Abstract
Four-dimensional (4D) biofabrication techniques aim to dynamically produce and control three-dimensional (3D) biological structures that would transform their shapes or functionalities with time, when a stimulus is imposed or cell post-printing self-assembly occurs. The evolution of 3D branching patterns via self-assembly of cells is critical for the 4D biofabrication of artificial organs or tissues with branched geometry. However, it is still unclear how the formation and evolution of these branching patterns are biologically encoded. Here, we study the biofabrication of lung branching structures utilizing a simulation model based on Turing instability that raises a dynamic reaction–diffusion (RD) process of the biomolecules and cells. The simulation model incorporates partial differential equations of four variables, describing the tempo-spatial distribution of the variables in 3D over time. The simulation results present the formation and evolution process of 3D branching patterns over time and also interpret both the behaviors of side-branching and tip-splitting as the stalk grows and the fabrication style under an external concentration gradient of morphogen, through 3D visualization. This provides a theoretical framework for rationally guiding the 4D biofabrication of lung airway grafts via cellular self-organization, which would potentially reduce the complexity of future experimental research and number of trials.
Highlights
Three-dimensional (3D) printing in health science mainly aims to mimic biological functions [1,2,3]
Further research for the 4D biofabrication may rely on the 3D culture techniques [3,27,40] that are essentially constructing and regulating the dynamic structures composed of numerous cells
bone morphogenetic protein-4 (BMP4) has several features that qualify it as a potential activator morphogen in this model
Summary
Three-dimensional (3D) printing in health science mainly aims to mimic biological functions [1,2,3]. Cytoskeletal tension mediated by Rho signaling plays a role during cleft formation in lung branching Another form of the mechanics-based model is the 3D vertex model [33], which enables the quantitative simulation of multicellular morphogenesis based on single cell mechanics involving various cellular activities, such as cell contraction, growth, rearrangement, division, and death. In addition to the simulation and discussion on the evolution of 3D structures, we present and discuss the law governing the change of 3D bifurcation patterns in 2D parameter domains, the fabrication style under an external concentration gradient of morphogen, and the limitations of this prediction model These studies are more extensive when compared to our previous paper [37]. The simulation results and analysis provide a theoretical framework of the 3D and 4D fabrication of branching structures for lung or kidney in a cellular self-organization manner
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