Growth of tumours with stem cells: The effect of crowding and ageing of cells

Effects of a Differentiating Therapy on Cancer-Stem-Cell-Driven Tumors

“…The growing recognition of the importance of understanding the processes underpinning CSC-fueled tumor growth has led to the formulation of a number of mathematical models [22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41]. These models offer insights into growth and differentiation rates, cell population fractions, lateral inhibition, and chemo-and radio-therapy effects, to cite a few processes.…”

A two-component model of the red blood cell membrane and other mathematical models in medicine

“…In addition, coarse-grained models have been developed to save computing effort (PIVKIN; KARNIADAKIS, 2008). For a comprehensive review of RBC cytoskeleton modeling details, we refer the reader to (MEACCI et al, 2021). As yet displayed in the Figure 32, mathematically we can consider for the nodes a set of vertex points X = {X j | X j ∈ R 3 ⊂ Ω, with j = 1 .…”

“…Plot [If[d < dstar,DLJ[dstar,eps,r0] mathematical point of view, this corresponds to assuming that the replication potential of each cell may depend on its position, in the sense that it can be hindered by the presence of other cells in its vicinity. This fact has been incorporated in different classes of models: (i) models that can be classified "agent-based" i.e., considering the evolution of each cell, using computer simulations and/or cellular automata methods ((MONTEAGUDO;SANTOS, 2014;MONTEAGUDO;SANTOS, 2015;, and the review (BOONDIREK; TRIAMPO; NUTTAVUT, 2010)), (ii) models that introduce partial differential equations and integral terms to take into account the space-dependence of the cellular dynamics (BORSI et al, 2015a;MANCINI;PRIMICERIO, 2016), (iii) models that are "mean field approximations" of the dynamics of individual cells, taking as unknown the averaged density of each sub-population and modifying the compartmental schemes of the population dynamics multiplying the replication potential by a monotonic function of the density of cells, decreasing to zero when all available space is filed by other cells (BETTERIDGE et al, 2006;BUSCAGLIA, 2021).…”