A Mathematical Framework for Developing Freezing Protocols in the Cryopreservation of Cells

Dalwadi, Mohit P.; Waters, Sarah L.; Byrne, Helen M.; Hewitt, Ian

doi:10.1137/19m1275875

Cited by 14 publications

(6 citation statements)

References 45 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…In doing so, we derive a novel free boundary condition that arises from the underlying biological mechanisms included in the discrete model. While the discrete model is suitable for describing cell-level observations and phenomena [15,29], the continuum limit description is suitable to describe tissue-level dynamics and is more amenable to analysis [30][31][32].…”

Section: Introductionmentioning

confidence: 99%

A free boundary mechanobiological model of epithelial tissues

et al. 2020

View full text Add to dashboard Cite

In this study, we couple intracellular signalling and cell-based mechanical properties to develop a novel free boundary mechanobiological model of epithelial tissue dynamics. Mechanobiological coupling is introduced at the cell level in a discrete modelling framework, and new reaction–diffusion equations are derived to describe tissue-level outcomes. The free boundary evolves as a result of the underlying biological mechanisms included in the discrete model. To demonstrate the accuracy of the continuum model, we compare numerical solutions of the discrete and continuum models for two different signalling pathways. First, we study the Rac–Rho pathway where cell- and tissue-level mechanics are directly related to intracellular signalling. Second, we study an activator–inhibitor system which gives rise to spatial and temporal patterning related to Turing patterns. In all cases, the continuum model and free boundary condition accurately reflect the cell-level processes included in the discrete model.

show abstract

Section: Introductionmentioning

confidence: 99%

A free boundary mechanobiological model of epithelial tissues

et al. 2020

View full text Add to dashboard Cite

show abstract

“…given by a classical one-phase Stefan condition ds(t)/dt = −κ∂u(s(t), t)/∂x [25][26][27][28][29][30][31][32][33], has been called the Fisher-…”

Section: Various Mathematical Extensions Have Been Proposed To Overco...mentioning

confidence: 99%

Non-vanishing sharp-fronted travelling wave solutions of the Fisher-Kolmogorov model

El‐Hachem¹,

McCue²,

Simpson³

2021

Preprint

View full text Add to dashboard Cite

The Fisher-KPP model, and generalisations thereof, are simple reaction-diffusion models of biological invasion that assume individuals in the population undergo linear diffusion with diffusivity D, and logistic proliferation with rate λ. For the Fisher-KPP model, biologically-relevant initial conditions lead to long-time travelling wave solutions that move with speed c = 2 √ λD. Despite these attractive features, there are several biological limitations of travelling wave solutions of the Fisher-KPP model. First, these travelling wave solutions do not predict a well-defined invasion front. Second, biologically-relevant initial conditions lead to travelling waves that move with speed c = 2This means that, for biologically-relevant initial data, the Fisher-KPP model can not be used to study invasion with c 2 √ λD, or retreating travelling waves with c < 0. Here, we reformulate the Fisher-KPP model as a moving boundary problem on x < s(t) and show that this reformulated model alleviates the key limitations of the Fisher-KPP model. Travelling wave solutions of the moving boundary problem predict a well-defined front, and can propagate with any wave speed, −∞ < c < ∞. Here, we establish these results using a combination of high-accuracy numerical simulations of the time-dependent partial differential equation, phase plane analysis and perturbation methods. All software required to replicate this work is available on GitHub.

show abstract

“…Moving-boundary problems of this type are traditionally used to model physical and industrial processes [26][27][28][29][30]. Indeed, the boundary condition (1.3) is analogous to the classical Stefan condition [31] for a material undergoing phase change, where κ is the inverse Stefan number.…”

Section: Introductionmentioning

confidence: 99%

The Effect of Geometry on Survival and Extinction in a Moving-Boundary Problem Motivated by the Fisher-KPP Equation

Tam,

Simpson

2022

Preprint

View full text Add to dashboard Cite

The Fisher-Stefan model involves solving the Fisher-KPP equation on a domain whose boundary evolves according to a Stefan-like condition. The Fisher-Stefan model alleviates two practical limitations of the standard Fisher-KPP model when applied to biological invasion. First, unlike the Fisher-KPP equation, solutions to the Fisher-Stefan model have compact support, enabling one to define the interface between occupied and unoccupied regions unambiguously. Second, the Fisher-Stefan model admits solutions for which the population becomes extinct, which is not possible in the Fisher-KPP equation. Previous research showed that population survival or extinction in the Fisher-Stefan model depends on a critical length in one-dimensional Cartesian or radially-symmetric geometry. However, the survival and extinction behaviour for general two-dimensional regions remains unexplored. We combine analysis and level-set numerical simulations of the Fisher-Stefan model to investigate the survival-extinction conditions for rectangular-shaped initial conditions. We show that it is insufficient to generalise the critical length conditions to critical area in two-dimensions. Instead, knowledge of the region geometry is required to determine whether a population will survive or become extinct.

show abstract

A Mathematical Framework for Developing Freezing Protocols in the Cryopreservation of Cells

Cited by 14 publications

References 45 publications

A free boundary mechanobiological model of epithelial tissues

A free boundary mechanobiological model of epithelial tissues

Non-vanishing sharp-fronted travelling wave solutions of the Fisher-Kolmogorov model

The Effect of Geometry on Survival and Extinction in a Moving-Boundary Problem Motivated by the Fisher-KPP Equation

Contact Info

Product

Resources

About