A model-based approach to generating annotated pressure support waveforms

For the patient model, we select the validated model of Athanasiades [3]. This model is similar to the model of Bates [6], but it includes turbulence, nonlinear relationships, airway collapse, and visco-elastic properties.

The model of Athanasiades was chosen because it is a validated model for maximumum effort tests with parameters that can be partly re-used. It can model expiratory flow limitation using a collapsible resistance and compliance, which is an important feature in COPD patients and patients suffering from obesity. Moreover, since non-linear equations are used to account for the lung and chest wall compliance, the effect of applying PEEP and inspiratory pressure is modeled more realistically, it is also required to model fibrosis, ARDS, COPD and obese patients properly. Viscous damping is an important feature in pressure waves, and therefore needs to be included in the model. The model includes turbulence in the upper airways which is especially an important feature for obese patients.

More complex models are available that also include these effects. However, clinical parameters are often estimated using one-lung models, and it is therefore convenient to use a one-lung model, such that these parameters can be re-used.

Given all the above requirements, the model complexity and number of parameters therefore seems reasonable.

The patient model (Fig. 1) consists of three variable resistances modeling the upper airways (\(R_u\)), collapsible airways (\(R_c\)), and small airways (\(R_s\)). The resistance of the upper airway \(R_u\) is given by a nonlinear flow-dependent Rohrer resistor, which accounts for turbulence:where \(A_u\) is the linear resistance of the upper airways, \(K_u\) is a constant, and \(\dot{V}_{cw}\) the airflow rate.

The resistance of the collapsible airway \(R_c\) varies with the volume of the collapsible airway segment \(V_c\), and is given by:where \(K_c\) is a constant and \(V_{cmax}\) is the maximum volume of the collapsible airways.

The resistance of the small airways \(R_s\) captures the dependency of the small airway resistance on the alveolar volume \(V_A\) [3]:where \(A_s\), \(K_s\), \(B_s\), and \(V^*\) are constants and RV is the residual volume of the lung.

The variable capacitor \(C_c\) models the compliance of the collapsible airway segment. Athanasiades et al. [3] modeled this by a piece-wise continuous function. To make the implementation in a circuit simulator possible, we replace this function by a twice differentiable function, which has the same (sigmoidal) shape in the physiological region:where \(V_{cmax}\) is the maximum volume of the collapsible airways, \(A_c\), \(B_c\), and \(D_c\) are patient dependent constants, and \(P_c\) is the pressure over the capacitor \(C_c\).

\(C_{cw}\) is the compliance of the chest wall. The volume of the chestwall \(V_{cw}\) is modeled by a sigmoid function [3]:where TLC is the total lung capacity (the maximum value of the sigmoid function), RV the residual volume (the minimum value of the sigmoid function), \(P_{cw}\) the pressure in the chest wall, and \(A_{cw}\) (the shift of the curve) and \(B_{cw}\) (related to the slope of the curve) are patient dependent constants.

For the alveolar volume \(V_A\), we replace the original curve with the exponential curve determined empirically by Venegas et al. [36], which describes the normal lung and different disease archetypes:where \(A_l\), \(B_l\) and \(D_l\) are patient dependent constants and \(P_t\) is the transmural pressure. Together with \(C_l\), the linear \(C_{ve}\) and \(R_{ve}\) form a nonlinear Kelvin body that mimics the visco-elastic properties of the lung and chest wall. \(C_{ve}\) and \(R_{ve}\) are constants and are chosen such to mimic available literature. Note that the order of the Kelvin body and chest wall compliance is switched as compared to Athanasiades et al. [3]. This is done to ensure that lung and chest wall volumes are equal during simulation.

Finally, \(\mathrm {P_{mus}}\) models the effect of the respiratory muscle activity. We use a rounded trapezoid with a different slope for the rising edge and falling edge (Fig. 2), which is similar to measured patient muscle effort. We also added a sine wave to this signal, with an amplitude between 0.25 and 1 \(\hbox {cmH}_2\)O and a frequency between 1 and 2 Hz, to model the cardiac oscillations often observed in ventilator waveforms.

