# Echocardiographic Calculations and Case Examples

Echocardiographic Calculations and Case Examples

Terence Hill

Richard A. Grimm

I. INTRODUCTION

In this chapter, we will review the calculations used to quantitatively assess valvular stenosis and regurgitation by Doppler echocardiography. We will first review the necessary equations and data that must be acquired, along with how the results are calculated and used to assess valvular stenosis or regurgitation severity. We will also discuss potential pitfalls in performing these calculations. Finally, we will present several cases that demonstrate how to apply these calculations using real echocardiographic data.

II. CALCULATIONS: AORTIC VALVE

A. Aortic stenosis

1. Aortic stenosis (AS) severity is assessed by Doppler and two-dimensional (2D) echocardiographic imaging capabilities. Peak aortic flow velocity, peak aortic valve (AV) gradient, mean AV gradient, aortic valve area (AVA), and the dimensionless index (DI) all in combination with 2D appearance of the valve are required to derive a determination of stenosis severity. The aortic flow velocity is a measured variable that is acquired using continuous-wave (CW) Doppler echocardiography with the cursor aligned parallel to flow across the AV from either the apical 5-chamber (A5C) or apical 3-chamber (A3C) window. Additionally, data can be acquired from the right parasternal border, suprasternal notch, and subcostal windows. A dedicated Doppler Pedoff probe can be used to assure maximal velocities are obtained from each imaging plane. The highest values obtained, reported as Doppler velocities, are usually underestimated when images are off axis, as only the component of the velocity vector parallel to the Doppler signal is measured. The peak aortic gradient is calculated from the peak velocity, usually using the simplified Bernoulli equation (if subaortic velocity is <1.5 m/s):

ΔP = 4V2

where ΔP is the peak instantaneous gradient across the valve and V is the Doppler flow velocity. The mean aortic gradient is calculated as the mean velocity over time of left ventricular (LV) ejection.

2. The AVA is calculated by the continuity equation:

AVA = CSA(LVOT) × VTI(LVOT)/VTI(AV)

3. The three main components of this equation include the LV outflow tract (LVOT) diameter, subaortic flow, and transvalvular flow (both approximated by the velocity-time integral or VTI). The LVOT diameter measurement is necessary to determine the cross-sectional area (CSA) of the LVOT. This is calculated from the LVOT diameter measured from the parasternal long-axis view just below the
AV. The LVOT is assumed to be circular, hence allowing for the calculation of the CSA as follows: CSALVOT = (D(LVOT)/2)2 × π. VTILVOT is a representation of subvalvular systolic flow and is measured as the area under the Doppler velocity versus time curve during ventricular systole. The Doppler measurement for this parameter is obtained using pulsed wave (PW) Doppler across the AV (typically in the A5C or A3C window), with a sample volume located 0.5-1 cm on the ventricular side of the AV. VTIAV is representative of flow across the AV and is obtained using CW Doppler across the AV, in multiple imaging windows, and measuring the area under the Doppler velocity versus time curve in systole. It is very important to note that the measured LVOT diameter has a major impact on the calculated valve area as the diameter is squared in the equation, and hence the potential error is magnified. In the event of uncertainty of measurement, one can simply report the ratio of subaortic to transvalvular maximum velocity, which is referred to as the velocity ratio or DI.

DI = V(LVOT)/V(AV)

4. Not infrequently, there will be a discrepancy between the calculated AVA, the DI, and the AV gradients, where an AVA calculated as <1.0 cm2 and the gradients not being significantly elevated suggest severe disease. This can indicate a low-flow state, an error in measurement, or an error in Doppler velocity data sampling. Low-flow states can result from many causes, including an abnormally low LV systolic function, low output due to small ventricular cavities, atrial fibrillation, mitral regurgitation (MR), diastolic dysfunction, hypertensive heart disease, or increased valvuloarterial impedance. In order to appropriately identify these patients, it is important to calculate the stroke volume (SV) and index it to body size. The stroke volume index (SVI) is as follows (BSA = body surface area):

