Doppler Cardiology for Dummies Doppler Cardiology for Dummies A comprehensive review of Doppler echocardiography George Thomas, Cardiologist. Fellow, Indian Academy of Echocardiography. E-mail: [email protected] A review of Doppler echocardiography - for the beginner to the expert. Intended for physicians and cardiac sonologists. For educational purposes only. Fig 1. Christian Johann Doppler HISTORICAL PERSPECTIVE When the trumpets sounded, the army shouted, and at the sound of the trumpet, when the men gave a loud shout, the wall collapsed. (Read the full story here) Joshua 6:20, Holy Bible The power of sound was known since Biblical times.Doppler echocardiography is based on a physical property of sound which was first scientifically validated by Christian Johann Doppler (Fig 1).[1] Doppler was born on November 29, 1803 in Salzburg Austria to Johann and Theresa Doppler. He was groomed to get into the family stonemason business. However due to occupational pneumoconiosis he could not continue his work as a stonemason. He was a brilliant student at school.

In 1822 his mathematics professor urged him to pursue mathematics at a higher level. So, Doppler studied mathematics at the Polytechnic Institute in Vienna. After two and a half years at the school, Doppler decided that he did not like the education system there and he continued to privately study mathematics with a tutor. At the age of 21, after finishing his secondary education, Doppler worked as a mathematics tutor and began writing scientific papers. Doppler died of lung disease on 17 March 1853 at the age of 50, in Venice, Italy. During Doppler’s lifetime, it was well known that the pitch of a sound would vary if the object was moving relative to a listener. It was observed in train horns that the sound would increase in pitch as it approached and decrease as it went away. Doppler’s genius was in explaining the phenomenon scientifically. In order to measure this effect, Doppler performed a strange experiment. He hired a group of trumpeters to play from a moving train car. He then had musicians with nearly perfect pitch recognition listen to the trumpets as the train travelled towards and away from them.

The changes in pitch were noted for the different conditions, and this experiment paved the way for the physics of what is now known as the ‘Doppler Effect’. Although the Doppler effect was originally observed for sound, it eventually was found to hold true for light and all forms of electromagnetic radiation as well. In 1842 he presented his paper "On the Coloured Light of Double Stars and Certain Other Stars of the Heavens," illustrating the Doppler effect in astronomical studies. He explained that the perceived change of frequency in light and sound waves was due to the relative motion of the source and the observer. His ideas helped pave the way for the idea that the universe is expanding, and made it possible to follow weather patterns by tracking electromagnetic radio waves. The medical use of Doppler effect came about in the 1950’s almost along with the medical use of ultrasound. In the mid 50‘s several Japanese investigators such as Satomura, Yoshida, and Nimura at Osaka University were using Doppler technology to examine the heart.

They began publishing their work in the mid 1950’s.[2] In those days the Doppler recordings were thought to come from the heart tissues and no signals were attributed to blood flow. Consequently the Doppler technique did not interest the cardiologists then! In December 1955, Satomura published his first paper on the subject entitled "A new method of the mechanical vibration measurement and its application". In this paper he demonstrated that Doppler signals can be retrieved from the heart when insonated with 3 MHz ultrasonic waves. Together with Ziro Kaneko, they constructed the Doppler flow meter to measure the velocities in blood vessels. Lindstrom and Edler in 1969 demonstrated the use of continuous wave Doppler. Later in the same year Baker and Peronneaux introduced the pulse wave Doppler. Marco Brandestini is credited for the introduction of colour Doppler in 1981. A major development in Doppler came when Holen and Hatle demonstrated that one could derive hemodynamic information from Doppler ultrasound. They noted that one could use a modified version of the Bernoulli equation to detect gradients across stenotic valves.

The method of measurement of the pressure gradient of aortic stenosis using the Doppler principle was the first clinical application that probably established Doppler echocardiography as a clinically important technique. Isaaz and group introduced the concept of tissue Doppler in 1989. Thomas postulated the concept of low velocity flow Doppler in 2004. Fig-2. The Doppler Principle. In the top panel note a stationary police car emitting a siren sound. There is no frequency change here. In the middle panel the same car is in motion. The frequency increases in the direction of motion. The situation in the lower panel is akin to medical Doppler. A speed detection radar sends a beam towards a moving vehicle. A vehicle coming in the direction of the radar reflects the wave at a higher frequency, while a vehicle going away reflects at a lower frequency. THE DOPPLER PRINCIPLE [3] Doppler effect is the apparent difference between the frequency at which an energy wave leaves a source and at which they reach an observer, caused by relative motion of the observer and/or the wave source.

This phenomenon is used in astronomical measurements, in Mössbauer effect studies, in radar, modern navigation, Leslie rotating speaker systems and medicine. If an ultrasonic wave is reflected off a moving object, the frequency of the resulting wave will be changed. More specifically, if an object is moving toward the source, the frequency of the reflected wave will be increased; and if the object is moving away from the source, the frequency of the reflected wave will be decreased (Fig 2). The amount of the frequency shift can be used to determine the velocity of the moving object. Different energies can be used for the purpose. In the classic case of the whistling train, sound Doppler shift is observed. In radar, electromagnetic waves are used. In sonar, ultrasound is used. Important applications are burglar alarms, speed detector radars and the ultrasonic flow meter. This last application has found use in medicine – the present topic of discussion. In lighter vein: A physicist was once caught for crossing a red (lower frequency of light waves) traffic light. He used his genius and tried to fool the traffic policeman.

He said that the signal appeared green (higher frequency) due to the Doppler shift when he was moving towards the signal and so he should not be fined. The smart policeman thought for a moment. With the basic physics knowledge he learnt at school he realized that the speed of the car should be approaching the speed of light for it to happen. He fined him for over speeding! Fig-3. Features of a wave DOPPLER IN CARDIOLOGY [4,5] Doppler is used to study blood flow. Doppler systems measure the characteristics of disturbed flow: direction, turbulence and velocity. This enables examiners to differentiate between normal and abnormal flow patterns and to quantify those characteristics. These are helpful in determining the severity of abnormal hemodynamics.[6] Doppler echocardiography provides an accurate assessment of the severity of many cardiac disorders and has therefore assumed an integral role in the clinical evaluation of cardiac patients. There are excellent guidelines to properly record and quantify Doppler studies.[7] According to the Doppler principle moving blood particles alter the frequency of reflected ultrasound.

