A multiphysics hybrid continuum - agent-based model of in vitro vascularized organoids

Organoids are 3D in vitro models that fulfill a hierarchical function, representing a small version of living tissues and, therefore, a good approximation of cellular mechanisms. However, one of the main disadvantages of these models is the appearance of a necrotic core due to poor vascularization. The aim of this work is the development of a numerical framework that incorporates the mechanical stimulation as a key factor in organoid vascularization. Parameters, such as fluid velocity and nutrient consumption, are analyzed along the organoid evolution.

The mathematical model created for this purpose combines continuum and discrete approaches. In the continuum part, the fluid flow and the diffusion of oxygen and nutrients are modeled using a finite element method approach. Meanwhile, the growth of the organoid, blood vessel evolution, as well as their interaction with the surrounding environment, are modeled using agent-based methods.

Continuum model outcomes include the distribution of shear stress, pressure and fluid velocity around the organoid surface, in addition to the concentration of oxygen and nutrients in its interior. The agent models account for cell proliferation, differentiation, organoid growth and blood vessel morphology, for the different case studies considered.

Two main conclusions are achieved in this work: (i) the results of the study quantitatively predict in vitro data, with an enhanced blood vessel invasion under high fluid flow and (ii) the diffusion and consumption model parameters of the organoid cells determine the thickness of the proliferative, quiescent, hypoxic and necrotic layers.