- Open Access
A new CFD based non-invasive method for functional diagnosis of coronary stenosis
© The Author(s) 2018
Received: 10 October 2017
Accepted: 17 March 2018
Published: 22 March 2018
Accurate functional diagnosis of coronary stenosis is vital for decision making in coronary revascularization. With recent advances in computational fluid dynamics (CFD), fractional flow reserve (FFR) can be derived non-invasively from coronary computed tomography angiography images (FFRCT) for functional measurement of stenosis. However, the accuracy of FFRCT is limited due to the approximate modeling approach of maximal hyperemia conditions. To overcome this problem, a new CFD based non-invasive method is proposed.
Instead of modeling maximal hyperemia condition, a series of boundary conditions are specified and those simulated results are combined to provide a pressure-flow curve for a stenosis. Then, functional diagnosis of stenosis is assessed based on parameters derived from the obtained pressure-flow curve.
The proposed method is applied to both idealized and patient-specific models, and validated with invasive FFR in six patients. Results show that additional hemodynamic information about the flow resistances of a stenosis is provided, which cannot be directly obtained from anatomy information. Parameters derived from the simulated pressure-flow curve show a linear and significant correlations with invasive FFR (r > 0.95, P < 0.05).
The proposed method can assess flow resistances by the pressure-flow curve derived parameters without modeling of maximal hyperemia condition, which is a new promising approach for non-invasive functional assessment of coronary stenosis.
Functionally significant stenosis generally causes angina symptoms, and is associated with inducible ischemia and impaired outcome. Therefore, it should be revascularized. While, if a stenosis has no functional significance, medical treatment is quite excellent . Therefore, determining the functional significance of a coronary stenosis plays a pivotal role in decision making in coronary revascularization . Fractional flow reserve (FFR) is considered as the gold standard for assessment of functional measurement of stenosis [2, 3]. It is a pressure derived index and defined as the ratio between the distal and proximal pressure of the stenosis at maximal hyperemia . A cut-off value of 0.75–0.8 is employed to indicate the functionally significant stenosis . FFR-guided strategy has been proved to be safety and also has been demonstrated to be both cost-effective and cost-saving [5–7]. However, FFR is an invasive procedure and requires pharmacologic intervention to induce maximal hyperemia, which limits its in-hospital utilization [2, 8]. To overcome this problem, a novel technology that combines coronary computed tomography angiography (cCTA) and computational fluid dynamics (CFD) has been developed [9–11]. By using the CFD method, an accurate reconstruction of coronary flow and pressure fields can be obtained from cCTA images, and then, the coronary diagnostic index (CT-derived computed FFR, FFRCT) can be derived without additional medications [9, 12–15]. Multiple clinic trials have demonstrated that the performance of FFRCT was superior to cCTA stenosis for diagnosing ischemic lesions [16–21]. The use of FFRCT is showed to reduce the overall use of invasive angiography and more and more researchers suggest that FFRCT can be the gatekeeper to the cardiac catheterization laboratory .
To overcome this problem, a new CFD based non-invasive approach for functional measurement of stenosis is proposed. It is based on an invasive non-dimensional index, pressure drop coefficient (CDP), which combining both the pressure and flow velocity information. CDP is defined as the ratio of trans-stenotic pressure drop to distal dynamic pressure during maximal hyperemia . Compared with pressure-derived indices (FFR), CDP directly quantifies the hemodynamic behavior of a stenosis section . Thus, the presence of microvascular disease has limited impact on CDP [27–29]. However, due to the limitation of the invasive procedure (the viscous loss is not considered in order to get a result with a single measurement; the flow velocity is measured, but not the flow rate), CDP is still dependent on the flow rate across a stenosis . Although previous studies reported that CDP were useful during both basal and hyperemia condition, the cutoff values were quite different in those two conditions [27, 30]. Additional, guide wire insertion has great impact on flow patterns, and reliable measurement of flow velocity is also technically difficult . Fortunately, those limitations of CDP can be overcame by combining with CFD method. The viscous loss can be included with multiple measurements, simply by specifying different boundary conditions; flow rates also can be accurately obtained without the influence of guide wire insertion. Unlike FFRCT, the proposed approach do not need to model the hyperemia condition. Instead, the stenosis flow with a series of flow rates will be simulated and the pressure-flow relationships is obtained. Then, f and s in Eq. 1 can be estimated and further employed to functional measurement of stenosis.
