Comparison of 1D and 3D Models for the Estimation of Fractional Flow Reserve

Abstract

In this work we propose to validate the predictive capabilities of one-dimensional (1D) blood flow models with full three-dimensional (3D) models in the context of patient-specific coronary hemodynamics in hyperemic conditions. Such conditions mimic the state of coronary circulation during the acquisition of the Fractional Flow Reserve (FFR) index. Demonstrating that 1D models accurately reproduce FFR estimates obtained with 3D models has implications in the approach to computationally estimate FFR. To this end, a sample of 20 patients was employed from which 29 3D geometries of arterial trees were constructed, 9 obtained from coronary computed tomography angiography (CCTA) and 20 from intra-vascular ultrasound (IVUS). For each 3D arterial model, a 1D counterpart was generated. The same outflow and inlet pressure boundary conditions were applied to both (3D and 1D) models. In the 1D setting, pressure losses at stenoses and bifurcations were accounted for through specific lumped models. Comparisons between 1D models (FFR1D) and 3D models (FFR3D) were performed in terms of predicted FFR value. Compared to FFR3D, FFR1D resulted with a difference of 0.00 ± 0.03 and overall predictive capability AUC, Acc, Spe, Sen, PPV and NPV of 0.97, 0.98, 0.90, 0.99, 0.82, and 0.99, with an FFR threshold of 0.8. We conclude that inexpensive FFR1D simulations can be reliably used as a surrogate of demanding FFR3D computations.

Fractional Flow Reserve Evaluated as Metric of Coronary Stenosis — A Mathematical Model Study

“…Similarly, 296 lesions were studied (15) and the authors compared (by linear regression) various clinically relevant measures, including diameter stenosis (R = 0.565), lesion length (R = 0.306), reference vessel cross sectional area (R = 0.195), and the myocardial supply area subtended by the coronary vessel under study (R = 0.504). In an attempt to further simplify calculations a 1D model was compared with a 3D model, and found to yield nearly similar findings for FFR (16). Findings reported in 38 studies (17) are summarized in Figure 9 which further illustrates the discrepancy between FFR and diameter-based indicators of coronary luminal obstruction.…”

Non-invasive fractional flow reserve: a comparison of one-dimensional and three-dimensional mathematical modeling effectiveness

“…В ходе анализа литературных источников удалось найти одну схожую публикацию. В исследовании [13] сравнивали одномерную и трехмерную модели с точки зрения прогнозирования значения КТ ФРК. В исследование были включены 20 пациентов и построены 29 трехмерных математических моделей коронарного русла: 9 на основании данных КТ КА и 20 на основании данных, полученных при выполнении внутрисосудистого ультразвука.…”

“…Результаты представленного исследования несколько хуже, чем в процитированной выше работе, однако следует отметить, что дизайн этого исследования отличался от предложенного авторами. Кроме того, в работе [13] использовался алгоритм построения трехмерной модели, предложенный самими исследователями, а не методика HeartFlow  , как в настоящей работе.…”

Mathematical modelling of atherosclerosis

“…In these cases two-scale 1D-3D models should be applied [50,58,125,129,165]. On the other hand, for estimation of the relative pressure drop across the stenosis, its asymmetry produces no appreciable difference [21,33].…”