SVI = CSA(LVOT) × VTI(LVOT)/BSA

5. Generally, a SVI of less than 35 mL/m2 is consistent with a low-flow state. In patients with poor LV function, a dobutamine stress echocardiogram can be performed to determine if there is a fixed versus “pseudo”stenosis. This test either will confirm a truly severe AS (increase in gradient with persistently unchanged AVA) or can unmask pseudostenosis (no increase in gradient with an AVA that increases with dobutamine). Furthermore, the SVI can be calculated at rest and with stress. An increase in SV with dobutamine of greater than 20% is considered a favorable contractile reserve, whereas an increase in SV of less than 20% confers poor prognosis. Combining these variables, we can grade AS accordingly as shown in Table 21.1.

6. Common pitfalls in accurately determining AS severity are derived from improper or suboptimal Doppler sampling, and error in tracing or measurement of Doppler signals. Other pitfalls include confusing a mitral regurgitant jet signal by CW Doppler with a transvalvular aortic flow from an A5C view, which can happen if the CW tracing is misaligned to capture MR (which is in the same direction as the aortic flow). However, this can usually be recognized by the parabolic nature of the MR tracing, the longer duration of systole incorporating the isovolumic contraction and relaxation periods, as well as a peak velocity typically of at least 5 m/s. Additionally, the CW tracing can represent flow acceleration in a location along the beam other than the AV, usually from subaortic stenosis such as a subaortic membrane or LVOT obstruction (i.e., in hypertrophic cardiomyopathy). This error can be identified by examining the contour of the tracing, as in valvular stenosis the tracing will be triangular, while a dynamic LVOT obstruction is classically more “dagger” shaped. Careful assessment of the color flow Doppler map should be examined to ensure that the location of flow acceleration is at the valve
level consistent with valvular stenosis, as opposed to lower in the LVOT and more consistent with subvalvular stenosis. It may also be helpful to take several PW tracings from various points in the LV cavity to determine the location at which the velocity increases. Furthermore, attention should be paid to the morphology of the AV, as a very high gradient without significant calcification of the AV or restricted opening should prompt further scrutiny. Planimetry of the AV (usually in the parasternal short-axis [PSAX] window) can help, but is very operator dependent and prone to error in measurement. A typical LVOT diameter for patients with a trileaflet AV is approximately 2 cm, so for measurements significantly smaller or larger than 2 cm, the images should be reviewed with a particularly skeptical “eye.” This should be a prime consideration when there is disagreement between the AVA and DI (which does not include the LVOT measurement).

TABLE 21.1 Quantitative Assessment of Aortic Stenosis (AS)

 Aortic Sclerosis Mild AS Moderate AS Severe AS Peak velocity (m/s) ≤ 2.5 2.6-2.9 3.0-4.0 >4.0 Peak gradient (mm Hg) 27-34 35-64 >64 Mean gradient (mm Hg) <20 20-40 >40 Aortic valve area (cm2) >1.5 1.0-1.5 <1.0 Dimensionless index >0.5 0.25-0.5 <0.25

B. Aortic insufficiency

1. While aortic insufficiency (AI) will frequently be assessed semiquantitatively, it can be quantitatively assessed by measuring the vena contracta (VC), calculating the regurgitant orifice area (ROA), as well as regurgitant volume (RV) and regurgitant fraction (RF) by volumetric methods. The VC is measured as the narrowest point in the regurgitant jet at the leaflet level in diastole, as observed on color flow Doppler, at a Nyquist limit of 50-60 cm/s. The ROA is a physiologic estimate of the regurgitant defect area that would be necessary to produce the amount of observed regurgitation. It is calculated by first measuring the proximal isovelocity surface area (PISA) radius obtained using color flow Doppler of the AI regurgitant jet. The PISA is observed as a hemispherical color flow disturbance within the regurgitant jet on the aortic side of the valve. After measuring the PISA (typically in the right parasternal or A3C window), the ROA is calculated as follows:

