Geometric characteristics of the patients’ coronary arteries
The 20 patient-specific coronary geometries were reconstructed. Among all, the 4 typical geometries were taken as examples as illustrated in Fig. 1. Isolated stenosis was found in case 1 and case 4 with significant difference in the length of the lesions. For case 1, the stenosis was in the middle of the left anterior descending coronary artery of length 3.28 mm; for case 4, the stenosis was in the middle of the right coronary artery of length 8.34 mm. On the other hand, serial stenoses were found in (i) case 2 of lengths 3.98 and 2.32 mm distributed at the bifurcation of the LAD and distal daughter branch, and (ii) case 3 of length 4.84 and 2.11 mm distributed at the adjacent bifurcation in the LAD. The severity of the stenosis at the locations of measurement was then calculated from the reconstructions; the stenosis percentage based on cross sectional area reduction of the four cases were 56.25% in case 1, 49.54 and 54.97% for the proximal and distal stenosis in case 2, 67.2 and 35.23% for the proximal and distal stenosis in case 3, and 62.3% in the middle of RCA in case 4.
Validation of the calculation
The hemodynamic simulations were performed in the 20 patient-specific coronary arterial geometries to investigate the performance of FFRCT in the functional assessment of complex stenosis. Validation of the calculation was made by comparing the calculated FFR at the location similar to the measurements, wherein the invasive FFRs were taken downstream to the stenosis in all cases. The mean ± SD of the error between FFRCT and FFR was − 0.023 ± 0.015. Taking the FFR < 0.8 as indicator of ischemic-related stenosis, the true positive and true negative values of FFRCT was 11/12 (91%) and 8/8 (100%), respectively. FFRCT values in the four example cases were 0.84, 0.67, 0.74 and 0.81, respectively. The corresponding FFR values were 0.83, 0.68, 0.79 and 0.88, respectively. The error between the FFRCT and the FFR in the four cases were 1.2, − 1.4, 6.3, and − 3.4%, the mean standard deviation of the error was − 0.0067 ± 0.042. As can be noted, good agreement was achieved between the calculations and the measurements.
Pressure distributions in the patient-specific coronary arteries
The time average pressure distribution in one cycle for the all cases were calculated (the four typical cases were taken as examples as illustrated in Fig. 2). The pressure drop was not significant at the bifurcation in the normal segments; comparing the left coronary arteries and right coronary arteries, the appearance was similar. Significant blood pressure variations were concentrated at the culprit stenosis, and the pressure drop was negatively proportional to the severity of the stenosis (as indicated by the arrows in Fig. 2).
Correlation between the pullback curve and the coronary geometries
The pressure values along the target vessels were extracted following the center-line of the vessels, and sampled at uniform distance to form the pullback curves. The distance between sampling points was determined to be half of the length of significant stenosis in the vessel. The locations of the beginning of the pullback curves were determined according to the patient-specific DSA images. The sampling procedure was also performed on the FFR pullback curve in each case, for evaluation of the accuracy of the calculations. The spearmen test showed good agreements to the overall pullback curves in the all cases (mean ± SD was 0.84 ± 0.102 with p value < 0.01, patient-wise). Particularly, for the 4 example cases, the correlation factor was 0.951, 0.923, 0.809, and 0.969, respectively, with p < 0.01, as indicated by Fig. 3). On the other hand, slight overestimation was found for the calculation in case 2 (with mean difference ± SD was − 0.0021 ± 0.02652) and underestimations were found for the remaining cases (with mean difference ± SD of 0.00993 ± 0.00557, 0.01477 ± 0.01654, and 0.009 ± 0.00775 for case 1, case 3 and case 4, respectively) according to the Bland–Altman test (Fig. 3).
The pattern and the values of the calculated pullback curves are evaluated by overlapping to the invasive FFR pullback curves from the measurements for the example cases (Fig. 4). The solid line represents the FFR and the dashed line with circle marks represents the FFRCT. Some variations in the patterns of the pullback curves were found among the cases. For instance, in case 1, the FFR value represents the pressure distribution in the stenotic left coronary artery; there appears to be a sudden increase from below 0.85 to above 0.88 at the normalized length of 0.25 from the distal beginning, which is an indication of the pressure variation between the immediate downstream and the immediate upstream of the distal stenosis. Within the same segment, the calculated pullback curve is less fluctuating compared to the measurement curve. Following the fast pressure recovery to 0.98 at the normalized length of 0.625, a plateau is observed along the measurement curve (FFR = 0.93), which indicates the pressure variation to the proximal stenosis. A delay is observed in the calculated curve. The calculated underestimation is mainly distributed proximal to the proximal stenosis.
