Abstract
Measurements of Young’s moduli are mostly evaluated using strong assumptions, such as sample homogeneity and isotropy. At the same time, descriptions of measurement parameters often lack detailed specifications. Many of these assumptions are, for soft hydrogels especially, not completely valid and the complexity of hydrogel microindentation demands more sophisticated experimental procedures in order to describe their elastic properties more accurately. We created an algorithm that automates indentation data analysis as a basis for the evaluation of large data sets with consideration of the influence of indentation depth on the measured Young’s modulus. The algorithm automatically determines the Young’s modulus in indentation regions where it becomes independent of the indentation depth and furthermore minimizes the error from fitting an elastic model to the data. This approach is independent of the chosen elastic fitting model and indentation device. With this, we are able to evaluate large amounts of indentation curves recorded on many different sample positions and can therefore apply statistical methods to overcome deviations due to sample inhomogeneities. To prove the applicability of our algorithm, we carried out a systematic analysis of how the indentation speed, indenter size and sample thickness affect the determination of Young’s modulus from atomic force microscope (AFM) indentation curves on polyacrylamide (PAAm) samples. We chose the Hertz model as the elastic fitting model for this proof of principle of our algorithm and found that all of these parameters influence the measured Young’s moduli to a certain extent. Hence, it is essential to clearly state the experimental parameters used in microindentation experiments to ensure reproducibility and comparability of data.
Highlights
The ability of cells to sense and react to mechanical cues of their evironment has been largely accepted by the scientific community and is currently the focus of many research projects
We have developed and evaluated a new algorithm that automates the analysis of microindentation experiments by taking into account the dependence of Young’s modulus on indentation depth
We have demonstrated the applicability of this algorithm by a systematic analysis of the effect of several indentation parameters, such as indentation speed and indenter size, on the measured Young’s modulus of PAAm samples
Summary
The ability of cells to sense and react to mechanical cues of their evironment has been largely accepted by the scientific community and is currently the focus of many research projects. The step towards quantitative and comparable results does lie in a more sophisticated discrete theoretical description, but in more complex and statistically inspired experimental procedures For this purpose, the AFM is the perfect tool, since it allows the implementation of indentation experiments down to piconewton precision, but it is able to scan surfaces in the micrometer range, making it possible to measure the elasticity of substrates at many different positions. Our strategy to automate the analysis of indentation curves with respect to the influence of the indentation depth on the measured Young’s modulus allows a more comprehensive description of the elasticity of soft biomaterials It will facilitate the computation of elasticity maps and allow the measurement of the elastic properties of substrates on a spatial scale similar to that of cellular interactions. This method has a broad applicability as it is independent of the applied elastic theory and indenting device
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