1. Numerical modelling of affected zone for cerebral aneurysm A.A.Cherevko, A.P.Chupakhin, A.L.Krivoshapkin, A.K.Khe, K.Y.Orlov, P.A.Seleznev Lavrentyev Institute of Hydrodynamics SB RAS Meshalkin Novosibirsk Scientific Research Institute of Circulation Pathology 6th Russian workshop on mathematical models and numerical methods in biomathematics

2. Outline Purposes and stages of work Medical information 3D-reconstruction of the cerebral vascular system Hemodynamic modeling Assessment of the region of influence of the aneurysm on hydrodynamic characteristics Determination of influence on the aneurysm high blood pressure ( Hypertension) and low blood pressure (Hypotension)

3. Stages of work 3D- geometric reconstruction of circulation of the cerebral vascular system with and without aneurysm based on tomograms (data from Meshalkin Novosibirsk Scientific Research Institute of Circulation Pathology ) Hemodynamic modeling based on the software package ANSYS-CFX using the 3D- geometric reconstruction Assessment of the region of influence of the aneurysm on hydrodynamic characteristics. Determination of pressure’s influence on the aneurysm (high blood pressure and low blood pressure) Purposes

4. An aneurysm is a weak area in the wall of a blood vessel that causes the blood vessel to bulge or balloon out. Locations of aneurysm’s appearance :arterial bifurcations, space of anatomical changes of vessel’s structure, arteriovenous malformations. The major factors: structural changes in the arteries, hemodynamics, wall biomechanics. A person may have an aneurysm without having any symptoms Symptoms : double vision,loss of vision,headaches,eye pain,neck pain,stiff neck Repair an aneurysm: Clipping and endovascular repair is most often done. It usually involves a "coil" or coiling, this is a less invasive way to treat some aneurysms.

5. Benchmark data – Computed tomography (CT) and magnetic resonance imaging (MRI) scans of the brain Thickness- 0.8 mm, amount of scans-150 for each model Reconstruction of two models of the cerebral vascular system with aneurysm on Middle cerebral artery(model А) Anterior communicating artery’s bifurcation(model В). Size of each aneurysm is about 4 mm. 3D-reconstruction

6. Seg3D и ITK-SNAP RESAMPLE tool to change and improve the resolution of the tomograms in SEG 3D program ITK-Snap program to build 3D-geometry of the cerebral vascular system with aneurysms

7. ITK-SNAP The methodology behind SNAP is called snake evolution. The term snake is used to refer to a closed curve (or surface in 3D) that represents a segmentation. In snake evolution methods, the snake evolves from a very rough estimate of the anatomical structure of interest to a very close approximation of the structure, as illustrated in the figure below Уравнение построения фронта(змеи):,where α –propagation coefficient β – curvature coefficient к - curvature - luminance - velocity of spreading

8. Reconstructed 3D-Model before smoothing Specific layered features. Possibly presence of artifacts – excess parts which are not vessels and also splicing of vessels

9. Final 3D-Model with aneurysm Model A Aneurysm on the Middle cerebral artery Model B Aneurysm on the Anterior communicating artery’s bifurcation

10. Final 3D-Model without aneurysm Model A Without Aneurysm on the Middle cerebral artery Model B Without Aneurysm on the Anterior communicating artery’s bifurcation

11. The main stage of work- hydrodynamic calculation - ANSYS CFX software which consists of six components that take a geometry and mesh and pass the information required to perform a hydrodynamic analysis Hemodynamic modeling. ANSYS-CFX

12. The mesh consists of tetrahedrons. The mesh is automatically refined based on geometry curvature. This will result in larger elements on flat planar surfaces and smaller elements in areas of high curvature. Model A: quantity of nodes- 195226, quantity of elements– 1019089. Model B: quantity of nodes - 208691, quantity of elements - 1070303. Mesh generation with aneurysm CFX — Meshing (ANSYS ICEM CFD) AB

13. Mesh generation without aneurysm CFX — Meshing (ANSYS ICEM CFD) Model A : quantity of nodes - 18754, quantity of elements - 990567 Model B : quantity of nodes -196536, quantity of elements-1006249, B

14. Mathematical Statement of the Problem Blood flow described by the Navier-Stokes equations for three-dimensional motion of an incompressible, viscous Newtonian fluid where v - velocity, p - pressure, ν - the kinematic viscosity, Ω - the internal volume of the computational domain, including the configuration of the vessels in the form of the tee and the aneurysm. γ = ∂ Ω - boundary wall of the vessel. Boundary conditions: Where and - velocity and pressure -

15. Computational area. Steady State ANSYS CFX — Pre. Model А Diameter of the biggest vessel is 5 mm (Input), Diameter of the smallest - 1,02 mm (Output2) Boundary Conditions: V=100 cm/s on Input, P=40 mmHg on Output(3,5), P=35 mmHg on Output4, P=30 mmHg on Output(1,2).

