### Гологуш Т.С. Черевко А.А. Петренко И.А. Остапенко В.В.

## Two-phase filtration as a model of embolization of arteriovenous malformation

### Reporter: Гологуш Т.С.

Arteriovenous malformation (AVM) is a complex and dangerous malformation of cerebral vessels. Endovascular embolization of AVM is an effective treatment for such pathologies. Nevertheless, there is still a risk of AVM rupture during the operation and within a few days after its termination. The purpose of this work is to model the embolization process and build an optimization algorithm for embolization of AVM.

Arteriovenous malformation can be adequately modeled by a porous medium due to the fact that it consists of a chaotic disordered entanglement of degenerate vessels of various small diameters (from 0.01 to 1 cm) that carry out bypassing blood from the artery to the vein. The embolization process is described in this model by introducing another liquid (glue) immiscible to the first one into a porous medium filled with liquid (blood).

The process of embolization in the one-dimensional approximation is described by the Buckley-Leverett equation, which is solved numerically with the aid of a new modification of the Cabaret scheme. To test the suitability of the method for calculating the embolization tasks, numerical experiments were performed in which the main points of the embolization process were modeled and calculations were compared with the exact solutions [1].

The proposed model of optimal embolization has two new principal features.

1. The embolization process requires a restriction of the specific load on the AVM node during embolization [2]. This requirement follows from neurosurgical practice and is justified on the hydraulic model of embolization of AVM. It is formulated in the form of a restriction on the energy dissipated in the AVM per unit time, referred to the volume of the AVM.

2. The process of embolization is described as an optimal control process, in which, by controlling the concentration of the glue at the entrance to the AVM, it is necessary to achieve the maximum possible embolization during a finite time when the restriction is performed.

It is shown that the optimal control consists of intervals in which either the blood saturation at the entrance to the AVM reaches the minimum acceptable value, which means the maximum supply of the glue, or during the embolization the maximum permissible load is constantly maintained.

The work was supported by the grant of the Government of the Russian Federation No. 14.W03.31.0002.

BIBLIOGRAPHY

1. Cherevko A.A, Gologush T.S., Ostapenko V. V., Petrenko I.A., Chupakhin A.P. Modeling process of embolization arteriovenous malformation on the basis of two-phase filtration model // J. Phys .: Conf. Ser. 2016. Volume 722. Conference 1.

2. Krivoshapkin AL, Panarin VA, Orlov K.Yu., Berestov VV, Shayakhmetov TS, Gorbatykh AV, Kislitsin DS, Chupakhin AP, Cherevko AA, Khe AK, Sergeev GS, Chebykin DV Algorithm for preventing hemodynamic hemorrhages during embolization of cerebral arteriovenous malformations // BULLETIN OF SB RAS. 2013. Т. 33. С. 65-73.

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