Opinions

Reply to: Four-dimensional flow MRI for evaluation of post-stenotic turbulent flow in a phantom: comparison with flowmeter and computational fluid dynamics

by Jihoon Kweon, PhD and Dong Hyun Yang, MD (donghyun.yang@gmail.com)

Kweon, J., Yang, D.H., Kim, G.B. et al. (2016) Four-dimensional flow MRI for evaluation of post-stenotic turbulent flow in a phantom: comparison with flowmeter and computational fluid dynamics. Eur Radiol 26: 3588.

Aug 8, 2017

Dear Editor,

We appreciate the interest in our publication entitled “Four-dimensional flow MRI for evaluation of post-stenotic turbulent flow in a phantom: comparison with flowmeter and computational fluid dynamics”[1] The authors raised the issues of definition of Reynold decomposition and PC-MRI turbulence mapping.
In turbulent flows, Reynolds decomposition is a common technique to evaluate velocity fluctuations. As the authors presented, the fluctuating velocity is defined as {u^'}=u-\bar{u} , the difference between instantaneous velocity u and mean velocity \bar{u}. We calculated the root-mean-square (rms) of u^' using the common definition as

〖u'〗_{rms}= \sqrt(\frac{1}{N} \sum_〖u'〗^2 )=\sqrt(\frac{1}{N} \sum(u-\bar{u})^2 )  [Equation 1]

Using the authors’ notations, the definition for PC-MRI velocity can be translated as

〖u'〗_{rms}= \sqrt(\frac{1}{N} \sum_〖u'〗^2_{PC-MRI})=\sqrt(\frac{1}{N} \sum(u_{PC-MRI}-\bar{u}_{PC-MRI})^2 ) [Equation 2]

If the rms of u, instead of u^', is plotted as indicated, the highest value will appear at the most stenosed region. However, we agree that u_{PC-MRI} as an outcome of time-averaging in a voxel loses the turbulent characteristics mostly and high 〖u'〗_{rms} values in Figure 5 were largely affected by the artifact due to low signal-to-noise ratio [2]. Interpretation of our data about velocity fluctuations should be limited when analyzing u_{PC-MRI} as is, and MR turbulent mapping can be performed within a feasible time by applying refined methods as the authors stated.
In the last decade, novel techniques have been developed to evaluate the turbulent characteristics using 4D PC-MRI, which allow faster and more accurate acquisition of flow patterns [3-5]. These techniques applied to measurement of cardiovascular blood flows in vivo have been used to find a correlation between turbulent flow patterns and diagnostic parameters [6; 7]. Together with introduction of a more elaborate method [8], MR turbulent mapping will offer more opportunities to implement 4D PC-MRI in clinical situations and facilitate better understanding of cardiovascular physiology beyond a direct interpretation of flow measurement as in our work.

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