomographic image of the thorax was obtained during a static breath hold at 30 cmH₂O (Siemens SOMATOM Force, Erlangen, Germany). The airway tree was then manually segmented from the acquired 3D image using 3d slicer (version 5.6.2, Boston, MA) and truncated from the proximal third of the trachea (to exclude the endotracheal tube) to up to half of the fifth-generation airway segments (Fig. 2). All airway segments were truncated to retain as much length as possible to allow the internal flow to reach a fully developed state. The resulting airway tree consisted of 23 peripheral outlets. Each outlet was assigned to one of six lobes: left cranial, left caudal, right cranial, right middle, right accessory, and right caudal [35]. The outlet-lobe correspondence is shown in Fig. 2.

Fig. 2.

The truncated geometry based on the segmented geometry of the porcine airway tree for CFD simulation with outlet orders and dashed colored ellipses for symbolic lobe locations (outlet-lobe correspondence: 1, 2—right cranial; 3, 4—right middle; 5—right accessory; 6, 7, 8, 9, 10, 11, 12, 13—right caudal; 14, 15, 16—left cranial; and 17, 18, 19, 20, 21, 22, 23—left caudal) (Color version online)

Boundary Conditions.

Before applying the CMV and MFV flow waveforms to the CFD simulation, they were adjusted to zero-mean flow by offsetting the positive and negative flow volumes. The CMV and MFV waveforms were then imposed in sequence as boundary conditions at the trachea inlet of the CFD model, assuming a uniform flow profile. In the simulation, dynamic pressure variations at each of the 23 outlets of the airway segments were induced by the effects of downstream parenchymal tissue elastances (E_d) and peripheral resistance (R_d) and were applied as boundary conditions. Their values were determined by subtracting tissue elastance (E) and tissue resistance (R) of the truncated model from the values of total parenchymal tissue elastance (E_total) and total tissue resistance (R_total). Specifically, E_d = E_total − E and R_d = R_total − R. Because the truncated model was treated as nonelastic, the downstream parenchymal tissue elastances accounted for the total lung tissue elastance (E_total), i.e., E = 0 or E_d = E_total. The value of E_total was determined to be 14.93 cmH₂O L⁻¹, based on the linear regression on the sampled airway flow and transpulmonary pressure waveforms from the animal experiment [36], and R_total represents both peripheral airway resistance and total lung tissue resistance [37]. The value for R_total was approximated based on the structural damping hypothesis of Fredberg and Stamenovic [38], which assumes that energy dissipation and energy storage within the lung tissue are coupled within its stress-bearing elements

$$R_{\text{total}}=\eta \hspace{0.17em}\frac{E_{\text{total}}}{2\pi \hspace{0.17em}f}$$ (1)

where $\eta$ denotes the lung tissue hysteresivity, and f denotes the fundamental ventilation frequency in Hz. For both the CMV and MFV waveforms, f was assumed to be 0.27 Hz, while η was empirically set to a value of 0.19, based on previously reported values in the literature [38–40]. The resultant $R_{\text{total}}$ was therefore assumed to be 1.67 cmH₂O s L⁻¹ for both the CMV and MFV waveforms.

With a specific flow waveform at the inlet and zero pressure at outlets, CFD calculations were implemented. The resulting flow and volume at the inlet were then obtained as inputs for the multiple linear regression (inverse model algorithm) [36,41] that yielded resistance R of 0.26 cmH₂O s L⁻¹ and inertance I of 0.01 cmH₂O s² L⁻¹ for the CMV, and resistance R of 0.51 cmH₂O s L⁻¹ with the same inertance I for the MFV. The resultant downstream tissue elastance (E_d) and resistance (R_d) were 14.93 cmH₂O L⁻¹ and 1.41 cmH₂O s L⁻¹ for the CMV, and 14.93 cmH₂O L⁻¹ and 1.16 cmH₂O s L⁻¹ for the MFV, respectively. The contribution of resultant downstream gas inertia was neglected, due to its negligible value in the lung periphery over this frequency range (i.e., less than 10 Hz).

