(K-409) Quantifying Formation of the Fractal Pattern of Airways in the Lung

Thursday, October 12, 2023

9:30 AM – 10:30 AM PDT

Location: Exhibit Hall - Row K - Poster # 409

Presenting Author(s)

JK

Jake J. Klimek

Student
Department of Chemical and Biological Engineering, Princeton University
Princeton, New Jersey, United States

Co-Author(s)

IL

Isabella P. Leite

Graduate Student
Lewis Sigler Institute for Integrative Genomics, Princeton University, United States
TK

Trishala Kumar

Student
Department of Physics, Princeton University, United States
SP

Sarah V. Paramore

Graduate Student
Department of Molecular Biology, Princeton University, United States
KG

Katharine Goodwin

Graduate Student
Lewis Sigler Institute for Integrative Genomics, Princeton University, United States
SB

Samhita P. Banavar

Postdoctoral Research Fellow
Department of Chemical and Biological Engineering, Princeton University, United States

Last Author(s)

CN

Celeste M. Nelson

Professor
Departments of Chemical and Biological Engineering and Molecular Biology, Princeton University, United States

Introduction: The mammalian lung consists of a highly stereotyped branched network of airways typically described as fractal in nature. When mature, the lungs are characterized by a self-similar bronchial tree, wherein each subsequent generation of branches is a scaled-down replicate of the parental branch. Surprisingly, however, daughter branches have similar diameters and lengths as their parent branches when they are first formed, suggesting that the fractal pattern arises from remodeling during lung maturation. In humans, abnormal growth of the airways during development can lead to potentially fatal birth defects like pulmonary hypoplasia, which is characterized by significantly underdeveloped lungs. With this in mind, characterizing the mechanisms by which the embryonic airway epithelium grows (in both the longitudinal and radial directions) is thus essential for understanding how the complex fractal patterns of the bronchial tree are formed. Previous work in our group found that first-generation branches throughout the lung widen at similar rates but lengthen at different rates during development. Here, our objective was to extend our analysis to higher branch generations by semi-automatically quantifying morphometric parameters in the entire bronchial tree. Indeed, quantitatively characterizing fractal pattern formation may inform the morphogenetic underpinnings of congenital lung disorders and inspire future clinical solutions.

Track: Tissue Engineering
Sub-Track: Developmental Biology and Morphogenesis of Engineered Tissues

Materials and Methods: We created and implemented a novel approach to semi-automatically quantify morphometric parameters (branch generation, length, and width) in the entire bronchial tree. Our method first leverages Imaris software to generate a multi-scale diameter filament from confocal microscopy z-stacks of dissected control mouse embryonic lungs stained for E-cadherin. Filament generation captures the branched morphology of the entire epithelium and only requires the specification of three parameters (tracheal, maximum airway, and minimum airway diameters). The filament contains a network of nodes that are connected along the longitudinal axis of the airways. Key data are embedded within each node, including its Cartesian coordinates in space, connectivity to other nodes, and local radius. The inherent unidirectional outgrowth and lack of loops in the bronchial tree allows the filament network to be interpreted as a directed acyclic graph (DAG). Consequently, we adapted directed graph theory approaches to automatically classify branches by lobe or generation and extract morphometric parameters from the generated filament network. Automated in MATLAB, we assign each filament node its degree to identify branch points and terminal ends. Subsequently, we employ breadth- and depth-first search algorithms to directionally traverse the filament network, isolating branches by generation and by stereotyped lobe (cranial, medial, left, and accessory). Upon branch identification, airway length and diameter are automatically obtained. We used this approach to analyze embryonic day (E) 12, E13, and E14 lungs to quantitatively characterize the entire bronchial tree during development.

Results, Conclusions, and Discussions: Using Imaris and directed graph theory approaches allowed for the semi-automatic generation of multi-scale diameter filaments and identification of first-generation branches in stereotyped lobes of the developing mouse lung. Because the seed-point generation and short-path algorithm employed by Imaris rely on local image intensity, high-quality microscopy images were essential for accurate filament generation. Fractal dimension of the bronchial tree (determined by a box counting method) was found to increase with the number of terminal ends (a proxy for developmental time) according to the power law y = a * x^b, where a = 1.83 (0.02) and b = 0.043 (0.002). Future work will continue to examine how airway length and diameter vary throughout development. Beyond application to control lungs, our pipeline to rapidly determine branch dimensions can be used to quickly quantify defects in the developing bronchial tree. There is also an opportunity to extend our approach to other organs with branched structures, providing further insight without requiring advanced tools like optical projection tomography.

Our work is a step toward elucidating the sophisticated interplay between the biochemical and biomechanical mechanisms that regulate and control the spatiotemporal dynamics of mammalian lung morphogenesis. Regardless of the complexity of the lung of interest, only three parameters were necessary to generate a multi-scale diameter filament and perform DAG analysis to quantify branch dimensions by generation and/or by lobe. Whereas many approaches to measure individual branches quickly become intractable in more developed lungs, our efficient and robust method significantly reduces both the time needed to quantify airway dimension and the potential bias that exists when taking measurements manually. Indeed, our reliable, high-throughput approach to morphometric analysis may rapidly accelerate discovery of the origins of fractal pattern formation in the lungs and inspire technologies or therapies that have a positive clinical impact.