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Research Papers

Reduced Order Models for Transstenotic Pressure Drop in the Coronary Arteries

[+] Author and Article Information
Mehran Mirramezani

Department of Mechanical Engineering,
University of California,
Berkeley, CA 94720;
Department of Mathematics,
University of California,
Berkeley, CA 94720

Scott L. Diamond

Department of Chemical and
Biomolecular Engineering,
Institute for Medicine and Engineering,
University of Pennsylvania,
Philadelphia, PA 19104

Harold I. Litt

Department of Radiology,
Perelman School of Medicine
of the University of Pennsylvania,
Philadelphia, PA 19104

Shawn C. Shadden

Department of Mechanical Engineering,
University of California,
Berkeley, CA 94720
e-mail: shadden@berkeley.edu

1Corresponding author.

2Technically, FFR = (PdistPv/PaoPv), although central venous pressure (Pv < 8 mmHg) is often assumed negligible.

Manuscript received June 22, 2018; final manuscript received November 13, 2018; published online January 18, 2019. Assoc. Editor: Ching-Long Lin.

J Biomech Eng 141(3), 031005 (Jan 18, 2019) (11 pages) Paper No: BIO-18-1292; doi: 10.1115/1.4042184 History: Received June 22, 2018; Revised November 13, 2018

The efficacy of reduced order modeling for transstenotic pressure drop in the coronary arteries is presented. Coronary artery disease is a leading cause of death worldwide and the computation of pressure drop in the coronary arteries has become a standard for evaluating the functional significance of a coronary stenosis. Comprehensive models typically employ three-dimensional (3D) computational fluid dynamics (CFD) to simulate coronary blood flow in order to compute transstenotic pressure drop at the arterial stenosis. In this study, we evaluate the capability of different hydrodynamic models to compute transstenotic pressure drop. Models range from algebraic formulae to one-dimensional (1D), two-dimensional (2D), and 3D time-dependent CFD simulations. Although several algebraic pressure-drop formulae have been proposed in the literature, these models were found to exhibit wide variation in predictions. Nonetheless, we demonstrate an algebraic formula that provides consistent predictions with 3D CFD results for various changes in stenosis severity, morphology, location, and flow rate. The accounting of viscous dissipation and flow separation were found to be significant contributions to accurate reduce order modeling of transstenotic coronary hemodynamics.

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References

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Figures

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Fig. 1

Schematic of image-based 3D model of an aorta and coronary arteries coupled to closed-loop lump parameter (0D) models of the heart, pulmonary arteries, and systemic and coronary circulations

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Fig. 2

Simulation results for image-based 3D CFD coronary modeling: (a) image-based geometry with 24 coronary outlets, (b) computed aortic pressure waveform, (c) computed pressure-volume loops of the left and right ventricles, (d) typical computed left coronary artery flow waveform with minimum flow in systole and maximum flow in diastole, and (e) typical computed right coronary artery flow waveform with commensurate peaks in systole and diastole

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Fig. 3

Comparison of results for models with 50%, 75%, and 90% idealized stenosis: (a), (d), (g) computed FFR distribution throughout the coronary trees from 3D CFD, (b), (e), (h) comparison of pressure drop across the respective coronary stenosis for four different algebraic models and the full 3D CFD simulation, and (c), (f), (i) comparison of pressure drop across the respective coronary stenosis obtained from algebraic model 3 (0D), 1D, multiring (2D), and the full 3D CFD simulation

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Fig. 4

Comparison of results for models with asymmetric stenoses: (a) computed FFR distribution from 3D CFD for a 73% asymmetric stenosis, (b) pressure drop across stenosis for model 3 (0D) and full 3D CFD simulation for the 73% asymmetric stenosis, (c) computed FFR distribution from 3D CFD for a 90% asymmetric stenosis, and (d) pressure drop across stenosis between model 3 (0D) and full 3D CFD simulation for the 90% asymmetric stenosis

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Fig. 5

Comparison of models for patient-specific coronary stenoses: (a) computed FFR distribution for a patient with two consecutive stenosis in the left anterior descending (LAD) coronary artery with maximum value of 70%, (b) pressure drop across the consecutive stenoses from the algebraic model 3 (0D) and full 3D simulation, (c) computed FFR distribution for a patient-specific 88% stenosis in the left anterior descending (LAD) coronary artery, (d) pressure drop across the patient-specific 88% stenosis for algebraic model 3 (0D) and full 3D simulation, (e) computed FFR distribution for a patient-specific 84% stenosis in the right coronary artery (RCA), and (f) pressure drop across the patient-specific 84% stenosis for algebraic model 3 (0D) and full 3D simulation

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Fig. 6

Results of 1D simulations of flow and pressure in an idealized common carotid artery from our in-house solver and benchmark [37]: (a) imposed inlet flow rate, (b) computed inlet pressure, (c) computed flow rate at the vessel midpoint, and (d) computed pressure difference between the inlet and outlet

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Fig. 7

Comparison of velocity profiles from the analytical linear Womersley solution (dashed line) and multiring method (solid lines) at x = 25 cm and different time points

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