Flow quantification

Abstract

IntroductionFlow measurements have been possible in ultrasound ever since the advent of Doppler; however, the measurements have been problematic and error prone. This has lead to compromises in the flow measurements that have generally been performed. These compromises have included flow velocity measurements, which are a direct outgrowth of Doppler, rather than true volume flow, and semi-quantitative parameters such as resistive indices (RIs) and pulsatility indices (PIs). Flow velocities have direct value in that conservation of volume flow due to autoregulating areas produces increases in local flow velocities at areas of stenosis. Such changes have proven very useful for the diagnosis. Also because of the Bernoulli equation, peak flow velocities can be used to estimate pressure drops in the correct circumstances such at the aortic and pulmonary valves. Although attractive because they are simple to perform, RIs and PIs have very frequently provided less than totally useful information. This may be because these measurements are only empirical, and really do not measure what they are claim to, i. e. vascular resistance. Ultimately, one would like to measure flow directly, and recent developments have moved closer to this goal. Measuring flow volumeThe first volume flow estimates were made with Doppler. The ubiquitous Doppler equation is:where Df is the Doppler shifted frequency, v is the velocity of the blood flow, c is the speed of sound, f o is the carrier frequency of the Doppler and Q is the Doppler angle. Solving for velocity and opening the range gate to include the entire width of a blood vessel, one can estimate the mean velocity through the range gate. By assuming the vessel is circular in cross section, one can estimate the radius of the blood vessel, calculate the cross-sectional area of the vessel, and by multiplying flow determine the mean velocity through the cross section by the area of the cross section. Although true in theory, these estimates lead to many problems in practice. Firstly, the cross section is almost never circular making the area estimate imprecise, and secondly, the velocity profile is hardly ever cylindrically symmetric, making the velocity sampling assumptions wrong. The usual machine-programmed volume estimating routines assume a circular cross section. Even if this assumption is correct, the effect of the error multiplies with small radii. The fractional error is DA/A = 2Dr/r, where A is area and r is radius. Thus, for example, if a vessel has a radius of 5 mm and the error in measuring the radius is 1 mm, then the fractional error will be 40 %. Such problems alone have discouraged use of this method. An additional problem is estimating the Doppler angle, yet, certain angle-independent flow techniques can theoretically decrease this problem. However, major issues still remain. A novel solution to this problem had been proposed some years ago by Hottinger and Meindl [1]. They proposed using two different beam profiles to solve the geometry problem. They used a beam with larg...

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