Unsteady hemodynamic simulation of cerebral aneurysms

А.А.Cherevko, А.P.Chupakhin, А.А.Yanchenko ( IGiL SB RAS, NSU)

• Place the appearance of aneurysms: bifurcation of vessels, space anatomical changes structure of vessels, next to the arteriovenous malformation.

• The reasons of occurrence: structural changes in the arteries, hemodynamic factor, mechanical damage of the vessel wall.

• Found in 0.3-5% of the adult population, a rare occurrence in children.

• Aneurysmal wall material differs from the material of a healthy vessel wall.

Aneurysm - a diverticulum the arterial wall due to its stretching

Endovascular treatment of aneurysms

Аневризма

treatment: embolization stenting

riskiness:rupturerecanalization

aneurysm

catheter

Aneurysms hemodynamic modeling

• Preoperative simulation should be carried out quickly enough - 1-2 days

• The most simple and effective model, giving sufficient accuracy • Geometry of aneurysm - tomography data (NNIIPK)

• Flow parameters - intravascular pressure and velocity sensor (NNIIPK )

• CFD calculations – ANSYS (IGiL, NSU computer cluster)

What hemodynamic parameters determine the effectiveness of the operation?

What is the safe range of variation of these parameters?

Stages of work: • Reconstruction of the geometry from the CT scan• Numerical simulation of hemodynamics with fixed walls of the vessel • Simulation of the stress-strain state of the wall using the pressure distribution

obtained in the previous stage of the calculation

Vessel geometry

before after controla year later

Progressive rectification of bifurcation

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 an aneurysm located at the bifurcation. γ = ∂ Ω - boundary wall of the vessel. Boundary conditions:

where vreal and preal - speed and pressure, taken from the sensor during operation.

Гin - cross section of the parent vessel tee; Г1out, Г2out - cross sections of child

vessels

The computational domain (Before surgery)

Clinical velocity and pressure data

Hydrodynamics

computational grid

Used computational grid of tetrahedra. When mesh refinement is 5 times - deviation of pressure is less than 1%, slightly larger deviations (up to 5%) observed in the values of the velocity modulus. Further refinement grid has almost no influence on the result.

streamlines (up to stenting)

High speeds, vorticity within the aneurysm.

Streamlines (after stenting)

Reducing the area of maximum speed. The appearance of "almost circular" vortex.

Streamlines (control a year later)

Weak vorticity, velocity decreased.

WSS (up to stenting)

Clearly visible zones of large WSS on bends (not on the cupola!).

WSS (after stenting)

Zones of large WSS decreased.

WSS (control a year later)

Zone of high stress is very small, almost all within the normal range (1.5-2 Pa).

Energy flux (up to stenting)

Loss of energy flux is ~ 9%, which is quite a large value at longer tee is approximately equal to 2 cm

Energy flux (after stenting)

After surgery, vascular geometry is restored almost to the health and loss constitute ~ 4%.

Energy flux (control a year later)

Energy loss is ~ 1%.

mechanics

wall parameters

vessel aneurysm

Young's modulus 1 МPа 1.2 МPа

Poisson's ratio 0.49 0.49

wall thickness 4,e-4 m 1,e-4 m

Unsteady calculation. Aneurysm's zone has a different properties.

Total deformation and von-Mises stress (up to stenting)

Maxima concentrated on the aneurysm's cupola.Compared with the stationary calculations: maximum deformations slightly

increased. Stress are increased (4.335e5 against 3.0894e5). Localization of maximums is not changed.

Total deformation and von-Mises stress (after stenting)

Maximum values decreased slightly.Compared with the stationary calculations: Localization of maximums is not

changed.

Total deformation and von-Mises stress (control a year later)

The maximum strain decreased by 2 times, the maximum stress at 1/3.

Comparison of simulation results. (Maxima of displacement and von- Mises stress)

before after a year later

Steady 9.3551e-1 mm3.0894e5 Pа

8.2307e-1 mm3.1445e5 Pа

4.6604e-1 mm2.2557e5 Pа

Transient 1.3116 mm4.3346e5 Pa

1.0937 mm4.1624e5 Pa

6.1321e-1 mm2.9726e5 Pa

1 mm Hg = 133.322 Pа

conclusions

• Maxima of stresses and displacements in the steady and unsteady calculations based differ in magnitude, but do not differ by location.

• To identify "dangerous places" stationary calculation with allocation of area of the aneurysm can be used.

• To find the magnitudes of stresses and displacements need to use unsteady calculations with allocation of area of the aneurysm.

• Unsteady calculation without separation zone of the aneurysm is not sufficiently accurate

• Time costs: Steady calculation: a few minutes Transient calculation: 3 hours for 1 simulation

second

Thank you for your attention!