A conservative algorithm for parabolic problems in domains with moving boundaries

Novak, Igor L.; Slepchenko, Boris M.

doi:10.1016/j.jcp.2014.03.014

Cited by 13 publications

(24 citation statements)

References 34 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…30 Level set methods have been applied to implicitly track the movement of cell boundaries, 31 and VCell (see Connecting to Molecular Effects) recently added front-tracking capabilities. 32,33 These are among the most computationally intensive cell-based methods, but they are useful for coupling detailed cell mechanics to fluid and solid tissue mechanics.…”

Section: A Survey Of Cell-based Modeling Methodsmentioning

confidence: 99%

“…Many discrete models include systems of ordinary differential equations (ODEs) to model molecular processes in individual cells. 35,36 VCell can simulate reacting flows of many proteins within a single detailed cell, 32,33 and many modeling packages (eg, Chaste, 37 CompuCell3D, 38 and EPISIM 39 ) support systems biology markup language (SBML) to include systems of ODEs that simulate molecular effects in individual cells. Others use discrete models within individual agents: Gerlee and Anderson 40 used small neural networks to simulate individual cell phenotypic "decisions" on the basis of microenvironmental inputs, whereas PhysiBoSS 41 combines the Boolean network modeling approach of MaBoSS 42,43 with PhysiCell 21 to simulate molecular processes in individual cells.…”

Section: A Survey Of Cell-based Modeling Methodsmentioning

confidence: 99%

See 1 more Smart Citation

A Review of Cell-Based Computational Modeling in Cancer Biology

Metzcar

Wang

Heiland

et al. 2019

JCO Clinical Cancer Informatics

318

270

View full text Add to dashboard Cite

Cancer biology involves complex, dynamic interactions between cancer cells and their tissue microenvironments. Single-cell effects are critical drivers of clinical progression. Chemical and mechanical communication between tumor and stromal cells can co-opt normal physiologic processes to promote growth and invasion. Cancer cell heterogeneity increases cancer’s ability to test strategies to adapt to microenvironmental stresses. Hypoxia and treatment can select for cancer stem cells and drive invasion and resistance. Cell-based computational models (also known as discrete models, agent-based models, or individual-based models) simulate individual cells as they interact in virtual tissues, which allows us to explore how single-cell behaviors lead to the dynamics we observe and work to control in cancer systems. In this review, we introduce the broad range of techniques available for cell-based computational modeling. The approaches can range from highly detailed models of just a few cells and their morphologies to millions of simpler cells in three-dimensional tissues. Modeling individual cells allows us to directly translate biologic observations into simulation rules. In many cases, individual cell agents include molecular-scale models. Most models also simulate the transport of oxygen, drugs, and growth factors, which allow us to link cancer development to microenvironmental conditions. We illustrate these methods with examples drawn from cancer hypoxia, angiogenesis, invasion, stem cells, and immunosurveillance. An ecosystem of interoperable cell-based simulation tools is emerging at a time when cloud computing resources make software easier to access and supercomputing resources make large-scale simulation studies possible. As the field develops, we anticipate that high-throughput simulation studies will allow us to rapidly explore the space of biologic possibilities, prescreen new therapeutic strategies, and even re-engineer tumor and stromal cells to bring cancer systems under control.

show abstract

Section: A Survey Of Cell-based Modeling Methodsmentioning

confidence: 99%

Section: A Survey Of Cell-based Modeling Methodsmentioning

confidence: 99%

A Review of Cell-Based Computational Modeling in Cancer Biology

Metzcar

Wang

Heiland

et al. 2019

JCO Clinical Cancer Informatics

318

270

View full text Add to dashboard Cite

show abstract

“…Numerical solutions of the ZV and ZS models were obtained using a generalized version of a mass-conservative algorithm originally developed for solving parabolic equations in moving domains with known kinematics [ 30 ]. The method has been shown to converge in space with an order close to 2 in L 2 -norm and ensures exact local mass conservation.…”

