Objective: In order to take a decision about the revascularization approach to be adopted, it is of fundamental importance to determine whether coronary artery stenoses induce ischemia or not. An index, named (Fractional Flow Reserve), based on pressure measurements has been proposed to this aim and is usually interpreted in terms of flows. The objective of this work is to compute simultaneously pressures and flow rates in the coronary network of patients with three-vessel disease, in order to study more precisely the relationship between these two quantities. Approach: 22 patients have been included in the study. Some pressure and flow rate measurements were collected during by-pass surgery. These clinical data allow determining parameters for a patient’s specific model, based on the electric/hydraulic analogy. Collateral pathways are included in the model, as well as the severity of the disease and the impact of revascularization. Main Results: For patients with stenoses on LAD, LCx, LMCA and occlusion of the RCA, the flow rate delivered to the right territory is of course a function of the aortic pressure, the left stenoses severity, and the pressure distal to the thrombosis. But it mainly depends on the capillary and collateral resistances, and on the proportion between them. Abnormal microvascular hemodynamics, may be present in patients with non-hemodynamic significant lesions as assessed by the pressure ratio. Complete revascularization with the 3 grafts is demonstrated to be fully justified. The direction of collateral flows may be reversed, depending on the pressure gradient. In any case, they remain low and become negligible when the 3 grafts are operating. Significance: Surgical decision based only on pressure measurements may miss some real hemodynamic problems due to the considered stenosis. This risk is even greater in case of serial stenoses.
References
[1]
Pijls, N., Van Son, J.A., Kirkeeide, R.L., De Bruyne, B. and Gould, K.L. (1993) Experimental Basis of Determining Maximum Coronary, Myocardial, and Collateral Blood Flow by Pressure Measurements for Assessing Functional Stenosis Severity before and after Percutaneous Transluminal Coronary Angioplasty. Circulation, 87, 1354-1367. https://doi.org/10.1161/01.CIR.87.4.1354
[2]
Abuouf, Y., Ookawara, S. and Ahmed, M. (2020) Analysis of the Effect of Guidewire Position on Stenosis Diagnosis Using Computational Fluid Dynamics. Computers in Biology and Medicine, 121, Article ID: 103777.
https://doi.org/10.1016/j.compbiomed.2020.103777
[3]
Taylor, Ch., Fonte, T. and Min, J. (2013) Computational Fluid Dynamics Applied to Cardiac Computed Tomography for Noninvasive Quantification of Fractional Flow Reserve: Scientific Basis. Journal of the American College of Cardiology, 61, 2233-2241. https://doi.org/10.1016/j.jacc.2012.11.083
[4]
Morris, P., Van De Vosse, F., Lawford, P., Hose, R. and Gunn, J. (2015) Virtual (Computed) Fractional Flow Reserve, Current Challenges and limitations. JACC: Cardiovascular Interventions, 8, 1009-1017.
https://doi.org/10.1016/j.jcin.2015.04.006
[5]
Freiman, M., Nickisch, H., Schmitt, H., Maurovich-Horvat, P., Donnelly, P., Vembar, M. and Goshen, L. (2018) A Functionally-Personalized Boundary Condition Model to Improve Estimates of Fractional Flow Reserve with CT (CT-FFR). Medical Physicss, 45, 1170-1177. https://doi.org/10.1002/mp.12753
[6]
Fayssal, I., Moukalled, F., Alam, S. and Isma’eel, H. (2018) An Outflow Boundary Condition Model for Noninvasive Prediction of Fractional Flow Reserve in Diseased Coronary Arteries. Journal of Biomechanical Engineering, 140, Article ID: 041004 (13 p.). https://doi.org/10.1115/1.4038250
[7]
Garcia, D., Harbaoui, B., Van De Hoef, T., Meuwissen, M., Nijjer, S., Echavarria-Pinto, M., Davies, J., Piek, J. and Lantelme, P. (2019) Relationship between FFR, CFR and Coronary Microvascular Resistance—Practical Implications for FFR-Guided Percutaneous Coronary Intervention. PLoS ONE, 14, e0208612.
https://doi.org/10.1371/journal.pone.0208612
[8]
Quarteroni, A. and Veneziani, A. (2003) Analysis of a Geometrical Multiscale Model Based on the Coupling of ODEs and PDEs for Blood Flow Simulations. Multiscale Modeling & Simulation, 1, 173-195.
https://doi.org/10.1137/S1540345902408482
[9]
Olufsen, M. and Nadim, A. (2004) On Deriving Lumped Models for Blood Flow and Pressure in the Systemic Arteries. Mathematical Biosciences and Engineering, 1, 61-80. https://doi.org/10.3934/mbe.2004.1.61
[10]
Maasrani, M., Verhoye, J., Corbineau, H. and Drochon, A. (2008) Analog Electrical Model of the Coronary Circulation in Case of Multiple Revascularizations. Annals of Biomedical Engineering, 36, 1163-1174.
