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Research Papers

An Outflow Boundary Condition Model for Noninvasive Prediction of Fractional Flow Reserve in Diseased Coronary Arteries

[+] Author and Article Information
Iyad A. Fayssal

Computational Mechanics Laboratory,
Mechanical Engineering Department,
American University of Beirut,
Riad El-Solh,
Beirut 1107 2020, Lebanon
e-mail: iaf04@mail.aub.edu

Fadl Moukalled

Professor
Mechanical Engineering Department,
American University of Beirut,
Riad El-Solh,
Beirut 1107 2020, Lebanon
e-mail: fmukalled@aub.edu.lb

Samir Alam

Professor
Department of Internal Medicine,
American University of Beirut,
Riad El-Solh,
Beirut 1107 2020, Lebanon
e-mail: salam@aub.edu.lb

Hussain Isma'eel

Associate Professor
Department of Internal Medicine,
American University of Beirut,
Riad El-Solh,
Beirut 1107 2020, Lebanon
e-mail: hi09@aub.edu.lb

1Corresponding author.

Manuscript received April 14, 2017; final manuscript received October 16, 2017; published online January 23, 2018. Assoc. Editor: C. Alberto Figueroa.

J Biomech Eng 140(4), 041004 (Jan 23, 2018) (13 pages) Paper No: BIO-17-1154; doi: 10.1115/1.4038250 History: Received April 14, 2017; Revised October 16, 2017

This paper reports on a new boundary condition formulation to model the total coronary myocardial flow and resistance characteristics of the myocardial vascular bed for any specific patient when considered for noninvasive diagnosis of ischemia. The developed boundary condition model gives an implicit representation of the downstream truncated coronary bed. Further, it is based on incorporating patient-specific physiological parameters that can be noninvasively extracted to account for blood flow demand to the myocardium at rest and hyperemic conditions. The model is coupled to a steady three-dimensional (3D) collocated pressure-based finite volume flow solver and used to characterize the “functional significance” of a patient diseased coronary artery segment without the need for predicting the hemodynamics of the entire arterial system. Predictions generated with this boundary condition provide a deep understanding of the inherent challenges behind noninvasive image-based diagnostic techniques when applied to human diseased coronary arteries. The overall numerical method and formulated boundary condition model are validated via two computational-based procedures and benchmarked with available measured data. The newly developed boundary condition is used via a designed computational methodology to (a) confirm the need for incorporating patient-specific physiological parameters when modeling the downstream coronary resistance, (b) explain the discrepancies presented in the literature between measured and computed fractional flow reserve (FFRCT), and (c) discuss the current limitations and future challenges in shifting to noninvasive assessment of ischemia.

