Multiscale Computational Modelling and Analysis of Cancer Invasion

Trucu, Dumitru; Domschke, Pia; Gerisch, Alf; Chaplain, M. A. J.

doi:10.1007/978-3-319-42679-2_5

Cited by 8 publications

(12 citation statements)

References 49 publications

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“…Thus, denoting the micro-scale densities of uPA by a(y, τ ), PAI-1 by p(y, τ ), and plasmin by m(y, t), and proceeding as in [58], in brief, the dynamics of the tumour invasive edge proteolytic micro-processes can be is described as follows. Per unit time, the uPA molecular population a(•, •) changes through diffusion (with a random motility coefficient D a ) while being produced (at a rate ψ 12 ) and bound by cancer cells' uPA receptors (uPAR) (at a rate ψ 13 ), as well as being inhibited by PAI-1 density p(•, •) (at a rate ψ 11 ).…”

Section: The Microscopic Proteolytic Dynamics and The Macro-micro Doumentioning

confidence: 99%

Multiscale modelling of cancer response to oncolytic viral therapy

Alzahrani

Eftimie

Trucu

2019

Mathematical Biosciences

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Oncolytic viruses (OV) are viruses that can replicate selectively within cancer cells and destroy them. While the past few decades have seen significant progress related to the use of these viruses in clinical contexts, the success of oncolytic therapies is dampened by the complex spatial tumour-OV interactions. In this work, we present a novel multiscale moving boundary modelling for the tumour-OV interactions, which is based on coupled systems of partial differential equations both at macro-scale (tissue-scale) and at micro-scale (cell-scale) that are connected through a double feedback link. At the macro-scale, we account for the coupled dynamics of uninfected cancer cells, OV-infected cancer cells, extracellular matrix (ECM) and oncolytic viruses. At the same time, at the micro scale, we focus on essential dynamics of urokinase plasminogen activator (uPA) system which is one of the important proteolytic systems responsible for the degradation of the ECM, with notable influence in cancer invasion. While sourced by the cancer cells that arrive during their macro-dynamics within the outer proliferating rim of the tumour, the uPA micro-dynamics is crucial in determining the movement of the macro-scale tumour boundary (both in terms of direction and displacement magnitude). In this investigation, we consider three scenarios for the macro-scale tumour-OV interactions. While assuming the usual context of reaction-diffusion-taxis coupled PDEs, the three macro-dynamics scenarios gradually explore the influence of the ECM taxis over the tumour-OV interaction, in the form of haptotaxis of both uninfected and infected cells populations as well as the indirect ECM taxis for the oncolytic virus. Finally, the complex tumour-OV interactions is investigated numerically through the development a new multiscale moving boundary computational framework. While further investigation is needed to validate the findings of our modelling, for the parameter regimes that we considered, our numerical simulations indicate that the viral therapy leads to control and decrease of the overall cancer expansion and in certain cases this can result even in the elimination of the tumour.

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Section: The Microscopic Proteolytic Dynamics and The Macro-micro Doumentioning

confidence: 99%

Multiscale modelling of cancer response to oncolytic viral therapy

Alzahrani

Eftimie

Trucu

2019

Mathematical Biosciences

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“…Herein, we present a similar derivation in order to augment the generality of this framework and present a modelling form capable of capturing the intricacies, and important heterogeneous features of SARs. Compared to [5,34] we introduce new metabolic structural variables and conjugated advection fluxes that are derived from the continuity equation and Liouville's theorem. These variables are needed for modelling stimulated amplification in SARs.…”

Section: Sensing and Reciprocating Systems And Their Mathematical Trementioning

confidence: 99%

“…Throughout this model, we assume a homogeneous and constant concentration of biological pathogen, such that IFN response is consistently encouraged. We have chosen illustrative values for the binding rates, consistently with previous models [5,34], but with the difference that we consider here the negative feedback loop of the IFN system between the metabolic state of the cell and the binding of molecular species to the surface. In this respect, we consider binding to be non-dimensionalised and that feedback causes the maximal binding rate to decrease linearly with the metabolic state of the cell such that the range of values of y for which positive binding exists is given by y < 1 − α.…”

Section: Unthresholded Binding Modelmentioning

confidence: 99%

Signal Propagation in Sensing and Reciprocating Cellular Systems with Spatial and Structural Heterogeneity

et al. 2018

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Sensing and reciprocating cellular systems (SARs) are important for the operation of many biological systems. Production in interferon (IFN) SARs is achieved through activation of the Jak-Stat pathway, and downstream upregulation of IFN regulatory factor (IRF)-7 and IFN transcription, but the role that high- and low-affinity IFNs play in this process remains unclear. We present a comparative between a minimal spatio-temporal partial differential equation model and a novel spatio-structural-temporal (SST) model for the consideration of receptor, binding, and metabolic aspects of SAR behaviour. Using the SST framework, we simulate single- and multi-cluster paradigms of IFN communication. Simulations reveal a cyclic process between the binding of IFN to the receptor, and the consequent increase in metabolism, decreasing the propensity for binding due to the internal feedback mechanism. One observes the effect of heterogeneity between cellular clusters, allowing them to individualise and increase local production, and within clusters, where we observe 'subpopular quiescence'; a process whereby intra-cluster subpopulations reduce their binding and metabolism such that other such subpopulations may augment their production. Finally, we observe the ability for low-affinity IFN to communicate a long range signal, where high affinity cannot, and the breakdown of this relationship through the introduction of cell motility. Biological systems may utilise cell motility where environments are unrestrictive and may use fixed system, with low-affinity communication, where a localised response is desirable.

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“…However, since cancer invasion is a complex multiscale phenomenon occurring across different spatial and temporal scales, it is important to capture and model these multiscale processes also for tumour-OV interactions. The last two decades have seen the development of various mathematical models for multiscale cancer dynamics [1,34,39,48,49,50]. Nevertheless, there are not many multiscale mathematical models for oncolytic viral therapies and tumour-viral interactions; among the very few multiscale models we mention those in [3,4,37,38].…”

Section: Introductionmentioning

confidence: 99%

Non-local multiscale approaches for tumour-oncolytic viruses interactions

Alsisi¹,

Eftimie²,

Trucu

2020

Math Appl Sci Eng

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Oncolytic virus (OV) therapy is a promising treatment for cancer due to the OVs selective ability to infect and replicate inside cancer cells, thus killing them, without harming healthy cells. In this work, we present a new non-local multiscale moving boundary model for the spatio-temporal cancer-OV interactions. This model explores an important double feedback loop that links the macro-scale dynamics of cancer-virus interactions and the micro-scale dynamics of proteolytic activity taking place at the tumour interface. The cancer cell-cell and cell-matrix interactions are assumed to be nonlocal, while the cell-virus interactions are assumed local. With the help of this model we investigate computationally various cancer treatment scenarios involving oncolytic viruses (i.e., the effect of injecting the OV inside the tumour, or outside it). Moreover, we investigate the effect of different cell-cell and cell-matrix interaction strengths on the success of OV spreading throughout the tumour, and the effect of constant or density-dependent virus diffusion coefficients on viral spread.

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Multiscale Computational Modelling and Analysis of Cancer Invasion

Cited by 8 publications

References 49 publications

Multiscale modelling of cancer response to oncolytic viral therapy

Multiscale modelling of cancer response to oncolytic viral therapy

Signal Propagation in Sensing and Reciprocating Cellular Systems with Spatial and Structural Heterogeneity

Non-local multiscale approaches for tumour-oncolytic viruses interactions

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