An Immersed Boundary Method for a Contractile Elastic Ring in a Three-Dimensional Newtonian Fluid

Lee, Seunggyu; Jeong, Darae; Lee, Wanho; Kim, Junseok

doi:10.1007/s10915-015-0110-8

Cited by 5 publications

(2 citation statements)

References 38 publications

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“…The authors also resorted to several numerical experiments to demonstrate the viability of the method used in modelling the two mentioned processes 6 . Similar works can be found in, 105106 and 107 . In all of them, cytokinesis is modulated and the contractile ring is assumed.…”

Section: Mathematical and Computational Modelsmentioning

confidence: 83%

Computationally modelling cell proliferation: A review

Barbosa

Belinha

Jorge

et al. 2023

Numer Methods Biomed Eng

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Cell proliferation is vital for the development and homeostasis of the human body. For such to occur, cells go through the cell cycle during which they replicate their genetic material and ultimately complete cellular division, when one cell divides into two new cells with equal genetic material. However, if there are some errors or abnormalities during the cell cycle that disrupt the balance between cell death and proliferation, severe problems can occur, such as tumour development, which is currently one of the leading causes of death in the world. Nowadays, mathematical and computational models are used to understand and study several biological mechanisms and processes, namely cellular proliferation. Over the last forty-five years, several models have attempted to describe cell proliferation and its regulation. Due to the complexity of the process, numerous assumptions and simplifications have been considered. This work presents a review of some of these models, focusing mainly on mammalian or generic eukaryotic models. Previously published continuum, discrete and hybrid approaches are presented and compared, in order to understand and highlight the relevance and capabilities of these models, their shortcomings and future challenges.

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Section: Mathematical and Computational Modelsmentioning

confidence: 83%

Computationally modelling cell proliferation: A review

Barbosa

Belinha

Jorge

et al. 2023

Numer Methods Biomed Eng

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“…The conventional IB method usually uses the Navier–Stokes equations to represent the structure’s motion; however, the transport equation for simple implementation and immediate reaction from the generated force was the only part used in our simulation. The details of the forcing formula were referred to in Lim and Kim (2011) 16 and Lee et al (2016) 17 . The following equations describe the energies and forces of the longitudinal and circular muscle motions: where E circular is the elastic shrinking energy of the circular bundles, F circular is the force accounting for variational derivatives, F longitudinal is the tethered shrinking force of the longitudinal bundles, X is the fiber position, s is the parametrization, t is time, and σ and k T are the coefficients relating to the energy and force, respectively.…”

Section: Methodsmentioning

confidence: 99%

The three muscle layers in the pyloric sphincter and their possible function during antropyloroduodenal motility

Hur

Lee

Kang

et al. 2021

Sci Rep

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This study was conducted to determine the muscular arrangement of the human pyloric sphincter using a comprehensive approach that involved microdissection, histology, and microcomputed tomography (micro‐CT). The stomachs of 80 embalmed Korean adult cadavers were obtained. In all specimens, loose muscular tissue of the innermost aspect of the sphincter wall ran aborally, forming the newly found inner longitudinal muscle bundles, entered the duodenum, and connected with the nearby circular bundles. In all specimens, approximately one-third of the outer longitudinal layer of the sphincter entered its inner circular layer, divided the circular layer into several parts, and finally connected with the circular bundles. Anatomical findings around the sphincter were confirmed in micro-CT images. The sphincter wall comprised three layers: an inner layer of longitudinal bundles, a middle layer of major circular and minor longitudinal bundles, and an outer layer of longitudinal bundles. The stomach outer longitudinal bundles were connected to the sphincter circular bundles. The inner longitudinal bundles of the sphincter were connected to the adjacent circular bundles of the duodenum.

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Mathematical Model of Contractile Ring-Driven Cytokinesis in a Three-Dimensional Domain

Lee

2018

Bull Math Biol

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In this paper, a mathematical model of contractile ring-driven cytokinesis is presented by using both phase-field and immersed-boundary methods in a three-dimensional domain. It is one of the powerful hypotheses that cytokinesis happens driven by the contractile ring; however, there are only few mathematical models following the hypothesis, to the author's knowledge. I consider a hybrid method to model the phenomenon. First, a cell membrane is represented by a zero-contour of a phase-field implicitly because of its topological change. Otherwise, immersed-boundary particles represent a contractile ring explicitly based on the author's previous work. Here, the multi-component (or vector-valued) phase-field equation is considered to avoid the emerging of each cell membrane right after their divisions. Using a convex splitting scheme, the governing equation of the phase-field method has unique solvability. The numerical convergence of contractile ring to cell membrane is proved. Several numerical simulations are performed to validate the proposed model.

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An Immersed Boundary Method for a Contractile Elastic Ring in a Three-Dimensional Newtonian Fluid

Cited by 5 publications

References 38 publications

Computationally modelling cell proliferation: A review

Computationally modelling cell proliferation: A review

The three muscle layers in the pyloric sphincter and their possible function during antropyloroduodenal motility

Mathematical Model of Contractile Ring-Driven Cytokinesis in a Three-Dimensional Domain

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