Computational Modelling of Cancer Development and Growth: Modelling at Multiple Scales and Multiscale Modelling

Abstract

In this paper, we present two mathematical models related to different aspects and scales of cancer growth. The first model is a stochastic spatiotemporal model of both a synthetic gene regulatory network (the example of a three-gene repressilator is given) and an actual gene regulatory network, the NF-[Formula: see text]B pathway. The second model is a force-based individual-based model of the development of a solid avascular tumour with specific application to tumour cords, i.e. a mass of cancer cells growing around a central blood vessel. In each case, we compare our computational simulation results with experimental data. In the final discussion section, we outline how to take the work forward through the development of a multiscale model focussed at the cell level. This would incorporate key intracellular signalling pathways associated with cancer within each cell (e.g. p53-Mdm2, NF-[Formula: see text]B) and through the use of high-performance computing be capable of simulating up to [Formula: see text] cells, i.e. the tissue scale. In this way, mathematical models at multiple scales would be combined to formulate a multiscale computational model.

Identification of Significant Gene Signatures and Prognostic Biomarkers for Patients With Cervical Cancer by Integrated Bioinformatic Methods

“…A possible reason might be that MCM5 was present throughout the cell cycle of proliferating cells but not in nonproliferating quiescent cells. 39 With the progress of the tumor, tumor proliferation in situ is slow, 40 , 41 leading to the decreasing of MCM5 expression. According to the NCCN (National Comprehensive Cancer Network) guidelines of cervical cancer ( https://www.nccn.org ), surgical indications would become scarce for those patients with advanced stage IIB.…”

A Review of Cell-Based Computational Modeling in Cancer Biology

“…48 (F) A CBM of tumor cords growing around a blood vessel and showing a reversed structure with viable tissue in the interior. Adapted with permission from Szymańska et al 49…”

Nonlinear dynamics in tumor-immune system interaction models with delays

“…We should emphasize that the literature on modeling tumor-immune system interactions is huge, see reviews by Anderson and Maini [7], Cristini et al [31], dePillis et al [34], Eftimie et al [47], Freedman [53], Friedman [54], Konstorum et al [72], Mahlbacher et al [84], Szymańska et al [110], Wilkie [120], and books of d'Onofrio et al [41], Eladdadi et al [48], and Kuang et al [73]. In order to understand the nonlinear dynamics in particular various bifurcations in the tumor-immune system interaction models, we focused only on two-dimensional delay differential equations.…”

“…In order to simulate the host's own immune response to destroy and eliminate tumor cells, various types of mathematical models have been proposed, see for example Adam and Bellomo [3], Arciero et al [8], Byrne et al [24], de Pillis et al [35], Dritschel et al [43], Frascoli et al [52], Hu and Jang [64], Kirschner and Panetta [70], Kuznetsov et al [74], Lejeune et al [78], Nani and Freedman [92], Nikolopoulou et al [93], Owen and Sherratt [94], Robertson-Tessi et al [100], Stepanova [109], and the references cited therein. We refer to reviews by Anderson and Maini [7], Cristini et al [31], dePillis et al [34], Eftimie et al [47], Freedman [53], Friedman [54], Konstorum et al [72], Mahlbacher et al [84], Szymańska et al [110], Wilkie [120] and the references cited therein on modeling tumor-immune system interactions and tumor growth, proceedings of d'Onofrio et al [41] and Figure 1. Three processes in cancer immunoediting: (a) Elimination corresponds to immunosurveillance; (b) Equilibrium represents the process by which the immune system iteratively selects and/or promotes the generation of tumor cell variants with increasing capacities to survive immune attack; (c) Escape is the process wherein the immunologically sculpted tumor expands in an uncontrolled manner in the immunocompetent host.…”