Conference Agenda

Acute Respiratory Distress Syndrome (ARDS) is a critical condition. For patients suffering from this pathology, mechanical ventilation (MV) is needed to ensure sufficient ventilation and oxygenation. Intensivists have several therapeutic tools at their disposal to design an adapted MV. However, they still face several issues in their decision-making when designing it:

• High variability between patients
• Limits in the understanding of the underlying mechanisms

That is why MV design is still mostly experience-based. In order to improve the understanding of ARDS lung biomechanics and physiology, a coupled physio-mechanical computational framework was conceived and implemented.

The model is a lumped-parameter model which is conceptually simple and has a limited number of degrees of freedom in order to keep the computational burden low. The discretization of the lung is made into 2N compartments called Respiratory Units (R.U.), with N being the number of generations of the trachea-bronchial tree considered. The geometry and physical properties of each R.U. are based on the patient's CT-scan and lung segmentation. Throughout a simulation, two submodels are run: the mechanical and the physiological ones. In the mechanical model, each R.U. is able to inflate and deflate according to the input MV and a non-linear compliance. The R.U. can also collapse and reopen to embody atelectasis. In the physiological model, gas exchanges (O2 and CO2) consequent to the inflation computed in the mechanical model are calculated for each R.U. This model allows the simulation of the patient's oxygenation, including phenomena such as hypoxic vasoconstriction. Notably, the coupling between the two submodels allows for the simulation of the ventilation-perfusion mismatch, which is data of high clinical significance.

First results showed that the model behaves as expected qualitatively. Clinically observed phenomena were reproduced. For instance, from a biomechanical point of view, recruitment in dorsal areas and lung homogenization when positioning the patient prone were reproduced. Concerning the physiological model, the discrepancy between tidal volume increase and oxygenation improvement was simulated and explained.

These results are promising and demonstrate the ability of the model to capture part of the ARDS lung biomechanics and physiology. However, the model's validity is currently not validated against patient data, and in its current form, it provides qualitative results only. Future work will aim first to identify the most influential parameters through a global sensitivity analysis. Then, an inverse method framework will be developed to tune this reduced set of parameters based on patient data to make quantitative predictions

Pulmonary capillary perfusion and gas exchange are critical physiological processes that occur at the alveolar level and are fundamental to sustaining life. Current computational simulations of these phenomena often rely on simplified, low-dimensional mathematical models that do not directly account for the alveolar morphology [1]. These models typically involve simplified representations of the complex chemical reactions between O2​-CO2​ and hemoglobin. While such models offer general insights, they frequently fail to capture the intricate nature of chemical reactions within pulmonary capillary blood flow in realistic geometries. Additionally, they overlook the significant impact of microstructural morphology on overall pulmonary function. In this work, we introduce a coupled continuum model to simulate pulmonary perfusion and gas exchange in alveolar geometries [2]. We further include complex gas and hemoglobin dynamics within realistic geometries of alveolar tissue [3]. To achieve this, we derive a set of governing equations that include a two-way Hill-like relationship to describe the interaction between gas partial pressures and hemoglobin saturations. We employ a non-linear finite-element approach to solve the resulting boundary-value problem numerically. This approach enables us to simulate and validate key physiological fields such as blood velocity, oxygen and carbon dioxide partial pressure, and hemoglobin saturation in idealized and complex geometries. We also conduct sensitivity studies to examine the influence of blood speed and acidity variations on these key physiological fields. Notably, we extend our simulations to anatomical alveolar domains reconstructed from 3D computed-tomography images of murine lungs. Our simulations reveal that morphological variations within these domains lead to significant changes in O2​ and CO2​diffusing capacity, which can be related to pulmonary chronic diseases.

Acknowledgements: This work was supported by the Agencia Nacional de Investigación y Desarrollo, Chile, through grant FONDECYT 1220465.

[1] Clark, A. R., Burrowes, K. S., & Tawhai, M. H. (2021). Integrative computational models of lung structure-function interactions. Comprehensive Physiology, 11(2), 1501–1530. https://doi.org/10.1002/cphy.c200011

[2] Zurita, P., & Hurtado, D. E. (2022). Computational modeling of capillary perfusion and gas exchange in alveolar tissue. Computer Methods in Applied Mechanics and Engineering, 399, 115418. https://doi.org/10.1016/j.cma.2022.115418

[3] Herrera, B., & Hurtado, D. E. (2025). Modeling pulmonary perfusion and gas exchange in alveolar microstructures. Computer Methods in Applied Mechanics and Engineering, 433, 117499. https://doi.org/10.1016/j.cma.2024.117499

Introduction: Computational lung modeling has become an essential tool for virtually analyzing respiratory mechanics and disease progression in individual patients, providing detailed insights into key variables such as deformation, stress, and pressure distributions [1]. Despite its advantages, the high computational cost of current organ simulations, often requiring several hours, restricts their use in clinical settings. To overcome this challenge, machine learning (ML) has shown promise in accelerating predictions through surrogate models. However, most existing approaches are limited to the study of structured grids, fixed domains, or parameterized geometries. Graph Neural Networks (GNNs) have recently gained attention for their inherent ability to adapt to intricate and irregular geometries. In this study, we propose a GNN-based framework to develop efficient spatiotemporal surrogates of finite element lung models under mechanical ventilation. Our approach is designed to handle diverse and complex lung geometries, while remaining generalizable to patient-specific boundary conditions.

