Usefulness of velocity profiles based on 3D cine PC MR used as boundary conditions for computational fluid dynamics of an intracranial aneurysm : investigation with the aid of simulated data set Haruo Isoda 1, Yuki Onishi 2, Yasuo Takehara 3, Toshiyasu Shimizu 4, Kohei Aoki 2, Takashi Kosugi 4, Kenji Amaya 2, Harumi Sakahara 5 1 Department of Radiological and Medical Laboratory Sciences, Nagoya University Graduate School of Medicine, Nagoya, Japan 2 Department of Mechanical and Environmental Informatics, Tokyo Institute of Technology, Graduate School of Information Science and Engineering, Tokyo, Japan; 3 Department of Radiology, Hamamatsu University Hospital, Hamamatsu, Japan; 4 Renaissance of Technology Corporation, Hamamatsu, Japan; 5 Department of Radiology, Hamamatsu University School of Medicine, Hamamatsu, Japan BACKGROUND Hemodynamics, especially wall shear stress (WSS), plays a v ery important role in the initiation, progression and rupture of intracranial aneurysms. Human hemodynamic analysis mainly includes MR fluid dyn amics (MRFD) based on 3D cine phase-contrast MR imaging and Computational fluid dynamics (CFD). They have several merits and deficits. MR-based CFD, which uses flow information of 3D cine PC MR as boundary conditions, provides us with intracranial an eurysmal hemodynamics with high spatial resolution and hi gh temporal resolution. However, adequate inlet region len gth can not be obtained, because imaging slab of 3D cine P C MR is limited due to relatively longer imaging time. Inlet velocity profile boundary conditions (BC) or flow volu me BC are thought to affect the results of MR-based CFD. PURPOSE

The purpose of our study was to perform CFD with v elocity profile inlet BC and flow volume inlet BC wit h the aid of simulated 3D cine PC MR data set of an i ntracranial aneurysm, and to compare velocities, str eamlines and WSS obtained from the two types of C FD, using the true 3D data set as a gold standard. Materials and Methods CFD STL data from digital angiogram (DA) of a lt. IC-PC aneurysm with a 15mm diameter obtained from 70 year old pt. with SAH Calculation condition Blood density: 1054[kg/m3] Blood viscosity: 0.00384[kg/(m s)] Inlet boundary condition: flow volume, 0.003[kg/s] Outlet boundary condition: Pressure, 0[Pa] Newtonian fluid Steady flow Non-slip boundary condition Vascular wall: rigid Volume corrected velocity profile inlet BC

Velocity profile Flow volume outlet BC + Gaussian noise CFD Flow volume for 10 sections each 3 segments CFD with volume corrected velocity profile inlet BC Calculation domain Flow volume information CFD Flow volume inlet and outlet BC Simulated 3D cine PC MR data

Gold standard Elongation of inlet region Calculation domain Overview of this study CFD with flow volume inlet BC Comparison Flow vector Streamlines WSS CFD STL data from digital angiogram (DA) of a lt. IC-PC aneurysm with a 15mm diameter obtained from 70 year old pt. with SAH Calculation condition Blood density: 1054[kg/m3] Blood viscosity: 0.00384[kg/(m s)] Inlet boundary condition: flow volume, 0.003[kg/s] Outlet boundary condition: Pressure, 0[Pa] Newtonian fluid

Steady flow Non-slip boundary condition Vascular wall: rigid Volume corrected velocity profile inlet BC Velocity profile Flow volume outlet BC + Gaussian noise CFD Flow volume for 10 sections each 3 segments CFD with volume corrected velocity profile inlet BC Calculation domain Flow volume information

CFD Flow volume inlet and outlet BC Simulated 3D cine PC MR data Gold standard Elongation of inlet region Calculation domain Overview of this study CFD with flow volume inlet BC Comparison Flow vector Streamlines WSS CFD STL data from digital angiogram (DA) of a lt. IC-PC aneurysm with a 15mm diameter obtained from 70 year old pt. with SAH

