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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 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
1D Haemodynamic Models
Haemodynamic Models 3D models
Haemodynamic Models 3D models 1D models
1D Models Enhanced External Counterpulsation (EECP) • 1 hour and more • whole body (legs - heart)
1D Models 1D-3D coupling
Blood flow circulation model 1) Mass balance 2)Momentum balance
Blood flow circulation model 1) Mass balance 2)Momentum balance
Blood flow circulation model 1) Mass balance 2)Momentum balance
Blood flow circulation model 1) Mass balance 2)Momentum balance Wall state
Blood flow circulation model 1) Mass balance 2)Momentum balance Wall state Pedley, Luo, 1998 Favorsky, Mukhin
Blood flow circulation model 1) Mass balance 2)Momentum balance Wall state
Blood flow circulation model 1) Mass balance 2)Momentum balance Wall state 3)Bifurcations
Blood flow circulation model 1) Mass balance 2)Momentum balance Wall state 3)Bifurcations
Blood flow circulation model 1) Mass balance 2)Momentum balance Wall state 3)Bifurcations
Blood flow circulation model 1) Mass balance 2)Momentum balance Wall state 3)Bifurcations Compatibility conditions
Blood flow circulation model 1) Mass balance 2)Momentum balance Wall state 3)Bifurcations Compatibility conditions
Blood flow circulation model 1) Mass balance 2)Momentum balance Wall state 3)Bifurcations 4)Numerical method
Gaussian pulse Straight long vessel Left boundary Right boundary - no reflection
Gaussian pulse Discontinuous Galerkin
Gaussian pulse Locally Conservative Galerkin
Gaussian pulse Discontinuous Galerkin Locally Conservative Galerkin
Gaussian pulse Grid Characteristic 1st order Grid Characteristic 2nd order
Gaussian pulse Grid Characteristic 1st order Grid Characteristic 2nd order
Gaussian pulse Grid Characteristic 1st order Grid Characteristic 2nd order
Gaussian pulse. Amplitude Grid Characteristic 2nd order (exponent) Grid Characteristic 2nd order (sqrt)
Gaussian pulse. Distance traveled Grid Characteristic 2nd order (exponent) Grid Characteristic 2nd order (sqrt) Discontinuous Galerkin (sqrt)
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)
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
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
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
\Silicon-tube model Koen S. Matthys, JordiAlastruey, JoaquimPeiro, et. al., 2007 Inlet: Q=Q(t) Outlets: R
\Thoracic aorta (15) GC Exp GC Exp Q, ml/s P, kPa Time, s Time, s
Right carotid (3) DG • GC 1st
Discussion • Variety of 1d models • Different methods, wall state equations, etc. • Toro, Muller