The magnitude of this Doppler shift relates to the velocity of the blood particles, whereas the polarity of the shift reflects the direction of blood flow toward (positive) or away (negative) from the transducer. The Doppler equation states that the Doppler shift (F) is directly proportional to the velocity blood particles (v), the transducer frequency (f), and the cosine of the angle of incidence (θ) and is inversely proportional to the velocity of sound in tissue (c). The Doppler equation can be derived for blood flow velocity (see Box). When solving the Doppler equation, an angle of incidence of 0 degrees (cosine = 1.0) is assumed for cardiac applications.

BOX Let the velocity of sound be = c Let the velocity of sound emitting moving object be= v Let the frequency of sound = f Let the observed frequency = F So observed wavelength= c/F The wavelength of sound would be= c/f The distance travelled by the object in this period=v/f Distance between waves= c/f – v/f = c/F Or, c/F = (c-v)/f Or F-f= fc/(c-v)-f (by arranging the terms and simplifying) Or the change in frequency Δf= fv/(c-v) Because the speed of sound (c) in blood is approximately 1560 m/s and the highest velocities (v) of interest in the heart are under 10 m/s, this v can be omitted in the final equation. Thus, Δf=fv/c meaning the change in frequency is equal to the fundamental frequency multiplied by the ratio of the velocity of the object and the speed of sound. This is true only if the observation is in line of the moving object. If it is at an angle θ the relationship is related to the cosine of the angle.

Thus, Δf=cosθfv/c.(Fig-4) In the case of medical applications, the moving object (blood particles) itself does not emit sound. It reflects the sound emitted by the transducer. Thus the effect occurs twice – once when received by the blood particles and second after reflection. This will result in adding a factor of 2 to the equation. Thus Δf=2cosθfv/c. Thus the Doppler signal is dependent on: (1) Blood velocity: as velocity increases, so does the Doppler frequency. (2) Ultrasound frequency: higher ultrasound frequencies give increased Doppler frequency. But, lower ultrasound frequencies have better penetration. (3) The choice of frequency is a compromise between better sensitivity to flow or better penetration. (4) The angle of insonation: the Doppler velocity estimation is most accurate when the Doppler ultrasound beam is aligned (Cos00 or Cos1800=1) to the flow direction. This is of the utmost importance in the use of Doppler ultrasound. Fig-4. Cosine correction. If the Doppler velocity measurement v is done at an angle q, then the actual velocity would be vcosq Fig-5. Laminar and turbulent flows.

In laminar flow the fluid moves in concentric circles with maximum velocity at the center. In turbulent flow the fluid moves in a disorganized manner with eddies and vortices. Apart from flow velocity, another aspect is the detection of abnormal flows or turbulence (Fig-5). The normal flow in a smooth tubing is laminar. Pressure differences can occur any where along the path of blood flow. Interaction of blood with higher velocity and lower pressure with blood of lower velocity and higher pressure produces turbulence. The critical number at which turbulence will occur is the called the Reynold’s number. As blood velocity increases, from an increase in either ejection force or some obstruction, the critical Reynold's number is reached and turbulence occurs. This turbulence may be relatively short in length or may extend considerably if the obstruction is severe. Turbulence generates sound waves (murmurs and bruits) that can be heard with a stethoscope. Because higher velocities enhance turbulence, audible sounds resulting from turbulence become louder whenever blood flow is increased across the valve or vessel. Elevated cardiac outputs, even across anatomically normal valves, can cause physiological murmurs because of turbulence.

These types of turbulence may not cause significant ultrasound frequency shifts and may not be detected by Doppler at the conventional frequencies. Such a phenomenon explains the paradox of murmur without Doppler abnormalities. The relation of the degree of obstruction and the rate of flow of the fluid is given by the Poiseuille's Law. It states that the rate of flow is proportional to the fourth power of the radius of the tube. BOX Reynolds Number The Reynolds number (Re) predicts the onset of turbulence and is by given by the equation: Re= (VxDxρ)/η where V=velocity, D=diameter, ρ=density of blood and η=viscosity of blood. The Reynolds number is a dimensionless factor that indicates whether fluid flow will be turbulent If the Reynolds’s number > 2000 then the flow is turbulent, if < 2000 it is laminar. Poiseuille's Law The rate of flow through a pipe can be found from Poiseuille's Law. A simplified equation is flow Q∞R4 .

From this equation, we can see that the rate of flow is proportional to the fourth power of the radius, so a small decrease in the diameter of a tube will result in a very large decrease in the flow rate. Osborne Reynolds Osborne Reynolds (1842 - 1912) was born in Belfast. His father was the Rev. Osborne Reynolds. Reynolds had great mathematical ability and a deep insight into the physical fundamentals. His researches led to the publication of many papers of outstanding interest. His works covered turbulent flow, hydraulic modelling, hydrodynamic lubrication, friction, heat transfer, and many other topics. He demonstrated the famous Reynolds effect by injecting a thin trace of ink into water flowing along a glass pipe in a tank; by varying the diameter of the pipe and the velocity of the water in the tube, Reynolds developed a relationship between these quantities and the viscosity which changes the laminar to turbulent flow. His later works established the equations which govern turbulence and which are still used as the basis of the modern computerised analysis known as computational fluid mechanics. Jean Poiseuille Jean Poiseuille (1797-1869) was born in Paris and studied at the Ecole Polytechnique.

He studied the flow of liquid through tubes, and found that rate of flow depended on the diameter and length of the tube and pressure difference between the ends. He formulated an equation known as Poiseuille's law describing the relationship. The unit of viscosity (resistance to flow) is named the ‘poise’ in his honour. Poiseuille improved on earlier measurements of blood pressure by using a mercury manometer and filling the connection to the artery with potassium carbonate to prevent coagulation. He used this instrument, known as a hemodynamometer, to show that blood pressure rises during expiration (breathing out) and falls during inspiration (breathing in). Currently, Doppler echocardiography consists of 4 modalities: continuous wave Doppler, pulsed wave Doppler, colour Doppler imaging and power Doppler. Continuous wave and pulse wave together can be called spectral Doppler. Current ultrasound systems can also apply the Doppler principle to assess velocity within cardiac tissue. The moving target in this case is tissue, such as myocardium, that has higher amplitude of backscatter ultrasound and a lower velocity compared with red blood cells.

