Letter by Dasi et al Regarding Article, “Effect of Chronotropy and Inotropy on Stitch Tension in the Edge-to-Edge Mitral Repair”
To the Editor:
Timek et al concluded that the septal-lateral (SL) diameter rather than hemodynamic parameters are the main determinants of “Alfieri stitch” force (ASF) during diastole.1 We found that the arguments presented were not convincing because of an insufficiently detailed hemodynamic characterization. The purely statistical analysis of the problem, excluding instantaneous flow rate data, undermines the potential scientific impact of the excellent in vivo experiments. To elaborate on our criticism, we present a brief summary of the physics that determines ASF, arguments based on the data of Timek et al, and previous data2 that corroborate the physics we describe, and we recommend an analysis to correctly identify the main determinant.3
Diastolic ASF is the force necessary to prevent the fluid pressure that acts on the leaflets from opening them to their natural configuration. Fluid pressure on the leaflets is directly proportional to the upstream momentum flux, ρQV, where ρ is the blood density, Q is the diastolic flow rate, and V is the mean annular blood velocity; which in turn can be shown to be ρQ2MAA−1 from continuity, where MAA is the mitral annular area. The use of dimensional analysis3 yields the same with
where the proportionality constant k is dependent on the precise geometric shape and Reynolds number. Therefore, the 3 determinants of ASF are Q, MAA and SL, and identifying the main determinant of these requires quantification of the sensitivity of ASF to each of these 3 determinants, which was lacking in the article by Timek et al.1
Even with omission of instantaneous flow rate, the data corroborate the physics and provide physical insight. In Figure 2, during diastole t=(−250,−50), MAA clearly decreased with pacing (well beyond noise level), and tension clearly increased (>20%). Given that cardiac output and SL changed insignificantly, this result corroborates the inverse relationship with MAA, also previously demonstrated.2 In Figure 3, during early diastole t=(−250,−150), ASF markedly increased whereas MAA and SL remained unchanged from CaCl2 infusion. Because flow increased, this finding corroborates ASF∝Q2, also demonstrated previously.2 However, it is interesting that in the later half of diastole t=(−150,0), ASF slightly decreased with a simultaneous decrease in both MAA and SL. This can be attributed to the decrease in SL. Fully understanding this phenomenon needs the position data of the stitch and the instantaneous flow rate, which were not presented. Furthermore, the above arguments related to Figures 2 and 3 are subject to statistics that have not been presented.
From the above, it is our opinion that crucial instantaneous flow rate data, which may be derivable,4,5 need to be examined, because cardiac output carries little information, especially relative to the peak force event. In addition, a deeper understanding could be gained by averaging ASF and each of the 3 determinants over t=(−250,−50), (−250,−150), (−150,0) and comparing them statistically to gain a full understanding of the in vivo mechanics.