1. Date of download: 9/19/2016 Copyright © ASME. All rights reserved. From: Multiscale Modeling of Cardiovascular Flows for Clinical Decision Support Appl. Mech. Rev. 2015;67(3):030804-030804-11. doi:10.1115/1.4029909 Schematic of a RCR (Windkessel) circuit for modeling the 0D domain vasculature. The wall distensibility is modeled by including a capacitor, which stores blood as pressure increases. Pressure drop due to viscous dissipation is modeled using two resistors to model the proximal and distal vessels. Figure Legend:

2. Date of download: 9/19/2016 Copyright © ASME. All rights reserved. From: Multiscale Modeling of Cardiovascular Flows for Clinical Decision Support Appl. Mech. Rev. 2015;67(3):030804-030804-11. doi:10.1115/1.4029909 Comparison between a closed loop and open loop lumped-parameter model. A dirichlet BC is prescribed at the inlet in the open loop configuration, fixing the flow rate to a user-defined value (or waveform in the case of unsteady flow), whereas flow rate dynamically changes depending on the coupled behavior of the 3D and 0D domains in the closed loop configuration. With the closed loop configuration, additional information, for example, cardiac work load or pressure volume loops, can be extracted from the 0D domain. Figure Legend:

3. Date of download: 9/19/2016 Copyright © ASME. All rights reserved. From: Multiscale Modeling of Cardiovascular Flows for Clinical Decision Support Appl. Mech. Rev. 2015;67(3):030804-030804-11. doi:10.1115/1.4029909 Schematic of time marching in the 3D and 0D domains. The 0D domain sends corrected Pi,n+1 and Q j,n+1 to the 3D domain and receives Q i,n and Pj,n and the corrected Q i,n+1 and Pj,n+1 values from the 3D domain. Simulation is performed iteratively and proceeds to the next time step only when the coupled system is converged. Neumann boundary (i ∈ η h ) values are colored blue and Dirichlet boundary (j ∈ η g ) values are colored red. Figure Legend:

4. Date of download: 9/19/2016 Copyright © ASME. All rights reserved. From: Multiscale Modeling of Cardiovascular Flows for Clinical Decision Support Appl. Mech. Rev. 2015;67(3):030804-030804-11. doi:10.1115/1.4029909 Schematic of a 2D model with backflow at a Neumann boundary. Three velocity profiles (green/solid, blue/dashed, and red/dot-dash) are shown with different levels of flow reversal, but similar net-flow. All three profiles can satisfy conservation of mass, causing the flow to become unstable as it transitions from the green toward the red profile. This issue is resolved by adding an outward traction proportional to the inward velocity. Figure Legend:

5. Date of download: 9/19/2016 Copyright © ASME. All rights reserved. From: Multiscale Modeling of Cardiovascular Flows for Clinical Decision Support Appl. Mech. Rev. 2015;67(3):030804-030804-11. doi:10.1115/1.4029909 Schematic of flow in a bifurcating vessel with resistance BC at outlets and inflow condition at the inlet. For high resistance values, flow split to the right and left branches highly depends on the BC, rather than the 3D geometry. The domination of outlet BCs in determining the entire flow solution leads to an ill-conditioning problem stemming from a few dominant eigenvalues coming from the boundaries. Figure Legend:

6. Date of download: 9/19/2016 Copyright © ASME. All rights reserved. From: Multiscale Modeling of Cardiovascular Flows for Clinical Decision Support Appl. Mech. Rev. 2015;67(3):030804-030804-11. doi:10.1115/1.4029909 Comparison of cost and convergence criteria for explicit, implicit, and implicit-with-preconditioner coupling schemes for a cylinder with resistance outflow BC and prescribed inflow BC. Explicit denotes the case in which KBCab is neglected. Implicit denotes the case in which KBCab is included in the formulation, but the preconditioner described in Sec. 4 is not considered. Imp + PC denotes the case in which KBCab is included in the formulation and used to construct the preconditioner in Eq. (16). Significant improvements in both cost and stability are achieved using implicit coupling and preconditioning methods tailored to account for outflow resistance. Figure Legend:

7. Date of download: 9/19/2016 Copyright © ASME. All rights reserved. From: Multiscale Modeling of Cardiovascular Flows for Clinical Decision Support Appl. Mech. Rev. 2015;67(3):030804-030804-11. doi:10.1115/1.4029909 Modeling process for virtual surgery, beginning with model construction from imaging data followed by virtual surgery (a) and the patient-specific stage one models for two patients (b). The example shown compares the Hemi-Fontan and Glenn surgeries in single ventricle palliation, as well as surgical correction of pulmonary stenosis. Figure Legend:

8. Date of download: 9/19/2016 Copyright © ASME. All rights reserved. From: Multiscale Modeling of Cardiovascular Flows for Clinical Decision Support Appl. Mech. Rev. 2015;67(3):030804-030804-11. doi:10.1115/1.4029909 Examples of open (upper) and closed (lower) loop BC configurations for a patient-specific model of the Y-graft Fontan procedure. Reprinted with permission from Physics of Fluids [72]. Figure Legend:

9. Date of download: 9/19/2016 Copyright © ASME. All rights reserved. From: Multiscale Modeling of Cardiovascular Flows for Clinical Decision Support Appl. Mech. Rev. 2015;67(3):030804-030804-11. doi:10.1115/1.4029909 Example of a closed loop lumped parameter network coupled to a patient-specific model of coronary artery bypass graft surgery (upper) and a simulated WSS field (lower) (contours WSS magnitude min 0, max 15 dynes/cm 2 ) Figure Legend: