Hemodynamic Calculations

 Fellow – TEE Review Workshop – Hemodynamic Calculations 2013 Mary Beth Brady, MD, FASE Director, Intraoperative TEE Program Johns Hopkins School of Medicine At the conclusion of the workshop, the participants will be able to 1) apply the simplified Bernoulli equation to estimate valvular gradients and valve area 2) compute stroke volume and cardiac output utilizing 2D and Doppler technology 3) calculate intracardiac pressures 4) list the benefits and limitations of the above techniques. Bernoulli Equation Pulsed wave (PW) and continuous wave (CW) Doppler provide measurements of velocity. In our case, we are interested in the velocity of red blood cells traveling within cardiac chambers. These velocities can be used to provide estimations of pressure gradients, which in turn can be used to estimate transvalvular pressure gradients and valve areas. In general, the velocity of fluid traveling through a narrowed orifice depends on the size of the orifice. Simply put, the narrower the orifice – the higher the velocity. Bernoulli described this in more complicated terms with his mathematical equation △P = 1/2p(v22-­‐ v12) + p(dv/dt)dx + R(v) 1/2p(v22-­‐ v12) = Convection acceleratoin p(dv/dt)dx = Flow acceleration R(v) = viscous Friction Fortunately, this complicated mathematical equation can be greatly simplified for use in echocardiography. First, convection acceleration can be simplified. The density of blood is 1.06 x 103 kg/m3 and is designated by the symbol p. The velocities distal and proximal to the area of interest are v2 and v1 respectively. With lesions of clinical significance, v2 is far greater than v1. Keeping this in mind and noting that both terms are squared, the contribution of v1 can be ignored, so that v22-­‐v12 can be simplified to merely v22. Flow acceleration can be ignored in clinical settings. Our interest is in peak flows, and during peak flow, the flow acceleration is nonexistent. Finally, R(V) represents the degree of energy lost due to viscous friction. Viscous friction is a function of blood viscosity and velocity. This term is insignificant for orifices with an area greater than 0.25 cm2 in that blood flow is thought to be constant in that setting. Therefore, this term can also be ignored. In summary, both flow acceleration and viscous friction can be ignored under most physiological conditions and convection acceleration can be simplified. As a result, the Bernoulli equation can be 1 | P a g e modified t to a more simple Bernoulli equation, which is △P = 1/2pv22. Converting to mmHg, the equation simplifies to △P = 4v22, known as the simplified Bernoulli equation. Transvalvular Gradients One of the most clinically significant applications of the simplified Bernoulli equation is measuring the peak velocity of red blood cells moving through a discrete lesion in order to estimate transvlavular gradients. For example, the degree of aortic stenosis can be quantified using this formula. CW Doppler interrogation of the AV in TG LAX view. The peak velocity is 3.6 m/sec and the calculated gradient (using the simplified Bernoulli equation) is 4(3.6m/sec)2 = 52.1mmHg. There are many potential sources of error associated with this technique. Technical errors can lead to an underestimation of the transvalvular pressure gradient. The most common of these errors is inadequate beam alignment. Aligning the ultrasound beam in any way which is not parallel to blood flow results in an underestimation of velocity and therefore an underestimation of the transvalvular gradient. If possible, interrogating the area of interest in multiple views is recommended. In addition, reviewing multiple Doppler profiles (5 for regular rhythm and 10 for irregular rhythm) is recommended. Depending on the blood flow under investigation, velocity can be measured by PW or CW Doppler. In order to avoid the issue of aliasing which can occur with PW Doppler, CW Doppler is recommended if the velocity is high. Of course, the disadvantage of CW Doppler is range ambiguity in that CW Doppler measures the highest velocity along the beam: there is the potential of interrogating the wrong flow signal. It is important to note that Doppler technology measures instantaneous gradients. Often as is the case of aortic stenosis, the peak pressure in the left ventricle does not occur at the same time in the cardiac cycle as in the aorta. In this case, the simplified Bernoulli equation may indeed overestimate the degree of aortic stenosis. In a similar vein, the degree of aortic stenosis will be overestimated if the velocity of v1 is ignored but should not be ignored because the velocity is too high. For example if there is some degree of narrowing in the LVOT, v1 will be relatively high. As v1 is squared in the formula, ignoring this (high value) 2 would significantly overestimate the degree of valvular stenosis. If v1 (the velocity across the LVOT in the example of AS) is ≥ 1.5 cm/sec, it is recommended to use the modified Bernoulli equation, 2 | P a g e which includes measuring v1 and using it in the modified Bernoulli equation. The modified Bernoulli