Lung heterogeneity and deadspace volume in animals with acute respiratory distress syndrome using the inspired sinewave test

Abbreviations

ARDS	Acute respiratory distress syndrome
ELV	Effective lung volume measured by the IST (l)
fp,i	Perfusion fraction to the lung compartment i
fv,i	Ventilation fraction to the lung compartment i
Q$_{\textrm{p}}$	Blood flow measured by the IST (l min–1)
VT	Tidal volume (ml)
VA	Alveolar lung volume (l)
VDIST	Deadspace volume measured by the IST (ml)
$VD_{SF_{_{6}}}$	Deadspace volume measured by the SF6 (ml)
PEEP	Positive end-expiratory pressure
$\dot{V}$	Ventilation (l min–1)
$\dot{Q}$	Perfusion (l min–1)

Acute respiratory distress syndrome (ARDS) is characterized by pulmonary inflammation and carries significant morbidity and mortality (Summers et al 2016). The prognosis of ARDS has improved within the past decades, with in-hospital mortality rates decreasing from 90% in the 1970s to approximately 30% in a recent study (de Prost et al 2011). Guidelines for mechanical ventilation have probably contributed to this result by reducing ventilator-induced lung injury. The mainstay of ventilator treatment is a reduction in tidal volume (V_T ) and inspiratory and driving pressures, thereby reducing the stress and strain applied to the lungs. But there is currently no conclusive way to determine optimal ventilation for an individual patient at the bedside.

In ARDS the lung is mechanically very heterogeneous, causing heterogeneous and harmful ventilation. However, if lung mechanics could be homogenized [such as by positive end-expiratory pressure ( PEEP) titration and lung recruitment], the result could be more homogeneous, and thus less harmful, lung ventilation. Lung heterogeneity is the unequal distribution of airflow (ventilation) relative to the size of the lung regions to which it is distributed or to gas exchange to the bloodstream (perfusion) (West 2012). There are no simple methods that can be used at the bedside to evaluate lung heterogeneity or to quantify the effect of different manoeuvres and ventilator settings on lung homogeneity (Stahr et al 2016, Mountain et al 2018). The measurement of lung homogeneity could potentially benefit ventilated patients.

The inspired sinewave test (IST) was introduced as a non-invasive test which requires no cooperation from patients being tested and does not involve ionizing radiation. The IST applies a forced oscillation of a low dose of N₂O tracer gas with a sinusoidal period which can be determined by the user. The results of the IST provide lung function parameters including deadspace volume (VD), effective lung volume (ELV) and pulmonary blood flow (Q_p ) (Phan et al 2017b, Crockett et al 2019, Bruce et al 2018, Hahn and Farmery 2003, Clifton et al 2013). The IST results, including VD and ELV, provide suggestions for optimizing the ventilator setting. Furthermore, it is proposed that by using two tracer gas frequencies, the IST can quantify the ventilatory heterogeneity of the lung. In a previous study, the IST in combination with data from another lung function test (plethysmography) was able to detect changes in ventilatory heterogeneity which occur normally with age in healthy participants (Bruce et al 2018). In other research in simulated patients, the IST showed the potential to identify that simulated patients had emphysema (ventilation heterogeneity) and pulmonary embolism (perfusion heterogeneity) (Tran et al 2020). There is thus the possibility of developing the IST such that lung heterogeneity could be determined solely from the IST data without recourse to other techniques.

We therefore developed a model to quantify the degree of lung heterogeneity using the IST. We then performed experiments in anaesthetized piglets using only the heterogeneity obtained using the IST. The experiments included measurements before and after the lung was damaged by following the saline lavage protocol (ARDS model). We also compared the absolute VD measured by the IST with that obtained by SF₆ washout.

2.1. Measurement protocol

2.2. Inspired sinewave test heterogeneity indices

In the IST analysis the VD inside the lung, VD_IST, was first measured using the modified Bohr method (Phan et al 2017a). Secondly, ELV and Q_p were calculated from a model assuming one well-mixed lung compartment (Bruce et al 2018).

Theory dictates that in a completely homogeneously ventilated and perfused lung, the values of ELV and Q_p recovered from the IST are independent of the tracer gas period used. The IST accuracies of ELV and Q_p values are published elsewhere (Bruce et al 2019, Crockett et al 2020). However, as the degree of heterogeneity increases, the ELV and Q_p values (based on the assumption of perfect homogeneity) begin to diverge from true values; moreover, those values recovered from periods of 60 s and 180 s also diverge from each other. Consequently, the ratio of these latter values provides an index of the degree of heterogeneity. The IST ventilatory and perfusion heterogeneity ratio of the lung are given by the following expressions:

$$\begin{equation} \textrm{IST}_{\textrm{Vent-Heterogeneity}} = \frac{\textrm{ELV}_{180\ \mathrm{s}}}{\textrm{ELV}_{60\ \mathrm{s}}} \end{equation} \tag{ 1 }$$

$$\begin{equation} \textrm{IST}_{\textrm{Perf-Heterogeneity}} = \frac{{Q}_{p60\ \mathrm{s}}}{{Q}_{p180\ \mathrm{s}}} \end{equation} \tag{ 2 }$$

where $\textrm{ELV}_{180\ \mathrm{s}}/\textrm{ELV}_{60\ \mathrm{s}}$ are the effective lung volumes measured by IST with tracer gas periods of 180 s or 60 s, and similarly for Q_p .

2.3. Lung heterogeneity simulation model

A heterogeneous lung was simulated by compartments, including three serial deadspace compartments (Harrison et al 2017), two alveolar compartments (tidal compartments) (Hahn and Farmery 2003, Whiteley et al 2003, Whiteley et al 2001) and five compartments to present the whole body (lung, viscera fast, viscera liver, lean and fat) (Baker and Farmery 2011). All compartments were linked together by conservation of mass equations. The significance of this simulation was as a suitable test for the IST and it also had clear settings in two tidal lung compartments to quantify lung heterogeneity. The simulated patient weighs 70 kg, with a lung volume of 2.5 l and pulmonary blood flow of 5.0 l min^–1.

The volume fractions of the two tidal lung compartments were fixed at 0.1 and 0.9. Ventilation and perfusion fractions to the first lung compartment (0.1 fraction of volume) were changed to f_v and f_p . The ventilation and perfusion fractions to the second compartment (0.9 fraction of volume) were calculated by 1 − f_v and 1 − f_p .

Due to the model setting, the lung was homogeneous when f_{v 1} = 0.1 and f_{p 1} = 0.1. An increase in value of f_{v 1} caused the mismatch of the ventilation and higher lung ventilation heterogeneity. Similarly, when f_{p 1} increased, the lung perfusion heterogeneity also increased. A schematic diagram of the lung simulation is presented in figure 1. The full process of model development and the modelling parameters are described in Appendix A.

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2.4. Ethical approval

2.5. Lung injury

2.6. Statistical analysis

The ability to measure lung heterogeneity in the IST was assessed using the simulated heterogeneous lungs (figure 2). The difference between control and ARDS lungs in the IST ventilation and perfusion heterogeneity ratios was analysed by statistical tests (figure 4). Six of the 13 animals had measurements at PEEP 15 and 20 cmH₂O. Additionally, a total of n = 72 paired VD measurements in 13 pigs at four different PEEP levels were analysed. Statistical analyses revealed that VD_IST and VD_SF6 was not different in both control and ARDS lungs.

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3.1. IST lung heterogeneity values in simulated data

3.2. IST heterogeneity indices: a comparison between control and injured animals

3.3. Deadspace volume: a comparison of IST with SF₆

Figure 5 shows the relationship and correlation between VD measured by the IST and the SF₆ test. In general, VD increased when the PEEP was raised, and the ARDS group had larger VDs than controls (panels (a) and (b)). SF₆ measurements showed smaller variations than IST ones. There was a robust relationship between $\textrm{VD}_{\textrm{IST}}$ and $\textrm{VD}_{\textrm{SF6}}$: the linear regression slope was 0.87 with R² = 0.5 in the control group (panel (c)). The volume bias was 9 ml (limits of agreement −79 to 57 ml) in controls and similarly 10 ml (limits of agreement −51 to 32 ml) in ARDS lungs (figures 5(e) and (f)).

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This research shows the ability of the IST to measure lung heterogeneity and absolute VD in uninjured lungs and the ARDS model of lung injury compared with the 'gold standard' SF₆ washout technique. The IST heterogeneity indices have the potential to identify ARDS from control subjects with reasonable diagnostic accuracy; the AuC being $0.85\,(p\lt0.001)$ at a PEEP of 10 cmH₂O. Additionally, VD measured by the IST had a small bias (10 ml) compared with values measured by the SF₆ technique.

A previous study of lung heterogeneity in human patients measured by the IST did not achieve any significant results because of the wide variability in the severity of conditions in the study population. Our research in animals, in which we were able to standardize and control the degree of lung injury more reliably, proved more insightful. Bruce et al showed that ventilation heterogeneity could be determined using the IST values in combination with plethysmography results (Bruce et al 2018). However, in this study, for the first time, we used only the IST to measure the heterogeneity of the lung without the need for plethysmography. We implemented a simulation model and used it to understand the IST heterogeneity indices and their boundaries. Healthy simulated lung should have an IST heterogeneity ratio of 1, although healthy human subjects would not quite achieve this.

