Kontomaris Stylianos Vasileios, Malamou Anna, Stylianou Andreas
Cancer Mechanobiology and Applied Biophysics Group, School of Sciences, European University Cyprus, 2404 Nicosia, Cyprus.
School of Electrical and Computer Engineering, National Technical University of Athens, 15773 Athens, Greece.
Micromachines (Basel). 2024 Sep 29;15(10):1209. doi: 10.3390/mi15101209.
When testing biological samples with atomic force microscopy (AFM) nanoindentation using pyramidal indenters, Sneddon's equation is commonly used for data processing, approximating the indenter as a perfect cone. While more accurate models treat the AFM tip as a blunted cone or pyramid, these are complex and lack a direct relationship between applied force and indentation depth, complicating data analysis. This paper proposes a new equation derived from simple mathematical processes and physics-based criteria. It is accurate for small indentation depths and serves as a viable alternative to complex classical approaches. The proposed equation has been validated for ℎ < 3 (where h is the indentation depth and R is the tip radius) and confirmed through simulations with blunted conical and pyramidal indenters, as well as experiments on prostate cancer cells. It is a reliable method for experiments where the tip radius cannot be ignored, such as in shallow indentations on thin samples to avoid substrate effects.
在用金字塔形压头通过原子力显微镜（AFM）纳米压痕测试生物样品时，通常使用斯涅登方程进行数据处理，即将压头近似为一个完美的圆锥体。虽然更精确的模型将AFM探针视为钝圆锥体或棱锥体，但这些模型很复杂，且施加力与压痕深度之间缺乏直接关系，使数据分析变得复杂。本文提出了一个源自简单数学过程和基于物理标准的新方程。它在小压痕深度时是准确的，并且是复杂经典方法的可行替代方案。所提出的方程已在ℎ < 3（其中h是压痕深度，R是探针半径）的情况下得到验证，并通过钝圆锥体和棱锥体压头的模拟以及前列腺癌细胞实验得到证实。对于探针半径不可忽略的实验，例如在薄样品上进行浅压痕以避免基底效应的实验，它是一种可靠的方法。
