

The Gorlin Equation Revisited  Is this Equation Being Correctly to Assess Aortic Valve Area?
Neelakantan Saikrishnan^{1}, ChoonHwai Yap^{1}, Stamatios Lerakis^{2}, Ajit P. Yoganathan^{1}. Objective: The Gorlin equation is used clinically for obtaining the Aortic Valve Area (AVA) using catheter measurements. However, this equation contains simplifying assumptions that could lead to misdiagnosis of severity of Aortic Stenosis (AS) if not used correctly. The objective of this study is to present the equation from fundamental fluid mechanics principles to aid in its proper use. Methods: Starting from the Bernoulli equation, the basis and methodology of the derivation of the Gorlin equation are described. Previous studies which have used this equation incorrectly are noted to demonstrate pitfalls of wrong use of this equation. Using free streamline theory as proposed by Kirchhoff (1869) and the method of conformal mapping, an estimate for the contraction coefficient (C_{c}) used in the equation is obtained. This coefficient is calculated for a variety of orifice shapes, designed to simulate various disease conditions of the AV. The equation also contains the cardiac output (Q) and transvalvular pressure gradient (ΔP), and multiple studies have used combinations of mean Q, root mean square (RMS) Q, mean ΔP or mean √(ΔP) to calculate AVA. This study also compares and contrasts the use of these different terms. Results: A correction factor of 44.3 has been widely used clinically, but this implicitly assumes C_{c} = 0.85. From free streamline theory, it is shown that this value can vary between 0.621.0 for a range of AV orifice shapes. Further, C_{c} only depends on the orifice geometry, making it practical for use with clinical echocardiography, where leaflet dynamics can be observed. Finally, the use of Q_{RMS} and mean ΔP appears to be the best combination from a fluid mechanics perspective. Conclusion: The Gorlin equation provides a simple yet powerful method to assess the severity of AS using catheter data, but it has been used incorrectly in many studies thus far. We present a more accurate representation of this equation, and we expect that this should provide a more consistent and reliable estimate of the severity of AS. We hope that by revisiting the Gorlin equation, we can set the platform for more elaborate studies based on energy loss concepts. Back to 2011 Program 

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