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Title: Curvature distribution and autocorrelations in elliptic cylinders and cones

Abstract

Not all micro-vessels (MV) are traditionally circular and there are examples of elliptic cylindrical MVs in life sciences, particularly if projected with a slant. Similarly, certain biological structures, ferroelectric liquid crystals, aluminum oxide clusters and witherite crystallites’ crosssection appear to be elliptical cones. We studied the mean curvature (H) distribution of these elliptic morphological structures with geometric parameter such as eccentricity; e (ratio of semi-minor to semi-major axes) and a measure of how much diagonal section deviates from circularity and height (h) in case of cones. By means of topographical cues, we defined the curvature-curvature autocorrelation function (gk) and applied this notion to mean curvature (H) of circular and elliptical cylinders and cones. The Fourier transform of correlation function, i.e. “curvature factor” is analogous to “structure factor (or Patterson function)” in X-ray and neutron scattering intensity. It elucidates critically important information related to surface curvature fluctuation relevant to shape (geometry), network and phase transformation. The latter is induced by cells under mechanical stress, occurring in many soft systems (polymeric liquid crystals, foams, bubbles) and biological tissues, particularly cell walls of primary and branched vessels bed in microvasculature that distributes blood within tissue during hypertension and migraines. This perspective is usefulmore » in a sustained release of angiogenic/vasculogenic factors and relevant for precision medicine and engineered microvessels and tissues in vitro and in vivo extended cellular processes. The quantitative analysis carried out in this work facilitates our understanding of the mechanical mechanisms associated with thrombosis during surgery that typically occur in bent or stretched MVs due to microenvironment such as localized shear stresses and biochemical factors.« less

Authors:
ORCiD logo [1];  [2]
+ Show Author Affiliations
  1. Western Kentucky Univ., Bowling Green, KY (United States). Dept. of Physics & Astronomy,
  2. Los Alamos National Lab. (LANL), Los Alamos, NM (United States). Theoretical Division and Center for Nonlinear Studies
Publication Date:
Research Org.:
Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
Sponsoring Org.:
USDOE Laboratory Directed Research and Development (LDRD) Program
OSTI Identifier:
1566114
Report Number(s):
LA-UR-19-23839
Journal ID: ISSN 2158-3226
Grant/Contract Number:  
89233218CNA000001
Resource Type:
Accepted Manuscript
Journal Name:
AIP Advances
Additional Journal Information:
Journal Volume: 9; Journal Issue: 8; Journal ID: ISSN 2158-3226
Publisher:
American Institute of Physics (AIP)
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; Material Science

Citation Formats

Gupta, Sanju, and Saxena, Avadh. Curvature distribution and autocorrelations in elliptic cylinders and cones. United States: N. p., 2019. Web. doi:10.1063/1.5106380.
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Gupta, Sanju, & Saxena, Avadh. Curvature distribution and autocorrelations in elliptic cylinders and cones. United States. https://doi.org/10.1063/1.5106380
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Gupta, Sanju, and Saxena, Avadh. Thu . "Curvature distribution and autocorrelations in elliptic cylinders and cones". United States. https://doi.org/10.1063/1.5106380. https://www.osti.gov/servlets/purl/1566114.
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@article{osti_1566114,
title = {Curvature distribution and autocorrelations in elliptic cylinders and cones},
author = {Gupta, Sanju and Saxena, Avadh},
abstractNote = {Not all micro-vessels (MV) are traditionally circular and there are examples of elliptic cylindrical MVs in life sciences, particularly if projected with a slant. Similarly, certain biological structures, ferroelectric liquid crystals, aluminum oxide clusters and witherite crystallites’ crosssection appear to be elliptical cones. We studied the mean curvature (H) distribution of these elliptic morphological structures with geometric parameter such as eccentricity; e (ratio of semi-minor to semi-major axes) and a measure of how much diagonal section deviates from circularity and height (h) in case of cones. By means of topographical cues, we defined the curvature-curvature autocorrelation function (gk) and applied this notion to mean curvature (H) of circular and elliptical cylinders and cones. The Fourier transform of correlation function, i.e. “curvature factor” is analogous to “structure factor (or Patterson function)” in X-ray and neutron scattering intensity. It elucidates critically important information related to surface curvature fluctuation relevant to shape (geometry), network and phase transformation. The latter is induced by cells under mechanical stress, occurring in many soft systems (polymeric liquid crystals, foams, bubbles) and biological tissues, particularly cell walls of primary and branched vessels bed in microvasculature that distributes blood within tissue during hypertension and migraines. This perspective is useful in a sustained release of angiogenic/vasculogenic factors and relevant for precision medicine and engineered microvessels and tissues in vitro and in vivo extended cellular processes. The quantitative analysis carried out in this work facilitates our understanding of the mechanical mechanisms associated with thrombosis during surgery that typically occur in bent or stretched MVs due to microenvironment such as localized shear stresses and biochemical factors.},
doi = {10.1063/1.5106380},
journal = {AIP Advances},
number = 8,
volume = 9,
place = {United States},
year = {2019},
month = {8}
}
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Journal Article:
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https://doi.org/10.1063/1.5106380
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Figures / Tables:

FIG. 1 FIG. 1: (A) Human vascular system showing blood flow in blood vessels with elliptical cross-sectional overlay with semi-major (a) and semi-minor axes (b). (B) Optical micrographs of silica-witherite aggregates, viewed between crossed polarizers (with a sensitive tint plate in place). The continuous color changes within the aggregate are evidence ofmore » preferred orientations of optically anisotropic material within the aggregates (witherite crystallites). Trumpet-bell shaped sheet (600 μm field of view). (C) Interstitial mineralization reflecting mineralized redundant basement membrane (arrow) (scale bar=15 μm; Ref. 52). (D) Shown is an elliptical cone with height h and other parameters.« less
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