This new application is under investigation.[8] BOX PROPERTIES OF A GOOD SONIC REFLECTOR Strong Doppler shifted signals are required for reliable flow measurement. The amplitude of the Doppler shifted signals is largely related to the suitability of the sonic scatterers in the flow. In the case of blood the sonic scatterers are blood cells and colloidal molecules. Of late artificially introduced contrast agents are used to enhance Doppler signals.[9] The properties of a good reflector are: a)The scattering material must have an acoustic impedance* different from the fluid. b)There must be some particles large enough to cause longitudinal scattering. c)For a given tube size, the longitudinal scattering must have sufficient energy to overcome the Rayleigh (energy wasting) scattering caused by smaller particles. d)The scattering material must travel at the same velocity as the fluid for good accuracy. * The acoustic impedance (Z) of a material is defined as the product of density (p) and acoustic velocity (V) of that material or Z = pV Fig-6. Features of Doppler spectral display. Note the spectral broadening the second tracing with the window being filled with ‘noise’.

DOPPLER INSTRUMENTATION An oscillator circuit delivering a variable voltage to the piezoelectric ceramic crystals of the transducer produces the ultrasound energy. The reflected Doppler ultrasound is passed through the quadrature detector and high-pass filtering. The quadrature detector resolves the frequency shift between the transmitted and received frequencies and thus determines the direction. In pulse wave Doppler, pulsing is achieved by an electronic transmission gate. Besides it is passed through a low-pass filter (determining the highest frequency without aliasing) and the sample and hold unit. High-pass filtering is required to remove high amplitude but low frequency artefacts arising from tissues and movement of the probe (if hand-held). Such a procedure will unavoidably lose low frequency Doppler signals from slowly moving blood, which may be of clinical significance. Next, the demodulated and filtered Doppler frequency shift signals are digitized in the analogue to digital converter. The continuous analogue Doppler signal is thus converted into a series of discrete digital signals. These are sent through the ‘FFT analyser’. This part of a Doppler ultrasound instrument analyses the spectrum of Doppler frequency shifts using the mathematical method of fast Fourier transform (FFT).

The analyser transforms the Doppler signals into a time velocity spectral display, showing how the full spectrum of blood-flow velocities varies with time. The FFT analyser resolves the composite, multifrequency Doppler signal into its component frequencies, transforming the signal from an amplitude versus time (time domain) format into an amplitude versus frequency (frequency domain) format. Thus finally the continuous spectrum of the original analogue Doppler signal is divided into a certain number of frequency intervals. The higher the frequency interval, the better the resolution of the analyser. The display of the spectral wave form is as follows: X-axis = time; Y-axis = estimated velocity blood flow with direction relative to baseline (flow toward - above (+) and flow away - below (-)); the ‘Z’-axis = brightness of screen pixels is proportional to amplitude of returning reflections from blood cells. If the returning signal is stronger the amplitude or brightness of the displayed signal will be higher. The spectral display consists of an envelope and a window (Fig-6). When there is turbulent flow the window area gets filled – a phenomenon known as spectral broadening.

The filtered Doppler signal, which normally is in the audible frequency range is fed into (stereo) speakers or headphones so that directional effect may be appreciated through sound outputs from the respective speakers. In the case of colour Doppler an additional step of autocorrelation is involved. Jean Baptiste Joseph Fourier Fourier transform is named after Joseph Fourier (1768-1830). Fourier was born in France. He was the son of a tailor, and was educated by the Catholic order of the Benedictines. The commissions in the military scientific corps were reserved for the elite, and being ineligible he took up a job as a mathematics lecturer in the army. He took a prominent part in his own district in promoting the Revolution, and was rewarded by an appointment in 1795 in the Normal school, and subsequently by a chair in the Polytechnic school. Fourier went with Napoleon on his Eastern expedition in 1798, and was made governor of Lower Egypt. He contributed several mathematical papers to the Egyptian Institute at Cairo, with a view of weakening English influence in the East. In 1787 Fourier decided to train for the priesthood and joined a Benedictine abbey.

His interest in mathematics continued, however he was unsure if he was making the right decision in training for the priesthood. He is best known for initiating the investigation of Fourier series and their application. The Fourier transform is an integral transform that re-expresses a function in terms of sinusoidal basis functions, i.e. as a sum or integral of sinusoidal functions multiplied by some coefficients ("amplitudes"). In signal processing and related fields, the Fourier transform is typically thought of as decomposing a signal into its component frequencies and their amplitudes. BOX MAJOR COMPONENTS OF A DOPPLER SYSTEM Analogue to digital converter Quadrature detector Sample and hold unit Fig-7. Continuous Wave Doppler. Here there are 2 separate crystals one for transmitting and another for receiving the signals. CONTINUOUS WAVE DOPPLER This is probably the earliest use of Doppler in clinical cardiology. In this method two ultrasound crystals are integrated in one transducer - one for transmission and another for reception (Fig-7). The two crystals are usually mounted at a slight angle to one another to ensure overlap of the outgoing (transmitted) and incoming (received) beam of ultrasound.

The region of overlap is usually several centimetres long and comprises the sensitive volume at which blood-flow velocities may be detected. Because echoes from all depths within the sensitive volume will be analysed it is impossible to separate Doppler signals from different depths. This is the main disadvantage of continuous wave Doppler as compared to pulsed Doppler ultrasound. The main advantage as compared to pulsed Doppler is much higher measurable velocities due to lack of aliasing. Relatively inexpensive stand alone Doppler ultrasound systems (Pedoff) are available which employ continuous wave probes to give Doppler output without the addition of B-mode images. BOX Very high velocities can be measured -no aliasing. Dedicated CW transducers are cheap and very sensitive. Good temporal resolution – can examine flow waveform. Allows calculations of velocity and and other indices. Allows better documentation and recognition of flow patterns. Disadvantages No spatial resolution May not be possible to detect small turbulences because of normal spectral broadening. Fig-8. Pulse Wave Doppler. Here the transducer has just one crystal which does both the transmission and reception PULSE WAVE DOPPLER Here only one crystal is used for both transmission and reception (Fig-8).