In case 2, a gradual increase is found from the distal end to normalized length of 0.625, the FFR/FFRCT increased from 0.68/0.67 to 0.79/0.79, respectively. According to the DSA images, the distal end located at the downstream of the distal stenosis in the left anterior descending branch of the left coronary artery, and the proximal stenosis was located at the proximal bifurcation of the left coronary artery. The slow recovery of the pressure distribution coincides with the segment between two significant stenoses.
For case 3, slow pressure recovery is also found between the two stenoses in the left anterior descending branch of the left coronary artery. The measurement shows that FFR increased from 0.79 to 0.83 from the distal end to the normalized length of 0.75; the pullback curve could reproduce the pressure level at the two significant stenoses. However, the rate of the pressure recovery from the calculation diverged from the measurement during this segment. The measurement FFR curve fluctuated above 0.8, with a wide pulse between the normalized length of 0.25 and 0.625, followed by a significant short pulse to 0.9 before the normalized length of 0.75; the corresponding geometric characteristics were the proximal stenosis distal to the nearby bifurcation. On the other hand, the calculation presented a pressure drop at the distal stenosis at the bifurcation, followed by a slow pressure recovery until the proximal stenosis.
For case 4, the FFR value recovered from 0.88 to 0.92 over the distal stenosis, which is 0.91 for the calculation at the normalized length of 0.2. Following a plateau along the normalized length of 0.2 to 0.8, a recognizable overestimation is found in the calculation compared to the measurement (an average 3% error comparing FFRCT to FFR along the pullback curves). The corresponding segment begins from the significant stenosis at the mid-right coronary artery to the proximal.
A significant drop of FFRCT was found in the cases with single stenosis (case 4 in Fig. 4), on the contrary, a plateau was found in serial stenosis (case 2 and 3 in Fig. 4). Therefore, 14 cases were identified with serial stenosis and grouped that the correlation between radius and FFRCT were evaluated. Spearman test showed that mean ± SD per patient over the 14 cases was 0.9 ± 0.35, p < 0.01). Four cases with serial stenoses were showed as examples here that the radiuses of the stenotic arteries were overlapped to the FFRCT (Fig. 5). FFRCT pullback curves showed plateau between serial stenoses (as showed in a, b and c in Fig. 5). However, as the distance became small between stenoses, the plateau was replaced by a delay of pressure recovery instead (as showed in d in Fig. 5). The correlation between variation rate of the radius and the FFRCT was also tested that the mean ± SD of spearman correlation per cases was 0.56 ± 0.08, p < 0.0001.
Correlation of wall shear stress to the pressure variations
Time average wall shear stress (TAWSS) was evaluated in the stenotic branches, and their variations along the branches are illustrated in Fig. 6. In the figure, H1, H2, H3, H4 indicate high TAWSS, and the L1, L2, L3, L4 indicate low TAWSS for each case. Significant high TAWSS was found in the stenosis area in cases 2, 3 and 4, except for case 1. High TAWSS is also found to be distributed along the branches, as for instance, where the curvature was found in case 1 (labeled with a solid star in H1) and the daughter branches proximal to the bifurcations (labeled with a hollow star in H4).
On the other hand, significant low TAWSS was seen to be located at various sites, including immediate downstream of the stenosis (labeled with a solid star in L1 for case 1), immediate upstream of the stenosis (labeled with a solid star in L2 for case 2) and at the area of the bifurcations (labeled with a solid star in L1 for case 1, a hollow star in L3 for case 3, and a solid star in L4 for case 4).
The maximum TAWSS at the stenosis was 22.07, 57.14, 8.69, 11.6 Pa for cases 1, 2, 3 and 4, respectively; minimum TAWSS at the significant low TAWSS area was 1.2, 1.5, 1.4 and 1.21 Pa for cases 1, 2, 3, and 4, respectively.
Outcomes of the actual vs. simulated interventions performed for case 3
Treatment had been performed in the stenosis of hemodynamic significance for case 3 (Fig. 7A, B). For the serial stenoses (in case 3, a stent of length equals to the arterial segment between bifurcations was placed to restore the cross-section area of the lumen. Invasive FFR was measured immediately following the PCI procedure and the FFR value along the vessel from the distal stenosis to the ostium of the LAD was recorded (Additional file 1).
Virtual revascularization by virtual stenting was then performed in the image-based reconstruction of the stenoses (Fig. 7C). For the virtual revascularization, the stenotic lumen was repaired, and the cross-section areas of the repaired lumen equaled to the average of the cross-section areas of the immediate upstream and downstream of the stenosis. The pullback curve was then calculated, as shown in Fig. 7. The FFRCT pullback curve was overlapped to the measurement curve as shown in Fig. 7D. The pattern of the FFRCT pullback curve shows good agreement with the FFR (the spearmen correlation factor was over 0.93 with p value < 0.01).