相关论文: On a cross-diffusion hybrid model: Cancer Invasion…
In this work we propose and investigate a family of models, which admits as particular cases some well known mathematical models of tumor-immune system interaction, with the additional assumption that the influx of immune system cells may…
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…
Cell invasion and spatial pattern formation are two distinct manifestations of cellular self-organisation in development, regeneration, and disease. Here, we develop and analyse a unified theoretical framework that links these two seemingly…
The investigation of tumor invasion and metastasis dynamics is crucial for advancements in cancer biology and treatment. Many mathematical models have been developed to study the invasion of host tissue by tumor cells. In this paper, we…
Multicellular collective migration is a ubiquitous strategy of cells to translocate spatially in diverse tissue environments to accomplish a wide variety of biological phenomena, viz. embryonic development, wound healing, and tumor…
Stochastic simulation methods can be applied successfully to model exact spatio-temporally resolved reaction-diffusion systems. However, in many cases, these methods can quickly become extremely computationally intensive with increasing…
Current biological knowledge supports the existence of a secondary group of cancer cells within the body of the tumour that exhibits stem cell-like properties. These cells are termed Cancer Stem Cells (CSCs}, and as opposed to the more…
Cross-diffusion systems arise as hydrodynamic limits of lattice multi-species interacting particle models. The objective of this work is to provide a numerical scheme for the simulation of the cross-diffusion system identified in [J.…
Phase-field models of tumour growth have proved useful as theoretical tools to investigate cancer invasion. A key implicit assumption underlying mathematical models of this type which have so far been proposed, though, is that cells in the…
We show that propagation speeds in invasion processes modeled by reaction-diffusion systems are determined by marginal spectral stability conditions, as predicted by the marginal stability conjecture. This conjecture was recently settled in…
Uncontrolled growth of tumor cells in confined spaces leads to the accumulation of compressive stress within the tumor. Although the effects of tension within 3D extracellular matrices on tumor growth and invasion are well established, the…
We investigate the long-time dynamics and optimal control problem of a diffuse interface model that describes the growth of a tumor in presence of a nutrient and surrounded by host tissues. The state system consists of a Cahn-Hilliard type…
Tumor growth, which plays a central role in cancer evolution, depends on both the internal features of the cells, such as their ability for unlimited duplication, and the external conditions, e.g., supply of nutrients, as well as the…
Cancer cell invasion is recognised as one of the hallmarks of cancer and involves several inner-related multiscale processes that ultimately contribute to its spread into the surrounding tissue. In order to gain a deeper understanding of…
In this work, we present and analyze a mathematical model for tumor growth incorporating ECM erosion, interstitial flow, and the effect of vascular flow and nutrient transport. The model is of phase-field or diffused-interface type in which…
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…
Diffusion models are important in tissue engineering as they enable an understanding of molecular delivery to cells in tissue constructs. As three-dimensional (3D) tissue constructs become larger, more intricate, and more clinically…
Breast cancer invasion into adipose tissue strongly influences disease progression and metastasis. The degree of cancer cell invasion into adipose tissue depends on numerous biochemical and physical properties of cancer cells, adipocytes,…
The early stages of the collective invasion may occur by single mesenchymal cells or hybrid epithelial-mesenchymal cell groups that detach from cancerous tissue. Tumors may also emit invading protrusions of epithelial cells, which could be…
In this work, we present a phase-field model for tumour growth, where a diffuse interface separates a tumour from the surrounding host tissue. In our model, we consider transport processes by an internal, non-solenoidal velocity field. We…