Doppler Effect PDF

The Doppler Effect The Doppler Effect is the change 19 - Doppler in frequencies of a wave secondary to motion in th...

The Doppler Effect The Doppler Effect is the change 19 - Doppler in frequencies of a wave secondary to motion in the wave’s source Wave’s Source = The thing that is making sound This includes sound bouncing off that thing. If we bounce sound off something, that thing is considered to be “making” the sound. The Doppler Effect When an object that is creating waves moves, the direction of that motion tends to change the shapes of the waves Waves traveling in the same direction as the moving object will have a higher frequency Waves travelling the opposite Lower Stationary Moving direction as the moving object will Frequency Higher Sound Source Sound Source have a lower frequency Frequency  Doppler Frequencies This is also how RADAR and SONAR work! The frequency changes in those waves being given off by a moving source RADAR comes out of the tower with a known frequency When those waves hit the airplane and bounce off, their frequency is These changed changed based on the Airplane’s frequencies are called movement direction and speed “Doppler Frequencies” Doppler Shift A “Sonic Boom” is what occurs if a sound source Fundamental Frequency travels faster than the The amount of difference between sound waves travelling ahead of it! The frequency of the Transducer / the Transducer Frequency Operating frequency / Transmitted (Fundamental Frequency) Frequency and the Reflected Frequency (from the Red Blood Cell) What the sound frequency begins as The faster an object moves, the greater the Fundamental Frequency With this knowledge, we from the Transmitter can tell how fast Doppler Effect, with something is moving by increasingly higher comparing the original frequencies ahead and Reflected Doppler ”RADAR Tower” lower frequencies Frequency from Frequency to the behind the moving object Frequency bouncing off the reflector Reflected Frequency The Doppler Effect is Doppler Shift Equation also used by Weather DS = RF – FF Radar to track the The frequency of the sound waves motion of storm systems being reflected off of the RBC DS = Doppler Shift (Hz) RF = Reflected Frequency (Hz) The known frequency of the RADAR tower is compared to the frequency of the FF = Fundamental Frequency (Hz) waves reflected off water particles in the air If the DS is a positive number, the RBC is moving toward the Tx We’ll do the same thing, except with blood cells If the DS is a negative number, the instead of rain! RBC is moving away from the Tx Doppler Shift Equation (Simplified) Doppler Notes You are operating a 4MHz Transducer. You Doppler is used to determine Blood receive back a frequency of 2.7 MHz Velocity Was the RBC you reflected your waves from coming toward you or away from you? Velocity = Speed + Direction Speed Shift = Reflected – Original 2.7 Shift = 2.7 – 4.0 4 Speed = How fast Direction 4 MHz Shift = -1.3 Direction = Which way Negative Shift = Going AWAY from the Transducer 4.0 The pulse we sent Doppler determines how fast This is the reason that Doppler has a (+) sign MHz (by the degree of the shift) above baseline and a (-) sign below baseline The pulse 2.7 Doppler determines which way we got back MHz (by the positive or negative shift) Doppler Shift Equation (Expanded) Doppler Shift Equation (Expanded) DS = ( 2 x V x FF x Cos ) ÷ C Doppler Shift and Velocity have a Direct Relationship Direct Relationship DS = Doppler Shift (Hz) with Doppler Shift Doppler Shift and Transducer Frequency V = Blood Velocity (cm/s) have a Direct Relationship FF = Fundamental Frequency (Hz) Doppler Shift and Cosine have a Direct Relationship Cos = Cosine of the Doppler Angle Doppler Shift and Prop. Speed have an Inverse Relationship Inverse Relationship C = Propagation Speed with Doppler Shift Doppler Equation Notes Here the equation has been reorganized to solve for Blood Velocity Sound Beam Direction vs Flow Direction Doppler Shift and Velocity have a Parallel = When two planes are Direct Relationship (important) oriented toward each other in such a DS = RF - FF way that they will not cross This is how we determine velocity of the blood, when we measure it Parallel to Flow = When the angle of the doppler beam is as close to matching the angle of flow as The machine solves for “Blood possible (0 degree angle) Velocity” using the Doppler Shift Equation Perpendicular = When two planes cross at a 90 degree angle Transducer Frequency, Cosine and Prop Speed are known values to Perpendicular to Flow = When the the machine doppler beam’s angle is oriented 90 degrees from the angle of flow  The Doppler Angle is travelling The doppler signal out from the Tx in a Fan-Shape gets weaker the closer identical to the Scan Lines of the the angle of incidence Curvilinear Probe gets to 90º Red flow is making (+) Doppler Shifts moving toward the Tx Smallest Angles Strongest Signals Largest Angle Worst Signal Blue flow is making (-) Doppler Shifts moving Notice the color of the blood flow away from the Tx Strength of the doppler signal is through this abdominal Aorta reliant on angle, not direction! (Blood is flowing from Left-to-Right) Cosine Cosine This Angle = 60º The cosine of an angle is a logarithmic Measured Velocity = True Velocity x Cos function used in mathematics If the true velocity through a vessel is… Here, we only need