## Lv

where EF is ejection fraction, LV EDV is left ventricular end-diastolic volume, and LV ESV is left ventricular end-systolic volume.

Normal values for ejection fraction are approx 55-65%, and cardiac output can be estimated by multiplying the volume ejected with each beat (stroke volume) by the heart rate using the equation

where CO is cardiac output, HR is heart rate, and SV is stroke volume.

### 3.3. Doppler Ultrasound

The Doppler principle, described by Christian Johann Doppler in 1843, states that the frequency of transmitted sound is altered when the source of the sound is moving (2). The classic example is the change in pitch of a train whistle as it moves, getting higher as it approaches the receiver and lower as it moves away from it. This change in frequency, or Doppler shift, also occurs when the source of sound is stationary, and the waves are reflected off a moving target, including red blood cells in the vasculature. The shift in frequency is related to the velocity of the moving target, as well as the angle of incidence, and is described by the equation fd =

where fd is the observed Doppler frequency shift, f0 is the transmitted frequency, c is the velocity of sound in human tissue at 37°C (~1560 m/s), V is blood flow velocity, and 0 is the intercept angle between the ultrasound beam and the blood flow.

Using this principle, Doppler ultrasound can be used to estimate the velocity of blood flow in the human heart and vasculature noninvasively. Using a modified Bernoulli equation in which pressure drop is equal to four times the velocity squared (4 V2), Doppler ultrasound can also be used to estimate chamber pressures and gradients and to provide significant noninvasive hemodynamic data.

### 3.4. Continuous Wave Doppler

Continuous wave Doppler is performed using a single transducer with two separate elements for transmission and reception of sound waves, so that there is continuous monitoring of the Doppler shift. This technique allows detection of very high velocity blood flow, but does not allow localization of the site of velocity shift along the line of interrogation (1).

### 3.5. Pulsed Wave Doppler

Pulsed wave Doppler uses bursts of ultrasound alternating with pauses to detect Doppler shift in a localized region. The timing between the generation of the ultrasound wave and detection of the reflected wave determines the depth of interrogation. Pulsed wave Doppler is useful to measure velocity changes in a region defined by 2D echocardiography; however, the spatial resolution limits the velocity shifts detected. In general, the maximal velocity shift detectable is one-half of the Doppler sampling rate (pulse repetition frequency) and is designated the Nyquist limit (1). The maximal sampling rate is determined by the distance of the sampling site from the transducer and the transducer frequency, so that sampling from a transducer position nearer to the region to be interrogated and using a lower frequency transducer will improve the detection and localization of higher velocity flow (1).

### 3.6. Color Doppler Flow Mapping

Color Doppler flow mapping uses the principles of pulsed Doppler to examine multiple points along the scan lines. The mean velocity and direction of these signals are calculated and then displayed, superimposed on a 2D image. By convention, flow directed toward the transducer is red, and flow directed away from the transducer is blue. Accelerated or turbulent flow is given a different color, typically yellow and green. Color flow mapping is valuable because of the large amount of information that can be obtained in a single image. It can also aid in the localization of flow acceleration, quantitation of valvular regurgitation, visualization of intracardiac shunting, or assessment of arterial connections. Information obtained from color Doppler can also be refined by pulsed wave Doppler and continuous wave Doppler interrogation.

3.7. Quantification of Pressure Gradients Using Doppler Shift Measurements

Today, quantification of pressure gradients using Doppler echocardiography can provide hemodynamic information that could previously be obtained only by invasive cardiac catheter-ization. Specifically, the Bernoulli equation (3,7) defines the relationship between velocity shift across an obstruction and the pressure gradient caused by the obstruction. For practical purposes, the proximal velocity is neglected, and the simplified equation becomes:

pressure difference = distal velocity squared x 4 This is a valuable way to estimate pressure drops across obstructive valves or pressure differences between chambers (i.e., based on the velocity of valvar regurgitation or intracar-diac shunting).

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