https://doi.org/10.1007/s10439-008-9500-5
[11]
Maasrani, M., Abouliatim, I., Harmouche, M., Verhoye, J., Corbineau, H. and Drochon, A. (2011) Patients’ Specific Simulations of Coronary Fluxes in Case of Three-Vessel Disease. Journal of Biomedical Science and Engineering, 4, 34-45. https://doi.org/10.4236/jbise.2011.41005
[12]
Verhoye, J., De La Tour, B., Drochon, A. and Corbineau, H. (2005) Collateral Flow Reserve and Right Coronary Occlusion: Evaluation during Off-Pump Revascularization. Interactive CardioVascular and Thoracic Surgery, 4, 23-26. https://doi.org/10.1510/icvts.2004.093088
[13]
Verhoye, J., Abouliatim, I., Drochon, A., De La Tour, B., Leclerq, Ch., Leguerrier, A. and Corbineau, H. (2007) Collateral Blood Flow between Left Coronary Artery Bypass Grafts And chronically Occluded Right Coronary Circulation in Patients with Triple Vessel disease. European Journal of Cardio-Thoracic Surgery, 31, 49-54. https://doi.org/10.1016/j.ejcts.2006.09.033
[14]
Morris, P., Soto, D., Feher, J., Rafiroiu, D., Lungu, A., Varma, S., Lawford, P., Hose, R. and Gunn, J. (2017) Fast Virtual Fractional Flow Reserve Based upon Steady-State Computational Fluid Dynamics Analysis. Results from the VIRTU-Fast Study. JACC: Basic to Translational Science, 2, 434-446.
https://doi.org/10.1016/j.jacbts.2017.04.003
[15]
Pietrabissa, R., Mantero, S., Marotta, T. and Menicanti, L. (1996) A Lumped Parameter Model to Evaluate the Fluid Dynamics of Different Coronary Bypasses. Medical Engineering and Physics, 18, 477-484.
https://doi.org/10.1016/1350-4533(96)00002-1
[16]
Wang, J.Z., Tie, B., Welkowitz, W., Kostis, J. and Semmlow, J. (1989) Incremental Network Analogue Model of the Coronary Artery. Medical and Biological Engineering and Computing, 27, 416-422.
https://doi.org/10.1007/BF02441434
[17]
Harmouche, M., Maasrani, M., Verhoye, J., Corbineau, H. and Drochon, A. (2014) Coronary Three-Vessel Disease with Occlusion of the Right Coronary Artery: What Are the Most Important Factors That Determine the Right Territory Perfusion? IRBM, 35, 149-157. https://doi.org/10.1016/j.irbm.2013.11.002
[18]
Spaan, J., Kolyva, C., Van Der Wijngaard, J., Ter Wee, R., Van Horssen, P., Piek, J. and Siebes, M. (2008) Coronary Structure and Perfusion in Health and Disease. Philosophical Transactions of the Royal Society A, 366, 3137-3153. https://doi.org/10.1098/rsta.2008.0075
[19]
Harmouche, M., Anselmi, A., Maasrani, M., Mariano, Ch., Corbineau, H., Verhoye, J. and Drochon, A. (2014) Coronary Three Vessel Disease Hydrodynamics: Simulations Including the Time-Dependence of the Microvascular Resistances. Advances in Biomechanics and Applications, 1, 279-292.
https://doi.org/10.12989/aba.2014.1.4.279
[20]
Nijveldt, R., Beek, A., Hirsch, A., Stoel, M., Hofman, M., Umans, V., Algra, P., Twisk, J. and Van Rossum, A. (2008) Functional Recovery after Acute Myocardial Infarction: Comparison between Angiography, Electrocardiography, and Cardiovascular Magnetic Resonance Measures of Microvascular Injury. Journal of the American College of Cardiology, 52, 181-189. https://doi.org/10.1016/j.jacc.2008.04.006
[21]
Marcheix, B., Van den Eynden, F., Demers, P., Bouchard, D. and Cartier, R. (2008) Influence of Diabetes Mellitus on Long-Term Survival in Systematic Off-Pump Coronary Artery Bypass Surgery. Annals of Thoracic Surgery, 86, 1181-1188. https://doi.org/10.1016/j.athoracsur.2008.06.063
[22]
Wit, M., De Mulder, M., Jansen, E. and Umans, V. (2013) Diabetes Mellitus and Its Impact on Long-Term Outcomes after Coronary Artery Bypass Graft Surgery. Acta Diabetologica, 50, 123-128.
