doppler ultrasonic technique

8/14/2019 Doppler Ultrasonic Technique

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MEDICAL ENGNEERING SYSTMS

Doppler ultrasonic technique

Doppler ultrasound technique, was originally applied in the medical fieldand dates back more then 30 years. The use of pulsed emissions hasextended this technique to other fields and has open the way to newmeasuring techniques in fluid dynamics. The term "Doppler ultrasoundvelocimetry" implies that the velocity is measured by finding theDoppler frequency in the received signal, as it is the case in LaserDoppler velocimetry. In fact, in ultrasonic pulsed Doppler velocimetry,this is never the case. Velocities are derived from shifts in positionsbetween pulses, and the Doppler effect plays a minor role.Unfortunately, many publications, even recent ones, fails to make thedistinction, resulting in erroneous system description and fallacious

interpretation of the influence from various physical effects.

Functioning principles of pulsed Doppler ultrasound

In pulsed Doppler ultrasound, instead of emitting continuous ultrasonicwaves, an emitter sends periodically a short ultrasonic burst and areceiver collects continuously echoes issues from targets that may bepresent in the path of the ultrasonic beam. By sampling the incomingechoes at the same time relative to the emission of the bursts, the shiftof positions of scatterers are measured. Let assume a situation, asillustrated in the figure below, where only one particle is present along

the ultrasonic beam.

From the knowledge of the time delay Td between an emitted burst andthe echo issue from the particle, the depth p of this particle couldcomputed by:


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where c is the sound velocity of the ultrasonic wave in the liquid.If theparticle is moving at an angle q regarding the axis of the ultrasonicbeam, its velocity could be measured by computing the variation of itsdepth between two emissions separated in time by Tprf:

The time difference (T2-T1) is always very short, most of the time lowerthan a microsecond. It is advantageous to replace this timemeasurement by a measurement of the phase shift of the received echo.

where fe is the emitting frequency. With this information the velocity ofthe target is expressed by:

This last equation gives the same result as the Doppler equation. Butone should always be aware that the phenomena involved are not thesame. assume that the particles are randomly distributed inside theultrasonic beam. The echoes issue from each particle are thencombined together in a random fashion, giving a random echo signal.Hopefully, a high degree of correlation exists between differentemissions. This high correlation degree is put in advance in all digitalprocessing techniques used in Signal Processing's Ultrasonic Dopplervelocimeter to extract information, such as the velocity.

Doppler EffectINTODUCTION:

B-mode imaging is based on the reflection and scatter of

ultrasound at interfaces and intrinsic organic structures. Theinformation carriers that make Doppler sonography possible are the

red blood cells (erythrocytes) inside the vessels, which move towards

the transducer or away from it at various speed. The Doppler effect

is named after the physicist Christian Johann Doppler (1803 1853).

Doppler physically interpreted and mathematically expressed the

fact that the light of stars moving towards the earth undergoes a shift

towards blue (shorter wavelength), and that the light of stars moving

away from the earth undergoes a shift towards red (longer

wavelength).


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In a similar way, the sound waves generated from the erythrocytesand the echo signals returning to the transducer experience a slight

frequency shift f with regard to the transmit frequency f. The

frequency shift f depends on the magnitude and direction of the

blood flow velocity v. The scatter echoes from within the vessels are

weaker than the signals obtained from the interfaces of vessels,

organs, and tissues, by a factor of 100 to 1000. For their detection

and processing a very sensitive system technique is needed.

The Doppler equation (forSpectral Dopplerand Color Doppler)describes the relation between f and v:

f = 2 f/c v cos

where c is the velocity of sound (at an average of 1540 m/s in tissue), v

the blood flow velocity to be analyzed and the angle of incidence in

relation to the axis of the vessel. The factor 2 takes into account that

the Doppler effect is observed twice: once when the moving blood


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cells receive the transmit signal from the probe, and the second time,

when the probe receives the echo from the blood cells.