ROA = 2π(rPISA)2 × Valiasing/VAI Jet

where rPISA is the measured radius of the PISA (as described earlier), Valiasing is the Nyquist limit set when the PISA is measured, and VAI Jet is the peak velocity of the AI jet, measured using the CW Doppler sampling across the AV. The RV and RF are calculations of the approximate total volume (RV) or percentage (RF) of blood flow through the regurgitant orifice compared with the total SV ejected from the left ventricle. In a normal heart with no regurgitant valves, the blood entering the left ventricle through the mitral valve (MV) is equal to the blood
exiting the left ventricle through the AV. The SV is the quantity of blood that exits and enters the heart on each and every beat. Therefore, in a normal heart:

SVLVOT = SVMV Inflow

because all blood enters through the MV and exits through the LVOT (AV). The SV moving through any portion of the heart is defined as

SV = CSAarea of interest × VTIarea of interest

and

CSA = 2πr2

Therefore, substituting these equations, for the normal heart:

πrLVOT2 × VTILVOT = πrMV2 × VTIMV inflow

where rLVOT is the LVOT radius, rMV is the MV radius, and VTIMV inflow is the VTI of the MV inflow. The MV radius is calculated from the annular diameter, which is measured in the apical 4-chamber (A4C) window during mid-diastole (just after the leaflets begin to close). The VTI of the MV inflow is measured by positioning the sample volume of the PW Doppler cursor just inside of the MV. In the case of AI, blood enters the heart both from the regurgitant lesion (the volume of AI is defined as the RV) and through the MV, while both the RV and the mitral inflow exit through the LVOT. Therefore, for AI:

πrLVOT2 × VTILVOT = πrMV2 × VTIMV inflow + RV

RV = πrLVOT2 × VTILVOTπrMV2 × VTIMV inflow

2. Once the RV is determined, RF is calculated as the ratio of the RV to the total SV (which for AI is the LVOT SV):

RF = RV/(πrLVOT2 × VTILVOT) × 100.

3. Alternatively, RV can be calculated using the ROA (calculated from the PISA) and the VTI of the AI jet, using the equation:

RV = ROA × VTIAI Jet

This equation can be somewhat less cumbersome, but relies on an accurately measured ROA and accurately sampled and measured AI Doppler signal. Severity of AI can be described quantitatively using Table 21.2.

TABLE 21.2 Quantitative Assessment of Aortic Insufficiency

 Parameter Mild Moderate Severe VC (cm) <0.3 (<25% LVOT diameter) 0.31-0.6 >0.6 (>65% LVOT diameter) ROA (cm2) <0.10 0.1-0.29 ≥ 0.30 RV (mL) <30 30-59 ≥ 60 RF (%) <30 30-49 ≥ 50 LVOT, left ventricular outflow tract; RF, regurgitant fraction; RV, regurgitant volume; ROA regurgitant orifice area; VC, vena contracta.

4. In aortic regurgitation, Doppler quantification has several potential sources of measurement error typically related to suboptimal image quality or acquisition technique. When there are multiple or eccentric AI jets, the VC can be under- or overestimated. The PISA can frequently be a challenge to measure as the hemisphere of the isovelocity flow is often difficult to identify. Additionally, measurement using PISA does not perform as well in patients with aneurysmal ascending aortas, or with cusp perforation or commissural leak. These limitations primarily apply to noncentral and eccentrically directed jets of regurgitation.

5. RV and RF measurements using PW Doppler volumetric techniques are accurate only in the absence of any significant MR or intracardiac shunt. For these calculations to be most accurate, the only inflow into the ventricle needs to come through the MV, and the only outflow through the AV. Furthermore, the equations rely on several different measurements including both the LVOT and MV annulus, which are assumed to be circular (a less valid assumption particularly for the MV). Any significant measurement error can cause wide variation in this calculation. Again, when assessing AV insufficiency it is important to remember that the length of the AI jet by color flow mapping does not correlate well with severity. Finally, flow reversal in the proximal descending aorta may result from other disease conditions such as patent ductus arteriosus or arteriovenous fistula. As a reminder, an integrative approach, incorporating several of these parameters, is the rule in echocardiography whenever generating an overall assessment of valvular dysfunction severity.