The IST has shown potential strengths, including working as a bedside monitor and diagnostic tool. Firstly, it can be used with spontaneously ventilating subjects. In this research, mechanically ventilated animals were investigated. Further study in ventilated patients could improve development of the IST. The IST also can measure the size of a 'baby lung' (equivalent to a small well-ventilated compartment) and results compare well with SF₆ and CT scan data in ventilated animals (Crockett et al 2020). We show that the heterogeneity of the lung changes with applied PEEP; this is of potential interest to the bedside clinician seeking to optimize ventilator settings. Secondly, at the appropriate ventilator setting significant differences between control and ARDS conditions were distinguishable (AuC = 0.85). The results of this study could pave the way for study of disease classification at the bedside using lung heterogeneity. Patients could benefit as a result of better-informed ventilation settings and the reduction of ventilator-induced lung injury (Nieman et al 2017, Brochard et al 2017).

In addition, this study reveals the ability of the IST to measure the absolute VD; it compares well with the SF₆ wash-in–washout method. The correlation between the two methods had a slope of 0.87 (R² = 0.5) and the limits of agreements were from −51 ml to 32 ml in control lungs. Clinically, deadspace volume has a strong association with mortality risk in patients with ARDS, wherein the risk of death increased by 22% for every 0.05 increase in VD:V_T (Kallet et al 2017).

We implemented a lung simulation to show how lung heterogeneity can be captured by the IST. However, the simulation and our work contain limitations. A lung simulation with two alveolar compartments may not be enough to represent the complexity of real-life lung heterogeneity. In figure 2, the heterogeneity index is only valid between certain limits of ventilatory misdistribution (within the grey zone) Outside this region, the simulations break down as described above (in the results, section 3). Of note, whereas in the simulation perfect homogeneity gives a heterogeneity index of 1, healthy subjects do not achieve this value (it being closer to 2). This is not surprising given that even in healthy people ventilation is not perfectly uniformly distributed. A better simulation including the effects of hypoxic pulmonary vasoconstriction could be developed in the future (Whiteley et al 2003, Alford et al 2010). Furthermore, only six animals were studied at PEEP 15 and 20 cmH₂O because, in two cases, the pigs were too unstable to tolerate such high levels of PEEP and these experiments were undertaken in parallel with the collection of data for other studies. Further research could explore IST heterogeneity indices at higher PEEP levels.

The IST is a potentially translatable research tool. This research examined the utility of the IST in measuring lung heterogeneity and VD in ventilated lungs at the bedside. Accurate measurement of VD could help in the prognostication of acute lung injury/ARDS. Furthermore, measurement of the heterogeneity of the lung might be used to quantify the extent of lung injury and inform ventilatory therapy. Our results support further development of these IST heterogeneity indices and their translation to classify lung diseases.

A quantitative method for measuring lung heterogeneity was introduced and explored in animal models. The IST ventilation and perfusion heterogeneity ratios have the potential to inform and optimize mechanical ventilation strategy at the bedside in real time. This work provides a fundamental foundation for the study of lung heterogeneity in clinical trials. The IST can also measure VD with small bias compared with the values measured by the SF₆ technique. Further research is required to determine how the IST could be used to inform mechanical ventilation.

The authors are grateful for the important contribution from veterinary anaesthetists Christian Dancker and William McFadzean, and for the technical assistance by Hanne McPeak and Kristina Britchford.

This project was funded by the National Institute for Health Research, grant number II-LA-0214-20 005.

The lung simulation consisted of three space compartments, two tidal lung compartments and five body compartments with a shunt block. In the two tidal lung compartments, the fraction of lung volume was fixed at 0.1 and 0.9. Parameters for the lung simulation are summarized in table A1. This lung simulation has been described and validated elsewhere (Tran et al 2020).

