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Review Article

Multiscale Modeling of Cardiovascular Flows for Clinical Decision Support

[+] Author and Article Information
Alison L. Marsden, Mahdi Esmaily-Moghadam

Department of Mechanical
and Aerospace Engineering,
University of California, San Diego,
La Jolla, CA 92093

Manuscript received August 19, 2014; final manuscript received February 19, 2015; published online April 8, 2015. Assoc. Editor: Gianluca Iaccarino.

Appl. Mech. Rev 67(3), 030804 (May 01, 2015) (11 pages) Paper No: AMR-14-1063; doi: 10.1115/1.4029909 History: Received August 19, 2014; Revised February 19, 2015; Online April 08, 2015

Patient-specific cardiovascular simulations can provide clinicians with predictive tools, fill current gaps in clinical imaging capabilities, and contribute to the fundamental understanding of disease progression. However, clinically relevant simulations must provide not only local hemodynamics, but also global physiologic response. This necessitates a dynamic coupling between the Navier–Stokes solver and reduced-order models of circulatory physiology, resulting in numerical stability and efficiency challenges. In this review, we discuss approaches to handling the coupled systems that arise from cardiovascular simulations, including recent algorithms that enable efficient large-scale simulations of the vascular system. We maintain particular focus on multiscale modeling algorithms for finite element simulations. Because these algorithms give rise to an ill-conditioned system of equations dominated by the coupled boundaries, we also discuss recent methods for solving the linear system of equations arising from these systems. We then review applications that illustrate the potential impact of these tools for clinical decision support in adult and pediatric cardiology. Finally, we offer an outlook on future directions in the field for both modeling and clinical application.

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References

Figures

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Fig. 1

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.

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Fig. 2

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.

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Fig. 3

Schematic of time marching in the 3D and 0D domains. The 0D domain sends corrected Pi,n+1 and Qj,n+1 to the 3D domain and receives Qi,n and Pj,n and the corrected Qi,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 (iηh) values are colored blue and Dirichlet boundary (jηg) values are colored red.

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Fig. 4

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.

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Fig. 5

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.

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Fig. 6

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.

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Fig. 7

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.

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Fig. 8

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].

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Fig. 9

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/cm2)

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