The global downstream properties E_d and R_d values were then partitioned across the six lobes, based on their relative lobar volume percentages, determined by the average of their end-inspiratory and end-expiratory volumes as reported by Gallifant et al. [42] (Table 1). Hughes et al. demonstrated an approximate linear relationship between airway diameter and cube root of lung volume [43], which was used to further distribute the lobar elastance $E_{\text{dlobe}}\hspace{0.17em}$and lobar resistance $R_{\text{dlobe}}$, defined by Eqs. (2) and (3) down to each outlet at a specific lobe, respectively,

$${E_{\text{dlobe}}\left(i\right)=E}_{\mathrm{d}}/\left(V_{\text{lobe}}\left(i\right)/V_{\text{total}}\right)$$ (2)

$${R_{\text{dlobe}}\left(i\right)=R}_{\mathrm{d}}/\left(V_{\text{lobe}}\left(i\right)/V_{\text{total}}\right)$$ (3)

Table 1.

Lung and lobar volume percentages for a pig in supine position [42]

	Percentage of total lung volume (%)
Total lung	100
Right lung	62.30
Right cranial lobe	15.71
Right caudal lobe	17.93
Right accessory lobe	7.31
Right middle lobe	22.01
Left lung	37.70
Left cranial lobe	17.59
Left caudal lobe	19.45

where $E_{\text{dlobe}}\left(i\right)$, $R_{\text{dlobe}}\left(i\right)$, and $V_{\text{lobe}}\left(i\right)$ denote the downstream lobar elastance, downstream lobar resistance, and lobar volume, respectively, at the $i\hspace{0.17em}$th outlet, and $V_{\text{total}}$ indicates the total lung volume. Equations (2) and (3) describe how the global downstream elastance and peripheral resistance are distributed among the six lobes based on each lobe's volume as a percentage of the total lung volume. Elastance is inversely related to compliance, which generally scales with volume—a larger lobe tends to be more compliant, thus contributing less to overall elastance. Similarly, peripheral airway and tissue resistances tend to decrease with increasing volume, meaning larger lobes generally offer less resistance to flow compared to smaller lobes, assuming similar levels of strain stiffening [40,44]. Such approximations are reasonable for healthy lungs or simplified lung models [41], although they neglect the impact of mechanical heterogeneity in the airways or parenchymal tissues [45]. Given the definition of lobar lung elastance in Eq. (2) and lobar resistance in Eq. (3), the elastances and resistances subtending each airway outlet were then further defined as

$$E_{\mathrm{d}}\left(i\right)=E_{\text{dlobe}}\left(i\right)/({A\left(i\right)}^{3/2}/{\sum }_{j=1}^{n\left(i\right)}{A\left(j\right)}^{3/2})$$ (4)

$$R_{\mathrm{d}}\left(i\right)=R_{\text{dlobe}}\left(i\right)/({A\left(i\right)}^{3/2}/{\sum }_{j=1}^{n\left(i\right)}{A\left(j\right)}^{3/2})$$ (5)

where $A\left(i\right)$ indicates the area of cross section of the $i\hspace{0.17em}$th outlet and $n\left(i\right)\hspace{0.17em}$denotes the number of outlets within the lobe of the $i\hspace{0.17em}$th outlet, with j varying from 1 to $n\left(i\right).\hspace{0.17em}$Equations (4) and (5) thus assume that within-lobe volumes subtending each outlet scale according to airway diameter [43].

The CFD simulation was performed with the pressure boundary conditions contributed by $E_{\mathrm{d}}\left(i\right)$ and $R_{\mathrm{d}}\left(i\right)$ at each outlet, along with the corresponding inlet boundary condition. With the flow value ( $\dot{V}(i,\hspace{0.17em}t)$) provided from each outlet by the solver at every time-step, the dynamic boundary condition at each outlet is

$$P\left(i,\hspace{0.17em}t\right)=E_{\mathrm{d}}\left(i\right){\int }_0^{t_0}\dot{V}(i,\hspace{0.17em}t)\hspace{0.17em}dt+R_{\mathrm{d}}\left(i\right)\hspace{0.17em}\dot{V}(i,\hspace{0.17em}t)$$ (6)

where $t$ represents virtual time, and ${\hspace{0.17em}t}_0$ denotes total simulated time. Note that Eq. (6) assumes any positive end-expiratory pressure (i.e., prestress) is negligible during these simulations.

Computational Fluid Dynamics Schemes.

