The fractal geometry of bronchial trees differs by strain in mice

Exploiting mechanisms for hierarchical branching structure of lung airway

The lung airways exhibit distinct features with long, wide proximal branches and short, thin distal branches, crucial for optimal respiratory function. In this study, we investigated the mechanism behind this hierarchical structure through experiments and modeling, focusing on the regulation of branch length and width during the pseudoglandular stage. To evaluate the response of mouse lung epithelium to fibroblast growth factor 10 (FGF10), we monitored the activity of extracellular signal-regulated kinase (ERK). ERK activity exhibited an increase dependent on the curvature of the epithelial tissue, which gradually decreased with the progression of development. We then constructed a computational model that incorporates curvature-dependent growth to predict its impact on branch formation. It was demonstrated that branch length is determined by the curvature dependence of growth. Next, in exploring branch width regulation, we considered the effect of apical constriction, a mechanism we had previously proposed to be regulated by Wnt signaling. Analysis of a mathematical model representing apical constriction showed that branch width is determined by cell shape. Finally, we constructed an integrated computational model that includes curvature-dependent growth and cell shape controls, confirming their coordination in regulating branch formation. This study proposed that changes in the autonomous property of the epithelium may be responsible for the progressive branch morphology.

Physiological impacts of computed tomography airway dysanapsis, fractal dimension, and branch count in asymptomatic never smokers

Dysanapsis, a mismatch between airway tree caliber and lung size, contributes to a large variation in lung function on spirometry in healthy subjects. However, it remains unclear whether other morphological features of the airway tree could be associated with the variation in lung function independent of dysanapsis. This study used lung cancer screening chest computed tomography (CT) and spirometry data from asymptomatic never smokers. Dysanapsis and the complexity of airway tree geometry were quantified on CT by measuring airway to lung ratio (ALR) and airway fractal dimension (AFD). Moreover, total airway count (TAC), ratio of airway luminal surface area to volume (SA/V), longitudinal tapering and irregularity of the radius of the internal lumen from the central to peripheral airways (Tapering index and Irregularity index) were quantified. In 431 asymptomatic never smokers without a history of lung diseases, lower ALR was associated with lower forced expiratory volume in 1 s (FEV₁) and FEV₁/forced vital capacity (FEV₁/FVC). The associations of ALR with AFD and TAC (r = 0.41 and 0.13) were weaker than the association between TAC and AFD (r = 0.64). In multivariable models adjusted for age, sex, height, and mean lung density, lower AFD and TAC were associated with lower FEV₁ and FEV₁/FVC independent of ALR, whereas SA/V and Tapering index were not. These results suggest that the smaller airway tree relative to a given lung size and the lower complexity of airway tree shape, including lower branch count, are independently associated with lower lung function in healthy subjects.NEW & NOTEWORTHY This study showed that fractal dimension and total airway count of the airway tree on computed tomography are associated with lung function on spirometry independent of a smaller airway for a given lung size (dysanapsis) in asymptomatic never smokers without a history of lung diseases. In addition to dysanapsis, the morphometric complexity of the airway tree and the airway branch count may cause a substantial variation of lung function in these subjects.

Fgf10/Fgfr2b Signaling Orchestrates the Symphony of Molecular, Cellular, and Physical Processes Required for Harmonious Airway Branching Morphogenesis

Airway branching morphogenesis depends on the intricate orchestration of numerous biological and physical factors connected across different spatial scales. One of the key regulatory pathways controlling airway branching is fibroblast growth factor 10 (Fgf10) signaling via its epithelial fibroblast growth factor receptor 2b (Fgfr2b). Fine reviews have been published on the molecular mechanisms, in general, involved in branching morphogenesis, including those mechanisms, in particular, connected to Fgf10/Fgfr2b signaling. However, a comprehensive review looking at all the major biological and physical factors involved in branching, at the different scales at which branching operates, and the known role of Fgf10/Fgfr2b therein, is missing. In the current review, we attempt to summarize the existing literature on airway branching morphogenesis by taking a broad approach. We focus on the biophysical and mechanical forces directly shaping epithelial bud initiation, branch elongation, and branch tip bifurcation. We then shift focus to more passive means by which branching proceeds, via extracellular matrix remodeling and the influence of the other pulmonary arborized networks: the vasculature and nerves. We end the review by briefly discussing work in computational modeling of airway branching. Throughout, we emphasize the known or speculative effects of Fgfr2b signaling at each point of discussion. It is our aim to promote an understanding of branching morphogenesis that captures the multi-scalar biological and physical nature of the phenomenon, and the interdisciplinary approach to its study.

Fractal Analysis of Lung Structure in Chronic Obstructive Pulmonary Disease

Chest CT is often used for localizing and quantitating pathologies associated with chronic obstructive pulmonary disease (COPD). While simple measurements of areas and volumes of emphysema and airway structure are common, these methods do not capture the structural complexity of the COPD lung. Since the concept of fractals has been successfully applied to evaluate complexity of the lung, this review is aimed at describing the fractal properties of airway disease, emphysema, and vascular abnormalities in COPD. An object forms a fractal if it exhibits the property of self-similarity at different length scales of evaluations. This fractal property is governed by power-law functions characterized by the fractal dimension (FD). Power-laws can also manifest in other statistical descriptors of structure such as the size distribution of emphysema clusters characterized by the power-law exponent D. Although D is not the same as FD of emphysematous clusters, it is a useful index to characterize the spatial pattern of disease progression and predict clinical outcomes in patients with COPD. The FD of the airway tree shape and the D of the size distribution of airway branches have been proposed indexes of structural assessment and clinical predictions. Simulations are also useful to understand the mechanism of disease progression. Therefore, the power-law and fractal analysis of the parenchyma and airways, especially when combined with computer simulations, could lead to a better understanding of the structural alterations during the progression of COPD and help identify subjects at a high risk of severe COPD.