Vascular geometry reconstruction
Besides the reconstructed patient-specific models, several idealized coronary stenosis models are also created. As shown in Fig. 1b, two types of stenosis are modeled: concentric shaped stenosis and eccentric shaped stenosis. For each types, seven models with the AS% of 65, 70, 75, 80, 85, 90 and 95% are created. These idealized stenosis sections are modeled as 3D pipes with a diameter of 3 mm and the stricture length is kept to be two diameters for all models.
Instead of providing approximate boundary conditions for pulsatile flow simulation (as FFRCT), a series of boundary conditions with specified pressures and resistances are applied for steady flow simulation. In the proposed method, a static pressure (88 mmHg) is applied to the inlet. For each outlets, a lumped parameter model with only one resistance is coupled (Fig. 1c). The resistance represents the microvascular resistance. The “form–function” relationship (which relates the resistance of a downstream vessel to the vessel size at each outlet) is assumed to derive the values of microvascular resistance for each outlets with a given total distal microvascular resistance [9, 31]. Finally, a series values of total distal microvascular resistance are specified, providing different outlet boundary conditions for each steady flow simulation. The total distal microvascular resistance is set to be 240 (mmHg s/cm3) at first, and then reduced to 87.5, 75.0, 62.5, 50.0, 37.5 and 25.0%. Thus, for one case, steady flow is simulated seven times with seven different total distal microvascular resistances. Since only one outlet exists in each idealized models, the outlet may not be coupled to the lumped parameter model to enforce the “form–function” relationship. Thus, a more simple boundary conditions can be applied to get the pressure-flow curves. For idealized models, a relative zero pressure is assumed at the outlet and a series of static pressure is applied at the inlet. The inlet static pressure is set to be 0.5 mmHg at first, and then increased by 0.5 mmHg each time, until it reaches 11 mmHg.
ANSYS FLUENT V14 (ANSYS Inc.) was used to perform flow simulations. The blood was modeled as an incompressible Newtonian fluid. The dynamic viscosity is set to be 3.5 cP and the density to be 1050 kg/m3. The k–ω shear stress transport turbulence model was adopted for turbulence modeling of the low Reynolds number flow in stenosis arteries . Mesh independence was judged by comparing both the computed velocities and the pressure. For each case, further grid refinement (doubled mesh resolution) led to < 1% relative error in velocity and pressure profiles.
Validation with FFR
To further validate the proposed method, six patients who undergo both FFR and cCTA scans are employed. FFRs are measured with pressure wire (St. Jude Medical, Inc.) by experienced invasive cardiologists. cCTA images are acquired and six 3D coronary models with stenosis in LAD are reconstructed as described in “Vascular Geometry Reconstruction”. Parameters derived from the simulated pressure-flow curve are compared with the invasive FFR.
A promising noninvasive method was proposed for assessing of hemodynamic significance of coronary stenosis. Anatomy information of a stenosis is first derived from the cCTA images; and then, the pressure-flow relationship of a stenosis is obtained by using CFD method. Unlike previous invasive (FFR and CDP) or noninvasive method (FFRCT) which evaluating the stenosis at a specific flow rate (maximum hyperemia), the proposed method characters the hemodynamic stenosis at a series of flow rate. The main advantages of the proposed method are: (1) it is a non-invasive functional diagnosis method; (2) do not need to model the maximum hyperemia condition; (3) fully characters the pressure-flow behavior of a stenosis within normal physiological range. The proposed method is validate in six patients who undergo both FFR and cCTA scans, and all the proposed four parameters have linear and significant correlations with invasive FFR.
Compared with cCTA
It was reported that anatomic assessments of stenosis evaluated by cCTA had significant correlation with those evaluated by digital subtraction angiography . Although cCTA alone can accurately detect anatomically obstructive coronary stenosis, it cannot define the hemodynamic significance of a stenosis due to the complex relationship between stenosis and flow . The spatial characteristics of stenosis have great impact on flow [41–43]. Even for stenosis with similar AS%, the pressure-flow behaviors still can be different due to the different shapes of stenosis (as shown in Figs. 2 and 4). With the anatomic models obtained by cCTA, a further CFD analysis is performed to fill the gap between anatomically obstructive and hemodynamic significance. In the proposed method, pressure-flow curves are obtained and further employed to define the hemodynamic significance. It characters the nonlinear relationship between the flow rate and the pressure drop across a stenosis, reflecting the flow resistances of a given stenosis. A sharper curve represents a larger flow resistance, while more flat curve means smaller flow resistance. As shown in Fig. 4, severe stenosis defined by cCTA can have a relative smaller flow resistance, but it cannot be known before the pressure-flow curve obtained. Several parameters are derived from the curves to quantify the flow resistance. As compared with AS%, flow resistance has a more direct relationship with the radius of a stenosis . Thus, from the results, moderate correlations are observed when correlated these parameters with AS%, but linear and significant correlations are obtained when correlated with MLA.
