Measuring Valve Gradients and Areas

Although echocardiographic valve area determinations have taken the primary role in noninvasive assessment, it is important to remember that the standard on which echocardiography is based is the catheter-based hemodynamic data, which include aortic and left ventricular (LV) pressures and the measurement of cardiac output (CO). The original calculations of mitral and aortic valve stenosis have remained vital for >70 years.1Gorlin R. Gorlin S.G. Hydraulic formula for calculation of the area of the stenotic mitral valve, other cardiac valves, and central circulatory shunts.I Am Heart J. 1951; 41: 1-29https://doi.org/10.1016/0002-8703(51)90002-6Crossref PubMed Scopus (1142) Google Scholar In brief, invasively obtained transvalvular pressure gradients and the calculation of valve areas require the following:•An appropriate catheter and recording system for the accurate measurement of pressures2Dean L.S. Kern M.J. Getting from A to C: from pressure waves to graphic display to interpretation.J Soc Cardiovasc Angiogr Interv. 2022; 1100034https://doi.org/10.1016/j.jscai.2022.100034Abstract Full Text Full Text PDF Google Scholar above and below the valve under study•Simultaneous transvalvular pressures should be obtained whenever possible. See alternatives to the dual lumen catheter3Kern M.J. The Langston is gone for now (no more dual lumen pigtail for aortic valve assessment). Now what? Cath Lab Digest.www.hmpgloballearningnetwork.com/site/cathlab/content/langston-gone-now-no-more-dual-lumen-pigtail-aortic-valve-assessment-now-what-includes-video-discussionDate accessed: June 18, 2022Google Scholar•A hemodynamic recording system capable of calculating the mean gradient and valve area or one may use peak-to-peak gradients for aortic stenosis if a mean gradient is not available (see below)•An accurate CO measurement•An understanding of the underpinnings of the formulas that are used to make valve area calculations There are 2 formulas that can be used to calculate valve area—the Gorlin and Hakki formulas. The gold (perhaps old as well) standard is the Gorlin formula, first published in 1951.1Gorlin R. Gorlin S.G. Hydraulic formula for calculation of the area of the stenotic mitral valve, other cardiac valves, and central circulatory shunts.I Am Heart J. 1951; 41: 1-29https://doi.org/10.1016/0002-8703(51)90002-6Crossref PubMed Scopus (1142) Google Scholar Since then, other formulas have been proposed and, although a bit simpler, are all based on the original study by Gorlin and Gorlin.1Gorlin R. Gorlin S.G. Hydraulic formula for calculation of the area of the stenotic mitral valve, other cardiac valves, and central circulatory shunts.I Am Heart J. 1951; 41: 1-29https://doi.org/10.1016/0002-8703(51)90002-6Crossref PubMed Scopus (1142) Google Scholar To understand the history, we must turn the clock back to the early beginnings of invasive cardiac catheterization and cardiovascular surgery. There was a need to assess valvular heart disease, predominantly rheumatic, at a time before cardiopulmonary bypass and echocardiography were available. One needed to know who would need surgery (done by closed mitral commissurotomy in the beating heart). The Gorlin formula was developed for this very reason. Based on fundamental hydraulics, a valve area (cm2) was equal to flow (mL/s) across the valve divided by the square root of the pressure difference (ie, the gradient or ΔP) across the valve × 2 constants. The first constant is the discharge coefficient, an empirical constant of 1 for the aortic valve and 0.7 for the mitral valve (these were assigned arbitrarily to improve data fit). The second constant is 44.5, which is a blood acceleration factor (square root of 2 × gravity acceleration factor, 980 cm/s2). Only the flow across the valve during valve opening is used. For aortic stenosis, flow was equal to CO (mL/min) divided by the fraction of flow for each heartbeat during systole (ie, heart rate HR, beats/min × the systolic ejection period SEP, point of aortic valve opening on LV curve to the dichotic notch of aortic valve closure) (Figure 1A, left side). For mitral stenosis, flow was equal to CO (mL/min) divided by the fraction of flow during diastole (ie, HR × the diastolic filling period point on the LV curve where the mitral valve opens to end of the “a” before isovolumetric contraction, s/beat) (Figure 1A, right side). In 1972, Cohen and Gorlin4Cohen M.V. Gorlin R. Modified orifice equation for the calculation of mitral valve area.Am Heart J. 1972; 84: 839-840Crossref PubMed Scopus (137) Google Scholar revised the original formula and suggested the use of 0.85 for the mitral valve (instead of 0.7) as the discharge coefficient. The modern Gorlin formula is as follows:Aortic valve area = CO (mL)/(SEP × HR × 44.3 × √mean gradient)Mitral valve area = CO (mL)/(DFP × HR × 0.85 × 44.3 × √mean gradient), where DFP = diastolic filling period •Accurate valve area calculation requires accurate measurement of CO. Note that in low flow states, valve areas may be underestimated.•For low flow states, dobutamine can be used to increase the CO and hence the gradient for better assessment.•Gorlin formulas use mean gradients and not peak gradients (which are used for the Hakki aortic stenosis formula, see below).•The calculated valve area does not depend on the HR in the same way that echocardiographic calculations require because HR and the mean gradient are intrinsic to the Gorlin formulas.•With irregular rhythms, such as atrial fibrillation, averaging the data over 10 beats rather than using a single beat is more accurate.•Significant valvular regurgitation will cause an underestimation of the valve area because routine CO measurements do not account for the true flow across the valve (CO in valvular regurgitation is usually higher than actually measured).•Unlike echocardiographic measurements, the left ventricular end diastolic pressure (LVEDP) is actually measured, which can potentially “unmask” diastolic dysfunction. For example, consider a mean mitral valve gradient of 30 mm Hg with an LVEDP of 20 mm Hg. Following successful balloon valvuloplasty, the mean mitral valve gradient is reduced to 5 mm Hg but the LVEDP is still 20 mm Hg. No wonder your patient still has symptoms! (Figure 1D) In 1981, A-Hamid Hakki, a cardiology fellow at Hahnemann University, after planimetering 60 aortic valve tracings and 40 mitral valve tracings, proposed that the Gorlin formula should be simplified because the factor HR × SEP × 44.3 (the Gorlin constant) was always “1.” Hakki et al5Hakki A.H. Iskandrian A.S. Bemis C.E. et al.A simplified valve formula for the calculation of stenotic cardiac valve areas.Circulation. 1981; 63: 1050-1055https://doi.org/10.1161/01.cir.63.5.1050Crossref PubMed Google Scholar then published the simplified Gorlin formula, using the peak LV–peak aortic pressures (or mean). The Hakki valve area formula is as follows: AVAHakki or MVAHakki = CO/ √ peak − peak (LV-Ao) or mean (mitral) gradient, where AVA = aortic valve area, MVA = mitral valve area, and Ao = aortic (Figure 1B) Hakki data have a very strong correlation to the Gorlin formula (Figure 1C).6Kern M.J. Aortic valve areas: Gorlin or Hakki? Cath Lab Digest.https://www.hmpgloballearningnetwork.com/site/cathlab/content/aortic-valve-areas-gorlin-or-hakkiDate accessed: May 19, 2022Google Scholar It remains highly accurate except in patients with significant bradycardia (100 beats/min).Pearls in briefPearl #1: Invasive hemodynamics of valvular stenoses are the gold standard on which other techniques, such as echocardiography, are based. Pearl #2: Accurate assessment of CO is critical. Underestimation of CO is a major pitfall in calculations when there is significant valvular regurgitation. Pearl #3: An understanding of the formulas used to calculate valve area allows one to not only interpret the data but also to understand when there is an issue with the accuracy of the measurement and how to troubleshoot the problem. Pearl #4: Do not forget the importance of knowing diastolic function (LVEDP) in the care of your patients post percutaneous or surgical valve procedures. The author(s) declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article. This research did not receive any specific grant from funding agencies in the public, commercial, or not-for-profit sectors.