Fig 9 - uploaded by Yuriria Cortés Poza
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Minimum entropy values reached when applying radiotherapy on a simulated tumor that has grown under the support of 100 different vascular network configurations (each point corresponds to one of the networks). The horizontal axis indicates a metric for the networks: (a) degree centrality, (b) betweenness centrality, (c) page rank, and (d) clustering coefficient. The vertical axis represents the minimum entropy obtained (smaller entropies correspond to better treatment outcomes). Radiotherapy parameter values used were í µí»¾ 0,rad = 0.05, í µí»¼ rad = 0.1, í µí»½ rad = 0.05, í µí± = 1, í µí± í µí±,rad = 0.35, í µí± 0,rad = 0.2, í µí± í µí± ,rad = 0.5.
Contexts in source publication
Context 1
... treatment was administered to the developing tumor. In this case, however, the effectiveness of the treatment was assessed by computing the minimum entropy in the generated sequence of tumor images. Therapies applied to the tumor decrease entropy; thus, a lower minimum in entropy will be observed in cases where the treatment is most effective. Fig. 9 shows how initial network metrics relate to the minimum tumor entropy value reached when applying the radiotherapy treatment. ...
Context 2
... as the Internet facilitate information traffic, and these types of networks tend to present few nodes with high degree centralities [40]. Finally, high page-rank nodes can create stops for proliferating cells since many high transit paths are directed to them. Thus, a high average page rank could prevent the efficient spreading of tumor cells. Fig. 9 illustrates the comparison between vascular network properties and the minimum tumor entropy values achieved upon application of radiotherapy treatment. The results indicate that higher treatment effectiveness is observed when the therapy is administered to tumors growing along with networks that offer less support to tumor growth. ...
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.
