Cellular Automata-Based Modeling of Three-Dimensional Multicellular Tissue Growth

Computationally modelling cell proliferation: A review

“…On the other hand, some approaches have also been used to simulate the population dynamics of proliferating cells, 62 like in the works developed by Frame K. K. and Hu W 63 . and by Cherry R. S. and Papoutsakis E. T 64 .…”

“…These types of models are simple and allow to obtain detailed mathematical analyses that are commonly applied to study cell dynamics 62 . However, these models might not be completely accurate because they move columns or rows of cells in order to make room for newborn cells 95 …”

“…Furthermore, it was also assumed that cell division occurs when the conditions s < s threshold and z > z threshold are satisfied since the biomolecular machinery necessary to conclude the cell cycle is triggered when these two conditions are achieved. 16 On the other hand, some approaches have also been used to simulate the population dynamics of proliferating cells, 62 like in the works developed by Frame K. K. and Hu W. 63 and by Cherry R. S. and Papoutsakis E. T. 64 In this first work, the authors described the growth rate based on cell density, which is given by:…”

“…Discrete models are usually called cell-based models, where both space and time are discrete. 62 To study cell proliferation, different approaches can be used to describe the processes involved in it and, since some of these models can only be solved analytically, different numerical integration methods can be used to achieve an approximate solution. Some examples are the cellular automata, cellular Potts, cell-vertex and off-lattice cell-based models.…”

Integrative lymph node-mimicking models created with biomaterials and computational tools to study the immune system

“… (1) Simulate many interactions at the individual level to uncover emergent behavior at the whole-population level; (2) Stochastic gene expression [ 94 ]; (3) Tissue formation and morphogenesis [ 95 ]; (4) Mammary stem cell subpopulation dynamics [ 96 ]; (5) Inflammation pathways [ 97 , 98 ]; (6) Immune system dynamics [ 99 , 100 ]; (7) Tumor models [ 101 ]; (8) Cell migration [ 102 , 103 ]; (9) Chemotaxis [ 104 , 105 ] Boolean network A discrete set of boolean variables which can be presented by a graph of linked nodes (1) Gene regulatory networks [ [106] , [107] , [108] ]; (2) Interaction between pathogens and different cytokines [ 109 ] Cellular automaton c A discrete spatio-temporally extended dynamical system that includes identically programmed automaton cells and interacting units with a finite number of discrete states. (1) 3D multicellular tissue growth [ 110 ]; (2) Cell behaviors and activities (e.g., neurons and fibroblasts); (3) Cardiac model [ 111 ]; (4) Tissue growth [ 112 ] Cellular Potts model (CPM) A lattice-based model where a cell can be described using a cluster of points, allowing capture of cell shape changes. The movement of the points/cluster around the lattice is governed by calculation of force equations and energy of the system therefore considering cell state and the grid environment.…”