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Dynamics of individual and collective cells with fluid flow is an important and attractive topic in both the areas of fluid science and biomedical engineering. The kinetic theory-based lattice Boltzmann model is presented to describe the multicellular dynamics coupled with fluid flows. In the model, the Bhatnagar–Gross–Krook (BGK) Boltzmann equation is extended to describe both cellular and fluid dynamics. Through the Chapman–Enskog analysis, the BGK–Boltzmann equation for cells can be recovered to the phase field equation, capturing the intricate processes of cell motion and deformation. Simultaneously, the BGK–Boltzmann equation governing fluid dynamics can be recovered to the Navier–Stokes equations, enabling accurate representation of fluid flow characteristics. Both BGK–Boltzmann equations are directly discretized into the lattice Boltzmann scheme, providing an efficient and robust computational approach. After model validation and verification, the dynamical behavior of an individual cell and multicellular spheroids in shear flows were sequentially investigated. Apart from the observation of elongation and rotation of multicellular spheroids, quantitative analyses were conducted across several key factors. The results show that the physical properties of cells and flow significantly impact the rheology of multicellular spheroids, and this effect is related to intercellular interactions. Furthermore, the morphogenesis of multicellular aggregate under the influence of inflow was investigated, revealing the remarkable cellular deformation along with the formation of a cavity. This study demonstrates the potentiality of the proposed kinetic theory based method in simulating microscopic biofluidic systems, providing a novel numerical tool to explore the intricate interactions between cells and their hydrodynamical environments.
Wu et al. (Tue,) studied this question.