The normal cardiac valves offer little resistance to blood flow even when flow velocity is high.When stenosis develops, the valve orifice offers greater resistance to flow resulting in a pressure drop (pressure gradient) across the valve. At any given stenotic orifice size, greater flow across the valve produces a greater pressure gradient across the valve. Based on this concept, the Gorlin formula was derived for calculation of cardiac valve orifices from flow and pressure gradient data.
Gorlin Formula
Formula I: First Hydraulic Formula (Toricelli’s law)
F = AVCc
Where, F = flow rate
A = orifice area
Cc = coefficient of orifice contraction
Rearranging this formula, we get:
A =F/VCc
Wherein A is the orifice area.
Formula II: Second Hydraulic Formula
This relates to pressure gradient and velocity of flow:
V2 = (Cv)2 2gh or V = (Cv) 2gh
Wherein, V = velocity of flow
Cv = coefficient of velocity
g = acceleration due to gravity (980 cm/sec/sec)
h = pressure gradient in cm of H 2 O
Combining these two equations, we get:
The final equation for calculation of valve orifice area A in cm 2 is:
Where, CO = Cardiac output in cm 3 / min
DFP = diastolic filling period (sec/beat)
(measured directly form LV/PCW/LA tracings)
SEP = systolic ejection period (sec/beat)
HR = heart rate (beats/min)
C = empirical constant
P = pressure gradient
Mitral Valve Orifice Area
The normal mitral valve orifice in an adult is 4-5cm 2 when the valve is completely open in diastole. When the mitral valve orifice area is 1.0 cm 2 , then there will be a significant resting gradient across the valve and any requirement for increase cardiac output leads to an increase in LA and PCW pressure and results in Pulmonary edema. This therefore, represents “critical mitral valve orifice area”.
The formula for calculating mitral valve orifice area is:Where P = mean transmitral pressure gradient, and MVA = mitral valve area. Thus when the cardiac output is doubled, the transmitral gradient is quadrupled (if HR and DFP remain constant).
Aortic Valve Orifice Area
An aortic valve orifice area of < 0.7cm 2 leads to angina, syncope or heart failure in a patient with aortic stenosis and constitutes critical aortic stenosis. The aortic valve orifice can be calculated using the formula:
Assessment of Tricuspid and Pulmonary Orifice Areas
Due to the rarity of tricuspid stenosis and pulmonary stenosis, no general agreement exists on what constitutes critical orifice area in these cases. Generally a gradient of 5mmHg causes venous hypertension. In the case of pulmonary stenosis, gradients of < 50mmHg are well tolerated.
Gradients of >100mmHg require intervention. Gradients between 50-100mmHg merit correction depending on the case.
Alternatives to Gorlin Formula
Hakki et al proposed a simplified formula for calculation of valve orifice area and had found good correlation. This formula may not be useful in substantial tachycardia.
Assessment of Valvular Regurgitation
The severity of valvular regurgitation is generally graded by visual assessment, although calculation of the regurgitant fraction is used occasionally.
Visual Assessment of Regurgitation
Valvular regurgitation may be assessed visually by determining the relative amount of radiographic contrast medium that opacifies the chamber proximal to its injection.
Seller’s Classification of Regurgitation
Grade of regurgitation Description
+ Minimal regurgitant jet seen. Clears rapidly from proximal chamber with each beat.
++ Moderate opacification of proximal chamber, clearing with subsequent beast.
+++ Intense opacification ofproximal chamber, becoming equal to that of distal chamber.
++++ Intense opacification of proximal chamber, becoming denser than that of the distal chamber. Opacification often persists over the entire series of images obtained.
Regurgitant Fraction
A gross estimate of the degree of valvular regurgitation may be obtained by determining the regurgitant fraction (RF).
Regurgitant Stroke Volume It is defined as the difference between the angiographic stroke volume and the forward stroke
volume.The RF is that portion of angiographic stroke volume that does not contribute to the net cardiac output.
