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Hydraulic model of cerebral arteriovenous malformations

Published online by Cambridge University Press:  16 May 2016

S. V. Golovin ,
A. K. Khe  and
K. A. Gadylshina
S. V. Golovin*
Affiliation:
Lavrentyev Institute of Hydrodynamics, Novosibirsk, Russia Novosibirsk State University, Novosibirsk, Russia
A. K. Khe
Affiliation:
Lavrentyev Institute of Hydrodynamics, Novosibirsk, Russia Novosibirsk State University, Novosibirsk, Russia
K. A. Gadylshina
Affiliation:
Novosibirsk State University, Novosibirsk, Russia
*
†Email address for correspondence: [email protected]
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Abstract

The paper presents a model of a cerebral vascular system including two types of vessel networks (arterial and venous) joined by a porous medium as a substitute to a microcapillary system. The aim of the paper is to reproduce numerically experimental data on endovascular measurements of fluid velocity and pressure in the afferent artery and the efferent vein of the arteriovenous malformation (AVM). The suggested model qualitatively simulates all the main features of the experimental $vp$-diagrams: presence of the time shift between velocity and pressure waves, semicircular shape of the diagram, difference in the direction of circulation in the arterial and venous parts and upper-left drift of the diagram during the embolisation of the AVM. The velocity–pressure time shift is analysed on the modelling example of pulsation flow within a vessel in a cylindrical porous medium. The demonstrated adequacy of the model allows its further use for simulation of various strategies of AVM treatment, haemorrhage risk estimations, etc.

JFM classification

Biological Fluid Dynamics: Blood flow Waves/Free-surface Flows: Hydraulics Low-Reynolds-number flows: Porous media
Type
Papers
Information
Journal of Fluid Mechanics , Volume 797 , 25 June 2016 , pp. 110 - 129
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Copyright
© 2016 Cambridge University Press 