16. Computational area. Steady State ANSYS CFX — Pre. Model В Diameter of the biggest vessel is 4,87 mm (InputRight), Diameter of the smallest - 0,412 mm (OutputRight2). Boundary Conditions: v=100 cm/s on InputLeft, InputRight, P=40mmHg on OutputLeft1, OutputRight1, P=35mmHg on OutputLeft(2,31,31), OutputRight(2,3), P=30mmHg on OutputLeft4, OutputRight4

17. Assessment of the area of influence of the aneurysm on hydrodynamic characteristics

18. Comparative analysis Allocation of pressure for Model A Variations in the pressure are not observed(1,19% with respect to maximum value). Point of max value moves on 2,6 mm, min – 2.8 mm

19. Comparative analysis Allocation of pressure for Model B Variations ~2%, point of max value moves on 3 mm, min – 2.4 mm

20. Comparative analysis Allocation of velocity for Model A Variations - 20 cm/s (6% with respect to maximum value) in the region of the location of the aneurysm. Point of max value moves on 4.6 mm, min – 1.4 mm

21. Variations in velocity is small (4% with respect to maximum value), point of max value moves on 5.1 mm, point of min value remains at the same location Comparative analysis Allocation of velocity for Model B

22. Comparative analysis Allocation of wall shear stress (WSS) for Model A Little changes (≈6%) about 0-0,2 mm Hg. Point of max value moves on 5.2 mm, min – 4.6 mm

23. Changes are not observed, point of max value move on 5.7 mm, min - 5 mm Comparative analysis Allocation of wall shear stress (WSS) for Model B

24. ∆maxDistance(mm) Pressuremm Hg1.2365 (1,19%)2.6345 Velocitycm/s16.904 (5,5%)4.6423 WSSmm Hg0.03 (0,96%)5.2397 ∆minDistance(mm) Pressuremm Hg2.8991 (2,81%)2.8523 Velocitycm/s2.68359 (0,88%)1.4523 WSSmm Hg0.07 (2,25%)4.6324 Model A Changes for max and min values in the cerebral vascular system with and without aneurysm Distance is length between points with max value (or min value) on the cerebral vascular system with and without aneurysm

25. ∆maxDistance(mm) Pressuremm Hg1.5207 (1,83%)2.9944 Velocitycm/s14.811 (4,61%)5.1318 WSSmm Hg0.05 (2,9%)5.6795 ∆minDistance(mm) Pressuremm Hg0.9074 (1,09%)2.493 Velocitycm/s6.48087 (1,99%)0.7345 WSSmm Hg0.02 (1,17%)5.0148 Model B

26. Pressure Velocity WSS Distance is length between points with max value (or min value) on the cerebral vascular system with and without aneurysm

27. Summary points Uniform pressure distribution for models with aneurysm; Velocity and pressure don’t change in the transition from the model with aneurysm to the model without aneurysm; Influence of the aneurysm on hydrodynamic characteristics is local; Aneurysm affects locally, in the future we can restrict by the area of influence of the aneurysm, which extends to 25 mm along the vessel on both sides of the aneurysm (outside the "zone of influence" of data changes are small).

28. Determination of influence on the aneurysm high blood pressure (hypertension) and low blood pressure (hypotension)

29. Comparative analysis Allocation of pressure for Model A. Modeling hypertension (increase of pressure on outlets on 30%) Pressure increases throughout model. Locally elevated pressure is not observed

30. Allocation of pressure for Model B. Modeling hypertension (increase of pressure on outlets on 30%) Pressure increases throughout model. Locally elevated pressure is not observed Comparative analysis

31. Allocation of velocity for Model А. Modeling hypertension (increase of pressure on outlets on 30%) Flow reconstructs at a distance 4 cm (or 10 diameters of aneurysm) Comparative analysis

32. Allocation of velocity for Model B. Modeling hypertension (increase of pressure on outlets on 30%) Flow reconstructs at a distance 2 cm (or 5 diameters of aneurysm) Comparative analysis Changes of velocity close to the aneurysm are 5-10 cm/s between max values for each model

33. Allocation of wall shear stress (WSS) for Model А. Modeling hypertension( increase of pressure on outlets on 30%) Comparative analysis Changes of WSS close to the aneurysm are not observed

34. Allocation of wall shear stress (WSS) for Model B. Modeling hypertension( increase of pressure on outlets on 30%) Comparative analysis Place of locally elevated WSS near the basis of aneurysm Essential changes of WSS -0.2 mm Hg or 27 Pa (difference 30%)

35. Values of MAX and MIN of important hemodynamic parameters around the aneurysm for Model A Values of basic parameters around the aneurysm Bench mark +30% for values of pressure on outlets -30% for values of pressure on outlets Max WSS (mm Hg)0,5 0,4 Min WSS (mm Hg)0,0030,0040,003 Max velocity (cm/s)130135121 Max pressure (mm Hg)708057 Min pressure (mm Hg)647552

36. Values of MAX and MIN of important hemodynamic parameters around the aneurysm for Model B Values of basic parameters around the aneurysm Bench mark +30% for values of pressure on outlets -30% for values of pressure on outlets Max WSS (mm Hg)1,050,980,9 Min WSS (mm Hg)0,00180,00190,0016 Max velocity (cm/s)146155140 Max pressure (mm Hg)50,35842 Min pressure (mm Hg)35,54430 Linear changes

37. Summary points Little changes of max and min values of WSS WSS is locally elevated close to the aneurysm on the arterial bifurcation Linear changes of pressure on walls of vessel close to the aneurysm (4 mm) and also throughout model Linear changes of max velocity values close to the aneurysm Reconstruction of flow at the distance 4 cm (or 10 diameters of aneurysm) for model A and at the distance 2 cm (or 5 diameters of aneurysm) for model B Modeling of high blood pressure ( Hypertension) and low blood pressure (Hypotension) has shown changes of basic hemodynamic parameters: Make an assumption that aneurysm on arterial bifurcation could be more danger than aneurysm on the vessel’s wall. During modeling of the brain’s vascular system can consider local areas close to the aneurysm (about 10 diameters of aneurysm)

38. Thank you for your attention!

39. ANSYS Geometry Model A of the cerebral vascular system consists of two unconnected parts. It is an anatomical peculiarity of patient.The generate of mesh and the calculation have performed only for the component with aneurysm.