From the fractal structure of the lungs to diagnosing COPD
Dagmar Iber and her team at the Department of Biosystems Science and Engineering in Basel aim to understand how the lungs develop in the foetus so they are fully functional by the time the baby is born. Her computer-based method could, in the future, help improve the diagnosis of certain respiratory diseases.
As soon as a baby squeezes through the birth canal and enters the world, it begins to cry and takes its very first breath. Therefore, the lungs must function right from the outset. Like most organs, a baby’s lungs are fully operational at birth – containing millions of airway branches and tens of millions of tiny air sacs (alveoli). As the newborn grows, only the number of alveoli will multiply, while no new airway generations will be added to the lung tree. The “bronchial tree” is fully formed and ready for life when the baby is born.
But how are the lungs formed during embryonic and foetal development? And most importantly, how is the remarkable fractal structure of the bronchial tree created in which the trachea branches into two primary bronchi, then again and again into smaller bronchi and bronchioles in such a way that every branch – whether large or small – appears almost identical under a microscope? A team led by Dagmar Iber, a professor at ETH Zurich’s Department of Biosystems Science and Engineering (BSSE) in Basel, is now shedding light on these highly complex processes. These new findings could, in the future, improve the diagnosis of lung conditions, such as chronic obstructive pulmonary disease, or COPD.
Dagmar Iber’s team is working to understand how the linear information in hereditary DNA is translated into three-dimensional structures. “That is our basic question.” The lung is ideally suited for these studies because its structure is, on one hand, simple – the branches always follow the same pattern – but, on the other hand, highly complex, as the bronchi divide into two sub-branches about 24 times from the trachea down to the finest bronchioles. These new branches are, on average, 20 percent narrower each time. The question is: which factors and biophysical processes control this pattern formation during lung development? Or, as Iber puts it: “How does this fractal structure develop right up to a baby’s first cry?”
The earliest research on branched biological transport systems dates back over a hundred years. In the 1910s, Walter Rudolf Hess, a physiologist from the Swiss canton of Thurgau and later a Nobel Prize laureate, suggested that in symmetrical blood vessel branches, the daughter branches should be 20 percent narrower to optimise blood flow. Just over ten years later, American physiologist Cecil Murray generalised Hess’s principle to asymmetric trees and also proposed ideal branching angles. “But the Hess-Murray Law doesn’t only apply to blood vessels; it also applies to lungs,” says Iber.
Scientists have faced significant challenges in the anatomical annotation and measurement of the human lung. In the early 1960s, Swiss anatomist and former rector of the University of Bern, Ewald Weibel, was the first to measure a resin cast of the bronchial tree; however, narrower branches broke off and were missing. Similarly, in a computed tomography (CT) scan, only the thick branches of the first ten generations of airways are visible. Meanwhile, using other techniques, only the smallest branches and alveoli can be observed. Just under four years ago, a team at the European Synchrotron Radiation Facility in Grenoble used X-rays to visualise the complete lung structure, from the primary bronchi to the alveoli. But until now, no comprehensive analysis of the 3D images has been undertaken.
For their own research project on lung development, Iber’s team employed a variety of methods. The foundation of their work was animal experiments involving healthy mice. In mice, lung development begins on day 10 after conception, and by day 16.5 – just under three days before birth – all branches are formed. Malte Mederacke, a doctoral student in Iber’s group, dissected and prepared lungs from mouse embryos at different stages of development, and created 3D images using light sheet fluorescence microscopy. To do this, he had to euthanise the pregnant females (seven in total) at specific times and remove the embryos (52 in total). This procedure is regarded as not distressing for the animals, as no intervention is performed on live animals (severity degree 0).
Together with Kevin Yamauchi, a postdoctoral researcher in Iber’s group, Mederacke developed an AI-based software called SkelePlex to analyse 3D lung images. This enabled them to depict and quantify the architecture of a developing lung, down to the finest branches. The tool allowed the researchers to visualise the dynamic process by which the wall thickness and diameter of pulmonary vessels constantly change during development, ensuring the formation of an optimally adapted lung.
