## INTRODUCTION

This chapter discusses the use of the Doppler principle and the modified Bernoulli equation for the assessment of gradients and regurgitations caused by stenotic or insufficient valves, as well as the evaluation of physiologic or pathologic communications within the circulatory system. These principles are applied to clinical bedside decision making in the context of neonatal functional echocardiography.

An important application of echocardiography is its use in analyzing the direction and velocity of blood flow within the heart and the blood vessels, and the difference in pressure values (pressure gradient) between these chambers. As described in Chapter 1, these measurements are possible thanks to the Doppler principle and the Bernoulli equation. The Doppler principle is used to derive information about velocity of blood flow, and this information can then be applied to the Bernoulli equation to extrapolate an estimation of pressure gradients.

* Videos can be accessed at http://PracticalNeonatalEcho.com.

## DOPPLER PRINCIPLE

The Doppler principle states that, to a stationary observer, the original frequency of sound emitted from a source is altered when the source of the sound is moving. The difference in frequency is called the Doppler shift. For echocardiography, the stationary observer is the transducer, emitting the ultrasound waves at a given frequency and receiving the returning ultrasound waves. The red cells within the bloodstream are the moving objects that reflect the incident sound waves and therefore serve as the “source” responsible for producing the Doppler shift. The returning signals will have a higher frequency (positive numerical value) if the red cells are moving toward the transducer, and a lower frequency (negative numerical value) if moving away from the transducer (Figure 6-1).

###### FIGURE 6-1.

Doppler shift; fo = transmitted frequency, fr = reflected frequency, V = velocity of red blood cells, Θ = Doppler angle.

The Doppler shift (or frequency difference) is calculated using the following formula:

$Doppler shift (Fd)=2 × Ft × V × Cos θC$

where:

• Fd = Doppler shift (frequency difference)

• 2 = Factor used because there are two shifts: one because the wave incident on the moving red blood cells is Doppler shifted and an additional shift because the reflection is from a moving object.

• Ft = Frequency of transmitted beam (transducer frequency)

• V = Velocity of the blood

• Cos θ = Cosine of angle of incidence (insonation) between the ultrasound beam and the blood flow

• C = Speed of sound in human tissue (1540 m/sec or m/s)

The importance of the angle of incidence θ becomes obvious when one considers the following:

For ...

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