We have added a voltage source \(\mathrm {PipPEEP}\) and a very high resistance \(R_d\) to ensure correct initial conditions of the equal lung and chest wall volume and to avoid floating nodes.

Athanasiades et al. [3] use measurements of four different healthy test subjects to fit four parameter sets. We take this set of parameters as our baseline. To create a diverse dataset with different types of critically ill patients, we have selected the following types of patients: Obese patients, patients suffering from ARDS, COPD patients, and patients with idiopathic fibrosis. By using available clinical data in the literature, we propose the following changes in the lung mechanics as compared to the “healthy” archetype:Based on these descriptions, we compose a set of requirements for every patient archetype (Table 1). We hand-tune the parameters of the model to meet these requirements, and represent the different disease conditions, creating a more diverse set of parameters. The parameter sets are available in the supplementary information.

The ventilator model is shown in Fig. 3. The node below \(R_{et}\) is connected to the wire above \(R_{u}\) in Fig. 1.

The ventilator model consists of the following parts:The pressure and the flow in ventilated patients are usually measured at the proximal location after the Y-piece but before the endotracheal tube, this is also where we measure the pressure at the airway opening (labeled ’sensor’ in Fig. 3). The effect of the parasitics of the tubing is very important for modeling the specific waveform characteristics measured at the sensor.

During PSV, the ventilator triggering (delivery of \(P_{insp}\)) and cycling (switching from \(P_{insp}\) to PEEP) are initiated by the patient. If the patient starts inspiration, air starts flowing into the lung and the pressure at the sensor becomes lower than PEEP. Triggering can therefore be achieved by putting a threshold on the flow or the pressure. Cycling is usually done when the flow reaches a percentage of the peak flow (usually 10-80 percent). Ideally, the ventilator would trigger and cycle exactly at the same time as the patient’s start and end of inspiration effort. If the trigger and cycle timings differ too much from the inspiration time of the patient, we are observing an asynchrony.

To classify whether a breath is an asynchrony or a regular breath, the time between the start of patient inspiration and ventilator triggering (start-inspiration delay) and the end of patient inspiration and ventilator cycling (end-inspiration delay) need to fall into certain margins. We employ the same margins as Bakkes et al. [5]:Since delayed inspiration occurs during triggering, and late cycling and early cycling occur during cycling, also combinations of delayed inspiration and early cycling, and delayed inspiration and late cycling can be present during one breath.

In clinical data, the start and end of patient inspiration are usually difficult to determine precisely without an esophageal balloon manometry. In the simulation, the patient and ventilator are fully controlled. We know exactly when patient inspiration started and ended and when the ventilator triggered and cycled, which creates sets of completely annotated waveforms.

Before generating the waveforms, we check whether the model parameters are tuned correctly according to Table 1. We compare \(R_{insp}\), \(R_{exp}\), compliances, and lung volumes in the model to the values reported in the literature. RV and TLC can directly be observed from the model parameters. FRC can be calculated by calculating the volume at \(P_t+P_c= -P_{cw}\). We define \(R_{exp}\) and \(R_{insp}\) as the sum of \(R_u\), \(R_c\), and \(R_s\) during expiration and inspiration at low flow. \(C_{tot}\) is calculated by taking the slope of the combined lung-chest wall pressure–volume curve of the model at FRC. We report the values using zero end-expiratory pressure (ZEEP), except for COPD where we report the values using PEEP and \(P_{insp}\).

After this initial verification, a synthetic dataset with more than 60.000 breaths was created, using the implementation of the model in LT Spice XVII [26]. The disease type of the patient was randomly selected. The input muscle waveform \(\mathrm {P_{mus}}\) is generated by MATLAB R2019b [23] using the parameters in Table 2.

