Outline

1. NUMERICAL MODELLING OF PULSE WAVE PROPAGATION IN THE CARDIOVASCULAR SYSTEMJordi AlastrueyDepartments of Aeronautics & BioengineeringImperial College London, U.K.

2. Study of the compensatory ability of the complete circle of Willis and its most frequent anatomical variations to compensate for occlusions of the inflow arteries. www.health.allrefer.com Outline 1. Formulation 2. Validation 3. Clinical application:

3. The 1-D model

4. 1-D Governing equations of incompressible & Newtonian fluid within an elastic tube Governing equations Conservation of mass Conservation of momentum Tube law

5. System of hyperbolic equations. • Discontinuous Galerkin scheme with a spectral/hp spatial discretisation and a second-order Adams-Bashforth time-integration. • Solution of Riemann problems at interfaces within each artery and at the boundaries, including the bifurcations. • For further details: Numerical solution Sherwin et al (2003), J. Eng. Math., 47, 217-250

6. Validation of the model

7. Ghent Imperial Arterial Network Test P. Segers & P. Verdonck University of Ghent, Belgium K.H. Parker, J. Peiró, S.J. Sherwin, K. Matthys & J. Alastruey Imperial College London, U.K. A.W. Khir Brunel University, U.K.

8. Experimental set up • 1:1 replica of the 37 largest conduit arteries. • Arteries made of silicon. • Blood: mixture of water and glycerol.

9. Experimental set up • 1:1 replica of the 37 largest conduit arteries. • Arteries made of silicon. • Blood: mixture of water and glycerol.

10. Experimental set up • 1:1 replica of the 37 largest conduit arteries. • Arteries made of silicon. • Blood: mixture of water and glycerol.

11. Experimental set up • 1:1 replica of the 37 largest conduit arteries. • Arteries made of silicon. • Blood: mixture of water and glycerol.

12. E = 1.2 MPa Geometry & elasticity for the 1-D simulation • Diameters and wall thicknesses measured using a micro screw after having dissected the model. • Lengths measured with a ruler. • Elastic modulus determined from an extension test. Stress (Pa) Working range Strain

13. Input boundary condition • Harvard pulsatile pump at the inlet of the ascending aorta. 3.1 l/min, 70 beats/min systole/diastole = 35/65 • Approximated by the first 20 harmonics.

14. Output boundary conditions • Resistance elements consisting of a stiff tube (Ø = 2mm) connected to an overflow reservoir. • 16 terminal branches

15. Comparison at the aortic arch II

16. Comparison at the abdominal aorta III

17. Comparison at the right iliac-femoral

18. Comparison at the left renal

19. Comparison at the left posterior tibial

20. The circle of Willis

21. The cerebral circulation www.health.allrefer.com ACoA Carotids PCoAs Vertebrals OBJECTIVE: to study the collateral ability of the circle of Willis after occlusion of a carotid or vertebral artery. *

22. The cerebral circulation Lippert and Pabst (1985). Arterial variations in man. Bergmann www.health.allrefer.com ACoA Carotids PCoAs Vertebrals *

23. Velocity in MCA www.health.allrefer.com Normal conditions ACA ACoA Velocity in the cerebral arteries MCA PCoAs PCA

24. www.health.allrefer.com Normal conditions ACA ACoA Velocity in the cerebral arteries MCA PCoAs PCA • The system does not require the collateral pathways through the communicating arteries to adequately perfuse the brain in normal conditions and in anatomical variations involving the communicating arteries.

25. Carotid occluded www.health.allrefer.com Normal conditions ACA ACoA Velocity in the cerebral arteries MCA PCoAs PCA • The communicating arteries become important to maintain sufficient brain perfusion in cases of missing ACA (A1) or PCA (P1) or when a carotid or vertebral artery is occluded.

26. Lippert and Pabst (1985). Arterial variations in man. Bergmann www.health.allrefer.com ACA • The occlusion of a vertebral artery is less critical than the occlusion of an internal carotid artery, even in the PCAs. ACoA Mean cerebral outflows MCA PCoAs PCA • If an ICA is occluded, the absence of the ACoA is more critical than the absence of both PCoAs. • The worst scenario is a configuration without the first segment of an ACA combined with an occlusion of the contra lateral ICA. 16.4

27. Conclusions • The 1-D formulation is able to accurately capture the main features of pulse wave propagation in the experimental set up (measured parameters, not fitted!). • This work has increased our confidence in applying the 1-D formulation to clinically relevant studies, but has also shown its limitations: very sensitive to the calibre of the arteries, to the elastic modulus, and the boundary conditions. • The model of the circle of Willis allows us to understand blood flow patterns and distributions throughout the brain. • If used with patient-specific data, it can predict the haemodynamic effect of clinical interventions such as carotid endarterectomy, angioplasty and stenting. • Simulation of local flows in detail if coupled to a 3-D simulation.

28. Acknowledgements Dr. K. Matthys Prof. K.H. Parker Dr. J. Peiró Prof. S.J. Sherwin Prof. P. Segers Prof. P. Verdonck Dr. A. Khir Technical staff at Ghent University EU grant HPRN-CT-2002-00270

29. Pressure & Flow measurements • Pressures measured with micro-tip catheter transducers and flows with ultrasonic flow probes at about 70 locations. Micro-tip catheter Ultrasonic flow probe

30. Comparison at the ascending aorta

31. Mean cerebral outflows

32. Lippert and Pabst (1985). Arterial variations in man. Bergmann www.health.allrefer.com Velocity in the ACoA (normal conditions) ACA ACoA Non-invasive detection of anatomies MCA PCoA PCA Velocity in the left PCoA (normal conditions) 16.4