Aortic valve area calculation
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EditorInChief: C. Michael Gibson, M.S., M.D. [1]; Associate Editor(s)InChief: Cafer Zorkun, M.D., Ph.D. [2]; Lakshmi Gopalakrishnan, M.B.B.S. [3]; Usama Talib, BSc, MD [4]
Overview
Aortic valve area calculation is an indirect method of determining the area of the aortic valve. The calculated aortic valve orifice area is currently one of the measures for evaluating the severity of aortic stenosis. A valve area of less than 0.8 cm² is considered to be severe aortic stenosis.^{[1]}^{[2]}
There are many ways to calculate the valve area of aortic stenosis. The most commonly used methods involve measurements taken during echocardiography. For interpretation of these values, the area is generally divided by the body surface area, to arrive at the patient's optimal aortic valve orifice area.
Cardiac Catheterization
Gorlin Equation
Grolin Equation can be used to calculate Aortic Valvular functional dynamics.^{[3]}^{[4]}
 In 1951, S.G. Gorlin and Dr. Richard Gorlin, were the first to develop a formula to calculate the cardiac valvular orifices using the flow and pressuregradient data.
 The Gorlin equation states that the aortic valve area is equal to the blood flow through the aortic valve during ventricular systole divided by the systolic pressure gradient across the valve times a constant.
 The flow across the aortic valve is calculated by taking the cardiac output (measured in liters/minute) and dividing it by the heart rate (to give output per cardiac cycle) and then dividing it by the systolic ejection period measured in seconds per beat (to give flow per ventricular contraction).
Aortic Valve Area (cms^{2}) = (Stroke volume (mL/beat) ÷ Systolic ejection period (secs/beat)) ÷ ( 44.3 x square root of mean systolic pressure gradient between the left ventricle and aorta (mm Hg))
Simplified Equation: Aortic valve area = (Cardiac output/Heart rate) ÷ (44.3 x Sq rt mean systolic pressure gradient x Systolic ejection period) → AVA = Cardiac output ÷ (44.3 x Heart rate x Systolic ejection period x Sq rt mean systolic pressure gradient)
 The Gorlin equation is related to blood flow across the valve. Therefore, in cases of low cardiac output, the valve area may be erroneously calculated as stenotic. Therefore, the measurement of the true gradient may be accomplished by temporarily increasing the cardiac output by the infusion of positive inotropic agents, such as dobutamine.
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Example: An individual undergoes left and right heart cardiac catheterization as part of the evaluation of aortic stenosis. The following hemodynamic parameters were measured. With a heart rate of 80 beats/minute and a systolic ejection period of 0.33 seconds, the cardiac output was 5 liter/minute. During simultaneous measurement of pressures in the left ventricle and aorta (with the use of one catheter in the left ventricle and a second in the ascending aorta), the mean systolic pressure gradient was measured at 50 mm Hg. What is the valve area as measured by the Gorlin equation?  
Answer:

Hakki Equation
 The Hakki equation is a simplification of the Gorlin equation, relying on the observation that in most cases, the numerical value of 44.3 x heart rate (bpm) x systolic ejection period (secs) is ≈1000.^{[5]}
 The resulting simplified formula is:
Aortic Valve Area (cms^{2}) = (Cardiac output (liters/minute)) ÷ (Square root of mean systolic pressure gradient between the left ventricle and aorta (mmHg))
Example: An individual undergoes left and right cardiac catheterization for the evaluation of aortic stenosis. Measurements includes an aortic pressure of 120/60, left ventricular pressure of 170/15, cardiac output of 3.5 liters/minute. What is the aortic valve area?  
Answer: The peak gradient between the left ventricle and aorta is 50 mm Hg → Aortic Valve Area = (3.5) ÷ (Sq root of 50) = 0.496 cms^{2} 
Echocardiography
Planimetry
Planimetry is the tracing out of the opening of the aortic valve in a still image obtained during echocardiographic acquisition during ventricular systole, when the valve is supposed to be open. While this method directly measures the valve area, the image may be difficult to obtain due to artifacts during echocardiography, and the measurements are dependent on the technician who has to manually trace the perimeter of the open aortic valve. Because of these reasons, planimetry of aortic valve is not routinely performed.^{[6]}
Continuity Equation
The role of continuity equation in diagnosing Aortic Stenosis can be understood with the following details. ^{[7]}
 The continuity equation states that the flow in one area must equal the flow in a second area if there are no shunts in between the two areas.