equation △P = 4(v22-­‐v12). (Patients with high cardiac output states, such as those with significant aortic regurgitation, often have LVOT velocities > 1.5 cm/sec.) The velocity of the LVOT can be measured using CW Doppler to interrogate flow across the aortic valve and the LVOT. The peak velocity represents the velocity across the aortic valve. The lower envelope velocity represents the velocity across the LVOT. CW Doppler interrogation of the AV in TG LAX view. The peak velocity(across the aortic valve) is 3.6 m/sec and the lower velocity(across the LVOT) is 1m/sec (see arrow) In patients with low EF, the gradient measured using the simplified Bernoulli equation may underestimate the severity of the valvular stenosis. Simply put, the patient may not be able to generate a high gradient even in the face of significant stenosis. In this case, the continuity equation may be better suited for evaluation of aortic stenosis. (See continuity equation section) Stroke Volume and Cardiac Output Calculation Doppler measurements can be used to quantify stroke volume and cardiac output. Simple hemodynamic formulas are used. These somewhat noninvasive techniques correlate well with other more invasive methods. While using these formulas, it is important to differentiate between blood flow velocity, volumetric flow and stroke volume (SV). One helpful way to keep these straight is remembering the units of measurement for each. Blood flow velocity is the speed at which blood travels and is measured in cm/sec. The amount of blood that is flowing per second is known as the volumetric flow and is measured in cm3/sec. Finally, SV is the amount of blood flowing in a single cardiac cycle and is expressed as cm3/cycle. The product of flow velocity and the cross sectional area (CSA) of an orifice is the flow rate through that orifice. The mathematical formula is simple: Flow = Velocity x CSA During times of constant flow, the velocity measured at any point in time can be used in the equation. Throughout the cardiac cycle, blood flow is not constant but is pulsatile. In order to overcome this, individual velocities are sampled over one cardiac cycle and the sum of theses velocities is 3 | P a g e integrated over time. This is known as the time velocity integral (VTI). This velocity integrated over time is a measure of distance and is expressed in centimeters. The second variable is the cross sectional area of the orifice through which the blood flows. It is measured in cm2. The product of the 2 variables is SV. Of course, SV multiplied by HR is cardiac output. SV = VTI x CSA cm3 = cm x cm2 CO = SV x HR cm3/min = cm3 x /min SV and CO can be measured at multiple locations. The most reliable and easily measured is at the level of the aortic valve, with flow measured through the left ventricular outflow tract (LVOT). Flow at this site is normally laminar, which makes Doppler estimation more accurate. In addition, the aortic valve is an attractive site for measurements in that the CSA does not vary much throughout the cardiac cycle, while other structures do. The pulmonary valve is also an attractive site for measurement, although Doppler alignment may be a bit challenging. Flow = Velocity x CSA Flow (SV) = VTI x CSA of aortic valve The CSA of the aortic valve may be measured using planimetry of the short axis view of the valve. Measurement error is a concern as changes in gain setting can affect measurement. A more commonly used approach is to measure the diameter of the LVOT which is measured in the midesophageal long axis view of the valve. (see below, LVOT diameter measures 1.87cm) The area of the circle is πr2. The LVOT diameter is measured, so D/2 replaces r in the formula such that Area = πr2 Area = π(D/2)2 or Area = 3.14/4 (D)2 4 | P a g e Area = 0.7854(D)2 In order to lessen potential error, multiple measurements of the LVOT should be conducted: the largest measurement usually corresponds to the correct diameter. Measurements of the LVOT are usually conducted during systole, although the annular size does not vary greatly throughout the cardiac cycle so the exact timing is less critical than measurements taken at other sites. VTI of the LVOT can be measured using pulse wave Doppler with the sample volume positioned in the LVOT just proximal to the aortic valve. The transgastric and/or deep transgastric long axis views are best for these measurements. Flow (SV) = VTI x CSA of aortic valve SV= VTI x 0.7854(D)2 CO= VTI x 0.7854(D)2 x HR Flow (SV) = VTI x CSA of aortic valve SV= VTI x 0.7854(D)2 SV = 25.8 cm x .785 (1.8cm)2 SV = 66cm3 3