This method allows a sample volume or "gate" to be positioned on the grey-scale image. To provide a localised velocity measurement, the instrument transmits a pulse that is 6 wavelengths to 40 wavelengths long - depending on the desired length of the sample volume. The received signal is gated so that the time elapsed between the transmission of the pulse and the opening of the gate determines the depth of the velocity measurement, i.e., the position of the sample volume. Short pulses of ultrasound are transmitted with a certain frequency, the pulse repetition frequency (PRF). Between pulse transmissions, echoes are continuously returning to the transducer, but most of them are not analysed. A receiver gate opens only once between each pulse transmission to allow estimation of the Doppler frequency shift from only one predetermined range along the ultrasound beam, the sample volume. To ensure that the signals originate only from the small sample volume only small samples of signal are fed through the receiver gate once between pulse transmissions. The time delay from pulse transmission to opening of the receiver gate is regulated by the range delay, and the time period the gate is open, is regulated by the length delay. The small samples of the demodulated Doppler signal pass the receiver gate once per pulse repetition period.

A low-pass filter removes frequencies above the Nyquist limit (1/2 PRF), and a high-pass filter (wall filter) is added to remove unwanted high-amplitude, low-frequency signals. Low pulse repetition frequencies are usually employed in cardiac examinations. The transmission is at a low frequency (low pulsed repetition frequency, LPRF), such that one small area (sample volume) along the ultrasound beam is interrogated. The reflected ultra-sound is used to calculate the velocity, direction and depth. However, the maximum velocity, which can be recorded, is severely limited by the Nyquist limit. So, abnormally elevated velocities cannot be measured Pulsed Doppler transmitted at a higher frequency (high pulse repetition frequency, HPRF) offers a compromise between continuous wave and LPRF Doppler. HPRF allows measurement of velocities as high as continuous wave, but because there is more than one pulse along the beam, there is some difficulty in estimating depth. However, the multiple sample volumes are usually displayed on the monitor showing that there is more than one source of velocity measurement. A variation of this method is called the multigate pulse Doppler.

Here velocities as high as 3.5 to 5 m/sec can be measured with the additional ability to identify one of the gates as the site of origin. Pulse wave Doppler has an inherent phenomenon called aliasing. Aliasing is an erroneous frequency estimation occurring when the sampling frequency is less than twice the frequency to be measured (Fig-9). According to the Nyquist criterion the sampling frequency should be at least twice the frequency being sampled. In other words if you want to measure the frequency of a repetitive event by sampling the event, then you have to sample the event at a frequency at least twice the frequency of the event itself. In pulse wave Doppler, the pulse repetition frequency PRF (the sampling frequency), must be at least twice the maximum Doppler frequency shift to be measured. Thus the maximum measurable frequency is equal to half the sampling frequency. This is the so-called Nyquist limit. The Nyquist Limit is the threshold that determines the maximum detectable frequency shift for pulsed wave Doppler instruments, including colour flow. This limit occurs because pulsed wave instruments "sample" and therefore do not record "everything" that occurs. The Doppler signal will "alias" when the Nyquist Limit is exceeded.

Nyquist Limit (maximum frequency shift) = PRF / 2 . Aliasing may be seen as frequency wrap around in pulsed Doppler spectral displays (Fig-10) or as mosaic in colour Doppler. Aliasing may be a problem to measure velocities accurately. But it is also a useful phenomenon as it makes it easy to qualitatively detect high velocities at the aliasing frequency. Similarly, aliasing is a property used in the PISA method of flow quantification. Spectral Doppler (continuous wave and pulse wave) waveforms can also be used for qualitative analysis by way of pattern recognition. This qualitative analysis of the flow waveform morphology can be useful in conditions like hypertrophic obstructive cardiomyopathy where there is a dynamic left ventricular outflow obstruction. The classical ‘sabre’ shaped left ventricular outflow Doppler waveform of hypertrophic obstructive cardiomyopathy is diagnostic. Similarly the transmitral Doppler patterns can be used for diagnostic and prognostic purposes (see below). These observations are independent of the beam/flow angle as no velocity measurements are made. Harry Nyquist The Nyquist limit is named after Harry Nyquist (1889-1976), a Swedish - American physicist.

Harry was born to Lars Jonsson and Katrina in Sweden. His father thought that the name Jonsson was too common resulting in mail delivery problems. So he changed his name to a difficult sounding/spelling Nyquist. Although he was born into a poor shoemaker family, Harry showed great promise as a mathematician. After migrating to the USA, he published the landmark paper "Certain topics in Telegraph Transmission Theory," in 1928. This paper described the criteria for what we know today as sampled data systems. The Nyquist theorem stated that for periodic functions, if you sampled at a rate that was at least twice as the frequency of the signal of interest, then no information (data) would be lost upon reconstruction. Nyquist is also credited for pioneering the “information theory” of digital transmission, which is the basis for the information technology revolution and the invention of the fax machine. BOX Can determine the region of flow disturbance. Detailed analysis of distribution of flow possible. Good temporal resolution – can examine flow waveform. Allows calculation of the angle of the Doppler beam. Superior ability to distinguish laminar and turbulent flow. Allows calculations of velocity and and other indices. Allows better documentation and recognition of flow patterns. Disadvantages May be difficult to position sample volume.

Limited by the PRF – difficult to measure high velocities due to aliasing. Fig-9. Aliasing. The upper panel shows how a wave (top) will appear (bottom) if analysed with almost the same frequency. Note the distorted shape. In the lower panel the same wave is analysed at twice the frequency. Note how the shape approaching the original. Fig-10. Aliasing. The upper tracing shows a transmitral pulse wave tracing case of mitral regurgitation. Note the aliasing signals (black arrows). The same valve interrogated with a continuous wave Doppler. Note the absence of aliasing. Also note the spectral broadening that is normal in the case of continuous wave Doppler. Fig-11. Colour Flow Doppler. This is a variety of pulse wave Doppler. Multiple points in the ‘region of interest’ are analysed and colour coded rapidly. COLOUR DOPPLER [10] This technique estimates the average velocity of flow by colour coding the information (Fig-11). The direction of blood flow is assigned the colour red or blue, usually indicating flow toward or away from the ultrasound transducer. Usually this is represented by convention as blue-away and red-towards the transducer.

