Directionality of Macrophages Movement in Tumour Invasion: A Multiscale Moving-Boundary Approach

Abstract

Invasion of the surrounding tissue is one of the recognised hallmarks of cancer (Hanahan and Weinberg in Cell 100: 57–70, 2000. 10.1016/S0092-8674(00)81683-9), which is accomplished through a complex heterotypic multiscale dynamics involving tissue-scale random and directed movement of the population of both cancer cells and other accompanying cells (including here, the family of tumour-associated macrophages) as well as the emerging cell-scale activity of both the matrix-degrading enzymes and the rearrangement of the cell-scale constituents of the extracellular matrix (ECM) fibres. The involved processes include not only the presence of cell proliferation and cell adhesion (to other cells and to the extracellular matrix), but also the secretion of matrix-degrading enzymes. This is as a result of cancer cells as well as macrophages, which are one of the most abundant types of immune cells in the tumour micro-environment. In large tumours, these tumour-associated macrophages (TAMs) have a tumour-promoting phenotype, contributing to tumour proliferation and spread. In this paper, we extend a previous multiscale moving-boundary mathematical model for cancer invasion, by considering also the multiscale effects of TAMs, with special focus on the influence that their directional movement exerts on the overall tumour progression. Numerical investigation of this new model shows the importance of the interactions between pro-tumour TAMs and the fibrous ECM, highlighting the impact of the fibres on the spatial structure of solid tumour.

Collective Cell Migration in a Fibrous Environment: A Hybrid Multiscale Modelling Approach

“…To this end, we start each simulation with a single cancer cell with well defined properties located at a point (x 0 1 , x 0 2 ) (that will be defined for each simulations) of the computational domain Y [−1280mm, 1280mm] × [−1280mm, 1280mm], and any alteration from this will be stated accordingly. Then, this single cancer cell is considered to be embedded within the following (scaled) non-fibre ECM environment [19][20][21][22][23]:…”

“…We employ here a hybrid modeling framework [15] that combines the off-lattice agent based model MultiCell-LF [16][17][18] to represent the cells, and a multi-scale continuous framework [19][20][21][22][23] to represent the microenvironment. To facilitate the description of this multi-scale hybrid model, let us first introduce some useful notations from both frameworks.…”

“…Besides the cell-cell interactions described above, of particular importance, are the cell-ECM adhesions [28][29][30][31] that we explore here through a cell-non-fibre ECM adhesion [32][33][34][35] as well as a cell-fibre ECM adhesion [36,37]. In the existing literature [19][20][21][22][23][38][39][40][41][42], this type of interaction is usually modelled by a non-local adhesion integral with a sensing region B(0, R) of radius R. Since in our hybrid model the two phase ECM is modelled in a continuous manner using densities, we can adopt this approach to describe the present cell-ECM interactions. To this end, let us define the cell-ECM adhesion force/velocity for an arbitrary cell C i as…”

“…Ultimately, this enables us to appropriately construct the integral of the step functions associated with each annulus sector S ] whose value is given by a linear combination of the mean-values. Finally, these mean values are used to obtain the numerical approximation for F ECM i by following the numerical steps described in full in [19,22,23].…”

A level-set approach for a multi-scale cancer invasion model

“…In this work we present a new formulation of the link that connects the two scales of the tumour dynamics that was considered in the initial multiscale moving boundary modelling approach presented in [73] as well as in the multiscale cancer invasion modelling developments that followed [4,5,6,71,52,62,63,64,65,67,72]. In particular, the movement of the tumor boundary is here defined by a velocity field instead of a displacement of the interface.…”