1. 1 Mathematical modeling of blood flow in translational medicine (1) Moscow Institute of Physics and Technology (2) Institute of Numerical Mathematics Workgroup on modelling blood flow and vascular diseases Simakov Sergey 1,2 7th Conference on Mathematical Modelling and Computational Methods in Biomathematics Moscow, INM RAS, 30.10.2015 The work was supported by Russian Science Foundation Grant No 14-31-00024 (New Laboratories)

2. 2 1D Systemic Blood Flow Model

3. 3 Global blood flow 1) Mass balance 2) Momentum balance 3) Junctions 3.1 3.2a 2a) 2b) 3.2b 3.2c

4. 4 Vessel wall elasticity Pedley, Luo, 1998 Modelling Analytic approximation Yu. Vassilevski, S Simakov, V. Salamatova, T. Dobroserdova, Blood Flow Simulation in Atherosclerotic Vascular Network Using Fiber-Spring Representation of Diseased Wall, Math. Mod. In Nat. Phenom., 6(5):333-349, 2011

5. 5 Wall elasticity adaptation to average pressure T T Physiological conditions: autoregulation Mechanism: shear stress NO production endothelial layer permeability

6. 6 Gravity and Autoregulation S S Head Leg Auotregulation Collapsible tube

7. 7 Biomedical Applications: Angiosurgery Enchanced External Counterpulsation Fractional Flow Reserve Cerebral Flow

8. 8 Angiosurgery (stenting)

9. 9 Vascular surgery: stenosis treatment MRI/CT Ultrasound dopplerography Computational model: 1D vascular structure Functional parameters fitting (elasticity, resistance) Simulations

10. 10 Stenosis treatment: boundary conditions and identification Boundary conditions Input (arteries): Output (veins): Parameters identification Ultrasound measurements (before surgery!) Angles between vessels at bifurcations Large vessels – rigid walls, small vessels – more elastic Occlusion – decreased lumen, high resistance

11. 11 Stenosis treatment: 1D vascular domain reconstruction

12. 12 Stenosis treatment Patient-specific MRI and Doppler ultrasound data thanks to I.M. Sechenov First Moscow State Medical University (Ph.Kopylov, et.al.) S.Simakov, T.Gamilov, Yu.Vassilevskii, Yu.Ivanov, P.Kopylov, Patient specific haemodynamics modeling after occlusion treatment in leg, Mat. Mod. Nat. Phen, 2014

13. 13 Enhanced External Counterpulsation (EECP)

14. 14 EECP review Ischemia Arterial Hypertension Cardiovascular insufficiency Indications Risk factors Aneurisms rupture Atherosclerotic plaques rupture Varicose veins Individual EECP strategy is required!!!

15. 15 A B C EECP model Wall state equation Cardiac cycle 0 1 systole diastole

16. 16 Patient-specific EECP treatment simulations

17. 17 EECP optimization: sensitivity analysis Impact of myocardial pressureImpact of arterial stiffness Impact of autoregulation response rate T.Gamilov, S.Simakov, Modelling of coronary flow stimulation by enchanced external counterpulsation, Int. J. Num. Met. Biomed. Eng (under review)

18. 18 Virtual Fractional Flow Reserve Assesment

19. 19 Fractional Flow Reserve Review endovascular intervention expensive transducer Solution: Virtual FFR assessment basing on non-invasively collected data (CT scans, systolic/diastolic pressure, heart rate …) Clinical measurements require F.Yu. Kopylov, A.A. Bykova, Yu. V. Vassilevskii, S.S. Simakov, Role of measurement of fractional flow reserve in coronary artery atherosclerosis, Terapevticheskii Arkhiv, 87(9):106-113, 2015

20. 20 Fractional Flow Reserve 1D vascular domain reconstruction

21. 21 Fractional Flow Reserve T.Gamilov, Ph. Kopylov, R. Pryamonosov, S.Simakov, Virtual fractional flow reserve assessment in patient-specific coronary networks by 1D haemodynamic model, Russ. J. Num. Anal. Math. Mod., 2015

22. 22 Cerebral Flow: Carotid Stenosis Treatment

23. 23 Cerebral Flow 1D vascular domain reconstruction Patient APatient B

24. 24 Cerebral Flow LeftRight model (cm/s) measured (cm/s) error (%) model (cm/s) measured (cm/s) error (%) Patient A Common Carotid Art. (No 26, 3) 5055951545,5 Internal Carotid Art. (No 27, 86) 7267724022010 Patient B Common Carotid Art. (No 13, 36) 51581260567 Internal Carotid Art. (No 19, 28) 130963558555 Before treatment (with stenosis)

25. 25 Cerebral Flow After treatment (stenting) Vessel's indexVelocity, cm/s Patient APatient BPatient APatient BNorm Common Carotid Art.3, 262, 13605950-104 Internal Carotid Art.27, 8619, 28486032-100 External Carotid Art.74-75, 12-1329-31, 14-16609037-105 Vertebral Art.42, 555, 10503520-61 Subcluvian Art.54-52-50, 56-60-6440, 3-4, 41-43-46989560-150

26. 26 Conclusions Adequate tool for local and systemic blood flow analysis is developed Successful patient-specific simulations cover Femoral artery stenting EECP impact to the blood flow Virtual FFR assessment Carotid artery stenting Full automatization of the presented algorithm and validation with more clinical cases are required to translate this research to the bedside

27. 27 Thank You!