This can be remembered using the mnemonic BART (Blue-away, Red-towards). The Doppler signals, which are superimposed on real time grey scale images, are colour coded to reveal the velocity (frequency shift) and direction of blood flow (phase shift). The shade and intensity of colour can correlate with the velocity of flow. Colour flow Doppler is an adaptation of HPRF. Numerous sample volumes are overlaid on a 2-D or 3-D echocardiogram and the direction of flow is recorded on the screen as either red or blue, depending on whether the flow direction was towards or away from the transducer. Some indication of the velocity is given by the brightness of the colour. Flow, which is turbulent, having no definite direction, is displayed as a third colour, e.g. green or yellow known as variance. Each calculated mean velocity is the result of a number of individual velocity samples. The range of velocities (minimum to maximum) sampled at a given interval show variation similar to the spectral width on a spectral analysis of peak velocities. The additional hue (usually green/yellow) added to the colour map indicates the degree of variance in the sampled frequency shifts (Fig-12).

To produce a 'flow image' the amplitude, phase and frequency contents of the returned echoes across an area called the ‘region of interest’ are captured and very rapidly analysed. Japanese researchers first introduced a phase detector based on an autocorrelation technique in which the changing phase of the received signal gave information about changing velocity along the ultrasonic beam. This provided a rapid means of frequency estimation to be performed in real-time. The basis of the autocorrelation detector is that the echo reflections from stationary targets have corresponding changes with time, whereas sequential echo reflections from moving targets have corresponding changes in the relative phase. The autocorrelaton detector produces an output signal that depends on the relative phases of consecutive pairs of received echo. Thus, the returning echoes themselves are their own references for phase comparison. The autocorrelation detector functions by multiplying two returning echoes. The output from the autocorrelator has constant amplitude except where consecutive waves have phase differences. In colour Doppler processors, a parallel and separate process of velocity and velocity variance are made. The value of the velocity variance can be considered to be a measure of the width of the Doppler frequency spectrum, which increases with the degree of flow disturbance.

The final processor in the circuitry, the colour processor, assigns luminance, hue and saturation to the display, following one of the designated colour-coding schemes. These colour maps also display a scale, which indicates the colour assignment for blood flow direction and velocity. With the advent of three-dimensional echocardiography, it is possible to get a flow map in a three dimensional format (Figs-13,14). There are automatic flow quantification algorithms based on colour flow technology.[11] Limited by PRF and subject to aliasing. Records mean velocities only. Slower frame rate. No spectral information. Fig-12. Colour flow mapping in the case mitral regurgitation. Note the flow away from the transducer (blue) with some aliasing (reds) and variance (green-yellow) Fig-13. A 3D colour Doppler study from the same patient as Fig-12. The extent of the regurgitation can be better delineated in terms of volume and 3-dimensional shape. This image can be rotated in any direction and can also be cut at any level. The myocardial image has been suppressed to facilitate the evaluation of the flow. Fig-14.

3D Doppler study of a case of severe MR. The image has been cropped from a full volume rendering without myocardial image supression. Fig-15. Power Doppler study of the left ventricle. Note the cavity being filled thus facilitating the detection of intracardiac masses. POWER DOPPLER In this modality the amplitude, or power, of Doppler signals rather than the frequency shift are displayed (Fig-15). This allows detection of a larger range of Doppler shifts and thus better visualization of small vessels and slow flows, but at the expense of directional and velocity information. Power Doppler is also referred to as energy Doppler, amplitude Doppler or Doppler angiography. The magnitude of the Doppler output is displayed rather than the Doppler frequency signal. Power Doppler does not display flow direction or different velocities. It is often used in conjunction with frame averaging to increase sensitivity to low flows and velocities. Hybrid colour flow modes incorporating power and velocity data are also available from some manufacturers. These can also have improved sensitivity to low flow. While standard colour Doppler is generally based on a mean frequency shift, power Doppler displays the total integrated Doppler power in colour.

In fact in power Doppler the hue and the brightness of the colour signal represent the total energy of the Doppler signal. Conventional colour Doppler is based on the mean Doppler frequency shift and therefore related to the directional component of the velocity of the blood. Thus, it is affected by inherent limitations like Doppler angle dependence and aliasing. Power Doppler output is calculated on the base of the integrated power Doppler spectrum. The hue and the brightness represent the power in the Doppler signal, which is relate to the number of blood cells. In the power Doppler mode the colour map indicates the colour assignment for blood cell amplitude. Power Doppler noise gets assigned to a homogeneous background (usually dark - blue), even when the gain is increased greatly over the level at which conventional colour Doppler image is obscured. Power Doppler image is unaffected by aliasing because the integral of the power spectrum is the same whether the signal wraps around or not. The major disadvantage is that power Doppler does not allow the detection of direction and velocity of blood flow. Power Doppler is used mainly in vascular studies and is used to “fill” cavities (eg left ventricle) to delineate masses (eg thrombus). BOX Fig-16.

Tissue Doppler showing both tissue Doppler Imaging and pulse tissue Doppler waveforms TISSUE DOPPLER Tissue Doppler is a by-product of colour flow technology. In colour flow, tissue signals are suppressed and flow signals are analyzed. The reverse is true in tissue Doppler.[8] Doppler velocities associated with tissue motion are slower than blood flow. Flow signals are eliminated on the basis of signal amplitude. The amplitude of tissue motion is about 40 db greater than the corresponding flow amplitude. Blood flow imaging applies a high pass filter to exclude the strong but low frequency tissue signals before the signal is input into an autocorrelator that estimates velocity. Erroneous filter settings could cause the autocorrelator to include components of tissue signals so that tissue velocities become encoded. This principle has been legitimised to colour code tissue motion and we get an ‘image’ which is entirely Doppler information. Tissue Doppler includes both pulsed tissue Doppler and colour tissue Doppler (also known as Doppler tissue imaging or tissue velocity imaging). Tissue Doppler echocardiography is further explained here A comparison of flow and tissue Doppler is given below: Flow Doppler Overall utility great ?Utility Fig -17.