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References

Pijls, N. H. J. , de Bruyne, B. , Peels, K. , van der Voort, P. H. , Bonnier, H. J. R. M. , Bartunek, J. , and Koolen, J. J. , 1996, “ Measurement of Fractional Flow Reserve to Assess the Functional Severity of Coronary-Artery Stenoses,” N. Engl. J. Med., 334, pp. 1703–1708. [CrossRef] [PubMed]
Meijboom, W. B. , Van Mieghem, C. A. , van Pelt, N. , Weustink, A. , Pugliese, F. , Mollet, N. R. , Boersma, E. , Regar, E. , van Geuns, R. J. , de Jaegere, P. J. , Serruys, P. W. , Krestin, G. P. , and de Feyter, P. J. , 2008, “ Comprehensive Assessment of Coronary Artery Stenoses: Computed Tomography Coronary Angiography Versus Conventional Coronary Angiography and Correlation With Fractional Flow Reserve in Patients With Stable Angina,” J. Am. Coll. Cardiol., 52(8), pp. 636–643. [CrossRef] [PubMed]
Yong, A. S. , Ng, A. C. , Brieger, D. , Lowe, H. C. , Ng, M. K. , and Kritharides, L. , 2011, “ Three-Dimensional and Two-Dimensional Quantitative Coronary Angiography, and Their Prediction of Reduced Fractional Flow Reserve,” Eur. Heart J., 32(3), pp. 345–353. [CrossRef] [PubMed]
Taylor, C. A. , Fonte, T. A. , and Min, J. K. , 2013, “ Computational Fluid Dynamics Applied to Cardiac Computed Tomography for Noninvasive Quantification of Fractional Flow Reserve: Scientific Basis,” J. Am. Coll. Cardiol., 61(22), pp. 2233–2241. [CrossRef] [PubMed]
Min, J. K. , Berman, D. S. , Budoff, M. J. , Jaffer, F. A. , Leipsic, J. , Leon, M. B. , Mancini, G. B. , Mauri, L. , Schwartz, R. S. , and Shaw, L. J. , 2011, “ Rationale and Design of the DeFACTO (Determination of Fractional Flow Reserve by Anatomic Computed Tomographic AngiOgraphy) Study,” J. Cardiovasc. Comput. Tomogr., 5(5), pp. 301–309. [CrossRef] [PubMed]
Koo, B. K. , Erglis, A. , Doh, J. H. , Daniels, D. V. , Jegere, S. , Kim, H. S. , Dunning, A. , DeFrance, T. , Lansky, A. , Leipsic, J. , and Min, J. K. , 2011, “ Diagnosis of Ischemia-Causing Coronary Stenoses by Noninvasive Fractional Flow Reserve Computed From Coronary Computed Tomographic Angiograms: Results From the Prospective Multicenter DISCOVER-FLOW (Diagnosis of Ischemia-Causing Stenoses Obtained Via Noninvasive Fractional Flow Reserve) Study,” J. Am. Coll. Cardiol., 58(19), pp. 1989–1997. [CrossRef] [PubMed]
LaDisa, J. F. , Figueroa, C. A. , Vignon-Clementel, I. E. , Kim, H. J. , Xiao, N. , Ellwein, L. M. , Chan, F. P. , Feinstein, J. A. , and Taylor, C. A. , 2011, “ Computational Simulations for Aortic Coarctation: Representative Results From a Sampling of Patients,” ASME J. Biomech. Eng., 133(9), p. 091008. [CrossRef]
Wei, X. , Ghosh, S. K. , Taylor, M. E. , Johnson, V. A. , Emini, E. A. , Deutsch, P. , Lifson, J. D. , Bonhoeffer, S. , Nowak, M. A. , Hahn, B. H. , Shaw, G. M. , and Saag, M. S. , 1995, “ Viral Dynamics in Human Immunodeficiency Virus Type 1 Infection,” Nature, 373(6510), pp. 117–122. [CrossRef] [PubMed]
Wu, H. , Ding, A. A. , and De Gruttola, V. , 1998, “ Estimation of HIV Dynamic Parameters,” Stat. Med., 17(21), pp. 2463–2485. [CrossRef] [PubMed]
Adams, M. C. , Turkington, T. G. , Wilson, J. M. , and Wong, T. Z. , 2010, “ A Systematic Review of the Factors Affecting Accuracy of SUV Measurements,” Am. J. Roentgenol., 195(2), pp. 310–320. [CrossRef]
Sun, N. , Torii, R. , Wood, N. B. , Hughes, A. D. , Thom, S. A. , and Xu, X. Y. , 2009, “ Computational Modeling of LDL and Albumin Transport in an In Vivo CT Image-Based Human Right Coronary Artery,” ASME Biomech. Eng., 131(2), p. 021003. [CrossRef]
Min, J. K. , Taylor, C. A. , Achenbach, S. , Koo, B. K. , Leipsic, J. , Nørgaard, B. L. , Pijls, N. J. , and De Bruyne, B. , 2015, “ Noninvasive Fractional Flow Reserve Derived From Coronary CT Angiography: Clinical Data and Scientific Principles,” JACC Cardiovasc. Imaging, 8(10), pp. 1209–1222. [CrossRef] [PubMed]
West, G. B. , Brown, J. H. , and Enquist, B. J. , 1997, “ A General Model for the Origin of Allometric Scaling Laws in Biology,” Science, 276(5309), pp. 122–126. [CrossRef] [PubMed]
Choy, J. S. , and Kassab, G. S. , 2008, “ Scaling of Myocardial Mass to Flow and Morphometry of Coronary Arteries,” J. Appl. Physiol., 104(5), pp. 1281–1286. [CrossRef] [PubMed]
Beck, K. C. , Randolph, L. N. , Bailey, K. R. , Wood, C. M. , Snyder, E. M. , and Johnson, B. D. , 2006, “ Relationship Between Cardiac Output and Oxygen Consumption During Upright Cycle Exercise in Healthy Humans,” J. Appl. Physiol., 101(5), pp. 1474–1480.
