Geodesic
Mathematical model of left ventricle during the process of contraction
Vestnik Sankt-Peterburgskogo universiteta. Prikladnaâ matematika, informatika, processy upravleniâ, no. 4 (2013), pp. 66-72 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

The paper is devoted to mathematical modeling of left ventricle (LV) work during contraction and blood ejection to the blood vessel system. As opposed to preceding works actual left ventricle contours obtained by means of ultrasonic investigation was used in the construction of a proposed model. In addition the algorithm of contraction was constructed in such a manner that the blood stream volume flowing from the model corresponded to the experimentally measured stream volume ejected through the LV outlet hole, whose diameter stayed constant. For this purpose the special model parameter was defined for control of the contraction process. The dependence of this parameter on time was obtained as a result of the integral equation in which the desired function entered both in explicit and implicit forms and also entered the variable limit of integration. This desired function was obtained by means of the special algorithm for numerical solution. As a result the integral characteristic of the contraction process was obtained which may be used as additional information of pathology cases of LV work. Bibliogr. 4. Il. 10.
Keywords: left ventricle, mathematical model, integral characteristic of contraction process, integral equation, numerical solution. 
@article{VSPUI_2013_4_a7,
     author = {V. P. Tregubov and A. O. Radichkina},
     title = {Mathematical model of left ventricle during the process of contraction},
     journal = {Vestnik Sankt-Peterburgskogo universiteta. Prikladna\^a matematika, informatika, processy upravleni\^a},
     pages = {66--72},
     year = {2013},
     number = {4},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VSPUI_2013_4_a7/}
}
TY  - JOUR
AU  - V. P. Tregubov
AU  - A. O. Radichkina
TI  - Mathematical model of left ventricle during the process of contraction
JO  - Vestnik Sankt-Peterburgskogo universiteta. Prikladnaâ matematika, informatika, processy upravleniâ
PY  - 2013
SP  - 66
EP  - 72
IS  - 4
UR  - http://geodesic.mathdoc.fr/item/VSPUI_2013_4_a7/
LA  - ru
ID  - VSPUI_2013_4_a7
ER  - 
%0 Journal Article
%A V. P. Tregubov
%A A. O. Radichkina
%T Mathematical model of left ventricle during the process of contraction
%J Vestnik Sankt-Peterburgskogo universiteta. Prikladnaâ matematika, informatika, processy upravleniâ
%D 2013
%P 66-72
%N 4
%U http://geodesic.mathdoc.fr/item/VSPUI_2013_4_a7/
%G ru
%F VSPUI_2013_4_a7
V. P. Tregubov; A. O. Radichkina. Mathematical model of left ventricle during the process of contraction. Vestnik Sankt-Peterburgskogo universiteta. Prikladnaâ matematika, informatika, processy upravleniâ, no. 4 (2013), pp. 66-72. http://geodesic.mathdoc.fr/item/VSPUI_2013_4_a7/

[1] Radichkina A. O., “Mathematical modelling of the heart left ventricle”, Trudy 41 mezhdunar. nauch. konferencii aspirantov i studentov, Izd. Dom S.-Peterb. un-ta, S.-Petersburg, 2010, 349–352

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

[3] Radichkina A. O., Tregubov V. P., “Mathematical modelling of the left ventricle systole contraction”, Ustoychivost' i processy urpavleniya, Vseros. konferenciya, posvyaschennaya 80-letiu so dnya rozhdeniya V. I. Zubova, Tezisy dokladov (S.-Petersburg, 2010), 272–273

[4] Richard G., “Wise Geometrical models of left ventricular contraction from MRI of the normal and spontaneously hypertensive rat heart”, J. Phys. Med. Biol., 44 (1999), 2657–2676 | DOI