The governing equations for the gas flow are continuity equation

$$\nabla ·\mathbf{\text{u}}\hspace{0.17em}=0$$ (7)

and the 3D Navier–Stokes equation

$$\frac{\partial \mathbf{\text{u}}}{\partial t}+(\mathbf{\text{u}}·\nabla )\mathbf{\text{u}}=-\frac{1}{\rho }\nabla P+n\left({\nabla }^2\mathbf{\text{u}}\right)$$ (8)

where $\nabla$ is the vector differential operator, $\mathbf{\text{u}}$ denotes the flow velocity vector, and $P$, $\rho$, and $\nu$ denote pressure, fluid density, and kinematic viscosity, respectively. The value of $\rho$ was set at 1.225 kg m⁻³, while the value of $\nu$ was set at 1.48 × 10⁻⁵ m² s⁻¹.

The flow field was discretized using nearly 3.5 × 10⁶ tetrahedral cells, with five incremental sublayers near the sidewall, at an incremental ratio of 1.2, and the thickness of the first sublayer was set at 0.1 mm. Figure 3 shows a close-up magnification of the grids at the smallest outlet (i.e., outlet 10). The mesh sensitivity was confirmed by comparing the pressure and flow variations in the models using 1.5 × 10⁶ to 5.4 × 10⁶ tetrahedral grids, with a grid increment of approximately 1 × 10⁶. The mesh with 3.5 × 10⁶ tetrahedral grids provided stable computational iterations, and the results differed from those of the 5.4 × 10⁶ tetrahedral grids by less than 1%. The turbulence was modeled using the Navier–Stokes equations incorporating the k–ω shear-stress transport model. The governing equations were solved by employing the pressure-implicit with splitting of operators algorithm, with a time-step size of 0.5 ms for convergence sensitivity of the dynamic boundary condition at the outlets. The airway wall was assumed to be rigid, with a no-slip boundary condition. Numerical computations were carried out using a commercial solver (ansys/fluent 2023 R2), with dynamic pressure boundary conditions implemented in the c programing language that were compiled by the built-in compiler of ansys/fluent. Due to the small time-step required to capture the dynamics at end-inspiration and end-expiration, each ventilation case took nearly 40 h to compute on a standard local computer. However, this computation time could be significantly reduced through parallel processing or high-performance computing. The computational specifications for the simulations are listed in Table 2.

Fig. 3.

A close-up magnification of the grids at outlet 10, with a hydraulic diameter of 1.56 mm

Table 2.

Specifications of the CFD computations

Settings	Specifications
Analysis type	Transient flow
Turbulent model	k–ω shear-stress transport
Algorithm for pressure–velocity	Pressure-implicit with splitting of operators
Wall condition	No-slip
Inlet BC	Forced flow
Outlet BC	Dynamic pressure BC
Mesh type	Tetrahedral
Mesh number	3.5 × 106
Mesh sublayers	5 with increment ratio of 1.2
Time-step	5 × 10−4 s
Simulation time	11.11 s (22,222 time-steps)
Solver	ansys/fluent 2023 R2
CPU	Intel(R) Core(TM) i7-4770 3.4 GHz
Number of cores	6
Memory	8 GB
Calculation time per case	∼40 h

Data Analysis Methodology.

Three breaths were simulated for each scenario, with no notable differences observed among them. Therefore, the results from the second breath were selected as representative examples. Upon completion of the CFD computation, pressure variations were recorded for both CMV and MFV simulations. The elastic pressure component was determined by multiplying the downstream elastance by the accumulated flow (volume), while the resistive pressure component was calculated by multiplying the resistance by the flow at each inlet and outlet. At peak inhalation and peak exhalation of the second breath cycle, shear stress on the airway wall, velocity vectors, and turbulence kinetic energy (TKE) were recorded across the model. At end-inspiration and end-expiration of the second breath cycle (the terms “end-inspiration” and “end-expiration” here refer to the instants when the flow at inlet reaches zero following the inspiration and expiration, separately), flow streamlines within the model were recorded to visualize the “out-of-phase” flow (i.e., pendelluft). The resultant pressure and flow across the inlet and all outlets were analyzed in the frequency-domain using the discrete Fourier transform (DFT), with a window length of 22,222 data points, corresponding to three breath cycles at 0.27 Hz, and a frequency resolution of 2 kHz, in accordance with the CFD solving time-step.