When analysing this data, the researchers observed that two biophysical factors, in particular, played a significant role. The first is the shear force exerted when a liquid flows through a tube. The flow velocity is highest at the centre of the vessel and decreases towards the walls – the resulting velocity gradient at the vessel wall generates wall shear stress. Using the SkelePlex tool, the researchers demonstrated that as the tubes begin to widen during embryonic development, the relative diameters of successive tubes are adjusted so that the wall shear stress is approximately uniform across the entire bronchial tree. Walter Rudolf Hess and Cecil Murray had already noted that a branching architecture with uniform wall shear stress enables transport with minimal energetic cost.
Another factor is circumferential (or hoop) stress. It arises from the pressure difference between the luminal and external sides of the tube, which strains the wall. Airflow through the bronchial tree is driven by a pressure gradient between the airways and the alveoli, while the external pressure is relatively constant. As a result, the transmural pressure varies along the bronchial tree. Circumferential stress decreases with decreasing transmural pressure and tube radius, and with increasing wall thickness, and vice versa.
Using a SkelePlex analysis, the researchers demonstrated that wall thickness varies along the bronchial tree so that circumferential stress remains approximately uniform throughout the entire structure, from the smallest bronchioles to the primary bronchi. Clearly, it is vital that these two parameters – wall shear stress and circumferential stress – remain uniform to develop a lung that is as efficient as possible.
These new findings would not have emerged without the initial animal experiments. “We would never have been able to discover these things without the mouse embryo data,” says Iber. For all subsequent experiments in the project, the BSSE researchers relied on 3R methods, which aim to replace, reduce, or refine animal testing. “Simulation models allow us to get more out of the animal data and better transfer it to humans,” says Iber.
For some of their analyses, Iber and her team even exploited a fourth “R”: reuse. For one, the data on the earliest stages of lung development in mice were sourced from an earlier publication. In addition, the researchers relied on 20-year-old data from an experiment conducted on juvenile dogs in the United States to verify their findings from the mouse embryos. This data came from a study, in which juvenile dogs in Texas underwent lung lobectomy, leading to significant compensatory lung growth until lung volume was fully restored to normal. Using the SkelePlex tool, Iber’s team analysed the raw data from Texas and found that the observed compensatory growth followed the same principles as embryonic development.
Iber and her team also examined the human lungs, with particular focus on samples from patients with COPD. COPD is the third leading cause of death worldwide, after cardiovascular disease and cancer, but Iber notes that it can be difficult to diagnose correctly. It is typically identified by ruling out other respiratory conditions. Although it is well established that the thickness of airway walls increases in patients with COPD, the variability within a single bronchial tree and between individuals is too large to allow for a definitive diagnosis based on a single case.
For their current study, Iber’s team analysed chest CT scans from over 500 COPD patients and more than 40 healthy individuals, provided by Basel University Hospital and Siemens Healthineers. Using their findings on wall shear stress and circumferential stress, the team was able to better distinguish the two cohorts based on tube diameter and wall thickness. However, the separation between the cohorts is still insufficient for a reliable COPD diagnosis.
Iber hopes that the data from Grenoble will help bridge the gap. The dataset includes lung CT scans from both COPD patients and healthy controls. Her team plans to analyse these with SkelePlex to identify quantitative biomarkers that can reliably detect COPD. They also aim to create synthetic lungs through computer simulations (“in silico”) to improve the diagnosis and understanding of the deadly respiratory disease. Yet this is only the beginning: Iber’s ambitions go further. “My goal is to develop a digital twin - a computer model that reproduces embryonic or even organ development in silico, and that others can use as well,” she says.
Related scientific publication
external page The emergence of the fractal bronchial tree
Malte Mederacke, Kevin A. Yamauchi, Nikolaos Doumpas, Laura Schaumann, Jonathan Sperl, Thomas Weikert, D. Merrill Dane, Connie C. W. Hsia, Maurice Pradella, Jens Bremerich, Roman Vetter, Dagmar Iber (2025). Cell Systems