The Nyquist Limit

Doppler echocardiography is often used to assess stenotic or regurgitant valves. Two types of doppler signals are used- pulsed wave doppler (PWD) and continuous wave doppler (CWD). Both serve different purposes and can be viewed as complementary.

PWD is used as a localising tool. It accurately detects that a systolic murmur is, for example, a consequence of aortic stenosis rather than mitral regurgitation. By producing a spectral image, PWD demonstrates a direction of flow towards or away from the tranducer. A spectral wave of aortic stenosis would, for example, be directed away from a transducer placed at the apex. In the case of PWD, a single transducer does both the sending and receiving.

Echocardiography relies on the shift in ultrasound frequency caused by red cells flowing towards or away from the transducer. This is called doppler shift and is given by F= 2Fo.v.cos theta/c, where Fo is the transmitted frequency, v denotes velocity of blood flow, theta is the angle between the transducer and plane of flow and c is the velocity of ultrasound waves in the medium in use, in this case, blood. When the transducer is parallel to the direction of flow, theta is 0, and cos theta is 1. Thus F= 2Fo. v/c.

Note that the doppler shift, i.e, the detected change in frequency is proportional to twice the emitted frequency. This illustrates an important limitation of PWD called "Nyquist limit". The Nyquist limit is always half the sampling frequency. That is to say that the maximum frequency accurately detectable with a sampling frequency of f is f/2. If emitted frequency is more than the Nyquist limit for the sampling frequency, than a phenomenon called "aliasing" occurs, where the recorded spectral wave is cut off at its peak and appears on the other side of the baseline (mimicking combined stenosis and regurgitation in the case of pure stenosis, for example), thus giving a distorted image. One way of reducing aliasing is by reducing the "sample volume", i.e. by placing the transducer as close to the valve being examined as possible. Thus, the ultrasound waves have to travel a shorter distance, thus raising the frequency at which sampling occurs, and thus the Nyquist limit.

CWD overcomes this shortcoming by using 2 transducers- one to transmit, and one to receive. There is thus no Nyquist limit. CWD is thus used to measure high velocity flows, such as through a severely stenotic valve (velocity being a function of Doppler shift in the above equation). Using the modified Bernoulli equation, one can estimate the pressure change across a defective heart valve. Thus Delta P (change in pressure)= 4 V^2. For example, if blood is flowing through a stenotic aortic valve at 4m/s, the pressure differential across the valve is 64 mm Hg.

The limitation of CWD is that while it can measure, it cannot localise. Thus, it is likely to confuse AS with MR if the jets happen to be in range. This distinction is only achievable by PWD, which samples a limited frame. In practice therefore, one should localise the jet with PWD, taking care to avoid aliasing and then measure the velocity and thus delta P with CWD.