MODEL STUDIES OF BLOOD FLOW IN BASILAR ARTERY WITH 3D LASER DOPPLER ANEMOMETER Biomedical Engineering Sergey Frolov, Tambov State Technical University, Russia Sergey Sindeev, Tambov State Technical University, Russia Dieter Liepsch, Munich University of Applied Sciences, Germany Andrea Balasso, Technical University of Munich, Germany Sergey Proskurin, Tambov State Technical University, Russia Anton Potlov, Tambov State Technical University, Russia

Актуальность Brain aneurysm suffers 3-5 % of adult population Topicality More then 60 % die from ruptured aneurysm (stroke) Biomedical Engineering

Aneurysm Кафедра «Биомедицинская техника» Protrusion of the arterial wall due to its stretching or thinning Biomedical Engineering

Current state Causes of aneurysm development and growth are not fully studied Researchers suggest that key role in aneurysm development play violation of local and global hemodynamics Biomedical Engineering

Flow-diverters Problem of choice Biomedical Engineering

Morphology «classic» ≈ % cases deviations Biomedical Engineering

Multiscale model of basilar artery hemodynamics Biomedical Engineering

Multiscale model of basilar artery hemodynamics Biomedical Engineering

Compartments of cardiovascular system Cardiovascular system is a set of compartments (elastic chambers) Every chamber is characterized by blood volume in it and pressure Link between chambers is characterized by blood flow Biomedical Engineering

0D model 14 chamber model Pulsating heart Heart as a source of pressure Valves with backflow Flow inertia Biomedical Engineering

System of global hemodynamics simulation (bmt.tstu.ru/cvs) Biomedical Engineering

Link «Left ventricle – aorta» Biomedical Engineering

Multiscale model of basilar artery hemodynamics Biomedical Engineering

1D model №Artery№ 1Ascending aorta25Left carotid 2Aortic arch 126Right carotid 3Aortic arch 227Left external carotid 4Thoracic aorta 128Right external carotid 5Thoracic aorta 229Right vertebral 6Abdominal aorta A30Left vertebral 7Intercostals31Right internal carotid 1 8Coelic32Left internal carotid 9Gastric33Basilar 10Splenic34Right posterior cerebral artery1 11Hepatic35Left posterior cerebral artery 1 12Left subclavian 136Right posterior cerebral artery 2 13Left subclavian 237Right posterior communicating artery 14Left radius 138Right internal carotid 2 15Left ulnar 139Right middle cerebral artery 16Left ulnar 240Right anterior cerebral artery 1 17Left interosseous41Right anterior cerebral artery 2 18Brachiocephalicus42Anterior communicating artery 19Right subclavian 143Right brachial 20Right subclavian 244Left anterior cerebral artery 1 21Right radius45Left middle cerebral artery 22Right ulnar 146Left internal carotid 2 23Right interosseous47Left posterior communicating artery 24Right ulnar 248Left posterior cerebral artery 2 Biomedical Engineering

Approach Arterial tree is a set of elementary regions Number of elementary regions may be N>48 Number of equations is 3*N Biomedical Engineering

Festdaten 1212 i-2i-1 i i+1 i+2 i – elementary region; Elasticity; Inertia; Resistance; Unstrained volume; Stiffness [mmHg/ sm 3 ]; [mmHg*s 2 / sm 2 ]; [Тоrr *s / sm 2 ]; [sm 3 ]; Conductivity; Length; Cross sectional area Volume;[sm 3 ]; Pressure; [mmHg]; Blood flow;[sm 3 /s]; Parameters Functions Approach Biomedical Engineering

Multiscale model of basilar artery hemodynamics Biomedical Engineering

3D model Navier-Stokes equations Continuity equation Boundary conditions Initial conditions Biomedical Engineering

Parallel computing 8 parts Domain Decomposition Computational mesh spits on N parts. Every part is computed by it’s own thread Technology: MPI + OpenMP Programming language: С++ Libraries: Intel MKL, Trilinos, LifeV Solver: GMRES Preconditioner: Domain Decomposition Timestep: s. Precision: 1e-10 Problem of choice of number N*, that T min Biomedical Engineering

3D model of bifurcations Geometrical model PressureVelocity field Velocity profileVelocity Biomedical Engineering

Experimental setup 3D Laser Doppler Anemometer measure blood velocity in elastic vessel model. It gives opportunity to estimate stent influence on blood flow Biomedical Engineering

Principle of LDA Biomedical Engineering Signal conditioner Flow Signal Processing unit: Laser HeNe Photomultiplier PC

Measurements Biomedical Engineering The flow velocity is measured with a 1-component laser Doppler anemometer system equipped with a 5mW He-Ne laser with a wavelength of 632.8nm. The laser Doppler anemometer does not disturb the flow and is not affected by temperature, pressure or fluid density. It offers a high spatial (focus point less than 70 µm) and temporal (1ms) resolution. Velocity measurements are performed in the model at different cross sections allowing a 2D or a 3D-flow-reconstruction.

Measurements Biomedical Engineering Blood cannot be used as a fluid for LDA measurements, because the laser light is absorbed by the red cells. The model fluid have a similar flow behavior as blood, a refraction index of n =1.41 to match the refraction index of the silicon rubber model wall. The fluid and the model wall have to be transparent so that the laser beam can pass undisturbed the medium. A 58% aqueous glycerol mixture with Separan AP45 and Separan AP302 (a macromolecular polyacrylamide) with a dynamic viscosity of 8mPas is used. The mixture shows viscoelastic flow behavior similar to the non-Newtonian characteristics of blood.

Realistic vessel model Biomedical Engineering

Scheme of experimental setup An overflow chamber (3) filled with the perfusion mixture gives the constant inflow pressure to the model (10). A computer-controlled piston pump (1) superimposes a dynamic pressure gradient needed to obtain systolic and diastolic pressures in the inflow section of 80 mmHg and 145 mmHg respectively. Pressure transducers (9) monitor the amplitude and frequency of the pulse wave. The outflow of the model is connected to a reservoir of variable height (11) to allow control of the flow volume. Biomedical Engineering

Thanks for attention Biomedical Engineering