Important Formula for Regurgitant Valvular Lesions
Regurgitant stroke volume = angiographic stroke volume – forward stroke volume
RF = (Angiographic stroke volume – Forward stroke volume)/Angiographic stroke volume
Forward stroke volume = Cardiac Output Heart Rate
Correlation Between Degree of Regurgitation and Regurgitant Fraction
Degree of regurgitation Regurgitant fraction
1+ ? 20 per cent
2+ 21 to 40 per cent
3+ 41 to 60 per cent
4+ > 61 per cent
Gorlin Formula
Formula I: First Hydraulic Formula (Toricelli’s law)
F = AVCc
Where, F = flow rate
A = orifice area
Cc = coefficient of orifice contraction
Rearranging this formula, we get:
A =F/VCc
Wherein A is the orifice area.
Formula II: Second Hydraulic Formula
This relates to pressure gradient and velocity of flow:
V2 = (Cv)2 2gh or V = (Cv) 2gh
Wherein, V = velocity of flow
Cv = coefficient of velocity
g = acceleration due to gravity (980 cm/sec/sec)
h = pressure gradient in cm of H 2 O
Combining these two equations, we get:
The final equation for calculation of valve orifice area A in cm 2 is:
Where, CO = Cardiac output in cm 3 / min
DFP = diastolic filling period (sec/beat)
(measured directly form LV/PCW/LA tracings)
SEP = systolic ejection period (sec/beat)
HR = heart rate (beats/min)
C = empirical constant
P = pressure gradient
Mitral Valve Orifice Area
The normal mitral valve orifice in an adult is 4-5cm 2 when the valve is completely open in diastole. When the mitral valve orifice area is 1.0 cm 2 , then there will be a significant resting gradient across the valve and any requirement for increase cardiac output leads to an increase in LA and PCW pressure and results in Pulmonary edema. This therefore, represents “critical mitral valve orifice area”.
The formula for calculating mitral valve orifice area is:Where P = mean transmitral pressure gradient, and MVA = mitral valve area. Thus when the cardiac output is doubled, the transmitral gradient is quadrupled (if HR and DFP remain constant).
Aortic Valve Orifice Area
An aortic valve orifice area of < 0.7cm 2 leads to angina, syncope or heart failure in a patient with aortic stenosis and constitutes critical aortic stenosis. The aortic valve orifice can be calculated using the formula:
Assessment of Tricuspid and Pulmonary Orifice Areas
Due to the rarity of tricuspid stenosis and pulmonary stenosis, no general agreement exists on what constitutes critical orifice area in these cases. Generally a gradient of 5mmHg causes venous hypertension. In the case of pulmonary stenosis, gradients of < 50mmHg are well tolerated.
Gradients of >100mmHg require intervention. Gradients between 50-100mmHg merit correction depending on the case.
Alternatives to Gorlin Formula
Hakki et al proposed a simplified formula for calculation of valve orifice area and had found good correlation. This formula may not be useful in substantial tachycardia.
Assessment of Valvular Regurgitation
The severity of valvular regurgitation is generally graded by visual assessment, although calculation of the regurgitant fraction is used occasionally.
Visual Assessment of Regurgitation
Valvular regurgitation may be assessed visually by determining the relative amount of radiographic contrast medium that opacifies the chamber proximal to its injection.
Seller’s Classification of Regurgitation
Grade of regurgitation Description
+ Minimal regurgitant jet seen. Clears rapidly from proximal chamber with each beat.
++ Moderate opacification of proximal chamber, clearing with subsequent beast.
+++ Intense opacification ofproximal chamber, becoming equal to that of distal chamber.
++++ Intense opacification of proximal chamber, becoming denser than that of the distal chamber. Opacification often persists over the entire series of images obtained.
Regurgitant Fraction
A gross estimate of the degree of valvular regurgitation may be obtained by determining the regurgitant fraction (RF).
Regurgitant Stroke Volume It is defined as the difference between the angiographic stroke volume and the forward stroke
volume.The RF is that portion of angiographic stroke volume that does not contribute to the net cardiac output.
Important Formula for Regurgitant Valvular Lesions
Regurgitant stroke volume = angiographic stroke volume – forward stroke volume
RF = (Angiographic stroke volume – Forward stroke volume)/Angiographic stroke volume
Forward stroke volume = Cardiac Output Heart Rate
Correlation Between Degree of Regurgitation and Regurgitant Fraction
Degree of regurgitation Regurgitant fraction
1+ ? 20 per cent
2+ 21 to 40 per cent
3+ 41 to 60 per cent
4+ > 61 per cent
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