LETTER TO THE EDITOR
Space and time dependency of inertial and convective contribution to the transmitral pressure drop during ventricular filling
Giovanni Tonti, MDa,
Gianni Pedrizzetti, PhDa,
Paolo Trambaiolo, MDa and
Alessandro Salustri, MD, PhD
a Via Circonvallazione Occidentale N. 145, 67039 Sulmona, Italy
giatonti{at}arc.it
We have read with much interest the recent article by Firstenberg et al. (1), which provides new insights into the comprehension of noninvasive assessment of transmitral pressure drop. In their Figure 2, the investigators display a graph demonstrating how the inclusion of inertial term in the pressure calculation allows an estimation of pressure drop across the mitral valve closely related to the invasive measurements. In contrast, the application of the steady formulation of the Bernoulli equation implies a relevant underestimation of the pressure value with a relevant phase lag of the pressure curve. However, the relative role of convective and inertial terms for pressure generation is strongly dependent on the space and temporal distribution of the two terms, thus the Doppler-derived curve of pressure represented in their Figure 2 represents only a particular case and should not be taken as a reference for normal condition.
We have previously evaluated the pressure maps derived from the solution of Eulero equations applied on numerical transformed color Doppler M-mode images of the left ventricular inflow (2,3). Because the inertial and convective terms have different space-time distribution and derive from different phenomenon (acceleration and potential of velocity, respectively), care must be taken when interpreting the transmitral pressure difference between two points. In fact, inertial drop is unaffected by the distance between measurement points when these are sufficiently outside the mitral jet core. In contrast, the convective force plays a role only when the second point is within the jet core; otherwise, its contribution is negligible.
The graph of pressure drop reported in Figure 2 of Firstenberg et al. (1) study and computed between points 5 cm apart can be misleading and of difficult interpretation because it is not linked to a space-time map of pressure. A relevant positive contribution of convection is shown there, which is always between 0.5 and 1 mm Hg during the entire filling period. This means that the velocity in the ventricle, at a distance of 3 cm from the mitral plane, must be always >25 cm/s, even in the diastasic period, which for a normal heart rate and normal flow propagation velocity is not a common finding. In addition, it is also difficult to understand how the total pressure may remain positive during the deceleration phase of the E-wave. In fact, because the inertial contribution is the flow acceleration, during deceleration the pressure increases along the direction of flow; thus, a negative atrium-ventricular pressure difference can be predictable.
From the space-temporal maps, we calculated the pressure difference among three pairs of points at different distances, and the respective results are plotted in Figure 1. As we can see, the convective term disappears when the points are separated by 5 cm (2 cm inside the atrium to 3 cm in the ventricle), a distance similar to the example by Firstenberg et al. (1). In our example, the two points are outside the jet core, and the pressure drop is zero at the maximum of mitral velocity. Figure 1 shows little changes when the two points are closer (1 cm in the atrium and 2 cm in the ventricle). In contrast, an important convective effect appears only when the second point is placed inside the jet (1 cm into the ventricle). In this case, the pressure presents a comparable influence of both terms. However, even in this case, pressure at the E-wave still presents an inversion of sign at the end of the deceleration when inertia is negative and velocity (convection) goes to zero.
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Figure 1 Computed pressure difference during left ventricular filling in normal conditions. Measurement points are (upper) 2 cm in the atrium, above the mitral plane, and 3 cm in the ventricle; (middle) 1 cm in the atrium and 2 cm in the ventricle; (lower) 1 cm in the atrium and 1 cm in the ventricle. Total pressure difference is reported with a thick, continuous line; the inertial (dashed line) and convective (dash-dot line) contributions are also reported separately. The thin, continuous line is the reference velocity at the mitral plane.
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In conclusion, we underline how convective and inertial terms of pressure are dependent from the relative position of measurement points. Space allocation of convective and inertial forces by the analysis of the atrioventricular velocity field allows a better interpretation of pressure map in hemodynamic terms.
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References
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1. Firstenberg MS, Vandervoort PM, Greenberg NL, et al. Noninvasive estimation of transmitral pressure drop across the normal mitral valve in humans: importance of convective and inertial forces during left ventricular filling. J Am Coll Cardiol. 2000;36:1942–1949[Abstract/Free Full Text]
2. Tonti G, Fedele F, Manfredi RM, et al. Numerical models for supporting non-invasive investigation of left atrium-ventricle system. J Cardiovasc Diagn Proc. 1998;15:283–285
3. Tonti G, Riccardi G, Denaro FM, Trambaiolo P, Salustri A. From digital image processing of color Doppler M-mode maps to noninvasive evaluation of the left ventricular diastolic function: a dedicated software package. Ultrasound Med Biol. 2000;26:603–611[Medline]
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