Color LVFD ('tissue' Doppler) from apical 4-chamber view. Note the velocity scale showing a maximum velocity of 5.6 cm/sec. Observe the lower velocities collecting towards the apex with some aliasing. This can be used to identify low flow thrombogenic states. LOW VELOCITY FLOW DOPPLER This is an application of tissue Doppler (Fig 17). Here the low velocity flow signals are studied using tissue Doppler settings. For further details check this article . DOPPLER VELOCITY DETERMINATION To estimate the clinically relevant Doppler velocity the following steps are required: 1. You must have prior knowledge of the line of motion of the object. Only if you know this ‘direction’, you can apply the interrogating signal along the path of motion. This is because of the directional bias of Doppler. 2. Next you will know the direction of motion – whether the object is moving towards the interrogating signal or away. 3. Only after the first two steps you can measure the clinically significant peak velocity. Thus the primary step is to know the line of motion. For example we know for sure that the blood moves from left atrium to left ventricle.

At the mitral valve this is a free linear motion towards the apex. That is why we place the sample volume at the mitral valve from the apical views. That is also why we do not measure the mitral flow velocity from the parasternal views (see figure above) . Next we come to learn whether the blood is flowing towards or away from the transducer. After all these steps it is possible to measure the clinically significant peak velocity. BOX ERRORS IN DOPPLER VELOCITY MEASUREMENTS Theoretically once the Doppler beam is aligned to the direction of flow, reliable velocities can be estimated using the Doppler methods. However in spite of these precautions technical errors can occur.[12,13] 1. Errors can occur in the formation of the Doppler beam due to element damage. On the reception side, the erroneous filter settings may eliminate/create some signals. 2. Errors can arise in the measurement due to eccentricity of flow. The flow may not be in the anticipated direction in some pathological states. 3. Errors can arise in the calculation packages provided by the manufacturers for analysis of the Doppler spectrum (for instance, velocity time integral).

This should be always kept in mind where the calculated result does not match the clinical situation. INFORMATIONS DERIVED FROM DOPPLER Based on the above discussion it is clear that the following information can be derived from Doppler: 1. Is there motion? Does the object move? This is a random application of Doppler. It will not be possible to determine the accurate velocity of the object. This is what is done in power Doppler. 2. What is the direction of motion? Is it moving towards or away from the interrogating signal? 3. To measure the clinically significant peak velocity we must have a clear-cut line of motion. Application of Doppler along this line enables us to measure the velocity. In cardiology, Doppler is primarily used to study the direction of motion and it is complimentary to ultrasound imaging. This can be explained by an example. Suppose you have a thickened valve on imaging, even without Doppler you know it is stenosed. The Doppler information could then, in ideal circumstances, provide an extra parameter of the severity of the lesion. On the other hand, if you have a ‘normal’ looking valve you can never know if it is incompetent.

Here Doppler information could provide enormous information if the flow direction is abnormal. Thus Doppler provides substantial information if used judiciously. The Doppler methods use mathematical formulae to indirectly study motion that cannot be directly measured. Examples are movements of stellar bodies and in the present context movements of blood cells. We use the indirect method based on Doppler principle because we cannot ‘image’ blood cells by imaging. When the imaging of blood cells become possible, Doppler studies would probably be relegated to the background. CLINICAL APPLICATIONS Doppler methods are useful to derive hemodynamic information non-invasively[14]. They can be used for measuring intracardiac pressures, quantifying valve stenosis or regurgitation, [15,16] evaluating shunts and chamber properties. It is also useful in evaluating prosthetic valves.[17 ] Tenuous Doppler catheters are available to study intra coronary flows. [18] Fig-18. The Continuity Equation.

The flow across a narrowed orifice A2 can be calculated by the relation V1A1=V2A2 PRESSURE GRADIENTS AND STENOTIC LESIONS Once the velocity of blood flow is determined, this information can be used to determine pressure gradients an orifice using the Bernoulli equation. The original Bernoulli equation contains multiple variables like convective acceleration and viscous friction. A simplified form the Bernoulli equation states that the pressure gradient across an orifice = 4v2, where v= the peak velocity of flow through the orifice. The Bernoulli formula is adequate in most clinical situations.[19,20] However it may not be accurate if the proximal velocity is greater than 1.5 m/s, in the presence of 2 stenotic areas in the same path and with long stenotic lesions. With the currently available software it is possible to measure the peak, mean and the velocity time integral. The area of a stenotic orifice can be calculated by the continuity equation (Fig-18).

In the case of mitral valve pressure half-time (PHT) is another method of determining valve area.[21] Pressure half-time represents the time that the maximal pressure gradient takes to decrease by one half. In terms of velocity, this time is equivalent to the time that the peak velocity drops by 30%. Studies have established an inverse relation between PHT and mitral valve area (MVA) and from this relation the following empirical equation is derived MVA = 220/PHT. There are built in software for calculating the ‘valve area' by PHT (Fig-19). While reporting the ‘area’ of a valve by Doppler methods it is better to say ‘effective orifice size’ rather than ‘valve area’ which should be reserved for planimetric measurements. This is because all estimates using Doppler are subject to hemodynamic variables.[22 ] Daniel Bernoulli Daniel Bernoulli was born in the year 1700 in the Netherlands into a family of illustrious mathematicians. His father Johann, a famous mathematician, was determined that Daniel should become a businessman. However Daniel was totally against this. His father relented but certainly did not let Daniel study mathematics.

That was because there was no money in mathematics and so he sent Daniel to Basel University to study medicine. He completed his doctorate in medicine in 1720. Nevertheless, Johann taught Daniel some mathematics, which he applied in medicine. His doctoral thesis was on the mechanics of breathing where he applied mathematical physics to medicine. His medical work on the flow of blood and blood pressure also gave him an interest in fluid flow. Daniel made several mathematical theories. One important work, which Daniel produced, was one on probability and political economy. Daniel deduced that the moral value of the increase in a person's wealth is inversely proportional to the amount of that wealth. He then assigns probabilities to the various means that a person has to make money and deduces an increase in moral expectation. However the equation for which he is famous was published in 1738. This important work was his work on hydrodynamics. Even the term itself is based on the title of the work which he produced called Hydrodynamica. This work contains for the first time the correct analysis of water flowing from a hole in a container. This was based on the principle of conservation of energy, which he had studied with his father.

