ISSN: 2375-3846
American Journal of Science and Technology  
Manuscript Information
 
 
A Research Proposal in Mathematical Modeling Applied to Heart and Mathematical Concepts of Mechanisms of Heart
American Journal of Science and Technology
Vol.1 , No. 1, Publication Date: Jul. 7, 2014, Page: 30-35
1761 Views Since July 7, 2014, 2214 Downloads Since Apr. 14, 2015
 
 
Authors
 
[1]    

Mersedeh Karvandi , Taleghani Hospital, ShahidBeheshti University of Medical Sciences, Tehran, Iran.

[2]    

Saeed Ranjbar , Taleghani Hospital, ShahidBeheshti University of Medical Sciences, Tehran, Iran.

[3]    

Mehrdad Shahshahani , School of Mathematics, Statistics and Computer Sciences of Sharif University of technology, Tehran Iran.

[4]    

Arash Rastegar , School of Mathematics, Statistics and Computer Sciences of Sharif University of technology, Tehran Iran.

[5]    

Seyed Ahmad Hassantash , Modarres Hospital, Institute of Cardiovascular Research, ShahidBeheshti University of Medical Science, Tehran, Iran.

[6]    

Mahnoosh Foroughi , Modarres Hospital, Institute of Cardiovascular Research, ShahidBeheshti University of Medical Science, Tehran, Iran.

[7]    

Fariba Ranjbar , School of Mathematics, Statistics and Computer Sciences of University of Tehran, Tehran, Iran.

 
Abstract
 

As stated by Jacques Hadmard in 'science and hypothesis', mathematical creation and mathematical intelligence are not without connection with creation in general and with general intelligence. A great proportion of prominent mathematicians have been creators in other fields. One of the greatest, Gauss, carried out important and classical experiments on magnetism; and Newton's fundamental discoveries in optics are well known. And Leibniz influenced by their mathematical abilities on philosophical ones. The research proposals we propose here, are motivated by our background and previous research, and are supposed to indicate my general directions in forthcoming research. Following Poincare, each research subject is formed by an attempt to link two fields in sciences, in order to contribute to at least one of the two. In this proposal, always the mathematical part is the part which takes the benefit. We will try to explain an abstract for each problem and give motivations for importance of the corresponding research direction together with a prediction of expected progress. We hope that the expository style of this proposal does not hurt the scientific value of its predictions. This proposal is addressed to experts in mathematical modeling applied to medicine.


Keywords
 

Mathematical Modeling, Mathematics of Heart, Left Ventricular Modeling of Heart, Direction of Blood Flow Path Inside the Left Ventricle of Heart, Cardiac Digital Image Processing Mathematically Based Software, Virtual Heart


Reference
 
[01]    

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.

[02]    

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.

[03]    

Le Grice 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.

[04]    

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.

[05]    

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.

[06]    

Truesdell C.A. A critical summary of developments in nonlinear elasticity. Journal of rational mechanics, 1952; 1:125-300.

[07]    

Truesdell C.A. A critical summary of developments in nonlinear elasticity. Journal of rational mechanics, 1953; 2: 593-616.

[08]    

Heimdal A. 4D Strain: Advanced research application for quantitative echocardiography. GE Healthcare. 2011.

[09]    

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.

[10]    

Badano LP, Lang RM, Zamorano JL Textbook of Real-Time Three-Dimensional Echocardiography. Springer-Verlag London Ltd, London, 2011

[11]    

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.

[12]    

Ranjbar S. Karvandi M. Ajzachi M. System and method modeling left ventricle of heart. US Patent 2013; patent number 8,414,490.

[13]    

Geu-Ru Hong G. R., Pedrizzetti G., Giovanni Tonti G et al. Characterization and quantification of Vortex Flow in the Human Left Ventricle by contrast echocardiography using vector particle Image velocimetry.JACC: Cardiovascular imaging. 2008; 1: 705-717.

[14]    

A, Houle H., Pedrizzetti G., Tonti G et al. Echocardiographic Particle Image Velocimetry: A novel technique for quantification of left ventricular blood vorticity pattern. J Am SocEchocardiogr. 2010; 23: 86- 94.

[15]    

Belohlavek M. Vortex formation time: an emerging echocardiographic index of left ventricular filling efficiency? European Heart Journal – Cardiovascular Imaging.2012 13: 367–369.

[16]    

Hendabadi S. Bermejo J. Benito Y et al. Topology of Blood Transport in the Human Left Ventricle by Novel Processing of Doppler Echocardiography. Journal of Annals of Biomedical Engineering.2013; 10: 39-53.

[17]    

Ranjbar S., Karvandi M., Hassantash S. A. A Novel Mathematical Fluid Dynamic of Left Ventricular Dilated Cardiomyopathy.Poster presentation at AmericanEcho. 2012; Abstract: P2-89.

[18]    

Re′kaFaludi R. K., SzulikM,hooge Jan D et al. Left ventricular flow patterns in healthy subjects and patients with prosthetic mitral valves: An in vivo study using echocardiographic particle image velocimetry. The Journal of Thoracic and Cardiovascular Surgery.2009 139: 1501-1510.

[19]    

Van Rijk-Zwikker GL., DelemarreBJ., Huysmans HA. The orientation of the bileafletCarboMedics valve in the mitral position determines left ventricular spatial flow patterns. Eur J Cardiothorac Surg. 1996;10: 13-20.

[20]    

Kheradvar A., Gharib M. Influence of ventricular pressure drop on mitral annulus dynamics through the process of vortex ring formation. Ann Biomed Eng. 2007; 35: 50-64.

[21]    

Karvandi M., Ranjbar S., Hassantash S. A. Achievability of the Assessment of the Mitral Valve Leaflets by Mathematical Equations of Inelasticity Based EchocardiographyPoster presentation at Americanecho. 2012; Abstract: P2-92.





 
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