 In practical terms, the blood flow from the left ventricular outflow tract is compared to the blood flow at the level of the aortic valve.
 Using echocardiography, the aortic valve area calculated using the time velocity integral (TVI) which is the most accurate and preferred method.
 The blood flow through the LVOT (i.e., left ventricular stroke volume (cm^{3} or cc), can be calculated by measuring the LVOT diameter (cm), squaring that value, multiplying the value by 0.78540 giving cross sectional area of the LVOT (cm^{2})and multiplying that value by the LVOT TVI (cm), measured on the spectral Doppler display using pulsedwave Doppler.
 From these, it is easy to calculate the aortic valve area (cm^{2}) of the aortic valve by simply dividing the stroke volume (cm^{3}) by the aortic valve time velocity integral (cm) measured on the spectral Doppler display using continuouswave Doppler.
Aortic Valve Area (cms^{2}) = { (LVOT Diameter^{2} x 0.78540 x LVOT Time Velocity Integral) ÷ (Aortic Valve Time Velocity Integral) }
Example: An individual undergoes transthoracic echocardiography for the evaluation of a systolic ejection murmur with delayed carotid upstroke noted on physical examination. During echocardiography, the following measurements were made: LVOT diameter of 2 cm, LVOT TVI of 24 cm, and an Aortic Valve TVI of 50 cm. What is the aortic valve area?  
Answer:

 The weakest aspect of this calculation is the variability in measurement of LVOT area, because it involves squaring the LVOT dimension. Therefore, it is crucial for the sonographer to take great care in measuring the LVOT diameter.
References
 ↑ Charlson E, Legedza A, Hamel M (2006). "Decisionmaking and outcomes in severe symptomatic aortic stenosis". J Heart Valve Dis. 15 (3): 312–21. PMID 16784066.
 ↑ "Survival in elderly patients with severe aortic stenosis is dramatically improved by aortic valve replacement: results from a cohort of 277 patients aged >/=80 years". Eur J Cardiothorac Surg. PMID 16950629.
 ↑ James D. Thomas & Nicholas Furiasse (2016). "Exercise Testing in Paradoxical LowFlow Aortic Stenosis: Where Is the Truth?". JACC. Cardiovascular imaging. doi:10.1016/j.jcmg.2016.05.012. PMID 27568123. Unknown parameter
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ignored (help)  ↑ GORLIN R, GORLIN SG (1951). "Hydraulic formula for calculation of the area of the stenotic mitral valve, other cardiac valves, and central circulatory shunts. I". American Heart Journal. 41 (1): 1–29. PMID 14799435. Unknown parameter
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(help)  ↑ Hakki AH, Iskandrian AS, Bemis CE, Kimbiris D, Mintz GS, Segal BL, Brice C (1981). "A simplified valve formula for the calculation of stenotic cardiac valve areas". Circulation. 63 (5): 1050–5. PMID 7471364. Retrieved 20120412. Unknown parameter
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ignored (help)  ↑ Michael A. Fierro & Ian J. Welsby (2016). "Identification of Severe Mitral Stenosis Using RealTime ThreeDimensional Transesophageal Echocardiography During an Left Ventricular Assist Device Insertion". Anesthesia and analgesia. 123 (5): 1089–1093. doi:10.1213/ANE.0000000000001551. PMID 27984244. Unknown parameter
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ignored (help)  ↑ John B. Chambers, Denise Parkin, James Roxburgh, Vinayak Bapat & Christopher Young (2016). "A comparison of two forms of the continuity equation in the Trifecta bovine pericardial aortic valve". Echo research and practice. 3 (1): 25–28. doi:10.1530/ERP160007. PMID 27249811. Unknown parameter
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ignored (help)