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... two different tips collide at the exact location of the grid. In this situation, the two of them will merge, simulating a process known as anastomosis. In terms of the model, one will be removed from , while the remaining one will be left to evolve. The algorithm used to update the angiogenesis automaton at each step has been summarized in Fig. ...
Citations
... We show that the additional modelling assumptions in our ABM can have a significant effect on the tumour's response to radiotherapy. Due to its prevalence in the clinic, there are many mathematical models of tumour responses to radiotherapy (for example, [61][62][63][64][65][66]). We follow [58,62,67], by simulating radiotherapy with the linear quadratic model. We show that even this simple implementation of radiotherapy, when integrated within our ABM, produces a complex treatment and recovery landscape. ...
We develop a multiscale agent-based model (ABM) to investigate the effect that mechanical interactions between proliferating tumour cells and the surrounding vasculature have on the oxygen supply to the tumour microenvironment (TME), the tumour’s growth dynamics, and its response to radiotherapy. Our model extends existing models of tumour spheroid growth by incorporating vessel deformation due to mechanical forces between vessel walls and neighbouring tumour cells. These forces generate an effective pressure which compresses vessels, driving occlusion and pruning. This, in turn, leads to a hypoxic oxygen landscape which stimulates angiogenesis.
A key feature of our model is the treatment of mechanical cell interactions with the tumour microenvironment, which we represent with two forces. The first is Stokes’ drag which is widely used in ABMs to represent resistance to cell movement. The second is a friction force which accounts for resistance due to the continual breaking and reforming of cell-extracellular matrix (ECM) adhesions. The importance of this friction force is demonstrated by numerical simulation. When Stokes’ drag dominates, pressure gradients dissipate across the tissue and vessel compression is negligible. By contrast, as the strength of the friction force increases, larger pressure gradients form, leading to significant vessel compression.
We perform extensive numerical simulations to investigate how model parameters that control vascular remodelling and friction influence tumour vascularisation, which we spatially quantify using the cross-pair correlation function. This, in turn, alters the oxygen landscape and drives changes in tumour morphology. Finally, we highlight the importance of accounting for both mechanisms when simulating tumour responses to treatment with radiotherapy. We observe that vascular remodelling critically alters the tumour’s susceptibility to treatment and post-radiotherapy regrowth. Tumour regrowth is especially impacted by vessel remodelling, with certain vascular landscapes able to rebound quickly post-radiotherapy, resulting in fast tumour regrowth.
