Curvature distribution and autocorrelations in elliptic cylinders and cones
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’ cross-sectio...
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| Format: | Article |
| Language: | English |
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AIP Publishing LLC
2019-08-01
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| Series: | AIP Advances |
| Online Access: | http://dx.doi.org/10.1063/1.5106380 |
| _version_ | 1818928715025874944 |
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| author | Sanju Gupta Avadh Saxena |
| author_facet | Sanju Gupta Avadh Saxena |
| author_sort | Sanju Gupta |
| collection | DOAJ |
| description | 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’ cross-section 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. |
| first_indexed | 2024-12-20T03:33:18Z |
| format | Article |
| id | doaj.art-18f4fed402ec41c5a4a64e92f99dedee |
| institution | Directory Open Access Journal |
| issn | 2158-3226 |
| language | English |
| last_indexed | 2024-12-20T03:33:18Z |
| publishDate | 2019-08-01 |
| publisher | AIP Publishing LLC |
| record_format | Article |
| series | AIP Advances |
| spelling | doaj.art-18f4fed402ec41c5a4a64e92f99dedee2022-12-21T19:54:56ZengAIP Publishing LLCAIP Advances2158-32262019-08-0198085304085304-810.1063/1.5106380020908ADVCurvature distribution and autocorrelations in elliptic cylinders and conesSanju Gupta0Avadh Saxena1Department of Physics & Astronomy, Western Kentucky University, Bowling Green, Kentucky 42101, USATheoretical Division and Center for Nonlinear Studies, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USANot 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’ cross-section 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.http://dx.doi.org/10.1063/1.5106380 |
| spellingShingle | Sanju Gupta Avadh Saxena Curvature distribution and autocorrelations in elliptic cylinders and cones AIP Advances |
| title | Curvature distribution and autocorrelations in elliptic cylinders and cones |
| title_full | Curvature distribution and autocorrelations in elliptic cylinders and cones |
| title_fullStr | Curvature distribution and autocorrelations in elliptic cylinders and cones |
| title_full_unstemmed | Curvature distribution and autocorrelations in elliptic cylinders and cones |
| title_short | Curvature distribution and autocorrelations in elliptic cylinders and cones |
| title_sort | curvature distribution and autocorrelations in elliptic cylinders and cones |
| url | http://dx.doi.org/10.1063/1.5106380 |
| work_keys_str_mv | AT sanjugupta curvaturedistributionandautocorrelationsinellipticcylindersandcones AT avadhsaxena curvaturedistributionandautocorrelationsinellipticcylindersandcones |