Modeling of cardiovascular system hemodynamics with cerebral aneurysm

S. V. Sindeev ; S. V. Frolov

Matematičeskoe modelirovanie, Tome 28 (2016) no. 6, pp. 98-114.

Résumé

Method of multiscale hemodynamics modeling is presented which allows coupling of mathematical models of hemodynamics with a different level of detail for pre-operational evaluation of condition of patients with cerebral aneurysm. Simulation results can be used by physician for developing of a strategy and tactics of a treatment according to individual features of cardiovascular system of a patient.

Détail

Keywords: cerebral circulation, cardiovascular system model, aneurysm genesis, multiscale mathematical model, model of global hemodynamics, model of arterial tree hemodynamics, model of cerebral artery hemodynamics, high performance computing.

Bibliographie

[1] S. E. Kornelik, E. K. Borzenko, A. N. Grishin, M. A. Bubenchikov, V. I. Stolyarov, “Formation and destruction of erythrocyte rouleau in a vessel with local bulge”, Mathematical models and computer simulations, 1:1 (2009), 1–10 | DOI

[2] H. J. Steiger, D. W. Liepsch, A. Poll, H. J. Reulen, “Hemodynamic stress in terminal saccular aneurysms: a laser-Doppler study”, Heart and vessels, 1988, no. 4, 162–169 | DOI

[3] F. Dorn, F. Niedermeyer, A. Balasso, D. Liepsch, T. Liebig, “The effect of stents on intra-aneurysmal hemodynamics: in vitro evaluation of a pulsatile aneurysm using laser Doppler anemometry”, Neuroradiology, 2011, no. 4, 267–272 | DOI | MR

[4] V. A. Lischuk, Matematicheskaya teoriya krovoobrascheniya, Meditsina, M., 1991, 256 pp.

[5] S. V. Frolov, S. V. Sindeev, V. A. Lischouk, D. Sh. Gazizova, “Hemodynamics modeling of the cardiovascular system with a pulsating heart”, Transactions TSTU, 13:3 (2012), 546–551

[6] E. V. Astrahanceva, V. Yu. Gidaspov, D. L. Reviznikov, “Matematicheskoe modelirovanie gemodinamiki krupnih krovenosnyh sosudov”, Mathem. modelir., 17:8 (2005), 61–80 | Zbl

[7] A. Ya. Bunicheva, M. A. Menyailova, S. I. Mukhin, N. V. Sosnin, A. P. Favorskii, “Studying the influence of gravitational overloads on the parameters of blood flow in vessels of greater circulation”, Mathematical models and computer simulations, 5:1 (2013), 81–91 | DOI | MR

[8] N. V. Abakumov, I. V. Ashmetkov, N. B. Esikova, V. B. Koshelev, S. I. Mukhin, N. V. Sosnin, V. F. Tishkin, A. P. Favorskii, A. B. Khrulenko, “Metodika matematicheskogo modelirovaniia serdechnososudistoi sistemy”, Matematicheskoe modelirovanie, 12:2 (2000), 106–117 | Zbl

[9] V. A. Lukshin, Matematicheskoe modelirovanie tserebralnoy gemodinamiki, Dissertatsiya ... kand. fiz.-mat. nauk, MGU im. M. V. Lomonosova, M., 2004

[10] V. B. Koshelev, S. I. Mukhin, T. V. Sokolova, N. V. Sosnin, A. P. Favorskii, “Matematicheskoe modelirovanie gemodinamiki serdechno-sosudistoi sistemy s uchetom vliianiia neiroreguliatsii”, Matematicheskoe modelirovanie, 19:3 (2007), 15–28 | MR

[11] S. I. Muhin, Matematicheskoe modelirovanie gemodinamiki, Avtoreferat dissertatsii ... dokt. fiz.-mat. nauk, MGU im. M. V. Lomonosova, M., 2008

[12] D. V. Ivanov, O. A. Fomkina, “Opredelenie postoyannyih dlya modeley Neo–Guka i Muni–Rivlina po rezultatam eksperimentov na odnoosnoe rastyazhenie”, Mehanika. Matematika, Sb. nauch. tr., Izd-vo Sarat. un-ta, Saratov, 2008, 114–117

[13] D. V. Ivanov, O. A. Fomkina, “Determination of mechanical properties of Willis circle arteries”, Russian Journal of Biomechanics, 12:4 (2008), 71–78 | MR

[14] D. V. Ivanov, “Issledovanie arteriy villizievogo kruga v norme i pri patologii”, Izvestiya Saratovskogo un-ta. Novaya seriya. Matematika. Mehanika. Informatika, 10:1 (2010), 35–43 | MR

[15] D. V. Ivanov, Teoretiko-eksperimentalnoe issledovanie vliyaniya mehanicheskih faktorov na vozniknovenie i patogenez anevrizm arteriy villizievogo kruga, Avtoreferat dissertatsii ... kand. fiz.-mat. nauk, SGU im. N. G. Chernyishevskogo, Saratov, 2010