Typical values for the breathing rates, and trigger and cycling thresholds are reported in Table 3. PEEP and \(P_{insp}\) are chosen in such a way that the tidal volume is 0.4-0.6 L during a normal breath.

To ensure balanced classes and enough training examples for the machine learning algorithm, each class of asynchronies has the same number of breaths. The asynchrony type of each breath is easily retrieved since the timing of the patient and ventilator are saved. Low-pass filtered white noise (bandwith 15 Hz) with a signal-to-noise ratio (SNR) between 15 and 16 was added to the pressure and an SNR between 30 and 31 to the flow.

Although we started with 60.000 breaths, the method can quickly generate more breaths. On a single core of an Intel Core i7 7th Gen, the program runs 4.7 times real-time (including the initialization of the muscle waveform in MATLAB). In other words, for 10 s of simulation, 2.1 s of execution time is required.

Validation of the obtained dataset is not a trivial task. Therefore we include a variety of tests from airway and lung parameters, evaluation of the waveforms by experienced clinicians and using an existing validated neural network model.

The authors visually compared the synthetic waveforms to clinical data that were obtained from patients after cardiac surgery [13]. The local Institutional Review Board (R16.054) associated with Catharina Hospital Eindhoven approved the use of patient-related waveforms for medical research. The clinical data contained all asynchronies, which were also visually compared to the asynchronies in the synthetic data.

A survey was sent to 16 experienced clinicians from two different instituations to check whether they were able to differentiate the simulated waveforms and the previously mentioned clinical waveforms. The clinicians assessed 32 samples, which were 16 clinical and 16 synthetic waveforms. Both 16 clinical waveforms and 16 synthetic waveforms were randomly selected from both datasets. The first 16 samples were the same for every clinician. The last 16 samples were unique for every clinician. The clinicians determined whether the provided waveforms were a simulated waveform or a clinical waveform. To statistically test whether they were able to differentiate the two, Fisher’s exact test was used, for which a \(p < 0.05\) was considered to be significant. Fisher’s exact test tests whether the difference between two proportions in a 2 \(\times\) 2 contingency table is significant.

As a last test, we apply the neural network trained on clinical data proposed in Bakkes et al. [5] to the synthetic dataset. In the orignal paper [5], the machine learning algorithm was trained and tested on the same (small) labeled clinical dataset. It is therefore not known how well this algorithm generalizes when applied to a different dataset. The algorithm is a one-dimensional version of the U-net architecture and detects the start and end of patient inspiration in unlabeled pressure, flow, and volume waveforms when esophageal pressure is not available. The network consists of four contracting and expanding layers and is trained using the adam optimizer in conjuction with categorical cross-entropy as a loss function [5]. 4275 labeled clinical breaths were used to train the network using 300 epochs. The 60.000 synthetic waveforms were only used for validation.

Since we know the true timing of the synthetic dataset, we report the true positive rate (TPR), positive predictive value (PPV), and root-mean-squared error (RMSE) of the algorithm, which are defined in the following way:where \(S_{i}\) is the true start time of patient inspiration and \(\hat{S}_{i}\) is the estimated start time by the machine learning algorithm.where \(E_{i}\) is the true end of patient inspiration and \(\hat{E}_{i}\) is the estimated end time by the machine learning algorithm.

This test, including all its presented evaluation metrics (Eq. 7–10) gives us information both about the ability of the algorithm to generalize and about the quality and abnormalities of our synthetic dataset.

Table 4 shows the target range of \(R_{insp}\), \(R_{exp}\), \(C_{tot}\), and of the lung volumes and the values obtained from the model. The values for the “Healthy” archetype are not tuned but obtained from Athanasiades et al. [3], and therefore differ more from the target values, but are still in the acceptable range. We defined the acceptable range as 0.5 L from the target value for the RV, 1 L for FRC, and 1 L for TLC. For \(R_{insp}\) and \(R_{exp}\), 1.5 cmH2O/L/s from the target is acceptable, for \(C_{tot}\) 0.01 L/cmH2O is.

