Epithelial tissues maintain structural integrity through a balance between cell-cell adhesion and cortical contractility. Disruption of E-cadherin-mediated adhesion is a hallmark of metastatic progression, yet the physical mechanisms by which local molecular defects escalate into global tissue destabilization remain poorly understood. Traditional theoretical studies have focused on the density...
In this talk, I will introduce a modelling approach for single and collective cell migration through confined non-isotropic environments using geometric surface partial differential equations. By assuming that cell migration is driven by cell surface biochemical processes and surface mechanics, the evolution law of the cell and nuclear envelope is modelled through a force balance equation...
Biological tissues are often subjected to forces. In many cases, such as tumor growth or skin contraction, it is crucially important to model the state of tissues that are exposed to forces in order to improve or optimize therapies for different pathologies. The simplest models use linear elasticity as a constitutive law. This linearity enables the use of the superposition principle and the...
Cancer invasion emerges from coupled interactions between tumour cells and the extracellular matrix (ECM), where fibre architecture, remodelling, and microenvironmental cues jointly regulate migration and growth. Building on our earlier PhysiCell framework for collagen-density-dependent spheroid invasion, we present a hybrid discrete-continuous model that incorporates fibre orientation,...
In this talk we illustrate two-interrelated models of, respectively, onset of tumor angiogenesis \cite{m1}ย and of the effect of an antiangiogenesis therapy \cite{m1}. The key component of the model is a chemotactic mechanism (CM) for new vessel cells sprouting induced by pro-angiogenic factors secreted by the tumor. Our approach is based on a statistical mechanics and it takes into the account...
Cell migration is a complex biological process underlying phenomena such as wound healing, tissue morphogenesis, and cancer invasion. A key component of this process is the formation and turnover of focal adhesions, which provides a mechanical coupling between the cytoskeleton and the extracellular matrix. Actin filaments anchored at focal adhesions generate forces on the cell membrane,...
Motivated by a mechanical model of tumor encapsulation, we derive a generalized volume-filling cross-diffusion system for the components of tissue structures. The equations are formally derived from mass conservation laws and force balances in a multiphase approach. The model provides a general framework for studying tissue structures, and we show the analytical well-posedness of the system in...
Cells exert forces in their direct environment and cause the deformation of the tissue, which can result in severe consequences in some diseases such as contractures in burn injuries. Various mathematical models --- particularly in various scales ---- have been developed aiming to understand the biomechanics. In most of our work, we used the immerse boundary approach based on a superposition...
Cell-tissue interactions, including both chemical and mechanical interactions, are essential and crucially important for various biological processes, such as functioning organs, regenerating tissues and regulating cellular behaviours. In the past years, mathematical modelling has shown its great potential to further understand the biology and then predict the behaviours of cells and tissue,...
