Doppler Physics

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“It is almost to be accepted with certainty that this will -in the not too distant future- offer astronomers a welcome means to determine the movements and distances of such stars “
Christian Andreas Doppler, from the paper ‘On the coloured light of the double stars and certain other stars of the heavens’, 25 May 1842, Royal Bohemian Society of Sciences, Prague.

Definition

Doppler echocardiography is a diagnostic ultrasound based technique that is widely used for measuring blood flow velocities in the different sectors of the cardiocirculatory system and, from these data, to obtain a noninvasive hemodynamic assessment of patients with known or suspected cardiovascular disease.


Contents

History of Doppler Echocardiography

In 1842, an Austrian professor of mathematics and physics, Christian Andreas Doppler, presented results of his investigations in the field of astronomy at the Royal Bohemian Society of Sciences (Prague), without any hints that they would have become one of the basic principles of modern ultrasound diagnostics[1]. More than a century later, in October 1958, prof. Shigeo Satomura from University of Osaka (Japan), presented a paper entitled "Study of blood flow in vessels by ultrasonics" at the meeeting of Japanese Acoustics Society. This paper was about the measurement of blood flow velocities in peripheral and extracranial brain-supplying vessels using ultrasounds. In 1962, prof. Kanemasa Kato demonstrated that: Doppler signals from blood were actually produced by waves reflected from moving red blood cells; output voltage correlated with the number of particles; and the frequency of the detected sound correlated with the speed of the flow. In 1963, the Osaka group derived the flow velocity waveforms that are used widely today from spectral flow analysis. However, Doppler echocardiography was not used clinically until the late 1970s. Holen and Hatle were the first clinicians to apply this technique to measure the pressure gradient in patients with mitral stenosis [2][3].

The Doppler Effect

In clinical routine, Doppler echocardiography is used used to measure velocities and direction of blood flow in the heart chambers and vessels according to the Doppler effect, which was described by Christian Doppler. He discovered that stars appear of different colours when observed from a constant position on earth. He suggested that all stars emitt a common white light and the different colours we observe are due to both the motion of the star and the motion of the observer. These motions cause a change in the frequency shift of the light reaching the observer which is known as ‘Doppler effect’ [4][5][6][7].The “Doppler effect” can apply to any wave in which the source or the observer is moving with respect to the other. The frequency shift is directly proportional to the velocity difference between the source and the observer. The Doppler principle states that the frequency of the reflected ultrasound is altered by a moving target in a way that if a sound source moves toward the observer, the reflect sound frequency increases, conversely if the source moves away from the observer, the reflected sound frequency decreases.

Figure-1. The Doppler effect. Schema indicating the Doppler effect in relation to blood flow: the transmitted ultrasounds showed as ƒt and v is the velocity of the red blood cells. Angle-dependence of Doppler analysis is also displayed (Modified from reference 9)

With Doppler echocardiography, a high frequency ultrasound (2 to 5 MHz) beam is directed towards the red blood cells flowing in the circulatory system, the transducer determines the frequency shift (Δƒ) which is the difference between the frequency of the transmitted ultrasound (ƒt) and the frequency of the received one (ƒr). The Doppler equation relates the velocity of the moving red blood cells to the Doppler shift:

Δƒ = (2ƒt . v . cosɵ)/c

where v is the velocity of the moving target, ƒt the frequency of the transmitted ultrasound, ɵ is the angle between the direction of ultrasound beam and the direction of the moving target. and c is the velocity of sound in blood (1.540 m/s). Doppler shift (Δƒ = ƒt - ƒr ) is expressed in Hertz.


This equation shows that an accurate measurement of blood flow velocity critically depends on the alignment of the Doppler beam as parallel as possible to the direction of the blood flow (Figure-1).

Figure-2. PW Doppler recording of left ventricular outflow velocity obtained from apical window. Since flow is away from transducer, velocities are displayed below baseline. A thin vertical line after the flow profile results from aortic valve closing.


Blood flow velocity can be calculated using the Doppler equation:

v = (Δƒ . c)/ (2ƒt . cosɵ)

Currently, three Doppler echocardiography modalities are available for clinical use: pulsed wave (PW) Doppler (Figure-2), continuous wave (CW) Doppler (Figure-3) and colour Doppler flow imaging (Figure-4).