Calculation condition Blood density: 1054[kg/m3] Blood viscosity: 0.00384[kg/(m s)] Inlet boundary condition: flow volume, 0.003[kg/s] Outlet boundary condition: Pressure, 0[Pa] Newtonian fluid Steady flow Non-slip boundary condition Vascular wall: rigid Volume corrected velocity profile inlet BC Velocity profile Flow volume outlet BC + Gaussian noise CFD Flow volume for 10 sections each 3 segments CFD with volume corrected

velocity profile inlet BC Calculation domain Flow volume information CFD Flow volume inlet and outlet BC Simulated 3D cine PC MR data Gold standard Elongation of inlet region Calculation domain Overview of this study CFD with flow volume inlet BC Comparison Flow vector Streamlines WSS

CFD STL data from digital angiogram (DA) of a lt. IC-PC aneurysm with a 15mm diameter obtained from 70 year old pt. with SAH Calculation condition Blood density: 1054[kg/m3] Blood viscosity: 0.00384[kg/(m s)] Inlet boundary condition: flow volume, 0.003[kg/s] Outlet boundary condition: Pressure, 0[Pa] Newtonian fluid Steady flow Non-slip boundary condition Vascular wall: rigid Volume corrected velocity profile inlet BC Velocity profile Flow volume outlet BC + Gaussian noise

CFD Flow volume for 10 sections each 3 segments CFD with volume corrected velocity profile inlet BC Calculation domain Flow volume information CFD Flow volume inlet and outlet BC Simulated 3D cine PC MR data Gold standard Elongation of inlet region Calculation domain Overview of this study

CFD with flow volume inlet BC Comparison Flow vector Streamlines WSS CFD STL data from digital angiogram (DA) of a lt. IC-PC aneurysm with a 15mm diameter obtained from 70 year old pt. with SAH Calculation condition Blood density: 1054[kg/m3] Blood viscosity: 0.00384[kg/(m s)] Inlet boundary condition: flow volume, 0.003[kg/s] Outlet boundary condition: Pressure, 0[Pa] Newtonian fluid Steady flow Non-slip boundary condition Vascular wall: rigid Volume corrected velocity profile inlet BC

Velocity profile Flow volume outlet BC + Gaussian noise CFD Flow volume for 10 sections each 3 segments CFD with volume corrected velocity profile inlet BC Calculation domain Flow volume information CFD Flow volume inlet and outlet BC Simulated 3D cine PC MR data

Gold standard Elongation of inlet region Calculation domain Overview of this study CFD with flow volume inlet BC Comparison Flow vector Streamlines WSS CFD STL data from digital angiogram (DA) of a lt. IC-PC aneurysm with a 15mm diameter obtained from 70 year old pt. with SAH Calculation condition Blood density: 1054[kg/m3] Blood viscosity: 0.00384[kg/(m s)] Inlet boundary condition: flow volume, 0.003[kg/s] Outlet boundary condition: Pressure, 0[Pa]

Newtonian fluid Steady flow Non-slip boundary condition Vascular wall: rigid Volume corrected velocity profile inlet BC Velocity profile Flow volume outlet BC + Gaussian noise CFD Flow volume for 10 sections each 3 segments CFD with volume corrected velocity profile inlet BC Calculation domain Flow volume information

CFD Flow volume inlet and outlet BC Simulated 3D cine PC MR data Gold standard Elongation of inlet region Calculation domain Overview of this study CFD with flow volume inlet BC Comparison Flow vector Streamlines WSS CFD STL data from digital angiogram (DA) of a lt. IC-PC aneurysm with a 15mm diameter obtained from 70 year old pt. with SAH

Calculation condition Blood density: 1054[kg/m3] Blood viscosity: 0.00384[kg/(m s)] Inlet boundary condition: flow volume, 0.003[kg/s] Outlet boundary condition: Pressure, 0[Pa] Newtonian fluid Steady flow Non-slip boundary condition Vascular wall: rigid Volume corrected velocity profile inlet BC Velocity profile Flow volume outlet BC + Gaussian noise CFD Flow volume for 10 sections each 3 segments CFD with volume

corrected velocity profile inlet BC Calculation domain Flow volume information CFD Flow volume inlet and outlet BC Simulated 3D cine PC MR data Gold standard Elongation of inlet region Calculation domain Overview of this study CFD with flow volume inlet BC Comparison Flow vector Streamlines