CO = 66cm x 80 = 5280 cm3 CO= VTI x 0.7854(D)2 x HR Valve Area Calculation As mentioned earlier, patients with low EF may not be able to generate a significant pressure gradient even if they have significant aortic stenosis. In these patients, valvular stenosis may be more accurately measured using the continuity equation. 5 | P a g e Simply put, the continuity equation boils down to “what goes in, must come out.” The volume that enters the stenotic area equals the volume which leaves the area. By measuring these volumes, we can calculate the unknown area, which in this case is the area of the aortic valve. SV(LVOT) = SV(AV) VTI(LVOT) x CSA(LVOT) = VTI(AV) x CSA(AV) All but the CSA of the aortic valve are directly measured. Solving for CSA(AV) the formula becomes CSA(AV) = VTI(LVOT) x CSA(LVOT) ÷ VTI(AV) CSA(AV) = VTI(LVOT) x CSA(LVOT) ÷ VTI(AV) CSA(AV) = 24.3 cm x .784 (1.8cm)2 ÷ 96.4cm = .64cm2 6 | P a g e Intracardiac Pressure Calculations The simplified Bernoulli equation △P = 4v22 can be used to evaluate intracardiac pressures. In this case, △P = p1 – p2, the pressure difference between the proximal and distal cardiac chambers. Doppler technology permits direct measure of the velocity of flow between the 2 chambers. If etiher the proximal or distance pressure can be measured or estimated, simple algebra permits calculation of the alternative pressure. Commonly the right ventricular pressure (RVSP) is measured in this fashion, but pulmonary artery pressures (both mean and diastolic), left atrial pressure and left ventricular end diatolic pressure can also be estimated. Right Ventricular Systolic Pressure The velocity of blood flowing through the tricuspid valve during systole (tricuspid regurgitant velocity) reflects the pressure gradient between the right atrium and the right ventricle. The faster the velocity; the higher the pressure gradient. CW Doppler is utilized to measure the peak velocity of the TR jet and is used as v2. Right atrial pressure (RAP) is estimated or central venous pressure (CVP) is measured and can be used p2. Thus, the Bernoulli equation can be expressed as p1 – p2 = 4v22 RVSP – RAP = 4(TR velocity) 2 Solving for RVSP using simple algebra RVSP = 4(TR velocity) 2 + RAP CVP can be used in place of RAP RVSP = 4(TR velocity) 2 + CVP In the absence of pulmonic stenosis and right ventricular outflow tract obstruction, RVSP and pulmonary artery systolic pressure (PASP) are essentially the same so that RVSP or PASP = 4(TR velocity) 2 + CVP One of the limitations of this technique is that there must be a regurgitant jet or the calculation cannot be made. Thus, if the patient does not have TR, the RVSP cannot be estimated. 7 | P a g e RVSP = 4(2.5)2 + 10 = 25 + 10 = 35mmHg Interestingly, in patients with a left-­‐to-­‐right shunt, RVSP can be estimated measuring the velocity of the ventricular septal defect jet between the left ventricle and the right ventricle during systole. p1 – p2 = 4v22 LVSP – RVSP = 4(VSD velocity)2 Using simple algebra and assuming that left ventricular systolic pressure (LVSP) is similar to measured systolic blood pressure (SBP), the formula becomes RVSP = SBP -­‐ 4(VSD velocity)2 CW Doppler interrogation through VSD. If the patient’s SBP is 140mmHg, using the above formula of RVSP = SBP -­‐ 4(VSD velocity)2, the RVSP = 140 – 77 = 63mmHg Pulmonary Artery Mean Pressure The velocity of the pulmonic regurgitation jet during diastole reflects the pressure gradient between the RV and the pulmonary artery and is measured using CW Doppler. p1 – p2 = 4v22 PAMP-­‐ RVP = (early PR velocity) 2 During diastole RVP and RAP are essentially the same. CVP can replace RAP and can be measured or estimated. Using simple algebra, the formula becomes PAMP = (early PR velocity) 2 + CVP 8 | P a g e Pulmonary Artery Diastolic Pressure The velocity of the pulmonic regurgitation jet measured suing CW Doppler at end diastole reflect the pressure gradient between the pulmonary artery and the RV at end diastole. This can be used to calculate pulmonary artery diastolic pressure (PADP). p1 – p2 = 4v22 PADP – RVP = 4(late PR velocity) 2 During diastole, RVP is essentially the same as RAP. CVP can be used in place of RAP. Using simple alegebra, the equation becomes PADP = 4(late PR velocity) 2 + CVP Of note, parallel interrogation of the PR jet can be challenging with the limitations of TEE manipulation. Left Atrial Pressure Flow across the mitral valve can be used to estimate left atrial pressure (LAP). The gradient between the left atrium and the left ventricle is reflected in the peak velocity of the mitral regurgitation (MR) jet. p1 – p2 = 4v22 LVP – LAP = 4(MR velocity)2 Assuming LVP is similar to SBP and using simple algebra, the equation becomes LAP = SBP -­‐ 4(MR velocity)2 The MR jet can be measured in the midesophageal views utilizing CW or PW Doppler depending on the velocity. In the presence of aortic stenosis or obstruction of the LV outflow tract, the formula cannot be used as SBP will not accurately estimate LVP. Left Ventricular End Diastolic Pressure LVECP can be measured in if aortic regurgitation is present and its velocity can be measured. The peak end diastolic velocity of an AR jet reflects the difference in pressure between the left ventricle and the aorta during diastole. p1 – p2 = 4v22 ADP – LVEDP = 4(AR velocity) 2 Using simple algebra and replacing ADP with DBP, the formula becomes LVEDP = DBP -­‐ 4(AR velocity) 2 Brady, MB. Basic Echo Doppler. IN: Practical Ultrasound in Anesthesia, Critical Care and Pain Management. Eds. PM Hopkins, A. Bodenham, ST Reeves. Marcel, Dekker, Taylor & Francis. Chapter 9. 2008 9 | P a g e 10 | P a g e