Du Bois, D. , and Du Bois, E. F. , 1916, “ Clinical Calorimetry Tenth Paper a Formula to Estimate the Approximate Surface Area if Height and Weight be Known,” Arch. Intern. Med., 6(2), pp. 863–871.
Jacobs, P. L. , Nash, M. S. , and Mintz, C. D. , 1999, “ Assessment of Fractional Expired Gases and Air Flow by an Ambulatory Metabolic Analyzer,” J. Exercise Physiol., 2(4), pp. 20–28. https://www.asep.org/asep/asep/jacobcol.pdf
Wilson, R. F. , Wyche, K. , Christensen, B. V. , Zimmer, S. , and Laxson, D. D. , 1990, “ Effects of Adenosine on Human Coronary Arterial Circulation,” Circulation, 82(5), pp. 1595–1606. [CrossRef] [PubMed]
Kaufmann, P. A. , and Camici, P. G. , 2005, “ Myocardial Blood Flow Measurement by PET: Technical Aspects and Clinical Applications,” J. Nucl. Med., 46(1), pp. 75–88. http://jnm.snmjournals.org/content/46/1/75 [PubMed]
Murray, C. D. , 1926, “ The Physiological Principle of Minimum Work I. The Vascular System and the Cost of Blood Volume,” Proc. Natl. Acad. Sci. U.S.A., 12(3), pp. 207–214. [CrossRef] [PubMed]
Kim, H. J. , Vignon-Clementel, I. E. , Coogan, J. S. , Figueroa, C. A. , Jansen, K. E. , and Taylor, C. A. , 2010, “ Patient-Specific Modeling of Blood Flow and Pressure in Human Coronary Arteries,” Ann. Biomed. Eng., 38(10), pp. 3195–3209. [CrossRef] [PubMed]
Figueroa, C. A. , Vignon-Clementel, I. E. , Jansen, K. E. , Hughes, T. J. , and Taylor, C. A. , 2006, “ A Coupled Momentum Method for Modeling Blood Flow in Three-Dimensional Deformable Arteries,” Comput. Methods Appl. Mech. Eng., 195(41), pp. 5685–5706. [CrossRef]
Moukalled, F. , Mangani, L. , and Darwish, M. , 2016, The Finite Volume Method in Computational Fluid Dynamics, Springer, Cham, Switzerland. [CrossRef]
Patankar, S. V. , 1980, Numerical Heat Transfer and Fluid Flow, McGraw-Hill, New York.
Guyton, A. C. , Jones, C. E. , and Coleman, T. B. , 1973, Circulatory Physiology: Cardiac Output and Its Regulation, WB Saunders Co, Philadelphia, PA.
Edwards, 2010, Quick Guide to Cardiopulmonary Care, W. T. McGee, J. M. Headley, and J. A. Frazier, eds., Edwards Lifesciences LLC, Irvine, CA, pp. 164–165.
De Cort, S. C. , Innes, J. A. , Barstow, T. J. , and Guz, A. , 1991, “ Cardiac Output, Oxygen Consumption and Arteriovenous Oxygen Difference Following a Sudden Rise in Exercise Level in Humans,” J. Physiol., 441(1), pp. 501–512. [CrossRef] [PubMed]
Schindler, T. H. , Zhang, X. L. , Prior, J. O. , Cadenas, J. , Dahlbom, M. , Sayre, J. , and Schelbert, H. R. , 2007, “ Assessment of Intra-and Interobserver Reproducibility of Rest and Cold Pressor Test-Stimulated Myocardial Blood Flow With 13N-Ammonia and PET,” Eur. J. Nucl. Med. Mol. Imaging, 34(8), pp. 1178–1188. [CrossRef] [PubMed]
Schelbert, H. R. , 2012, “ Positron Emission Tomography Measurements of Myocardial Blood Flow: Assessing Coronary Circulatory Function and Clinical Implications,” Heart, 98(7), pp. 592–600. [CrossRef] [PubMed]
Prior, J. O. , Allenbach, G. , Valenta, I. , Kosinski, M. , Burger, C. , Verdun, F. R. , Bischof Delaloye, A. , and Kaufmann, P. A. , 2012, “ Quantification of Myocardial Blood Flow With 82Rb Positron Emission Tomography: Clinical Validation With 15O-Water,” Eur. J. Nucl. Med. Mol. Imaging, 39(6), pp. 1037–1047. [CrossRef] [PubMed]
Gewirtz, H. , 2012, “ PET Measurement of Adenosine Stimulated Absolute Myocardial Blood Flow for Physiological Assessment of the Coronary Circulation,” J. Nucl. Cardiol., 19(2), pp. 347–354. [CrossRef] [PubMed]
Gould, K. L. , Lipscomb, K. , and Hamilton, G. W. , 1974, “ Physiologic Basis for Assessing Critical Coronary Stenosis: Instantaneous Flow Response and Regional Distribution During Coronary Hyperemia as Measures of Coronary Flow Reserve,” Am. J. Cardiol., 33(1), pp. 87–94. [CrossRef] [PubMed]
Dodge, J. T. , Brown, B. G. , Bolson, E. L. , and Dodge, H. T. , 1992, “ Lumen Diameter of Normal Human Coronary Arteries. Influence of Age, Sex, Anatomic Variation, and Left Ventricular Hypertrophy or Dilation,” Circulation, 86(1), pp. 232–246. [CrossRef] [PubMed]
Østergaard, L. , Granfeldt, A. , Secher, N. , Tietze, A. , Iversen, N. K. , Jensen, M. S. , Andersen, K. K. , Nagenthiraja, K. , Gutiérrez-Lizardi, P. , Mouridsen, K. , Jespersen, S. N. , and Tønnesen, E. K. , 2015, “ Microcirculatory Dysfunction and Tissue Oxygenation in Critical Illness,” Acta Anaesthesiol. Scand., 59(10), pp. 1246–1259. [CrossRef] [PubMed]

