On the monotonicity of the CABARET scheme approximating a scalar conservation law with a convex flux

Zyuzina, N. A.; Остапенко, В. В.

doi:10.1134/s1064562416010282

Cited by 13 publications

(3 citation statements)

References 8 publications

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“…It is shown 34 that the correction of fluxes ( 37 ) is not sufficient to preserve the local monotonicity of the difference solution at the - th time layer, which is necessary for the absence of non-physical oscillations on the shocks. Therefore, if at the n -th time layer in the vicinity of the grid node the difference solution is locally monotone, an additional correction of the numerical fluxes is performed where …”

Section: Methodsmentioning

confidence: 99%

Optimal control problem arising in mathematical modeling of cerebral vascular pathology embolization

Sharifullina

Cherevko

Остапенко

2022

Sci Rep

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Arteriovenous malformation (AVM) of the brain is a congenital vascular abnormality, in which the arterial and venous blood pools are intertwined and directly connected. This dangerous disease causes a high risk of intracranial hemorrhage and disrupts brain functioning. The preferred method of AVM treating is embolization, which is the endovascular filling of abnormal AVM vessels with a special embolic agent. Despite the fact that this method is widely used in neurosurgery, in some cases its use is accompanied by perioperative AVM vessels rupture. In this regard, the aim of this work is to study the optimal scenarios for multi-stage AVM embolization from the effectiveness and safety of the procedure point of view. Mathematically, the joint movement of blood and embolic agent in the AVM body is described on the basis of a one-dimensional two-phase filtration model, which takes into account the redistribution of blood to surrounding healthy vessels. For the numerical solution of the resulting integro-differential system of equations, a monotonic modification of the CABARET scheme is used. To find optimal embolization scenarios, the optimal control problem with phase constraints arising from medicine is formulated. A modified particle swarm optimization method is used to solve this problem numerically. This technique is used to obtain optimal embolization scenarios on the basis of real patients clinical data collected during neurosurgical operations.

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Section: Methodsmentioning

confidence: 99%

Optimal control problem arising in mathematical modeling of cerebral vascular pathology embolization

Sharifullina

Cherevko

Остапенко

2022

Sci Rep

View full text Add to dashboard Cite

show abstract

“…Currently, for numerical simulations of spatially multidimensional gas-dynamic [40] and hydraulic [41] flows, the two-layer in time form of the CABARET scheme [42] is widely used. The monotonicity of this scheme for approximation of scalar conservation law with convex flux was studied in [43] and with a non-convex flux in [27]. In the present paper, for Buckley-Leverett equations (2.2) and (2.4) numerical solution the monotonic modification of the CABARET scheme proposed in [27,44] will be used.…”

Section: Methodsmentioning

confidence: 99%

Modelling of the arteriovenous malformation embolization optimal scenario

et al. 2020

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Cerebral arteriovenous malformation (AVM) is a congenital brain vessels pathology, in which the arterial and venous blood channels are connected by tangles of abnormal blood vessels. It is a dangerous disease that affects brain functioning causing the high risk of intracerebral haemorrhage. One of AVM treatment methods is embolization—the endovascular filling of the AVM vessel bundle with a special embolic agent. This method is widely used, but still in some cases is accompanied by intraoperative AVM vessels rupture. In this paper, the optimal scenario of AVM embolization is studied from the safety and effectiveness of the procedure point of view. The co-movement of blood and embolic agent in the AVM body is modelled on the basis of a one-dimensional two-phase filtration model. Optimal control problem with phase constraints arising from medicine is formulated and numerically solved. In numerical analysis, the monotone modification of the CABARET scheme is used. Optimal embolization model is constructed on the basis of real patients' clinical data collected during neurosurgical operations. For the special case of embolic agent, input admissible and optimal embolization scenarios were calculated.

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“…By analogy to paper [10], it is possible to show that the offered modification of the CABARET scheme is monotonous [11] that provides its high resolution at shock capturing calculation.…”

Section: Initial-boundary Problem Of Embolizationmentioning

confidence: 99%

Modeling process of embolization arteriovenous malformation on the basis of two-phase filtration model

Cherevko

Gologush

Остапенко

et al. 2016

J. Phys.: Conf. Ser.

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Abstract. Arteriovenous malformation is a chaotic disordered interlacement of very small diameter vessels, performing reset of blood from the artery into the vein. In this regard it can be adequately modeled using porous medium. In this model process of embolization described as penetration of non-adhesive substance ONYX into the porous medium, filled with blood, both of these fluids are not mixed with each other. In one-dimensional approximation such processes are well described by Buckley-Leverett equation. In this paper Buckley-Leverett equation is solved numerically by using a new modification of Cabaret scheme. The results of numerical modeling process of embolization of AVM are shown.

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On the monotonicity of the CABARET scheme approximating a scalar conservation law with a convex flux

Cited by 13 publications

References 8 publications

Optimal control problem arising in mathematical modeling of cerebral vascular pathology embolization

Optimal control problem arising in mathematical modeling of cerebral vascular pathology embolization

Modelling of the arteriovenous malformation embolization optimal scenario

Modeling process of embolization arteriovenous malformation on the basis of two-phase filtration model

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