DOPPLER SHIFT

DOPPLER SHIFT UNSEEN POWERFUL TECHNOLOGY FROM ASTRONOMY TO BLOOD FLOW IN OUR ARTERIES

When I was a young lad, I was deeply interested in trains railways and especially in steam locomotives. I used to tell my father that I wanted to be a steam engine driver. Belching and spewing steam and smoke gave an extra image for the steam locomotives. When starting the engine, the driver with one hand lifts the throttle handle the engine moves forward, with his other hand pulls the string of the steam whistle leans backward through his window to make sure that all attached wagons are coming with his engine. It is a great sight to remember. The central character in this discussion is THE WISTLE.

Now consider yourself standing on a railway platform and an express train which does not stop at your station comes whistling at full speed you start hearing the whistle faintly at a distance. As the train comes nearer and nearer the whistle sound will be harsher and harsher as the train moves away from you the whistle sound will become fainter and fainter. As the train approaches you the whistle sound get compressed into high frequency short wavelength and as it moves away from you the sound waves become relaxed into long wavelength low frequency sound waves (In the ambulance figure above the same phenomenon is depicted). The compression and stretching of waves emitted by a moving object is called DOPPLER EFFECT OR DOPPLER SHIFT This change or shift was observed and a scientific explanation and a mathematical formalization was given by the Austrian physicist Christian Johann Doppler in 1850 hence the name DOPPLER SHIFT(DS). DS is used right from astronomy to medicine. In medicine. It allows to measure the blood flow in arteries and veins and echocardiogram. The Doppler shift or effect occurs not only for sound but for any wave when there is relative motion between the observer and source. Doppler shifts occur in the frequency of sound, light and water waves. Doppler shifts can be used to determine velocity such as when ultrasound is reflected from blood in a medical diagnostic. The relative velocities of stars and galaxies is determined by the shift in frequencies of light received from them and has implied much about the origin of the Universe.

It is interesting to note that in Doppler ultrasound since we are transmitting and receiving a reflection, the actual shift is TWICE the shift.

ANGLE EFFECTS – We normally assume the blood is flowing directly towards the ultrasound transducer. In practice this does not happen. So, we have to correct for the direction of blood flow. This is done with simple trigonometry. If theta is the angle between the ultrasound beam and blood flow, the component of velocity towards beam is

V towards transducer = V x cos theta

(This figure was specially composed and drawn by our darling daughter Sukanya Subramanian and our darling grand daughter Maya Anandi Hari Krishna. I express my heartfelt thanks to them)

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This figure illustrates the Doppler angle theta and the right-angled triangle formed by the beam with blood flow. The flow towards the beam is thus

V x cos theta

The Doppler shift is a change in frequency and phase of the reflected signal by a moving object. It could be moving car, flowing blood in the body or a moving star in the galaxy. Now let us look into the movement of blood in artery. Doppler shift frequency is determined according to the frequency following equation.

Fd= (Fr-Fo) = 2F0V (cos theta)/C, where V is the velocity of blood flow Cos theta is the cosine of the angle between the FDA path of the ultrasound beam and the flow od blood and C is the average speed of ultrasound in soft tissue(1540m/sec). There are actually two Doppler shifts that occur (hence the number 2 in the numerator). For moving targets first act as sound recipient and then as the source as ultrasound strikes it and reflects back towards the transducer. By rearranging the equation, we can solve for velocity

V = C Fd/2F0(cos theta)

An ultrasound transducer which I used for my experiments looks like the diaphragm of a common stethoscope. It encloses a piezoelectric crystal which is usually quartz. When applied electrical potential it vibrates and sends out ultrasound waves. That is the emitter. Transducer also encloses another quartz crystal which receives reflected ultrasound waves converts them to electrical signals and is called receiver. So, a transducer contains both emitter and receiver quartz crystals. The transducer is electrically stimulated sending continuous ultrasound waves, aimed at a stream of flowing blood or cardiac tissue. When the emitted ultrasound signal strikes the red blood cells a small proportion of its energy is reflected back to the transducer. If the target (blood cells) is travelling towards transducer, the frequency of the reflected ultrasound is greater than the emitted frequency. The increase in frequency is called POSITIVE DOPPLER SHIFT. If the blood is moving away from the transducer, the reflected frequency is lower and is knowns NRGATIVE DOPPLER SHIFT. The difference between the emitted (Fo) and the reflected (Fr) ultrasound frequencies is termed DOPPLER SHIFT FREQUENCY (Fd) is calculated according to the following equation

Fd = (Fr – Fo) = 2Fo x V (cos theta)/C

Where V is the velocity of blood

Cos theta is the cosine of angle between the ultrasound beam and blood flow and C is the average speed of ultrasound in soft tissues (1540 m/sec). There are actually two DOPPLER SHIFTS THAT OCCUR (HENCE THE NUMBER 2 IN THE NUMERATOR). For the moving target like blood first acts as the ultrasound recipient and then as the source of ultrasound strikes it and reflects back towards the transducer. By rearranging the equation above we solve the velocity of blood as

V = C x Fd/2Fo (cos theta)

The same equation can be applied for the cop detecting the speed of the speeding car.

DOPPLER RADAR

Doppler radar is different from regular radar that it uses the Doppler shift or effect to measure the velocity and movement of the objects whereas regular radar simply detects the presence and range of objects. The Doppler shift or effect is the change in the frequency or wavelength of a wave in relation to the motion of source or observer. These radars are very much needed for high-speed trains in India to avoid head on collisions of trains.

DOPPLER SHIFT IN ASTRONOMY

The American astronomer Edwin Hubble Observed that the light of faraway stars in other galaxies appears to be systematically red shifted. This redshift has two important characteristics

1, The red shift appears in all galaxies independent of the direction observed. This means galaxies are moving away from earth.

2. The greater the distance to galaxies, the more intense the redshift (that is the faster they move away).

DOPPLER SHIFT IN LIGHT

Objects emitting light with a certain frequency “fs” will experience a frequency shift (the same as with sound). If the source of light moves away from the observer the observed light appears to have a larger wavelength (less frequency). This effect is called RED SHIFT (a name used for sound and other waves but it comes from light radiation).

Hubble’s experiment and observation help us to understand that the universe is expanding, which shed some light on the origin and evolution of universe

THE ORIGIN OF UNIVERSE

In 1929, Edwin Hubble noticed that light coming from almost every galaxy he studied was shifted to the red end of the spectrum. He argued that only galaxies moving away from our galaxy could produce these RED SHITS This led to the theory that the universe is expanding ultimately to support the BIG BANG THEORY OF THE ORIGIN OF UNIVERSE. To honour his contributions to astronomy NASA has launched and stationed a massive space telescope to see deep into the universe. This telescope is appropriately named as HUBBLE TELESCOPE

The other uses of Doppler shits in medicine

In the place of X-rays ultrasound waves for Doppler shift are used to see the wellbeing of foetus in mother’s womb.

In addition to this ultrasound Doppler shift is used to detect medically oriented problems in different parts of the human body

MY EXPERIENCE

Way back in mid 1980s one of my graduate students for his M.Sc. thesis studied the Doppler shift in velocity of ultrasound waves through Sorghum vulgare stems for tis resistant and susceptibility to charcoal rot disease.

One of my scientist friends from Electronic Corporation of India developed ultrasound flaw detector of railway tracks way back in 1970s using Doppler shift.

I have in this article only scrapped the tip of the iceberg called DOPPLER SHIFT. Many more inventions and developments will come in future.

Professor K.A.Balasubramanian

Ph.D. (IARI NEW DELHI) Ph.D. (LONDON) DIC (LONDON)