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## Doppler Physics and Instrumentation

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**Topics**• Doppler effect • Doppler equation • Doppler Modes • Doppler Artifacts**Scattering of Ultrasound by RBC’s**• Red blood cells • Diameter: 7µm • Raleigh scatterers • Smaller than ultrasound wavelength (0.1-0.7 mm)**Scattering of Ultrasound by RBC’s**• The Intensity of the Raleigh Scatterers is • determined by: • Transducer frequency • Scatterer density • Scatterer size • Scatterer acoustic impedance**The Doppler Effect**Doppler shift is a change in frequency caused by the relative movement of the sound source or the reflector. Transducer is the sound wave source. Red Blood Cells are the reflector RBC’s can be: • stationary • moving towards the transducer • moving away from the transducer**Doppler Shift**fo fr = fd fr fo fo - = = 0 fr Stationery Reflectors**Doppler Shift**fr fo > fd fr fo = - +ve shift = fo fr Reflectors moving towards Sound source**Doppler Shift**fr fo < fd fr fo = = = - ve shift fo fr Reflectors moving away from sound source**Doppler Equation**2f0vcos fd = c • fd = Doppler shifted frequency • fo = transducer frequency • v = blood velocity • = beam flow angle • c = speed of sound in tissue (1540 m/s)**Cos **1.00 Cos 0 90 **Beam Flow Angle**• Ø = 0° • Parallel to flow - Optimum shift • Ø = 1° to 89° • Shift is reduced • Ø = 90° • Perpendicular to flow - No shift**Beam Flow Angle**• Best Doppler angle is parallel to flow and closest to 0 • Angle is effected by • organ position • patient position • transducer position**Reflector Velocity**The Doppler shift can be used to calculate the velocity of a column of moving RBCs if the following is known: • fo = transducer frequency • = beam flow angle • c = speed of sound in tissue (1540 m/s)**Reflector Velocity**fdc v = 2f0cos**Doppler Modes**• Pulsed Wave Doppler • Continuous Wave Doppler • Color Doppler • Power Doppler**Pulsed Doppler**A C A = PRP B = Pulse Duration C= Reception Time B**Pulsed Doppler**• The # of cycles per pulse is determined by: • Strength of the excitation voltage. • Electro-mechanical efficiency. • The damping characteristics.**Pulsed Doppler**Pulsed Duration = period x cycles per pulse PRP = PD + Reception Time PRF = # of pulses per second PRP = 1/PRF Duty Factor = PD PRP**Range Equation**Distance = velocity x time**Range Equation**Velocity = speed of sound in soft tissue. Distance = reflector distance. Time = time it takes the sound wave to reach reflector.**Range Equation**Time that can be measured is the go – return time. The actual time = go-return time 2**Range Equation**Reflector distance = velocity x go-return time 2**Aliasing**• The inability of a PD transducer to detect large Doppler shift is known as aliasing.**Aliasing**• The sampling rate = PRF • Maximum PRF is determine by the go- return time. • Deeper vessels requires longer go-return time • and thus a lower PRF.**Aliasing**• Low sampling rate results large signal • changes occurring between samples • Acquired sample lacks information • regarding these fast changes.**Aliasing**Low Sampling Rate Received information sampled too infrequently Measurement Errors (aliasing)**Pulsed Doppler**Receiver Gated Receiver circuits only open for a short interval during every pulse cycle.**Pulsed Doppler**Receiver Gated Receiver circuits only open for a short interval during every pulse cycle.**Spectral Analysis**• Returning signal from volume of RBCs contains • range of frequencies. • These range of frequencies are called the • FREQUENCY SPECTRUM. • Analysis of this spectrum will separate this • complex signals into its component parts.**Spectral Analysis**• The component frequencies are converted • into velocity information. • This allow for quantitative analysis of the • range of RBC’s velocities.**Fast Fourier Transform**• Digital method of spectrum analysis. • Mathematical technique. Complex wave is • broken down into a series of simpler sine wave. • Analog Doppler signal is digitized in a ADC**Fast Fourier Transform**• 5- 10 microseconds samples of signal are • processed using the FFT algorithm. • Digital component frequencies are converted • back into a analog signal by a DAC. • Signal is displayed.**Spectral Display**Doppler Signals Analysis FFT Quadrature Phase Detector Positive Shift Negative Shift Channel A Channel B Audio Channel A Audio Channel B Spectral Display Below the Baseline Spectral Display Above the Baseline**Spectral Display**• X- axis – time information • Y- axis – frequency/velocity information. • Z- axis – amplitude information.**Spectral Display**Frequency, y-axis Amplitude Z- axis Sonic Window Time, x axis**Spectral Display**• Velocity Measurements • Peak systolic velocity • End-diastolic velocity • Mean velocity – calculated by taken the area • under the curve.**Spectral Display**Systolic Peak Velocity Velocity Mean Velocity End Diastolic Velocity Time**Doppler Spectrum Assessment**• Assess the following: • Presence of flow • Direction of flow • Amplitude • Window • Pulsatility**Doppler Spectrum Assessment**Check for Flow Flow Detected No Flow Detected Check Sensitivity Check SV Placement Check Beam- flow angle Sensitive Decreased Sensitivity Improve Sensitivity**Doppler Spectrum Assessment**• Sensitivity can be improved by: • Increasing power or gain. • Decreasing the velocity scale. • Decreasing the reject or filter. • Slowly increasing the SV size.**Doppler Spectrum Assessment**• Direction of Flow • Pulsed Doppler use quadrature phase • detection to provide bidirectional Doppler • information.**Doppler Spectrum Assessment**• Flow can either be: • Mono-phasic • Bi-phasic • Tri-phasic • Bidirectional**Spectral Display**Mono-phasic Flow Flow on just on side of the Baseline. Frequency Time**Spectral Display**Bi-phasic Flow Flow start on one side of the Baseline and then crosses to the other. Frequency Time**Spectral Display**Tri-phasic Flow Flow start on one side of the baseline side, then crosses to the other, then returns to the original side. Frequency Time**Spectral Display**Bidirectional Flow Flow which occurs simultaneously on both sides of the baseline. Frequency Time**Doppler Spectrum Assessment**• Amplitude • The spectrum displays echo amplitude by varying the • brightness of the display. • The amplitude of the echoes are determined by: • Echo intensity • Power • Gain • Dynamic range**Spectral Display**Low amplitude Frequency Time