https://doi.org/10.1007/s00592-010-0223-3
[23]
Schmitz, C., Ashraf, O., Schiller, W., Preusse, Cl., Esmailzadeh, B., Likungu, J.A., Fimmers, R. and Welz, A. (2003) Transit Time Flow Measurement in On-Pump and Off-Pump Coronary Artery Surgery. Journal of Thoracic and Cardiovascular Surgery, 126, 645-650. https://doi.org/10.1016/S0022-5223(03)00018-7
[24]
Takami, Y. and Takagi, Y. (2018) Roles of Transit Time Flow Measurement for Coronary Artery Bypass Surgery. Journal of Thoracic and Cardiovascular Surgery, 66, 426-433. https://doi.org/10.1055/s-0037-1618575
[25]
Kaku, D., Nakahira, A., Hirai, H., Sasaki, Y., Hosono, M., Bito, Y., Suehiro, Y. and Suehiro, S. (2013) Does Rich Coronary Collateral Circulation Distal to Chronically Occluded Left Anterior Descending Artery Compete with Graft Flow? Interactive CardioVascular and Thoracic Surgery, 17, 944-949. https://doi.org/10.1093/icvts/ivt337
[26]
Borowski, A., Godehardt, E. and Dalyanoglu, H. (2017) Surgical Decision Making for Revascularization of Chronically Occluded Right Coronary Artery. General Thoracic and Cardiovascular Surgery, 65, 17-24.
https://doi.org/10.1007/s11748-016-0702-8
[27]
Xie, X., Zheng, M., Wen, D., Li, Y. and Xie, S. (2018) A New CFD Based Non-Invasive Method for Functional Diagnosis of Coronary Stenosis. BioMedical Engineering OnLine, 17, Article No. 36.
https://doi.org/10.1186/s12938-018-0468-6
[28]
Zbinden, R., Zbinden, S., Billinger, M., Windecker, S., Meier, B. and Seiler, C. (2005) Influence of Diabetes Mellitus on Coronary Collateral Flow: An Answer to an Old Controversy. Heart, 91, 1289-1293.
https://doi.org/10.1136/hrt.2004.041236
[29]
Meier, P., Zbinden, R., Togni, M., Wenaweser, P., Windecker, S., Meier, B. and Seiler, C. (2007) Coronary Collateral Function Long after Drug-Eluting stent Implantation. Journal of the American College of Cardiology, 49, 15-20. https://doi.org/10.1016/j.jacc.2006.08.043
[30]
Coppel, R., Lagache, M., Finet, G., Rioufol, G., Gomez, A., Derimay, F., Malvé, M., Yazdani, S., Pettigrew, R. and Ohayon, J. (2019) Influence of Collaterals on True FFR Prediction for a Left Main Stenosis with Concomitant lesions: An in Vitro Study. Annals of Biomedical Engineering, 47, 1409-1421.
https://doi.org/10.1007/s10439-019-02235-y
[31]
Modi, B., Sankaran, S., Kim, H., Ellis, H., Rogers, C., Taylor, Ch., Rajani, R. and Perera, D. (2019) Predicting the Physiological Effect of Revascularization in Serially Diseased Coronary Arteries: Clinical Validation of a Novel CT Coronary Angiography-Based Technique. Circulation: Cardiovascular Interventions, 12, e007577.
https://doi.org/10.1161/CIRCINTERVENTIONS.118.007577
[32]
Lust, R., Zeri, R., Spence, P., Hopson, S., Sun, Y., Otaki, M., Jolly, S., Mehta, P. and Chitwood, W. (1994) Effect of Chronic Native Flow Competition on Internal Thoracic Artery Grafts. The Annals of Thoracic Surgery, 57, 45-50. https://doi.org/10.1016/0003-4975(94)90363-8
[33]
Wahl, A., Billinger, M., Fleisch, M., Meier, B. and Seiler, Ch. (2000) Quantitatively Assessed Coronary Collateral Circulation and Restenosis Following Percutaneous Revascularization. European Heart Journal, 21, 1776-1784.