Figure-3.CW Doppler recording of aortic valve velocity in patient with aortic stenosis. Aortic peak valve gradients, mean gradients and valve areas can be measured


The first two of them are also known as spectral Doppler [8][9][10]. The spectral Doppler display shows blood flow velocities plotted against time. By using this Doppler modality, flow velocity, flow direction (conventionally, spectra above the baseline indicate blood flowing towards the transducer, whereas spectra below the baseline indicate blood flowing away from the transducer) and the timing of the signal can be displayed.

Figure-4. Colour Doppler in parasternal short axis view at tricuspid valve. The green flow in systole inside the right atrium shows tricuspid regurgitation.

Pulsed-wave Doppler

Pulsed-wave Doppler consists of intermittent (pulsed) bursts of ultrasound at a frequency called the pulse repetition frequency (PRF). A single ultrasound crystal sends and receives sound beams. These intermittent pulsed bursts of ultrasound are reflected off the moving red blood cells and received at intervals between the transmitted pulses. Signals returning from different depths are received at different times. With the knowledge of the speed of ultrasound in cardiac tissue, the returning signals can be time-gated so that interrogation of blood flow can be acquired at a specific site (sample volume) that can be selected by the observer. Using PW Doppler echocardiography we can only measure velocities which are below a certain value, faster velocities cannot be displayed because of the aliasing phenomenon. The highest velocities that can be measured by PW Doppler are limited by the Nyquist limit which is determined by the PRF. The “Nyquist limit” is equal to one half the PRF, which is usually less than 2 m/s on current ultrasound machines. If the frequency shift is higher than Nyquist frequency, aliasing occurs. The PRF varies inversely with the depth of the sample volume. Therefore, to increase the velocities that can be measured with PW Doppler without aliasing, the sample volume should be placed closer to the transducer. In conclusion, PW Doppler is used to measure laminar low-velocity blood flow in a specific area. Typical PW Doppler velocity spectrum consists of a narrow spectral pattern during flow acceleration and deceleration and wider dispertion in the middle. Degree of dispersion indicates range of blood flow velocities detected within the sample volume. The most dense (brightest) portion depicts the velocity of the majority of blood cells, also known as the modal velocity. Less dense areas show the velocity of a smaller mass of blood cells. The outer edge of the dense envelope should be used for measuring velocities and velocity-time integral.

Nyquist limit = PRF/2

The primary use of PW Doppler is to assess velocities across normal valves or vessels to evaluate cardiac function or flow. Common clinical applications include calculation of cardiac output and regurgitant volumes, quantification of intracardiac shunts, and evaluation of diastolic function.

Continuous-wave Doppler

Continuous-wave Doppler uses a transducer with two ultrasound crystals, one continuously emitting ultrasounds and the other one continuously receiving the reflected signals. This modality permits to record high blood flow velocities (since it is not affected by the Nyquist limits) but does not allow precise localization of the site of origin of these velocities along the sound beam. CW Doppler is used for measuring high velocities across obstructed and/or regurgitant lesions. Continuous wave Doppler records the velocities of all the red blood cells moving along the course of the sound beam. Therefore, the recording shows a full spectral envelope where the outer border represents the velocities of the fastest moving target. Measurements of velocities should be taken from the outer border which is assumed to represent the stenotic jet velocity. Common clinical applications include measuring pressure gradients in stenotic native valves, estimating pulmonary artery systolic pressure and determining prosthetic valve gradients. Measurements of blood flow velocities, allows the calculation of pressure gradients using the modified Bernoulli equation:

Pressure gradient continuous-wave Doppler

Pressure gradient (ΔP) = 4.(v2²-v1²)

where v1 is the velocity of flow upstream the stenotic orifice, whereas v2 is the velocity of flow within the vena contracta.

Recommendations about recording spectral Doppler velocities

Accuracy of blood flow velocities measured by Doppler relies on the parallel orientation of the sound beam with the direction of flow. Although small (<20 degrees) deviations from perfect parallelism may cause only mild (<10%) errors in velocity measurements, when Doppler is used to calculate pressure gradients, this small error in velocity measurement is squared resulting in a significant underestimation of the pressure gradient.

Colour Doppler flow imaging

Colour Doppler flow imaging is based on PW Doppler technology by using multiple sampling sites (100-400) along multiple ultrasound beams (multigated) in order to display intracavitary blood flow using a colour map where colours are coded according to direction, mean velocity and extent of turbulence of flow (Figure-5).

