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Anesthesia & Analgesia:
doi: 10.1213/ANE.0000000000000233
Cardiovascular Anesthesiology: Echo Rounds

Subaortic Membrane and the “Unsimplified” Bernoulli Equation

Markin, Nicholas W. MD; Desjardins, Georges MD, FRCPC, FASE

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From the Department of Anesthesiology, University of Utah, Salt Lake City, Utah.

Accepted for publication January 24, 2014.

Consent for publication of this case has been granted by the patient.

Funding: None.

The authors declare no conflicts of interest.

Supplemental digital content is available for this article. Direct URL citations appear in the printed text and are provided in the HTML and PDF versions of this article on the journal’s Web site.

Reprints will not be available from the authors.

Address correspondence to Nicholas W. Markin, MD, Department of Anesthesiology, University of Utah, 1900 E 30 N, 3C444 SOM, Salt Lake City, UT 84132. Address e-mail to nick.markin@gmail.com.

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CASE REPORT

A 75-year-old woman, body surface area of 2.1 m2, presented for aortic valve replacement (AVR) secondary to reported dysfunction of her St. Jude 19-mm mechanical prosthetic valve (St. Jude Medical, St. Paul, MN) in the aortic position. Eight years before admission, the patient presented with fatigue and was found to have elevated transvalvular gradients on transthoracic echocardiography. She underwent AVR at that time because she was symptomatic; intraoperative transesophageal echocardiography (TEE) documented an elevated fixed left ventricular outflow tract (LVOT) obstruction with peak gradient of 48 mm·Hg (Fig. 1). On TEE, a subaortic membrane was seen and aliasing at this level with a transition from laminar flow to turbulent flow (Clips 1A and 1B, Video 1, see Supplemental Digital Content 1, http://links.lww.com/AA/A883). While the echocardiographic appearance of the valve did not suggest aortic stenosis, the valve was resected at that time, and a St. Jude bileaflet 19-mm mechanical prosthesis was placed in the aortic position in conjunction with resection of the subaortic membrane. The final peak gradient through this valve was 48 mm·Hg, and though the subaortic membrane appeared resected, the possibility for residual tissue causing elevated gradients should have been considered. No further procedures were done to mitigate the peak gradient of 48 mm·Hg through the mechanical prosthesis at that time.

Figure 1
Figure 1
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Over the subsequent years, the patient reported increasing fatigue. A follow-up transthoracic echocardiogram showed increasing transvalvular gradients up to 65 mm·Hg, suspicious for prosthetic valve dysfunction. As a result of these findings, she returned to the operating room for redo AVR. The present intraoperative TEE demonstrated normal appearance and function of the mechanical valve from the midesophageal aortic valve short-axis view and normal occluder motion from the deep transgastric view. Regrowth of the previously resected subvalvular membrane was seen in the midesophageal aortic valve long-axis view (Fig. 2A, Video 2, see Supplemental Digital Content 2, http://links.lww.com/AA/A884). Pulse wave Doppler was used in a step-wise approach from the deep transgastric view to determine the area of acceleration, but due to the Nyquist limit, pulse wave Doppler could not give an accurate velocity. Continuous-wave Doppler demonstrated elevated velocities and a double envelope (Fig. 2B), suggesting 2 areas of stenosis within the patient’s LVOT1: the subaortic membrane (2.7 m/s), and the mechanical valve in the aortic position (4 m/s) with a peak gradient of 64 mm·Hg. She otherwise had normal left ventricular size and systolic function and only mild mitral regurgitation.

Figure 2
Figure 2
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In the operating room, we used the 2 peak gradients of the double envelope seen on continuous-wave Doppler to solve for the peak gradient through the valve, which were within normal values for a St. Jude 19-mm valve. Also, the area of the valve was calculated by the continuity equation using an x-Plane derived cross-sectional area (CSA) of the LVOT at the level of the stenosis (Fig. 3). These results suggested that valve function was unchanged from the original procedure. The patient underwent aortotomy and subaortic membrane resection with the original 19-mm valve remaining in the aortic position. After uneventful separation from cardiopulmonary bypass, the subaortic membrane appeared fully resected. The LVOT peak gradient was 6 mm·Hg (1.2 m/s); however, the peak pressure gradient through the prosthetic valve was 49 mm·Hg, similar to the original peak gradient during the AVR 8 years prior. While the possibility of incomplete resection of the membrane was discussed with the surgeon, the LVOT gradient was reduced. Concerns regarding patient-prosthesis mismatch (PPM) were also discussed, but the surgical team elected to attempt no further intervention.

