1. Patient-specific Cardiovascular Modeling System using Immersed Boundary Technique Wee-Beng Tay a, Yu-Heng Tseng a, Liang-Yu Lin b, Wen-Yih Tseng c a High Performance Computing & Environmental Fluid Dynamic Laboratory, Department of Atmospheric Sciences, National Taiwan University, Taipei, Taiwan (yhtseng@as.ntu.edu.tw)yhtseng@as.ntu.edu.tw b National Taiwan University Hospital, Taipei, Taiwan c Center for Optoelectronic Biomedicine, National Taiwan University College of Medicine, Taipei, Taiwan * Special thanks to Peskin and Mcqueen for providing the CFD code

2. 3/3/20162 Outlines Introduction Introduction Patient-specific Cardiovascular Modeling System Patient-specific Cardiovascular Modeling System 4-D MRI system 4-D MRI system Numerical methods Numerical methods Results and discussions Results and discussions Conclusion and future work Conclusion and future work

3. 3/3/20163 Introduction Develop a CFD based, patient-specific cardiovascular modeling system Develop a CFD based, patient-specific cardiovascular modeling system Facilitate physicians’ diagnosis at early stage through hybrid CFD simulation and 4-D MRI Facilitate physicians’ diagnosis at early stage through hybrid CFD simulation and 4-D MRI Use Immersed boundary method (IBM) to simulate fluid-elastic interaction of heart Use Immersed boundary method (IBM) to simulate fluid-elastic interaction of heart Investigate the vortex dynamic and effects of reservoir pressure boundary condition (RPBC) on the flows in Left Ventricle (LV) Investigate the vortex dynamic and effects of reservoir pressure boundary condition (RPBC) on the flows in Left Ventricle (LV)

4. 3/3/20164 Patient-specific Cardiovascular Modeling System Methodology Methodology

5. 3/3/20165 Patient-specific Cardiovascular Modeling System 4-D phase contract magnetic resonance imaging (PC-MRI) system 4-D phase contract magnetic resonance imaging (PC-MRI) system –Currently at the National Taiwan University Hospital –Images acquired using an eight-channel phased-array body coil –Time-resolved 3D hemodynamic velocity fields –Allows one to reconstruct the 3D images of the heart over a cardiac cycle –Data comprises of both healthy volunteer as well as patients with cardiac problems for comparison

6. 3/3/20166 Patient-specific Cardiovascular Modeling System Image resolution at 192x256x8 Image resolution at 192x256x8 Extracted slice at z=3, T*=0.2 Extracted slice at z=3, T*=0.2 1T=1 heart cycle

7. 3/3/20167 Numerical Method – IBM Incompressible Navier-Stokes equations Incompressible Navier-Stokes equations (f represents force density) (f represents force density) Interaction between immersed boundary, fluid and boundary forces Interaction between immersed boundary, fluid and boundary forces (Lai and Peskin, 2000)

8. 3/3/20168 Numerical Method - IBM

9. 3/3/20169 Sensitivity of the pressure inflow conditions Reservoir pressure boundary condition (RPBC) Reservoir pressure boundary condition (RPBC) –5 sources of RPBC at (a) superior (b) inferior vena cava (c) pulmonary vein (d) artery (e) aorta

10. 3/3/201610 Sensitivity of the pressure inflow conditions Influence of reservoir pressure boundary condition (RPBC) Influence of reservoir pressure boundary condition (RPBC) –Investigate the effects/impacts of different pressure BC on the simulation results –Study vortex dynamics of left ventricle (LV) RunDescription 1constant RPBC, unmodified 2Similar to Run 1, except that the pulmonary vein (PV) pressure is 25% smaller 3Similar to Run 1, except that the PV pressure is 25% larger 4Varying RPBC, realistic data of a healthy volunteer over a heartbeat cycle (Abdallah, 2009)

11. 3/3/201611 Sensitivity of the pressure inflow conditions RPBC vs. T (Run 1 to 4) RPBC vs. T (Run 1 to 4)

12. 3/3/201612 Sensitivity of the pressure inflow conditions PV and Aorta RPBC vs. T (Run 1 to 4) PV and Aorta RPBC vs. T (Run 1 to 4)

13. 3/3/201613 Results and Discussions Higher pressure BC gives higher blood inflow at the PV Flow rates decrease and even reverse for all cases except Run 4 Decrease and reverse in flow rate for Run 1 to 3 despite mitral valve closure Hemodynamic comparison for PV Hemodynamic comparison for PV

