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:

Gupta, Sanju  ^[1];

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Saxena, Avadh ^[2]

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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:

2019-08-01

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