Original contributionOn MRI turbulence quantification☆
Introduction
While normal cardiovascular flow is predominately laminar, turbulent flow accompanies many forms of cardiovascular disease. In the human arterial tree, turbulence causes pressure drops over stenoses and may increase the risk for hemolysis [1] as well as platelet activation and thrombus formation [2], [3]. Additionally, ample evidence suggests that turbulence is involved in the pathogenesis of atherosclerosis [4], [5], [6]. With a growing awareness of the implications of abnormal hemodynamics, the demand for reliable tools for the quantitative assessment of blood flow disturbances is increasing [7].
Turbulent fluid motion can be described as “an irregular condition of flow in which the various quantities show a random variation with time and space coordinates, so that statistically distinct average values can be discerned” [8]. By employing ensemble, time or space averaging, a velocity component u can be statistically separated into the averaged mean velocity U and the fluctuating velocity u′ according to u=U+u′ [9]. The intensity of the velocity fluctuations can be quantified by the standard deviation (m/s). Under the ergodic hypothesis, ensemble, time and space averages are interchangeable [10]. This means for example that sampling over a spatial area that encompasses all turbulence space scales yields the same result as a convergent value sampled over time.
Several studies have investigated the effects of turbulent flow on the magnetic resonance imaging (MRI) signal in order to establish methods for quantifying turbulence [11], [12], [13], [14], [15], [16], [17], [18]. Recently, an in vitro study indicated good agreement between the turbulence quantities obtained by MRI and particle image velocimetry [19]. In addition, MR turbulence quantification was recently successfully applied in vivo for the first time [20]. Prior to this, MR methods for the quantification of turbulence have been sparingly applied [21]. This may partly be attributed to earlier limitations in scanner hardware; the advantages offered by modern MRI scanners, such as increased signal-to-noise ratio through the use of improved receiver coils and reduction of echo time through the use of high-performance gradients can be expected to increase their utilization. Moreover, usability may be enhanced by clarifying specific aspects of MR turbulence measurements that facilitate adequate application of the technique. Here, we will examine the practical consequences of some of the assumptions which underlie MR quantification of turbulence and investigate how intravoxel mean velocity variations and noise affect the turbulence estimates. All methods that utilize the MR signal magnitude for turbulence quantification are subjected to the same sources of error; however, different approaches for obtaining turbulence estimates may be differently affected.
The objective of this work was to investigate potential pitfalls and sources of error in MR measurements of turbulence quantities and to outline strategies for minimizing their effects. This was done by means of theoretical derivations and numerical simulations.
Section snippets
Theory
MRI flow quantification of the mean velocity, U, is a standard clinical tool and a powerful research tool that can be used to quantify different components of blood transiting the left ventricle [22], for example. The most common MR tool for quantification of flow is phase-contrast (PC) MRI [23] where bipolar gradients are used to apply flow sensitivity. Spins moving under the influence of a bipolar gradient accumulate phase according towhere γ is the gyromagnetic ratio, τ is
Materials and methods
An important assumption underlying MR turbulence methods is that |S(kv)| has a Gaussian distribution, even though other distributions may be used as well [18]. Also, MR methods for turbulence quantification require that the voxels are sampled in a way which sufficiently encompasses the turbulence scales. The conditions for this to hold are dependent on the nature of the flow in combination with imaging parameters. Intravoxel mean velocity variations will contribute to the distribution of s(u)
Results
Maps of the instantaneous axial velocity in a centerplane of the numerical flow phantom at three different time points (Fig. 1B) indicate that the largest temporal velocity variations are present around Z=3. The velocity over time at the centerline position Z=2.5 is plotted in Fig. 2.
A comparison between a simulated MR turbulence measurement (σIVSD), the root-mean-square deviation of the intravoxel velocities from their mean,σrms, and σtime as obtained by sampling the numerical flow field over
Discussion
In this study, fundamental aspects of the theory underlying MR turbulence measurements have been investigated. Methods for assessing the effects of noise and intravoxel mean velocity variations have been derived. By means of two different simulation approaches, the consequences of these sources of error on the MR signal used for turbulence quantification have been demonstrated.
In theory, MR methods for the quantification of turbulence seek to estimate σrms, the root-mean-square deviation of the
Conclusion
We have studied the practical consequences of important aspects of the theory underlying MR turbulence measurements and presented several findings that may facilitate future applications of the technique. The findings are applicable to all approaches for MR quantification of turbulence that use information contained in the MR signal magnitude. Data acquisition strategies suitable for turbulence quantification have been outlined. We have derived an expression that describes the impact of
Acknowledgments
The authors thank Nora Östrup and Pamela Vang for helpful comments on the manuscript.
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Grant support was provided by the Swedish Research Council and the Swedish Heart-Lung Foundation.