Daniel became famous and he shared the Grand prize of the Paris Academy with his father. His father was furious to think that his son had been rated as his equal and this resulted in a breakdown in relationships between the two. The outcome was that Daniel was banned from his father's house! BOX HEMODYNAMIC FORMULAE DERIVATIONS The Bernoulli Equation The Bernoulli Equation can be considered to be a derivation of the first Law of Thermodynamics for flowing fluids. Simply put, the law states that Energy cannot be created or destroyed. The "Bernoulli effect" is the lowering of fluid pressure in regions where the flow velocity is increased. In the high velocity flow through a constriction, kinetic energy must increase at the expense of pressure energy. The Bernoulli's equation relates the pressure, velocity, and height of a fluid at one point to the same parameters at a second point. The equation explains such things as how airplanes fly, and how cricket balls curve The first Law of Thermodynamics is often expressed as: Potential Energy+ Kinetic Energy=Constant. In the case of fluids Bernoulli's equation is usually stated as: Static Pressure + Dynamic Pressure =Constant.

Or Ps+ ½ρV2=K Or if the pressures at 2 points are P1 and P2 and the velocities V1 and V2 The pressure difference would be P1-P2=½ρV22 – ½ ρV12 (Ignoring static pressure) Therefore Pressure difference ΔP= 1/2ρ(V22-V12) Since the proximal velocity V1 is insignificant, we can omit it So the equation becomes ΔP =½ρV22 or ½ ρV2 The density of blood ρ = 1060 kg/m3, and the velocity in m/sec So, ΔP = ½ x 1060V2 = 530V2 kg/m2 Converting to mmHg by multiplying with a factor of 0.00735 makes it 3.9 or 4 (round off) So ΔP = 4V2 mmHg Continuity Equation While Bernoulli equation is the law of conservation of energy the Continuity equation is the conservation of mass.

If the area of the proximal segment is A1 and the distal segment is A2 and the velocities are V1 and V2 respectively, Then, A1V1=A2V2 Basically it means that flow in = flow out (Fig-18). Fig-19 : Pressure Half Time. Method of calculating the mitral valve area by the pressure half time method. . Fig-20. Principle of PISA (Proximal iso-velocity surface area). In this simplified diagram the first aliasing velocity v with a radius of r gives a PISA of 2pr2. This will give a flow of 2pr2v. REGURGITANT LESIONS Doppler is also used for detecting and evaluating valvular regurgitation. Many indices are available to assess the severity of regurgitation. Regurgitant volume, regurgitant fraction, and effective regurgitant orifice area are the commonly used indices. In the presence of valvular regurgitation, the flow through the affected valve is greater than through other competent valves. For example, in MR more volume will pass through the MV than through the aortic valve. The difference between the two represents the regurgitant volume.

Regurgitant fraction is derived from the regurgitant volume divided by the flow through the regurgitant valve. The calculation of regurgitant volume and regurgitant fraction can be achieved by measuring the flows through the regurgitant atrioventricular valve and competent ventriculoarterial valve. Effective regurgitant orifice area (EROA) is another index of regurgitation derived with the continuity equation: EORA = Regurgitant volume/Regurgitant VTI [23] In the case of aortic regurgitation pressure half time can also be used to quantify the lesion. Recording of aortic regurgitation jet by CW Doppler reflects the instantaneous pressure differential between the aorta and left ventricle. Thus, the rate of velocity decline is an index of severity of aortic regurgitation. Although this rate of decline may be measured as a slope, it is more commonly assessed by measuring pressure half time in a manner analogous to mitral stenosis; that is, the time taken for the peak velocity to decline by 30%.[24] The same methodology can be used for pulmonary regurgitation.[25] This flow spectrum can also be qualitatively analysed.

A steeper slope means a greater regurgitation. Colour flow Doppler imaging is ideal to detect regurgitant valve lesions.[26] The regurgitant area provides a semiquantitative idea of the severity. Trivial and mild degrees of regurgitation have thin jets that travel short distances while more severe lesions have broader jets covering larger areas. However there are several technical pitfalls in assessing the regurgitant area by colour flow. Regurgitant area should therefore be used with caution when assessing the severity of regurgitant lesions. 3 dimensional colour Doppler could provide volumetric data for the assessment of regurgitation. Analysis of the colour flow velocities within the regurgitant orifice could be more accurate than the colour jet area in evaluating severity of regurgitation.[26,27] Both the width and the area of the regurgitant jet at the valve orifice (ie, near the vena contracta) or immediately distal to the orifice relate well with other independent measurements of severity of regurgitation.

Using the flow velocity pattern proximal to the regurgitant orifice could provide a better measure of the severity of regurgitation.[28] Proximal flow acceleration occurs with the isovelocity “surfaces” assuming a hemispheric shape adjacent to the regurgitant orifice that can be visualized with colour Doppler (Fig-20). With the PISA method, flow rate is calculated as the product of the area of an isovelocity (surface of constant velocity), and the velocity. The transducer is sensitive only to velocities in the axial direction. Lowering the aliasing velocity (through baseline shifting) can produce the isovelocity surface. This is a region of distinct blue red colour reversal seen upstream from the orifice. The boundary, where colour reversal occurs, represents the contour of an isovelocity surface (surface where a single component of the velocity is constant). The velocity in this proximal isovelocity surface area (PISA) is equal to the aliasing velocity (Va). Regurgitant flow (in milliliters per second) can be derived from the PISA radius (r) as 2r2´Va.

Assuming the maximal PISA radius occurs simultaneously with the peak regurgitant flow and the peak regurgitant velocity (Vr), the EORA is derived as: EORA = (2r2´Va)/ Vr. Regurgitant volume can be estimated as EORA x VTI Other Uses RIGHT-SIDED PRESSURES The Bernoulli equation can be used to calculate a gradient between any high-pressure and low-pressure chamber. Tricuspid regurgitation is very common in pulmonary hypertension, which is demonstrated by an increase in right ventricular systolic pressure. By determining the peak velocity of a tricuspid regurgitation jet one can calculate the right ventricular to right atrial pressure gradient. Right ventricular systolic pressure by tricuspid regurgitation jet is a fairly good indicator of pulmonary arterial pressure provided there is no pulmonary stenosis. Pulmonary regurgitation indicates the instantaneous gradient between the pulmonary artery and the right ventricle. Thus, the pulmonary regurgitant velocity at end-diastole may also be used to derive the pulmonary artery diastolic pressure with the Bernoulli formula and by adding an estimate of mean right atrial pressure.

