scholarly journals On-lattice agent-based simulation of populations of cells within the open-source Chaste framework

2013 ◽  
Vol 3 (2) ◽  
pp. 20120081 ◽  
Author(s):  
Grazziela P. Figueredo ◽  
Tanvi V. Joshi ◽  
James M. Osborne ◽  
Helen M. Byrne ◽  
Markus R. Owen
Keyword(s):  
Tumour Growth ◽  
Current System ◽  
Reaction Diffusion ◽  
Multiple Scale ◽  
Reaction Diffusion Equations ◽  
Scale Model ◽  
Low Oxygen ◽  
Model Framework ◽  
Agent Based ◽  
Multi Scale

Over the years, agent-based models have been developed that combine cell division and reinforced random walks of cells on a regular lattice, reaction–diffusion equations for nutrients and growth factors; and ordinary differential equations for the subcellular networks regulating the cell cycle. When linked to a vascular layer, this multiple scale model framework has been applied to tumour growth and therapy. Here, we report on the creation of an agent-based multi-scale environment amalgamating the characteristics of these models within a Virtual Physiological Human (VPH) Exemplar Project. This project enables reuse, integration, expansion and sharing of the model and relevant data. The agent-based and reaction–diffusion parts of the multi-scale model have been implemented and are available for download as part of the latest public release of Chaste (Cancer, Heart and Soft Tissue Environment; http://www.cs.ox.ac.uk/chaste/), part of the VPH Toolkit (http://toolkit.vph-noe.eu/). The environment functionalities are verified against the original models, in addition to extra validation of all aspects of the code. In this work, we present the details of the implementation of the agent-based environment, including the system description, the conceptual model, the development of the simulation model and the processes of verification and validation of the simulation results. We explore the potential use of the environment by presenting exemplar applications of the ‘what if’ scenarios that can easily be studied in the environment. These examples relate to tumour growth, cellular competition for resources and tumour responses to hypoxia (low oxygen levels). We conclude our work by summarizing the future steps for the expansion of the current system.

scholarly journals A nonlinear multi-scale model for blood circulation in a realistic vascular system

2021 ◽  
Vol 8 (12) ◽  
Author(s):  
Ulin Nuha A. Qohar ◽  
Antonella Zanna Munthe-Kaas ◽  
Jan Martin Nordbotten ◽  
Erik Andreas Hanson
Keyword(s):  
Blood Flow ◽  
Blood Circulation ◽  
Vascular System ◽  
Scale Model ◽  
Model Framework ◽  
Fluid Exchange ◽  
Multi Scale ◽  
Proposed Model ◽  
Porous Media Model ◽  
Capillary Bed

In the last decade, numerical models have become an increasingly important tool in biological and medical science. Numerical simulations contribute to a deeper understanding of physiology and are a powerful tool for better diagnostics and treatment. In this paper, a nonlinear multi-scale model framework is developed for blood flow distribution in the full vascular system of an organ. We couple a quasi one-dimensional vascular graph model to represent blood flow in larger vessels and a porous media model to describe flow in smaller vessels and capillary bed. The vascular model is based on Poiseuille’s Law, with pressure correction by elasticity and pressure drop estimation at vessels' junctions. The porous capillary bed is modelled as a two-compartment domain (artery and venous) using Darcy’s Law. The fluid exchange between the artery and venous capillary bed compartments is defined as blood perfusion. The numerical experiments show that the proposed model for blood circulation: (i) is closely dependent on the structure and parameters of both the larger vessels and of the capillary bed, and (ii) provides a realistic blood circulation in the organ. The advantage of the proposed model is that it is complex enough to reliably capture the main underlying physiological function, yet highly flexible as it offers the possibility of incorporating various local effects. Furthermore, the numerical implementation of the model is straightforward and allows for simulations on a regular desktop computer.

scholarly journals Compartmental and spatial rule-based modeling with Virtual Cell (VCell)

2017 ◽  
Author(s):  
M. L. Blinov ◽  
J. C. Schaff ◽  
D. Vasilescu ◽  
I. I. Moraru ◽  
J. E. Bloom ◽  
...  
Keyword(s):  
Reaction Diffusion ◽  
Molecular Complexes ◽  
Reaction Diffusion Equations ◽  
Reaction Networks ◽  
The Novel ◽  
Modeling Framework ◽  
Rule Based ◽  
Agent Based ◽  
Virtual Cell ◽  
Stochastic Simulator