Results

Since this model did not include the regulated intrapleural pressures provided by the chest wall, diaphragm, and the other surrounding bodily structures, the resultant airway pressures approximated transpulmonary pressure. Figure 4(a) shows the variation of airway pressure at one of the outlets (outlet 21) over the second CMV breath cycle. Because of the similarity in pressure variations across all outlets and the inlet, only the result at one outlet is shown. Downstream elastic pressure dominated the total outlet pressure, peaking at about 7 cmH₂O for all the 23 outlets. Resistive pressure varied between −1.7 cmH₂O and 1.1 cmH₂O, leading the elastic pressure by 90 deg.

Fig. 4.

Pressure variation (black, marked as “P_total”) and its components (blue—elastic, marked as “P_elastic”; red—resistive, marked as “P_resistive”) at outlet 21 during CMV (a) and MFV (b) for the second breath (Color version online)

During MFV, the peak pressure at the outlet was slightly over 6 cmH₂O, which was predominately comprised of elastic and resistive components (Fig. 4(b)). The resistive pressure variation during MFV was more augmented compared to CMV, due to high flow rates associated with the higher frequency oscillations at 3.5 Hz and 7 Hz. A 90 deg phase difference between the elastic and the resistive pressures was also observed. The outlet pressures were roughly 1–2 cmH₂O lower than the inlet pressure, due to the resistive and inertial pressure drops across the airway tree.

Figure 5 depicts the sidewall shear stress at peak inspiration and expiration during the second breath cycle of the CMV and MFV modalities, which were induced by the near-wall flow rate and gas viscosity. MFV resulted in greater peak shear stress compared to CMV, due to greater flow rates at peak inspiration and peak expiration. The bifurcating region of the airway wall endured the highest shear stress at peak inspiration and the lowest at peak expiration. Figure 6 shows 3D rendering of velocity field, with velocity vectors on the 45 cross sections across the model at peak inspiration and peak expiration of the second breath cycle for CMV and MFV. MFV generated considerably greater peak flow velocities on the cross sections compared to CMV due to its greater transient flow rate. Figure 7 demonstrates the TKE across the cross sections at peak inspiration and peak expiration for both CMV and MFV. The TKE varies between the values at peak inspiration and expiration within a respiratory cycle. The intensity of turbulence in MFV was significantly higher than in CMV, indicating that considerably more turbulent eddies and chaotic fluctuations were produced during MFV.

Fig. 5.

Shear stress on the airway wall at four different instants during the second breath: (a) peak inspiration of CMV; (b) end-inspiration of CMV; (c) peak inspiration of MFV; and (d) end-expiration of MFV (Color version online)

Fig. 6.

Three dimensional rendering of velocity field with velocity vectors on 45 cross-sectional planes at four different instants during the second breath: (a) peak inspiration of CMV; (b) end-inspiration of CMV; (c) peak inspiration of MFV; and (d) end-expiration of MFV. (The velocity magnitude is represented by color.) (Color version online.)

Fig. 7.

Contour of turbulence kinetic energy on the 45 cross-sectional planes at four different instants during the second breath: (a) peak inspiration of CMV; (b) end-inspiration of CMV; (c) peak inspiration of MFV; and (d) end-expiration of MFV (Color version online)

One of the central objectives of this study was to investigate out-of-phase flow, or pendelluft. This phenomenon is best examined at two key temporal instants of MFV: end-inspiration and end-expiration, when the inlet (tracheal) flow rate approaches zero. At these moments, interregional flow within the lung can primarily be attributed to phase differences, which can be effectively visualized using streamlines, as they represent the instantaneous flow direction at a given time. Figure 8 demonstrates streamlines at both end-inspiration and end-expiration during CMV in the second breath cycle. CMV induced weak pendelluft at end-inspiration and minimal pendelluft at end-expiration, which may also be assessed by the velocity magnitude along the streamlines. Figures 9 and 10 demonstrate streamlines at end-inspiration and end-expiration, respectively, during MFV in the second breath cycle, with local magnification by velocity vectors at several locations. By comparing with CMV, MFV induced strong pendelluft that occurred at multiple locations, especially between right cranial lobe and the trachea (marked as ① in Figs. 9 and 10), among right middle, right accessory, and right caudal lobes (marked as ② in Figs. 9 and 10), between left cranial and left caudal lobes (marked as ③ in Figs. 9 and 10). Furthermore, the direction of pendelluft at end-inspiration was roughly opposite to those at end-expiration. Figures 8–10 give intuitive views on how much the flow phases differed each other at different lung regions during shifts between inspiration and expiration. The considerably stronger pendelluft in MFV implies more energy transfer among different frequency components and more effective gas mixing within the lung airway tree.

