International Journal of Medical Imaging

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Brief Communication: Mathematical Concepts of Mechanisms of Left Ventricular Myocardium

Received: 21 February 2014    Accepted:     Published: 20 March 2014
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Abstract

Background: How can mathematics help us to understand the mechanism of the cardiac motion? The best known approach is to take a mathematical model of the fibered structure, insert it into a more-or-less complex model of cardiac architecture, and then study the resulting fibers of activation that propagate through the myocardium. In our paper, we have attempted to create a novel software capable of demonstrate left ventricular (LV) model in normal hearts. Method: Echocardiography was performed on 70 healthy volunteers. Data evaluated included: velocity (radial, longitudinal, rotational and vector point), displacement (longitudinal and rotational), strain rate (longitudinal and circumferential) and strain (radial, longitudinal and circumferential) of all 16 LV myocardial segments. Using these data, force vectors of myocardial samples were estimated by MATLAB software, interfaced in the echocardiograph system. Dynamic orientation contraction (through the cardiac cycle) of every individual myocardial fiber could be created by adding together the sequential steps of the multiple fragmented sectors of that fiber. This way we attempted to mechanically illustrate the global LV model. Result: Our study shows that in normal cases myocardial fibers initiate from the posteriorbasal region of the heart, continues through the LV free wall, reaches the septum, loops around the apex, ascends, and ends at the superior-anterior edge of LV.Conclusion: We were able to define the whole LV myocardial model mathematically, by MATLAB software in normal subjects. This will enable physicians to diagnose and follow up many cardiac diseases when this software is interfaced within echocardiographic machines.

DOI 10.11648/j.ijmi.20140202.13
Published in International Journal of Medical Imaging (Volume 2, Issue 2, March 2014)
Page(s) 19-23
Creative Commons

This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.

Copyright

Copyright © The Author(s), 2024. Published by Science Publishing Group

Keywords

Echocardiography, Mathematical Modeling, 2D and 3D Speckle Tracking Method, MATLAB Software, Left Ventricular Myocardium, Force Vector Field

References
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[2] Abe Y, Kawagishi T, Ohuchi H, Takeguchi T, Nishiura M. Accurate detection of regional contraction using novel 3-dimensional speckle tracking technique. J Am CollCardiol2008; 51:A116.
[3] de Isla LP, Balcones DV, Fernandez-Golfın C, Marcos-Alberca P, Almerıa C, Rodrigo JL,MacayaC,ZamoranoJ.Three dimensional-wall motion tracking: a new and faster tool for myocardial strain assessment: Comparison with two-dimensional-wall motion tracking. J Am SocEchocardiogr 2009; 22:25–30.
[4] Saito K, Okura H, Watanabe N, Hayashida A, Obase K, Imai K. Comprehensive evaluation of left ventricular strain using speckle tracking echocardiography in normal adults: Comparison of three-dimensional and two-dimensional approaches. J Am SocEchocardiogr 2009; 22:25–30.
[5] D’Hooge J, Heimdal A, Jamal F. Regional strain and strain rate measurements by cardiac ultrasound: principles, implementation and limitations. Eur J Echocardiogr 2000; 1:54 –70.
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[9] Mor-Avi V. Lang R. M. Badano L. P. BelohlavekM.Cardim N. M. Derumeaux G. Current and Evolving Echocardiographic Techniques for the Quantitative Evaluation of Cardiac Mechanics: ASE/EAE Consensus Statement on Methodology and Indications Endorsed by the Japanese Society of Echocardiography. European Journal of Echocardiography 2011; 12, 167–205.
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Author Information
  • Taleghani Hospital, Shahid Beheshti University of Medical Sciences, Tehran, Iran

  • Modarres Hospital, Institute of Cardiovascular Research, Shahid Beheshti University of Medical Sciences, Tehran, Iran

  • Modarres Hospital, Institute of Cardiovascular Research, Shahid Beheshti University of Medical Sciences, Tehran, Iran

  • Modarres Hospital, Institute of Cardiovascular Research, Shahid Beheshti University of Medical Sciences, Tehran, Iran

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  • APA Style

    Mersedeh Karvandi, Saeed Ranjbar, Seyed Ahmad Hassantash, Mahnoosh Foroughi. (2014). Brief Communication: Mathematical Concepts of Mechanisms of Left Ventricular Myocardium. International Journal of Medical Imaging, 2(2), 19-23. https://doi.org/10.11648/j.ijmi.20140202.13

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    ACS Style

    Mersedeh Karvandi; Saeed Ranjbar; Seyed Ahmad Hassantash; Mahnoosh Foroughi. Brief Communication: Mathematical Concepts of Mechanisms of Left Ventricular Myocardium. Int. J. Med. Imaging 2014, 2(2), 19-23. doi: 10.11648/j.ijmi.20140202.13

