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It has been shown experimentally that contact interactions may influence the migration of cancer cells. Previous works have modelized this thanks to stochastic, discrete models (cellular automata) at the cell level. However, for the study…
Integrating experimental data into ecological models plays a central role in understanding biological mechanisms that drive tumor progression where such knowledge can be used to develop new therapeutic strategies. While the current studies…
Theoretical and computational tools that can be used in the clinic to predict neoplastic progression and propose individualized optimal treatment strategies to control cancer growth is desired. To develop such a predictive model, one must…
We study the mathematical properties of a general model of cell division structured with several internal variables. We begin with a simpler and specific model with two variables, we solve the eigenvalue problem with strong or weak…
We demonstrate the power of the genetic algorithms to construct the cellular automata model simulating the growth of 2-dimensional close-to-circular clusters revealing the desired properties, such as the growth rate and, at the same time,…
The spread of metastases is a crucial process in which some questions remain unanswered. In this work, we focus on tumor cells circulating in the bloodstream, the so-called Circulating Tumor Cells (CTCs). Our aim is to characterize their…
Stem cells, through their ability to produce daughter stem cells and differentiate into specialized cells, are essential in the growth, maintenance, and repair of biological tissues. Understanding the dynamics of cell populations in the…
We argue that volumetric growth dynamics of a solid cancer depend on the tumor system's overall surface extension. While this at first may seem evident, to our knowledge, so far no theoretical argument has been presented explaining this…
We study a tumor growth model in two space dimensions, where proliferation of the tumor cells leads to expansion of the tumor domain and migration of surrounding normal tissues into the exterior vacuum. The model features two moving…
The understanding of the macroscopic phenomenological models of the population growth at a microscopic level is important to predict the population behaviors emerged from the interactions between the individuals. In this work we consider…
Genetic mutations are footprints of tumour growth. While mutation data in bulk samples has been used to infer evolutionary parameters hard to measure in vivo, the advent of single-cell data has led to strong interest in the mutational…
Developing epithelial tissues coordinate cell proliferation and mechanical forces to achieve proper size and shape. As epithelial cells tightly adhere together to form the confluent tissue, the distribution of cell areas significantly…
This paper concerns multiphase models of tumor growth in interaction with a surrounding tissue, taking into account also the interplay with diffusible nutrients feeding the cells. Models specialize in nonlinear systems of possibly…
A macroscopic model of the tumor Gompertzian growth is proposed. The new approach is based on the energetic balance among the different cell activities, described by methods of statistical mechanics and related to the growth inhibitor…
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,…
In this paper, we propose a tumor growth model to incorporate and investigate the spatial effects of autophagy. The cells are classified into two phases: normal cells and autophagic cells, whose dynamics are also coupled with the nutrients.…
Tumor growth has a number of features in common with a physical process known as molecular beam epitaxy. Both growth processes are characterized by the constraint of growth development to the body border, and surface diffusion of…
Circulating tumor cell clusters play an important role in the metastatic cascade. These clusters can acquire a migratory and more invasive phenotype, and coordinate their motion to migrate as a collective. Before such clusters can form by…
Using formal asymptotic methods we derive a free boundary problem representing one of the simplest mathematical descriptions of the growth and death of a tumour or other biological tissue. The mathematical model takes the form of a closed…
Known as one of the hallmarks of cancer [30], cancer cell invasion of human body tissue is a complicated spatio-temporal multiscale process which enables a localised solid tumour to transform into a systemic, metastatic and fatal disease.…