III. CALCULATIONS: MITRAL VALVE

A. Mitral regurgitation

1. MR is interpreted in a similar manner to AI, yet quantitative measurements are used more commonly with MR than they are with AI. This is largely related to the fact that MR is more amenable to PISA identification and measurement. The ROA for MR is calculated using similar parameters as the ROA for AI:

ROA = 2π(rPISA)2 × Valiasing/VMR jet

Notably, when the Nyquist limit is set to 40, and the velocity of the MR jet is 5 m/s (which represents a 100 mm Hg pressure difference between LV and left atrium, as is a usual measurement for this value), the equation simplifies to:

ROA = (rPISA)2/2

The RV and RF are calculated similarly to the method described earlier for AI. Notably, however, because the MV is leaking, the SV of the MV inflow represents the total inflow, with the outflow being the SVLVOT and SVMR (which is the RV for the MV). Therefore,

RV = SVMV Inflow – SVLVOT

RV = πrMV2 × VTIMV inflowπrLVOT2 × VTILVOT

The total SV is now equal to the SVMV inflow, and so the RF is calculated as:

RF = RV/(πrMV2 × VTIMV inflow) × 100

As with AI, the RV can also be calculated using the ROA, where

RV = ROA × VTIMV jet

MR severity is described using the parameters mentioned in Table 21.3.

2. Pitfalls in measuring MR are similar to those in measuring AI. The PISA method may underestimate the ROA if suboptimally acquired or in multiple jets, or overestimate the MR severity in eccentric jets where constraint of the LV wall/myocardium deforms the isovelocity flow fields, as the equation assumes a perfectly
hemispheric PISA. Transesophageal echocardiography (TEE) may help to define anatomy more precisely. Also, the RF and RV measurements fail when there is significant aortic regurgitation, as they assume that the only flow into the LV on each heartbeat comes through the MV. Furthermore, when calculated using the inflow SV and outflow SV, the annular area equations assume a circular MV and AV annulus, which can be an additional source of error.

TABLE 21.3 Quantitative Assessment of Mitral Regurgitation

 Parameter Mild Moderate Severe Vena contracta width (cm) <0.3 0.3-0.69 ≥ 0.7 Regurgitant volume (mL) <30 30-59 ≥ 60 Regurgitant fraction <30 30-49 ≥ 50 Effective regurgitant orifice area (cm2) <0.2 0.2-0.39 ≥ 0.4

B. Mitral stenosis

1. Mitral stenosis severity is typically derived on the basis of quantification of the transmitral valve gradient and the MV area (MVA), similar to that of AS. The peak gradient (which is even less useful in describing mitral stenosis severity than it is in describing AS) is measured from the A4C window using a CW Doppler sampling across the MV. The mean gradient is measured as the integral of the CW tracing across the MV (both the E- and A-waves are included) during the diastolic filling period. MVA is best quantified directly as measured by planimetry (2D or 3D) or estimated using the empirically derived pressure half-time (PHT) formula:

MVA = 220/PHT

To measure the PHT, a line is drawn tracing the deceleration of the E-wave of the mitral inflow tracing from PW Doppler usually from the A4C window. The PHT is the calculated time it would take for the maximum value to become half. Because of the limitations of PHT, direct planimetry of the MV is measured from the PSAX. While planimetry can be very accurate, it requires technical acquisition and measurement expertise, as an accurate valve area must be traced precisely at the leaflet tips in a plane perpendicular to the mitral orifice. Off-axis or out-of-plane images will lead to inaccurate measurement (usually overestimation). Furthermore, windows can be limited because of calcification in degenerative MS. These limitations of planimetry can be overcome utilizing three-dimensional echocardiography, and in fact this is considered the optimal and preferred method for echocardiographic assessment of mitral stenosis severity, although it is not universally available. MV stenosis is classified using the parameters outlined in Table 21.4.

TABLE 21.4 Classification of Mitral Stenosis

 Parameter Progressive Severe Very Severe Valve area (cm2) >1.5 ≤1.5 <1.0 Mean gradient <5 >5-10 >10