Section: Models and Methodsmentioning

confidence: 99%

A free-boundary model of a motile cell explains turning behavior

et al. 2017

Self Cite

View full text Add to dashboard Cite

To understand shapes and movements of cells undergoing lamellipodial motility, we systematically explore minimal free-boundary models of actin-myosin contractility consisting of the force-balance and myosin transport equations. The models account for isotropic contraction proportional to myosin density, viscous stresses in the actin network, and constant-strength viscous-like adhesion. The contraction generates a spatially graded centripetal actin flow, which in turn reinforces the contraction via myosin redistribution and causes retraction of the lamellipodial boundary. Actin protrusion at the boundary counters the retraction, and the balance of the protrusion and retraction shapes the lamellipodium. The model analysis shows that initiation of motility critically depends on three dimensionless parameter combinations, which represent myosin-dependent contractility, a characteristic viscosity-adhesion length, and a rate of actin protrusion. When the contractility is sufficiently strong, cells break symmetry and move steadily along either straight or circular trajectories, and the motile behavior is sensitive to conditions at the cell boundary. Scanning of a model parameter space shows that the contractile mechanism of motility supports robust cell turning in conditions where short viscosity-adhesion lengths and fast protrusion cause an accumulation of myosin in a small region at the cell rear, destabilizing the axial symmetry of a moving cell.

show abstract

“…Geometries for cell simulations can be designed by hand, derived from microscope images (Schaff et al, 2000), or generated from machine-learned cell models (Majarian et al, 2019). Currently, there are only a few simulation tools that can model cellular biochemistry within dynamic morphologies (Angermann et al, 2012;Tanaka et al, 2015) and the computational treatment of reaction-diffusion processes within domains that exhibit moving boundaries is still a very active field of research (Wolgemuth and Zajac, 2010;Novak and Slepchenko, 2014). We note that models allowing moving boundaries (which usually represent the membrane) do not necessarily capture the biophysics of membrane dynamics (Figure 2d).…”

Section: Spatial Modeling Approachesmentioning

confidence: 99%

Quantifying the roles of space and stochasticity in computer simulations for cell biology and cellular biochemistry

Johnson

Chen

Faeder

et al. 2021

MBoC

View full text Add to dashboard Cite

Most of the fascinating phenomena studied in cell biology emerge from interactions among highly organized multi-molecular structures embedded into complex and frequently dynamic cellular morphologies. For the exploration of such systems, computer simulation has proved to be an invaluable tool, and many researchers in this field have developed sophisticated computational models for application to specific cell biological questions. However, it is often difficult to reconcile conflicting computational results that use different approaches to describe the same phenomenon. To address this issue systematically, we have defined a series of computational test cases ranging from very simple to moderately complex, varying key features of dimensionality, reaction type, reaction speed, crowding, and cell size. We then quantified how explicit spatial and/or stochastic implementations alter outcomes, even when all methods use the same reaction network, rates, and concentrations. For simple cases we generally find minor differences in solutions of the same problem. However, we observe increasing discordance as the effects of localization, dimensionality reduction, and irreversible enzymatic reactions are combined. We discuss the strengths and limitations of commonly used computational approaches for exploring cell biological questions and provide a framework for decision-making by researchers developing new models. As computational power and speed continue to increase at a remarkable rate, the dream of a fully comprehensive computational model of a living cell may be drawing closer to reality, but our analysis demonstrates that it will be crucial to evaluate the accuracy of such models critically and systematically.

show abstract

A conservative algorithm for parabolic problems in domains with moving boundaries

Cited by 13 publications

References 34 publications

A Review of Cell-Based Computational Modeling in Cancer Biology

A Review of Cell-Based Computational Modeling in Cancer Biology

A free-boundary model of a motile cell explains turning behavior

Quantifying the roles of space and stochasticity in computer simulations for cell biology and cellular biochemistry

Contact Info

Product

Resources

About