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FFR quantification in a left coronary artery using a three-element Windkessel model and the nonlinear viscoelastic property of blood

André A. Martins, Catarina F. Castro, Carlos C. António, Luísa C. Sousa and Sónia I. S. Pinto

Vol. 11 (2023), No. 3, 349–379
Abstract

Atherosclerosis is a cardiovascular disease that obstructs blood flow to the heart. The fractional flow reserve (FFR) is the gold standard in assessing the functional significance of an intermediate coronary lesion. The goal of this study is to noninvasively calculate a patient-specific FFR value, using hemodynamic simulations under conditions as realistic as possible, and to compare it with the invasively measured FFR in the hospital. Regarding the methodology, the main novelty of this work is the use of blood’s viscoelastic property in conjunction with a three-element windkessel model as a pressure boundary condition, in the hemodynamic simulations. No studies were found in the literature taking into account both assumptions simultaneously.

The three-element windkessel model was implemented in the present study through a user-defined function (UDF) in ANSYS software. This model has three parameters that require estimation. Three estimates were made, based either on the measured blood pressure of the patient-specific case, in the hospital, or on a higher blood pressure. Blood’s viscoelastic property is considered by using the simplified Phan-Thien–Tanner (sPTT) model.

The invasively measured FFR is of 0.93. The noninvasive FFR, calculated by using hemodynamic simulations, is of 0.91 in all scenarios for the estimation of the model parameters. This corresponds to a relative error of 2.15% in the FFR-value calculation.

The noninvasive calculation of the FFR value appears to have low sensitivity to the model’s parameter estimates. Thus, the geometry of the patient’s stenosis appears to be a determining factor in the FFR value calculation.

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Keywords
fractional flow reserve, left coronary artery, windkessel model, viscoelasticity, user-defined function, hemodynamic simulations
Mathematical Subject Classification
Primary: 65K05, 92C10
Milestones
Received: 13 October 2022
Revised: 27 January 2023
Accepted: 27 February 2023
Published: 15 November 2023

Communicated by Antonio Carcaterra
Authors
André A. Martins
Faculty of Engineering
University of Porto
Porto
Portugal
Catarina F. Castro
Faculty of Engineering
University of Porto
Porto
Portugal
Institute of Science and Innovation in Mechanical and Industrial Engineering (LAETA-INEGI)
Porto
Portugal
Carlos C. António
Faculty of Engineering
University of Porto
Porto
Portugal
Institute of Science and Innovation in Mechanical and Industrial Engineering (LAETA-INEGI)
Porto
Portugal
Luísa C. Sousa
Faculty of Engineering
University of Porto
Porto
Portugal
Institute of Science and Innovation in Mechanical and Industrial Engineering (LAETA-INEGI)
Porto
Portugal
Sónia I. S. Pinto
Faculty of Engineering
University of Porto
Porto
Portugal
Institute of Science and Innovation in Mechanical and Industrial Engineering (LAETA-INEGI)
Porto
Portugal