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    AMA Style

    Mersedeh Karvandi, Saeed Ranjbar, Seyed Ahmad Hassantash, Mahnoosh Foroughi. Brief Communication: Mathematical Concepts of Mechanisms of Left Ventricular Myocardium. Int J Med Imaging. 2014;2(2):19-23. doi: 10.11648/j.ijmi.20140202.13

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  • @article{10.11648/j.ijmi.20140202.13,
      author = {Mersedeh Karvandi and Saeed Ranjbar and Seyed Ahmad Hassantash and Mahnoosh Foroughi},
      title = {Brief Communication: Mathematical Concepts of Mechanisms of Left Ventricular Myocardium},
      journal = {International Journal of Medical Imaging},
      volume = {2},
      number = {2},
      pages = {19-23},
      doi = {10.11648/j.ijmi.20140202.13},
      url = {https://doi.org/10.11648/j.ijmi.20140202.13},
      eprint = {https://download.sciencepg.com/pdf/10.11648.j.ijmi.20140202.13},
      abstract = {Background: How can mathematics help us to understand the mechanism of the cardiac motion? The best known approach is to take a mathematical model of the fibered structure, insert it into a more-or-less complex model of cardiac architecture, and then study the resulting fibers of activation that propagate through the myocardium. In our paper, we have attempted to create a novel software capable of demonstrate left ventricular (LV) model in normal hearts. Method: Echocardiography was performed on 70 healthy volunteers. Data evaluated included: velocity (radial, longitudinal, rotational and vector point), displacement (longitudinal and rotational), strain rate (longitudinal and circumferential) and strain (radial, longitudinal and circumferential) of all 16 LV myocardial segments. Using these data, force vectors of myocardial samples were estimated by MATLAB software, interfaced in the echocardiograph system. Dynamic orientation contraction (through the cardiac cycle) of every individual myocardial fiber could be created by adding together the sequential steps of the multiple fragmented sectors of that fiber. This way we attempted to mechanically illustrate the global LV model. Result: Our study shows that in normal cases myocardial fibers initiate from the posteriorbasal region of the heart, continues through the LV free wall, reaches the septum, loops around the apex, ascends, and ends at the superior-anterior edge of LV.Conclusion: We were able to define the whole LV myocardial model mathematically, by MATLAB software in normal subjects. This will enable physicians to diagnose and follow up many cardiac diseases when this software is interfaced within echocardiographic machines.},
     year = {2014}
    }
    

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  • TY  - JOUR
    T1  - Brief Communication: Mathematical Concepts of Mechanisms of Left Ventricular Myocardium
    AU  - Mersedeh Karvandi
    AU  - Saeed Ranjbar
    AU  - Seyed Ahmad Hassantash
    AU  - Mahnoosh Foroughi
    Y1  - 2014/03/20
    PY  - 2014
    N1  - https://doi.org/10.11648/j.ijmi.20140202.13
    DO  - 10.11648/j.ijmi.20140202.13
    T2  - International Journal of Medical Imaging
    JF  - International Journal of Medical Imaging
    JO  - International Journal of Medical Imaging
    SP  - 19
    EP  - 23
    PB  - Science Publishing Group
    SN  - 2330-832X
    UR  - https://doi.org/10.11648/j.ijmi.20140202.13
    AB  - Background: How can mathematics help us to understand the mechanism of the cardiac motion? The best known approach is to take a mathematical model of the fibered structure, insert it into a more-or-less complex model of cardiac architecture, and then study the resulting fibers of activation that propagate through the myocardium. In our paper, we have attempted to create a novel software capable of demonstrate left ventricular (LV) model in normal hearts. Method: Echocardiography was performed on 70 healthy volunteers. Data evaluated included: velocity (radial, longitudinal, rotational and vector point), displacement (longitudinal and rotational), strain rate (longitudinal and circumferential) and strain (radial, longitudinal and circumferential) of all 16 LV myocardial segments. Using these data, force vectors of myocardial samples were estimated by MATLAB software, interfaced in the echocardiograph system. Dynamic orientation contraction (through the cardiac cycle) of every individual myocardial fiber could be created by adding together the sequential steps of the multiple fragmented sectors of that fiber. This way we attempted to mechanically illustrate the global LV model. Result: Our study shows that in normal cases myocardial fibers initiate from the posteriorbasal region of the heart, continues through the LV free wall, reaches the septum, loops around the apex, ascends, and ends at the superior-anterior edge of LV.Conclusion: We were able to define the whole LV myocardial model mathematically, by MATLAB software in normal subjects. This will enable physicians to diagnose and follow up many cardiac diseases when this software is interfaced within echocardiographic machines.
    VL  - 2
    IS  - 2
    ER  - 

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