1 Mathematical Assessment of Arterio-Venous Malformations Embolisation 1 Moscow Institute of Physics and Technology 2 Novosibirsk State University 3 Institute of Hydrodynamics SD RAS Simakov 1 S.S., Gorodnova 1 N.O., Chupakhin 2,3 A.P., Khe 2,3 A.K. Workshop on mathematical models and numerical methods in biomathematics 2013
2 Cardiovascular Loop
3 Motivation AVM embolisation: Mortality (1.5-3%) Disability (3.8-7%) Postoperative risk (5% during the next 5 years) Without treatment: Stroke at the age of years
4 Motivation
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6 1D Network Mathematical model of circulation
7 Global blood flow 1) Mass balance 2) Momentum balance 3) Boundary conditions at junctions Compatibility conditions along outgoing characteristics (finite difference discretisaztion) 3.3 equations Kholodov 2001,et. al.
8 Boundary conditions: vessels junction Equations set
9 Vessel wall elasticity Pedley, Luo, 1998 Analytic approximation
10 Vessel elasticity modeling
11 AVM Haemodynamics with 1D Approach
12 AVM
13 1D AVM scheme
14 Pressure distribution input output left route right route input left route output input left route occluded
15 Velocity distribution right route output input left route occluded
16 Relative measures of embolisation quality Pressure embolisation quality Velocity embolisation quality
17 1D AVM scheme
18 Pressure embolisation quality
19 Velocity embolisation quality
20 P-U diagrams before and after surgical embolisation
21 P-U diagrams before and after surgical embolisation
22 Q-E diagrams before and after surgical embolisation
23 Q-E diagrams before and after surgical embolisation
24 Arteries Before surgery Before After V-P Q-E
25 Arteries After surgery Before After V-P Q-E
26 Thank You!