Figure-5. Colour Doppler in apical long-axis view from the patient with severe mitral insufficiency due to ruptured papillary muscle post myocardial infarction. Turbulence is characterized by the difference between the mean velocity and individual flow velocities, is shown as green colour.

At each sampling volume, the frequency shift is measured, converted to a digital format and displayed as colour flow map superimposed on 2-dimensional imaging. A pair of pulses determines a phase shift; two phase shifts (three pulses) enable velocity estimation. More pulses are needed to increase accuracy or sensitivity to low velocities (slow smooth appearance). However, the number of pulses per sample volume is limited by a drop in frame rate. Frequency shift analysis with autocorrelation (comparison of a signal with itself in time to find a pattern) estimates mean velocity, variance (spread of velocities around the mean), and direction of flow. Conventionally, the blood flow directed towards the transducer is colour-coded in red and the flow directed away from the transducer is colour-coded in blue (Figure-6).

Figure-6. The pulmonary valve regurgitation is seen as a red flame towards the right ventricle in systole when viewed parasternal short-axis view.

Each colour has multiple shades and brighter shades are indicative of higher velocities within the Nyquist limit. If flow velocity is higher than the Nyquist limit, colour aliasing occurs which is depicted as colour reversal. Reducing the colour sector width (number of scan lines) and the depth of sampling result in increased temporal resolution of the colour flow. The degree of turbulence is characterized by the presence of variance, which is measured as the difference between the mean and individual flow velocities, and it is shown as green colour. Colour Doppler flow imaging modality visualizes jets and their direction, allowing fast detection of valvular regurgitation or intracardiac shunting with a spatial display in a two-dimensional plane. Additionally, it has an important role to calculate regurgitant volumes using the proximal isovelocity surface area (PISA) method. By combining the colour display of jets obtained using colour Doppler flow imaging and the high temporal resolution of M-mode echocardiography, we have a sensitive echocardiographic modality which allows to relate the valve motion to flow characteristics and assess the timing and duration of regurgitant jets (Figure-7). Furthermore, M-mode colour Doppler echocardiography has been utilized in assessing left ventricular filling dynamics (flow propagation velocity).


Figure-7. Colour M-mode of the mitral flow from the apical four chamber view during 2:1 atrioventricular block revealed retrograde flow into the left atrium after the blocked P-wave, which indicates holodiastolic mitral regurgitation (DMR).




References

  1. J Schwippel, Christian Doppler and the Royal Bohemian Society of Sciences. The Phenomenon of Doppler. Prague: 1992. pp 46–54.
  2. Holen J, Aaslid R, Landmark K, et al. Determination of pressure gradient in mitral stenosis with a non-invasive ultrasound Doppler technique. Acta Med Scand. 1976; 199:455-460.
  3. Hatle L, Brubakk A, Tromsdal A, et al. Noninvasive assessment of pressure drop in mitral stenosis by Doppler ultrasound. Br Heart J. 1978; 40:131-140.
  4. Yoshida T, Mori M, Nimura Y, Hikita G, Takagishi S, Nakanishi K, Satomura S. Analysis of heart motion with ultrasonic Doppler method and its clinical application. Am Heart J 1961; 61:61-75.
  5. Isaaz K, Thompson A, Ethevenot G, et al. Doppler echocardiographic measurement of low velocity motion of the left ventricular posterior wall. Am J Cardiol. 1989; 64:66-75.
  6. McDicken WN, Sutherland GR, Moran CM, et al. Colour Doppler velocity imaging of the myocardium. Ultrasound Med Biol. 1992; 18:651-654.
  7. Coman IM. Christian Andreas Doppler--the man and his legacy. Eur J Echocardiogr. 2005; 6:7-10.
  8. Nishimura RA, Tajik AJ. Quantitative hemodynamics by Doppler echocardiography: a noninvasive alternative to cardiac catheterization. Prog Cardiovasc Dis. 1994; 36:309-342.
  9. Anavekar NS, Oh JK. Doppler echocardiography: a contemporary review. J Cardiol. 2009; 54:347-358.
  10. Quiñones MA, Otto CM, Stoddard M, et al. Recommendations for quantification of Doppler echocardiography: a report from the Doppler Quantification Task Force of the Nomenclature and Standards Committee of the American Society of Echocardiography. J Am Soc Echocardiogr. 2002; 15:167-184.
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