Development of the Patientspecific Cardiovascular Modeling System using

Development of the Patient-specific Cardiovascular Modeling System using Immersed Boundary Technique Wee-Beng Taya, Yu-Heng Tsenga, Liang-Yu Linb, Wen-Yih Tsengc a. High Performance Computing & Environmental Fluid Dynamic Laboratory, Department of Atmospheric Sciences, National Taiwan University, Taipei, Taiwan (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

Outlines • Introduction • Patient-specific Cardiovascular Modeling System • 4 -D MRI system • Numerical Methods • Results from the cardiovascular heart models • Conclusion and future work 10/19/2021 2

Introduction • Develop a CFD based, patient-specific • • • cardiovascular modeling system Facilitate physicians’ diagnosis at early stage through the hybrid CFD simulation and 4 -D MRI Use Immersed boundary method (IBM) to simulate the fluid-elastic interaction of heart Investigate the vortex dynamic and effects of reservoir pressure boundary condition (RPBC) on the flows in Left Ventricle (LV) 10/19/2021 3

Patient-specific Cardiovascular Modeling System • Methodology Running of simulation using the original and modified CFD code Visualization and analysis of simulation results based KE, vorticity, hemodynamic, pressure and shear stress 10/19/2021 Obtaining of realistic data through the 4 DMRI system Comparison of CFD code’s results with realistic data 4

Patient-specific Cardiovascular Modeling System • 4 -D PC-MRI system – Images acquired using an eightchannel phased-array body coil – Allows one to reconstruct the 3 D images of the heart over a cardiac cycle – Time-resolved 3 D hemodynamic velocity fields – Data comprises of both healthy volunteer as well as patients with cardiac problems for comparison 10/19/2021 5

Patient-specific Cardiovascular Modeling System 10/19/2021 6

Patient-specific Cardiovascular Modeling system • Kinetic Energy (KE) of 4 D-MRI system 1 st peak of KE (left ventricle filling phase) 10/19/2021 2 nd peak of KE (atrial contraction phase) 7

Numerical Method – IBM (Mcqueen and Peskin, 2000) • Incompressible Navier-Stokes equations (f represents force density) • Interaction between immersed boundary, fluid and boundary forces 10/19/2021 8

Numerical Method - IBM • Fibers exert force onto • • the fluid Resulting velocity obtained by solving NS equations Return to calculate fiber’s velocity from surrounding fluid's velocity Shift fibers to new positions Repeat process 10/19/2021 9

Sensitivity of the pressure inflow conditions • Modified reservoir pressure boundary condition (RPBC) – examine the effects/impacts of different pressure BCs on the simulation results – Vortex formation in left ventricle (LV) Data set Data Type 1 Constant RPBC, unmodified 2 Similar to data set 1, except that the pulmonary vein (PV) pressure is 25% smaller 3 Similar to data set 1, except that the PV pressure is 25% larger 4 Varying RPBC, obtained from realistic data of a healthy volunteer over a heartbeat cycle (Abdallah, 2009) 10/19/2021 10

Boundary Conditions of IBM code 10/19/2021 11

Results and Discussions • Hemodynamic comparison for PV During initial LV filling phase, higher pressure BC gives higher PV blood inflow 10/19/2021 Towards end of LV filling phase, decrease and reverse in flow rate for all data sets except that of data set 4 (realistic pressure BC) 12

Results and Discussions • Inlet flow rate of patient data (Baccani et al. , 2002) Similar reverse flow rate, during systolic phase, at a later time compared to earlier data sets 10/19/2021 13

Results and Discussions • Hemodynamic comparison for aorta Minimal difference in flow rate of aorta for different data sets during initial filling of blood in the LV 10/19/2021 When systole phase begins , higher PV pressure for data set 3 (+25% PV) results in the highest outflow rate 14

Results and Discussions • Vorticity visualization 10/19/2021 15

Results and Discussions • Vorticity visualization – 2 D vorticity plots obtained by extracting a slice of the X vorticity at x=65. 0 – A pair of opposing signs vortices can be seen for all data sets – Left positively signed vortex (red) is stronger than the right negatively signed one (blue) – Right (blue) vortex interacts viscously with wall of LV, slows down and diminishes in size – Experiments by Fortini et al. (2008) show similar two vortices of opposite signs but negatively signed vortex (blue) is on left 10/19/2021 16

Results and Discussions • Vortex formation time Tv (Gharib et al. , 2006) – 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 10/19/2021 17

Results and Discussions • Vortex formation time Tv – EDV, ESV obtained by approximating heart as a 3 -D volume comprising of many polygons – by calculating the diameter of mitral annulus, which is represented as a 2 D surface Data set 1 2 3 4 Tv 2. 90 2. 23 0. 83 2. 11 – Expected value of Tv for healthy volunteer is 4. 0 (Gharib et al. , 2006) – Tv very sensitive to small differences in and EF. Power cube in equation causes small differences to be magnified. 10/19/2021 18

Results and Discussions • Kinetic Energy (KE) of data set 1 2 nd lower peak of KE (atrial contraction) 1 st higher peak of KE (LV filling) 10/19/2021 19

Results and Discussions • Kinetic Energy (KE) of 4 D-MRI system Similar 1 st peak of KE as data set 1 10/19/2021 Similar 2 nd peak of KE as data set 1 20

Results and Discussions • Kinetic Energy (KE) of data set 1 to 4 Two peaks in data set 2 (-25% PV), but the later peak is much higher than the first 10/19/2021 Data set 4 (realistic pressure BC) shows only one peak Data set 3 (+25% PV) similar to data set 121

Results and Discussions • Inlet flow rate of patient data (Baccani et al. , 2002) 1 st peak flow rate, similar to 1 st peak in KE during E -wave (LV filling) 10/19/2021 2 nd peak flow rate, similar to 2 nd peak in KE during A-wave (atrial contraction) 22

Results and Discussions • Pressure analysis 10/19/2021 23

Results and Discussions • Shear Stress analysis 10/19/2021 24

Conclusions • Simulation of heart using IBM • Modify original code to examine effect of • • reservoir pressure BC on different variables such as KE, vorticity etc Verify with experimental results from MRI and other means A more realistic reservoir pressure BC does not mean better results 10/19/2021 25

References • Abdallah, H. , "Pressures and the Heart: How Pressures Change in the • • Heart. " http: //www. childrensheartinstitute. org/educate/bloodprs/prchange. htm, 2009 Baccani, B. , Domenichini, F. , Pedrizzetti, G. , and Tonti, G. , "Fluid dynamics of the left ventricular filling in dilated cardiomyopathy, " in Journal of Biomechanics, Vol. 35, May 2002, pp. 665 -671 Fortini, S. , Querzoli, G. , Cenedese, A. , and Marchetti, M. , "The Effect of Mitral Valve on Left Ventricular Flow, " in 14 th Int Symp on Applications of Laser Techniques to Fluid Mechanics Lisbon, Portugal, 2008 Gharib, M. , Rambod, E. , Kheradvar, A. , Sahn, D. J. , and Dabiri, J. O. , "Optimal vortex formation as an index of cardiac health, " in Proceedings of the National Academy of Sciences of the United States of America, Vol. 103, Apr 2006, pp. 6305 -6308 Mc. Queen, D. M. and Peskin, C. S. , "A three-dimensional computer model of the human heart for studying cardiac fluid dynamics, " in Computer Graphics-Us, Vol. 34, Feb 2000, pp. 56 -60 10/19/2021 26

The End 10/19/2021 27

Q&A 10/19/2021 28