A 3D finite element model of ventral furrow invagination in the Drosophila melanogaster embryo

Article · May 2008with33 Reads
DOI: 10.1016/j.jmbbm.2007.10.002 · Source: PubMed
Abstract
The paper describes a mechanical model of epithelial tissue development in Drosophila embryos to investigate a buckling phenomenon called invagination. The finite element method is used to model this ventral furrow formation in 3D by decomposing the total deformation into two parts: an imposed active deformation, and an elastic passive deformation superimposed onto the latter. The model imposes as boundary conditions (i) a constant yolk volume and (ii) a sliding contact condition of the cells against the vitelline membrane, which is interpolated as a B-Spline surface. The active deformation simulates the effects of apical constriction and apico-basal elongation of cells. This set of local cellular mechanisms leads to global shape changes of the embryo which are associated with known gene expressions. Using the model we have tested different plausible hypotheses postulated to account for the mechanical behaviour of epithelial tissues. In particular, we conclude that only certain combinations of local cell shape change can successfully reproduce the invagination process. We have quantitatively compared the model with a 2D model and shown that it exhibits a more robust invagination phenomenon. The 3D model has also revealed that invagination causes a yolk flow from the central region to the anterior and posterior ends of the embryo, causing an accordion-like global compression and expansion wave to move through the embryo. Such a phenomenon cannot be described by 2D models.
    • "For the following calculations we have used E = 100Pa and ν = 0.4 , similar to the assumptions made in [8], and ρ 0 = 1000kgm −2 for the initial mass distribution. Furthermore, we have always set: "
    [Show abstract] [Hide abstract] ABSTRACT: Background During embryogenesis, chemical (morphogen) and mechanical patterns develop within tissues in a self-organized way. More than 60 years ago, Turing proposed his famous reaction-diffusion model for such processes, assuming chemical interactions as the main driving force in tissue patterning. However, experimental identification of corresponding molecular candidates is still incomplete. Recent results suggest that beside morphogens, also tissue mechanics play a significant role in these patterning processes. Results Combining continuous finite strain with discrete cellular tissue models, we present and numerically investigate mechanochemical processes, in which morphogen dynamics and tissue mechanics are coupled by feedback loops. We consider three different mechanical cues involved in such feedbacks: strain, stress, and compression. Based on experimental results, for each case, we present a feedback loop spontaneously creating robust mechanochemical patterns. In contrast to Turing-type models, simple mechanochemical interaction terms are sufficient to create de novo patterns. Conclusions Our results emphasize mechanochemical processes as possible candidates controlling different steps of embryogenesis. To motivate further experimental research discovering related mechanisms in living tissues, we also present predictive in silicio experiments. Reviewers Reviewer 1 - Marek Kimmel; Reviewer 2 - Konstantin Doubrovinski (nominated by Ned Wingreen); Reviewer 3 - Jun Allard (nominated by William Hlavacek).
    Full-text · Article · Dec 2016
    • "Two other pelvic floor conditions have been investigated and include SUI [32], and the modeling of child birth and its effect on the pelvic floor muscles. FE method, which involves the discretization of a complex irregular geometry into a finite number of elements, and subsequently applying appropriate BCs to analyze the mechanical behavior under different imposed conditions, has been widely used to model biological systems, such as heart, skeletal system, sensory organs, such as eyes and ears, soft tissues, and cells [15,17,22,99100101102103104105106107108109110111112113114. Pelvic floor changes due to prolapse and child birth have also been studied through FE modeling [Figure 3 shows a typical example of the numerical model of female pelvic system. "
    [Show abstract] [Hide abstract] ABSTRACT: Pelvic Organ Prolapse (POP) is an abnormality of the female pelvic anatomy due to events such as multiple child births, menopause and morbid obesity which may lead to weakening of the pelvic floor muscles and musculoconnective tissues. POP leads to “dropping” of the pelvic organs namely the bladder, uterus and rectum into the vaginal canal and eventual protrusion, causing vaginal pain, pressure, difficulty emptying the bladder and rectum, and sexual dysfunction. Each year, close to 300,000 POP surgeries are performed in the U.S., out of which, more than 60\% of patients may face relapse conditions. A closer look into the problem reveals that POP surgery failures may be attributed mainly to the lack of understanding among medical practitioners on the mechanics of prolapse. In the literature, there have been attempts in the engineering community to understand prolapse using phenomenological computational modeling. This paper reviews the development and study of these numerical models aimed at understanding the mechanics of POP. The various computational challenges related to geometry creation, material modeling, finite element modeling and boundary conditions will be discussed and significant future research directions will also be highlighted in this review.
    Full-text · Article · Jul 2015
    • "Here, we have chosen the active strain approach since it appears to be more robust from a mathematical point of view than the active stress one [37]. Additionally, its physiological relevance has already been shown in several biological context [28,38394041. In the fluid phase (i.e. the cytoplasm), the deformation gradient F f is also multiplicatively decomposed asFigure 2. Scheme of the generalized Maxwell model used to describe the viscoelastic behaviour of the cell. "
    [Show abstract] [Hide abstract] ABSTRACT: Cell migration, a fundamental mechanobiological process, is highly sensitive to the biochemical and mechanical properties of the environment. Efficient cell migration is ensured by the intrinsic polarity of the cell, which triggers a transition from an isotropic to an anisotropic configuration of the acto-mysion filaments responsible for the protrusion–contraction movement of the cell. Additionally, polarity may be highly influenced by the substrate rigidity, which results in a phenomenon called durotaxis. In the present work, we propose a two-dimensional finite element model able to capture three main features of cell migration: durotaxis, cell polarity and anisotropy. The cell is modelled as a continuum able to develop cyclic active strains regulated by the polymerization and depolymerization of the acto-myosin filaments and synchronized with the adhesion forces between the cell and the substrate underneath. A generalized Maxwell model is used to describe the viscoelastic behaviour of the cell constituted by a solid anisotropic branch with active strains (i.e. the acto-myosin filaments) and a fluid viscoelastic branch (i.e. the cytoplasm). Several types of substrate have been tested which are homogeneously soft or stiff or include both regions. The numerical results have been qualitatively compared with experimental observations showing a good agreement and have allowed us to find the mechanical link between durotaxis, cell polarity and anisotropy.
    Full-text · Article · Apr 2015
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