Topological Invariance of Biological Development

Presnov, E.; Isaeva, V. V.; Kasyanov, Nikolay

doi:10.1007/s10516-013-9216-5

Cited by 9 publications

(10 citation statements)

References 49 publications

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“…Technologies, which create graphical representations of mathematical concepts, nonlinear dynamics, fractal geometry, and topology, make them visual for architects and give an opportunity to "translate" modern scientific terminology into the language of architectural theory and export concepts of interdisciplinary science not only in biology [15,16], but also in architecture theory. New spatial forms of architecture, created by means of a computer, can be called the "virtual style" or "virtual architecture".…”

Section: Information Technologiesmentioning

confidence: 99%

Research on the Similarities of Morphogenesis in Architecture and Nature

Kasyanov¹

2020

Proceedings of the 2nd International Conference on Architecture: Heritage, Traditions and Innovations (AHTI 2020)

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This article highlights some of the patterns and trends of form building in the architecture of the early third millennium. An interdisciplinary approach, integrating different fields of science, contributes to the identification of morphogenetic parallelism in living and non-living nature, which is essential in the study of some aspects of architectural theory and practice. The study of the spatial possibilities of architecture, involving different methods of morphological analysis and changing the previous understanding of the functionality, provides new approaches to the formation of the architectural environment of the future. Further development of computer modeling methodology, including the use of cognitive technologies, and artificial intelligence, the study of which lies at the junction of technical and natural sciences, social and humanitarian areas of knowledge, is very relevant. Approaches that integrate modern technologies allow creating new forms of virtual architecture, potentially applicable for real construction. This should contribute to the creation of a comfortable, ecologically, and aesthetically harmonious living environment.

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Section: Information Technologiesmentioning

confidence: 99%

Research on the Similarities of Morphogenesis in Architecture and Nature

Kasyanov¹

2020

Proceedings of the 2nd International Conference on Architecture: Heritage, Traditions and Innovations (AHTI 2020)

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“…The cleavage results in a pattern of cellular contacts on the surface of an embryo that is a discrete cell [10]. After third division (8 blastomeres) the field pattern of cellular contacts on the embryo surface becomes topologically inhomogeneous inevitably that means the symmetry breaking of the discrete cell field.…”

Section: Topological Singularities and Symmetry Transformations In Eamentioning

confidence: 99%

Topology in Biology: Singularities and Surgery Transformations in Metazoan Development and Evolution

Isaeva¹,

Kasyanov²,

Presnov³

2014

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The review presents a topological description and interpretation (analysis) of some events in metazoan development and evolution through the use of well-known mathematical concepts and theorems (using topological approach). It is the topological language that can provide strict and adequate description of various phenomena in developmental and evolutionary transformations. Topological singularities inevitably arising and transforming during early development destroy the preexisting pattern of symmetry. The symmetry breaking of preexisting spatial pattern plays a critical role in biological morphogenesis in development and evolution. Some events of early development are interpreted in terms of symmetry breakdown and related to well-known mathematical theorems. A topological inevitability of some developmental events through the use of classical topological concepts is discussed. The topological approach makes it possible to consider the succession of spherical surgeries, which change the topological genus of an animal body surface. We model the biological shape as a set of smooth, closed, oriented surfaces-membrane or epithelial layers. Membrane and epithelial surfaces are boundary layers, interfaces between a living structure and its environment, ensuring metabolism. Toroid forms as well as fractal structures in metazoans can be considered as functionally optimized biological design and attractors in biological morphogenesis. The epithelial surface is an interface between the internal medium of an organism and the outside environmental medium; topological and fractal transformations during metazoan evolution and development increase this interface, ensuring better adaptation of organism to the environment. Fractal structures as well as toroid forms can be considered as a functionally optimized design in Metazoa. Topological methodology reveals a certain set of topological rules constraining and directing biological morphogenesis during evolution and development. V. V. Isaeva et al.2665

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“…We also plot the square root and cube root of total aortic area and volume, respectively. Remarkably, these scalings also collapse onto lines, proving that globally all aortas are generalized cylinders with aortic area and volume scaling as A T ∼ 2πc 2 and V ∼ πc 3 , where we used the reparameterization L ∼ c . The proportionality constant c ∼ 15 can be obtained from the linear fits and independently verified by defining L as the centerline length of each segmentation and inverting the reparameterization.…”

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confidence: 95%

“…The problem of morphogensis is deeply linked to the stability of growing structures; René Thom postulated that the precise mathematical form of any morphological process is defined by topologic homeomorphisms [2,3,66]. Topology is now a fundamental tool in the classification of rapidly changing shapes and structures in developmental biology [4].…”

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confidence: 99%

The Geometric Evolution of Aortic Dissections: Predicting Surgical Success using Fluctuations in Integrated Gaussian Curvature

Khabaz

Sankary

Yuan

et al. 2022

Preprint

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Cross-sectional imaging, such as computed tomography (CTA) scans, provide unparalleled visualization of aortic anatomy. However, despite the immense geometric and anatomic detail provided by CTA imaging, surgeons continue to interact with this data in a linear and dimensionally reduced feature space. Aortic pathologies such as aneurysms and dissections are clinically quantified using a single scalar: maximum aortic diameter. To date, not feature of aortic shape has reproducibly captured what surgeons often describe qualitatively when looking at CT scans or when in the operating room observing the physical anatomy. Shape along with size plays a central role in differentiating normal from diseased aortas. We defined a geometric feature space using tools of modern differential geometry that incorporate shape and size. We show that size can be parameterized by l, the radial aortic extent commonly taken as aortic diameter. Size invariant shape is quantified by performing a Gauss map of local regions on the aortic surface and calculating the variance of the total integrated curvature (δK) across each aorta. While we do not inherently study aortic stability as it relates to clinical rupture in this paper, aortas appearing at high δK are clinically classified by size and qualitative appearance as high risk. It is therefor interesting to conjecture that divergence in the (δK,l)-space is a sign of aortic topologic instability. Projection into (δK, l)-space provides two independent variables that show a natural division of the data as it transitions from size to shape dominated behavior, an indictor of aortic fragility.

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Topological Invariance of Biological Development

Cited by 9 publications

References 49 publications

Research on the Similarities of Morphogenesis in Architecture and Nature

Research on the Similarities of Morphogenesis in Architecture and Nature

Topology in Biology: Singularities and Surgery Transformations in Metazoan Development and Evolution

The Geometric Evolution of Aortic Dissections: Predicting Surgical Success using Fluctuations in Integrated Gaussian Curvature

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