Figure 3
Figure 3
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DISCUSSION

This case presents the challenges of determining the cause of increased gradients, given the complex scenario: regrowth of the subaortic membrane, dysfunction of the mechanical prosthesis, or both. In addition, the St. Jude 19-mm valve was likely too small for her body surface area, but because she had this in place for many years, PPM was not considered to be the cause of the increasing transvalvular gradients.

Calculation of intracardiac pressures through the use of the simplified Bernoulli equation is a hallmark of echocardiography. The equation is often presented in its simplified form:

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Simplification assumes a constant value for blood mass, energy loss secondary to viscosity, and a proximal velocity below 1.5 m/s. This case demonstrated a proximal velocity (V1) greater than 1.5 m/s, which would require the use of the modified Bernoulli equation (where V2 is the distal velocity).2 Our patient demonstrated an elevated proximal velocity presumed in the LVOT at 2.7 m/s, and a peak gradient of 4.0 m/s. Using these values, the actual peak gradient through the mechanical prosthetic is calculated as:

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The “unsimplified” Bernoulli equation calculates the actual peak transvalvular gradient to be within the normal report range, 42 ± 10 mm·Hg.3

In the midesophageal aortic valve long-axis view, the x-Plane feature allows CSA measurements of the LVOT at the level of the membrane (Figure 3).4 Using the continuity equation, the effective orifice area (EOA) of the valve is solved using the CSA of the LVOT and the LVOT volume-time integral (VTI) as traced in the double envelope. The result approximates the expected EOA based on valve type and size (1.5 ± 0.1 cm2):3

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Using this EOA, the indexed size for this patient is 0.6 cm2/m2, which is under the upper limit for acceptable size and consistent with that of PPM.5

This case also illustrates the discrete nature of these subaortic membranes and their ability to regrow6 (Fig. 2A); our patient had regrowth within 8 years. Subaortic membranes can present as membranous (approximately 5%) and tunnel-type (approximately 15%), further divided into short-segment and long-segment tunnels.6

Concern for PPM is an aspect of this case that makes the determination of the elevated gradients difficult to interpret. We were fortunate to have the TEE from her previous operation to assist in understanding the performance of this patient’s mechanical prosthesis. Based on the indexed valve area of 0.6 cm2/m2, the size is below a valve size of 0.65 cm2/m2, consistent with that of severe PPM.5 The historical peak gradient does not discount PPM as a cause of elevated gradients, but it confirms that the valve function has not changed. Certainly, the patient demonstrates findings consistent with that of severe PPM, but our surgeon did believe that a larger valve could be placed safely.

The differential diagnosis for early-peaking systolic gradient through the LVOT should include aortic valvular stenosis, but additional diagnoses, though rare, such as fixed subvalvular obstruction or supravalvular aortic stenosis should be considered.2 Patients with relatively small CSA of the proximal ascending aorta may demonstrate significant pressure recovery, exaggerating the severity of the stenosis as measured by Doppler.7 In addition, PPM must be considered, especially when the indexed valve area is under 0.65 cm2/m2.5 The reduction in afterload seen with AVR in patients with severe aortic stenosis could result in dynamic outflow obstruction from systolic anterior motion of the mitral valve or mid-cavitary obliteration from the hypertrophied left ventricle. The assessment of valvular disease is complex, and in the presence of elevated proximal velocities, the echocardiographer should remember the unsimplified Bernoulli equation. E

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Clinicians Key Teaching Points

By Kent H. Rehfeldt, MD, Donald Oxorn, MD, and Martin J. London, MD

* Bernoulli principle of fluid dynamics states that according to the law of conservation of energy, an increase in velocity occurs simultaneously with a decrease in pressure, resulting in an increase in pressure gradient. Using Doppler imaging, measurement of the peak velocity across a stenotic aortic valve (V2) can be related to the peak pressure decrease (the gradient across the valve), ΔP. This is commonly measured using the simplified Bernoulli equation, ΔP = 4(V2)2 where V2 represents the peak flow velocity at, or distal to, the assumed site of stenosis. This simplified equation ignores the contribution of blood viscosity and the velocity proximal to the presumed area of narrowing (V1), since this is smaller than V2 (usually <1 m/s).

* When V1 exceeds 1.5 m/s, the proximal pressure should be calculated and subtracted from the peak pressure gradient equation to avoid overestimation of the true peak pressure gradient. Thus, the corrected Bernoulli equation becomes ΔP = 4[(V2)2 − (V1)2] or ΔP = 4(V2)2 − 4(V1)2.

