A Geometric Method for Determining Shape of Bird Eggs

Baker, Douglas E.

doi:10.1093/auk/119.4.1179

Cited by 14 publications

(3 citation statements)

References 2 publications

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“…To extract shape descriptors of the FGF gradient, an isoline at 1/e of the maximal concentration was fit to the ovoid function [Baker, 2002], using the scipy.optimize.curve_fit function. The ovoid function offers a simple formula to approximate asymmetric elliptical shapes (similar to those observed experimentally), with the ellipticity T encoding the shape aspect ratio, and the asymmetry λ the reciprocal blunting of one end and sharpening of the opposing end of the shape.…”

Section: Baseline/physiologic Parameter Valuesmentioning

confidence: 99%

A chemo-mechanical model of endoderm movements driving elongation of the amniote hindgut

Oikonomou,

Cirne,

Nerurkar

2023

Preprint

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While mechanical and biochemical descriptions of development are each essential, integration of upstream morphogenic cues with downstream tissue mechanics remains understudied in many contexts during vertebrate morphogenesis. A posterior gradient of Fibroblast Growth Factor (FGF) ligands generates a contractile force gradient in the definitive endoderm, driving collective cell movements to form the hindgut. Here, we developed a two-dimensional chemo-mechanical model to investigate how mechanical properties of the endoderm and transport properties of FGF coordinately regulate this process. We began by formulating a 2-D reaction-diffusion-advection model that describes the formation of an FGF protein gradient due to posterior displacement of cells transcribing unstable Fgf8 mRNA during axis elongation, coupled with translation, diffusion, and degradation of FGF protein. This was used together with experimental measurements of FGF activity in the chick endoderm to inform a continuum model of definitive endoderm as an active viscous fluid that generates contractile stresses in proportion to FGF concentration. The model replicated key aspects of hindgut morphogenesis, confirms that heterogeneous - but isotropic - contraction is sufficient to generate large anisotropic cell movements, and provides new insight into how chemo-mechanical coupling across the mesoderm and endoderm coordinates hindgut elongation with outgrowth of the tailbud.

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Section: Baseline/physiologic Parameter Valuesmentioning

confidence: 99%

A chemo-mechanical model of endoderm movements driving elongation of the amniote hindgut

Oikonomou,

Cirne,

Nerurkar

2023

Preprint

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“…As a starting point, one can embody structurally a certain engineering object in the shape of an egg through use of its respective mathematical model. Despite fairly extensive research in this field for ∼70 years (e.g., Preston, 1953 ; Carter, 1968 ; Todd and Smart, 1984 ; Smart, 1991 ; Baker, 2002 ; Troscianko, 2014 ; Biggins et al, 2018 ; Pike, 2019 ), the Narushin’s ( Narushin, 2001b ) and Hügelschäffer’s ( Petrović and Obradović, 2010 ; Petrović et al, 2011 ; Obradović et al, 2013 ) models have recently gained the most attention. While the former is thought to be more applicable in thin-walled shell structures ( Zhang et al, 2017a ; b , 2019 , 2021 , 2022 ), the latter has been more adapted to architectural and construction design ( Petrović et al, 2011 ; Maulana et al, 2015 ).…”

Section: Introductionmentioning

confidence: 99%

Egg-inspired engineering in the design of thin-walled shelled vessels: a theoretical approach for shell strength

Narushin¹,

Romanov

Griffin

2022

Front. Bioeng. Biotechnol.

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A novel subdiscipline of bionics is emerging in the form of ‘egg-inspired engineering’ through the use of egg-shaped ovoids as thin-walled tanks and building structures. Hügelschäffer’s and Narushin’s models of egg geometry are highly applicable within this proposed subdiscipline. Here we conducted a comparative analysis between the two models with respect to some of the most important egg parameters. These included contents volume, shell volume, and the location of the neutral axis along the shell thickness. As a first step, theoretical studies using the Narushin’s model were carried out due to the lack (or limited amount) of data on the geometric relationships of parameters and available calculation formulae. Considering experimental data accumulated in the engineering and construction industries, we postulate a hypothesis that there is a correlation between location of the neutral axis and the strength of the walls in the egg-shaped structure. We suggest that the use of Narushin’s model is preferable to Hügelschäffer’s model for designing thin-walled shelled vessels and egg-shaped building structures. This is due to its relative simplicity (because of the requirement for only two initial parameters in the basic equation), optimal geometry in terms of material costs per unit of internal capacity, and effective prerequisites for shell strength characteristics.

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“…Most often, this function was determined by directly measuring the tested eggs, after which the data was subjected to a mathematical processing using the least squares method. As a result, a function could be deduced that, unfortunately, would be adequate only to those eggs that were involved in an experiment ( Baker, 2002; Troscianko, 2014; Pike, 2019 ). Some authors ( Todd and Smart, 1984; Biggins et al, 2018 ) applied the circle equation instead of ellipse as the basic formula, but the principle of empirical determination of the function f ( x ) remained unchanged.…”

Section: Introductionmentioning

confidence: 99%

A universal formula for avian egg shape

Narushin

Romanov

Griffin

2020

Preprint

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The bird's oomorphology has far escaped mathematical formulation universally applicable. All bird egg shapes can be laid in four basic geometric figures: sphere, ellipsoid, ovoid, and pyriform (conical/pear-shaped). The first three have a clear mathematical definition, each derived from expression of the previous, but a formula for the pyriform profile has yet to be inferred. To rectify this, we introduced an additional function into the ovoid formula. The subsequent mathematical model fits a completely novel geometric shape that can be characterized as the last stage in the evolution of the sphere-ellipsoid-Hügelschäffer's ovoid transformation applicable to any avian egg shape geometry. Required measurements are the egg length, maximum breadth, and diameter at the terminus from the pointed end. This mathematical description is invariably a significant step in understanding not only the egg shape itself, but how and why it evolved, thus making widespread biological and technological applications theoretically possible.

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A Geometric Method for Determining Shape of Bird Eggs

Cited by 14 publications

References 2 publications

A chemo-mechanical model of endoderm movements driving elongation of the amniote hindgut

A chemo-mechanical model of endoderm movements driving elongation of the amniote hindgut

Egg-inspired engineering in the design of thin-walled shelled vessels: a theoretical approach for shell strength

A universal formula for avian egg shape

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