Geodesic
Construction of a mechanical model of the human heart left ventricle in the process of its contraction
Vestnik Sankt-Peterburgskogo universiteta. Prikladnaâ matematika, informatika, processy upravleniâ, Tome 18 (2022) no. 3, pp. 402-409 Cet article a éte moissonné depuis la source Math-Net.Ru

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A detailed analysis of previous works on modeling the left ventricle (LV) of the human heart, starting with mechanical models in the form of the simplest three-dimensional figures (cylinder, sphere, ellipsoid of rotation) and ending with models using real contours of the human heart obtained by ultrasound examination of the human heart. A way of constructing a mechanical LV model based on the processing of its dynamic images obtained using computer and magnetic resonance imaging was proposed. Digitization of these images was carried out using numerical methods developed to create a finite element model were implemented in the CMISS system, which allows the use of finite element analysis methods to solve various complex problems. To avoid the need to operate with huge arrays of numbers (up to 10 thousand numerical values at each time of the MRI study) characteristic points of the three-dimensional LV image were selected and spline interpolation of the model framework written in C++ using the Cmgui module was performed. To describe the work of the mechanical model of LV reduction, the main components of this process were identified: transverse compression, longitudinal contraction and twisting. To describe them, simple mathematical characteristics were used.
Keywords: human heart, left ventricle, mechanical model, longitudinal contraction, twisting.
Mots-clés : transverse compression 
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V. P. Tregubov; N. K. Egorova. Construction of a mechanical model of the human heart left ventricle in the process of its contraction. Vestnik Sankt-Peterburgskogo universiteta. Prikladnaâ matematika, informatika, processy upravleniâ, Tome 18 (2022) no. 3, pp. 402-409. http://geodesic.mathdoc.fr/item/VSPUI_2022_18_3_a8/

[1] Hu Zh., Metaxas D., Axel L., “Functional imaging and modeling of the heart”, Intern. Workshop on Functional Imaging and Modeling of the Heart. FIMH 2005, 369–383

[2] Sallin E., “Fiber orientation and ejection fraction in the human LV”, Biophysical Journal, 9 (1969), 954–964 | DOI

[3] Hu Zh., “In vivo strain and stress estimation of the heart left and right ventricles from MRI images”, Medical Image Analysis, 7 (2003), 435–444 | DOI | Zbl

[4] Chadwick R. S., “Mechanics of the left ventricle”, Journal of Biophysics, 39 (1982), 279–288 | DOI | MR

[5] Shoucri R. M., “The pressure-volume relation and the mechanics of left ventricular contraction”, Japanese Heart Journal, 31 (1990), 713–729 | DOI

[6] Shoucri R. M., “Theoretical study of pressure-volume relation in left ventricle”, American Journal of Physiology, 260 (1991), H282–H291

[7] Shoucri R. M., “Active and passive stresses in the myocardium”, American Journal of Physiology, 279 (2000), H2519–H2528

[8] Shoucri R. M., “The calculation of the intramyocardial stress”, Technology and Health Care, 10 (2002), 11–22 | DOI

[9] Shoucri R. M., “Equivalence of two approaches to study the stress-strain relation in the myocardium”, WIT Transactions on Biomedicine and Health. Modelling in Medicine and Biology, 13 (2009), 3–16 | DOI

[10] Le Rolle V., Carrault G., Richard P.-Y., Pibarot Ph., Durand L.-G., Hernández A. I., “A tissue-level electromechanical model of the left ventricle: Application to the analysis of intraventricular pressure”, Acta Biotheoretica, 57:4 (2009), 457–478 | DOI

[11] Mirsky I., McGill P. L., Janz R. F., “Mechanical behavior of ventricular aneurisms”, Bulletin of Mathematical Biology, 40:4 (1978), 451–464 | DOI

[12] Campbell K. B., Simpson A. M., Campbell S. G., Granzier H. L., Slinker B. K., “Dynamic left ventricular elastance: a model for integrating cardiac muscle contraction into ventricular pressure-volume relationships”, Journal of Applied Physiology, 104 (2008), 958–975 | DOI

[13] Kerckhoffs R. C. P., Faris O. P., Bovendeerd P. H. M., Prinzen F. W., Smits K., McVeigh E. R., Arts T., “Electromechanics of paced left ventricle simulated by straightforward mathematical model: comparison with experiments”, American Journal of Physiology. Heart and Circulatory Physiology, 289:5 (2005), H1889–H1897 | DOI

[14] Radichkina A., Tregubov V., “Mathematical simulation of the left ventricle during the systole contraction”, Biomechanics, Intern. Conference of the Polish Society of Biomechanics, Book of abstracts (Warsaw, 2010), 2010, 185–186

[15] Tregubov V. P., Radichkina A. O., “Mathematical modeling of the kinematics of the left ventricle of the human heart in the process of its contraction”, Vestnik of Saint Petersburg University. Series 10. Applied Mathematics. Computer Science. Control Processes, 2013, no. 4, 67–73 (In Russian)