Initial cell position was: (A-C) (0,0). Open in a separate window Figure 5: Simulation results at final time = 28 days with random fibres, sensing radius = 50 = 0, cell-fibre ECM adhesion S= 0 and with (A) 10% : 90%, (B) 20% : 80%, (C) 30% : 70% fibres and non-fibres ECM ratios. moving tumour aggregations have elongate shapes (resembling to clusters, strands or files). We also show that the cell sensing radius impacts tumour shape only when there is a low ratio of fibre to non-fibre ECM components. Finally, we investigate the impact of different ECM fibre orientations corresponding to different tissues, on the overall tumour invasion of these neighbouring tissues. away [28]), and how this perception can impact the overall tumour shape. Moreover, it is still not fully understood how the various tissue types can impact the migration of tumour cells and tumour aggregations (as tumours can develop at the boundaries of different tissues with different characteristics). The goal of this study is to investigate migration cell Masitinib ( AB1010) patterns in various tissues with different levels of ECM fibres and different alignment levels, as we vary: (i) cells sensing radius, (ii) cell-cell and cell-ECM adhesion strengths, (iii) the orientation of ECM fibres and the ratio of fibres to non-fibres ECM components, (iv) the structure of the domain, with various tissue patches that have different fibre orientations. To this end, we consider a hybrid multi-scale modelling approach where cells are modeled as discrete entities while the ECM (with its two phases: fibrous and non-fibrous) is continuous. We show that this hybrid model can reproduce a variety of cell migration types ([23, 22, 4] to represent the cells, and a multi-scale continuous framework [42, 43, 44, 48, 49] to represent the microenvironment. To facilitate the description of this multi-scale hybrid model, let us first KPSH1 antibody introduce some useful notations from both frameworks. The model is defined within a maximal tissue cube with = 2 and time interval [0, the cell radius, the current cell age, the cell maturation age (denotes the number of neighbouring cancer cells at time {1,, [0, [0, is the usual indicator function, and describes the spatial region occupied by the body of an individual cell within the neighbourhood B( C 0 (which is proportional to the spatial step-size of the discretised computational domain (Multi-Cell Lattice-Free) model, several individually-regulated life processes are included, such as cell ageing, cell growth, cell division, cell-cell and cell-ECM interactions, and cell contact inhibition. 2.1.1. The cell cycle The lifespan of each cell is traced with the current cell age that progresses at the same rate as time, and cell maturation age that is assigned at the cell birth and varies slightly between the cells to avoid synchronization of cell divisions. The cell cycle is divided into the usual four phases [1]: the G1 phase (gap 1) during which the cells are growing in size, the S phase (synthesis) when biological cells replicate their DNA, the G2 phase (gap Masitinib ( AB1010) 2) in which cells complete the growth and replication processes in preparation for the M phase (mitosis) in which cells physically divide into two daughter cells. Following ours and others previous work, the length of the cell cycle is divided as follows: G1 (45% of the whole cell cycle), S (35%), G2 (15%), and M (5%), respectively [23, 22, 51]. Within the figures, we indicate the phase of an individual cell by different colours, of a growing cell is increasing linearly until it reaches the size of the mature cell is an angle randomly chosen from [0, 2is the maximal cell radius. The Masitinib ( AB1010) initial ages of the two new cells are set Masitinib ( AB1010) to zero and are inherited from the mother cell maturation age with a small noise term is the division age of the mother cell. Finally, both initial radii of the daughter cells are set to 0.65in the specified neighbourhood of radius = 4.5again denotes the indicator function and is the set of all cancer cells that are close to the cell {1, , for an arbitrary cell as represents the maximum range within which a cell can establish adhesive bonds with the surrounding ECM constituents, 0 and S 0 are assumed to be the constant cell-non-fibre ECM and cell-fibre ECM adhesion strengths, respectively. Furthermore, in Eq. (5) is the unit radial vector biased by the orientation of the fibres, within the sensing region B(0, which is given by given in (5). To this end, we adopt the partitioning of the sensing.
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