Compared with FFRCT
CFD is applied in both FFRCT and proposed method to provide the hemodynamic information of a stenosis. For FFRCT, pressure drop during maximal hyperemia is employed ; while for our method, pressure-flow relationship is derived. With a given flow rate, the pressure drop across the stenosis can be determined from its pressure-flow relationship. Thus, FFRCT can be derived from the obtained pressure-flow relationship if the exact flow rate during maximal hyperemia is known. However, the main problem for CFD based method is that there is no additional measurement about the flow rate during maximal hyperemia . Although clinical trials (DISCOVER-FLOW, DeFACTO and NXT) demonstrated that FFRCT improved diagnostic accuracy in differentiating ischemic stenosis as compared with cCTA alone [19–21], the performance is still unsatisfactory when compared with invasive FFR. One possible reason is that FFRCT has to employ several physiological models to estimate an approximate maximal hyperemia condition. Instead of modeling maximal hyperemia condition, a series of boundary conditions are specified and those simulated results are combined to provide a pressure-flow curve in proposed method. By this way, the accuracy do not rely on the modeling of maximal hyperemia condition. Additionally, pressure-flow relationship represents the flow resistances of a stenosis, which is determined mainly by its anatomical morphology. A functionally significant stenosis will increase the flow resistances and lead to a decrease in distal perfusion pressure, further cause ischemia [23, 43]. Thus, flow resistance maybe a more essential index for functional measurement of stenosis, as compared with pressure derived index.
Compared with CDP
CDP is a parameter which incorporates both pressure and flow variations . By ignoring the viscous friction effect and replacing the flow rate as flow velocity in Eq. (1), the expansion loss (s) can be approximately obtained with a single measurement of pressure drop and flow velocity. In the presence of microvascular dysfunction and submaximal hyperemia, both the pressure drop and the flow velocity will decreased, leading to a significant increase of pressure-derived parameters (FFR and FFRCT), but it has a limited impact on CDP . Ideally, the flow rate should have little impact on CDP. However, due to the assumptions made by CDP, the measured values in basal and hyperemic conditions are still quite different . Additionally, it is also difficult to measure the flow velocity accurately. Fortunately, those problem can be overcome by the proposed CFD based method. By combining several measurements, both the viscous friction (f) and expansion loss (s) can be estimated and the pressure-flow relationship can be obtained. With the CFD method, the flow rate also can be measured without the impact of guide wire insertion. It is reported that CDP has the ability to localize the differential culpability for flow impediment: translesional or microvascular [27–29]. But in proposed method, it is noninvasive and only the anatomy information derived from cCTA is used, thus the microvascular disease is excluded and it is concentrated to evaluate the culpability for flow impediment of translesional stenosis.
In this paper, a CFD based non-invasive method is proposed for functional measurement of coronary stenosis, which do not need to model the maximal hyperemia condition. However, only six patients are employed to validate with current “gold standard” invasive FFR. Besides, due to lack of FFR data, currently there is no cut-off value for those parameters derived from pressure-flow curves. Even though, this is a first approach to functional measurement of coronary stenosis non-invasively without modeling the maximal hyperemia conditions. Given this advantage over FFRCT, we believe that it will have a promising role in clinical practice. Still, further validations need to be performed, especially corrected with FFR. To limit the computational time, steady state flow is simulated to get the pressure-flow curves. However, blood flow is pulsating, which is inconsistence with steady state flow assumption. Fortunately, current “gold standard” invasive FFR is based on time-averaged pressure measured over several cardiac cycles , and previous studies also demonstrated that FFRCT obtained by using steady state flow simulation still performed well . Additionally, the boundary conditions used for pulsating flow simulation in FFRCT is derived from lumped parameter models, which is also inconsistence with real conditions [11, 46]. Thus, steady state flow is simulated in our method.
XX contributed to the experimental design, analysis of data. MZ and DW contributed to the cCTA data analysis. YL and SX carried out the experiments and the statistical analysis. XX provided final approval of the version of submitted manuscript. All authors read and approved the final manuscript.
The authors gratefully acknowledge the support provided by the National Natural Science Foundation of China (Grant Nos. 61601368, 81471663), the Natural Science Basic Research Plan in Shaanxi Province of China (2017JQ6012) and the Fundamental Research Funds for the Central Universities (No. 3102017jc11002).
The authors declare that they have no competing interests.
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