Materials and methods: Using CT scans, we created a dataset consisting of N different 3D lung meshes from different patients {M₁,M₂,…,M_N} and conducted finite element simulations of lung behavior under mechanical ventilation [2]. The simulation outputs included the spatiotemporal displacement and alveolar pressure fields over a ventilation cycle of duration T. To accelerate these model predictions, we developed and trained a Graph Neural Network (GNN) architecture named LungGraphNet (LGN). This model adapts each patient-specific lung mesh into a computational graph structure G=(V,E), where V represents the nodes and E the corresponding connecting edges. The physical boundary conditions essential to describe the problem are embedded as nodes and edges features into this graph representation. Once trained, LGN serves as a surrogate model capable of performing inference on a new and unseen lung geometry G_i​, accurately predicting the spatiotemporal response and reconstructing the evolution of respiratory signals under mechanical ventilation.

Results: The LGN displayed high accuracy in predicting spatiotemporal displacement and alveolar pressure fields, achieving a relative error of less than 5% across all patient cases in the test set, compared to the ground-truth simulation values. During inference, the surrogate model generated predictions for arbitrary lung geometries in less than 2 seconds, which is approximately 4800 times faster than the finite element simulations and without requiring retraining.

Discussion and Conclusions: The proposed framework offers an efficient solution for patient-specific lung modeling. The significant speed-up achieved by our surrogate model makes it a promising tool for the potential use of virtual lung analysis in both clinical practice and research.

References:

1. Neelakantan S et al. (2022), JR Soc. Interface. 19(191), 20220062

2. Avilés N, Hurtado D (2022), Frontiers in Physiology. 13, 984286.

Acknowledgements: The authors would like to thank the National Agency for Research and Development (ANID), graduate fellowship ANID BECAS/DOCTORADO NACIONAL #21220063, and Pontificia Universidad Católica de Chile, for providing financial support to this project.

The lung is a complex system that serves as an interface for the exchange of gases between the ambient air and the bloodstream. Its main function is to oxygenate the blood and remove carbon dioxide through its tree-like structure. Once oxygen enters the bloodstream, hemoglobin becomes its principal carrier. However, the affinity of hemoglobin for oxygen is influenced by the concentration of carbon dioxide in the blood, leading to a competition between the two gases to bind with hemoglobin. This phenomenon is known as the Haldane and Bohr effects.

The study of gas transport mechanisms and respiratory gases exchange with blood is a fundamental step to better understand how this complex system works. For this, a gas transport model has been developed. It is driven by the applied pressure on the lung and is composed of advection-diffusion-reaction PDEs for each gas species in one dimension. This model, contrary to its 0D counterpart [1], naturally accounts for the mixing of gases along the bronchial tree and introduces a time delay as the gases have to be transported before reaching the alveoli. Furthermore, it also takes into account the strong interaction between oxygen and carbon dioxide in the blood thanks to a coupled ODE system that represents the nonlinear coupling in the diffusion of the gases in the blood.

This model ultimately allows for the computation of the amount of oxygen and carbon dioxide exchanged with the blood over time along with their arterial partial pressures. The data predicted by the model are fully consistent with the physiological responses expected in the healthy case. Additionally, we explore how both the 1D model and its 0D counterpart respond to different breathing patterns by examining two types of applied pleural pressure—piecewise constant and piecewise exponential—across various breathing periods, inspiratory ratios, and pressure amplitudes.

Moreover, this model is used to consider optimal control scenarios by minimizing a cost function in order to find optimal breathing scenarios. This involves exploring which cost functions the observed stereotypical breathing scenario may optimize. The underlying assumption is that optimal breathing should be a combination of several criteria: low effort, minimal lung distension, while maintaining the carbon dioxide arterial partial pressure at a given level. By investigating these cost functions, the model can provide insights into the most efficient breathing patterns that balance these criteria, further enhancing our understanding of respiratory physiology and paving the way for more effective breathing therapies.

[1] L. Boudin, C. Grandmont, B. Grec, and S. Martin. A coupled model for the dynamics of gas exchanges in the human lung with Haldane and Bohr’s effects. Journal of Theoretical Biology, 573:111590, 2023.