A 3-D model of tumor progression based on complex automata driven by particle dynamics

Abstract

The dynamics of a growing tumor involving mechanical remodeling of healthy tissue and vasculature is neglected in most of the existing tumor models. This is due to the lack of efficient computational framework allowing for simulation of mechanical interactions. Meanwhile, just these interactions trigger critical changes in tumor growth dynamics and are responsible for its volumetric and directional progression. We describe here a novel 3-D model of tumor growth, which combines particle dynamics with cellular automata concept. The particles represent both tissue cells and fragments of the vascular network. They interact with their closest neighbors via semi-harmonic central forces simulating mechanical resistance of the cell walls. The particle dynamics is governed by both the Newtonian laws of motion and the cellular automata rules. These rules can represent cell life-cycle and other biological interactions involving smaller spatio-temporal scales. We show that our complex automata, particle based model can reproduce realistic 3-D dynamics of the entire system consisting of the tumor, normal tissue cells, blood vessels and blood flow. It can explain phenomena such as the inward cell motion in avascular tumor, stabilization of tumor growth by the external pressure, tumor vascularization due to the process of angiogenesis, trapping of healthy cells by invading tumor, and influence of external (boundary) conditions on the direction of tumor progression. We conclude that the particle model can serve as a general framework for designing advanced multiscale models of tumor dynamics and it is very competitive to the modeling approaches presented before.

Cancer models, genomic instability and somatic cellular Darwinian evolution

“…[146] employ an agent-based approach to model tumour growth, migration and cell death; a similar approach is adopted by Wcisło et al . [147], who also modelled vascular growth. Macklin et al .…”

A Hybrid Model of the Role of VEGF Binding in Endothelial Cell Migration and Capillary Formation

“…As discussed in detail in Jackson and Zheng (2010), Zheng et al (2013), existing models of tumor-induced angiogenesis can be characterized as continuous approaches (Balding and McElwain, 1985; Byrne and Chaplain, 1995, 1996; Anderson and Chaplain, 1998a,b; Holmes and Sleeman, 2000; Levine et al, 2001; Arakelyan et al, 2002; Sleeman and Wallis, 2002; Manoussaki, 2003; Plank and Sleeman, 2003, 2004; Plank et al, 2004; Levine and Nilsen-Hamilton, 2006; Schugart et al, 2008; Billy et al, 2009; Xue et al, 2009; Travasso et al, 2011), wherein cells are assumed to have a continuous distribution; discrete or hybrid models (Stokes and Lauffenburger, 1991; Anderson and Chaplain, 1998b; Tong and Yuan, 2001; Plank and Sleeman, 2003, 2004; Sun et al, 2005; Bartha and Rieger, 2006; Gevertz and Torquato, 2006; Frieboes et al, 2007; Milde et al, 2008; Capasso and Morale, 2009; Owen et al, 2009; Perfahl et al, 2011), wherein cells are modeled as individual agents and diffusible chemicals are modeled as a continuum; and cell-based formulations (Peirce et al, 2004; Bauer et al, 2007; Bentley et al, 2009; Qutub and Popel, 2009; Wcislo et al, 2009; Jackson and Zheng, 2010; Liu et al, 2011) wherein explicit incorporation of different properties of individual cells allows collective behavior of cell clusters to be predicted from the behavior and interactions of individual cells. Reviews of these models that appeared in or before 2009 can be found in Mantzaris et al (2004), Peirce (2008), Qutub et al (2009).…”

Growth of mixed cancer cell population – in silico the size matters

“…Alternative states of the cell cycle (like quiescent cells/resting cells state) are not introduced (Monteagudo & Santos, 2015), nor the immunology response (Alemani et al, 2012), nor the effects of the other, non-cancerous cells (fibroblasts) (Picco et al, 2017). The nutrients' uptakes (Bunimovich-Mendrazitsky et al, 2015), cellular motility (Kumar et al, 2016), adhesion, tissue pressure, cellular metabolism (Ascolani & Liò, 2019), chemotaxis and hypotaxis (Tzedakis et al, 2015), tissue vascularity (Wcisło et al, 2009), and other factors are also omitted. However, what causes the greatest uncertainty is the lack of the experimental data that could support our findings.…”