Computational models of airway branching morphogenesis

Abstract

The bronchial network of the mammalian lung consists of millions of dichotomous branches arranged in a highly complex, space-filling tree. Recent computational models of branching morphogenesis in the lung have helped uncover the biological mechanisms that construct this ramified architecture. In this review, we focus on three different theoretical approaches – geometrical modeling, reaction-diffusion modeling, and continuum mechanical modeling – and discuss how, taken together, these models have identified the geometrical principles necessary to build an efficient bronchial network, as well as the patterning mechanisms that specify the airway geometry in the developing embryo. We emphasize models that are integrated with biological experiments and suggest how recent progress in computational modeling has advanced our understanding of airway branching morphogenesis.

Spontaneous calcium activity in metanephric mesenchymal cells regulates branching morphogenesis in the embryonic kidney

“…The embryonic kidney continues to grow after a reduction of calcium signals, but with a lower probability for branching. Our data are in line with and support theoretical studies demonstrating that branching morphogenesis can be described as a stochastic and self-organizing process (4). Release of diffusible morphogenic factors at the UB-MM interface could modify and control the stochastic process that drives branching morphogenesis and lead to a self-organized morphology of the kidney (5–7).…”

“…In a series of theoretical studies, it has recently been proposed that morphogenesis in kidney, lung, and mammary glands can be described as a self-organized process (3) with stochastic components that are modified and controlled by signaling molecules (4–6). This description is supported by several studies of the embryonic kidney, where it has been demonstrated that genetically controlled and programmed events play a role for proper branching morphogenesis (7).…”

AVATREE: An open-source computational modelling framework modelling Anatomically Valid Airway TREE conformations

“…Deriving airway diameter as a relation of branching features facilitates full determination of the geometry given skeletal representations. Several studies mention scaling properties [33][34][35][36] for the airway diameters so that the average diameter D of a given airway at generation G is the product of the diameter of the trachea D 0 . Furthermore, Kamiya et al [37] validated the relation between airway diameter and branching angles and, Kitaoka et al [2] proposed a branching model allowing the prediction of the relationship between branching angle and flow rate and between airway length and diameter.…”

Multiscale dynamics of branching morphogenesis

“…calling for different theoretical (Table 1) and experimental approaches. Here, we aim to review our current understanding of branching morphogenesis, highlighting the generic design principles that can be abstracted at different scales ( Figure 1) and across organs [3][4][5] .…”