## Role of Continuity Equation Is Unsuitable for Low-Gradient Aortic Stenosis

Accurate assessment of low-gradient aortic stenosis has come into sharper focus with the advent of transcatheter aortic valve replacement for calcific aortic stenosis (AS). When the mean transvalvular gradient exceeds 40 mm Hg, there is little question about the severity of AS, and hence the accuracy of aortic valve area (AVA) measurement using the Doppler echocardiography–based continuity equation is rarely questioned. However, when the mean aortic valve gradient is <35 mm Hg, there is a tendency to rely on the estimated AVA to classify stenosis severity. Indeed, a number of publications have reported on patients with severe AS, defined as AVA < 1.0 cm ^{2 }or corrected for body surface area as <0.6 cm ^{2 }/m ^{2 }. This reliance on Doppler-derived AVA for an accurate assessment of AS severity needs to be questioned. Alternative approaches to confirm AS severity might need to be considered.

The application of the continuity equation (i.e., left ventricular outflow tract [LVOT] area × LVOT velocity-time integral [VTI] = AVA × aortic valve VTI) necessitates accurate measurement of LVOT area, precise placement of the pulse Doppler sample volume to obtain the VTI, and interrogation of AS jet velocity using continuous-wave Doppler to obtain trans–aortic valve VTI. An experienced sonographer is able to record accurate and reproducible LVOT and aortic valve VTI. The least accurate parameter is LVOT area, which is derived from a single diameter at the level of the annulus using the assumption of circular geometry. Imaging by computed tomographic angiography (CTA) dealt a major blow to this assumption. Indeed, the annular shape is often ovoid or irregular ( Figure 1 ), and actual annular area measurements by CTA are quite disparate from these derived by echocardiographic diameter.

Table 1 shows the disparities in annular area derived by echocardiography versus those measured by CTA in six consecutive patients undergoing transcatheter aortic valve replacement. LVOT area by the echocardiographic method is consistently smaller by an aggregate average of 32%. This would translate into the numerator in the continuity equation (i.e., LVOT area × VTI) being 32% smaller by echocardiography than by CTA, which in turn results in the AVA derived by echocardiographic assessment of LVOT being 32% smaller. It is thus apparent that a significant number of patients with true AVAs between 1.0 and 1.4 cm ^{2 }may have calculated AVAs < 1.0 cm ^{2 }using the continuity equation and may thus be considered to have severe AS. This potential for misclassification has important consequence on the management of elderly symptomatic patients.

Patient | Annular area (cm ^{2 }) |
LVOT VTI | BSA (m ^{2 }) |
SVI (mL/m ^{2 }) | ||
---|---|---|---|---|---|---|

Echocardiography | CT | Echocardiography | CT | |||

1 | 3.14 | 4.14 | 21.0 | 1.5 | 44 | 58 |

2 | 3.75 | 5.4 | 16.1 | 1.7 | 35 | 51 |

3 | 4.15 | 5.57 | 14.1 | 2.0 | 29 | 39 |

4 | 3.46 | 4.32 | 14.7 | 1.9 | 27 | 33 |

5 | 3.46 | 4.72 | 20.7 | 1.7 | 42 | 57 |

6 | 2.83 | 3.44 | 25.0 | 1.7 | 42 | 51 |

## An Approach to Improve on the Application of the Continuity Equation during Low-Dose Dobutamine Stress Echocardiography

Although intravenous dobutamine infusion can be used to help evaluate the severity of AS in some circumstances, it is important to emphasize the differences between this application and the conventional dobutamine stress protocol used to detect inducible myocardial ischemia. Typically, conventional dobutamine stress echocardiography involves increasing the rate of dobutamine infusion in 3-min stages, up to a maximum of 40 μg/kg/min, with the addition of atropine as needed to reach a desired double product. In contrast, dobutamine-induced stress used to evaluate low-gradient AS involves a more deliberate approach, based on a 6- to 8-min infusion of dobutamine at a given dose to observe desirable hemodynamic effects, with a cautious increase in the infusion rate not to exceed a maximum dose of 20 μg/kg/min. The increase in left ventricular contractile function results in increased stroke volume (LVOT area × VTI) and the observed effect on mean transvalvular gradient (AS VTI). In true severe AS, an increase in stroke volume results in increased mean gradient, whereas in pseudo-severe AS, the gradient fails to rise concomitantly with increased flow. However, there are several cases that do not fall into these discrete diagnostic categories. To understand this conundrum, we need to examine differences between the continuity equation and the Gorlin equation used in cardiac catheterization laboratories. The continuity equation, in its simplest form, states that

AVA = Stroke volume ( i .e ., LVOT area × VTI ) Mean gradient ( i .e ., AS VTI ) .

Instead, the Gorlin equation, which is usually used with invasive hemodynamics to calculate valve area, states that

AVA = Stroke volume ÷ Ejection time K × Mean gradient .