Fig. 8.

Flow streamlines within the airway tree at end-inspiration (a) and end-inspiration (b)during CMV, with colors representing velocity magnitudes (Color version online)

Fig. 9.

Flow streamlines within the airway tree at end-inspiration during MFV, with colors representing velocity values. Three regions exhibiting strong pendelluft are marked as ①, ②, and ③, and are magnified on the right side with velocity vectors (Color version online).

Fig. 10.

Flow streamlines within the airway tree at end-expiration during MFV, with colors representing velocity values. Three regions exhibiting strong pendelluft are marked as ①, ②, and ③, and are magnified on the right side with velocity vectors (Color version online).

To quantify further the effects of pendelluft during CMV and MFV, the pressure and flow across the inlet and all outlets were analyzed in frequency-domain. Figure 11 demonstrates the pressure and flow magnitude spectra at the inlet and a representative outlet (outlet 17) for both CMV and MFV in magnitude. For these calculations, the pressure and flow at the inlet and all outlets were recorded, then converted to their frequency-domain equivalents using the DFT to quantify magnitude in both flow and pressure. During CMV, both flow and pressure magnitudes peaked at 0.27 Hz, with attenuating harmonics as frequency increased (Figs. 11(a) and 11(b)). Figures 11(c) and 11(d) show the pressure and flow magnitude spectra at the inlet and outlet 17 during MFV, with both spectra demonstrating expected peaks at 0.27 Hz, 3.5 Hz, and 7 Hz.

Fig. 11.

Variation of pressure and flow magnitudes at the inlet and a representative outlet (outlet 17) in frequency-domain: (a) pressure magnitudes during CMV; (b) flow magnitudes during CMV; (c) pressure magnitudes during MFV; and (d) flow magnitudes during MFV (Color version online)

To quantify the inlet–outlet phase differences in pressure and flow during MFV, the high frequency 3.5 Hz and 7 Hz components were extracted from the MFV waveform using the DFT. The magnitude of these two individual oscillatory components (i.e., single frequency oscillatory ventilation, or SFOV) was determined by the distribution of volume (integrated by flow at trachea) in frequency-domain at 3.5 Hz and 7 Hz, then applied separately to the inlet of the CFD model as the input flow boundary condition, while the boundary conditions for the outlets remained unchanged. The computational results of pressure and flow at inlet and outlets were compared to the phase distributions at the same frequencies during MFV, aiming at quantifying the contribution to the phases of the high frequency components and the interactions between them and the base ventilation frequency (i.e., 0.27 Hz).

Figure 12 demonstrates inlet–outlet pressure phase differences and flow phase differences during CMV, 3.5 Hz-only SFOV, 7 Hz-only SFOV, and MFV at the corresponding three frequencies. Figures 12(a) and 12(b) show that, in both pressure and flow, considerably greater phase differences between inlet and outlets occurred during MFV at 0.27 Hz, comparing to the ones during CMV. It suggests that the inlet–outlet phase differences at 0.27 Hz during MFV were augmented, which indicates that the base 0.27 Hz component was considerably influenced by the 3.5 Hz and/or 7 Hz components, possibly through nonlinear mechanisms of the gas flow and the interaction between the internal gas and the airway wall. In addition, the augmentation of phase differences at the low frequency may cause more asymmetrical flow patterns, thus enhancing gas mixing and ventilation efficiency. By contrast, the inlet–outlet phase differences in pressure and flow during the 3.5 Hz-only SFOV were comparable to those observed during MFV at 3.5 Hz across all outlets, with neither condition showing a consistent overall dominance (Figs. 12(c) and 12(d)). However, the inlet–outlet phase differences in pressure and flow during the 7 Hz-only SFOV were clearly greater than those during MFV at the corresponding frequency, as shown in Figs. 12(e) and 12(f). This suggests that the 7 Hz component had significant influence on the base 0.27 Hz component during MFV. Alternatively, the kinetic energy was transferred from the 7 Hz component to the base 0.27 Hz component, contributing to the increase in inlet–outlet pressure and flow differences at 0.27 Hz. Such a nonlinear mechanism may be a contributing factor to the enhanced out-of-phase flow at the base frequency during MFV, which may benefit gas mixing during mechanical ventilation.