The frequency shift f measured by Doppler techniques in the

following also referred to asDoppler frequency is a direct measurefor v. For a given magnitude of v, the frequency shift f will be

higher with the selection of a higher transmit frequency f.

f also depends on the angle of incidence: f is at its highest when the

incident sound beam is directed parallel to the vessel axis. At

perpendicular incidence, cos = 0, i.e., no Doppler signal is obtained.

To calculate the velocity v from the Doppler frequency f, the angle

must be measured in the B-mode or Color Doppler image and an

angle correction must be made.

The Doppler effect increases or reduces the echo signal frequency f

coming from the vessel by f, depending on the direction of blood

flow. That means that the echo signal frequency also contains the

information on the direction of flow (bi-directional Doppler). For the

evaluation of echo signals, the flow velocities towards the transducer

are usually displayed on the positive axis in the Spectral Doppler

curve (encoded red when Color Doppler is used). They are displayed

on the negative axis and encoded blue in Color Doppler, when theflow is directed away from the probe.

The Doppler frequencies f measured within the frequency range of

2 10 MHz and at physiological flow velocities of several mm/s up to

1 2 m/s, are in the audible range between 50 Hz and 16 kHz and are

thus directly accessible to the ear as audio signals.

Advantages and limitations

The main advantage of pulsed Doppler ultrasound is its capability tooffer spatial information associated to velocity values. Unfortunately, asthe information is available only periodically, this technique suffers fromthe Nyquist theorem. This means that a maximum velocity exists foreach pulse repetition frequency (Prf):


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In addition to the velocity limitation, there is a limitation in depth. Theultrasonic burst travels in the liquid at a velocity which depends on thephysical properties of the liquid. The pulse repetition frequency givesthe maximum time allowed to the burst to travel to the particle and backto the transducer. This gives a maximum depth of:

From the above two equations, we could see that increasing the timebetween pulses (TPRF) will increase the maximum measurable depth,but will also reduce the maximum velocity which can be measured. Themaximum velocity and maximum depth are thus related according to thefollowing equation:


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Ultrasound scattering

The ultrasonic waves generated by the transducer are more or lessconfined in a narrow cone. As they travel in this cone they may bereflected or scattered when they touch a particle having a different

acoustic impedance. The acoustic impedance is defined by:

where is the density and c the sound velocity.

If the size of the particle is bigger than the wave length, the ultrasonicwaves are reflected and refracted by the particle. In such a case thedirection of propagation and the intensity of the ultrasonic waves areaffected. But if the size of the particle is much smaller than the wavelength an other phenomena appears, which is named scattering. In sucha case, a very small amount of the ultrasonic energy is reflected in alldirection. The intensity and the direction of propagation of the incomingwaves are practically not affected by the scattering phenomena.Ultrasonic Doppler velocimetry needs therefore particles smaller thanthe wave length.


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Doppler Waveforms and Vascular Resistance

The velocity vs. time display of the Doppler spectrum or the velocity

curves deduced from it yield information on the differences and

changes of peripheral vascular resistance. At a constant blood

pressure P, conclusions may be drawn on the perfusion (indirect

method) from the relation between volume flow Q and vascular

resistance R (see figure 2006).

The waveform of a low resistance vesselis marked by a higher end-

diastolic flow velocity and low pulsatility. Pulsatility is defined as therelation between systolic and end-diastolic velocity. The lower the

end-diastolic velocity, the higher is the vascular resistance.

The waveform of a high resistance vesselshows a low to disappearing

end-diastolic velocity and a high pulsatility. The triphasic flow profile

is typical of peripheral vessels in the extremities.

From the envelope curves of the Spectral Doppler, vascular resistance

andpulsatility indices can be deduced to obtain the actual vascularresistance .