AbstractIn rule-based modeling, molecular interactions are systematically specified in the form of reaction rules that serve as generators of reactions. This provides a way to account for all the potential molecular complexes and interactions among multivalent or multistate molecules. Recently, we introduced rule-based modeling into the Virtual Cell (VCell) modeling framework, permitting graphical specification of rules and merger of networks generated automatically (using the BioNetGen modeling engine) with hand-specified reaction networks. VCell provides a number of ordinary differential equation (ODE) and stochastic numerical solvers for single-compartment simulations of the kinetic systems derived from these networks, and agent-based network-free simulation of the rules. In this work, compartmental and spatial modeling of rule-based models has been implemented within VCell. To enable rule-based deterministic and stochastic spatial simulations and network-free agent-based compartmental simulations, the BioNetGen and NFSim engines were each modified to support compartments. In the new rule-based formalism, every reactant and product pattern and every reaction rule are assigned locations. We also introduce the novel rule-based concept of molecular anchors. This assures that any species that has a molecule anchored to a predefined compartment will remain in this compartment. Importantly, in addition to formulation of compartmental models, this now permits VCell users to seamlessly connect reaction networks derived from rules to explicit geometries to automatically generate a system of reaction-diffusion equations. These may then be simulated using either the VCell partial differential equations (PDE) deterministic solvers or the Smoldyn stochastic simulator.

A multi-scale agent-based model for avascular tumour growth

Biosystems ◽  
2021 ◽  
Vol 206 ◽  
pp. 104450
Author(s):  
Sounak Sadhukhan ◽  
P.K. Mishra ◽  
S.K. Basu ◽  
J.K. Mandal
Keyword(s):  
Tumour Growth ◽  
Agent Based Model ◽  
Agent Based ◽  
Multi Scale

scholarly journals A Novel Method for Simulating the Extracellular Matrix in Models of Tumour Growth

2012 ◽  
Vol 2012 ◽  
pp. 1-11 ◽  
Author(s):  
Alina Toma ◽  
Andreas Mang ◽  
Tina A. Schuetz ◽  
Stefan Becker ◽  
Thorsten M. Buzug
Keyword(s):  
Extracellular Matrix ◽  
Tumour Growth ◽  
Reaction Diffusion ◽  
Reaction Diffusion Equations ◽  
Spatiotemporal Model ◽  
Simplified Approach ◽  
Degrading Enzymes ◽  
Novel Method ◽  
Matrix Degrading Enzymes

A novel hybrid continuum-discrete model to simulate tumour growth on a cellular scale is proposed. The lattice-based spatiotemporal model consists of reaction-diffusion equations that describe interactions between cancer cells and their microenvironment. The fundamental ingredients that are typically considered are the nutrient concentration, the extracellular matrix (ECM), and matrix degrading enzymes (MDEs). The in vivo processes are very complex and occur on different levels. This in turn leads to huge computational costs. The main contribution of the present work is therefore to describe the processes on the basis of simplified mathematical approaches, which, at the same time, depict realistic results to understand the biological processes. In this work, we discuss if we have to simulate the MDE or if the degraded matrix can be estimated directly with respect to the cancer cell distribution. Additionally, we compare the results for modelling tumour growth using the common and our simplified approach, thereby demonstrating the advantages of the proposed method. Therefore, we introduce variations of the positioning of the nutrient delivering blood vessels and use different initializations of the ECM. We conclude that the novel method, which does not explicitly model the matrix degrading enzymes, provides means for a straightforward and fast implementation for modelling tumour growth.

scholarly journals Quantifying the driving factors for language shift in a bilingual region

2017 ◽  
Vol 114 (17) ◽  
pp. 4365-4369 ◽  
Author(s):  
Katharina Prochazka ◽  
Gero Vogl
Keyword(s):  
Cellular Automata ◽  
Differential Equations ◽  
Large Scale ◽  
Language Shift ◽  
Reaction Diffusion ◽  
Agent Based Modeling ◽  
Reaction Diffusion Equations ◽  
Agent Based ◽  
Using Data ◽  
A Minor

Many of the world’s around 6,000 languages are in danger of disappearing as people give up use of a minority language in favor of the majority language in a process called language shift. Language shift can be monitored on a large scale through the use of mathematical models by way of differential equations, for example, reaction–diffusion equations. Here, we use a different approach: we propose a model for language dynamics based on the principles of cellular automata/agent-based modeling and combine it with very detailed empirical data. Our model makes it possible to follow language dynamics over space and time, whereas existing models based on differential equations average over space and consequently provide no information on local changes in language use. Additionally, cellular automata models can be used even in cases where models based on differential equations are not applicable, for example, in situations where one language has become dispersed and retreated to language islands. Using data from a bilingual region in Austria, we show that the most important factor in determining the spread and retreat of a language is the interaction with speakers of the same language. External factors like bilingual schools or parish language have only a minor influence.

scholarly journals New Resolution Strategies for Multi-scale Reaction Waves: Optimal Time Operator Splitting and Space Adaptive Multiresolution

2011 ◽  
Vol 14 (1) ◽  
Author(s):  
Max Duarte ◽  
Marc Massot ◽  
Frédérique Laurent ◽  
Stéphane Descombes ◽  
Christian Tenaud ◽  
...  
Keyword(s):  
Numerical Simulation ◽  
Source Term ◽  
Operator Splitting ◽  
Reaction Diffusion ◽  
Time Operator ◽  
Reaction Diffusion Equations ◽  
Optimal Time ◽  
Time Step ◽  
Multi Scale ◽  
Reaction Fronts

