Populations
This study was approved by the ethical review committee of the First Affiliated Hospital of Jinan University (Guangzhou, Guangdong, China). Since this study is a retrospective study, the informed consent was waived and anonymized data were used for analysis. Coronary CTA performed less than 60 days before scheduled non-emergent ICA and FFR measurement was required for inclusion. Exclusion criteria included individuals who were unable to provide informed consent; complete occlusion of the coronary arteries; significant arrhythmia; non-cardiac illness with life expectancy <2 years; pregnant state; previous coronary intervention or coronary bypass surgery; allergy to iodinated contrast; contraindications to beta-blocking agents, nitroglycerin, or adenosine; and suspected acute coronary syndrome. Eventually, 29 patients in total were included in this study. The average age ranged from 54 to 82 years old (68.1 years old ± 8.4 years), and the patients were diagnosed with cardiovascular disease between March 15, 2013 and June 23, 2015.
Coronary CTA acquisition and analysis
Coronary CTA was performed using an MDCT volumetric scanner with 320-detector rows (Aquilion ONE, Toshiba, Otawara, Japan). All the procedures followed the Society of Cardiovascular Computed Tomography guidelines [20]. Oral beta-blockers were administered, targeting a heart rate of <60 beats/min. CCTA data were obtained at both systole and diastole. Experienced radiologists evaluated luminal diameter stenosis in each coronary artery segment using an 18-segment coronary model before ICA [21]. Significant obstruction was defined as luminal stenosis >50% in the main coronary arteries.
ICA and FFR measurement
ICA was performed according to a standard protocol when the severity of stenosis in a major coronary artery was quantified as more than 50% [22]. Invasive FFR was performed to obtain physiology measurements for clinical indications in significant stenosis. According to the protocol, an FFR pressure wire (PressureWire Aeris/Certus, St. Jude Medical, St. Paul, USA) was positioned distal to the stenosis of interest, at least 3 cm downstream of the lesion, and then hyperaemia was induced by intravenous infusion of adenosine at 140 μg/kg/min [23]. FFR was calculated by dividing the mean distal coronary pressure (mPd) by the mean aortic pressure (mPa) during hyperaemia. The FFR was considered diagnostic of ischaemia at a threshold of 0.80 or less [24].
Model establishment
Patient-specific coronary arterial geometries were reconstructed from 29 sets of CTA image data. By dividing the cross-sectional area of the stenosis by the normal segment proximal to the lesion, 36 lesions were identified as a stenosis by anatomic evaluation. Details of the coronary geometries were determined by the distribution of the contrast agent. Because the coronary lumen was compressed during systole and was unable to be distinguished from the surrounded tissue, the diastole data were used for geometric reconstruction. Vessels were reconstructed offline using Mimics, commercial 3-D reconstruction software (Materialise NV, Leuven, Belgium). The mesh of the geometries was generated using a non-structural mesh with tetrahedron elements. The mesh independence test was performed such that different densities of the meshes were generated in one model. The mesh sizes ranged from coarse (approximately 17,100 nodes with 85,600 elements) to fine (approximately 32,800 nodes with 545,820 elements) such that five mesh sizes were generated in total, as shown in Fig. 1. CFD simulation was performed using each mesh, and the maximum velocities from the calculation were considered indexes from which the values were obtained at the same point of the geometry (the centre of the aortic ostium). Convergence of the test was obtained when the difference of the values between two mesh densities was less than 0.1%. The test results indicated that the standard of the finer mesh approach was appropriate for simulations.
CFD configuration and FFRCTA computation
Focusing on the haemodynamics in the coronary artery at the peak flow velocity phase, the flow distribution was assumed to be fully developed in this study. Assumptions were made regarding the simulations that the blood flow was incompressible, laminar and Newtonian; the blood viscosity and density were constant at 0.0035 Pa s and 1056 kg/m3, respectively [25].
The momentum and mass conservation of flow was solved using Navier–Stokes governing equations as follows:
$$ \uprho \left( {\frac{\text{du}}{\text{dt}} + {\text{u}} \cdot \nabla {\text{u}}} \right) = - \nabla p + \upmu \nabla^{2} {\text{u}} + f, $$
(1)
$$ - \nabla \cdot {\text{u }} = \, 0, $$
(2)
where ρ is the density of blood, u is the velocity field, p is the pressure, μ is the viscosity, and f is the body force per unit volume. All data were obtained while the patients were at rest, and because an external force was not involved, f was assumed to be zero [26].
Because pulsatile flow simulation was applied in the present study, the lumped parameter model was implemented for the outflow boundaries. The lumped parameter model (LPM) consisted of resistances and compliances. To achieve the physiological flow condition in arteries, patient-specific parameter values were calculated according to the literature [19, 27]. In brief, the mean flow rate to the coronary arteries was calculated based on the average physiological condition that the flow to the coronary arteries consumed 4% of the stroke volume and the ratio of the blood flow between the left and right coronary arteries was 7 to 3 [28]; the relationship between the resistance of each outlet and the total flow in the coronary arteries was determined by the scale of the branch and the mean inlet pressure/flow rate [19]. Then, the resistances of the LPM of each outlet were calculated according to the relationship of the resistances between normal upstream and downstream. The walls of the vessels were assumed to be rigid and to have no-slip boundaries. The normal flow rate of the aorta ostium was implemented at the inflow boundary [27]. For comparison of the accuracy and the effectiveness, the steady state method [19] was also implemented to calculate FFRSS in the present study.
Simulations were carried out using COMSOL Multiphysics (COMSOL AB, Stockholm, Sweden), and a multifrontal massively parallel sparse direct solver (MUMPS) was applied to the simulations. FFRCTA was calculated by dividing the average pressure at the stenosis by that at the ostium of the coronary artery. The pressure waveform was extracted from the simulations (e.g., Fig. 2), and FFRCTA was calculated over one heart cycle period, similar to the measurement procedure during clinical practice. The FFRCTA based on the simplified method was calculated under the same condition of the computational platform, and the values were extracted directly from the calculations.
Statistical analysis
Pearson correlation and Bland–Altman plots were performed to investigate the relationships between FFRCTA and invasive FFR on a per-vessel basis. Invasive FFR was used as the gold standard (FFR ≤ 0.8) to assess the diagnostic performance of FFRCTA and the luminal diameter stenosis. A patient was considered positive if any vessel had FFR ≤0.8, and the vessel with the most adverse clinical status was selected to represent a given patient (minimum FFR, minimum FFRCTA and maximum CCTA stenosis). FFRCTA ≤0.8 was used as the threshold to identify the ischaemic lesions in this study, as well as stenosis >50%. Diagnostic performance on a per-patient and -vessel basis was analyzed, including accuracy, sensitivity, specificity, positive predictive value (PPV), negative predictive value (NPV), positive likelihood ratio (+LR), and negative likelihood ratio (−LR). The area under the receiver-operator characteristics curve (AUC) was also measured for CCTA stenosis and FFRCTA. The AUCs were compared by the DeLong method. A P value less than 0.05 was deemed to be statistically significant. All the analyses were performed on SPSS (version 14, Chicago, IL, USA) and MedCalc Software (MedCalc, Mariakerke, Belgium).