University Bordeaux, CNRS, Bordeaux INP, I2M, UMR 5295, F-33400, Talence, France; Arts et Metiers Institute of Technology, CNRS, Bordeaux INP, Hesam Universite, I2M, UMR 5295, F-33400 Talence, France; Institut Universitaire de France (IUF), France.
Institut Curie, Université PSL, Sorbonne Université, CNRS UMR168, Physique des Cellules et Cancer, 75005 Paris, France.
Acta Biomater. 2024 Nov;189:449-460. doi: 10.1016/j.actbio.2024.09.043. Epub 2024 Oct 1.
The micro-pipette aspiration technique is a classical experiment used to characterize the physical properties of inert fluids and biological soft materials such as cellular aggregates. The physical parameters of the fluid, as viscosity and interfacial tension, are obtained by studying how the fluid enters the pipette when the suction pressure is increased and how it relaxes when the suction pressure is put to zero. A mathematical model representative of the experiment is needed to extrapolate the physical parameters of the fluid-like matter; however, for biological materials as cells or cell aggregates mathematical models are always based on strong starting hypotheses that impact the significance of the identified parameters. In this article, starting from the bi-constituent nature of the cell aggregate, we derive a general mathematical model based of a Cahn-Hilliard-Navier-Stokes set of equations. The model is applied to describe quantitatively the aspiration-retraction dynamics of a cell-aggregate into and out of a pipette. We demonstrate the predictive capability of the model and highlight the impact of the assumptions made on the identified parameters by studying two cases: one with a non-wetting condition between the cells and the wall of the pipette (classical assumption in the literature) and the second one, which is more realistic, with a partial wetting condition (contact angle θ = 150°). Furthermore, our results provide a purely physical explanation to the asymmetry between the aspiration and retraction responses which is alternative to the proposed hypothesis of an mechano-responsive alteration of the surface tension of the cell aggregate. STATEMENT OF SIGNIFICANCE: Our study introduces a general mathematical model, based on the Cahn-Hilliard-Navier-Stokes equations, tailored to model micro-pipette aspiration of cell aggregates. The model accounts for the multi-component structure of the cell aggregate and its intrinsic viscoelastic rheology. By challenging prevailing assumptions, particularly regarding perfect non-wetting conditions and the mechano-responsive alteration of cell surface tension, we demonstrate the reliability of the mathematical model and elucidate the mechanisms at play, offering a purely physical explanation for observed asymmetries between the aspiration and retraction stages of the experiment.
微管吸吮技术是一种经典的实验方法，用于表征惰性流体和生物软物质（如细胞聚集体）的物理特性。通过研究当抽吸压力增加时流体如何进入微管以及当抽吸压力为零时流体如何松弛，可获得流体的物理参数，如粘度和界面张力。需要一个代表性的实验数学模型来推断类似流体物质的物理参数；然而，对于细胞或细胞聚集体等生物材料，数学模型始终基于对识别参数有重大影响的强起始假设。在本文中，我们从细胞聚集体的双组成性质出发，基于 Cahn-Hilliard-Navier-Stokes 方程组推导出一个通用的数学模型。该模型用于描述细胞聚集体进入和退出微管的抽吸-回缩动力学。我们通过研究两种情况来证明模型的预测能力，并突出对所识别参数的假设的影响：一种是细胞与微管壁之间的不润湿条件（文献中的经典假设），另一种是更现实的部分润湿条件（接触角θ=150°）。此外，我们的结果为抽吸和回缩响应之间的不对称性提供了一种纯粹的物理解释，这替代了细胞聚集体表面张力的机械响应改变的假设。
我们的研究引入了一个基于 Cahn-Hilliard-Navier-Stokes 方程的通用数学模型，旨在模拟细胞聚集体的微管吸吮。该模型考虑了细胞聚集体的多组分结构及其固有粘弹性流变学。通过挑战普遍的假设，特别是关于完美不润湿条件和细胞表面张力的机械响应改变的假设，我们证明了数学模型的可靠性，并阐明了起作用的机制，为实验中观察到的抽吸和回缩阶段之间的不对称性提供了一种纯粹的物理解释。