[16] O. E. Pavlova, D. V. Ivanov, A.A. Gramakova, K. M. Morozov, I. I. Suslov, “Gemodinamika i mehanicheskoe povedenie bifurkatsii sonnoy arterii s patologicheskoy zavisimostyu”, Izvestiya Saratovskogo universiteta. Novaya seriya. Matematika. Mehanika. Informatika, 10:2 (2010), 66–75 | Zbl

[17] D. V. Ivanov, A. V. Dol, O. E. Pavlova, A. V. Aristambekova, “Modelling of human circle of Willis in normal state and with pathology”, Russian J. of Biomechanics, 17:3(61) (2013), 40–52

[18] A. Valencia, A. Contente, M. Ignat, J. Mura, E. Bravo, R. Rivera, J. Sordo, “Mechanical test of human cerebral aneurysm sample obtained from surgical clipping”, J. of Mechanics in Medicine and Biology, 2010, no. 3, 28–42

[19] K. Balakhovsky, M. Jabareen, K. Y. Volokh, “Modeling rupture of growing aneurysms”, Journal of Biomechanics, 47 (2014), 653–658 | DOI

[20] C. J. Boyle, A. B. Lennon, P. J. Prendergast, “Application of a mechanobiological simulation technique to stents used clinically”, Journal of Biomechanics, 46:5 (2013), 918–924 | DOI

[21] A. J. Geers, I. Lararbide, H. G. Morales, A. F. Frangi, “Approximating hemodynamics of cerebral aneurysms with steady flow simulations”, Journal of Biomechanics, 47 (2014), 178–185 | DOI

[22] Y. Long, H. Yu, Z. Zhuo, Y. Zhang, Y. Wang, X. Yang, H. Li, “A geometric scaling model for assessing the impact of aneurysm size ratio on hemodynamic characteristics”, Biomedical Engineering Online, 17 (2014), 13–17

[23] M. L. Baharaglu, C. M. Schirmer, D. A. Hoit, B. L. Gao, A. M. Malek, “Aneurysm inflow-angle as a discriminant for rupture in sidewall cerebral aneurysms: morphometric and computational fluid dynamic analysis”, Stroke, 41:7 (2010), 1423–1430 | DOI

[24] J. Xiang, S. K. Natarajan, M. Tremmel, D. Ma, J. Mocco, L. N. Hopkins, A. H. Siddiqui, E. L. Levy, H. Meng, “Hemodynamic-morphological discriminants for intracranial aneurysm”, Stroke, 42:1 (2011), 144–152 | DOI

[25] A. M. Gambaruto, J. Janela, A. Moura, A. Sequeira, “Sensitivity of hemodynamics in a patient specific cerebral aneurysm to vascular geometry and blood rheology”, Mathematical Biosciences and Engineering, 8:2 (2011), 409–423 | DOI | MR | Zbl

[26] P. I. Begun, Biomehanicheskoe modelirovanie ob'ektov protezirovaniya, uchebnoe posobie, Politehnika, SPB., 2011, 464 pp.

[27] S. Tateshima, A. Chien, J. Sayre, J. Cebral, F. Vinuela, “The effect of aneurysm geometry on the intra-aneurysmal flow condition”, Neuroradiology, 52:12 (2010), 1135–1141 | DOI

[28] S. Schnell, S. A. Ansari, P. Vakil, M. Wasielewski, M. L. Carr, M. C. Hurley, B. R. Bendok, H. Batjer, T. J. Caroll, J. Carr, M. Markl, “Three-dimensional hemodynamics in intracranial aneurysms: influence of size and morphology”, J. of Magnetic Resonance Imaging., 39:1 (2014), 120–131 | DOI

[29] X. Wang, X. Li, “Biomechanical behavior of cerebral aneurysm and its relation with the formation of intraluminal thrombus: a patient-specific modelling study”, Computer Methods in Biomechanics and Biomedical Engineering, 16:11 (2013), 1127–1134 | DOI

[30] V. B. Parashin, G. P. Itkin, Biomehanika krovoobrascheniya, Ucheb. posobie, ed. S. I. Schukin, Izd-vo MGTU im. N. E. Baumana, M., 2005, 224 pp.

[31] P. N. Watton, A. Selimovic, N. B. Raberger, P. Huang, G. A. Holzapfel, Y. Ventikos, “Modelling evolution and the evolving mechanical environment of saccular cerebral aneurysms”, Biomechanics and Modeling in Mechanobiology, 10:1 (2011), 109–132 | DOI

[32] M. Steinhauser, Computational multiscale modeling of fluids and solids, Springer-Verlag, Berlin–Heidelberg, 2008, 428 pp. | Zbl

[33] V. A. Lischouk, E. V. Mostkova, “Systema zakonomernostey serdca”, Klinicheskaya fiziologiya crovoobracheniya, 2006, no. 1, 16–21 | MR

[34] V. A. Lischouk, S. V. Frolov, D. Sh. Gazizova, L. V. Sazykina, S. N. Makoveev, “Matematicheskaya model sosuda v obyknovennih proizvodnyh kak instrument dlya issledovaniya sosudistoy patologii. Ch. 2”, Klinicheskaya fiziologiya krovoobrascheniya, 2007, no. 1, 64–70