The data obtained for the other archetypes correspond well to measured airway and lung parameters [2, 4, 7, 9, 17, 18, 21, 29].

Figure 4 shows a normal PSV breath and the four types of asynchronies in clinical data of patients after cardiac surgery (normal lung) [13]. The normal breath shows a rounded peak in the flow during the inspiration phase and a sharp peak in flow during the expiration phase. The pressure increases steeply when the ventilator triggers and the pressure decreases slowly during inspiration until the patient’s muscles relax, after which it increases faster. The flow shows an exponential pattern and the pressure monotonically decreases after cycling. During the early cycling in Fig. 4, the pressure shows a pressure minimum after cycling and characteristic deviation from the exponential flow pattern during expiration, i.e., a strong decrease in expiratory flow directly after cycling. Finally, the volume after the ventilator cycles does not decrease as fast as in the regular breath. Only when the patient stops inspiration the volume decreases at its regular pace. In the delayed inspiration recording in Fig. 4, the patient suffers from cardiac oscillations, causing some extra pressure above PEEP. This causes the ventilator to be late with triggering. Besides the late trigger, the delayed inspiration looks similar to the normal breath. The ineffective effort in Fig. 4 is shown between two regular breaths. During the ineffective effort, a drop in pressure is visible in the pressure at the airway opening, and a small increase in the flow is visible caused by the inspiration effort of the patient without ventilator triggering. During late cycling in Fig. 4 the ventilator cycles later than the patient stops inspiration. This is clearly seen from the shape of the flow during inspiration. The flow first has a rounded shape, but after the inspiration effort end-time the flow decreases in an exponential manner and it fails to reach the cycling threshold quickly. Therefore, the ventilator pressurization lasts longer than the patient’s effort.

Figure 5 provides a comparison of the clinical data, and the five simulated patient archetypes with different types of asynchronies. The automatically generated labeling is visible in the generated simulated waveforms. In the figure, ineffective efforts, late cycling, delayed inspiration, and a combination of delayed inspiration-late cycling and delayed inspiration-early cycling are visible. They show correspondence to the asynchronies in Fig. 4. The waveforms for the different patient archetypes show the typical characteristics that are expected based on Table 1. The PEEP and \(P_{insp}\) are set in such a way that 0.5-L tidal volume was reached, which often corresponds to the clinical target (depending on the bodyweight of the patient). However, due to some asynchronies, this cannot always be reached. Triggering and cycling thresholds were sometimes set slightly too high or too low to generate an asynchrony.

For COPD and obese patients, expiratory flow limitation is an important feature. Figure 6 shows the differences in the expiratory flows of a COPD patient and a healthy patient in more detail.

Figure 7 shows an example of mild and evident early cycling in more detail, both in clinical data and in the simulated data. In the case of subtle early cycling, the maximum of patient effort lies just before the point of ventilator cycling. This results in a flattened peak of the expiratory flow, but it does not have the distinct early cycling shape often seen in literature and which is also seen in Figs. 4 and 5. The last two columns show a more severe version of early cycling, where the maximum of the patient effort lies much further beyond the cycling point of the ventilator. This results in the typical early cycling shape with a bump in pressure and in expiratory flow.

Table  5 shows the  TPR, PPV, a \(\hbox {RMSE}_{\text {start}}\) and \(\hbox {RMSE}_{\text {end}}\) of the machine learning algorithm. The overall TPR is 94.3%, while the overall TPR of the algorithm validated on clinical data reported in Bakkes et al. [5] was 98%. The overall PPV on the synthetic data was 93.5%, while on the clinical data this was 98%. The PPV and TPR of the ineffective efforts are lower than average. The PPV is lower than the TPR in case of ineffective efforts since the algorithm identifies segments in the data that are not ineffective efforts (false positives). The \(\hbox {RMSE}_\text {end}\) for early cycling is higher than for the other asynchronies.

This study has some limitations.