Besides the forward velocity tracings from the pulmonary valve can provide indications of pulmonary hypertension by wave-form morphology. Here the acceleration time is shortened, and a mid-systolic notch in the flow velocity envelope is often present. An inverse curvilinear relation exists between the acceleration time and mean pulmonary arterial pressure. CALCULATION OF FLOW. Doppler velocity measurement when combined with a measured area can provide data regarding actual volumetric flow. Multiplying the cross-sectional area of the flow times the velocity time integral yields the actual volume of flow during that period. In the case of left ventricular outflow tract, this value then represents the stroke volume of the left ventricle. This, in turn, can be used to calculate cardiac output. Another method is to use the colour Doppler aliasing method. The basic step here is the determination of the proximal iso-velocity surface area (PISA). This is based on the principle that Flow converging to a restrictive area will accelerate as it nears it. Because of the relatively low Nyquist limit of colour flow Doppler imaging, this results in a semicircular aliasing limit where the colour flow signal will change. Using this line the area is calculated by treating it as a hemisphere.

Because the velocity at which flow aliases is known, the velocity of flow at that point is likewise known. From this, one can then calculate the actual volume of flow as velocity times surface area. This can be further used to calculate the area of a stenosed valve. The major limitation of the use of proximal isovelocity surface area is the assumption that flow moves in a hemispherical manner. This assumption is true only for flow converging on a relatively flat surface. If flow is channeled through a funnel, corrections must be made for a surface area less than a full hemisphere. In the case of left-to-right intracardiac shunts, flow measurements can calculate the pulmonic to systemic (Qp:Qs) flow ratio. Most machines have inbuilt software to calculate these parameters. Fig-19. Various diastolic patterns ASSESSING CHAMBER PROPERTIES Mitral inflow Doppler has been used to assess the left ventricular chamber properties also known as ‘diastolic function’. Conventional flow Doppler is by far the most widely used technique in assessing diastolic function. The left ventricular diastolic properties are usually studied.

The Doppler assessment include measuring the isovolumic relaxation time, peak E and A wave velocities, calculating the E-A ratio, measuring the deceleration time (based on the downward slope of the E wave), velocity time integral, diastolic filling time, flow propagation velocity, analysis of pulmonary or hepatic veins Doppler and calculation of tau This assessment must be done in patients who are in sinus rhythm, during which there are discrete E and A wave velocities of the mitral valve inflow. In normal individuals, early velocities exceed later velocities and the E to A ratio is typically greater than 1.2. Various Doppler patterns can be recognized (Fig-19).[29] The main patterns are Stage 1 or ‘Impaired relaxation’ pattern is demonstrated by a smaller E wave, a larger A wave, and increased deceleration time; Stage 2, or ‘pseudonormalization’ pattern denoted by an apparently normal E and A wave and deceleration time. However there is atrial reversal in the pulmonary veins during atrial systole; and stage 3 or ‘restrictive filling’ pattern is denoted by a very prominent E wave with a short deceleration time and a miniscule A wave.

Sometimes the mitral inflow Doppler exhibits a triphasic pattern. This could be due to slow heart rate or delayed myocardial relaxation.[30] More than diastolic function, Doppler patterns could be used for diagnostic and prognostic purposes. In patients with normal systolic function transmitral Doppler patterns have a diagnostic role. The ‘impaired relaxation’ pattern would point to diseases like hypertension, hypertrophic cardiomyopathy and ischaemic heart disease. These are more relevant in the younger individual because normal ageing also causes such patterns. ‘Restrictive filling’ pattern could point to restrictive cardiomyopathy or pericardial disease. In patients with impaired systolic function, these Doppler patterns can be used to assess the severity of the impairment and predict the prognosis. In cases of systolic dysfunction, the left ventricular Doppler filling patterns are a continuous variable reflecting the increasing left atrial pressures and left ventricular end diastolic pressures which proceeds to atrial failure in stage 3. As a corollary, in cases with wall motion abnormalities and apparently normal ejection fraction, a stage 1 pattern could indicate an early systolic dysfunction. Stage 3 is associated with the worst prognosis.

For further information check these: Fig-22. Left ventricular flow propagation by colour M-mode FLOW PROPAGATION VELOCITY Colour Doppler can record the blood flow from the mitral valve to the left ventricular apex in the apical 4-chamber view. An M-mode cursor placed along the flow can create a colour M-mode representation of flow (Fig-22). Adjusting the colour Doppler can highlight a colour edge. The slope thus obtained represents the propagation velocity of blood flowing toward the apex. This flow propagation velocity has been shown to relate inversely with the time constant of LV relaxation and to be fairly insensitive to changes in left atrial pressures.[31,32] The late diastolic flow propagation (atrial flow) has also been used in a similar manner.[33 ] Fig-23. Principle of calculating the Tei index. TEI INDEX A simple and practical method of assessing the global (systolic and diastolic) function is the calculation of the myocardial performance or Tei index.[34,35] The Tei index combines systolic and diastolic intervals and not dependant on Doppler velocities (Fig-23).

Thus it is less affected by hemodynamic variables. This index is defined as the sum of isovolumic contraction time (IVCT) and the isovolumic relaxation time (IVRT) divided by the ejection time (ET). A good Doppler tracing combining 2 mitral inflow spectra and left ventricular outflow is taken. Tei index is calculated as (a–b)/b, ‘a’ being the time between the end of the first mitral valve flow and the onset of the next, and ‘b’ being the ventricular outflow flow ejection time. A value <0.45 connotes a good function while >0.45 connotes a poor function. A value >0.6 connotes a definite hemodynamic impairment. The index can also be used for right ventricular performance in a similar manner.[36 ] The only draw back is that this index also needs age related corrections.[37] CONCLUSION Doppler methods are essential tools in the cardiovascular examination. As with other medical methodology a systematic approach is required to derive maximum information. Being a dynamic form of examination all the steps in this examination require diagnostic logic.

Starting from image acquisition to the choice of Doppler modality and the application of the same and ending with interpretation of results requires the application of a diagnostic algorithm. Knowledge of the limitations of Doppler is a further requirement for proper clinical judgement. By following such an approach, meaningful information can be derived from Doppler, which in turn will result in better patient management.

Question: The scientific principle which explains that in fluid flow an increase in velocity is associated with a decrease in pressure is named after which family of mathematicians and physicists?
Answer: Bernoulli