WSS RESULTS 1 Gold standard CFD with flow volume corrected velocity profile inlet BC CFD with flow volume inlet BC Comparison of velocity vector maps RESULTS 2 A B Gold standard A B CFD with flow volume corrected velocity profile inlet BC CFD with flow volume inlet BC Comparison of flow velocities at the inl et and at the portion 11mm down stre

am from the inlet REAULTS 3 Subtraction vector map of CFD with flow volume corrected flow velocity inlet BC from Gold standard Subtraction vector map of CFD with flow volume inlet BC from Gold standard Comparison of the velocity differences betwe en two types of CFD and gold standard RESULTS 4 Correlation coefficients in three velocity components X: 0.999317 Y: 0.996258 Z: 0.995104 CFD (mm/s) CFD (mm/s) Correlation coefficients in three velocity components X: 0.99929 Y: 0.999175 Z: 0.998979 Gold standard (mm/s)

Correlation chart between gold standard and CFD with flow volume corrected velocity profile inlet BC Gold standard (mm/s) Correlation chart between gold standard and CFD with flow volume inlet BC Comparison of correlation coefficients of velocities in in thre e velocity components between gold standard and two type s of CFD RESULTS 5 Correlation coefficient in vector length, 0.998213 CFD (mm/s) CFD (mm/s) Correlation coefficient in vector length, 0.992992 Gold standard (mm/s) Correlation chart between gold standard and CFD with flow volume corrected velocity profile inlet BC Gold standard (mm/s) Correlation chart between gold standard and CFD with flow volume inlet BC

Comparison of correlation coefficients of vector length bet ween gold standard and two types of CFD Number of vector point RESULTS 6 Angle difference (degrees) Angle differences of vectors of two types of CFD from those of gold standard at each corresponding point RESULTS 7 Gold standard CFD with flow volume corrected velocity profile inlet BC CFD with flow volume inlet BC Comparison of streamlines RESULTS 8 Gold standard CFD with flow volume corrected velocity profile inlet BC

Comparison of WSS CFD with flow volume inlet BC RESULTS 9 Correlation coefficient in WSS of the intracranial aneurysm, 0.981925 CFD CFD Correlation coefficient in WSS of the intracranial aneurysm, 0.995496 Gold standard Correlation chart between gold standard and CFD with flow volume corrected velocity profile inlet BC Gold standard Correlation chart between gold standard and CFD with flow volume inlet BC Comparison of correlation coefficients in WSS of the intracra nial aneurysm between gold standard and two types of CFD RESULTS 10 Correlation coefficient

in WSS of the parent artery, 0.952791 CFD CFD Correlation coefficient in WSS of the parent artery, 0.996069 Gold standard Correlation chart between gold standard and CFD with flow volume corrected velocity profile inlet BC Gold standard Correlation chart between gold standard and CFD with flow volume inlet BC Comparison of correlation coefficients in WSS of the parent artery betwee n gold standard and two types of CFD DISCUSSION 1 In practical MR-based CFD, adequate inlet regio n length can not be obtained, because imaging s lab of 3D cine PC MR is limited due to relatively l onger imaging time. In this simulation study, CFD with flow volume c orrected velocity profile inlet BC was superior to CFD with flow volume inlet BC for accurate veloc ity vectors and WSS in and around the aneurys m.

DISCUSSION 2 There were several limitations in this study. Number of patients and the location of the inlet was limited. Not pulsatile flow but steady flow Intracranial aneurysmal geometry for simulated MR-based CFD calculation in this study was the sa me as the true geometry used for Gold standard. In practical CFD, we usually cant help but use diff erent geometry from true vascular shape. We tho ught that such geometric differences from the tru e may affect the CFD results much more than bou ndary conditions. CONCLUSION CFD with flow volume corrected velocity profile inl et BC was superior to CFD with flow volume inlet B C in this simulation study for an intracranial aneury sm. Therefore, flow volume corrected velocity pro file inlet BC should be used for MR-based CFD of int racranial aneurysms. According to our results, we can obtain accurate 3D velocity vector fields from MR-based CFD using flo w volume corrected velocity profile inlet BC, where as 3D cine PC MR data sets from the human body c ontain errors.