Fig. 12.

Inlet–outlet phase differences in flow rate and pressure during CMV, 3.5 Hz-only SFOV, 7 Hz-only SFOV, and MFV at the three corresponding frequencies with outlet numbers: (a) inlet–outlet phase differences in flow rate during CMV and MFV at 0.27 Hz; (b) inlet–outlet phase differences in pressure during CMV and MFV at 0.27 Hz; (c) inlet–outlet phase differences in flow rate during 3.5 Hz only oscillation and MFV at 3.5 Hz; (d) inlet–outlet phase differences inpressure during 3.5 Hz only oscillation and MFV at 3.5 Hz; (e) inlet–outlet phase differences in flow rate during 7 Hz only oscillation and MFV at 7 Hz; and (f) inlet–outlet phase differences in pressure during 7 Hz only oscillation and MFV at 7 Hz (Color version online)

Discussion

Multifrequency ventilation has been proposed as a new ventilatory modality that may provide more uniform ventilation throughout a lung with asymmetric airway branching and/or heterogeneous mechanical properties [3,5,6,46,47]. The goal of MFV is to optimize gas exchange in ARDS and other forms of lung injury, while simultaneously preserving mechanical protection of the lung. The rationale for its use assumes that lung function and gas exchange can be improved, if multiple frequencies are applied to the airway simultaneously, due to more even distribution of ventilation to mechanically disparate lung regions. Accordingly, airflow phenomena within the airways during MFV are of significant interest, for a better understanding of the mechanical properties and effectiveness of MFV. CFD plays a crucial role in quantifying such airflow phenomena during MFV, by providing a detailed understanding of fluid dynamics within the healthy or diseased respiratory system. The dynamic outlet boundary condition employed in this study entails lobar volume differences, downstream elastance and resistance that were acquired by inverse model regression [36], which provides an effective and efficient way to build up realistic exit boundary condition for investigation of flow phenomena within upper or central lung airways.

Our computational results in Fig. 4 show that lung tissue elastance dominates airway outlet pressure during CMV. By contrast, the airway resistive pressure component becomes more significant during MFV due to the faster oscillatory components. Despite the significantly higher peak flow in MFV compared to CMV, the peak pressure in MFV is lower, suggesting that MFV may be less likely to cause ventilator-induced lung injury. This is particularly important for patients with compromised lung function, as it could contribute to improved patient comfort.

Multifrequency ventilation generates significantly higher shear stress on the lung wall at the moments of peak inspiration and peak expiration, as shown in Fig. 5, which could suggest that MFV might promote more dynamic movement of the lung tissue compared to CMV, potentially helping with the clearance of mucus and improving ventilation in certain areas of the lungs. This may be beneficial in patients with conditions like ARDS or chronic obstructive pulmonary disease, where mucus clearance and alveolar ventilation are compromised. The increased shear stress would need to be carefully monitored, especially in patients with vulnerable lung tissues or acute lung injury. While MFV offers advantages in terms of lower peak pressures, the higher shear stress may require more careful patient selection and adjustment of ventilation parameters to avoid over-stressing the lung tissues.

Multifrequency ventilation causes higher TKE throughout the lung compared to CMV, as illustrated in Fig. 7. Higher TKE generally indicates more turbulent flow, which can lead to better mixing of gas within the lung. This can be advantageous in improving the distribution of inhaled air, especially in areas of the lung that are poorly ventilated or have irregular airflow, such as in patients with obstructive lung diseases or atelectasis. The improved mixing can help ensure more homogeneous ventilation across the lung, potentially improving gas exchange.

