# Tuning the Cell and Biological Tissue Environment through Magneto-Active Materials
## 3 Theoretical and Computational Frameworks for Mechanically Mediated Biological Processes
### Modelling Mechanical Effects on Bone Development and Healing
These results showed the role of nutrient concentration, suggesting that low availability severely dampens the speed of bone density evolution, resulting in lower inner density, but eventually converging into the expected final state. Moreover, the depletion of nutrients can result in accelerated atrophy, and a much slower increase in density in key support areas. Modelling Mechanical Effects on Collective Cell Migration Underlying Morphogenesis Tissue Regeneration and Cancer Progression  
The modelling of collective cell migration processes has been addressed mainly during the last decade. In this sense, different approaches covering different physical descriptions and scales have been used to model collective cell migration [88]. The lattice and phase field models describe the shape of the system at the subcellular level; however, the former are not suitable for incorporating some relevant cellular interactions to describe collective cell migration. Particle models are based on the physics of particulate media as granular materials. Although with less details of the cell shape, these can capture anisotropies in the geometry and allow the study of how and what interactions determine the mechanical state of tension of a tissue. Finally, continuous models describe cells as a whole at the coarse-grained level on the multicellular scale. Continuum models are most effective at this scale, as they describe the physical forces, flow, and deformation patterns that mediate collective cell migration during certain processes: wound healing, tissue development, and metastasis, among others. These models are based on the coupling of different governing equations: mass balance (cell proliferation dynamics); mechanical balance between cells and ECM; cell polarisation dynamics; dynamics of actomyosin concentration; and chemical diffusion processes. Mechanical equilibrium is affected by other physicochemical processes and determines the evolution of cell migration and proliferation, imposing a balance between internal cell stresses and external mechanical sources. [PERSON] and [PERSON] [89]proposed a continuous model, modified by [PERSON] et al. [90], for collective cell migration during unrestricted epithelial spread, which is a key mechanism in embryogenesis and wound healing, to reproduce the spontaneous formation of finger-like protrusions. This model describes the tissue as a polarizable elastic layer that interacts chemically and mechanically. Within the tissue, various chemical species diffuse, generating an active force along the direction of polarisation. Furthermore, [PERSON] et al. [90] proposed a continuous active polar fluid model for epithelial propagation where they demonstrated that epithelial fingering can arise naturally from generic morphological instability in a fluid film driven by interfacial active forces. [PERSON] et al. [91] developed a continuous model to examine the internal variables that generate cell polarisation and oscillatory waves. In another work, [PERSON] and [PERSON] [8] formulated a model that shows how the mechanics of the continuum can serve to test hypotheses about collective cell migration, more specifically, about the mechanical consequences of cell polarisation and the force of propulsion during durotaxis. Regarding current modelling approaches in cancer cell biology, the papers can be consulted in the References section [92; 93].