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References

Abakumov, M. V., Ashmetkov, I. V., Esikova, N. B., Koshelev, V. B., Mukhin, S. I., Sosnin, N. V., Tishkin, V. F., Favorskii, A. P. & Khrulenko, A. B. 2000 A method of matematical modelling of cardiovascular system. Math. Modelling 12, 106–117 (in Russian).Google Scholar
Alastruey, J., Khir, A. W., Matthys, K. S., Segers, P., Sherwin, S. J., Verdonck, P. R., Parker, K. H. & Peiró, J. 2011 Pulse wave propagation in a model human arterial network: assessment of 1-D visco-elastic simulations against in vitro measurements. J. Biomech. 44 (12), 2250–2258.Google Scholar
van Beijnum, J., van der Worp, H. B., Buis, D. R., Salman, R. A.-S., Kappelle, L. J., Rinkel, G. J. E., van der Sprenkel, J. W. B., Vandertop, W. P., Algra, A. & Klijn, C. J. M. 2011 Treatment of brain arteriovenous malformations: a systematic review and meta-analysis. J. Am. Math. Assoc. 306 (18), 2011–2019.CrossRefGoogle ScholarPubMed
Caro, C. G., Pedley, T. J., Schroter, R. C. & Seed, W. A. 1978 The Mechanics of the Circulation. Oxford University Press.Google Scholar
Cattaneo, L. & Zunino, P. 2014 Computational models for fluid exchange between microcirculation and tissue interstitium. Netw. Heterog. Media 9 (1), 135–159.CrossRefGoogle Scholar
Chupakhin, A. P., Cherevko, A. A., Khe, A. K., Chebotnikov, A. V., Krivoshapkin, A. L., Orlov, K. Yu. & Panarin, V. A. 2014 Comprehensive study of hemodynamics of cerebral vessels in the presence of pathologies. In International Conference ‘Mathematical Modeling and High Performance Computing in Bioinformatics, Biomedicine and Biotechnology’, June 24–27, 2014, Novosibirsk, Russia. Abstracts, p. 24. Publishing House SB RAS Novosibirsk.Google Scholar
Chupakhin, A. P., Cherevko, A. A., Khe, A. K., Telegina, N. Yu., Krivoshapkin, A. L., Orlov, K. Yu., Panarin, V. A. & Baranov, V. I. 2012 Measurement and analysis of cerebral hemodynamic parameters in the presence of brain vascular anomalies. Circulation Pathology Cardiac Surgery 4, 27–31.Google Scholar
D’Angelo, C. & Quarteroni, A. 2008 On the coupling of 1d and 3d diffusion-reaction equations: application to tissue perfusion problems. Math. Models Meth. Appl. Sci. 18 (08), 1481–1504.CrossRefGoogle Scholar
Formaggia, L., Quarteroni, A. & Veneziani, A.(Eds) 2009 Cardiovascular Mathematics: Modeling and simulation of the Circulatory System. Springer.CrossRefGoogle Scholar
Gromeka, I. S.1882 On the theory of fluid motion in narrow cylindrical tubes. In Gromeka, I. S. 1952 Collected Works, pp. 149–171. Publishing House of the USSR Academy of Sciences (in Russian).Google Scholar
Gromeka, I. S.1883 On the propagation speed of fluid wave motion in elastic tubes. In Gromeka, I. S. 1952 Collected Works, pp. 172–183. Publishing House of the USSR Academy of Sciences (in Russian).Google Scholar
Guglielmi, G. 2008 Analysis of the hemodynamic characteristics of brain arteriovenous malformations using electrical models: baseline settings, surgical extirpation, endovascular embolization, and surgical bypass. Neurosurgery 63 (1), 1–11.Google Scholar
Hecht, F. 2012 New development in FreeFem++. J. Numer. Math. 20 (3–4), 251–265.CrossRefGoogle Scholar
Kholodov, A. S. 2001 Some dynamical models of external breathing and haemodynamics including their interaction and matter transport. In Computer Models and Medicine Progress (ed. Belotserkovskii, O. M. & Kholodov, A. S.), pp. 127–163. Nauka (in Russian).Google Scholar
Laakso, A., Dashti, R., Juvela, S., Niemelä, M. & Hernesniemi, J. 2010 Natural history of arteriovenous malformations: presentation, risk of hemorrhage and mortality. In Surgical Management of Cerebrovascular Disease, pp. 65–69. Springer.CrossRefGoogle Scholar
Litao, M. L. S., Pilar-Arceo, C. P. C. & Legaspi, G. D. 2012 AVM compartments: Do they modulate trasnidal pressures? An electrical network analysis. Asian J. Neurosurg. 7 (4), 174–180.Google Scholar
Mohr, J. P., Parides, M. K., Stapf, C., Moquete, E., Moy, C. S., Overbey, J. R., Salman, R. A.-S., Vicaut, E., Young, W. L., Houdart, E. et al. 2014 Medical management with or without interventional therapy for unruptured brain arteriovenous malformations (ARUBA): a multicentre, non-blinded, randomised trial. Lancet 383 (9917), 614–621.CrossRefGoogle ScholarPubMed
