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• W3037638234 abstract "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 <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML id=M1><mml:mi>i</mml:mi></mml:math>, and the diffusion coefficient <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML id=M2><mml:mi>D</mml:mi></mml:math> (electrical coupling or gap junction <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML id=M3><mml:mi>G</mml:mi></mml:math>). The relationship between NPR and <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML id=M4><mml:mi>G</mml:mi></mml:math> has been investigated in different dimensions, respectively. That is, for each fixed <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML id=M5><mml:mi>i</mml:mi></mml:math>, there is a formula to describe the relationship between NPR and <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML id=M6><mml:mi>G</mml:mi></mml:math>; and three formulas are required for the three dimensions. However, there is not a universal expression to describe the relationship among NPR, <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML id=M7><mml:mi>G</mml:mi></mml:math>, and <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML id=M8><mml:mi>i</mml:mi></mml:math> 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, <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML id=M9><mml:mi>i</mml:mi></mml:math>, and <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML id=M10><mml:mi>G</mml:mi></mml:math>; and then, employing the cftool in MATLAB, the explicit formulas are derived for different cases. In addition, the goodness of fit (<mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML id=M11><mml:msup><mml:mrow><mml:mi>R</mml:mi></mml:mrow><mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:msup></mml:math>) 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, <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML id=M12><mml:mi>i</mml:mi></mml:math>, and the <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML id=M13><mml:mi>G</mml:mi></mml:math> (<mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML id=M14><mml:mi>D</mml:mi></mml:math>) could be described by a universal formula, where the NPR scales with the <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML id=M15><mml:mi>i</mml:mi></mml:math> (the dimension) power of the product of the square root of <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML id=M16><mml:mi>G</mml:mi></mml:math> (<mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML id=M17><mml:mi>D</mml:mi></mml:math>) and a constant <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML id=M18><mml:mi>b</mml:mi></mml:math> which is dependent on the strength of the pacing cells and so on." @default.
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• W3037638234 date "2020-06-26" @default.
• W3037638234 modified "2023-10-14" @default.
• W3037638234 title "The Quantitative Relationship among the Number of the Pacing Cells Required, the Dimension, and the Diffusion Coefficient" @default.
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• W3037638234 doi "https://doi.org/10.1155/2020/3608015" @default.
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