Material hereditariness has been a topic of great interest since 20^th century. Indeed, several materials display a non-local time-dependent mechanical behaviour since they have memory of their past stress-strain history. This peculiarity led to the formulations of mathematical models, to characterise them, based on the use of fractional calculus; in such a way, it was possible to express the relations between stress and strain as non-local convolution integrals with power-law kernels to describe their time behaviour, in an appropriate way.

This non-locality in time was also considered from an energetic point of view. In fact, the work spent by these materials, during the loading phase, is recovered only in a partial way, during the unloading phase, and the remaining part is dissipated in the form of heat. This is the reason why, starting from the already established fractional-order models, a new formulation for the dissipation function, based on non-local convolution integrals, was proposed [1].

However, it was demonstrated that biological materials cannot be analysed by using the relations of linear hereditariness, since they display a non-linear behaviour even for low stress-strain levels. For this reason, in previous studies, the authors established new mechanical models to properly fit the non-linear fractional-order relations between stress and strain [2].

Consequently, the aim of this study is the extension of the dissipation to the framework of non-linear hereditariness involving fractional-order decaying functions.

[1] Deseri, L., et al., “Free energy and states of fractional-order hereditariness'', International Journal of Solids and Structures, 51(18), 3156-3167 (2014).

[2] Alotta, G., et al., “Exact mechanical hierarchy of non-linear fractional-order hereditariness'', Symmetr}, 12(4), 673 (2020).

Scaffold-based tissue engineering is a fast-growing field. Thereby, scaffolded spheroids are extensively utilized as building blocks, for facilitating the regeneration of defective tissue, due to their enhanced self-bioassembly and tissue fusion. For successful clinical application, scaffolds should be biocompatible. To that end, scaffolds made of cross-linkable gelatins and PCL-based resin were considered here. In terms of the scaffold shape, we focus in this study on truncated icosahedron shape–often referred to as “buckyballs”. Clearly, the geometric parameters of the scaffold influence the resulting mechanical stiffness and load-bearing capacity. The objective of this study was to study, numerically, the effect of the geometric parameters on the corresponding mechanical properties of buckyballs (i.e., the shape and the length of the struts making them up), while maintaining a porosity allowing for sufficient cell retention. The numerical studies were performed by means of the commercial Finite Element software Abaqus, relying on periodic homogenization based on appropriately chosen unit cells, in order to predict the stiffness tensor components of densely packed scaffolds. For the unit cells, linear Timoshenko beam elements (B31) were used, with linear elastic material behavior (considering varying Young’s moduli). Furthermore, circular, rectangular, square, and elliptical cross sections were chosen, while the overall buckyball size amounted to 200 µm. Six effective strain states were applied by adjusting periodic boundary conditions on master nodes of the unit cell to determine the effective stiffness. The buckyball stiffness turned out to be linearly dependent on the Young’s modulus of the material used to fabricate the scaffold. Interestingly, the rate of stiffness increase due to an increase in strut diameter is equal to the rate of stiffness decrease due to an increase in edge length. Hence, the ratio of cross-sectional size over the strut length turned out to be the key design parameter for buckyball optimization.

The biocompatibility of medical devices replacing biological tissues is related to the substitution of tissue function, and similarity in a number of physical, mechanical or structural parameters. Modelling the optimal scaffold, from the point of view of matter flow, energy and mass, has been the aim of numerous scientific papers for many years. In all this, it is not only the moment of implantation that is important, but above all the nature of the changes during the operation of such a device. The implanted device does not have the ability to adjust its properties to changing internal conditions: load values, chemical and biological properties of the intradural fluid associated with inflammation, for example. It is therefore important to determine the rate of change of its degradation in different environments, so that both the implant and its degradation products are not toxic to the living organism. The aim of this research is to determine both the structural and physical changes of the 3D-printed scapulae in different solutions simulating a biological environment. The test material consists of the PLLA/PGA copolymer scapes stored in PBS solution, a liquid with a pH of 4.0 and 7.0. In order to determine the resorption rate, each of the scapes was subjected to measurements every 30 days, in which the weight and geometry of the scapes and the pH of the solution were determined. A differential analysis based on a comparative method of mictrotomographically reconstructed scans (SkyScan 1172, Bruker) was carried out to analyse the changes occurring at each stage of material degradation.

Aortic dissection is a cardiovascular pathology that consists in the laceration of the innermost layer of the aortic wall (the tunica intima) with the consequent leakage of the blood into the other layers of the vessel, resulting in the creation of a “false lumen”. Even if this condition is quite rare, it represents one of the most serious cardiovascular diseases.

This is the reason why a previous study established a new biomechanical model of interface to predict the aortic dissection [1]; in particular, the mode I debonding problem was analysed. The aortic wall was modelled by using two Euler-Bernoulli beams clamped at one end, transversally loaded at the other one and joined together through a cohesive interface. The novelty of this approach consisted in the introduction of non-local terms [2], in the governing equation of the problem, to consider the forces transmitted by collagen fibres of non-adjacent elements.

However, even if the two beams were modelled as two elastic ones, it is proven that the aortic tissue displays a non-local time-dependent mechanical behaviour.Consequently, the aim of this study is to propose a new model to describe aortic dissection that considers the hereditary behaviour of the aortic wall, modelled by using two hereditary beams.Finally, some numerical simulations, with different values of non-local parameters, will be provided to demonstrate the goodness of the proposed model.

[1] Alotta, G., et al., "A non-local mode-i cohesive model for ascending thoracic aorta dissections (ATAD).”, 2018 IEEE 4th International Forum on Research and Technology for Society and Industry (RTSI). IEEE, 2018. p. 1-6, (2018).

[2] Di Paola, M., et al., "Physically-based approach to the mechanics of strong non-local linear elasticity theory.", Journal of Elasticity 97: 103-130, (2009).

Eosinophilic Sinusitis (ES) represents a unique subtype of paranasal sinusitis, characterized by nasal polyps near sinus openings due to chronic inflammation. The presence of nasal polyps complicates the treatment of sinusitis, often necessitating Endoscopic Sinus Surgery (ESS) as the condition progresses. However, residual inflammation in the sinus post-surgery can contribute to the recurrence of ES. Recently, vibrating nebulizers that deliver medication at specific frequencies have been introduced as a potential treatment for sinus inflammation, with particular anticipation for their application in case of ES. Nevertheless, the optimal vibration frequency to achieve maximal therapeutic benefit in nasal polyp cases remains unclear. This study utilized Computational Fluid Dynamics (CFD) to identify the most effective frequency of vibrating nebulizers for treating maxillary sinus inflammation in case of ES. Using medical imaging data from the target case, we simulated ESS of the nasal cavity and sinuses through virtual surgery. We analyzed airflow in the maxillary sinus, assuming drug diffusion based on post-surgical data. The inflow frequency of the nebulizer was adjusted at 0-125 Hz with 25 Hz increments to evaluate its impact on airflow within the maxillary sinus. Six control sections were defined: one at the natural ostium of maxillary sinus on each side, and two internal sections on each side. The frequency at which the largest Forward direction Volume Flow rate was observed in each inspection section was defined as the optimal frequency. The results revealed that 50Hz was the optimal frequency at the natural ostium, and a frequency range of 0-50Hz was optimal within the maxillary sinus under post-surgical conditions. Furthermore, changes in vibration frequency affected the direction of inflow and location of vortex, leading to varying optimal frequencies within the sinus. Therefore, utilizing CFD analysis to identify the optimal frequency for each specific inflammation site could improve therapeutic outcomes.