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Validation and testing of 1D haemodynamics models

Validation and testing of 1D haemodynamics models. Timur M. Gamilov 1,2,3 , Etienne Boileau 4 , , Sergey S. Simakov 1,2,3 ,. 1 Moscow Institute of Physics and Technology 2 MIPT Center for Human Physiology Studies

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Validation and testing of 1D haemodynamics models

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  1. Validation and testing of 1D haemodynamics models Timur M. Gamilov1,2,3, Etienne Boileau4, , Sergey S. Simakov1,2,3, 1 Moscow Institute of Physics and Technology 2 MIPT Center for Human Physiology Studies 3 The International Translational Medicine and Biomodelling Research team 4 Swansea University 6th Russian Workshop on Mathematical Models and Numerical Methods in Biomathematics, 4-th International Workshop on the Multiscale Modeling and Methods in Biology and Medicine,29.10.2014

  2. 1D Haemodynamic Models

  3. Haemodynamic Models 3D models

  4. Haemodynamic Models 3D models 1D models

  5. 1D Models Enhanced External Counterpulsation (EECP) • 1 hour and more • whole body (legs - heart)

  6. 1D Models 1D-3D coupling

  7. Blood flow circulation model 1) Mass balance 2)Momentum balance

  8. Blood flow circulation model 1) Mass balance 2)Momentum balance

  9. Blood flow circulation model 1) Mass balance 2)Momentum balance

  10. Blood flow circulation model 1) Mass balance 2)Momentum balance Wall state

  11. Blood flow circulation model 1) Mass balance 2)Momentum balance Wall state Pedley, Luo, 1998 Favorsky, Mukhin

  12. Blood flow circulation model 1) Mass balance 2)Momentum balance Wall state

  13. Blood flow circulation model 1) Mass balance 2)Momentum balance Wall state 3)Bifurcations

  14. Blood flow circulation model 1) Mass balance 2)Momentum balance Wall state 3)Bifurcations

  15. Blood flow circulation model 1) Mass balance 2)Momentum balance Wall state 3)Bifurcations

  16. Blood flow circulation model 1) Mass balance 2)Momentum balance Wall state 3)Bifurcations Compatibility conditions

  17. Blood flow circulation model 1) Mass balance 2)Momentum balance Wall state 3)Bifurcations Compatibility conditions

  18. Blood flow circulation model 1) Mass balance 2)Momentum balance Wall state 3)Bifurcations 4)Numerical method

  19. Validation and testing

  20. Gaussian pulse Straight long vessel Left boundary Right boundary - no reflection

  21. Gaussian pulse Discontinuous Galerkin

  22. Gaussian pulse Locally Conservative Galerkin

  23. Gaussian pulse Discontinuous Galerkin Locally Conservative Galerkin

  24. Gaussian pulse Grid Characteristic 1st order Grid Characteristic 2nd order

  25. Gaussian pulse Grid Characteristic 1st order Grid Characteristic 2nd order

  26. Gaussian pulse Grid Characteristic 1st order Grid Characteristic 2nd order

  27. Gaussian pulse. Amplitude Grid Characteristic 2nd order (exponent) Grid Characteristic 2nd order (sqrt)

  28. Gaussian pulse. Distance traveled Grid Characteristic 2nd order (exponent) Grid Characteristic 2nd order (sqrt) Discontinuous Galerkin (sqrt)

  29. Shock formation in a strait vessel ~ 0.4 s; 2 m (GC 1st order, Exponent wall state) ~ 0.57 s; 3.3 m (two-step Lax–Wendroff) Mathematical analysis of the quasilineareects in a hyperbolic model blood ow through compliant axi-symmetric vessels SuncicaCanic and EunHeui Kim Math. Meth. Appl. Sci. 2003; 26:1161–1186 (DOI: 10.1002/mma.407) ~ 0.478 s; 2.95 m (theory)

  30. Autoregulation Ed VanBavel, Jos P.M. Wesselman, Jos A.E. SpaanMyogenic, Activation and Calcium Sensitivity of Cannulated Rat Mesenteric Small Arteries. Circulation Research,1998 Rat artery

  31. Autoregulation Ed VanBavel, Jos P.M. Wesselman, Jos A.E. SpaanMyogenic, Activation and Calcium Sensitivity of Cannulated Rat Mesenteric Small Arteries. Circulation Research,1998 Rat artery Wall state adaptation: (only arteries) T T t Heart cycle

  32. Autoregulation Ed VanBavel, Jos P.M. Wesselman, Jos A.E. SpaanMyogenic, Activation and Calcium Sensitivity of Cannulated Rat Mesenteric Small Arteries. Circulation Research,1998 Rat artery Leg artery No autoregulation Cross-section With autoregulation time

  33. \Silicon-tube model Koen S. Matthys, JordiAlastruey, JoaquimPeiro, et. al., 2007 Inlet: Q=Q(t) Outlets: R

  34. \Thoracic aorta (15) GC Exp GC Exp Q, ml/s P, kPa Time, s Time, s

  35. Right carotid (3) DG • GC 1st

  36. Discussion • Variety of 1d models • Different methods, wall state equations, etc. • Toro, Muller

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