SIAM News Blog

Data Assimilation Framework Sheds Light on Ventilator-induced Lung Injury

By Lina Sorg

Acute respiratory distress syndrome (ARDS) occurs when fluid builds up in the air sacs of the lungs, preventing them from opening completely and depriving the body of necessary oxygen. The condition causes significant problems in clinical management and develops in roughly eight to 10 percent of patients in the intensive care unit. Most people with ARDS require intubation and mechanical ventilation in order to survive. “The problem is, when you put people on a mechanical ventilator, it inflates your lungs differently than your diaphragm does,” Jake Stroh of the University of Colorado Anschutz Medical Campus said. “So it increases the risk of ventilator-induced lung injury (VILI).” While some type of connection exists between VILI, ARDS, and patient-ventilator dyssynchrony (VD)—the inappropriate timing and delivery of a mechanical breath in response to patient lung function—this connection is not especially clear. For instance, normal breaths exhibit a somewhat regular relationship between pressure and volume; in VD-affected patients, this relationship begins to break down. As such, researchers hypothesize that VD invokes VILI and (by consequence) worsened cases of ARDS and poorer outcomes.

The lungs and ventilator collectively serve as a coupled, interactive biomechanical system. In this lung-ventilator system (LVS), the ventilator—assisted by the patient’s muscle contractions—provides forcing to the system. The lungs, which are composed of many small structures that are constantly opening and closing, act an internal compliant boundary in the middle of the breath. “The things that can be seen are observable outside of the human body, outside of the mouth between the ventilator and the human,” Stroh said. “You’re measuring the interaction between the lungs and the ventilator, but you’re also trying to represent something about this aggregate behavior as a bulk process.” 

Figure 1. Visual description of acute respiratory distress syndrome (ARDS) and its impact on the body. Public domain image.
During a minisymposium presentation at the 2022 SIAM Conference on Mathematics of Data Science, which took place in a hybrid format in San Diego, Calif., last week, Stroh introduced a data assimilation framework that models a wide variety of LVS behaviors. This framework recognizes trajectory waveform patterns that allow clinicians to identify the mismatch between patients and ventilator settings, which ultimately lessens the risk of VILI. “How can we represent the LVS sufficiently and efficiently for analysis of its evolution over hour/day scales from observed waveforms and ventilator setting data?” he asked.

Stroh began by outlining four basic limitations that hinder progress in the study and quantification of VD severity and its relation to VILI:

  • Stiffness, which relates to the problem’s multiscale nature since breath details occur at subseconds and produce effects that then manifest at timescales on the order of hours to days
  • Inferrability, which arises because the inference of nonlinear parameters is a slow and difficult process
  • Modelability/flexibility, as the standard relationships between pressure and volume that guide assumptions about an idealized version of the lung do not actually exist in a clinical environment
  • Interpretability, meaning that doctors and stakeholders must be able to interpret and understand the results, model components, and parameters.

Because both traditional and waveform models of the lung have their own drawbacks, Stroh relied on quasi-empirical modeling to address the aforementioned limitations. Such models have flexible inference with no explicit physiology and produce outputs that resemble waveforms. “We’re basically just using this in order to discretize the lung ventilator system data—the waveform data—into something that is much more compactly represented for use in downstream applications,” Stroh said.

Stroh employed an asynchronous ensemble Kalman filter and smoother to capture two- to 10-second windows of breathing patterns. He used these windows to identify parameter distributions and extract other bits of data, including waveform characterizations over the interval in question. “We have a lot of control over the intervals, so we can look at five seconds, 10 seconds, or whatever we think the relevant stationarity assumption is for the estimation at that time,” Stroh said.

Jake Stroh of the University of Colorado Anschutz Medical Campus presents a minisymposium talk entitled "Progression and Pathophysiology: Quantifying the Clinical Evolution of the Human Lung under Mechanical Ventilation," at the 2022 SIAM Conference on Mathematics of Data Science, which took place in San Diego, Calif., in September 2022. SIAM photo.
After extracting parameter summary vectors, Stroh identified groupings of the different parameters to estimate the distinct types of breath waveform shapes that appear. Using a t-distributed stochastic neighbor embedding (t-SNE) projection, he examined the identifiable groupings of breath types to understand patient activity at certain points in time. He then studied the various characteristics of the parameters that are associated with the group and “backed out” computational biomarkers of VD; doing so involved interpreting the parameters and clusters based on the appearance of their waveforms. “Even though there’s no physiology, we’re kind of sidestepping that by applying the model again to get back to something that represents a characterization of the waveform that a doctor could look at,” Stroh said. “This is still empirical. Its nonphysiological, but it’s somewhat interpretable and it gives us a foothold on detangling the influences of ventilator settings from those that are going on with the patient by themselves.”

Next, Stroh shared some of the model’s results in the form of eight hours of data that was assimilated in short time intervals, then assembled and summarized in 10-second increments. “We’ve basically operationalized the waveform system inside the LVS so we can map out what kinds of breaths are happening at different periods of time,” he said. “We can also somewhat see the ventilator setting effects on the different breath types.”

Stroh concluded his presentation with a discussion of ongoing obstacles that impede further progress. For example, some patients experience a lot of ventilator setting changes and exhibit many different breath types. Furthermore, assessing behavior across multiple types of patients requires that researchers normalize the situation or find some sort of standard way of comparing one patient to another. And the clinical domain is of course complicated by heterogeneity and interactivity, which lead to a lack of control from an experimental perspective.

Nevertheless, Stroh’s method allows for the representation and digitization of LVS waveforms in a fast, flexible, and inferable way. “We can now visualize the LVS trajectories and form hypotheses about them,” Stroh said. “We have identified clusters of the system that correspond to computational biomarkers—at least in terms of VD—where the domain experts on the outside can tell us what different breaths the waveform shapes correspond to. Though we don’t have a way to model them in a physiological setting yet, we at least know what the different breaths look like in a human setting.”

Lina Sorg is the managing editor of SIAM News.
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