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The Quantitative Relationship among the Number of the Pacing Cells Required, the Dimension, and the Diffusion Coefficient
The purpose of the paper is to derive a formula to describe the quantitative relationship among the number of the pacing cells required (NPR), the dimension i, and the diffusion coefficient D (electrical coupling or gap junction G). The relationship between NPR and G has been investigated in differe...
Autores principales: | , , |
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Formato: | Online Artículo Texto |
Lenguaje: | English |
Publicado: |
Hindawi
2020
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Materias: | |
Acceso en línea: | https://www.ncbi.nlm.nih.gov/pmc/articles/PMC7335384/ https://www.ncbi.nlm.nih.gov/pubmed/32685474 http://dx.doi.org/10.1155/2020/3608015 |
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author | Zhang, Yue Yin, Guisheng Wang, Kuanquan |
author_facet | Zhang, Yue Yin, Guisheng Wang, Kuanquan |
author_sort | Zhang, Yue |
collection | PubMed |
description | The purpose of the paper is to derive a formula to describe the quantitative relationship among the number of the pacing cells required (NPR), the dimension i, and the diffusion coefficient D (electrical coupling or gap junction G). The relationship between NPR and G has been investigated in different dimensions, respectively. That is, for each fixed i, there is a formula to describe the relationship between NPR and G; and three formulas are required for the three dimensions. However, there is not a universal expression to describe the relationship among NPR, G, and i together. In the manuscript, surveying and investigating the basic law among the existed data, we speculate the preliminary formula of the relationship among the NPR, i, and G; and then, employing the cftool in MATLAB, the explicit formulas are derived for different cases. In addition, the goodness of fit (R(2)) is computed to evaluate the fitting of the formulas. Moreover, the 1D and 2D ventricular tissue models containing biological pacemakers are developed to derive more data to validate the formula. The results suggest that the relationship among the NPR, i, and the G (D) could be described by a universal formula, where the NPR scales with the i (the dimension) power of the product of the square root of G (D) and a constant b which is dependent on the strength of the pacing cells and so on. |
format | Online Article Text |
id | pubmed-7335384 |
institution | National Center for Biotechnology Information |
language | English |
publishDate | 2020 |
publisher | Hindawi |
record_format | MEDLINE/PubMed |
spelling | pubmed-73353842020-07-17 The Quantitative Relationship among the Number of the Pacing Cells Required, the Dimension, and the Diffusion Coefficient Zhang, Yue Yin, Guisheng Wang, Kuanquan Biomed Res Int Research Article The purpose of the paper is to derive a formula to describe the quantitative relationship among the number of the pacing cells required (NPR), the dimension i, and the diffusion coefficient D (electrical coupling or gap junction G). The relationship between NPR and G has been investigated in different dimensions, respectively. That is, for each fixed i, there is a formula to describe the relationship between NPR and G; and three formulas are required for the three dimensions. However, there is not a universal expression to describe the relationship among NPR, G, and i together. In the manuscript, surveying and investigating the basic law among the existed data, we speculate the preliminary formula of the relationship among the NPR, i, and G; and then, employing the cftool in MATLAB, the explicit formulas are derived for different cases. In addition, the goodness of fit (R(2)) is computed to evaluate the fitting of the formulas. Moreover, the 1D and 2D ventricular tissue models containing biological pacemakers are developed to derive more data to validate the formula. The results suggest that the relationship among the NPR, i, and the G (D) could be described by a universal formula, where the NPR scales with the i (the dimension) power of the product of the square root of G (D) and a constant b which is dependent on the strength of the pacing cells and so on. Hindawi 2020-06-25 /pmc/articles/PMC7335384/ /pubmed/32685474 http://dx.doi.org/10.1155/2020/3608015 Text en Copyright © 2020 Yue Zhang et al. http://creativecommons.org/licenses/by/4.0/ This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. |
spellingShingle | Research Article Zhang, Yue Yin, Guisheng Wang, Kuanquan The Quantitative Relationship among the Number of the Pacing Cells Required, the Dimension, and the Diffusion Coefficient |
title | The Quantitative Relationship among the Number of the Pacing Cells Required, the Dimension, and the Diffusion Coefficient |
title_full | The Quantitative Relationship among the Number of the Pacing Cells Required, the Dimension, and the Diffusion Coefficient |
title_fullStr | The Quantitative Relationship among the Number of the Pacing Cells Required, the Dimension, and the Diffusion Coefficient |
title_full_unstemmed | The Quantitative Relationship among the Number of the Pacing Cells Required, the Dimension, and the Diffusion Coefficient |
title_short | The Quantitative Relationship among the Number of the Pacing Cells Required, the Dimension, and the Diffusion Coefficient |
title_sort | quantitative relationship among the number of the pacing cells required, the dimension, and the diffusion coefficient |
topic | Research Article |
url | https://www.ncbi.nlm.nih.gov/pmc/articles/PMC7335384/ https://www.ncbi.nlm.nih.gov/pubmed/32685474 http://dx.doi.org/10.1155/2020/3608015 |
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