COVID-19 has clearly highlighted the need for reliable, mathematical modeling-based predictions in epidemiology. Standard models in the field do not account for the time delay between infections and corresponding fatalities, and often, also the fact that the underlying model parameters evolve over time is neglected. In order to tackle this challenge from an innovative perspective inspired by hereditary mechanics, we conceptualize it as a “mechanobiological problem”, formulating a “aging infection-to-death-rate delay rule”, through which the fatality trends are computed from infection histories. In contrast to the aforementioned standard models in the field, our model does account for delay effects within pandemic dynamics and incorporates exponentially decaying country-/territory-/US state-specific fatality fractions, which are governed by the initial fatality fraction and the characteristic time of fatality decay. When compared to the kinetics approach, as it is standardly implemented in the traditional SIR models, our novel approach allows for better fatality predictions from recorded infection numbers than the death kinetics model for remarkable 93 % of the 228 countries, territories and US states considered in this study. Moreover, it shows promising capabilities for short-term fatality predictions, as the derived parameters of our hereditary mechanics-based model are fairly stable over extended periods of time. Thus, by focusing here on the aging nature of pandemics and evolving parameters, the precision of epidemiological predictions is clearly improved based on the proposed model, emphasizing the benefits of integrating mechanobiological principles into epidemiological modelling. This way, it seems possible to better address the complex challenges posed by dynamic infectious diseases like COVID-19.

The paper addresses the issue of computational modeling of the human abdominal wall based on in vivo studies. The motivation for the research are abdominal defects, such as hernias, and the problem of their effective repair. Often the repair is done with the use of synthetic implants, that typically do not mimic the mechanical properties of the human tissue they replace. This causes a state of stress, which may lead to the implant detaching and thus to the recurrence of the hernia.

The complex, multi-layered structure of the abdominal wall causes differences in the mechanical behavior of its various regions, which are easy to observe e.g., through different ranges of strains under physiological loads. This causes difficulties in adjusting the appropriate properties of implants used as substitutes for healthy tissue in the area of the defect (hernia). The complexity makes the structure not easy to model.

In this article we discuss the problems of computational modeling of the human abdominal wall based on experimental data collected on the surface of the abdominal wall during changes in intra-abdominal pressure. We define numerical models by means of finite element method. We analyse the impact of changes in the mechanical properties of various abdominal regions on the forces in the connection between the implant and the tissue. We relate the results of numerical studies to experimental data based on digital image correlation. We use neural networks (self-organizing maps) in the analysis, which helps to determine regions with similar mechanical behavior under the influence of intra-abdominal pressure change.

The mechanotrasduction of intracellular stimuli represents a fascinating aspect of mechanobiology since many different pathways may activate the gene expression of different kind of cells. The main parameters and phenomena activating the mechanotrasduction have to be fully uncovered so that therapeutic stimulation to capture self-healing by some specific pathologies is still a fondamental challenge in the field of biomedical engineering.

In this study the author aims to show that possible source of mechanotrasduction is the flutter-induced instability of primary cilia on the anchoraging cytoskeleton. In particular, the cilium is modelled as an Euler-Bernoulli cantilever beam clamped at one side and free on the other side that is completely equivalent to a Leipholtz column, in which the follower load is distributed along the ciliary axoneme. By finding the critical load for which this system becomes unstable, it is possible to link it to the velocity with which the extracellular fluid is tangentially distributed along the cilium. The analysis is carried out introducing a generalized version of the Ruth-Hurwitz criterion that may be used in presence of hereditary materials as the cilium fibers.

[1] Wang J.H., Thampatty B.P. 2006, An introductory review of cell mechanobiology. Biomech. Model. Mechanobiol. ;5:1–16. doi: 10.1007/s10237-005-0012-z.

[2] Ingber D.E., 2003, Mechanobiology and diseases of mechanotransduction. Ann. Med. ;35:564–577. doi: 10.1080/07853890310016333.

[3] Bologna, E., Zingales, M. (2018). Stability analysis of beck’s column over a fractional-order hereditary foundation. Proc. Of the R. Soc. Of London A: Math. Gen. 474(2218), 20180315