Multi-species viscous models for tissue growth: incompressible limit and qualitative behaviour

Degond, Pierre; Hecht, Sophie; Romanos, Michèle; Trescases, Ariane

doi:10.1007/s00285-022-01784-6

Cited by 3 publications

(5 citation statements)

References 47 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…As we scale up to the tissue-level, the computational expense of agent-based models increases, giving way for partial differential equation (PDE)-based models. Although PDE models have proven useful in unraveling morphogenic principles in embryonic development (19)(20)(21)24,31,32), their emphasis remains on PSM elongation. The involvement of mechanical forces in axis elongation highlights the need to address both intra-and inter-tissue mechanical interactions.…”

Section: Discussionmentioning

confidence: 99%

“…It is worth noting that our model system diverges from zebrafish, where tissue growth is restricted or absent during posterior body development, potentially explaining the disparities between the two models (14). Our continuum model, incorporating short and long-distance effects within and between highly proliferative tissues, reproduces embryonic tissue dynamics, including cell vortices resulting from our choice for the velocity viscous equation (24). Moreover, distinguishing tissues with differential growth potentials allowed us to predict the influence of the interactions between them, such as sliding or mutual shaping.…”

Section: Discussionmentioning

confidence: 99%

“…We adopt a partial-differential-equation (PDE)-based model in a 2D multi-tissue framework, which integrates differential biophysical properties that contribute to the dynamics of the tissues. Our model builds upon previous works (24) by considering that tissue growth is driven by cell proliferation and cell ingression from the progenitor zone.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Differential proliferation regulates multi-tissue morphogenesis during embryonic axial extension: Integrating viscous modeling and experimental approaches

Romanos,

Salisbury,

Stephan

et al. 2024

Preprint

Self Cite

View full text Add to dashboard Cite

The study of how mechanical interactions and different cellular behaviors affect tissues and embryo shaping has been and remains an important challenge in biology. Axial extension is a morphogenetic process that results in the acquisition of the elongated shape of the vertebrate embryonic body. Several adjacent tissues are involved in the process, including the tissues that form the spinal cord and musculoskeletal system: the neural tube and the paraxial mesoderm, respectively. Although we have a growing understanding of how each of these tissues elongates, we still need to fully understand the morphogenetic consequences of their growth and mechanical interactions. In this study, we develop a 2D multi-tissue continuum-based mathematical model to simulate and study how differential growth, tissue biophysical properties, and mechanical interactions affect the morphogenesis of the embryonic body during axial extension. Our model captures the long-term dynamics of embryonic posterior tissues previously observed in vivo by time-lapse imaging of bird embryos. It reveals the underestimated influence of differential tissue proliferation rates in inter-tissue interaction and shaping by capturing the relative impact of this process on tissue dynamics. We verified the predictions of our model in quail embryos by showing that decreasing the rate of cell proliferation in the paraxial mesoderm affects long-term tissue dynamics and shaping of both the paraxial mesoderm and the neighboring neural tube. Overall, our work provides a new theoretical platform to consider the long-term consequences of tissue differential growth and mechanical interactions on morphogenesis.

show abstract

Section: Discussionmentioning

confidence: 99%

Section: Discussionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Differential proliferation regulates multi-tissue morphogenesis during embryonic axial extension: Integrating viscous modeling and experimental approaches

Romanos,

Salisbury,

Stephan

et al. 2024

Preprint

Self Cite

View full text Add to dashboard Cite

show abstract

“…where u is the concentration of a phase and µ is called the chemical potential in material sciences but is often used as an effective pressure for living tissues [13,17]. Also, the interaction potential F (u) contained in this effective pressure term comprises the effects of attraction and repulsion between cells.…”

Section: 3mentioning

confidence: 99%

“…Let u 0 ≥ 0 be an initial datum with finite energy and entropy E(u 0 ), Φ(u 0 ) < ∞ defined in (1. 13) and (1.10).…”