https://doi.org/10.1053/euhj.2000.2129
[34]
Stein, P., Davis, Z., Sabbah, H. and Marzilli, M. (1979) Reduction of Coronary Flow in the Native Circulation after Bypass. Observations in a Hydraulic Model of the Cardiovascular System. The Journal of Thoracic and Cardiovascular Surgery, 78, 772-778. https://doi.org/10.1016/S0022-5223(19)38067-5
[35]
Guo, L., Steiman, D., Moon, B., Wan, W. and Millsap, R. (2001) Effect of Distal Graft Anastomosis Site on Retrograde Perfusion and Flow Patterns of Native Coronary Vasculature. The Annals of Thoracic Surgery, 72, 782-787. https://doi.org/10.1016/S0003-4975(01)02801-6
[36]
Nordgaard, H., Nordhaug, D., Kirkeby-Garstad, I., Lovstakken, L., Vitale, N. and Haaverstad, R. (2009) Different Graft Flow Patterns Due to Competitive Flow or Stenosis in the Coronary Anastomosis Assessed by Transit time Flowmetry in a Porcine Model. European Journal of Cardio-Thoracic Surgery, 36, 137-142.
https://doi.org/10.1016/j.ejcts.2009.02.036
[37]
Rockstroh, J. and Brown, B. (2002) Coronary Collateral Size, flow Capacity and Growth: Estimates from the Angiogram in Patients with Obstructive Coronary Disease. Circulation, 105, 168-173.
https://doi.org/10.1161/hc0202.102120
[38]
Pohl, T., Seiler, C., Billinger, M., Herren, E., Wustmann, K., Mehta, H., Windecker, S., Eberli, F. and Meier, B. (2001) Frequency Distribution of Collateral Flow and Factors Influencing Collateral Channel Development. Functional Collateral Channel Measurement in 450 Patients with Coronary Artery disease. Journal of the American College of Cardiology, 38, 1872-1878. https://doi.org/10.1016/S0735-1097(01)01675-8
[39]
Miyamoto, S., Fujita, M. and Sasayama, S. (2000) Bidirectional Function of Coronary Collateral Channels in Humans. International Journal of Cardiology, 75, 249-252. https://doi.org/10.1016/S0167-5273(00)00313-2
[40]
Berry, C., Balachandran, K., L’Allier, Ph., Lespérance, J., Bonan, R. and Oldroyd, K. (2007) Importance of Collateral Circulation in Coronary Heart Disease. European Heart Journal, 28, 278-291.
https://doi.org/10.1093/eurheartj/ehl446
[41]
Bhatnagar, U., Nelson, G. and Stys, A. (2019) Collateral Flow Reversal: Exploring Protective Role of Collateral Circulation in Acute Coronary Syndrome. South Dakota Medicine: The Journal of the South Dakota State Medical Association, 72, 174-177.
[42]
Werner, G., Ferrari, M., Heinke, S., Kuethe, F., Surber, R., Richartz, B. and Figulla, H. (2003) Angiographic Assessment of Collateral Connections in Comparison with Invasively Determined Collateral Function in Chronic Coronary Occlusions. Circulation, 107, 1972-1977. https://doi.org/10.1161/01.CIR.0000061953.72662.3A
[43]
Wang, J., Filipovic, M., Skarvan, K., Michaux, I., Schumann, R., Buser, P. and Seeberger, M. (2006) Transesophageal Doppler Echocardiographic Detection of Intramyocardial Collateral Flow to the Right Coronary Artery and Changes in the Flow to the Inferior Left Ventricular Wall Immediately after Coronary Artery Bypass Grafting. American Journal of Cardiology, 98, 1587-1592. https://doi.org/10.1016/j.amjcard.2006.07.034
[44]
Zimarino, M., D’Andreamatteo, M., Waksman, R., Epstein, S. and De Caterina, R. (2014) The Dynamics of the Coronary Collateral Circulation. Nature Reviews Cardiology, 11, 191-197.
https://doi.org/10.1038/nrcardio.2013.207
[45]
Govindaraju, K., Badruddin, I., Viswanathan, G., Ramesh, S. and Badarudin, A. (2013) Evaluation of Functional Severity of Coronary Artery Disease and Fluid Dynamics’ Influence on Hemodynamic Parameters: A Review. Physica Medica, 29, 225-232. https://doi.org/10.1016/j.ejmp.2012.03.008
[46]
Yamamoto, E., Saito, N., Matsuo, H., Kawase, Y., Watanabe, S., Bao, B., Watanabe, H., Higami, H., Nakatsuma, K. and Kimura. T. (2016) Prediction of the True Fractional Flow Reserve of Left Main Coronary Artery Stenosis with Concomitant Downstream Stenoses: In Vitro and in Vivo Experiments. EuroIntervention, 11, e1249-e1256.
https://doi.org/10.4244/EIJV11I11A246
[47]
Uus, A., Liatsis, P., Jawaid, M., Rajani, R. and Benderskaya, E. (2015) Assessment of Stenosis Introduced Flow resistance in CCTA-Reconstructed Coronary Arteries. 2015 International Conference on Systems, Signals and Image Processing, London, 10-12 September 2015, 313-320. https://doi.org/10.1109/IWSSIP.2015.7314238
