The data processing regarding AFM nanoindentation experiments on biological samples relies on the basic contact mechanics models like the Hertz model and the Oliver & Pharr analysis. Despite the fact that the two aforementioned techniques are assumed to provide equivalent results since they are based on the same underlying theory of contact mechanics, significant differences regarding the Young’s modulus calculation even on the same tested sample have been presented in the literature. The differences can be even greater than 30% depending on the used model. In addition, when the Oliver & Pharr analysis is used, a systematic greater Young’s modulus value is always calculated compared to the Hertzian analysis. In this paper, the two techniques are briefly described and two possible reasons that accurately explain the observed differences in the calculated value of the Young’s modulus are presented.

Atomic Force Microscopy nanoindentation method is a powerful technique that can be used for the nano-mechanical characterization of bio-samples. Significant scientific efforts have been performed during the last two decades to accurately determine the Young’s modulus of collagen fibrils at the nanoscale, as it has been proven that mechanical alterations of collagen are related to various pathological conditions. Different contact mechanics models have been proposed for processing the force–indentation data based on assumptions regarding the shape of the indenter and collagen fibrils and on the elastic or elastic–plastic contact assumption. However, the results reported in the literature do not always agree; for example, the Young’s modulus values for dry collagen fibrils expand from 0.9 to 11.5 GPa. The most significant parameters for the broad range of values are related to the heterogeneous structure of the fibrils, the water content within the fibrils, the data processing errors, and the uncertainties in the calibration of the probe. An extensive discussion regarding the models arising from contact mechanics and the results provided in the literature is presented, while new approaches with respect to future research are proposed.

Assume a rigid sphere that is slightly pushed towards an elastic half space. The applied force on the half space can be easily calculated using the basic theoretical tools provided by the Hertzian contact mechanics theory. It should be noted that the aforementioned analysis is valid under the condition that the deformation depth is significantly smaller compared to the sphere’s radius ( h ≪ R ). So, a significant question arises; what if the sphere is pushed deeper in the elastic half space (e.g. h > R )? In this paper, the aforementioned question is answered and a relative discussion regarding the application of the results is presented.

Measuring the mechanical properties (i.e., elasticity in terms of Young’s modulus) of biological samples using Atomic Force Microscopy (AFM) indentation at the nanoscale has opened new horizons in studying and detecting various pathological conditions at early stages, including cancer and osteoarthritis. It is expected that AFM techniques will play a key role in the future in disease diagnosis and modeling using rigorous mathematical criteria (i.e., automated user-independent diagnosis). In this review, AFM techniques and mathematical models for determining the spatial variability of elastic properties of biological materials at the nanoscale are presented and discussed. Significant issues concerning the rationality of the elastic half-space assumption, the possibility of monitoring the depth-dependent mechanical properties, and the construction of 3D Young’s modulus maps are also presented.

Atomic force microscopy (AFM) is a powerful tool that enables imaging and nanomechanical properties characterization of biological materials. Nanofibers are the structural units of many biological systems and their role in the development of advanced biomaterials is crucial. AFM methods have proven to be effective towards the characterization of fibers with respect to biological and bioengineering applications at the nanoscale. However, both the topographical and mechanical properties’ nanocharacterizations of single fibers using AFM are challenging procedures. In particular, regarding imaging procedures, significant artifacts may arise from tip convolution effects. The geometrical characteristics of the AFM tip and the nanofibers, and the fact that they have similar magnitudes, may lead to significant errors regarding the topographical imaging. In addition, the determination of the mechanical properties of nanofibers is also challenging due to their small dimensions and heterogeneity (i.e., the elastic half-space assumption is not valid in most cases). This review elucidates the origins of errors in characterizing individual nanofibers, while also providing strategies to address limitations in experimental procedures and data processing.