14. 3/3/201614 Results and Discussions Minimal difference in flow rate of aorta for different data sets during initial filling of blood in the LV When systole phase begins, there is a large outflow to deliver oxygenated blood to other parts of the body Hemodynamic comparison for aorta Hemodynamic comparison for aorta

15. 3/3/201615 Results and Discussions Magnitude of the PV flow rate from Run 1 is generally twice as high as that of Fortini et al Current outflow is about 5 times that of Fortini et al. Comparison with Fortini et al. results Comparison with Fortini et al. results

16. 3/3/201616 Results and Discussions 2-D Vorticity visualization and verification (Run 1) 2-D Vorticity visualization and verification (Run 1) 2-D vorticity plots obtained by extracting a slice of the Z vorticity at z=0.56A pair of opposing signs vortices can be seen for all data sets 2-D vorticity plots obtained by extracting a slice of the Z vorticity at z=0.56. A pair of opposing signs vortices can be seen for all data sets Similar experimental results from Fortini et al. and Gharib et al.

17. 3/3/201617 Results and Discussions 3-D Iso-surface vorticity magnitude visualization 3-D Iso-surface vorticity magnitude visualization T=0.06 – Flow entering LV, vortex rings start to get connected T=0.37 – Reached a more mature stage, vortices stabilized, showing connected vortex rings T=0.56 – Only left a small region of weak vorticity

18. 3/3/201618 Results and Discussions Vortex formation time T v Vortex formation time T v –A good indicator of the cardiac health of the patient –EDV = LV end-diastolic volume (LV filling), – = time-averaged mitral (annulus) valve diameter, –EF = ejection fraction, –ESV = LV volume at the end of systole (LV ejection), –SV = the stroke volume, difference between ESV and EDV (Gharib et al., 2006)

19. 3/3/201619 Results and Discussions Vortex formation time T v Vortex formation time T v –Expected value of T v for healthy volunteer is 3.3< T v <5.5 –T v very sensitive to small differences in . Power cube in equation causes small differences to be magnified. Run1234* TvTv 2.112.902.230.83

20. 3/3/201620 Results and Discussions Kinetic Energy (KE) of 4-D PC-MRI system Kinetic Energy (KE) of 4-D PC-MRI system 1 st peak of KE (initial diastole), higher 2 nd peak of KE (atrial contraction), lower

21. 3/3/201621 Results and Discussions Kinetic Energy (KE) of Run 1 (z=0.56 slice) Kinetic Energy (KE) of Run 1 (z=0.56 slice) 2 nd lower peak of KE (atrial contraction) 1 st higher peak of KE (LV filling)

22. Maximum KE vs. T for Run 1 to 4 Maximum KE vs. T for Run 1 to 4 3/3/201622 Results and Discussions Run 2 (- 25% PV) also has 2 peaks, but the later peak is much higher than the first Exceptionally high erroneous 3 rd peak from Run 3 Total of 3 peaks for Run 1 and 3, with 1 st peak higher than 2 nd Similar peaks for Run 4, but solution diverges after 0.8T

23. 3/3/201623 Results and Discussions Surface pressure analysis Surface pressure analysis Significant reduction in surface pressure after systole High surface pressure during systole, especially in the front

24. 3/3/201624 Results and Discussions Surface shear stress analysis Surface shear stress analysis High shear stress, now near apex of the heart High shear stress during systole, near the aorta

25. 3/3/201625 Conclusions and future work Patient specific cardiovascular modeling system Patient specific cardiovascular modeling system Simulation of heart using IBM Simulation of heart using IBM 4-D PC-MRI system 4-D PC-MRI system Investigate the effect of RPBC on different variables such as KE, vorticity etc Investigate the effect of RPBC on different variables such as KE, vorticity etc Verified with experimental results from MRI and other means through KE, vorticity Verified with experimental results from MRI and other means through KE, vorticity Visualization of pressure and shear stress distribution on heart surface Visualization of pressure and shear stress distribution on heart surface Further investigation of the realistic reservoir pressure BC is required Further investigation of the realistic reservoir pressure BC is required Future work to include input of patient specific data in CFD code Future work to include input of patient specific data in CFD code

26. 3/3/201626 The End