Towards non-invasive computational-mechanics and imaging-based diagnostic framework for personalized cardiology for coarctation

Figure 1. Reconstructed geometry and simulation domain. We used CT images from patients to segment and reconstruct the 3D geometries of the complete aorta. These 3-D geometries were used for investigating hemodynamic using computational fluid dynamics. Local flow dynamics is greatly influenced by upstream and downstream flow conditions that are absent in the flow simulation domain. The lumped-parameter model simulates the function of the left side of the heart. Time-dependent inlet flow (at ascending aorta) and outlet pressure (at descending aorta) position were obtained from lumped parameter modeling and applied as the transient boundary conditions. Boundary conditions of the aortic branches were adjusted to match the flow distribution.

Figure 2. Validation against catheter data. Catheter data and results of lumped parameter modeling (aorta and LV pressures and workloads) in Patient No. 1.

Figure 3. Velocity comparison. Velocity at different cross sections of the aorta, simulated using lattice Boltzmann method (LBM) and finite volume method (FVM).

Figure 4. Wall shear stress comparison. Wall shear stress (WSS) through the aorta, simulated using LBM and FVM.

Figure 5. Validation against Doppler echocardiography. Doppler echocardiography data and results of the computational framework (based on LPM and LBM) in Patients No. 1 to 3 in pre and post intervention status.

Figure 6. Modeling complex geometries in LBM. (a) Geometry of D3Q19 discrete velocity model with lattice vectors of ei (Eq. 2); (b) Details of bounce-back interpolation scheme (Here A and E are fluid nodes, B is solid nodes and D represents the location of an interpolated population): (I) The wall-node C is closer to the fluid-node A than to the solid-node B (q < 1/2). In this case, interpolations are required to construct post collision state at node D. We constructed the unknown quantities at node A from particles population at node D that will travel to node A after bouncing back off the wall. (II) The wall-node C is closer to the solid-node B than to the fluid-node A (q≥1/2). In this case, endpoint of propagation state (node D) lies between the boundary node (A) and the wall node (C) and the information of the particle leaving node A and arriving node D will be used to compute the unknown quantities at node A42,74,75.

Figure 7. Flow modeling in Patient No. 1. Computed velocity magnitude, turbulent kinetic energy (TKE) and time-averaged wall shear stress (TAWSS) using the computational framework (based on LPM and LBM) in pre and post intervention status in Patient No. 1. Patient No. 1 underwent intravascular stent intervention to correct the coarctation. Post intervention, the stent was deployed with residual stenosis due to malapposition of the stent proximal to the coarctation. Angiography post dilatation did not reveal a dissection or extravasation of contrast. The patient tolerated the procedure well without complication. The total shear stress exerted on the wall throughout the cardiac cycle was evaluated using the time-averaged wall shear stress (TAWSS) which is obtained as \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\rm{TAWSS}}=\frac{1}{{\rm{T}}}{\int }_{0}^{{\rm{T}}}|{\rm{\tau }}|{\rm{dt}}$$\end{document}TAWSS=1T∫0T|τ|dt. Here, T and τ are the cardiac cycle period and instantaneous wall shear stress,…

Figure 8. Flow modeling in Patient No. 2. Computed velocity magnitude, turbulent kinetic energy and time-averaged wall shear stress using the computational framework (based on LPM and LBM) in pre and post intervention status in Patient No. 2. Patient No. 2 underwent intravascular stent intervention to correct the coarctation which was coexisted with a major aneurysm downstream of the coarctation. Post intervention, the stent was successfully deployed without residual stenosis. Angiography and pressure measurement confirmed stent expansion with no extravasation, contrast staining or hemodynamic instability. There was no evidence of aneurysm and the patient tolerated the procedure well without complication.

Figure 9. Flow modeling in Patient No. 3. Computed velocity magnitude, turbulent kinetic energy and time-averaged wall shear stress using the computational framework (based on LPM and LBM) in pre and post intervention status in Patient No. 3. Patient No. 3 underwent bypass grafting intervention to correct the coarctation. The patient tolerated the procedure well without complication and the intervention was performed successfully.