We tackle the numerical simulation of reaction-diffusion equations modeling multi-scale reac- tion waves. This type of problems induces peculiar difficulties and potentially large stiffness which stem from the broad spectrum of temporal scales in the nonlinear chemical source term as well as from the presence of large spatial gradients in the reaction fronts, spatially very lo- calized. In this paper, we introduce a new resolution strategy based on time operator splitting and space adaptive multiresolution in the context of very localized and stiff reaction fronts. Based on recent theoretical studies of numerical analysis, such a strategy leads to a splitting time step which is not restricted neither by the fastest scales in the source term nor by restric- tive diffusive step stability limits, but only by the physics of the phenomenon. We thus aim at solving accurately complete models including all time and space scales of the phenomenon, considering large simulation domains with conventional computing resources. The efficiency is evaluated through the numerical simulation of configurations which were so far out of reach of standard methods in the field of nonlinear chemical dynamics for 2D spiral waves and 3D scroll waves as an illustration. Future extensions of the proposed strategy are finally discussed.

scholarly journals Pulse dynamics in reaction–diffusion equations with strong spatially localized impurities

2018 ◽  
Vol 376 (2117) ◽  
pp. 20170183 ◽  
Author(s):  
Arjen Doelman ◽  
Peter van Heijster ◽  
Jianhe Shen
Keyword(s):  
Reaction Diffusion ◽  
Multiple Scale ◽  
Reaction Diffusion Equations ◽  
Diffusion Equations ◽  
Scalar Case ◽  
Pulse Solution ◽  
Linear Reaction ◽  
Existence And Stability ◽  
Stability And Bifurcations ◽  
The Impact

In this article, a general geometric singular perturbation framework is developed to study the impact of strong, spatially localized, nonlinear impurities on the existence, stability and bifurcations of localized structures in systems of linear reaction–diffusion equations. By taking advantage of the multiple-scale nature of the problem, we derive algebraic conditions determining the existence and stability of pinned single- and multi-pulse solutions. Our methods enable us to explicitly control the spectrum associated with a (multi-)pulse solution. In the scalar case, we show how eigenvalues may move in and out of the essential spectrum and that Hopf bifurcations cannot occur. By contrast, even a pinned 1-pulse solution can undergo a Hopf bifurcation in a two-component system of linear reaction–diffusion equations with (only) one impurity. This article is part of the theme issue ‘Stability of nonlinear waves and patterns and related topics’.

Multi-Scale Modeling of Internal Mass Diffusion Limitations in CO Oxidation Catalysts

2015 ◽  
Vol 364 ◽  
pp. 92-103 ◽  
Author(s):  
J.E.P. Navalho ◽  
J.M.C. Pereira ◽  
J.C.F. Pereira
Keyword(s):  
Diffusion Model ◽  
Transport Coefficients ◽  
Reaction Diffusion ◽  
Scale Model ◽  
Computational Time ◽  
Reactor Model ◽  
Porous Catalyst ◽  
Diffusion Limitations ◽  
Multi Scale ◽  
Reaction Diffusion Model

This work applies a 3D multi-scale bottom-up approach for modeling the processes of diffusion and reaction-diffusion in porous catalyst layers. The performance of the random pore model to predict effective transport coefficients are compared with the results of the multi-scale diffusion model. The results of the 3D multi-scale diffusion model are employed in a 1D pseudo-homogeneous reaction-diffusion model with a relative good agreement with the 3D multi-scale reaction-diffusion model. Furthermore, the former multi-scale model was coupled to a full-scale reactor model with good results and high advantages in terms of computational time savings.

On a Nonlinear System of Reaction-Diffusion Equations

2006 ◽  
Vol 11 (2) ◽  
pp. 115-121 ◽  
Author(s):  
G. A. Afrouzi ◽  
S. H. Rasouli
Keyword(s):  
Weak Solution ◽  
Dirichlet Boundary ◽  
Smooth Boundary ◽  
Reaction Diffusion ◽  
Reaction Diffusion Equations ◽  
Dirichlet Boundary Conditions ◽  
Nonlinear Elliptic System ◽  
Positive Parameter ◽  
Nonlinear Elliptic ◽  
Positive Weak Solution

The aim of this article is to study the existence of positive weak solution for a quasilinear reaction-diffusion system with Dirichlet boundary conditions,− div(|∇u1|p1−2∇u1) = λu1α11u2α12... unα1n,   x ∈ Ω,− div(|∇u2|p2−2∇u2) = λu1α21u2α22... unα2n,   x ∈ Ω, ... , − div(|∇un|pn−2∇un) = λu1αn1u2αn2... unαnn,   x ∈ Ω,ui = 0,   x ∈ ∂Ω,   i = 1, 2, ..., n,  where λ is a positive parameter, Ω is a bounded domain in RN (N > 1) with smooth boundary ∂Ω. In addition, we assume that 1 < pi < N for i = 1, 2, ..., n. For λ large by applying the method of sub-super solutions the existence of a large positive weak solution is established for the above nonlinear elliptic system.

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