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The present study proposes a mathematical model elucidating some aspects of the bio-mechanical stimulus involved in bone remodelling, which, in our assumptions, acts as a diffusive signalling agent for bones. The proposed mathematical model aims to scrutinize the behaviour of bone tissues and their evolution over time by better understanding the mechanisms of bone remodelling and offering new theoretical tools for developing more effective and efficient treatment strategies for bone defects, trauma, or diseases. The bone remodelling process involves adapting bone mechanical properties in response to dynamic loads. This adaptation is achieved through the diffusive stimulus created by these loads. The result is a functional adaptation of the bone, wherein it acquires the mechanical properties required to withstand the loads to which it is subjected. This phenomenon has significant implications for the study of bone physiology and biomechanics. As such, it is a topic of great interest to researchers and practitioners in the fields of orthopaedics, sports medicine, and related disciplines. In this contribution, the mechanical behaviour is modelled through a generalized three-dimensional deformable continuum that also takes into account the porous nature of the bone tissue with a nonlinear constitutive law. Since we have focused the study on the model of the stimulus and its interplay with the evolution of the tissue, an isotropic material symmetry is adopted to simplify the problem. This formulation is promising because it permits the bone tissue to evolve depending on the time variability of the external mechanical loads, even if the source of the stimulus is assumed to be the strain energy density. The proposed model exhibits great potential, and its scope extends to several other applications, including the integration of anisotropic material symmetry and damage. Further research in this area can unlock new possibilities and enable the development of more advanced models with these new features. We plan future investigations to focus on these areas to exploit the full potential of this model entirely. [ABSTRACT FROM AUTHOR]

Considering the major role of confined cell migration in biological processes and diseases, such as embryogenesis or metastatic cancer, it has become increasingly important to design relevant experimental set-ups for in vitro studies. Microfluidic devices have recently presented great opportunities in their respect since they offer the possibility to study all the steps from a suspended to a spread, and eventually crawling cell or a cell with highly deformed nucleus. Here, we focus on the nucleus self-deformation over a micropillared substrate. Actin networks have been observed at two locations in this set-up: above the nucleus, forming the perinuclear actin cap (PAC), and below the nucleus, surrounding the pillars. We can then wonder which of these contractile networks is responsible for nuclear deformation. The cytoplasm and the nucleus are represented through the superposition of a viscous and a hyperelastic material and follow a series of processes. First, the suspended cell settles on the pillars due to gravity. Second, an adhesive spreading force comes into play, and then, active deformations contract one or both actin domains and consequently the nucleus. Our model is first tested on a flat substrate to validate its global behaviour before being confronted to a micropillared substrate. Overall, the nucleus appears to be mostly pulled towards the pillars, while the mechanical action of the PAC is weak. Eventually, we test the influence of gravity and prove that the gravitational force does not play a role in the final deformation of the nucleus. [ABSTRACT FROM AUTHOR]

Successfully simulating tissue evolution in bone is of significant importance in predicting various biological processes such as bone remodeling, fracture healing and osseointegration of implants. Each of these processes involves in different ways the permanent or transient formation of different tissue types, namely bone, cartilage and fibrous tissues. The tissue evolution in specific circumstances such as bone remodeling and fracturing healing is currently able to be modeled. Nevertheless, it remains challenging to predict which tissue types and organization can develop without any a priori assumptions. In particular, the role of mechano-biological coupling in this selective tissue evolution has not been clearly elucidated. In this work, a multi-tissue model has been created which simultaneously describes the evolution of bone, cartilage and fibrous tissues. The coupling of the biological and mechanical factors involved in tissue formation has been modeled by defining two different tissue states: an immature state corresponding to the early stages of tissue growth and representing cell clusters in a weakly neo-formed Extra Cellular Matrix (ECM), and a mature state corresponding to well-formed connective tissues. This has allowed for the cellular processes of migration, proliferation and apoptosis to be described simultaneously with the changing ECM properties through strain driven diffusion, growth, maturation and resorption terms. A series of finite element simulations were carried out on idealized cantilever bending geometries. Starting from a tissue composition replicating a mid-diaphysis section of a long bone, a steady-state tissue formation was reached over a statically loaded period of 10,000 h (60 weeks). The results demonstrated that bone formation occurred in regions which are optimally physiologically strained. In two additional 1000 h bending simulations both cartilaginous and fibrous tissues were shown to form under specific geometrical and loading cases and cartilage was shown to lead to the formation of bone in a beam replicating a fracture healing initial tissue distribution. This finding is encouraging in that it is corroborated by similar experimental observations of cartilage leading bone formation during the fracture healing process. The results of this work demonstrate that a multi-tissue mechano-biological model of tissue evolution has the potential for predictive analysis in the design and implementations of implants, describing fracture healing and bone remodeling processes. [ABSTRACT FROM AUTHOR]

Cell migration triggered by pseudopodia (or “false feet”) is the most used method of locomotion. A 3D finite element model of a cell migrating over a 2D substrate is proposed, with a particular focus on the mechanical aspects of the biological phenomenon. The decomposition of the deformation gradient is used to reproduce the cyclic phases of protrusion and contraction of the cell, which are tightly synchronized with the adhesion forces at the back and at the front of the cell, respectively. First, a steady active deformation is considered to show the ability of the cell to simultaneously initiate multiple pseudopodia. Here, randomness is considered as a key aspect, which controls both the direction and the amplitude of the false feet. Second, the migration process is described through two different strategies: the temporal and the spatial sensing models. In the temporal model, the cell “sniffs” the surroundings by extending several pseudopodia and only the one that receives a positive input will become the new leading edge, while the others retract. In the spatial model instead, the cell senses the external sources at different spots of the membrane and only protrudes one pseudopod in the direction of the most attractive one. [ABSTRACT FROM AUTHOR]