Author + information
- Pablo Martínez-Legazpi, MEng, PhD,
- Javier Bermejo, MD, PhD∗ (, )
- Yolanda Benito, DCS, DVM,
- Raquel Yotti, MD, PhD,
- Candelas Pérez del Villar, MD,
- Ana González-Mansilla, MD, PhD,
- Alicia Barrio, DCS, MBiol,
- Eduardo Villacorta, MD,
- Pedro Luis Sánchez, MD, PhD,
- Francisco Fernández-Avilés, MD, PhD and
- Juan C. del Álamo, AeEng, PhD
- ↵∗Department of Cardiology, Hospital General Universitario Gregorio Marañón, Dr. Esquerdo 46, Madrid 28007, Spain
We read with great interest the letter by Pedrizzetti and colleagues Because our study (1) has raised some concerns among these investigators, here we are pleased to reassure the readers of JACC about the validity of our findings.
The impact of a vortex on the intraventricular flow is conditioned by its effects on the chamber’s wall movements, which cannot be predicted a priori without considering the mechanical properties of the walls and the momentum exchange between the walls and the fluid. It is true that uncoupling these effects from the rest of the flow is a challenging task that must be accomplished while enforcing fluid dynamics conservation laws. We were aware of this issue from the very onset of our study design. Thus, we defined that a fraction of wall velocity is caused by the vortex. This fraction was entered as a single free parameter (lambda, in our Online Appendix) in our calculations.
Making use of a novel iterative method, we updated lambda until mass conservation was ensured. Briefly, we started the calculation of the vortex flow with the assumption of rigid walls and thus null lambda. This resulted in values of flow velocity between the tips of the mitral valve, which were not null. Inflow volume was measured by time integrating this localized velocity under a 1-dimensional flow assumption. Note that this 1-dimensional approximation has been routinely used by the authors of the letter (2,3) and by others (4) for measuring inflow and has provided important new insight into left ventricular physiology. Finally, we updated lambda and repeated the procedure until the new transmitral inflow volume matched the expansion volume dictated by lambda. Importantly, convergence was achieved in fewer than 5 iterations in all cases. Furthermore, convergence to the same value of lambda was achieved regardless of the initial assumption about wall motion (i.e., the same result was obtained for any initial value of lambda), and the measured inflow volume was only slightly altered by the change in boundary conditions.
By using this method we were able to demonstrate some of the physiological implications of intraventricular vorticity in a clinical scenario using clinical measurements. This was one of the major strengths of our paper, as emphasized by the reviewers and the accompanying editorial (5).
Regarding the second concern of Pedrizzetti and colleagues, which related to the conservation of momentum, we estimated the rotational velocity field directly from the measured velocity field. The latter is the result of the balance of fluid momentum pressure and the fluid-structure interaction with the ventricular walls. It is from the resultant velocities that we reconstructed the pressure gradient fields and not vice versa. This approach has also been used before by the authors of the letter to the editor (3).
Thus, no physical law was inappropriately used in our study. Although the numerical values reported are approximate, we would like to reinforce the validity of our results and their clinical implications.
Please note: All authors have reported that they have no relationships relevant to the contents of this paper to disclose.
- American College of Cardiology Foundation
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