Section: Introductionmentioning

confidence: 96%

Degenerate Cahn-Hilliard equation: From nonlocal to local

Elbar¹,

Skrzeczkowski²

2022

Preprint

View full text Add to dashboard Cite

We consider the nonlocal Cahn-Hilliard equation with degenerate mobility and smooth potential. As the scaling parameter related to nonlocality tends to zero, we prove that the equation converges to a local Cahn-Hilliard equation. The proof relies on compactness properties and an adapted result from Bourgain-Brezis-Mironescu and Ponce. 2020 Mathematics Subject Classification. 35K25. Key words and phrases. Degenerate Cahn-Hilliard equation; Nonlocal Cahn-Hilliard equation; Aggregation-Diffusion; Singular limit. J.S. was supported by the National Agency of Academic Exchange project "Singular limits in parabolic equations" no. BPN/BEK/2021/1/00044. Authors are grateful to Benoît Perthame for fruitful discussions and helpful suggestions that greatly improved this paper. (C) F 2 has bounded second derivative i.e. F ′′ 2 ∞ < ∞ and F 2 (u) ≥ −C 3 − C 4 u 2 where C 4 is sufficiently small: more precisely 4 C 4 < C p with C p is the constant in Lemma C.1.Moreover, we require one of the following: (D1) F 1 = 0 or (D2) F 1 has a k-growth, i.e. for some constants C 5 , C 6 , C 7 and C 8 we haveExample 1.2. The following potentials satisfy Assumption 1.1.(1) power-type potential F (u) = u γ used in the context of tumour growth models [9,15,17,34],(2) double-well potential F (u) = u 2 (u − 1) 2 which is an approximation of logarithmic doublewell potential often used in Cahn-Hilliard equation, see [32, Chapter 1],(3) any F ∈ C 2 such that for some interval I ⊂ R we have F ′′ (u) > a > 0 for u ∈ R \ I andfor all u ∈ R \ I, see Lemma A.3 for details.Note that (3) is a more general version of (2). Notation 1.3 (exponents s and k).In what follows we writeWe also define s = 2k k−1 and s ′ its conjugate exponent. Now, we define weak solutions of the nonlocal and local degenerate Cahn-Hilliard equation.

show abstract

Differential proliferation regulates multi-tissue morphogenesis during embryonic axial extension: integrating viscous modeling and experimental approaches

Romanos,

Salisbury,

Stephan

et al. 2024

Development

View full text Add to dashboard Cite

A major challenge in biology is to understand how mechanical interactions and cellular behavior affect the shapes of tissues and embryo morphology. The extension of the neural tube and paraxial mesoderm, which form the spinal cord and musculoskeletal system, respectively, results in the elongated shape of the vertebrate embryonic body. Despite our understanding of how each of these tissues elongates independently of the others, the morphogenetic consequences of their simultaneous growth and mechanical interactions are still unclear. Our study investigates how differential growth, tissue biophysical properties and mechanical interactions affect embryonic morphogenesis during axial extension using a 2D multi-tissue continuum-based mathematical model. Our model captures the dynamics observed in vivo by time-lapse imaging of bird embryos, and reveals the underestimated influence of differential tissue proliferation rates. We confirmed this prediction in quail embryos by showing that decreasing the rate of cell proliferation in the paraxial mesoderm affects long-term tissue dynamics, and shaping of both the paraxial mesoderm and the neighboring neural tube. Overall, our work provides a new theoretical platform upon which to consider the long-term consequences of tissue differential growth and mechanical interactions on morphogenesis.

show abstract

Multi-species viscous models for tissue growth: incompressible limit and qualitative behaviour

Cited by 3 publications

References 47 publications

Differential proliferation regulates multi-tissue morphogenesis during embryonic axial extension: Integrating viscous modeling and experimental approaches

Differential proliferation regulates multi-tissue morphogenesis during embryonic axial extension: Integrating viscous modeling and experimental approaches

Degenerate Cahn-Hilliard equation: From nonlocal to local

Differential proliferation regulates multi-tissue morphogenesis during embryonic axial extension: integrating viscous modeling and experimental approaches

Contact Info

Product

Resources

About