Brief Communication: Mathematical Concepts of Mechanisms of Left Ventricular Myocardium

Mersedeh Karvandi; Saeed Ranjbar; Seyed Ahmad Hassantash; Mahnoosh Foroughi

doi:doi:10.11648/j.ijmi.20140202.13

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Brief Communication: Mathematical Concepts of Mechanisms of Left Ventricular Myocardium

Mersedeh Karvandi, Saeed Ranjbar, Seyed Ahmad Hassantash, Mahnoosh Foroughi

Published in International Journal of Medical Imaging (Volume 2, Issue 2)

Received: 21 February 2014 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.

Published in	International Journal of Medical Imaging (Volume 2, Issue 2)
DOI	10.11648/j.ijmi.20140202.13
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), 2014. Published by Science Publishing Group

Keywords

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

References

[1]	Notomi Y, Lysyansky P, Setser RM, Shiota T, Popovic ZB, Martin-Miklovic MG, Joan A.W, Stephanie J.O, Neil L.G, Richard D. W, James D.T. Measurement of ventricular torsion by two-dimensional ultrasound speckle tracking imaging. J Am CollCardiol 2005; 45:34–41.
[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.
[6]	Urheim S, Edvardsen T, Torp H, Angelsen B, Smiseth OA. Myocardial strain by Doppler echocardiography.Validation of a new method to quantify regional myocardial function. Circulation 2000; 102:58–64.
[7]	Leitman M, Lysyansky P, Sidenko S, Shir V, Peleg E, Binenbaum M. Two dimensional strain—a novel software for real-time quantitative echocardiographic assessment of myocardial function. J Am SocEchocardiogr 2004; 17: 1–9.
[8]	Pirat B, Khoury DS, Hartley CJ, Tiller L, Rao L, Schulz DG. A novel featuretracking echocardiographic method for the quantitation of regional myocardial function: validation in an animal model of ische- mia-reperfusion. J Am CollCardiol 2008; 51:1–9.
[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.
[10]	Helle-Valle T, Crosby J, Edvardsen T, Lyseggen E, Amundsen BH, Smith HJ. New noninvasive method for assessment of left ventricular rotation: speckle tracking echocardiography. Circulation 2005; 112:49–56.
[11]	Opdahl A, Helle-Valle T, Remme EW, Vartdal T, Pettersen E, Lunde K. Apical rotation by speckle tracking echocardiography: a simplified bedside index of left ventricular twist. J Am SocEchocardiogr 2008; 21:1–8.
[12]	Kim DH, Kim HK, Kim MK, Chang SA, Kim YJ, Kim MA. Velocity vector imaging in the measurement of left ventricular twist mechanics: head-to-head one way comparison between speckle tracking echocardiography and velocity vector imaging. J Am SocEchocardiogr 2009; 22: 44 52.
[13]	Kim HK, Sohn DW, Lee SE, Choi SY, Park JS, Kim YJ. Assessment of left ventricular rotation and torsion with two-dimensional speckle tracking echocardiography. J Am SocEchocardiogr 2007; 20:45–53.
[14]	Zhou Z, Ashraf M, Hu D, Dai X, Xu Y, Kenny B. Three-dimensional speckle tracking imaging for left ventricular rotation measurement. An in vitro validation study. J Ultrasound Med 2010; 29:3–9.
[15]	LeGrice IJ, Takayama Y, Covell JW. Transverse shear along myocardial cleavage planes provides a mechanism for normal systolic wall thickening. Circ Res 1995; 77: 182–193.
[16]	Seo Y, Ishizu T, Enomoto Y, Sugimori H, Yamamoto M, Machino T. Validation of 3-dimensional speckle tracking imaging to quantify regional myocardial deformation. CircCardiovasc Imaging 2009; 2:1–9.
[17]	Moore CC, Lugo-Olivieri CH, McVeigh ER, Zerhouni EA. Three dimensional systolic strain patterns in the normal human left ventricle: characterization with tagged MR imaging. Radiology 2000; 214: 453–466.
[18]	Truesdell C.A. A critical summary of developments in nonlinear elasticity. Journal of rational mechanics, 1952; 1:125-300.
[19]	Truesdell C.A. A critical summary of developments in nonlinear elasticity. Journal of rational mechanics, 1953; 2: 593-616.
[20]	Heimdal A. 4D Strain: Advanced research application for quantitative echocardiography. GE Healthcare. 2011.
[21]	D’hooge, J., Heimdal, A., Jamal, F., Kukulski, T., Bijnens, B., Rademakers, F., Hatle, L., Suetens, P., Sutherland, G.R. "Regional strain and strain rate measurements by cardiac ultrasound: principles, implementation and limitations." Eur J Echocardiogr 2000; 1:70-154.
[22]	Grapsa J. Efthimiadis I. Pakrashi T. Dawson D. Punjabi P.P. hoyannopoulos P. N. Improvement of left ventricular longitudinal strain following surgical revascularization of ischemic cardiomyopathy and left ventricular ejection fraction < 30%: a 3D and speckle tracking study. Poster presentation at Euroecho 2012. Abstract: P449
[23]	Badano LP, Lang RM, Zamorano JL Textbook of Real-Time Three-Dimensional Echocardiography. Springer-Verlag London Ltd, London, 2011
[24]	Le Grice I, Hunter P, Young A, Small B. The architecture of the heart: a data-based model. Philos Trans R SocLond A Math PhysSci 2001; 35: 1217–1232.
[25]	Ranjbar S. Karvandi M. Ajzachi M. System and method modeling left ventricle of heart. US Patent 2013; patent number 8,414,490.

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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://article.sciencepublishinggroup.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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Author Information

Mersedeh Karvandi

Taleghani Hospital, Shahid Beheshti University of Medical Sciences, Tehran, Iran
Saeed Ranjbar

Modarres Hospital, Institute of Cardiovascular Research, Shahid Beheshti University of Medical Sciences, Tehran, Iran
Seyed Ahmad Hassantash

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

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://article.sciencepublishinggroup.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}
}

Copy | Download

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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