Standardization of Carotid Ultrasound
To the Editor:
In a recent publication1 the authors reported a significant contribution to the standardization and normalization of duplex scanning for carotid stenosis. My purpose is to add a simple fluid mechanics analysis that supports their ratio of time-averaged blood flow velocity measured in the internal carotid intrastenotic segment to the time-averaged velocity in the downstream normal arterial segment.
Applied to the internal carotid artery, the law of conservation of mass requires that the time-averaged blood flow through the stenotic segment equal that in the downstream normal segment. Using the NASCET method, the percent diameter stenosis is 100(1−D1/D2), where D1 and D2 are the internal diameters of the stenotic and normal segments, respectively. The time average blood flow is IID2V/4, where V is the spatial average velocity. Conservation of mass gives V1D12=V2D22, or V1/V2=[1/(1−% stenosis/100)]2 and % diameter stenosis=100[1−(V2/V1)1/2]. Because the velocities in this simple formulation are both time and spatial (cross-section) averages and duplex scanning focuses on midstream velocities, these equations can be used in 2 situations. The above equations are good approximations for internal carotid arteries with mild or no stenosis because the time-averaged flow through both the stenotic segment and the distal segment have similar parabolic velocity profiles.2 Comparative V1/V2 data from Figure 11 and the above equation for 0%, 25%, and 50% stenosis are 0.7 versus 1.0, 1.5 versus 1.8, and 3.0 versus 4.0, respectively. When % diameter stenosis exceeds 50%, the flow through the stenotic segment becomes turbulent, the velocity profile is blunted, and the mean velocity is close to the midstream velocity. For laminar flow in the downstream normal segment, the velocity profile is parabolic and the spatial mean velocity is one half the peak (midstream) velocity.2 For this clinically important range, V1/V2≅2[1/(1−% stenosis/100)]2 and % stenosis≅100[1−(V2/2V1)1/2]. Comparative data from Figure 1 and Table 2 and these equations for 60%, 70%, and 80% stenosis give V1/V2 values of 4.0 versus 3.1, 5.0 versus 5.6, and 10 versus 12.5, respectively. These simplistic theoretical results correspond with the author’s measured values and support the use of their velocity ratio.
However, there may be some drawbacks. We have found it difficult to obtain velocities in the normal downstream internal carotid artery in patients with high carotid bifurcations when the stenosis is long and when the artery is tortuous. The velocity in the normal downstream segment must be measured 4 to 5 cm distal to the stenosis to allow for reestablishment of a near-parabolic velocity profile. Because of flow into the external carotid artery, this method is not applicable to distal common carotid stenosis; however, in this case the ratio of the velocity in the stenotic common carotid segment to that in the more proximal normal common carotid artery is hemodynamically valid and should give acceptable results.
- Copyright © 1999 by American Heart Association
Dr Archie’s fluid mechanics analysis is based on the assumption that carotid artery stenoses are concentric. In this sense his model is simplistic: predicted velocity ratios are higher than measured ratios because of the asymmetric stenotic lumen. A 70% diameter reduction with concentric lumen yields higher velocity ratios than a 70% eccentric stenosis with higher cross-sectional area. Our data indicate that carotid stenoses are more or less eccentric. Because the individual shape of the stenotic lumen cannot be predicted from Doppler measurements, we must rely on the estimation from nonlinear regression analysis, as shown in Figure 1 in our article.R1 What Doppler really tells us is cross-sectional area reduction, not diameter stenosis.
Dr Archie points out that reference measurement in the high cervical internal carotid artery is sometimes difficult. Less than 5% of our patients were ineligible for distal velocity ratio measurement: with sensitive color Doppler systems and suitable curved array or sector probes (ie, the ATL C7-4 and P5-3 probes) we could show the internal carotid 4 to 5 cm downstream in the majority of our patients. Patients with distal carotid stenosis or common carotid stenosis were not included in our study, but application of a “reversed velocity ratio” gave good results in our clinical practice, as correctly supposed by Dr Archie.
Ranke C, Creutzig A, Becker H, Trappe H-J. Standardization of carotid ultrasound: a hemodynamic method to normalize for interindividual and interequipment variability. Stroke.. 1999;30:402–406.