Deciphering the interplay between biology and physics with a finite element method-implemented vertex organoid model: A tool for the mechanical analysis of cell behavior on a spherical organoid shell

Understanding the interplay between biology and mechanics in tissue architecture is challenging, particularly in terms of 3D tissue organization. Addressing this challenge requires a biological model enabling observations at multiple levels from cell to tissue, as well as theoretical and computational approaches enabling the generation of a synthetic model that is relevant to the biological model and allowing for investigation of the mechanical stresses experienced by the tissue. Using a monolayer human colon epithelium organoid as a biological model, freely available tools (Fiji, Cellpose, Napari, Morphonet, or Tyssue library), and the commercially available Abaqus FEM solver, we combined vertex and FEM approaches to generate a comprehensive viscoelastic finite element model of the human colon organoid and demonstrated its flexibility. We imaged human colon organoid development for 120 hours, following the evolution of the organoids from an immature to a mature morphology. According to the extracted architectural/geometric parameters of human colon organoids at various stages of tissue architecture establishment, we generated organoid active vertex models. However, this approach did not consider the mechanical aspects involved in the organoids’ morphological evolution. Therefore, we applied a finite element method considering mechanical loads mimicking osmotic pressure, external solicitation, or active contraction in the vertex model by using the Abaqus FEM solver. Integration of finite element analysis (FEA) into the vertex model achieved a better fit with the biological model. Therefore, the FEM model provides a basis for depicting cell shape, tissue deformation, and cellular-level strain due to imposed stresses. In conclusion, we demonstrated that a combination of vertex and FEM approaches, combining geometrical and mechanical parameters, improves modeling of alterations in organoid morphology over time and enables better assessment of the mechanical cues involved in establishing the architecture of the human colon epithelium.Author summary: This study explores the interplay between biology and mechanics in tissue architecture, particularly the 3D organization of human colonic epithelial organoid. The experimental approach focused on imaging in culture the organoids for 120 hours to follow their morphological maturation. From these images, the architectural and geometric parameters of the biological organoids were extracted and used to create in silico organoid by the vertex method. However, this method did not take into account the mechanical forces involved in the morphological evolution of the organoids. To overcome this limitation, a finite element method was applied to the vertex model. Using the Abaqus solver, mechanical constraints, such as those undergone by biological organoids, were simulated. The integration of FEM into the vertex model improved the correspondence between the biological model and the modeling, providing a more accurate representation of tissue deformations, cellular forces and mechanical tensions undergone by the biological organoid. This method enabled creation of a digital model of the human colon tissue to aid in understanding the roles of mechanical forces in establishing human colon tissue architecture over time.