Off-Lattice Agent-Based Models for Cell and Tumor Growth

Liedekerke, Paul Van; Buttenschön, Andreas; Drasdo, Dirk

doi:10.1016/b978-0-12-811718-7.00014-9

Cited by 24 publications

(17 citation statements)

References 110 publications

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“…One central issue we focused on is the possible overshoot for too large time steps for highly compressed cells right after cell division due to unphysically large force magnitudes. This problem is well known in the CBM methods developer community and different ways of dealing with it have been suggested (Van Liedekerke et al 2018;Schaller and Meyer-Hermann 2005). Since the solution does not necessarily become numerically unstable and obviously wrong (see Fig.…”

Section: Discussionmentioning

confidence: 99%

“…Runge-Kutta schemes unless the degree of the polynomial is chosen to match the order of the scheme (Ghaffarizadeh et al 2018). We also note here that the challenge is to resolve the transient solution right after cell division and while a higher-order scheme allows for larger time steps than the forward Euler method, another possible approach to improve efficiency is time step adaptivity (Schaller and Meyer-Hermann 2005;Van Liedekerke et al 2018;Atwell 2016). In such a setting it could be interesting to consider switching between implicit and explicit schemes during the course of a simulation.…”

Section: Discussionmentioning

confidence: 99%

“…Implementation-wise this is a very simple and efficient algorithm. However, it may lead to locally and transiently high, unphysical force values right after cell division (Schaller and Meyer-Hermann 2005;Van Liedekerke et al 2018). This can be seen as a consequence of the fundamental model assumption underlying the CBM, i.e.…”

Section: Cell Cycle Model and Cell Division Implementationmentioning

confidence: 99%

“…This can be seen as a consequence of the fundamental model assumption underlying the CBM, i.e. the assumption of pairwise cell interactions not being valid in highly compressed scenarios (Van Liedekerke et al 2018). In Van Liedekerke et al (2019) a multiscale approach based on deformable cell model simulations is used to correct forces for highly compressed structures.…”

Section: Cell Cycle Model and Cell Division Implementationmentioning

confidence: 99%

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Impact of Force Function Formulations on the Numerical Simulation of Centre-Based Models

et al. 2020

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Centre-based or cell-centre models are a framework for the computational study of multicellular systems with widespread use in cancer modelling and computational developmental biology. At the core of these models are the numerical method used to update cell positions and the force functions that encode the pairwise mechanical interactions of cells. For the latter, there are multiple choices that could potentially affect both the biological behaviour captured, and the robustness and efficiency of simulation. For example, available open-source software implementations of centre-based models rely on different force functions for their default behaviour and it is not straightforward for a modeller to know if these are interchangeable. Our study addresses this problem and contributes to the understanding of the potential and limitations of three popular force functions from a numerical perspective. We show empirically that choosing the force parameters such that the relaxation time for two cells after cell division is consistent between different force functions results in good agreement of the population radius of a two-dimensional monolayer relaxing mechanically after intense cell proliferation. Furthermore, we report that numerical stability is not sufficient to prevent unphysical cell trajectories following cell division, and consequently, that too large time steps can cause geometrical differences at the population level.

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Section: Discussionmentioning

confidence: 99%

Section: Discussionmentioning

confidence: 99%

Section: Cell Cycle Model and Cell Division Implementationmentioning

confidence: 99%

Section: Cell Cycle Model and Cell Division Implementationmentioning

confidence: 99%

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Impact of Force Function Formulations on the Numerical Simulation of Centre-Based Models

et al. 2020

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“…A different approach to incorporate stochasticity at a cellular level within mathematical models is to use an individual-based (IB) (or agent-based) modelling approach [10, 100]. This approach allows each cell to be described as an individual agent which follows a set of predetermined rules.…”

Section: Introductionmentioning

confidence: 99%

Modelling rheumatoid arthritis: A hybrid modelling framework to describe pannus formation in a small joint

Macfarlane

Chaplain

Eftimie

2021

Preprint

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Rheumatoid arthritis (RA) is a chronic inflammatory disorder that causes pain, swelling and stiffness in the joints, and negatively impacts the life of affected patients. The disease does not have a cure yet, as there are still many aspects of this complex disorder that are not fully understood. While mathematical models can shed light on some of these aspects, to date there are not many such models that can be used to better understand the disease. As a first step in the mechanistic understanding of RA, in this study we introduce a new hybrid mathematical modelling framework that describes pannus formation in a small proximal interphalangeal (PIP) joint. We perform numerical simulations with this new model, to investigate the impact of different levels of immune cells (macrophages and fibroblasts) on the degradation of bone and cartilage. Since many model parameters are unknown and cannot be estimated due to a lack of experiments, we also perform a sensitivity analysis of model outputs to various model parameters (single parameters or combinations of parameters). Finally, we connect our numerical results with current treatments for RA, by discussing our numerical simulations in the context of various drug therapies using, for example, methotrexate, TNF-inhibitors or tocilizumab, which can impact different model parameters.

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Biomechanical modelling of cancer: Agent‐based force‐based models of solid tumours within the context of the tumour microenvironment

Macnamara

2021

Comp Sys Onco

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Once cancer is initiated, with normal cells mutated into malignant ones, a solid tumour grows, develops and spreads within its microenvironment invading the local tissue; the disease progresses and the cancer cells migrate around the body leading to metastasis, the formation of distant secondary tumours. Interactions between the tumour and its microenvironment drive this cascade of events which have devastating, if not fatal, consequences for the human host/patient. Among these interactions, biomechanical interactions are a vital component. In this review paper, key biomechanical relationships are discussed through a presentation of modelling efforts by the mathematical and computational oncology community. The main focus is directed, naturally, towards lattice‐free agent‐based, force‐based models of solid tumour growth and development. In such models, interactions between pairs of cancer cells (as well as between cells and other structures of the tumour microenvironment) are governed by forces. These forces are ones of repulsion and adhesion, and are typically modelled via either an extended Hertz model of contact mechanics or using Johnson–Kendal–Roberts theory, both of which are discussed here. The role of the extracellular matrix in determining disease progression is outlined along with important cell‐vessel interactions which combined together account for a great proportion of Hanahan and Weinberg's Hallmarks of Cancer.

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Off-Lattice Agent-Based Models for Cell and Tumor Growth

Cited by 24 publications

References 110 publications

Impact of Force Function Formulations on the Numerical Simulation of Centre-Based Models

Impact of Force Function Formulations on the Numerical Simulation of Centre-Based Models

Modelling rheumatoid arthritis: A hybrid modelling framework to describe pannus formation in a small joint

Biomechanical modelling of cancer: Agent‐based force‐based models of solid tumours within the context of the tumour microenvironment

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