* In this case, using continuous-wave Doppler imaging via the deep transgastric window, elevated peak velocities and gradients across an aortic prosthesis were recorded in a patient who had undergone previous aortic valve replacement and subaortic membrane resection. The authors could ascribe a 4 m/s velocity to the aortic prosthesis and a 2.7 m/s velocity to the acceleration of blood past what appeared to be a recurrent subaortic membrane. The corrected Bernoulli equation yielded a peak prosthesis gradient of 34.8 mm·Hg, which was within normal limits for that prosthesis size; therefore, the valve was not replaced.

* When flow acceleration is measured or suspected proximal to a valve or prosthesis (proximal velocity >1.5 m/s), the corrected Bernoulli equation should be used to generate the true peak pressure gradient. If the proximal velocity is <1.5 m/s, its contribution to the peak pressure gradient is generally negligible and can be ignored.

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DISCLOSURES

Name: Nicholas W. Markin, MD.

Contribution: This author helped prepare the manuscript and create the figures and videos.

Attestation: Nicholas W. Markin approved the final manuscript.

Name: Georges Desjardins, MD, FRCPC, FASE.

Contribution: This author helped prepare the manuscript.

Attestation: Georges Desjardins approved the final manuscript.

This manuscript was handled by: Martin J. London, MD.

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REFERENCES

1. Maslow AD, Mashikian J, Haering JM, Heindel S, Douglas P, Levine R. Transesophageal echocardiographic evaluation of native aortic valve area: utility of the double-envelope technique. J Cardiothorac Vasc Anesth. 2001;15:293–9

2. Baumgartner H, Hung J, Bermejo J, Chambers JB, Evangelista A, Griffin BP, Iung B, Otto CM, Pellikka PA, Quiñones MAmerican Society of Echocardiography; European Association of Echocardiography. . Echocardiographic assessment of valve stenosis: EAE/ASE recommendations for clinical practice. J Am Soc Echocardiogr. 2009;22:1–23

3. Zoghbi WA, Chambers JB, Dumesnil JG, Foster E, Gottdiener JS, Grayburn PA, Khandheria BK, Levine RA, Marx GR, Miller FA Jr, Nakatani S, Quiñones MA, Rakowski H, Rodriguez LL, Swaminathan M, Waggoner AD, Weissman NJ, Zabalgoitia MAmerican Society of Echocardiography’s Guidelines and Standards Committee; Task Force on Prosthetic Valves; American College of Cardiology Cardiovascular Imaging Committee; Cardiac Imaging Committee of the American Heart Association; European Association of Echocardiography; European Society of Cardiology; Japanese Society of Echocardiography; Canadian Society of Echocardiography; American College of Cardiology Foundation; American Heart Association; European Association of Echocardiography; European Society of Cardiology; Japanese Society of Echocardiography; Canadian Society of Echocardiography. . Recommendations for evaluation of prosthetic valves with echocardiography and doppler ultrasound: a report From the American Society of Echocardiography’s Guidelines and Standards Committee and the Task Force on Prosthetic Valves, developed in conjunction with the American College of Cardiology Cardiovascular Imaging Committee, Cardiac Imaging Committee of the American Heart Association, the European Association of Echocardiography, a registered branch of the European Society of Cardiology, the Japanese Society of Echocardiography and the Canadian Society of Echocardiography, endorsed by the American College of Cardiology Foundation, American Heart Association, European Association of Echocardiography, a registered branch of the European Society of Cardiology, the Japanese Society of Echocardiography, and Canadian Society of Echocardiography. J Am Soc Echocardiogr. 2009;22:975–1014

4. Doddamani S, Bello R, Friedman MA, Banerjee A, Bowers JH Jr, Kim B, Vennalaganti PR, Ostfeld RJ, Gordon GM, Malhotra D, Spevack DM. Demonstration of left ventricular outflow tract eccentricity by real time 3D echocardiography: implications for the determination of aortic valve area. Echocardiography. 2007;24:860–6

5. Pibarot P, Dumesnil JG. Prosthesis-patient mismatch: definition, clinical impact, and prevention. Heart. 2006;92:1022–9

6. Choi JY, Sullivan ID. Fixed subaortic stenosis: anatomical spectrum and nature of progression. Br Heart J. 1991;65:280–6

7. Pibarot P, Dumesnil JG. Improving assessment of aortic stenosis. J Am Coll Cardiol. 2012;60:169–80

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