The aortic valve (AV) is a semilunar valve of the heart. The area of the aortic valve (AVA) is used for measuring the severity of the Aortic stenosis (AS). Measurements that are taken during echocardiography is used for the calculation of the AVA. Find the stroke volume (SV), cross-sectional (CSA) and AVA by entering the left ventricular outflow tract (LVOT), velocity time integral (VTI).

### Formula

If the Aortic valve area is less than 1 centimeter square, then the risk for the aortic stenosis disorder is high.

**Example**

If LVOT is 1, LVOT (VTI) is 2 cm and aortic valve VTI is 3 cm

**CSA** = 0.785 x 1 = 0.785 cm^{2}

**SV** = 0.785 * 1^{2} * 2 = 1.570 cc

**Aortic Valve Area** = 1^{2} * 0.78540 * 2/3 = 0.52 cm^{2}

Hence, the risk for Aortic Stenosis is Severe.

Derivation of valve area is based the continuity equation which states that the flow passing through the LVOT has to equal the flow through the AV. Echocardiographic derived measurements are based on maximal instantaneous gradient which provide a more accurate assessment then non-physiologic peak-to-peak gradients observed on invasive studies. In general, the VTI (cm) is felt provide a more accurate assessment of valve area however peak velocity (m/sec) can also be used.

The normal aortic valve area is 3-4 cm^{2}. Symptoms tend to not be apparent until the AS is severe (<1cm^{2}). If a patient presents with symptoms and the AVA is measured in the mild-moderate range alternative causes should be explored before attributing them to AS alone.

Aortic valve area calculation can be directly performed through planimetry during echocardiography or indirectly estimated through several equations based on clinical cardiological measurements.

AVA estimates are crucial in the diagnosis of aortic stenosis and its severity, along with the measurement of transvalvular flow and the determination of the magnitude and duration of the transvalvular pressure gradient.

**Continuity equation**

- AVA = LVOT diameter (in cm)
^{2}x 0.78540 x LVOT VTI (in cm) / Aortic Valve VTI (in cm)

**Gorlin equation**

- AVA = Cardiac Output (in mL/min) / (Heart rate in beats/min x Systolic ejection period in seconds x 44.3 x √Mean valvular gradient in mmHg)

**Hakki equation**

- AVA = Cardiac Output in L/min / √Peak to peak gradient in mmHg

### Determining aortic valve area

The aortic valve (one of the two semilunar valves of the heart) is situated between the left ventricle and the aorta. It is basically the last structure in the heart the blood goes through before entering the systemic circulation.

Aortic valve area calculation can be directly performed through planimetry during echocardiography or indirectly estimated through several equations based on clinical cardiological measurements.

Inadequate opening of the aortic valve, often resulting from calcification, leads to higher flow velocities through the valve and larger pressure gradients.

AVA estimates are crucial in the diagnosis of aortic stenosis and its severity, along with the measurement of transvalvular flow and the determination of the magnitude and duration of the transvalvular pressure gradient.

In adult individuals with normal aortic valves, the valve area is 3 to 4 cm^{2} and anything less than 1 cm^{2} is considered severe stenosis. The ACC/AHA 2006 Guidelines for the Management of Patients With Valvular Heart Disease define the following aortic stenosis severity degrees:

Aortic Stenosis Severity | AVA | Mean pressure gradient | Peak systolic flow velocity |
---|---|---|---|

Mild | > 1.5 cm^{2} |
< 25 mmHg | < 3 m/s |

Moderate | > 1.0 - 1.5 cm^{2} |
25 - 40 mmHg | 3 - 4 m/s |

Severe | ≤ 1.0 cm^{2} |
> 40 mmHg | > 4 m/s |

#### The continuity equation

The continuity equation for indirectly determining the aortic valve area is based on the assumption that the flow in one area must equal the flow in a second area (where no shunts exist). Which can be put in cardiac terms as the flow from the left ventricular outflow tract (LVOT) having to equal the flow at the level of the aortic valve.

**AVA = LVOT diameter ^{2} x 0.78540 x LVOT VTI / Aortic Valve VTI**

Where all measurements are in centimetre.

The accuracy of this equation is limited by the accuracy of the three measurements involved, especially that of the LVOT diameter which is then squared in the equation.

#### The Gorlin equation

Aortic valve area calculation by the Gorlin formula is an indirect method of determining AVA based on the flow through the valve during ventricular systole divided by the systolic pressure gradient across the valve times a constant (44.3). The below equation relies on the ratio of peak-to-peak instantaneous gradients.

**AVA = Cardiac Output / (Heart rate x Systolic ejection period x 44.3 x √Mean valvular gradient)**

**Where:**

- Aortic valve area is expressed in cm
^{2}; - Cardiac Output is expressed in mL/min;
- Heart rate is expressed in beats/min;
- Systolic ejection period is expressed in seconds;
- Mean valvular gradient is expressed in mmHg.
- Please note that at low cardiac output (less than 2,500 mL/min), the Gorlin equation tends to overestimate the degree of aortic stenosis.

#### The Hakki equation

This is a simplification of the Gorlin equation that assumes that in most cases, the numerical value of the product of the heart rate, systolic ejection period and constant is approximately 1000.

In consequence, if Heart rate x Systolic ejection period x 44.3 is approx. 1000, then the equation becomes:

**AVA = Cardiac output (in L/min) / √Peak to Peak Gradient in mmHg**

#### References

- Chambers JB, Sprigings DC, Cochrane T, Allen J, Morris R, Black MM, Jackson G. Continuity equation and Gorlin formula compared with directly observed orifice area in native and prosthetic aortic valves. Br Heart J. 1992; 67(2): 193–199.
- Hakki A, Iskandrian A, Bemis C, Kimbiris D, Mintz G, Segal B, Brice C. A simplified valve formula for the calculation of stenotic cardiac valve areas. Circulation. 1981; 63 (5): 1050–5.
- Rifkin RD. Physiological Basis of Flow Dependence of Gorlin Formula Valve Area in Aortic Stenosis: Analysis Using an Hydraulic Model of Pulsatile Flow. J Heart Valve Dis. 2000; 9(6):740-51.
- Gorlin R, Gorlin SG: Hydraulic formula for calculation of stenotic mitral valve, other cardiac valves, and central circulatory shunts. Am Heart J. 1961; 41:1-29.
- ACC/AHA 2006 Guidelines for the Management of Patients With Valvular Heart Disease: A Report of the American College of Cardiology/American Heart Association Task Force on Practice Guidelines (Writing Committee to Revise the 1998 Guidelines for the Management of Patients With Valvular Heart Disease): Developed in Collaboration With the Society for Cardiovascular Angiography and Interventions: Endorsed by the Society of Cardiovascular Anesthesiologists and the Society of Thoracic Surgeons. Circulation 2006; 114;84-231.