Flow of fluids within biological tissues often meets with resistance that causes a rate- and size-dependent material behavior known as poroelasticity. Characterizing poroelasticity can provide insight into a broad range of physiological functions, and is done qualitatively in the clinic by palpation. Indentation has been widely used for characterizing poroelasticity of soft materials, where quantitative interpretation of indentation requires a model of the underlying physics, and such existing models are well established for cases of small strain and modest force relaxation. We showed here that existing models are inadequate for large relaxation, where the force on the indenter at a prescribed depth at long-time scale drops to below half of the initially peak force (i.e., F(0)/F(∞) > 2). We developed an indentation theory for such cases of large relaxation, based on Biot theory and a generalized Hertz contact model. We demonstrated that our proposed theory is suitable for biological tissues (e.g., porcine liver, spleen, kidney, skin and human cirrhosis liver) with both small and large relaxations. The proposed method would be a powerful tool to characterize poroelastic properties of biological materials for various applications such as pathological study and disease diagnosis.

生物组织内的流体流动通常会遇到阻力，这种阻力会导致速率和尺寸相关的材料行为（称为多孔弹性）。表征孔隙弹性可以洞察广泛的生理功能，并且在临床中通过触诊定性地完成。压痕已被广泛用于表征软质材料的孔隙弹性，其中压痕的定量解释需要基础物理模型，而对于小应变和适度力松弛的情况，这种现有模型已经很好地建立了。我们在这里表明，现有模型不足以实现较大的松弛，长时间内在规定深度处压头上的力会降至初始峰值力的一半以下（即F（0）/ F（∞）> 2）。基于比奥理论和广义赫兹接触模型，我们针对这种大松弛情况开发了一种压痕理论。我们证明了我们提出的理论适用于大小不一的生物组织（例如猪肝，脾脏，肾脏，皮肤和人肝硬化肝）。所提出的方法将是表征生物学材料的多孔弹性特性以用于各种应用（例如病理研究和疾病诊断）的有力工具。