We formulate a phase field model aiming to describe cell diffusion in a soft tissue, especially focusing on their active behaviour in sensing near cells and the mechanical property of the surrounding environment, to orientate their diffusion. The derivation is provided in the framework of power balance and micro-balance expenditure and has general applicability to a system of active particles moving inside an elastic environment. The key feature of this framework is the constitutive expression of the chemical potential, made up of an energetic term, derived from a homogeneous convex free energy, and an active microforce that leads to a spinodal decomposition. The active part of the chemical potential is defined in accordance with [1]. Additionally, we supplement the microforce balance with the power conjugate to the rate of change of the concentration gradient, guiding the diffusion process to a different stationary limit pattern [2]. This vector field could potentially model any directional cue or bias characterizing the interaction between particles and the surrounding elastic environment. Finally, we show the descriptive capability of the derived model to predict the characteristic patterns observed during the evolution of liver fibrosis inside a hepatic lobule, which represents the functional unit of the hepatic tissue. The FEM numerical simulations reproduce the fibrotic patterns as a result of the motion of the fibroblasts inside the lobule.

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Pattern Formation Due to the Interactions Between Active Particles and an Elastic Medium

  • Filippo Recrosi,
  • Rodolfo Repetto,
  • Amabile Tatone,
  • Marcello Vasta

摘要

We formulate a phase field model aiming to describe cell diffusion in a soft tissue, especially focusing on their active behaviour in sensing near cells and the mechanical property of the surrounding environment, to orientate their diffusion. The derivation is provided in the framework of power balance and micro-balance expenditure and has general applicability to a system of active particles moving inside an elastic environment. The key feature of this framework is the constitutive expression of the chemical potential, made up of an energetic term, derived from a homogeneous convex free energy, and an active microforce that leads to a spinodal decomposition. The active part of the chemical potential is defined in accordance with [1]. Additionally, we supplement the microforce balance with the power conjugate to the rate of change of the concentration gradient, guiding the diffusion process to a different stationary limit pattern [2]. This vector field could potentially model any directional cue or bias characterizing the interaction between particles and the surrounding elastic environment. Finally, we show the descriptive capability of the derived model to predict the characteristic patterns observed during the evolution of liver fibrosis inside a hepatic lobule, which represents the functional unit of the hepatic tissue. The FEM numerical simulations reproduce the fibrotic patterns as a result of the motion of the fibroblasts inside the lobule.