Author + information
- Gianni Pedrizzetti, PhD,
- Pavlos P. Vlachos, PhD,
- William C. Little, MD,
- Fotis Sotiropoulos, PhD,
- Morteza Gharib, PhD and
- Arash Kheradvar, MD, PhD∗ ()
- ↵∗Department of Biomedical Engineering, and Medicine, University of California Irvine, 2410 Engineering Hall, Irvine, California 92697
With much interest, we read the recent article by Martínez-Legazpi et al. (1), which suggests insights into the role of diastolic vortex formation in filling of the left ventricle. We are delighted to see that fluid dynamics is increasing its presence in the clinical cardiology community and contributes to an improved understanding of cardiac function as underlined in the editorial comment (2).
The article by Martínez-Legazpi et al. (1) introduces a technique to evaluate the contribution of the left ventricular (LV) vortex to diastolic filling using intraventricular velocity estimated by 2-dimensional color Doppler echocardiography. They aimed to quantify the percentage of diastolic filling volume related to the LV vortex and tried to distinguish between normal and abnormal LV function. Their method is based on dividing the intraventricular velocity field into 2 components where one is the rotational flow, directly related to the presence of the LV vortex, and the other is irrotational, a mathematical approach known as Stokes decomposition widely applied in fluid dynamics.
Accordingly, Martínez-Legazpi et al. (1) first isolated the LV vortex and subsequently tried to adjust the corresponding velocity to account for the presence of the LV wall and mitral leaflets. Based also on the communication that we had with some of the authors, we understood that the method is initiated by computing the rotational velocity under the assumption that the LV wall is rigid, which should yield a zero volume for transmitral inflow. However, this results in an estimate of a new transmitral inflow volume that is nonzero. Then the method repeats the same procedure that always results in an inflow volume that is different from the expansion volume, and this process continues until the solution converges to a value.
One major concern with this method is that once the LV wall is assumed to be rigid and the ventricle is full of blood, it is physically impossible to achieve a nonzero transmitral inflow volume. Similarly, when the LV wall expands, its volume increase cannot differ from the transmitral inflow volume. The fact that these volumes differ during the individual iterative steps is a direct violation of the fundamental law of the conservation of mass, and reveals a questionable calculation in their method. This flaw calls into question the study’s methodology and subsequent results.
Moreover, according to the fluid dynamics conservation laws, the role of the LV vortex in diastolic filling volume cannot be evaluated merely by volumetric balances, but needs to be considered in conjunction with the corresponding momentum balances and intraventricular pressure gradients. Here, the second controversial notion introduced by Martínez-Legazpi et al. (1) stems from the decomposition of the pressure gradient into a rotational and an irrotational component. The analysis did not take into consideration that every gradient field is a conservative field by definition; hence, it has no rotational component. Therefore, the pressure decomposition presented in their analysis is rather improper for fluid dynamics, and we do not believe that it should be used for such a purpose.
In conclusion, this letter aims to bring attention to the analyses reported by Martínez-Legazpi et al. (1) and the supporting editorial views on the article (2). Although the concerns raised here are highly technical, we believe that they may have an impact on the validity of the reported methodology and results, and consequently, their clinical implications. We hope that the present letter clarifies these technical, albeit fundamentally significant, points on this published study (1).
Please note: Dr. Little is a consultant for Medtronic, CVRx, CorNovus, and CorAssist. All other authors have reported that they have no relationships relevant to the contents of this paper to disclose.
- American College of Cardiology Foundation
- Martínez-Legazpi P.,
- Bermejo J.,
- Benito Y.,
- et al.
- Sengupta P.P.,
- Narula J.,
- Chandrashekhar Y.