The ode45 solver and Simulink Matlab were chosen for simulation. Ten mixing compartments of deadspace are included in this model. The equation for each deadspace compartment during inspiration is

$$\begin{equation} V_{M,i}\frac{dF_{M,i}}{dt} = \dot{V}_{A}(t)(F_{M,i-1}(t)-F_{M,i}(t)) \end{equation} \tag{ A1 }$$

where i is the number of deadspace compartments (from 1 to 10) and $F_{(M,1)}(t) = F_{I}(t)$ and $F_{M,10}(t) = F_{IA}(t)$. V_M,i is the VD of compartment i and $\dot{V}_{A}(t)$ is the ventilation at time t. The equivalent equation during expiration is

$$\begin{equation} V_{M,i}\frac{dF_{M,i}}{dt} = \dot{V}_{A}(t)(F_{M,i}(t)-F_{M,i+1}(t)) \end{equation} \tag{ A2 }$$

where i is from 1 to 10 and $F_{M,1}(t) = F_{E}(t)$ and $F_{M,10}(t) = F_{A}(t)$. F_I , F_IA and F_E are the fractional concentrations of the tracer gas coming into the deadspace compartment, coming out from the deadspace compartment to the lung compartment and exhaled from the deadspace to the environment, respectively.

The deadspace compartments are serially connected with two parallel lung blocks. These lung blocks are generated from physiological equations of the tidal lung (Hahn and Farmery 2003) as follows. Inspiration:

$$\begin{equation} V_{A}(t) = f_{\textrm{Volume}}\times\bar{V}_{A}+\frac{V_{T}\times t}{t_{i}} . \end{equation} \tag{ A3 }$$

Expiration:

$$\begin{equation} V_{A}(t) = f_{\textrm{Volume}}\times\bar{V}_{A}+V_{T}\times \textrm{exp}(-\gamma(t-t_{i})) \end{equation} \tag{ A4 }$$

where γ is the rate constant of expiratory flow, V_A (t) is the alveolar volume, V_T is the tidal volume and t_i is the inspiration starting time. $\bar{V}_{A}$ is end-expired alveolar volume. In the first compartment $f_{\textrm{Volume}} = 0.1$ and in the second compartment f_Volume = 0.9.

All the compartments are linked together by governing equations which represent the equilibrium of the mass concentration of the tracer gas. $C_{\bar{v}}$ and C_a are the mixed venous and pulmonary end-capillary gas concentrations, respectively. In the first lung compartment inspiration is

$$\begin{equation} \frac{d}{dt}(V_{A}(t)F_{A}(t)) = f_{v}\dot{V}_{A,i}(t)F_{IA}(t)+f_{p}\dot{Q}_{p,i}(C_{\bar{v}}-C_{a}) \end{equation} \tag{ A5 }$$

and expiration

$$\begin{equation} \frac{d}{dt}(V_{A}(t)F_{A}(t)) = f_{v}\dot{V}_{A,i}(t)F_{A}(t)+f_{p}\dot{Q}_{p,i}(C_{\bar{v}}-C_{a}) .\end{equation} \tag{ A6 }$$

Each compartment has its own fraction of ventilation f_v and fraction of perfusion f_p (table A1). The body compartments of a standard human consist of five different tissues inside the human body with different tissue gas coefficients (Hahn et al 1993, Baker and Farmery 2011):

$$\begin{equation} V_{i}^{\ast}\frac{dC_{i}(t)}{dt} = \dot{Q}_{i}(C_{\bar{a}}(t)-C_{i}(t)) \end{equation} \tag{ A7 }$$

where $V_{i}^{\ast}$, C_i and $\dot{Q}_{i}$ are the equivalent blood volume, concentration of the tracer gas and blood flow rate of i compartment. V_i is given by the following equation, where V_(b,i) and V_(t,i) are the blood and tissue volumes of each body compartments and λ_(t,i) is the Ostwald tissue gas coefficient of each compartment (these values are given in Farmery (2008)):

$$\begin{equation} V_{i}^{\ast} = V_{b,i}+\frac{\lambda_{t,i}}{\lambda}V_{t,i} .\end{equation} \tag{ A8 }$$

The Ostwald coefficient is the relation between the concentrations of the tracer gas in the blood to the fractional concentration in the lung. λ is the blood-gas partition coefficient. The body temperature is assumed to be constant (37^°C), so the Ostwald coefficient is stable:

$$\begin{equation} C_{a} = \lambda\times F_{A} .\end{equation} \tag{ A9 }$$

Since, $\dot{Q}_{T} = \dot{Q}_{S}+\dot{Q}_{P}$. The mixed arterial concentration $C_{\bar{a}}$ is given below with $\dot{Q}_{S}$ being the shunt flow rate, $\dot{Q}_{P}$ the pulmonary blood flow rate and $\dot{Q}_{T}$ the total blood flow:

$$\begin{equation} C_{\bar{a}}(t) = \frac{\dot{Q}_{S}}{\dot{Q}_{T}}C_{\bar{v}}(t)+\frac{\dot{Q}_{p}}{\dot{Q}_{T}}C_{a}(t) .\end{equation} \tag{ A10 }$$