to know (3) 100 cm/s Cosine values: Measured with a doppler angle of 60º Angle : Cosine 0 degree : 1.0 MV = TV x Cos 60 degree: 0.5 MV = 100 x 0.5 90 degree: 0.0 MV = 50 cm/s The Cosine of the Angle and the In Vascular Ultrasound, the Cosine of the Angle is Doppler Shift are Directly Related Taken at 90º? maintained at 60º by the “Angle Correct” function. MV = TV x Cos The greater the cosine (closer to 0 MV = 100 x 0 So, the machine automatically doubles every value degrees) the greater the Doppler before putting it on the screen. This is why Shift MV = 0 (no velocity measured at all) maintaining an angle of 60º is important. Sound Beam Direction vs Flow Direction Types of Doppler Cosine and Doppler Shift have a (2) Main and (4) Subtypes: Direct Relationship Spectral Doppler The lower the angle, the greater Pulse Wave the cosine Continuous Wave Overlay Doppler The lower the angle, the greater the doppler shift Velocity Mode (Color) Power Doppler The differences between these two types of doppler (Spectral vs Overlay) are in how the Doppler Shift information is used Overlay Doppler Notice the flow is fastest in the center of Doppler Scan Line Angles the vessel and slowest A Doppler “package” in which the against the walls doppler shift and velocity information is presented in a colored box, laid-over the Notice how those grayscale image (overlay) colors are represented The “Color Map” There are 2 Subtypes of Overlay Slower Doppler: Color Box (Color Overlay) (Velocity Mode) Power Doppler Faster The Doppler Shift and Velocity information is animated with colors corresponding to a “Color Map” similar Doppler to the Gray Map of B-Mode Angle Different “Hues” (colors) represent different doppler shifts Flow Direction Spectral Doppler Continuous Wave Doppler A Doppler “package” in which the Requires (2) crystals to function doppler shift and velocity One crystal always transmitting information is presented on a One crystal always receiving Velocity / Time graph (one microphone and one speaker) Advantage (strength): There are (2) Subtypes of Spectral Can measure extremely high Doppler: velocities High Velocities in the Does not Alias Heart are why Echo makes such Pulsed Wave extensive use of CW! Disadvantage (weakness): Cannot sample doppler shifts from Continuous Wave specific depths Must sample the entire length of the doppler scan-line (the whole beam) Continuous Target Flow Wave Scan Line Pulse Wave Doppler Accessory Flow Requires only (1) crystal to function picked up by the other parts of the scan line The doppler pulse (a specific pulse only used for detecting doppler information) is fired down the scan line. Its reflected frequency is compared to the original, and doppler shifts are measured. Then, depth information is added in. Continuous Wave cannot discern depth, (Depth information for doppler is obtained as depth information the same way that depth information is requires a obtained for B-Mode 2D Grayscale) measurement of time, which requires pulses (13 us rule) = (1 cm depth = 13 us round- trip time) Pulse Wave Doppler Target Flow This selector is called the “Sample Volume” or the “Range Gate” Advantage: Able to sample doppler shift information from specific depths Pulse Wave flow is often characterized Disadvantage: by these “windows” making the Not useful for High-Velocity waveforms appear situations hollow Subject to Aliasing This is often a good thing, as turbulent flow does not create these uniform, clear “windows” Quantitative vs Qualitative Studies and Information taken with the Ultrasound machine can be “Quantitative” images or This is a sign that the flow is likely more “Qualitative” images turbulent, or that the sample volume is large, allowing many Quantitative = Things you can Notice the lack of clear different velocities to Measure (think Quantity) “windows” within these be present in the waveforms. recording Qualitative = Things you can Observe (think Quality) Quantitative vs Qualitative Aliasing Spectral Doppler is a Quantitative Observations The most common error associated Study with doppler ultrasound Overlay Doppler is a Qualitative Study An error that occurs when the doppler shift exceeds the Nyquist What is the value? Limit Spectral = Specific, math-ready Measurable Numbers numbers The Nyquist Limit: Look at different points in time on 1 image NL = PRF / 2 Overlay = Big Picture flow profiles (is it turbulent or parabolic, etc.) Live display of flow (it’s a video, real time) Aliasing The Nyquist Limits of the Pulse Wave If the velocity of the blood is high enough to create a value greater than the Nyquist Limit, the velocity information is unusable and false. This is considered an “Artifact” Artifact = False information displayed on the US study (Something that isn’t there, or isn’t shaped correctly, etc.) The velocities that cannot be properly displayed with the current Scale/PRF settings are “wrapped-around” to the other end of the spectrum  As the doppler shifts exceed the Nyquist limit, they are wrapped-around to the other The Nyquist Limits of side of the spectrum the Color Overlay The flow velocity exceeds the Nyquist Limit of the Color Notice that this creates areas where the Scale but not of the maximum positive color borders the Spectral Scale maximum negative color In this case Light-Blue touching Light-Orange This is why we see Aliasing in the Color Box but not on the PW Waveform!