The notion of fractals in tumour angiogenic sprout initiation model based on cellular automata

Tumour growth is considered chaotic, poorly controlled growth as its cells and vasculatures are irregular in shape. The vascular system of tumour is a complex network and its architectural complexity and geometrical characteristics cannot be defined with Euclidian geometry as it is only capable of expressing regular or smooth objects whereas, fractal geometry describes an object with irregularities and it is therefore well suited to quantify those morphological characteristics. In this paper, we develop a cellular automata (CA) based discrete model that tries to mimic all the features and make useful predictions of tumour angiogenesis with computer-coded rules. From the interactions of several species in 2-D tissue space, we study the effects of these various biological factors on the formation of the capillary sprouts. The model also captures anastomoses and branching phenomena in capillary blood vessels. It is observed that chemotaxis and randomness are the essential components for the capillary sprout motility whereas, haptotaxis works as an add-on feature. The model is also validated with partial sensitivity analysis. The fractal properties of the growing capillary sprouts in the model are investigated. The characterization of these fractal objects (capillary sprouts) is provided by the box-counting method. The model shows, the morphological change in the early stages of the vascularization process where the capillary sprouts are formed from the surrounding blood vessels. The model successfully simulates the morphological aspects of capillary vessel growth during tumour angiogenesis. The estimated fractal dimension is very close to the previously measured range. This is established our hypothesis about the fractal nature of vascular network pattern and our CA-based discrete model for capillary sprout initiation during tumour angiogenesis.(c) 2021 Elsevier Ltd. All rights reserved.

Automated summary

This paper develops a cellular automata-based model to simulate tumor angiogenesis and studies the effects of biological factors on the formation of capillary sprouts. The model successfully captures various phenomena in capillary blood vessels, including morphological changes and fractal characteristics.