Müller, L. O. & Toro, E. F. 2014 A global multiscale mathematical model for the human circulation with emphasis on the venous system. Intl J. Numer. Meth. Biomed. Engng 30 (7), 681–725.CrossRefGoogle ScholarPubMed
Ogilvy, C. S., Stieg, P. E., Awad, I., Brown, R. D., Kondziolka, D., Rosenwasser, R., Young, W. L. & Hademenos, G. 2001 Recommendations for the management of intracranial arteriovenous malformations: a statement for healthcare professionals from a special writing group of the stroke council, american stroke association. Circulation 103 (21), 2644–2657.Google Scholar
Papapanayotou, C. J., Cherruault, Y. & De La Rochefoucauld, B. 1990 A mathematical model of the circle of willis in the presence of an arteriovenous anomaly. Comput. Maths Applics. 20 (4), 199–206.CrossRefGoogle Scholar
Pedley, T. J. 1980 The Fluid Mechanics of Large Blood Vessels. Cambridge University Press.CrossRefGoogle Scholar
Penta, R., Ambrosi, D. & Quarteroni, A. 2015 Multiscale homogenization for fluid and drug transport in vascularized malignant tissues. Math. Models Meth. Appl. Sci. 25 (01), 79–108.CrossRefGoogle Scholar
Qureshi, M. U., Vaughan, G. D. A., Sainsbury, C., Johnson, M., Peskin, C. S., Olufsen, M. S. & Hill, N. A. 2014 Numerical simulation of blood flow and pressure drop in the pulmonary arterial and venous circulation. Biomech. Model. Mechanobiol. 13 (5), 1137–1154.CrossRefGoogle ScholarPubMed
Reymond, P., Bohraus, Y., Perren, F., Lazeyras, F. & Stergiopulos, N. 2011 Validation of a patient-specific one-dimensional model of the systemic arterial tree. Am. J. Physiol. Heart Circ. Physiol. 301 (3), H1173–H1182.CrossRefGoogle ScholarPubMed
Reymond, P., Merenda, F., Perren, F., Rüfenacht, D. & Stergiopulos, N. 2007 One dimensional model of the systemic arterial tree including cerebral circulation. In Proceedings of the ASME Summer Bioengineering Conference 2007, SBC 2007, pp. 207–208. American Society of Mechanical Engineers.CrossRefGoogle Scholar
Reymond, P., Merenda, F., Perren, F., Rüfenacht, D. & Stergiopulos, N. 2009 Validation of a one-dimensional model of the systemic arterial tree. Am. J. Physiol. Heart Circ. Physiol. 297 (1), H208–H222.CrossRefGoogle ScholarPubMed
Saatci, I., Geyik, S., Yavuz, K. & Cekirge, H. S. 2011 Endovascular treatment of brain arteriovenous malformations with prolonged intranidal Onyx injection technique: long-term results in 350 consecutive patients with completed endovascular treatment course. J. Neurosurg. 115 (1), 78–88.Google Scholar
Sherwin, S. J., Formaggia, L., Peiro, J. & Franke, V. 2003a Computational modelling of 1D blood flow with variable mechanical properties and its application to the simulation of wave propagation in the human arterial system. Intl J. Numer. Meth. Fluids 43 (6–7), 673–700.CrossRefGoogle Scholar
Sherwin, S. J., Franke, V., Peiró, J. & Parker, K. 2003b One-dimensional modelling of a vascular network in space-time variables. J. Engng Maths 47 (3/4), 217–250.CrossRefGoogle Scholar
Simakov, S. S., Gorodnova, N. O., Chupakhin, A. P. & Khe, A. K. 2013 Mathematical modelling of haemodynamics of arteriovenous malformations. In International Conference on Mathematical Control Theory and Mechanics, July 5–9, 2013, Suzdal, Russia. Abstracts, pp. 213–218. MIAN, Moscow.Google Scholar
Smith, F. T. & Jones, M. A. 2000 One-to-few and one-to-many branching tube flows. J. Fluid Mech. 423, 1–31.CrossRefGoogle Scholar
Smith, F. T. & Jones, M. A. 2003 AVM modelling by multi-branching tube flow: large flow rates and dual solutions. Math. Med. Biol. 20 (2), 183–204.CrossRefGoogle ScholarPubMed
Stieg, P. E., Batjer, H. H. & Samson, D.(Eds) 2006 Intracranial Arteriovenous Malformations. CRC Press.CrossRefGoogle Scholar
Telegina, N., Chupakhin, A. & Cherevko, A. 2013 Local model of arteriovenous malformation of the human brain. J. Phys.: Conf. Ser. 410, 012001.Google Scholar
White, A. H. & Smith, F. T. 2013 Computational modelling of the embolization process for the treatment of arteriovenous malformations (AVMs). Math. Comput. Model. 57 (5–6), 1312–1324.Google Scholar
Womersley, J. R. 1955 Method for the calculation of velocity, rate of flow and viscous drag in arteries when the pressure gradient is known. J. Physiol. 127 (3), 553–563.CrossRefGoogle ScholarPubMed