Additionally, a comparison between Fig. 8 with Figs. 9 and 10 indicates that more pendelluft occurs in the airways at end-inspiration and end-expiration during MFV, potentially enhancing gas mixing. In the context of mechanical ventilation, pendelluft refers to a rhythmic, bidirectional flow of gas between lung regions due to pressure differences during ventilation [48]. It helps promote gas exchange and prevent lung collapse by improving ventilation distribution in the lungs, particularly in patients with respiratory distress. Examining the behavior of steady streaming could provide valuable insights and help further elucidate the time-averaged flow characteristics during MFV, which is not addressed in the current study. The phase shifts revealed by Fig. 12 imply that enhanced pendelluft in MFV relies on the high-frequency components of the waveform, as well as nonlinear interactions among flow components at different frequencies (i.e., the interaction between the highest frequency component and the lowest frequency component). The kinetic energy shift from high frequencies to low frequencies in a nonlinear system may account for this phenomenon. Phase differences in either pressure or flow across different lung regions are known to occur during high-frequency ventilation [7], especially in the mechanically heterogeneous lung (e.g., ARDS or other forms of acute lung injury). While in MFV, the phase differences may be more complicated due to contributions and mutual interactions among flow components with different frequencies.

Limitations

Although the results of this study revealed basic characteristics of airflow in the central airways during CMV and MFV, there are several limitations of our numerical approach with respect to computation efficiency and lack of additional physiologic fidelity. First, the central airway walls were assumed to be rigid, and our simulations do not account for flow losses due to wall deformation [49,50]. However, airway wall deformation in the central airway tree is generally less than that within peripheral airways [51]. Second, the fluid medium in these internal gas flows was assumed to be incompressible, which may also impact the validity of our results during high pressure variations and flow velocities [50]. However, since the pressure and flow were relatively low in the simulation scenarios, the lack of gas compressibility may have negligibly influenced the generalizability of our interpretation of the results. Third, downstream elastances were simplified as constant values across all 3D airway outlets during ventilation, which does not account for potential volume- or frequency-dependent variations due to nonlinear tissue mechanics or surface tension effects, such as those influenced by surfactant dynamics [52]. Fourth, our approach did not include the chest wall or its mechanical interaction with airway flow and thus lacks some additional fidelity with in vivo porcine lungs. Also in our simulations, the flow during the entire ventilatory cycle was forced at the trachea, which is different from the passive exhalation due to the recoil of the lungs and chest wall during mechanical ventilation. However, since the forced exhalation of our simulations was obtained from the actual in vivo ventilator waveform data for this specific pig, we believe that it would have minimal effect on the internal flow patterns. Fifth, the assumptions regarding the distributions of peripheral resistances are elastances across and within lobes (i.e., Eqs. (2)–(5)) have not been validated, although such approximations may be reasonable for establishing outlet boundary conditions for the segmented 3D airway tree [53]. Finally, the effects of endotracheal tube were neglected in our simulations and thus ignored additional nonlinear flow dynamics that may occur due to increased resistance and inertance of the tube [54].

Conclusions

In this study, we simulated gas flow in a computational model of the porcine lung, consisting of a central airway tree segmented from a 3D volumetric computed tomographic image, along with dynamic peripheral boundary conditions. Simulated flow waveforms at the trachea included a CMV cycled at 0.27 Hz, and a MFV consisting of low-amplitude 3.5 Hz and 7.0 Hz sinusoidal components superimposed on the 0.27 Hz CMV component. Dynamic pressures at various airway segments were predicted based on the interactions of internal flows with downstream elastances and peripheral resistances. The resulting internal airflows were simulated and analyzed in both time- and frequency-domains. Our simulations indicate that compared to CMV, MFV results in stronger flow asymmetry at end-inspiration and end-expiration (i.e., pendelluft), as well as larger phase differences between the inlet and outlets for both pressure and flow at low frequencies. Our results are consistent with the notion that MFV has potential to enhance gas mixing, thus facilitating the efficiency of ventilation in the mammalian lung. Moreover, our simulations offer an effective methodology to reveal flow phenomena for specific airway regions across various mechanical ventilation modalities. These results also highlight the importance of applying realistic boundary conditions to such numerical airflow simulations.

Funding Data

• Office of the Assistant Secretary of Defense for Health Affairs, through the Peer Reviewed Medical Research Program (Award No. W81XWH-21-1-0507; Funder ID: 10.13039/100000090).

• Army Research Office Program (Award No. W911NF-23-1-0004; Funder ID: 10.13039/100000183).

• NIH (No. T32 HL144461; Funder ID: 10.13039/100000050).

Data Availability Statement

The datasets generated and supporting the findings of this article are obtainable from the corresponding author upon reasonable request.