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Mathematical Assessment of Arterio-Venous Malformations Embolisation

1 Moscow Institute of Physics and Technology 2 Novosibirsk State University 3 Institute of Hydrodynamics SD RAS. Workshop on mathematical models and numerical methods in biomathematics 2013. Mathematical Assessment of Arterio-Venous Malformations Embolisation.

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Mathematical Assessment of Arterio-Venous Malformations Embolisation

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  1. 1Moscow Institute of Physics and Technology 2Novosibirsk State University 3Institute of Hydrodynamics SD RAS Workshop on mathematical models and numerical methods in biomathematics 2013 Mathematical Assessment of Arterio-Venous Malformations Embolisation Simakov1 S.S., Gorodnova1 N.O.,Chupakhin2,3 A.P., Khe2,3 A.K.

  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 30-40 years

  4. Motivation

  5. Motivation

  6. 1D Network Mathematical model of circulation

  7. Global blood flow Kholodov 2001,et. al. 1) Mass balance 2)Momentum balance 3)Boundary conditions at junctions 3.1 3.2 Compatibility conditions along outgoing characteristics (finite difference discretisaztion) 3.3 equations equations

  8. Boundary conditions: vessels junction Equations set

  9. Vessel wall elasticity Analytic approximation Pedley, Luo, 1998

  10. Vessel elasticity modeling

  11. AVM Haemodynamics with 1D Approach

  12. AVM

  13. 1D AVM scheme

  14. Pressure distribution output output input input input left route left route left route occluded occluded occluded right route

  15. Velocity distribution output input left route occluded occluded occluded occluded occluded right route

  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. ArteriesBefore surgery V-P Q-E Before After

  25. ArteriesAfter surgery V-P Q-E Before After

  26. Thank You!

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