About this note
A plain-language summary of the 3 publications listed under this topic on Academic Publications (Topic-wise). Full citations are under References.
Why this matters
Every breath carries air down a branching tree of airways to the alveoli, tiny air sacs where oxygen crosses a thin membrane into blood in the surrounding capillaries. Chronic respiratory diseases such as chronic obstructive pulmonary disease (COPD), pneumonia, asthma and tuberculosis (TB) cause pulmonary congestion: mucus, fluid or infected tissue blocks parts of this tree, restricts airflow and reduces the oxygen reaching the blood. COPD is expected to become a major cause of disability and death worldwide, and in 2022 TB was the second leading cause of death from a single infectious agent after COVID-19 (Thangavelu and Narasimhan, 2025; Thangavelu and Narasimhan, 2024a).
A doctor would like practical answers. How much of the lung can be congested before blood oxygen becomes dangerously low? How much time is left before the patient deteriorates, and when might a ventilator be needed? Experiments on living lungs are impractical, so modelling is the natural route. Earlier models simulated airflow in parts of the lung, but none followed the air from the trachea to the alveoli and linked congestion on the air side to oxygen on the blood side. Building that link is the aim of this work with Aarthi Thangavelu at IIT Madras.
What we did
The lung as a porous medium
Instead of drawing every airway, we treat the lung as a porous medium, a solid matrix threaded with interconnected voids like a sponge, described by its porosity (the void fraction) and permeability (a measure of how easily fluid passes through it).
The airways branch in two through 23 generations, which we group into three zones. Zone 1 (generations 1 to 16) only conducts air; Zone 2 (17 to 19) conducts air and takes a small part in oxygen transfer; Zone 3 (20 to 23) is the respiratory zone where gas exchange happens. The lung becomes a truncated cone of porous material with porosity 0.893 and a different permeability in each zone, calculated from the Carman-Kozeny equation (a classical relation linking permeability to pore size and porosity) using real branch dimensions (Thangavelu and Narasimhan, 2025).
Two scales working together
Lung structures range from centimetres to micrometres, so we built two connected porous medium models, which the conference paper describes as bi-disperse: a porous medium whose solid part is itself porous (Thangavelu and Narasimhan, 2024b).
- The global model represents the whole lung on the air side. It solves the airflow over each breathing cycle and gives the air velocity reaching Zone 3.
- The local model is a representative elementary volume (a small sample large enough to represent average behaviour) placed at several locations in Zone 3. Here the roles swap: blood flows through the pores and alveolar air occupies the solid part, so its porosity is 1 − 0.893 = 0.107. It solves for the oxygen transported into the blood.
The air velocity from the global model feeds the local model, so a blockage upstream shows up directly as a change in blood oxygen, reported as the partial pressure of oxygen (pO2) entering the bloodstream. Fresh alveolar air is at about 100 mm Hg and deoxygenated blood at 40 mm Hg. Checked against published results, the predicted pO2 agreed within about ±1.35% to ±1.5% for normal breathing rates (Thangavelu and Narasimhan, 2025; Thangavelu and Narasimhan, 2024a).
Adding congestion: the three studies
Congestion is introduced by lowering the porosity and permeability of the affected region, down to a porosity of 0.002 (almost solid). Its growth is fed in as a linear or exponential pattern, and results are reported against the percentage of total disease time, so any disease with a known growth pattern can be simulated.
The conference study tested the idea with congestion growing to 10% and 50% of lung volume (Thangavelu and Narasimhan, 2024b). The TB study modelled the disease in clinical stages: an initial response by macrophages (immune cells that engulf bacteria), a growth stage, a latent stage held in check by immunity, and reactivation when weakened immunity lets the bacteria spread. It compared a healthy person whose immunity drops suddenly with an elderly person whose immunity declines gradually, and represented immunity-boosting treatment by raising permeability by 20% or 40% from the midpoint of the disease time (Thangavelu and Narasimhan, 2024a). The journal study examined congestion as in COPD, from 10% to 95% of lung volume, and also half the lung blocked to different intensities (Thangavelu and Narasimhan, 2025).
What we found
A blocked region starves of air (its alveolar air velocity falls from about 2.5 × 10⁻⁵ m/s to around 10⁻⁸ m/s) while open regions speed up to carry the same breath.
- A first warning. With 50% of the lung congested, pO2 fell below 80 to 85 mm Hg after about one sixth of the simulated time and hypoxemia (abnormally low blood oxygen) set in after 600 seconds, while 10% congestion stayed safe (Thangavelu and Narasimhan, 2024b).
- The 40% threshold. A healthy lung keeps the blood adequately oxygenated with up to 40% of its volume congested. At about that level hypoxemia sets in, with pO2 down by 36.5%, and greater congestion depletes blood oxygen within a few hours (Thangavelu and Narasimhan, 2025).
- Intensity matters as well as volume. With half the lung congested, blockage of up to 21.6% of its pores needs no medical help in an otherwise healthy person, but care is needed beyond 23.5% (Thangavelu and Narasimhan, 2025).
- Timing in TB. Severe infection (pO2 below 60 mm Hg) arrived at 86% of the disease time for a sudden fall in immunity and at 75% for a gradual one. A 20% immunity boost only delayed it (from 86% to 91%), while a 40% boost avoided it altogether, restoring haemoglobin oxygen saturation from about 84% to 95%. With the smaller boost, moderate infection arrived slightly earlier because the disease spreads exponentially, echoing clinical reports that early treatment can still turn fatal for a few patients (Thangavelu and Narasimhan, 2024a).
The global model is rigid and does not expand with each breath, and predicting disease growth relies on data from existing studies, so new diseases with little data cannot yet be simulated (Thangavelu and Narasimhan, 2025). Even so, the dual-scale approach gives in silico (computer-based) estimates of how much time a congested lung has, which can inform treatment of chronic respiratory diseases.
Related
- Bi-disperse Porous Media
- Drug Delivery in Human Organs
- Essentials of Heat and Fluid Flow in Porous Media
References
- Thangavelu, A. and Narasimhan, A., (2025) “Effects of Congestion in Human Lung Investigated Using Dual-Scale Porous Medium Models,” Int J Numer Meth Biomed Engng, 41: e3893. [ DOI: 10.1002/cnm.3893 | Abstract ]
- Thangavelu, A. and Narasimhan, A., (2024a) “Dual scale porous medium model of lung congestion caused by tuberculosis,” Heat and Mass Transfer 2024, 60:1523–1536. [ DOI: 10.1007/s00231-024-03504-w | Abstract ]
- Thangavelu, A., and Narasimhan, A., (2024b) “Numerical Modeling of the Effects of Congestion in Human Lungs,” In: Benim, A.C., Bennacer, R., Mohamad, A.A., Ocłoń, P., Suh, SH., Taler, J. (eds) Advances in Computational Heat and Mass Transfer. ICCHMT 2023. Lecture Notes in Mechanical Engineering. Springer, Cham. [ DOI: 10.1007/978-3-031-67241-5_6 ]