Figures

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Fig. 1

(a) Patient specific coronary CTA images (DICOM files); (b) coronary artery segmentation; (c) reconstructed 3D model of the left coronary arterial system; (d) generation of 3D mesh using a finite number of elements; (e) quantification of total coronary rest flow to the myocardium and calculation of downstream microvascular resistance; (f) inducing hyperemic condition. The graph shows variation of mean total coronary resistance index with intravenous adenosine infusion for arteries with normal and abnormal flow reserve (Wilson et al. [18]); (g) steady-state mass and momentum equations governing blood flow; (h) a selected example of simulated patient-specific FFR with two upstream (in left main) and downstream (in LAD) disease locations.

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Fig. 2

Block diagram of the overall coupled 3D-lumped numerical solution algorithm

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Fig. 3

(a) Normalized left MBF demand. The figure also displays the computed range of the constant characteristic of myocardial flow (Y0) affirming the dependency of Y0 on patient physiological parameters. (b) Normalized left myocardial downstream resistance computed from the quantified total left myocardial flow demand.

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Fig. 5

Predicted values of Qs/Qh and variation of maximum relative difference for all cases simulated under (a) rest and (b) hyperemic conditions. At any specific disease geometric severity (%DS), Qs/Qh values are the result of varying patient physiological parameters: LV mass, M, (M ranges from 100 to 250 g, incremented by 50 g) and HR fixed at 60 BPM, the CI and VO2I are varied over their reported normal ranges (CI is varied from 2500 to 4000 ml/min/m2, incremented by 500 ml/min/m2, and VO2I is varied from 120 to 160 ml/min/m2, incremented by 10 ml/min/m2). The maximum relative difference in the values of Qs/Qh at a specific %DS is calculated by Eq. (22).

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Fig. 4

(a) Predicted normalized mean flow for a single dog mapped over the measured data of Gould et al. [32]; (b) comparison between the predicted and measured average normalized mean flow for all dogs under rest and hyperemic conditions. The lines numbered (1–12) in the figure correspond to the correlations (third-order polynomials) obtained when simulating the dog models under hyperemic conditions. The lines for rest conditions are not numbered since they are close to each other, and it is hard to distinguish them.

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Fig. 6

(a) Correlation between FFR computed using the new boundary condition and the MBF per unit myocardial mass approach; ((b)–(d)) Bland–Altman plots (provided for comparison purposes) for assesing the agreement level between FFR_MBF0.6, FFR_MBF1, and FFR_MBF1.4 versus FFR_new_boundary_condition, respectively

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