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.

This paper involves the automation of a visual characterisation technique for corrosion in marine vessels, as it appears in the hull preventive coatings of marine vessels and their surfaces. We propose a module that maximizes the utilisation of features learned by a deep convolutional neural network to identify areas of corrosion and segment pixels in regions of inspection interest for corrosion detection. Our segmentation module is based on Eigen tree decomposition and information-based decision criteria in order to produce specific corroded spots—regions of interest. To assess performance and compare it with our method, we utilize several state-of-the-art deep learning architectures.The results indicate that our method achieves higher accuracy and precision while maintaining the significance score across the entire dataset. To the best of our knowledge, this is the first Eigen tree-based module in the literature in the context of trained neural network predictors for classifying corrosion in marine vessel images.

Hertzian mechanics is the most frequently used theory for data processing in Atomic Force Microscopy (AFM) indentation experiments on soft biological samples, due to its simplicity and significant scientific results previously published. For instance, using the Hertz model, it has been proven that there are significant differences in the mechanical properties of normal and cancerous tissues and that cancer cells’ invasive properties are correlated with their nanomechanical properties. However, many scientists are skeptical regarding the applicability of the Hertz theory to biological materials, as they are highly heterogeneous. The main critical question to be addressed is “what do we calculate” when fitting the force-indentation data to Hertz equations. Previous studies have shown that when using cylindrical, parabolic, or conical indenters, the fitting parameter is the average Young’s modulus. In this paper, it is demonstrated that it is also valid to fit equations derived from Hertzian mechanics to force-indentation data when testing soft, heterogeneous samples for any indenter geometry. The fitting factor calculated through this approach always represents the average Young’s modulus for a specific indentation depth. Therefore, Hertzian mechanics can be extended to soft heterogeneous materials, regardless of the indenter’s shape.

We propose an unsupervised method for eigen tree hierarchies and quantisation group association for segmentation of corrosion in marine vessel hull inspection via camera images. Our unsupervised approach produces image segments that are examined to decide on defect recognition. The method generates a binary decision tree, which, by means of bottom-up pruning, is revised, and dominant leaf nodes predict the areas of interest. Our method is compared with other techniques, and the results indicate that it achieves better performance for true- vs. false-positive area against ideal (ground truth) coverage.

Nonlinear oscillations are a challenging problem due to the high complexity of the underlying differential equations. This paper focuses on the nonlinear oscillator with cubic and harmonic restoring force as it represents a very general case. In particular, many well-known oscillators (e.g., the Duffing equation, the capillary oscillator, the cubic-quintic Duffing oscillator, the simple pendulum, etc) are subcases of it. Accurate solutions in terms of Fourier series functions for different oscillation amplitudes were derived using an energy-based numerical method and fitting processes. In addition, an analytical approach was developed by finding the derivative of the restoring force function at the point x = c 0 A , where A is the amplitude of the oscillation, and c 0 is a constant. Using this approach, the error was negligible (∼0.02–0.22%) even for A → ∞. The methods and solutions for the nonlinear oscillator with cubic and harmonic restoring force can be equally applied to all its subcases.