Author + information
- Don P. Giddens, PhD∗ ()
- ↵∗Reprint requests and correspondence:
Dr. Don P. Giddens, Georgia Institute of Technology and Emory University, Wallace H. Coulter Department of Biomedical Engineering, 3096 Woodwalk Drive SE, Atlanta, Georgia 30339-8472.
Fractional flow reserve (FFR) in the clinical setting is approximated by the ratio of distal to proximal pressure under hyperemic flow conditions (1) and used as a tool to identify functionally significant coronary artery lesions. There is increasing interest in developing methodologies to compute FFR using principles of fluid dynamics applied to vascular geometries derived either from noninvasive computed tomographic imaging or from angiographic images obtained during catheterization. The former approach is hypothesized to be useful in stratifying patients into possible revascularization procedures or optimal medical therapy, while the latter is postulated to have value by replacing the additional step of measuring FFR under hyperemic conditions. In this issue of JACC: Cardiovascular Interventions, Tu et al. (2) present results for computing FFR using angiographic images, an approach aimed at simplifying invasive procedures.
Accuracy in computing FFR has 3 essential components: 1) constructing an in silico model representing the 3-dimensional geometry of the region of interest (ROI); 2) prescribing inflow to the ROI and outflow in the arterial branches; and 3) implementing a computational method. It is in the approaches to each of these critical steps that various groups differ. For example, Heartflow (3) uses computed tomographic images, uses a sophisticated model to distribute outflow among coronary artery branches, and computes FFR from the unsteady Navier-Stokes equations. Because computed tomography gives no flow information, assumed flow rates are based on models derived for tissue perfusion requirements in a healthy population.
In contrast, Tu et al. (2) constructed vessel geometry from angiography, used a simple model for flow division to branches (4), and used an approximate algebraic computational method based on experimental studies of flow through single arterial stenosis models (5) to solve for pressure drop and FFR. Because this does not involve numeric solution of the Navier-Stokes equations, the computational time is essentially instantaneous once the geometry is obtained and segmented into “subsegments” (2). The investigators compare their computed FFR (denoted as QFR) with invasive FFR using 3 methods for specifying the flow, Q, into the ROI: 1) fQFR, hyperemic inflow assuming a fixed inflow velocity of 0.35 m/s; 2) cQFR, a “virtual” hyperemic flow determined from a model that relates measured flow under baseline conditions (from TIMI [Thrombolysis In Myocardial Infarction] frame count) to hyperemic flow; and 3) aQFR, measured hyperemic flow.
QFR values derived from these assumptions give comparable results by comparison with measured FFR. Computations are fast, and the investigators conclude that “cQFR does not require pharmacological hyperemia induction and bears the potential of a wider adoption of FFR-based lesion assessment through a reduction in procedure time, risk, and costs.” Their reported accuracy compares favorably with groups that use noninvasive computed tomographic FFR methods (3,6). This is perhaps not surprising: the image resolution of angiography is superior to that of computed tomography, and imposing an individualized hyperemic inflow is directly patient specific, because it is derived from actual measurement.
Computationally, avoiding the Navier-Stokes equations is novel, although not without considerable approximation. The investigators compute pressure drops along a vessel using a simple quadratic equation with empirically derived coefficients based on early experimental work in stenotic flows (5). Although details are sketchy, the pressure drop–flow velocity relationship is assumed to be(Equation 1)where DP is the pressure drop along an arterial subsegment, HFV is the mean hyperemic flow velocity, and c1 and c2 are empirical coefficients derived for each subject by using the vessel and stenosis geometry. This equation is integrated subsegment by subsegment over the ROI to compute a total pressure drop, from which QFR is determined using a reference aortic pressure.
The model selected for flow splitting into arterial branches is critically important in computing FFR accurately. The relationship between flow and vessel radius in normal subjects has been well studied and is often expressed as(Equation 2)where Qd and Qp are flows in daughter and parent branches, respectively, Rd and Rp are vessel radii, and a is a parameter such that 2 < a < 3. Murray’s law uses a = 3 and is based on minimizing energy losses, while a = 2 implies constant velocity between mother and daughter branches. Tu et al. (2) did not account for branch outflows directly but rather inferred these by assuming that velocity in an epicardial vessel is constant from mother vessel to daughter (e.g., a = 2). This assumption is based on a study by Ofili et al. (4) in which intravascular Doppler measurements of velocity were performed in 15 subjects with 28 angiographically normal coronary arteries, and it was found that proximal and distal mean velocities in each major epicardial artery (left anterior descending, left circumflex, and right coronary artery) were relatively constant along the lengths investigated.
Returning to the 3 key components for calculating FFR, Tu et al. (2) have: 1) derived 3-dimensional arterial geometries from 2 planar angiographic views; 2) used TIMI frame count to prescribe patient-specific hyperemic inflow (either measured directly or inferred from baseline) and assumed a constant mean velocity along an epicardial artery as their flow split model; and 3) adapted a semiempirical algebraic model for computing pressure drop. This methodology results in a very fast computational time.
But is this process sufficiently fast, accurate, and easy to use that it can replace measured FFR during angiography as a tool for deciding on revascularization? The methodology presented that circumvents using the Navier-Stokes equations was developed for single constrictions using in vitro experiments in stenosis models with varying degrees of obstruction and shape and relies on empirically derived coefficients to capture stenosis complexity (5). Although Tu et al. (2) do not discuss whether they used these empirical coefficients directly or modified these, it is likely that accuracy in this simplified model will be degraded for complex lesions. Additionally, the investigators analyzed single vessels, and patients with multivessel disease will undoubtedly be more challenging.
An assumption of constant mean velocity along a vessel as a model for flow division has been rarely used. Interestingly, the value of HFV used to compute fQFR (2) was 35 cm/s, whereas the average value found by Ofili et al. (4) for the left anterior descending coronary artery was 62 cm/s. Furthermore, patients with coronary artery disease may not follow the behavior of healthy subjects. For example, our group has intravascular ultrasound–derived Doppler measurements of proximal and distal velocity under baseline conditions in 80 patients with mild to moderate coronary artery disease (7), and there is considerable departure from a constant velocity relationship along a vessel. Because Tu et al. (2) assume a quadratic relationship between pressure drop and velocity, patient-specific deviations from a constant velocity model would be expected to affect computed QFR. This can be seen from the derivative of Equation 1:(Equation 3)which suggests a strong dependence of pressure gradient upon HFV. Departures of actual HFV along a vessel from an model in which HFV is constant would likely be exacerbated for patients with more obstructive lesions, multivessel lesions, and microvascular disease. These factors may in part account for the notable scatter in computed versus measured results.
The overall aim is to improve clinical decisions, recognizing that FFR is only one tool available. An important clinical question is “how good is good enough?” for computed FFR to replace measured FFR during coronary angiography. The rates of false positives and false negatives in this study are small, and improvement over a purely anatomic classification of >50% stenosis for discriminating functionally significant lesions is demonstrated for these patients. However, key assumptions in the methodology—particularly the use of constant HFV and the fluid dynamic approximations inherent in Equation 2—may not have broad applicability. Whether clinicians will adopt computing FFR during angiography in lieu of measuring this variable is yet to be determined.
↵∗ Editorials published in JACC: Cardiovascular Interventions reflect the views of the authors and do not necessarily represent the views of JACC: Cardiovascular Interventions or the American College of Cardiology.
Dr. Giddens has received internal grants from Georgia Tech and Emory University in areas of computational hemodynamics in coronary arteries; and is currently a paid consultant for Emory University on projects supported by Medtronic and Abbott Laboratories.
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