Computational study of oxygen concentration in human blood under the low-frequency disturbances

S. S. Simakov ; A. S. Kholodov

Matematičeskoe modelirovanie, Tome 20 (2008) no. 4, pp. 87-102.

Résumé

Complex dynamical model of the closed cardiovascular and respiratory systems including their interaction is considered in this work. An approach is proposed to substitute single-component model of the alveolar volume with multi-component model. Improved structure of the vascular network based on the experimantal data is represented. Resonance propertires of the alveolar volume are stadied using the proposed multi-component approach. Numerical results are represented showing oxygen concentration decrease in pulmonary circulation depending on the amplitude of the disturbances affecting the alveolar volume on its eigenfrequencies.

Bibliographie

[1] R. A. Baron, D. R. Richardson, Human Aggression, Kluwer Academic Publisher, 1994, 419 pp.

[2] S. N. Willich, K. Wegscheider, M. Stallmann, T. Keil, “Noise burden and the risk of myocardial infraction”, European Heart J., 27:3 (2006), 276–282 | DOI

[3] A. S. Kholodov, “Nekotorye dinamicheskie modeli vneshnego dykhaniya i krovoobrascheniya s uchetom ikh svyaznosti i perenosa veschestv”, Kompyuternye modeli i progress meditsiny, eds. O. M. Belotserkovskii, A. S. Kholodov, Nauka, M., 2001, 127–163

[4] I. V. Ashmetkov, A. Ya. Bunicheva, V. A. Lukshin i dr., “Matematicheskoe modelirovanie krovoobrascheniya na osnove programmnogo kompleksa CVSS”, Kompyuternye modeli i progress meditsiny, eds. O. M. Belotserkovskii, A. S. Kholodov, Nauka, M., 2001, 194–218

[5] M. V. Abakumov, K. V. Gavrilyuk, N. B. Esikov i dr., “Matematicheskaya model gemodinamiki serdechno-sosudistoi sistemy”, Differentsialnye uravneniya, 33 (1997), 892–898 | MR | Zbl

[6] I. V. Ashmetkov, S. I. Mukhin, N. V. Sosnin, A. P. Favorskii, “Kraevaya zadacha dlya LGD uravnenii na grafe”, Differentsialnye uravneniya, 40 (2004), 1–11 | MR

[7] V. P. Vorobev, Atlas anatomii cheloveka, Literatura, Minsk, 1998, 1472 pp.

[8] S. Standring, Gray's Anatomy: The Anatomical Basis of Medicine and Surgery, 39 edition, Churchill-Livingstone, 2004, 1600 pp.

[9] A. V. Evdokimov, A. S. Kholodov, “Kvazistatsionarnaya prostranstvenno raspredelennaya model zamknutogo krovoobrascheniya organizma cheloveka”, Kompyuternye modeli i progress meditsiny, eds. O. M. Belotserkovskii, A.S. Kholodov, Nauka, M., 2001, 164–193

[10] S. S. Simakov, A. S. Kholodov, A. V. Evdokimov, Y. A. Kholodov, “Matter transport simulations using 2D model of peripheral circulation coupled with the model of large vessels”, Proceedings of II International Conference on Computational Bioengineering, v. 1, eds. H. Rodrigues, M. Cerrolaza, IST Press, 2005, 479–490

[11] R. Shmidt, G. Trevs (red.), Fiziologiya cheloveka, t. 2, Mir, M., 2005, 314 pp.

[12] A. I. Dyachenko, “Issledovanie odnokomponentnoi modeli mekhaniki legkikh”, Meditsinskaya biomekhanika, t. 1, Riga, 1986, 147–152

[13] A. P. Favorskii, M. V. Abakumov, N. B. Esikov i dr., Matematicheskaya model serdechnososudistoi sistemy, preprint, MGU, M., 1998, 16 pp.

[14] S. S. Simakov, A. S. Kholodov, A. V. Evdokimov, Y. A. Kholodov, “Numerical simulations of cardiovascular diseases and global matter transport”, Proceeding of the International Conference Advanced Information and Telemedicine Technologies for Health, v. 2, Minsk, 2005, 188–192

[15] S. S. Simakov, A. S. Kholodov, Y. A. Kholodov et al., “Global dynamical model of the cardiovascular system”, Proceedings of the III European Conference on Computational Mechanics, ed. C. A. Mota Soares, 2006, 1464.1–1464.9

[16] S. S. Simakov, A. S. Kholodov, Y. A. Kholodov et al., “Computational study of the vibrating disturbances to the lung function”, Proceedings of the III European Conference on Computational Mechanics, eds. C. A. Mota Soares, 2006, 1467.1–1467.15

[17] Y. A. Kholodov, A. S. Kholodov, N. Kovshov et al., “Computational models on graphs for nonlinear hyperbolic and parabolic sytems of equations”, Proceedings of the III European Conference on Computational Mechanics, ed. C. A. Mota Soares, 2006, 2279.1–2279.19

[18] K. M. Magomedov, A. S. Kholodov, Setochno-kharakteristicheskie chislennye metody, Nauka, M., 1988, 290 pp. | MR

[19] A. S. Kholodov, A. I. Lobanov, A. V. Evdokimov, Raznostnye skhemy dlya resheniya zhestkikh obyknovennykh differentsialnykh uravnenii v prostranstve neopredelennykh koeffitsientov, M., 2001, 47 pp.

[20] W. Huang, R. T. Yen, M. McLaurine, G. Bledsoe, “Morphometry of the human pulmonary vasculature”, Journal of applied physiology, 81 (1996), 2123–2133 | MR

[21] Yu. M. Nikitin, A. I. Trukhanov (red.), Ultrazvukovaya dopplerovskaya diagnostika sosudistykh zabolevanii, Vidar, M., 1998, 432 pp.

[22] L. N. Tarasova, T. N. Kiseleva, A. A. Fokin, Glaznoi ishemicheskii sindrom, Meditsina, M., 2003, 176 pp.

[23] Ya. A. Bunicheva, V. A. Lukshin, S. I. Mukhin i dr., Chislennoe issledovanie gemodinamiki bolshogo kruga krovoobrascheniya, MAKS-Press, M., 2001, 21 pp. | MR

[24] V. A. Lukshin, S. I. Mukhin, T.V. Sokolova i dr., Matematicheskaya model gidrodinamiki tserebralnogo krovoobrascheniya, preprint, MAKS-Press, M., 2001, 20 pp.