Mechanical waves transfer energy through a medium and include transverse, longitudinal, and surface waves. The Doppler effect describes how the frequency of a wave is changed relative to an observer based on their motion. Doppler echocardiography uses ultrasound to examine the heart and blood flow by detecting changes in frequency from reflected sound waves, allowing determination of flow speed and direction. It is a non-invasive procedure with benefits over more invasive testing for diagnosing cardiovascular conditions.

1. Mechanical Waves
Doppler Effect
And its application
In medicine
Yuzbasheva Nihal 221B

2. A mechanical wave is a wave that is an oscillation of m
atter, and therefore transfers energy through a medium.
While waves can move over long distances, the movem
ent of the medium of transmission—the material—is limit
ed. Therefore, oscillating material does not move far fro
m its initial equilibrium position. Mechanical waves trans
port energy. This energy propagates in the same directio
n as the wave. Any kind of wave (mechanical or electro
magnetic) has a certain energy. Mechanical waves can b
e produced only in media which possess elasticity and in
ertia.
A mechanical wave requires an initial energy input. Once this
initial energy is added, the wave travels through the medium
until all its energy is transferred. In contrast, electromagnetic
waves require no medium, but can still travel through one.

3. There are three types of mechanical waves: transverse
waves, longitudinal waves, and surface waves
Transverse waves cause the medium to vibrate at a right an
gle to the direction of the wave or energy being carried by
the medium.
Longitudinal waves cause the medium to vibrate parallel t
o the direction of the wave. It consists of multiple compre
ssions and rarefactions. The rarefaction is the farthest dist
ance apart in the longitudinal wave and the compression i
s the closest distance together.
This type of wave travels along a
surface that is between two media.
An example of surface wave would
be waves in a pool, or in an ocean,
lake, or any other type of water bo
dy. There are two types of surface
waves, namely Rayleigh waves an
d Love waves.

4. That the frequency measured by an observer may be diff
erent from that emitted from the wave source due to the
relative motion between them is called Doppler Effect.
For the mechanical waves (we simply call them sound i
n the following text), classical treatment can give satisfie
d result that has been given by many textbooks and disc
ussed. It is:
uo, us, and v are the speeds of observer, sound source, and sound in
the medium respectively; fo and fs are the frequency measured by th
e observer and emitted by the sound source respectively.

5. If a source is stationary, it will emit sound waves that propagate
out from the source as shown below. As the receiver moves tow
ards the source, it will detect the sound coming from the source
but each successive sound wave will be detected earlier than it
would have if the receiver were stationary, due to the motion of t
he receiver in the LOS. Thus the frequency that each successiv
e wave front would be detected would be changed by this relativ
e motion where:
The observer’s motion causes him
to intercept more waves per second
than he would if he were standing
still.

6. Equation is only valid when the relative velocity is along t
he line connecting the wave source and the observer (w
hich is called wave vector). When this is not the case, uo
and us should be replaced with their velocity component
s that are parallel to the wave vector,. Therefore, Eq. is
replaced with
When the source and observer are approaching to each other, uo and us
are positive; otherwise, they are negative. One should notice that the moti
on of observer and or source has different effect on frequency change.

7. When the source of light is moving away from the
observer the wavelength of the emitted light will
appear to increase. We call this a redshift. Red because the
wave length is the longest.
When the source of light is moving towards the
observer the wavelength of the emitted light will
appear to decrease. We call this a Blueshift.

8. For sound, only the velocity component along the wave
vector direction affects the frequency. This is so called
longitudinal Doppler Effect. When observer and source
move perpendicularly to the wave vector direction (trans
versely), i.e., θ1 = θ2 = 90°, then fo = fs. So there is no
so called transverse Doppler Effect for sound waves.
In the case that the wave source and observer are approaching/re
ceding to each other, fo actually changes with time because the
angles change with time

9. For the electromagnetic waves (we simply call them light
in the following text) we have similar Doppler effect but
the different equation because
1) propagation of light doesn’t need medium so the light
velocity relative to the observer is always the same;
2) the period of the light may change for the observers
at different initial frame of reference (and time dilatio
n)

10. Doppler echocardiography is a procedure that uses ultraso-
und technology to examine the heart or blood vessels. An ech
ocardiogram uses high frequency sound waves to create an
image of the heart while the use of Doppler technology allow
s determination of the speed and direction of blood flow by
utilizing the Doppler effect.
An echocardiogram can, within certain limits, produce accura
te assessment of the direction of blood flow and the velocity o
f blood and cardiac tissue at any arbitrary point using the Dop
pler effect. One of the limitations is that the ultrasound beam
should be as parallel to the blood flow as possible.
Mitral valve

11. Unlike 1D Doppler imaging, which can only provide one-
dimensional velocity and has dependency on the beam t
o flow angle, 2D velocity estimation using Doppler ultras
ound is able to generate velocity vectors with axial and
lateral velocity components. 2D velocity is useful even if
complex flow conditions such as stenosis and bifurcation
exist. There are two major methods of 2D velocity estim
ation using ultrasound: Speckle tracking and crossed be
am Vector Doppler, which are based on measuring the ti
me shifts and phase shifts respectively.

12. Vector Doppler is a natural extension of the traditional 1
D Doppler imaging based on phase shift. The phase shif
t is found by taking the autocorrelation between echoes f
rom two consecutive firings. The main idea of Vector
Doppler is to divide the transducer into three apertures:
one at the center as the transmit aperture and two on ea
ch side as the receive apertures. The phase shifts meas
ured from left and right apertures are combined to give t
he axial and lateral velocity components. The positions a
nd the relative angles between apertures need to be tun
ed according to the depth of the vessel and the lateral p
osition of the region of interest.

13. Speckle tracking, which is a well-established method in v
ideo compression and other applications, can be used to
estimate blood flow in ultrasound systems. The basic ide
a of speckle tracking is to find the best match of a certai
n speckle from one frame within a search region in subs
equent frames. The decorrelation between frames is one
of the major factors degrading its performance. The dec
orrelation is mainly caused by the different velocity of pix
els within a speckle, as they do not move as a block. Thi
s is less severe when measuring the flow at the center, a
s the changing rate of the velocity is the lowest. The flow
at the center usually has the largest velocity magnitude,
called peak velocity. It is the most needed information in
some cases, such as diagnosing stenosis.

14. It should be noted here that there are no standards for
the display of color Doppler. Some laboratories show art
eries as red and veins as blue, as medical illustrators us
ually show them, even though some vessels may have p
ortions flowing towards and portions flowing away from t
he transducer. This results in the illogical appearance of
a vessel being partly a vein and partly an artery. Other la
boratories use red to indicate flow toward the transducer
and blue away from the transducer. Still other laboratorie
s prefer to display the sonographic Doppler color map m
ore in accord with the prior published physics with the re
d shift representing longer waves of echoes (scattered)
from blood flowing away from the transducer; and with
blue representing the shorter waves of echoes reflecting
from blood flowing toward the transducer
Colour Doppler scan of the common carotid artery

15. The main benefit of Doppler ultrasound is that it is less in
vasive than other procedures used to identify these type
s of medical problems. The ultrasound is perform on the
outside of the body and is not painful. Some discomfort
may be experienced as the transducer is used, but it is
often minimal. Because the ultrasound is not invasive, th
ere are fewer risks to using it as a diagnostic test and m
any patients are able to have serious conditions detecte
d without having to spend extensive time in the hospital.