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We give a very short introduction to discrete and continuum models for the evolutionary and spatial dynamics of cancer through two case studies: a model for the evolutionary dynamics of cancer cells under cytotoxic therapy and a model for…
We provide a review of recent advancements in nonlocal continuous models for migration, mainly from the perspective of its involvement in embryonal development and cancer invasion. Particular emphasis is placed on spatial nonlocality…
We propose a mathematical model for tumor invasion supported by angiogenesis and interactions with the surrounding tissue. For the model deduction we employ a multiscale approach starting from lower scales and obtaining by an informal…
Airborne pathogen transmission mechanisms play a key role in the spread of infectious diseases such as COVID-19. In this work, we propose a computational fluid dynamics (CFD) approach to model and statistically characterize airborne…
In recent years, there has been a spike in the interest in multi-phase tissue growth models. Depending on the type of tissue, the velocity is linked to the pressure through Stoke's law, Brinkman's law or Darcy's law. While each of these…
In processes such as embryo shaping, wound healing, and malignant cell invasion, epithelial cells transition between dispersed phases, where the cells move independently, and condensed phases, where they aggregate and deform to close gaps,…
During the last decades, medical observations and multiscale data concerning tumor growth are mounting. At the same time, contemporary imaging techniques well established in clinical practice, provide a variety of information on real-time,…
The lack of analytical models describing diffusion time dependence at intermediate time scales in complex tissue microstructure limits the accurate quantification of extracellular diffusivity and tissue microstructure. We introduce TRACED,…
Collagen fibers, an important component of the extracellular matrix (ECM), can both inhibit and promote cellular migration. {\it In-vitro} studies have revealed that the fibers' orientations are crucial to cellular invasion, while {\it…
The blood vascular system consists of blood vessels such as arteries, arterioles, capillaries and veins that convey blood throughout the body. The pressure difference which exists between the ends of the vessels provides the living force…
There is increasing interest in the analysis of biological tissue, its organization and its dynamics with the help of mathematical models. In the ideal case emergent properties on the tissue scale can be derived from the cellular scale.…
We investigate the dynamics of the Red Blood Cell (RBC) in microfluidic channels under oscillatory flows. The simulations employ a hybrid continuum-particle approach, in which the cell membrane and cytosol fluid are modeled using…
We propose and study a strongly coupled PDE-ODE-ODE system modeling cancer cell invasion through a tissue network under the go-or-grow hypothesis asserting that cancer cells can either move or proliferate. Hence our setting features two…
Collective migration dominates many phenomena, from cell movement in living systems to abiotic self-propelling particles. Focusing on the early stages of tumor evolution, we enunciate the principles involved in cell dynamics and highlight…
In this paper we study a model describing the growth of necrotic tumors in different regimes of vascularisation. The tumor consists of a necrotic core of death cells and a surrounding nonnecrotic shell. The corresponding mathematical…
Heterogeneity within tumour cell populations is associated with an increase in malignancy and appears to play an important role during cancer metastasis. Using in silico experiments, we study the interplay between collective behaviours and…
Cell extravasation is a crucial step of the metastatic cascade. In this process, the circulating tumor cells inside the blood vessels adhere to the cell monolayer of the blood vessel wall and passes through it, which allows them to invade…
We present a mathematical model, based on ordinary differential equations, for the evolution of solid tumors and their response to treatment. Specifically the effects of a cytotoxic agent and a monoclonal antibody are included as control…
The recent advances in cancer immunotherapy boosted the development of tumor-immune system models aiming to provide mechanistic understanding and indicate more efficient treatment regimes. However, the complexity of such models, their…
Understanding cancer cell differentiation is essential for advancing its detection, diagnosis, and treatment. Mathematical models significantly contribute to this by providing a theoretical framework to understand the complex interactions…