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Flow Velocity and Doppler Effect

Ultrasound imaging techniques for the detection of blood flow are

based mainly on the fact that the pulses generated by the transducerare reflected not only by motionless organ interfaces and structures

but also by the formations of red blood cells flowing in the vessels. If

it were possible to measure the spatial displacement s of this

formation within a time interval, e.g., the time 1 / PRF between two

pulses, the flow velocity could be calculated directly, but this direct

approach is not yet possible.

Therefore, ultrasound imaging makes use of theDoppler effect

(Christian Johann Doppler, 1803 1853): The frequency perceivedby an observer of light or sound traveling towards him is higher then

the perceived frequency from that same light or sound at rest. The

frequency from a source of light or sound moving away from the

observer is perceived as lower. The higher the relative velocity the

greater the difference in perceived frequencies. This frequency

difference is calledDoppler frequency shiftorDoppler frequency.

In ultrasound imaging, the transducer is both a source of sound

and an observer. If the flow is directed towards the transducer, i.e.,

the incident sound direction is opposite to the direction of flow (from

upper right to lower left on the graphic), the pressure wave generated

by the moving blood cells is compressed. Its wavelength is shorter

and consequently, its frequency is higher. If the flow is directed away

from the transducer (incedent sound direction from upper left to

lower right on the graphic), the echo sound wave is extended, i.e., its

frequency is lower.

The Doppler techniques in ultrasound imaging are basedupon the measurement and evaluation of the Doppler

frequency shift which, subsequently, makes it possible tocalculate the flow velocities that go with it

CW- and PW-Doppler

CW-Doppler (continuous wave) and PW-Doppler (pulsed wave) differ

in the way of signal acquisition, but have some similarities in signal


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processing and presentation of results. With CW-Doppler, the

piezoceramic elements of the (phased array) transducer are divided

into two groups, one of them continuously transmitting while the

other one simultaneously receives the incoming signals. With pencil

probes, the transducer element is divided into two. Due to thecontinuous operation, it is not possible to assign an echos point of

origin. On the other hand, very high flow velocities (e.g. a high-grade

valvular stenosis) can be analyzed unambiguously with CW-Doppler.

In simple Doppler units without duplex operation (i.e. without

support by B-mode imaging), CW-Doppler further simplifies the

detection of vessels supplied with blood.

PW-Doppler meets the requirement for measuring flow in user

selected areas of interest. One single group of array elements is usedboth for receiving and transmitting. They transmit sequences of

short pulses into the body, just as in B-mode imaging. After the pulse

has traveled to the selected sample site and back (travel time T), the

sample gate is opened for a short period of time, TR, to receive the

echoes. The size and depth of the sample volume in the B-mode or the

Color Doppler image can be controlled on the monitor and are

adjustable by the sonographer.

The pulse travel time T determines the shortest possible time interval

between two successive transmit pulses. Therefore thepulse repetition

frequencyPRFfor the transmit pulse cannot be set higher than 1/T

without jeopardizing the unambiguous depth assignment. Since the

applicable PRF values are also in the range of the Doppler

frequencies f, depth discrimination with the PW-Doppler is

achieved at the price of an ambiguous evaluation of higher flow

velocities, resulting in aliasingeffects. Also Color Doppler is a PW-

technique to which both the Doppler equation and the restrictions

concerning PRF are applicable.


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Direct Measurement of Volume Flow

TAV mean is equivalent to the average constant flow velocity and is the

basis for the direct, quantitative calculation of the volume flow Q:

Q = A TAVmean

where A = r2, the cross sectional area of the vessel at the samplingsite which is obtained from the vessel diameter 2 r measured in the B-

mode image. When interpreting these values with regard to the

volume flow Q, two critical sources of error must be considered:

First, the limited measuring accuracy of the vessel diameter,

especially in the case of very small vessels and second, the angle

correction error which depends on the angle of incidence.

Nota bene: TAVmax , i.e. the time averagedmaximum velocity, cannot

be utilized for the determination of the volume flow Q, since it would


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overestimate it. TAVmax is frequentlyused for the indirectevaluation

of organ perfusion.

doppler ultrasonic technique

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